/specs/lapack/lapack-20010525.patch

diff -uNr LAPACK.orig/BLAS/TESTING/cblat2.f LAPACK/BLAS/TESTING/cblat2.f
--- LAPACK.orig/BLAS/TESTING/cblat2.f	Thu Nov  4 14:23:26 1999
+++ LAPACK/BLAS/TESTING/cblat2.f	Fri May 25 15:57:46 2001
@@ -64,6 +64,10 @@
 *     Richard Hanson, Sandia National Labs.
 *     Jeremy Du Croz, NAG Central Office.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
@@ -126,7 +130,7 @@
 *
       READ( NIN, FMT = * )SUMMRY
       READ( NIN, FMT = * )NOUT
-      OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' )
+      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
       NOUTC = NOUT
 *
 *     Read name and unit number for snapshot output file and open file.
@@ -135,7 +139,7 @@
       READ( NIN, FMT = * )NTRA
       TRACE = NTRA.GE.0
       IF( TRACE )THEN
-         OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' )
+         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
       END IF
 *     Read the flag that directs rewinding of the snapshot file.
       READ( NIN, FMT = * )REWI
diff -uNr LAPACK.orig/BLAS/TESTING/cblat3.f LAPACK/BLAS/TESTING/cblat3.f
--- LAPACK.orig/BLAS/TESTING/cblat3.f	Thu Nov  4 14:23:26 1999
+++ LAPACK/BLAS/TESTING/cblat3.f	Fri May 25 15:58:08 2001
@@ -46,6 +46,10 @@
 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
 *     Sven Hammarling, Numerical Algorithms Group Ltd.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
diff -uNr LAPACK.orig/BLAS/TESTING/dblat2.f LAPACK/BLAS/TESTING/dblat2.f
--- LAPACK.orig/BLAS/TESTING/dblat2.f	Thu Nov  4 14:23:27 1999
+++ LAPACK/BLAS/TESTING/dblat2.f	Fri May 25 15:57:41 2001
@@ -63,6 +63,10 @@
 *     Richard Hanson, Sandia National Labs.
 *     Jeremy Du Croz, NAG Central Office.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
@@ -121,7 +125,7 @@
 *
       READ( NIN, FMT = * )SUMMRY
       READ( NIN, FMT = * )NOUT
-      OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' )
+      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
       NOUTC = NOUT
 *
 *     Read name and unit number for snapshot output file and open file.
@@ -130,7 +134,7 @@
       READ( NIN, FMT = * )NTRA
       TRACE = NTRA.GE.0
       IF( TRACE )THEN
-         OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' )
+         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
       END IF
 *     Read the flag that directs rewinding of the snapshot file.
       READ( NIN, FMT = * )REWI
diff -uNr LAPACK.orig/BLAS/TESTING/dblat3.f LAPACK/BLAS/TESTING/dblat3.f
--- LAPACK.orig/BLAS/TESTING/dblat3.f	Thu Nov  4 14:23:27 1999
+++ LAPACK/BLAS/TESTING/dblat3.f	Fri May 25 15:58:04 2001
@@ -43,6 +43,10 @@
 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
 *     Sven Hammarling, Numerical Algorithms Group Ltd.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
@@ -96,7 +100,7 @@
 *
       READ( NIN, FMT = * )SUMMRY
       READ( NIN, FMT = * )NOUT
-      OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' )
+      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
       NOUTC = NOUT
 *
 *     Read name and unit number for snapshot output file and open file.
@@ -105,7 +109,7 @@
       READ( NIN, FMT = * )NTRA
       TRACE = NTRA.GE.0
       IF( TRACE )THEN
-         OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' )
+         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
       END IF
 *     Read the flag that directs rewinding of the snapshot file.
       READ( NIN, FMT = * )REWI
diff -uNr LAPACK.orig/BLAS/TESTING/sblat2.f LAPACK/BLAS/TESTING/sblat2.f
--- LAPACK.orig/BLAS/TESTING/sblat2.f	Thu Nov  4 14:23:26 1999
+++ LAPACK/BLAS/TESTING/sblat2.f	Fri May 25 15:57:34 2001
@@ -63,6 +63,10 @@
 *     Richard Hanson, Sandia National Labs.
 *     Jeremy Du Croz, NAG Central Office.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
@@ -121,7 +125,7 @@
 *
       READ( NIN, FMT = * )SUMMRY
       READ( NIN, FMT = * )NOUT
-      OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' )
+      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
       NOUTC = NOUT
 *
 *     Read name and unit number for snapshot output file and open file.
@@ -130,7 +134,7 @@
       READ( NIN, FMT = * )NTRA
       TRACE = NTRA.GE.0
       IF( TRACE )THEN
-         OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' )
+         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
       END IF
 *     Read the flag that directs rewinding of the snapshot file.
       READ( NIN, FMT = * )REWI
diff -uNr LAPACK.orig/BLAS/TESTING/sblat3.f LAPACK/BLAS/TESTING/sblat3.f
--- LAPACK.orig/BLAS/TESTING/sblat3.f	Thu Nov  4 14:23:26 1999
+++ LAPACK/BLAS/TESTING/sblat3.f	Fri May 25 15:58:00 2001
@@ -43,6 +43,10 @@
 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
 *     Sven Hammarling, Numerical Algorithms Group Ltd.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
diff -uNr LAPACK.orig/BLAS/TESTING/zblat2.f LAPACK/BLAS/TESTING/zblat2.f
--- LAPACK.orig/BLAS/TESTING/zblat2.f	Thu Nov  4 14:23:27 1999
+++ LAPACK/BLAS/TESTING/zblat2.f	Fri May 25 15:57:52 2001
@@ -64,6 +64,10 @@
 *     Richard Hanson, Sandia National Labs.
 *     Jeremy Du Croz, NAG Central Office.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
@@ -127,7 +131,7 @@
 *
       READ( NIN, FMT = * )SUMMRY
       READ( NIN, FMT = * )NOUT
-      OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' )
+      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
       NOUTC = NOUT
 *
 *     Read name and unit number for snapshot output file and open file.
@@ -136,7 +140,7 @@
       READ( NIN, FMT = * )NTRA
       TRACE = NTRA.GE.0
       IF( TRACE )THEN
-         OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' )
+         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
       END IF
 *     Read the flag that directs rewinding of the snapshot file.
       READ( NIN, FMT = * )REWI
diff -uNr LAPACK.orig/BLAS/TESTING/zblat3.f LAPACK/BLAS/TESTING/zblat3.f
--- LAPACK.orig/BLAS/TESTING/zblat3.f	Thu Nov  4 14:23:27 1999
+++ LAPACK/BLAS/TESTING/zblat3.f	Fri May 25 15:58:16 2001
@@ -46,6 +46,10 @@
 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
 *     Sven Hammarling, Numerical Algorithms Group Ltd.
 *
+*     10-9-00:  Change STATUS='NEW' to 'UNKNOWN' so that the testers
+*               can be run multiple times without deleting generated
+*               output files (susan)
+*
 *     .. Parameters ..
       INTEGER            NIN
       PARAMETER          ( NIN = 5 )
@@ -104,7 +108,7 @@
 *
       READ( NIN, FMT = * )SUMMRY
       READ( NIN, FMT = * )NOUT
-      OPEN( NOUT, FILE = SUMMRY, STATUS = 'NEW' )
+      OPEN( NOUT, FILE = SUMMRY, STATUS = 'UNKNOWN' )
       NOUTC = NOUT
 *
 *     Read name and unit number for snapshot output file and open file.
@@ -113,7 +117,7 @@
       READ( NIN, FMT = * )NTRA
       TRACE = NTRA.GE.0
       IF( TRACE )THEN
-         OPEN( NTRA, FILE = SNAPS, STATUS = 'NEW' )
+         OPEN( NTRA, FILE = SNAPS, STATUS = 'UNKNOWN' )
       END IF
 *     Read the flag that directs rewinding of the snapshot file.
       READ( NIN, FMT = * )REWI
@@ -1962,6 +1966,7 @@
 *  3-19-92:  Initialize ALPHA, BETA, RALPHA, and RBETA  (eca)
 *  3-19-92:  Fix argument 12 in calls to ZSYMM and ZHEMM
 *            with INFOT = 9  (eca)
+*  10-9-00:  Declared INTRINSIC DCMPLX (susan)
 *
 *     .. Scalar Arguments ..
       INTEGER            ISNUM, NOUT
@@ -1980,6 +1985,8 @@
 *     .. External Subroutines ..
       EXTERNAL           ZGEMM, ZHEMM, ZHER2K, ZHERK, CHKXER, ZSYMM,
      $                   ZSYR2K, ZSYRK, ZTRMM, ZTRSM
+*     .. Intrinsic Functions ..
+      INTRINSIC          DCMPLX
 *     .. Common blocks ..
       COMMON             /INFOC/INFOT, NOUTC, OK, LERR
 *     .. Executable Statements ..
diff -uNr LAPACK.orig/INSTALL/make.inc.LINUX LAPACK/INSTALL/make.inc.LINUX
--- LAPACK.orig/INSTALL/make.inc.LINUX	Thu Nov  4 14:23:30 1999
+++ LAPACK/INSTALL/make.inc.LINUX	Fri May 25 15:58:36 2001
@@ -17,7 +17,7 @@
 #  desired load options for your machine.
 #
 FORTRAN  = g77 
-OPTS     = -funroll-all-loops -fno-f2c -O3
+OPTS     = -funroll-all-loops -O3
 DRVOPTS  = $(OPTS)
 NOOPT    =
 LOADER   = g77
diff -uNr LAPACK.orig/SRC/cbdsqr.f LAPACK/SRC/cbdsqr.f
--- LAPACK.orig/SRC/cbdsqr.f	Thu Nov  4 14:23:31 1999
+++ LAPACK/SRC/cbdsqr.f	Fri May 25 15:59:05 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     April 25, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -18,14 +18,26 @@
 *  Purpose
 *  =======
 *
-*  CBDSQR computes the singular value decomposition (SVD) of a real
-*  N-by-N (upper or lower) bidiagonal matrix B:  B = Q * S * P' (P'
-*  denotes the transpose of P), where S is a diagonal matrix with
-*  non-negative diagonal elements (the singular values of B), and Q
-*  and P are orthogonal matrices.
-*
-*  The routine computes S, and optionally computes U * Q, P' * VT,
-*  or Q' * C, for given complex input matrices U, VT, and C.
+*  CBDSQR computes the singular values and, optionally, the right and/or
+*  left singular vectors from the singular value decomposition (SVD) of
+*  a real N-by-N (upper or lower) bidiagonal matrix B using the implicit
+*  zero-shift QR algorithm.  The SVD of B has the form
+*  
+*     B = Q * S * P**H
+*  
+*  where S is the diagonal matrix of singular values, Q is an orthogonal
+*  matrix of left singular vectors, and P is an orthogonal matrix of
+*  right singular vectors.  If left singular vectors are requested, this
+*  subroutine actually returns U*Q instead of Q, and, if right singular
+*  vectors are requested, this subroutine returns P**H*VT instead of
+*  P**H, for given complex input matrices U and VT.  When U and VT are
+*  the unitary matrices that reduce a general matrix A to bidiagonal
+*  form: A = U*B*VT, as computed by CGEBRD, then
+*  
+*     A = (U*Q) * S * (P**H*VT)
+*  
+*  is the SVD of A.  Optionally, the subroutine may also compute Q**H*C
+*  for a given complex input matrix C.
 *
 *  See "Computing  Small Singular Values of Bidiagonal Matrices With
 *  Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
@@ -61,18 +73,17 @@
 *          order.
 *
 *  E       (input/output) REAL array, dimension (N)
-*          On entry, the elements of E contain the
-*          offdiagonal elements of of the bidiagonal matrix whose SVD
-*          is desired. On normal exit (INFO = 0), E is destroyed.
-*          If the algorithm does not converge (INFO > 0), D and E
+*          On entry, the N-1 offdiagonal elements of the bidiagonal
+*          matrix B.
+*          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E
 *          will contain the diagonal and superdiagonal elements of a
 *          bidiagonal matrix orthogonally equivalent to the one given
 *          as input. E(N) is used for workspace.
 *
 *  VT      (input/output) COMPLEX array, dimension (LDVT, NCVT)
 *          On entry, an N-by-NCVT matrix VT.
-*          On exit, VT is overwritten by P' * VT.
-*          VT is not referenced if NCVT = 0.
+*          On exit, VT is overwritten by P**H * VT.
+*          Not referenced if NCVT = 0.
 *
 *  LDVT    (input) INTEGER
 *          The leading dimension of the array VT.
@@ -81,21 +92,22 @@
 *  U       (input/output) COMPLEX array, dimension (LDU, N)
 *          On entry, an NRU-by-N matrix U.
 *          On exit, U is overwritten by U * Q.
-*          U is not referenced if NRU = 0.
+*          Not referenced if NRU = 0.
 *
 *  LDU     (input) INTEGER
 *          The leading dimension of the array U.  LDU >= max(1,NRU).
 *
 *  C       (input/output) COMPLEX array, dimension (LDC, NCC)
 *          On entry, an N-by-NCC matrix C.
-*          On exit, C is overwritten by Q' * C.
-*          C is not referenced if NCC = 0.
+*          On exit, C is overwritten by Q**H * C.
+*          Not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C.
 *          LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.
 *
-*  RWORK   (workspace) REAL array, dimension (4*N)
+*  RWORK   (workspace) REAL array, dimension (2*N) 
+*          if NCVT = NRU = NCC = 0, (max(1, 4*N-4)) otherwise
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
diff -uNr LAPACK.orig/SRC/cgebd2.f LAPACK/SRC/cgebd2.f
--- LAPACK.orig/SRC/cgebd2.f	Thu Nov  4 14:24:07 1999
+++ LAPACK/SRC/cgebd2.f	Fri May 25 15:59:27 2001
@@ -3,7 +3,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     May 7, 2001
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N
@@ -172,8 +172,9 @@
 *
 *           Apply H(i)' to A(i:m,i+1:n) from the left
 *
-            CALL CLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
-     $                  CONJG( TAUQ( I ) ), A( I, I+1 ), LDA, WORK )
+            IF( I.LT.N )
+     $         CALL CLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
+     $                     CONJG( TAUQ( I ) ), A( I, I+1 ), LDA, WORK )
             A( I, I ) = D( I )
 *
             IF( I.LT.N ) THEN
@@ -215,8 +216,9 @@
 *
 *           Apply G(i) to A(i+1:m,i:n) from the right
 *
-            CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAUP( I ),
-     $                  A( MIN( I+1, M ), I ), LDA, WORK )
+            IF( I.LT.M )
+     $         CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
+     $                     TAUP( I ), A( MIN( I+1, M ), I ), LDA, WORK )
             CALL CLACGV( N-I+1, A( I, I ), LDA )
             A( I, I ) = D( I )
 *
diff -uNr LAPACK.orig/SRC/cgees.f LAPACK/SRC/cgees.f
--- LAPACK.orig/SRC/cgees.f	Thu Nov  4 14:24:08 1999
+++ LAPACK/SRC/cgees.f	Fri May 25 15:59:55 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVS, SORT
@@ -89,10 +90,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,2*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (N)
 *
@@ -120,11 +120,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTST, WANTVS
+      LOGICAL            SCALEA, WANTST, WANTVS
       INTEGER            HSWORK, I, IBAL, ICOND, IERR, IEVAL, IHI, ILO,
      $                   ITAU, IWRK, K, MAXB, MAXWRK, MINWRK
       REAL               ANRM, BIGNUM, CSCALE, EPS, S, SEP, SMLNUM
@@ -150,7 +152,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVS = LSAME( JOBVS, 'V' )
       WANTST = LSAME( SORT, 'S' )
       IF( ( .NOT.WANTVS ) .AND. ( .NOT.LSAME( JOBVS, 'N' ) ) ) THEN
@@ -177,7 +178,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 2*N )
          IF( .NOT.WANTVS ) THEN
@@ -196,19 +197,17 @@
             MAXWRK = MAX( MAXWRK, HSWORK, 1 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -12
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGEES ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/cgeesx.f LAPACK/SRC/cgeesx.f
--- LAPACK.orig/SRC/cgeesx.f	Thu Nov  4 14:24:08 1999
+++ LAPACK/SRC/cgeesx.f	Fri May 25 16:00:18 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Do WS calculations if LWORK = -1 (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVS, SENSE, SORT
@@ -119,6 +120,10 @@
 *          this routine.  Note that 2*SDIM*(N-SDIM) <= N*N/2.
 *          For good performance, LWORK must generally be larger.
 *
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
 *  RWORK   (workspace) REAL array, dimension (N)
 *
 *  BWORK   (workspace) LOGICAL array, dimension (N)
@@ -144,6 +149,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
@@ -211,7 +218,7 @@
 *       in the code.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 2*N )
          IF( .NOT.WANTVS ) THEN
@@ -229,18 +236,24 @@
             HSWORK = MAX( K*( K+2 ), 2*N )
             MAXWRK = MAX( MAXWRK, HSWORK, 1 )
          END IF
+*
+*        Estimate the workspace needed by CTRSEN.
+*
+         IF( WANTST ) THEN
+            MAXWRK = MAX( MAXWRK, (N*N+1)/2 )
+         END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     &      INFO = -15
       END IF
-      IF( LWORK.LT.MINWRK ) THEN
-         INFO = -15
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGEESX', -INFO )
          RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/cgeev.f LAPACK/SRC/cgeev.f
--- LAPACK.orig/SRC/cgeev.f	Thu Nov  4 14:24:08 1999
+++ LAPACK/SRC/cgeev.f	Fri May 25 16:00:48 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -85,10 +86,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,2*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (2*N)
 *
@@ -103,11 +103,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
+      LOGICAL            SCALEA, WANTVL, WANTVR
       CHARACTER          SIDE
       INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, IRWORK, ITAU,
      $                   IWRK, K, MAXB, MAXWRK, MINWRK, NOUT
@@ -136,7 +138,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVL = LSAME( JOBVL, 'V' )
       WANTVR = LSAME( JOBVR, 'V' )
       IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
@@ -165,7 +166,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
             MINWRK = MAX( 1, 2*N )
@@ -185,19 +186,17 @@
             MAXWRK = MAX( MAXWRK, HSWORK, 2*N )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -12
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGEEV ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/cgeevx.f LAPACK/SRC/cgeevx.f
--- LAPACK.orig/SRC/cgeevx.f	Thu Nov  4 14:24:08 1999
+++ LAPACK/SRC/cgeevx.f	Fri May 25 16:01:10 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
@@ -166,10 +167,9 @@
 *          LWORK >= N*N+2*N.
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (2*N)
 *
@@ -184,12 +184,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
-     $                   WNTSNN, WNTSNV
+      LOGICAL            SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, WNTSNN,
+     $                   WNTSNV
       CHARACTER          JOB, SIDE
       INTEGER            HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXB,
      $                   MAXWRK, MINWRK, NOUT
@@ -219,7 +221,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVL = LSAME( JOBVL, 'V' )
       WANTVR = LSAME( JOBVR, 'V' )
       WNTSNN = LSAME( SENSE, 'N' )
@@ -259,7 +260,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'CGEHRD', ' ', N, 1, N, 0 )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
             MINWRK = MAX( 1, 2*N )
@@ -293,19 +294,17 @@
             MAXWRK = MAX( MAXWRK, 2*N, 1 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -20
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -20
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGEEVX', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/cgegs.f LAPACK/SRC/cgegs.f
--- LAPACK.orig/SRC/cgegs.f	Thu Nov  4 14:24:08 1999
+++ LAPACK/SRC/cgegs.f	Fri May 25 16:01:59 2001
@@ -5,7 +5,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR
@@ -23,83 +23,70 @@
 *
 *  This routine is deprecated and has been replaced by routine CGGES.
 *
-*  CGEGS computes for a pair of N-by-N complex nonsymmetric matrices A,
-*  B:  the generalized eigenvalues (alpha, beta), the complex Schur
-*  form (A, B), and optionally left and/or right Schur vectors
-*  (VSL and VSR).
-*
-*  (If only the generalized eigenvalues are needed, use the driver CGEGV
-*  instead.)
-*
-*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly
-*  speaking, a scalar w or a ratio  alpha/beta = w, such that  A - w*B
-*  is singular.  It is usually represented as the pair (alpha,beta),
-*  as there is a reasonable interpretation for beta=0, and even for
-*  both being zero.  A good beginning reference is the book, "Matrix
-*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
-*
-*  The (generalized) Schur form of a pair of matrices is the result of
-*  multiplying both matrices on the left by one unitary matrix and
-*  both on the right by another unitary matrix, these two unitary
-*  matrices being chosen so as to bring the pair of matrices into
-*  upper triangular form with the diagonal elements of B being
-*  non-negative real numbers (this is also called complex Schur form.)
-*
-*  The left and right Schur vectors are the columns of VSL and VSR,
-*  respectively, where VSL and VSR are the unitary matrices
-*  which reduce A and B to Schur form:
-*
-*  Schur form of (A,B) = ( (VSL)**H A (VSR), (VSL)**H B (VSR) )
+*  CGEGS computes the eigenvalues, Schur form, and, optionally, the
+*  left and or/right Schur vectors of a complex matrix pair (A,B).
+*  Given two square matrices A and B, the generalized Schur
+*  factorization has the form
+*  
+*     A = Q*S*Z**H,  B = Q*T*Z**H
+*  
+*  where Q and Z are unitary matrices and S and T are upper triangular.
+*  The columns of Q are the left Schur vectors
+*  and the columns of Z are the right Schur vectors.
+*  
+*  If only the eigenvalues of (A,B) are needed, the driver routine
+*  CGEGV should be used instead.  See CGEGV for a description of the
+*  eigenvalues of the generalized nonsymmetric eigenvalue problem
+*  (GNEP).
 *
 *  Arguments
 *  =========
 *
 *  JOBVSL   (input) CHARACTER*1
 *          = 'N':  do not compute the left Schur vectors;
-*          = 'V':  compute the left Schur vectors.
+*          = 'V':  compute the left Schur vectors (returned in VSL).
 *
 *  JOBVSR   (input) CHARACTER*1
 *          = 'N':  do not compute the right Schur vectors;
-*          = 'V':  compute the right Schur vectors.
+*          = 'V':  compute the right Schur vectors (returned in VSR).
 *
 *  N       (input) INTEGER
 *          The order of the matrices A, B, VSL, and VSR.  N >= 0.
 *
 *  A       (input/output) COMPLEX array, dimension (LDA, N)
-*          On entry, the first of the pair of matrices whose generalized
-*          eigenvalues and (optionally) Schur vectors are to be
-*          computed.
-*          On exit, the generalized Schur form of A.
+*          On entry, the matrix A.
+*          On exit, the upper triangular matrix S from the generalized
+*          Schur factorization.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of A.  LDA >= max(1,N).
 *
 *  B       (input/output) COMPLEX array, dimension (LDB, N)
-*          On entry, the second of the pair of matrices whose
-*          generalized eigenvalues and (optionally) Schur vectors are
-*          to be computed.
-*          On exit, the generalized Schur form of B.
+*          On entry, the matrix B.
+*          On exit, the upper triangular matrix T from the generalized
+*          Schur factorization.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of B.  LDB >= max(1,N).
 *
 *  ALPHA   (output) COMPLEX array, dimension (N)
+*          The complex scalars alpha that define the eigenvalues of
+*          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
+*          form of A.
+*
 *  BETA    (output) COMPLEX array, dimension (N)
-*          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the
-*          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j),
-*          j=1,...,N  are the diagonals of the complex Schur form (A,B)
-*          output by CGEGS.  The  BETA(j) will be non-negative real.
-*
-*          Note: the quotients ALPHA(j)/BETA(j) may easily over- or
-*          underflow, and BETA(j) may even be zero.  Thus, the user
-*          should avoid naively computing the ratio alpha/beta.
-*          However, ALPHA will be always less than and usually
-*          comparable with norm(A) in magnitude, and BETA always less
-*          than and usually comparable with norm(B).
+*          The non-negative real scalars beta that define the
+*          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
+*          of the triangular factor T.
+*
+*          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
+*          represent the j-th eigenvalue of the matrix pair (A,B), in
+*          one of the forms lambda = alpha/beta or mu = beta/alpha.
+*          Since either lambda or mu may overflow, they should not,
+*          in general, be computed.
 *
 *  VSL     (output) COMPLEX array, dimension (LDVSL,N)
-*          If JOBVSL = 'V', VSL will contain the left Schur vectors.
-*          (See "Purpose", above.)
+*          If JOBVSL = 'V', the matrix of left Schur vectors Q.
 *          Not referenced if JOBVSL = 'N'.
 *
 *  LDVSL   (input) INTEGER
@@ -107,8 +94,7 @@
 *          if JOBVSL = 'V', LDVSL >= N.
 *
 *  VSR     (output) COMPLEX array, dimension (LDVSR,N)
-*          If JOBVSR = 'V', VSR will contain the right Schur vectors.
-*          (See "Purpose", above.)
+*          If JOBVSR = 'V', the matrix of right Schur vectors Z.
 *          Not referenced if JOBVSR = 'N'.
 *
 *  LDVSR   (input) INTEGER
diff -uNr LAPACK.orig/SRC/cgegv.f LAPACK/SRC/cgegv.f
--- LAPACK.orig/SRC/cgegv.f	Thu Nov  4 14:24:08 1999
+++ LAPACK/SRC/cgegv.f	Fri May 25 16:02:21 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -22,22 +22,28 @@
 *
 *  This routine is deprecated and has been replaced by routine CGGEV.
 *
-*  CGEGV computes for a pair of N-by-N complex nonsymmetric matrices A
-*  and B, the generalized eigenvalues (alpha, beta), and optionally,
-*  the left and/or right generalized eigenvectors (VL and VR).
-*
-*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly
-*  speaking, a scalar w or a ratio  alpha/beta = w, such that  A - w*B
-*  is singular.  It is usually represented as the pair (alpha,beta),
-*  as there is a reasonable interpretation for beta=0, and even for
-*  both being zero.  A good beginning reference is the book, "Matrix
-*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
-*
-*  A right generalized eigenvector corresponding to a generalized
-*  eigenvalue  w  for a pair of matrices (A,B) is a vector  r  such
-*  that  (A - w B) r = 0 .  A left generalized eigenvector is a vector
-*  l such that l**H * (A - w B) = 0, where l**H is the
-*  conjugate-transpose of l.
+*  CGEGV computes the eigenvalues and, optionally, the left and/or right
+*  eigenvectors of a complex matrix pair (A,B).
+*  Given two square matrices A and B,
+*  the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
+*  eigenvalues lambda and corresponding (non-zero) eigenvectors x such
+*  that
+*     A*x = lambda*B*x.
+*
+*  An alternate form is to find the eigenvalues mu and corresponding
+*  eigenvectors y such that
+*     mu*A*y = B*y.
+*
+*  These two forms are equivalent with mu = 1/lambda and x = y if
+*  neither lambda nor mu is zero.  In order to deal with the case that
+*  lambda or mu is zero or small, two values alpha and beta are returned
+*  for each eigenvalue, such that lambda = alpha/beta and
+*  mu = beta/alpha.
+*  
+*  The vectors x and y in the above equations are right eigenvectors of
+*  the matrix pair (A,B).  Vectors u and v satisfying
+*     u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
+*  are left eigenvectors of (A,B).
 *
 *  Note: this routine performs "full balancing" on A and B -- see
 *  "Further Details", below.
@@ -47,56 +53,62 @@
 *
 *  JOBVL   (input) CHARACTER*1
 *          = 'N':  do not compute the left generalized eigenvectors;
-*          = 'V':  compute the left generalized eigenvectors.
+*          = 'V':  compute the left generalized eigenvectors (returned
+*                  in VL).
 *
 *  JOBVR   (input) CHARACTER*1
 *          = 'N':  do not compute the right generalized eigenvectors;
-*          = 'V':  compute the right generalized eigenvectors.
+*          = 'V':  compute the right generalized eigenvectors (returned
+*                  in VR).
 *
 *  N       (input) INTEGER
 *          The order of the matrices A, B, VL, and VR.  N >= 0.
 *
 *  A       (input/output) COMPLEX array, dimension (LDA, N)
-*          On entry, the first of the pair of matrices whose
-*          generalized eigenvalues and (optionally) generalized
-*          eigenvectors are to be computed.
-*          On exit, the contents will have been destroyed.  (For a
-*          description of the contents of A on exit, see "Further
-*          Details", below.)
+*          On entry, the matrix A.
+*          If JOBVL = 'V' or JOBVR = 'V', then on exit A
+*          contains the Schur form of A from the generalized Schur
+*          factorization of the pair (A,B) after balancing.  If no
+*          eigenvectors were computed, then only the diagonal elements
+*          of the Schur form will be correct.  See CGGHRD and CHGEQZ
+*          for details.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of A.  LDA >= max(1,N).
 *
 *  B       (input/output) COMPLEX array, dimension (LDB, N)
-*          On entry, the second of the pair of matrices whose
-*          generalized eigenvalues and (optionally) generalized
-*          eigenvectors are to be computed.
-*          On exit, the contents will have been destroyed.  (For a
-*          description of the contents of B on exit, see "Further
-*          Details", below.)
+*          On entry, the matrix B.
+*          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
+*          upper triangular matrix obtained from B in the generalized
+*          Schur factorization of the pair (A,B) after balancing.
+*          If no eigenvectors were computed, then only the diagonal
+*          elements of B will be correct.  See CGGHRD and CHGEQZ for
+*          details.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of B.  LDB >= max(1,N).
 *
 *  ALPHA   (output) COMPLEX array, dimension (N)
-*  BETA    (output) COMPLEX array, dimension (N)
-*          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the
-*          generalized eigenvalues.
+*          The complex scalars alpha that define the eigenvalues of
+*          GNEP.
 *
-*          Note: the quotients ALPHA(j)/BETA(j) may easily over- or
-*          underflow, and BETA(j) may even be zero.  Thus, the user
-*          should avoid naively computing the ratio alpha/beta.
-*          However, ALPHA will be always less than and usually
-*          comparable with norm(A) in magnitude, and BETA always less
-*          than and usually comparable with norm(B).
+*  BETA    (output) COMPLEX array, dimension (N)
+*          The complex scalars beta that define the eigenvalues of GNEP.
+*          
+*          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
+*          represent the j-th eigenvalue of the matrix pair (A,B), in
+*          one of the forms lambda = alpha/beta or mu = beta/alpha.
+*          Since either lambda or mu may overflow, they should not,
+*          in general, be computed.
+
 *
 *  VL      (output) COMPLEX array, dimension (LDVL,N)
-*          If JOBVL = 'V', the left generalized eigenvectors.  (See
-*          "Purpose", above.)
-*          Each eigenvector will be scaled so the largest component
-*          will have abs(real part) + abs(imag. part) = 1, *except*
-*          that for eigenvalues with alpha=beta=0, a zero vector will
-*          be returned as the corresponding eigenvector.
+*          If JOBVL = 'V', the left eigenvectors u(j) are stored
+*          in the columns of VL, in the same order as their eigenvalues.
+*          Each eigenvector is scaled so that its largest component has
+*          abs(real part) + abs(imag. part) = 1, except for eigenvectors
+*          corresponding to an eigenvalue with alpha = beta = 0, which
+*          are set to zero.
 *          Not referenced if JOBVL = 'N'.
 *
 *  LDVL    (input) INTEGER
@@ -104,12 +116,12 @@
 *          if JOBVL = 'V', LDVL >= N.
 *
 *  VR      (output) COMPLEX array, dimension (LDVR,N)
-*          If JOBVR = 'V', the right generalized eigenvectors.  (See
-*          "Purpose", above.)
-*          Each eigenvector will be scaled so the largest component
-*          will have abs(real part) + abs(imag. part) = 1, *except*
-*          that for eigenvalues with alpha=beta=0, a zero vector will
-*          be returned as the corresponding eigenvector.
+*          If JOBVR = 'V', the right eigenvectors x(j) are stored
+*          in the columns of VR, in the same order as their eigenvalues.
+*          Each eigenvector is scaled so that its largest component has
+*          abs(real part) + abs(imag. part) = 1, except for eigenvectors
+*          corresponding to an eigenvalue with alpha = beta = 0, which
+*          are set to zero.
 *          Not referenced if JOBVR = 'N'.
 *
 *  LDVR    (input) INTEGER
diff -uNr LAPACK.orig/SRC/cgelsd.f LAPACK/SRC/cgelsd.f
--- LAPACK.orig/SRC/cgelsd.f	Thu Nov  4 14:26:25 1999
+++ LAPACK/SRC/cgelsd.f	Fri May 25 16:03:27 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -64,7 +65,8 @@
 *
 *  A       (input/output) COMPLEX array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
-*          On exit, A has been destroyed.
+*          On exit, the first min(m,n) rows of A are overwritten with
+*          its right singular vectors, stored rowwise.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A. LDA >= max(1,M).
@@ -96,32 +98,24 @@
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *
 *  LWORK   (input) INTEGER
-*          The dimension of the array WORK. LWORK must be at least 1.
+*          The dimension of the array WORK. LWORK >= 1.
 *          The exact minimum amount of workspace needed depends on M,
-*          N and NRHS. As long as LWORK is at least
-*              2 * N + N * NRHS
-*          if M is greater than or equal to N or
-*              2 * M + M * NRHS
-*          if M is less than N, the code will execute correctly.
+*          N and NRHS.
+*          If M >= N, LWORK >= 2*N + N*NRHS.
+*          If M < N, LWORK >= 2*M + M*NRHS.
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
-*
-*
-*  RWORK   (workspace) REAL array, dimension at least
-*             10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
-*             (SMLSIZ+1)**2
-*          if M is greater than or equal to N or
-*             10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
-*             (SMLSIZ+1)**2
-*          if M is less than N, the code will execute correctly.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
+*  RWORK   (workspace) REAL array, dimension (LRWORK)
+*          If M >= N, LRWORK >= 8*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS.
+*          If M < N, LRWORK >= 8*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS.
 *          SMLSIZ is returned by ILAENV and is equal to the maximum
 *          size of the subproblems at the bottom of the computation
 *          tree (usually about 25), and
-*             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
+*              NLVL = INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1
 *
 *  IWORK   (workspace) INTEGER array, dimension (LIWORK)
 *          LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
@@ -145,13 +139,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
       COMPLEX            CZERO
       PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ) )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY
       INTEGER            IASCL, IBSCL, IE, IL, ITAU, ITAUP, ITAUQ,
      $                   LDWORK, MAXMN, MAXWRK, MINMN, MINWRK, MM,
      $                   MNTHR, NRWORK, NWORK, SMLSIZ
@@ -179,7 +174,6 @@
       MINMN = MIN( M, N )
       MAXMN = MAX( M, N )
       MNTHR = ILAENV( 6, 'CGELSD', ' ', M, N, NRHS, -1 )
-      LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
@@ -263,20 +257,17 @@
          END IF
          MINWRK = MIN( MINWRK, MAXWRK )
          WORK( 1 ) = CMPLX( MAXWRK, 0 )
-         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-            INFO = -12
-         END IF
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
 *
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGELSD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         GO TO 10
       END IF
-*
-*     Quick return if possible.
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
          RANK = 0
          RETURN
diff -uNr LAPACK.orig/SRC/cgelss.f LAPACK/SRC/cgelss.f
--- LAPACK.orig/SRC/cgelss.f	Thu Nov  4 14:24:09 1999
+++ LAPACK/SRC/cgelss.f	Fri May 25 16:03:50 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     April 25, 2001 
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -87,10 +87,9 @@
 *          LWORK >=  2*min(M,N) + max(M,N,NRHS)
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (5*min(M,N))
 *
@@ -164,7 +163,7 @@
 *       immediately following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 0
          MM = M
          IF( M.GE.N .AND. M.GE.MNTHR ) THEN
@@ -235,19 +234,18 @@
          MINWRK = MAX( MINWRK, 1 )
          MAXWRK = MAX( MINWRK, MAXWRK )
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
+     $      INFO = -12
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -12
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGELSS', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
          RETURN
       END IF
-*
-*     Quick return if possible
-*
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
          RANK = 0
          RETURN
@@ -512,8 +510,8 @@
             DO 40 I = 1, NRHS, CHUNK
                BL = MIN( NRHS-I+1, CHUNK )
                CALL CGEMM( 'C', 'N', M, BL, M, CONE, WORK( IL ), LDWORK,
-     $                     B( 1, I ), LDB, CZERO, WORK( IWORK ), N )
-               CALL CLACPY( 'G', M, BL, WORK( IWORK ), N, B( 1, I ),
+     $                     B( 1, I ), LDB, CZERO, WORK( IWORK ), M )
+               CALL CLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ),
      $                      LDB )
    40       CONTINUE
          ELSE
diff -uNr LAPACK.orig/SRC/cgesdd.f LAPACK/SRC/cgesdd.f
--- LAPACK.orig/SRC/cgesdd.f	Thu Nov 11 20:32:54 1999
+++ LAPACK/SRC/cgesdd.f	Fri May 25 16:08:03 2001
@@ -1,10 +1,11 @@
-      SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
-     $                   LWORK, RWORK, IWORK, INFO )
+      SUBROUTINE CGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
+     $                   WORK, LWORK, RWORK, IWORK, INFO )
 *
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBZ
@@ -119,12 +120,14 @@
 *          if JOBZ = 'S' or 'A',
 *                LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
 *          For good performance, LWORK should generally be larger.
-*          If LWORK < 0 but other input arguments are legal, WORK(1)
-*          returns the optimal LWORK.
+*
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (LRWORK)
-*          If JOBZ = 'N', LRWORK >= 7*min(M,N).
-*          Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 5*min(M,N)
+*          If JOBZ = 'N', LRWORK >= 5*min(M,N).
+*          Otherwise, LRWORK >= 5*min(M,N)*min(M,N) + 7*min(M,N)
 *
 *  IWORK   (workspace) INTEGER array, dimension (8*min(M,N))
 *
@@ -143,14 +146,16 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       COMPLEX            CZERO, CONE
-      PARAMETER          ( CZERO = ( 0.0E0, 0.0E0 ),
-     $                   CONE = ( 1.0E0, 0.0E0 ) )
+      PARAMETER          ( CZERO = ( 0.0E+0, 0.0E+0 ),
+     $                   CONE = ( 1.0E+0, 0.0E+0 ) )
       REAL               ZERO, ONE
-      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
+      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
+      LOGICAL            WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
       INTEGER            BLK, CHUNK, I, IE, IERR, IL, IR, IRU, IRVT,
      $                   ISCL, ITAU, ITAUP, ITAUQ, IU, IVT, LDWKVT,
      $                   LDWRKL, LDWRKR, LDWRKU, MAXWRK, MINMN, MINWRK,
@@ -162,15 +167,17 @@
       REAL               DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           CGEBRD, CGELQF, CGEMM, CGEQRF, CLACP2, CLACPY, 
-     $                   CLACRM, CLARCM, CLASCL, CLASET, CUNGBR, CUNGLQ, 
-     $                   CUNGQR, CUNMBR, SBDSDC, SLASCL, XERBLA
+      EXTERNAL           CGEBRD, CGELQF, CGEMM, CGEQRF,
+     $                   CLACP2, CLACPY, CLACRM, CLARCM,
+     $                   CLASCL, CLASET, CUNGBR, CUNGLQ,
+     $                   CUNGQR, CUNMBR, SBDSDC, SLASCL,
+     $                   XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       INTEGER            ILAENV
       REAL               CLANGE, SLAMCH
-      EXTERNAL           CLANGE, ILAENV, LSAME, SLAMCH
+      EXTERNAL           CLANGE, SLAMCH, ILAENV, LSAME
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          INT, MAX, MIN, SQRT
@@ -181,8 +188,8 @@
 *
       INFO = 0
       MINMN = MIN( M, N )
-      MNTHR1 = INT( MINMN*17.0E0 / 9.0E0 )
-      MNTHR2 = INT( MINMN*5.0E0 / 3.0E0 )
+      MNTHR1 = INT( MINMN*17.0 / 9.0 )
+      MNTHR2 = INT( MINMN*5.0 / 3.0 )
       WNTQA = LSAME( JOBZ, 'A' )
       WNTQS = LSAME( JOBZ, 'S' )
       WNTQAS = WNTQA .OR. WNTQS
@@ -190,7 +197,6 @@
       WNTQN = LSAME( JOBZ, 'N' )
       MINWRK = 1
       MAXWRK = 1
-      LQUERY = ( LWORK.EQ.-1 )
 *
       IF( .NOT.( WNTQA .OR. WNTQS .OR. WNTQO .OR. WNTQN ) ) THEN
          INFO = -1
@@ -221,19 +227,21 @@
          IF( M.GE.N ) THEN
 *
 *           There is no complex work space needed for bidiagonal SVD
-*           The real work space needed for bidiagonal SVD is BDSPAC,
-*           BDSPAC = 3*N*N + 4*N
+*           The real work space needed for bidiagonal SVD is BDSPAC
+*           for computing singular values and singular vectors; BDSPAN
+*           for computing singular values only.
+*           BDSPAC = 5*N*N + 7*N
+*           BDSPAN = MAX(7*N+4, 3*N+2+SMLSIZ*(SMLSIZ+8))
 *
             IF( M.GE.MNTHR1 ) THEN
                IF( WNTQN ) THEN
 *
 *                 Path 1 (M much larger than N, JOBZ='N')
 *
-                  WRKBL = N + N*ILAENV( 1, 'CGEQRF', ' ', M, N, -1,
-     $                    -1 )
-                  WRKBL = MAX( WRKBL, 2*N+2*N*
-     $                    ILAENV( 1, 'CGEBRD', ' ', N, N, -1, -1 ) )
-                  MAXWRK = WRKBL
+                  MAXWRK = N + N*ILAENV( 1, 'CGEQRF', ' ', M, N, -1,
+     $                     -1 )
+                  MAXWRK = MAX( MAXWRK, 2*N+2*N*
+     $                     ILAENV( 1, 'CGEBRD', ' ', N, N, -1, -1 ) )
                   MINWRK = 3*N
                ELSE IF( WNTQO ) THEN
 *
@@ -335,8 +343,11 @@
          ELSE
 *
 *           There is no complex work space needed for bidiagonal SVD
-*           The real work space needed for bidiagonal SVD is BDSPAC,
-*           BDSPAC = 3*M*M + 4*M
+*           The real work space needed for bidiagonal SVD is BDSPAC
+*           for computing singular values and singular vectors; BDSPAN
+*           for computing singular values only.
+*           BDSPAC = 5*M*M + 7*M
+*           BDSPAN = MAX(7*M+4, 3*M+2+SMLSIZ*(SMLSIZ+8))
 *
             IF( N.GE.MNTHR1 ) THEN
                IF( WNTQN ) THEN
@@ -447,24 +458,21 @@
             END IF
          END IF
          MAXWRK = MAX( MAXWRK, MINWRK )
+      END IF
+      IF( INFO.EQ.0 ) THEN
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGESDD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
-         IF( LWORK.GE.1 )
-     $      WORK( 1 ) = ONE
          RETURN
       END IF
 *
@@ -529,7 +537,7 @@
 *
 *              Perform bidiagonal SVD, compute singular values only
 *              (CWorkspace: 0)
-*              (RWorkspace: need BDSPAC)
+*              (RWorkspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
@@ -844,7 +852,7 @@
 *
 *              Compute singular values only
 *              (Cworkspace: 0)
-*              (Rworkspace: need BDSPAC)
+*              (Rworkspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
@@ -1040,7 +1048,7 @@
 *
 *              Compute singular values only
 *              (Cworkspace: 0)
-*              (Rworkspace: need BDSPAC)
+*              (Rworkspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', N, S, RWORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
@@ -1205,8 +1213,8 @@
       ELSE
 *
 *        A has more columns than rows. If A has sufficiently more
-*        columns than rows, first reduce using the LQ decomposition
-*        (if sufficient workspace available)
+*        columns than rows, first reduce using the LQ decomposition (if
+*        sufficient workspace available)
 *
          IF( N.GE.MNTHR1 ) THEN
 *
@@ -1245,7 +1253,7 @@
 *
 *              Perform bidiagonal SVD, compute singular values only
 *              (CWorkspace: 0)
-*              (RWorkspace: need BDSPAC)
+*              (RWorkspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
@@ -1531,8 +1539,8 @@
 *              (CWorkspace: need M*M)
 *              (RWorkspace: 0)
 *
-               CALL CGEMM( 'N', 'N', M, N, M, CONE, WORK( IVT ), LDWKVT,
-     $                     VT, LDVT, CZERO, A, LDA )
+               CALL CGEMM( 'N', 'N', M, N, M, CONE, WORK( IVT ),
+     $                     LDWKVT, VT, LDVT, CZERO, A, LDA )
 *
 *              Copy right singular vectors of A from A to VT
 *
@@ -1567,7 +1575,7 @@
 *
 *              Compute singular values only
 *              (Cworkspace: 0)
-*              (Rworkspace: need BDSPAC)
+*              (Rworkspace: need BDSPAN)
 *
                CALL SBDSDC( 'L', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
@@ -1763,7 +1771,7 @@
 *
 *              Compute singular values only
 *              (Cworkspace: 0)
-*              (Rworkspace: need BDSPAC)
+*              (Rworkspace: need BDSPAN)
 *
                CALL SBDSDC( 'L', 'N', M, S, RWORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, RWORK( NRWORK ), IWORK, INFO )
@@ -1934,9 +1942,15 @@
          IF( ANRM.GT.BIGNUM )
      $      CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
      $                   IERR )
+         IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM )
+     $      CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1,
+     $                   RWORK( IE ), MINMN, IERR )
          IF( ANRM.LT.SMLNUM )
      $      CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
      $                   IERR )
+         IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM )
+     $      CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1,
+     $                   RWORK( IE ), MINMN, IERR )
       END IF
 *
 *     Return optimal workspace in WORK(1)
diff -uNr LAPACK.orig/SRC/cgesvd.f LAPACK/SRC/cgesvd.f
--- LAPACK.orig/SRC/cgesvd.f	Thu Nov  4 14:24:09 1999
+++ LAPACK/SRC/cgesvd.f	Fri May 25 16:08:29 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU, JOBVT
@@ -114,12 +115,12 @@
 *          LWORK >=  2*MIN(M,N)+MAX(M,N).
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
-*  RWORK   (workspace) REAL array, dimension (5*min(M,N))
+*  RWORK   (workspace) REAL array, dimension
+*                                  (5*min(M,N))
 *          On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the
 *          unconverged superdiagonal elements of an upper bidiagonal
 *          matrix B whose diagonal is in S (not necessarily sorted).
@@ -137,6 +138,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       COMPLEX            CZERO, CONE
       PARAMETER          ( CZERO = ( 0.0E0, 0.0E0 ),
      $                   CONE = ( 1.0E0, 0.0E0 ) )
@@ -144,8 +147,8 @@
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
-     $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
+      LOGICAL            WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS, WNTVA,
+     $                   WNTVAS, WNTVN, WNTVO, WNTVS
       INTEGER            BLK, CHUNK, I, IE, IERR, IR, IRWORK, ISCL,
      $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
      $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
@@ -188,7 +191,7 @@
       WNTVO = LSAME( JOBVT, 'O' )
       WNTVN = LSAME( JOBVT, 'N' )
       MINWRK = 1
-      LQUERY = ( LWORK.EQ.-1 )
+      MAXWRK = 1
 *
       IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN
          INFO = -1
@@ -216,8 +219,7 @@
 *       real workspace. NB refers to the optimal block size for the
 *       immediately following subroutine, as returned by ILAENV.)
 *
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) .AND. M.GT.0 .AND.
-     $   N.GT.0 ) THEN
+      IF( INFO.EQ.0 .AND. M.GT.0 .AND. N.GT.0 ) THEN
          IF( M.GE.N ) THEN
 *
 *           Space needed for CBDSQR is BDSPAC = 5*N
@@ -543,24 +545,21 @@
                MAXWRK = MAX( MINWRK, MAXWRK )
             END IF
          END IF
+      END IF
+      IF( INFO.EQ.0 ) THEN
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGESVD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
-         IF( LWORK.GE.1 )
-     $      WORK( 1 ) = ONE
          RETURN
       END IF
 *
diff -uNr LAPACK.orig/SRC/cggbak.f LAPACK/SRC/cggbak.f
--- LAPACK.orig/SRC/cggbak.f	Thu Nov  4 14:24:10 1999
+++ LAPACK/SRC/cggbak.f	Fri May 25 16:09:01 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     February 1, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB, SIDE
@@ -109,10 +109,15 @@
          INFO = -3
       ELSE IF( ILO.LT.1 ) THEN
          INFO = -4
-      ELSE IF( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) THEN
+      ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
+         INFO = -4
+      ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
+     $   THEN
+         INFO = -5
+      ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
          INFO = -5
       ELSE IF( M.LT.0 ) THEN
-         INFO = -6
+         INFO = -8
       ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
          INFO = -10
       END IF
diff -uNr LAPACK.orig/SRC/cggbal.f LAPACK/SRC/cggbal.f
--- LAPACK.orig/SRC/cggbal.f	Thu Nov  4 14:24:10 1999
+++ LAPACK/SRC/cggbal.f	Fri May 25 16:09:22 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     April 12, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB
@@ -150,7 +150,7 @@
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
-         INFO = -5
+         INFO = -6
       END IF
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGGBAL', -INFO )
@@ -197,8 +197,8 @@
       IF( L.NE.1 )
      $   GO TO 30
 *
-      RSCALE( 1 ) = 1
-      LSCALE( 1 ) = 1
+      RSCALE( 1 ) = ONE
+      LSCALE( 1 ) = ONE
       GO TO 190
 *
    30 CONTINUE
@@ -256,7 +256,7 @@
 *     Permute rows M and I
 *
   160 CONTINUE
-      LSCALE( M ) = I
+      LSCALE( M ) = REAL( I )
       IF( I.EQ.M )
      $   GO TO 170
       CALL CSWAP( N-K+1, A( I, K ), LDA, A( M, K ), LDA )
@@ -265,7 +265,7 @@
 *     Permute columns M and J
 *
   170 CONTINUE
-      RSCALE( M ) = J
+      RSCALE( M ) = REAL( J )
       IF( J.EQ.M )
      $   GO TO 180
       CALL CSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
@@ -437,7 +437,7 @@
       DO 360 I = ILO, IHI
          IRAB = ICAMAX( N-ILO+1, A( I, ILO ), LDA )
          RAB = ABS( A( I, IRAB+ILO-1 ) )
-         IRAB = ICAMAX( N-ILO+1, B( I, ILO ), LDA )
+         IRAB = ICAMAX( N-ILO+1, B( I, ILO ), LDB )
          RAB = MAX( RAB, ABS( B( I, IRAB+ILO-1 ) ) )
          LRAB = INT( LOG10( RAB+SFMIN ) / BASL+ONE )
          IR = LSCALE( I ) + SIGN( HALF, LSCALE( I ) )
diff -uNr LAPACK.orig/SRC/cgges.f LAPACK/SRC/cgges.f
--- LAPACK.orig/SRC/cgges.f	Thu Nov  4 14:26:17 1999
+++ LAPACK/SRC/cgges.f	Fri May 25 16:09:43 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SORT
@@ -145,10 +146,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,2*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (8*N)
 *
@@ -173,6 +173,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
       COMPLEX            CZERO, CONE
@@ -181,7 +183,7 @@
 *     ..
 *     .. Local Scalars ..
       LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
-     $                   LQUERY, WANTST
+     $                   WANTST
       INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
      $                   ILO, IRIGHT, IROWS, IRWRK, ITAU, IWRK, LWKMIN,
      $                   LWKOPT
@@ -237,7 +239,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -264,7 +265,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       LWKMIN = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          LWKMIN = MAX( 1, 2*N )
          LWKOPT = N + N*ILAENV( 1, 'CGEQRF', ' ', N, 1, N, 0 )
          IF( ILVSL ) THEN
@@ -272,21 +273,17 @@
      $               -1 ) )
          END IF
          WORK( 1 ) = LWKOPT
+         IF( LWORK.LT.LWKMIN .AND. LWORK.NE.LQUERV )
+     $      INFO = -18
       END IF
 *
-      IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
-     $   INFO = -18
+*     Quick return if possible
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGGES ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
-      WORK( 1 ) = LWKOPT
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/cggesx.f LAPACK/SRC/cggesx.f
--- LAPACK.orig/SRC/cggesx.f	Thu Nov  4 14:26:17 1999
+++ LAPACK/SRC/cggesx.f	Fri May 25 16:10:00 2001
@@ -7,6 +7,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Do WS calculations if LWORK = -1 (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SENSE, SORT
@@ -167,6 +168,10 @@
 *          If SENSE = 'E', 'V', or 'B',
 *          LWORK >= MAX(2*N, 2*SDIM*(N-SDIM)).
 *
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
 *  RWORK   (workspace) REAL array, dimension ( 8*N )
 *          Real workspace.
 *
@@ -198,6 +203,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
       COMPLEX            CZERO, CONE
@@ -304,14 +311,22 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
+      IF( INFO.EQ.0 ) THEN
          MINWRK = MAX( 1, 2*N )
          MAXWRK = N + N*ILAENV( 1, 'CGEQRF', ' ', N, 1, N, 0 )
          IF( ILVSL ) THEN
             MAXWRK = MAX( MAXWRK, N+N*ILAENV( 1, 'CUNGQR', ' ', N, 1, N,
      $               -1 ) )
          END IF
+*
+*        Estimate the workspace needed by CTGSEN.
+*
+         IF( WANTST ) THEN
+            MAXWRK = MAX( MAXWRK, (N*N+1)/2 )
+         END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -21
       END IF
       IF( .NOT.WANTSN ) THEN
          LIWMIN = N+2
@@ -319,21 +334,18 @@
          LIWMIN = 1
       END IF
       IWORK( 1 ) = LIWMIN
-*
-      IF( INFO.EQ.0 .AND. LWORK.LT.MINWRK ) THEN
-         INFO = -21
-      ELSE IF( INFO.EQ.0 .AND. IJOB.GE.1 ) THEN
+      IF( INFO.EQ.0 .AND. IJOB.GE.1 ) THEN
          IF( LIWORK.LT.LIWMIN )
      $      INFO = -24
       END IF
 *
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGGESX', -INFO )
          RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/cggev.f LAPACK/SRC/cggev.f
--- LAPACK.orig/SRC/cggev.f	Thu Nov  4 14:26:17 1999
+++ LAPACK/SRC/cggev.f	Fri May 25 16:10:19 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -113,10 +114,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,2*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace/output) REAL array, dimension (8*N)
 *
@@ -133,6 +133,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
       COMPLEX            CZERO, CONE
@@ -140,7 +142,7 @@
      $                   CONE = ( 1.0E0, 0.0E0 ) )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
+      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR
       CHARACTER          CHTEMP
       INTEGER            ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
      $                   IN, IRIGHT, IROWS, IRWRK, ITAU, IWRK, JC, JR,
@@ -202,7 +204,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -228,25 +229,21 @@
 *       computed assuming ILO = 1 and IHI = N, the worst case.)
 *
       LWKMIN = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          LWKOPT = N + N*ILAENV( 1, 'CGEQRF', ' ', N, 1, N, 0 )
          LWKMIN = MAX( 1, 2*N )
          WORK( 1 ) = LWKOPT
+         IF( LWORK.LT.LWKMIN .AND. LWORK.NE.LQUERV )
+     $      INFO = -15
       END IF
 *
-      IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY )
-     $   INFO = -15
+*     Quick returns
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGGEV ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
-      WORK( 1 ) = LWKOPT
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/cggevx.f LAPACK/SRC/cggevx.f
--- LAPACK.orig/SRC/cggevx.f	Thu Nov  4 14:26:17 1999
+++ LAPACK/SRC/cggevx.f	Fri May 25 16:11:36 2001
@@ -7,6 +7,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
@@ -194,10 +195,9 @@
 *          If SENSE = 'N' or 'E', LWORK >= 2*N.
 *          If SENSE = 'V' or 'B', LWORK >= 2*N*N+2*N.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  RWORK   (workspace) REAL array, dimension (6*N)
 *          Real workspace.
@@ -247,6 +247,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
       COMPLEX            CZERO, CONE
@@ -254,8 +256,8 @@
      $                   CONE = ( 1.0E+0, 0.0E+0 ) )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY,
-     $                   WANTSB, WANTSE, WANTSN, WANTSV
+      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, WANTSB,
+     $                   WANTSE, WANTSN, WANTSV
       CHARACTER          CHTEMP
       INTEGER            I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
      $                   ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK, MINWRK
@@ -321,7 +323,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC,
      $    'S' ) .OR. LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) )
      $     THEN
@@ -354,7 +355,7 @@
 *       computed assuming ILO = 1 and IHI = N, the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'CGEQRF', ' ', N, 1, N, 0 )
          IF( WANTSE ) THEN
             MINWRK = MAX( 1, 2*N )
@@ -363,21 +364,17 @@
             MAXWRK = MAX( MAXWRK, 2*N*N+2*N )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -25
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -25
-      END IF
+*     Quick returns
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'CGGEVX', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/cgghrd.f LAPACK/SRC/cgghrd.f
--- LAPACK.orig/SRC/cgghrd.f	Thu Nov  4 14:25:42 1999
+++ LAPACK/SRC/cgghrd.f	Fri May 25 16:11:54 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ
@@ -20,16 +20,29 @@
 *
 *  CGGHRD reduces a pair of complex matrices (A,B) to generalized upper
 *  Hessenberg form using unitary transformations, where A is a
-*  general matrix and B is upper triangular:  Q' * A * Z = H and
-*  Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular,
-*  and Q and Z are unitary, and ' means conjugate transpose.
+*  general matrix and B is upper triangular.  The form of the generalized
+*  eigenvalue problem is
+*     A*x = lambda*B*x,
+*  and B is typically made upper triangular by computing its QR
+*  factorization and moving the unitary matrix Q to the left side
+*  of the equation.
+*
+*  This subroutine simultaneously reduces A to a Hessenberg matrix H:
+*     Q**H*A*Z = H
+*  and transforms B to another upper triangular matrix T:
+*     Q**H*B*Z = T
+*  in order to reduce the problem to its standard form
+*     H*y = lambda*T*y
+*  where y = Z**H*x.
 *
 *  The unitary matrices Q and Z are determined as products of Givens
 *  rotations.  They may either be formed explicitly, or they may be
 *  postmultiplied into input matrices Q1 and Z1, so that
-*
-*       Q1 * A * Z1' = (Q1*Q) * H * (Z1*Z)'
-*       Q1 * B * Z1' = (Q1*Q) * T * (Z1*Z)'
+*       Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H
+*       Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H
+*  If Q1 is the unitary matrix from the QR factorization of B in the
+*  original equation A*x = lambda*B*x, then CGGHRD reduces the original
+*  problem to generalized Hessenberg form.
 *
 *  Arguments
 *  =========
@@ -53,10 +66,11 @@
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
-*          It is assumed that A is already upper triangular in rows and
-*          columns 1:ILO-1 and IHI+1:N.  ILO and IHI are normally set
-*          by a previous call to CGGBAL; otherwise they should be set
-*          to 1 and N respectively.
+*          ILO and IHI mark the rows and columns of A which are to be
+*          reduced.  It is assumed that A is already upper triangular
+*          in rows and columns 1:ILO-1 and IHI+1:N.  ILO and IHI are
+*          normally set by a previous call to CGGBAL; otherwise they
+*          should be set to 1 and N respectively.
 *          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
 *
 *  A       (input/output) COMPLEX array, dimension (LDA, N)
@@ -70,33 +84,28 @@
 *
 *  B       (input/output) COMPLEX array, dimension (LDB, N)
 *          On entry, the N-by-N upper triangular matrix B.
-*          On exit, the upper triangular matrix T = Q' B Z.  The
+*          On exit, the upper triangular matrix T = Q**H B Z.  The
 *          elements below the diagonal are set to zero.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of the array B.  LDB >= max(1,N).
 *
 *  Q       (input/output) COMPLEX array, dimension (LDQ, N)
-*          If COMPQ='N':  Q is not referenced.
-*          If COMPQ='I':  on entry, Q need not be set, and on exit it
-*                         contains the unitary matrix Q, where Q'
-*                         is the product of the Givens transformations
-*                         which are applied to A and B on the left.
-*          If COMPQ='V':  on entry, Q must contain a unitary matrix
-*                         Q1, and on exit this is overwritten by Q1*Q.
+*          On entry, if COMPQ = 'V', the unitary matrix Q1, typically
+*          from the QR factorization of B.
+*          On exit, if COMPQ='I', the unitary matrix Q, and if
+*          COMPQ = 'V', the product Q1*Q.
+*          Not referenced if COMPQ='N'.
 *
 *  LDQ     (input) INTEGER
 *          The leading dimension of the array Q.
 *          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
 *
 *  Z       (input/output) COMPLEX array, dimension (LDZ, N)
-*          If COMPZ='N':  Z is not referenced.
-*          If COMPZ='I':  on entry, Z need not be set, and on exit it
-*                         contains the unitary matrix Z, which is
-*                         the product of the Givens transformations
-*                         which are applied to A and B on the right.
-*          If COMPZ='V':  on entry, Z must contain a unitary matrix
-*                         Z1, and on exit this is overwritten by Z1*Z.
+*          On entry, if COMPZ = 'V', the unitary matrix Z1.
+*          On exit, if COMPZ='I', the unitary matrix Z, and if
+*          COMPZ = 'V', the product Z1*Z.
+*          Not referenced if COMPZ='N'.
 *
 *  LDZ     (input) INTEGER
 *          The leading dimension of the array Z.
diff -uNr LAPACK.orig/SRC/chbgst.f LAPACK/SRC/chbgst.f
--- LAPACK.orig/SRC/chbgst.f	Thu Nov  4 14:23:31 1999
+++ LAPACK/SRC/chbgst.f	Fri May 25 16:12:55 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     January 9, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO, VECT
@@ -131,7 +131,7 @@
          INFO = -3
       ELSE IF( KA.LT.0 ) THEN
          INFO = -4
-      ELSE IF( KB.LT.0 ) THEN
+      ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
          INFO = -5
       ELSE IF( LDAB.LT.KA+1 ) THEN
          INFO = -7
diff -uNr LAPACK.orig/SRC/chgeqz.f LAPACK/SRC/chgeqz.f
--- LAPACK.orig/SRC/chgeqz.f	Thu Nov  4 14:24:13 1999
+++ LAPACK/SRC/chgeqz.f	Fri May 25 16:12:16 2001
@@ -1,43 +1,64 @@
-      SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB,
+      SUBROUTINE CHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
      $                   ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK,
      $                   RWORK, INFO )
 *
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 3, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ, JOB
-      INTEGER            IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
+      INTEGER            IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N
 *     ..
 *     .. Array Arguments ..
       REAL               RWORK( * )
-      COMPLEX            A( LDA, * ), ALPHA( * ), B( LDB, * ),
-     $                   BETA( * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )
+      COMPLEX            ALPHA( * ), BETA( * ), H( LDH, * ),
+     $                   Q( LDQ, * ), T( LDT, * ), WORK( * ),
+     $                   Z( LDZ, * )
 *     ..
 *
 *  Purpose
 *  =======
 *
-*  CHGEQZ implements a single-shift version of the QZ
-*  method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i)
-*  of the equation
-*
-*       det( A - w(i) B ) = 0
-*
-*  If JOB='S', then the pair (A,B) is simultaneously
-*  reduced to Schur form (i.e., A and B are both upper triangular) by
-*  applying one unitary tranformation (usually called Q) on the left and
-*  another (usually called Z) on the right.  The diagonal elements of
-*  A are then ALPHA(1),...,ALPHA(N), and of B are BETA(1),...,BETA(N).
-*
-*  If JOB='S' and COMPQ and COMPZ are 'V' or 'I', then the unitary
-*  transformations used to reduce (A,B) are accumulated into the arrays
-*  Q and Z s.t.:
-*
-*       Q(in) A(in) Z(in)* = Q(out) A(out) Z(out)*
-*       Q(in) B(in) Z(in)* = Q(out) B(out) Z(out)*
+*  CHGEQZ computes the eigenvalues of a complex matrix pair (H,T),
+*  where H is an upper Hessenberg matrix and T is upper triangular,
+*  using the single-shift QZ method.
+*  Matrix pairs of this type are produced by the reduction to
+*  generalized upper Hessenberg form of a complex matrix pair (A,B):
+*  
+*     A = Q1*H*Z1**H,  B = Q1*T*Z1**H,
+*  
+*  as computed by CGGHRD.
+*  
+*  If JOB='S', then the Hessenberg-triangular pair (H,T) is
+*  also reduced to generalized Schur form,
+*  
+*     H = Q*S*Z**H,  T = Q*P*Z**H,
+*  
+*  where Q and Z are unitary matrices and S and P are upper triangular.
+*  
+*  Optionally, the unitary matrix Q from the generalized Schur
+*  factorization may be postmultiplied into an input matrix Q1, and the
+*  unitary matrix Z may be postmultiplied into an input matrix Z1.
+*  If Q1 and Z1 are the unitary matrices from CGGHRD that reduced
+*  the matrix pair (A,B) to generalized Hessenberg form, then the output
+*  matrices Q1*Q and Z1*Z are the unitary factors from the generalized
+*  Schur factorization of (A,B):
+*  
+*     A = (Q1*Q)*S*(Z1*Z)**H,  B = (Q1*Q)*P*(Z1*Z)**H.
+*  
+*  To avoid overflow, eigenvalues of the matrix pair (H,T)
+*  (equivalently, of (A,B)) are computed as a pair of complex values
+*  (alpha,beta).  If beta is nonzero, lambda = alpha / beta is an
+*  eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP)
+*     A*x = lambda*B*x
+*  and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the
+*  alternate form of the GNEP
+*     mu*A*y = B*y.
+*  The values of alpha and beta for the i-th eigenvalue can be read
+*  directly from the generalized Schur form:  alpha = S(i,i),
+*  beta = P(i,i).
 *
 *  Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
 *       Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
@@ -47,83 +68,88 @@
 *  =========
 *
 *  JOB     (input) CHARACTER*1
-*          = 'E': compute only ALPHA and BETA.  A and B will not
-*                 necessarily be put into generalized Schur form.
-*          = 'S': put A and B into generalized Schur form, as well
-*                 as computing ALPHA and BETA.
+*          = 'E': Compute eigenvalues only;
+*          = 'S': Computer eigenvalues and the Schur form.
 *
 *  COMPQ   (input) CHARACTER*1
-*          = 'N': do not modify Q.
-*          = 'V': multiply the array Q on the right by the conjugate
-*                 transpose of the unitary tranformation that is
-*                 applied to the left side of A and B to reduce them
-*                 to Schur form.
-*          = 'I': like COMPQ='V', except that Q will be initialized to
-*                 the identity first.
+*          = 'N': Left Schur vectors (Q) are not computed;
+*          = 'I': Q is initialized to the unit matrix and the matrix Q
+*                 of left Schur vectors of (H,T) is returned;
+*          = 'V': Q must contain a unitary matrix Q1 on entry and
+*                 the product Q1*Q is returned.
 *
 *  COMPZ   (input) CHARACTER*1
-*          = 'N': do not modify Z.
-*          = 'V': multiply the array Z on the right by the unitary
-*                 tranformation that is applied to the right side of
-*                 A and B to reduce them to Schur form.
-*          = 'I': like COMPZ='V', except that Z will be initialized to
-*                 the identity first.
+*          = 'N': Right Schur vectors (Z) are not computed;
+*          = 'I': Q is initialized to the unit matrix and the matrix Z
+*                 of right Schur vectors of (H,T) is returned;
+*          = 'V': Z must contain a unitary matrix Z1 on entry and
+*                 the product Z1*Z is returned.
 *
 *  N       (input) INTEGER
-*          The order of the matrices A, B, Q, and Z.  N >= 0.
+*          The order of the matrices H, T, Q, and Z.  N >= 0.
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
-*          It is assumed that A is already upper triangular in rows and
-*          columns 1:ILO-1 and IHI+1:N.
-*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
-*
-*  A       (input/output) COMPLEX array, dimension (LDA, N)
-*          On entry, the N-by-N upper Hessenberg matrix A.  Elements
-*          below the subdiagonal must be zero.
-*          If JOB='S', then on exit A and B will have been
-*             simultaneously reduced to upper triangular form.
-*          If JOB='E', then on exit A will have been destroyed.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max( 1, N ).
-*
-*  B       (input/output) COMPLEX array, dimension (LDB, N)
-*          On entry, the N-by-N upper triangular matrix B.  Elements
-*          below the diagonal must be zero.
-*          If JOB='S', then on exit A and B will have been
-*             simultaneously reduced to upper triangular form.
-*          If JOB='E', then on exit B will have been destroyed.
+*          ILO and IHI mark the rows and columns of H which are in
+*          Hessenberg form.  It is assumed that A is already upper
+*          triangular in rows and columns 1:ILO-1 and IHI+1:N.
+*          If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.
+*
+*  H       (input/output) COMPLEX array, dimension (LDH, N)
+*          On entry, the N-by-N upper Hessenberg matrix H.
+*          On exit, if JOB = 'S', H contains the upper triangular
+*          matrix S from the generalized Schur factorization.
+*          If JOB = 'E', the diagonal of H matches that of S, but
+*          the rest of H is unspecified.
+*
+*  LDH     (input) INTEGER
+*          The leading dimension of the array H.  LDH >= max( 1, N ).
+*
+*  T       (input/output) COMPLEX array, dimension (LDT, N)
+*          On entry, the N-by-N upper triangular matrix T.
+*          On exit, if JOB = 'S', T contains the upper triangular
+*          matrix P from the generalized Schur factorization.
+*          If JOB = 'E', the diagonal of T matches that of P, but
+*          the rest of T is unspecified.
 *
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max( 1, N ).
+*  LDT     (input) INTEGER
+*          The leading dimension of the array T.  LDT >= max( 1, N ).
 *
 *  ALPHA   (output) COMPLEX array, dimension (N)
-*          The diagonal elements of A when the pair (A,B) has been
-*          reduced to Schur form.  ALPHA(i)/BETA(i) i=1,...,N
-*          are the generalized eigenvalues.
+*          The complex scalars alpha that define the eigenvalues of
+*          GNEP.  ALPHA(i) = S(i,i) in the generalized Schur
+*          factorization.
 *
 *  BETA    (output) COMPLEX array, dimension (N)
-*          The diagonal elements of B when the pair (A,B) has been
-*          reduced to Schur form.  ALPHA(i)/BETA(i) i=1,...,N
-*          are the generalized eigenvalues.  A and B are normalized
-*          so that BETA(1),...,BETA(N) are non-negative real numbers.
+*          The real non-negative scalars beta that define the
+*          eigenvalues of GNEP.  BETA(i) = P(i,i) in the generalized
+*          Schur factorization.
+*
+*          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
+*          represent the j-th eigenvalue of the matrix pair (A,B), in
+*          one of the forms lambda = alpha/beta or mu = beta/alpha.
+*          Since either lambda or mu may overflow, they should not,
+*          in general, be computed.
 *
 *  Q       (input/output) COMPLEX array, dimension (LDQ, N)
-*          If COMPQ='N', then Q will not be referenced.
-*          If COMPQ='V' or 'I', then the conjugate transpose of the
-*             unitary transformations which are applied to A and B on
-*             the left will be applied to the array Q on the right.
+*          On entry, if COMPZ = 'V', the unitary matrix Q1 used in the
+*          reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the unitary matrix of left Schur
+*          vectors of (H,T), and if COMPZ = 'V', the unitary matrix of
+*          left Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
 *
 *  LDQ     (input) INTEGER
 *          The leading dimension of the array Q.  LDQ >= 1.
 *          If COMPQ='V' or 'I', then LDQ >= N.
 *
 *  Z       (input/output) COMPLEX array, dimension (LDZ, N)
-*          If COMPZ='N', then Z will not be referenced.
-*          If COMPZ='V' or 'I', then the unitary transformations which
-*             are applied to A and B on the right will be applied to the
-*             array Z on the right.
+*          On entry, if COMPZ = 'V', the unitary matrix Z1 used in the
+*          reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the unitary matrix of right Schur
+*          vectors of (H,T), and if COMPZ = 'V', the unitary matrix of
+*          right Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
 *
 *  LDZ     (input) INTEGER
 *          The leading dimension of the array Z.  LDZ >= 1.
@@ -145,13 +171,12 @@
 *  INFO    (output) INTEGER
 *          = 0: successful exit
 *          < 0: if INFO = -i, the i-th argument had an illegal value
-*          = 1,...,N: the QZ iteration did not converge.  (A,B) is not
+*          = 1,...,N: the QZ iteration did not converge.  (H,T) is not
 *                     in Schur form, but ALPHA(i) and BETA(i),
 *                     i=INFO+1,...,N should be correct.
-*          = N+1,...,2*N: the shift calculation failed.  (A,B) is not
+*          = N+1,...,2*N: the shift calculation failed.  (H,T) is not
 *                     in Schur form, but ALPHA(i) and BETA(i),
 *                     i=INFO-N+1,...,N should be correct.
-*          > 2*N:     various "impossible" errors.
 *
 *  Further Details
 *  ===============
@@ -178,7 +203,7 @@
       REAL               ABSB, ANORM, ASCALE, ATOL, BNORM, BSCALE, BTOL,
      $                   C, SAFMIN, TEMP, TEMP2, TEMPR, ULP
       COMPLEX            ABI22, AD11, AD12, AD21, AD22, CTEMP, CTEMP2,
-     $                   CTEMP3, ESHIFT, RTDISC, S, SHIFT, SIGNBC, T,
+     $                   CTEMP3, ESHIFT, RTDISC, S, SHIFT, SIGNBC, T1,
      $                   U12, X
 *     ..
 *     .. External Functions ..
@@ -255,9 +280,9 @@
          INFO = -5
       ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN
          INFO = -6
-      ELSE IF( LDA.LT.N ) THEN
+      ELSE IF( LDH.LT.N ) THEN
          INFO = -8
-      ELSE IF( LDB.LT.N ) THEN
+      ELSE IF( LDT.LT.N ) THEN
          INFO = -10
       ELSE IF( LDQ.LT.1 .OR. ( ILQ .AND. LDQ.LT.N ) ) THEN
          INFO = -14
@@ -293,8 +318,8 @@
       IN = IHI + 1 - ILO
       SAFMIN = SLAMCH( 'S' )
       ULP = SLAMCH( 'E' )*SLAMCH( 'B' )
-      ANORM = CLANHS( 'F', IN, A( ILO, ILO ), LDA, RWORK )
-      BNORM = CLANHS( 'F', IN, B( ILO, ILO ), LDB, RWORK )
+      ANORM = CLANHS( 'F', IN, H( ILO, ILO ), LDH, RWORK )
+      BNORM = CLANHS( 'F', IN, T( ILO, ILO ), LDT, RWORK )
       ATOL = MAX( SAFMIN, ULP*ANORM )
       BTOL = MAX( SAFMIN, ULP*BNORM )
       ASCALE = ONE / MAX( SAFMIN, ANORM )
@@ -304,23 +329,23 @@
 *     Set Eigenvalues IHI+1:N
 *
       DO 10 J = IHI + 1, N
-         ABSB = ABS( B( J, J ) )
+         ABSB = ABS( T( J, J ) )
          IF( ABSB.GT.SAFMIN ) THEN
-            SIGNBC = CONJG( B( J, J ) / ABSB )
-            B( J, J ) = ABSB
+            SIGNBC = CONJG( T( J, J ) / ABSB )
+            T( J, J ) = ABSB
             IF( ILSCHR ) THEN
-               CALL CSCAL( J-1, SIGNBC, B( 1, J ), 1 )
-               CALL CSCAL( J, SIGNBC, A( 1, J ), 1 )
+               CALL CSCAL( J-1, SIGNBC, T( 1, J ), 1 )
+               CALL CSCAL( J, SIGNBC, H( 1, J ), 1 )
             ELSE
-               A( J, J ) = A( J, J )*SIGNBC
+               H( J, J ) = H( J, J )*SIGNBC
             END IF
             IF( ILZ )
      $         CALL CSCAL( N, SIGNBC, Z( 1, J ), 1 )
          ELSE
-            B( J, J ) = CZERO
+            T( J, J ) = CZERO
          END IF
-         ALPHA( J ) = A( J, J )
-         BETA( J ) = B( J, J )
+         ALPHA( J ) = H( J, J )
+         BETA( J ) = T( J, J )
    10 CONTINUE
 *
 *     If IHI < ILO, skip QZ steps
@@ -365,22 +390,22 @@
 *        Split the matrix if possible.
 *
 *        Two tests:
-*           1: A(j,j-1)=0  or  j=ILO
-*           2: B(j,j)=0
+*           1: H(j,j-1)=0  or  j=ILO
+*           2: T(j,j)=0
 *
 *        Special case: j=ILAST
 *
          IF( ILAST.EQ.ILO ) THEN
             GO TO 60
          ELSE
-            IF( ABS1( A( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
-               A( ILAST, ILAST-1 ) = CZERO
+            IF( ABS1( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+               H( ILAST, ILAST-1 ) = CZERO
                GO TO 60
             END IF
          END IF
 *
-         IF( ABS( B( ILAST, ILAST ) ).LE.BTOL ) THEN
-            B( ILAST, ILAST ) = CZERO
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+            T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
 *
@@ -388,30 +413,30 @@
 *
          DO 40 J = ILAST - 1, ILO, -1
 *
-*           Test 1: for A(j,j-1)=0 or j=ILO
+*           Test 1: for H(j,j-1)=0 or j=ILO
 *
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS1( A( J, J-1 ) ).LE.ATOL ) THEN
-                  A( J, J-1 ) = CZERO
+               IF( ABS1( H( J, J-1 ) ).LE.ATOL ) THEN
+                  H( J, J-1 ) = CZERO
                   ILAZRO = .TRUE.
                ELSE
                   ILAZRO = .FALSE.
                END IF
             END IF
 *
-*           Test 2: for B(j,j)=0
+*           Test 2: for T(j,j)=0
 *
-            IF( ABS( B( J, J ) ).LT.BTOL ) THEN
-               B( J, J ) = CZERO
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+               T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
 *
                ILAZR2 = .FALSE.
                IF( .NOT.ILAZRO ) THEN
-                  IF( ABS1( A( J, J-1 ) )*( ASCALE*ABS1( A( J+1,
-     $                J ) ) ).LE.ABS1( A( J, J ) )*( ASCALE*ATOL ) )
+                  IF( ABS1( H( J, J-1 ) )*( ASCALE*ABS1( H( J+1,
+     $                J ) ) ).LE.ABS1( H( J, J ) )*( ASCALE*ATOL ) )
      $                ILAZR2 = .TRUE.
                END IF
 *
@@ -423,21 +448,21 @@
 *
                IF( ILAZRO .OR. ILAZR2 ) THEN
                   DO 20 JCH = J, ILAST - 1
-                     CTEMP = A( JCH, JCH )
-                     CALL CLARTG( CTEMP, A( JCH+1, JCH ), C, S,
-     $                            A( JCH, JCH ) )
-                     A( JCH+1, JCH ) = CZERO
-                     CALL CROT( ILASTM-JCH, A( JCH, JCH+1 ), LDA,
-     $                          A( JCH+1, JCH+1 ), LDA, C, S )
-                     CALL CROT( ILASTM-JCH, B( JCH, JCH+1 ), LDB,
-     $                          B( JCH+1, JCH+1 ), LDB, C, S )
+                     CTEMP = H( JCH, JCH )
+                     CALL CLARTG( CTEMP, H( JCH+1, JCH ), C, S,
+     $                            H( JCH, JCH ) )
+                     H( JCH+1, JCH ) = CZERO
+                     CALL CROT( ILASTM-JCH, H( JCH, JCH+1 ), LDH,
+     $                          H( JCH+1, JCH+1 ), LDH, C, S )
+                     CALL CROT( ILASTM-JCH, T( JCH, JCH+1 ), LDT,
+     $                          T( JCH+1, JCH+1 ), LDT, C, S )
                      IF( ILQ )
      $                  CALL CROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
      $                             C, CONJG( S ) )
                      IF( ILAZR2 )
-     $                  A( JCH, JCH-1 ) = A( JCH, JCH-1 )*C
+     $                  H( JCH, JCH-1 ) = H( JCH, JCH-1 )*C
                      ILAZR2 = .FALSE.
-                     IF( ABS1( B( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
+                     IF( ABS1( T( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
                         IF( JCH+1.GE.ILAST ) THEN
                            GO TO 60
                         ELSE
@@ -445,35 +470,35 @@
                            GO TO 70
                         END IF
                      END IF
-                     B( JCH+1, JCH+1 ) = CZERO
+                     T( JCH+1, JCH+1 ) = CZERO
    20             CONTINUE
                   GO TO 50
                ELSE
 *
-*                 Only test 2 passed -- chase the zero to B(ILAST,ILAST)
-*                 Then process as in the case B(ILAST,ILAST)=0
+*                 Only test 2 passed -- chase the zero to T(ILAST,ILAST)
+*                 Then process as in the case T(ILAST,ILAST)=0
 *
                   DO 30 JCH = J, ILAST - 1
-                     CTEMP = B( JCH, JCH+1 )
-                     CALL CLARTG( CTEMP, B( JCH+1, JCH+1 ), C, S,
-     $                            B( JCH, JCH+1 ) )
-                     B( JCH+1, JCH+1 ) = CZERO
+                     CTEMP = T( JCH, JCH+1 )
+                     CALL CLARTG( CTEMP, T( JCH+1, JCH+1 ), C, S,
+     $                            T( JCH, JCH+1 ) )
+                     T( JCH+1, JCH+1 ) = CZERO
                      IF( JCH.LT.ILASTM-1 )
-     $                  CALL CROT( ILASTM-JCH-1, B( JCH, JCH+2 ), LDB,
-     $                             B( JCH+1, JCH+2 ), LDB, C, S )
-                     CALL CROT( ILASTM-JCH+2, A( JCH, JCH-1 ), LDA,
-     $                          A( JCH+1, JCH-1 ), LDA, C, S )
+     $                  CALL CROT( ILASTM-JCH-1, T( JCH, JCH+2 ), LDT,
+     $                             T( JCH+1, JCH+2 ), LDT, C, S )
+                     CALL CROT( ILASTM-JCH+2, H( JCH, JCH-1 ), LDH,
+     $                          H( JCH+1, JCH-1 ), LDH, C, S )
                      IF( ILQ )
      $                  CALL CROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
      $                             C, CONJG( S ) )
-                     CTEMP = A( JCH+1, JCH )
-                     CALL CLARTG( CTEMP, A( JCH+1, JCH-1 ), C, S,
-     $                            A( JCH+1, JCH ) )
-                     A( JCH+1, JCH-1 ) = CZERO
-                     CALL CROT( JCH+1-IFRSTM, A( IFRSTM, JCH ), 1,
-     $                          A( IFRSTM, JCH-1 ), 1, C, S )
-                     CALL CROT( JCH-IFRSTM, B( IFRSTM, JCH ), 1,
-     $                          B( IFRSTM, JCH-1 ), 1, C, S )
+                     CTEMP = H( JCH+1, JCH )
+                     CALL CLARTG( CTEMP, H( JCH+1, JCH-1 ), C, S,
+     $                            H( JCH+1, JCH ) )
+                     H( JCH+1, JCH-1 ) = CZERO
+                     CALL CROT( JCH+1-IFRSTM, H( IFRSTM, JCH ), 1,
+     $                          H( IFRSTM, JCH-1 ), 1, C, S )
+                     CALL CROT( JCH-IFRSTM, T( IFRSTM, JCH ), 1,
+     $                          T( IFRSTM, JCH-1 ), 1, C, S )
                      IF( ILZ )
      $                  CALL CROT( N, Z( 1, JCH ), 1, Z( 1, JCH-1 ), 1,
      $                             C, S )
@@ -497,42 +522,42 @@
          INFO = 2*N + 1
          GO TO 210
 *
-*        B(ILAST,ILAST)=0 -- clear A(ILAST,ILAST-1) to split off a
+*        T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a
 *        1x1 block.
 *
    50    CONTINUE
-         CTEMP = A( ILAST, ILAST )
-         CALL CLARTG( CTEMP, A( ILAST, ILAST-1 ), C, S,
-     $                A( ILAST, ILAST ) )
-         A( ILAST, ILAST-1 ) = CZERO
-         CALL CROT( ILAST-IFRSTM, A( IFRSTM, ILAST ), 1,
-     $              A( IFRSTM, ILAST-1 ), 1, C, S )
-         CALL CROT( ILAST-IFRSTM, B( IFRSTM, ILAST ), 1,
-     $              B( IFRSTM, ILAST-1 ), 1, C, S )
+         CTEMP = H( ILAST, ILAST )
+         CALL CLARTG( CTEMP, H( ILAST, ILAST-1 ), C, S,
+     $                H( ILAST, ILAST ) )
+         H( ILAST, ILAST-1 ) = CZERO
+         CALL CROT( ILAST-IFRSTM, H( IFRSTM, ILAST ), 1,
+     $              H( IFRSTM, ILAST-1 ), 1, C, S )
+         CALL CROT( ILAST-IFRSTM, T( IFRSTM, ILAST ), 1,
+     $              T( IFRSTM, ILAST-1 ), 1, C, S )
          IF( ILZ )
      $      CALL CROT( N, Z( 1, ILAST ), 1, Z( 1, ILAST-1 ), 1, C, S )
 *
-*        A(ILAST,ILAST-1)=0 -- Standardize B, set ALPHA and BETA
+*        H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHA and BETA
 *
    60    CONTINUE
-         ABSB = ABS( B( ILAST, ILAST ) )
+         ABSB = ABS( T( ILAST, ILAST ) )
          IF( ABSB.GT.SAFMIN ) THEN
-            SIGNBC = CONJG( B( ILAST, ILAST ) / ABSB )
-            B( ILAST, ILAST ) = ABSB
+            SIGNBC = CONJG( T( ILAST, ILAST ) / ABSB )
+            T( ILAST, ILAST ) = ABSB
             IF( ILSCHR ) THEN
-               CALL CSCAL( ILAST-IFRSTM, SIGNBC, B( IFRSTM, ILAST ), 1 )
-               CALL CSCAL( ILAST+1-IFRSTM, SIGNBC, A( IFRSTM, ILAST ),
+               CALL CSCAL( ILAST-IFRSTM, SIGNBC, T( IFRSTM, ILAST ), 1 )
+               CALL CSCAL( ILAST+1-IFRSTM, SIGNBC, H( IFRSTM, ILAST ),
      $                     1 )
             ELSE
-               A( ILAST, ILAST ) = A( ILAST, ILAST )*SIGNBC
+               H( ILAST, ILAST ) = H( ILAST, ILAST )*SIGNBC
             END IF
             IF( ILZ )
      $         CALL CSCAL( N, SIGNBC, Z( 1, ILAST ), 1 )
          ELSE
-            B( ILAST, ILAST ) = CZERO
+            T( ILAST, ILAST ) = CZERO
          END IF
-         ALPHA( ILAST ) = A( ILAST, ILAST )
-         BETA( ILAST ) = B( ILAST, ILAST )
+         ALPHA( ILAST ) = H( ILAST, ILAST )
+         BETA( ILAST ) = T( ILAST, ILAST )
 *
 *        Go to next block -- exit if finished.
 *
@@ -565,7 +590,7 @@
 *        Compute the Shift.
 *
 *        At this point, IFIRST < ILAST, and the diagonal elements of
-*        B(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
+*        T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
 *        magnitude)
 *
          IF( ( IITER / 10 )*10.NE.IITER ) THEN
@@ -577,33 +602,33 @@
 *           We factor B as U*D, where U has unit diagonals, and
 *           compute (A*inv(D))*inv(U).
 *
-            U12 = ( BSCALE*B( ILAST-1, ILAST ) ) /
-     $            ( BSCALE*B( ILAST, ILAST ) )
-            AD11 = ( ASCALE*A( ILAST-1, ILAST-1 ) ) /
-     $             ( BSCALE*B( ILAST-1, ILAST-1 ) )
-            AD21 = ( ASCALE*A( ILAST, ILAST-1 ) ) /
-     $             ( BSCALE*B( ILAST-1, ILAST-1 ) )
-            AD12 = ( ASCALE*A( ILAST-1, ILAST ) ) /
-     $             ( BSCALE*B( ILAST, ILAST ) )
-            AD22 = ( ASCALE*A( ILAST, ILAST ) ) /
-     $             ( BSCALE*B( ILAST, ILAST ) )
+            U12 = ( BSCALE*T( ILAST-1, ILAST ) ) /
+     $            ( BSCALE*T( ILAST, ILAST ) )
+            AD11 = ( ASCALE*H( ILAST-1, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD21 = ( ASCALE*H( ILAST, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD12 = ( ASCALE*H( ILAST-1, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            AD22 = ( ASCALE*H( ILAST, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
             ABI22 = AD22 - U12*AD21
 *
-            T = HALF*( AD11+ABI22 )
-            RTDISC = SQRT( T**2+AD12*AD21-AD11*AD22 )
-            TEMP = REAL( T-ABI22 )*REAL( RTDISC ) +
-     $             AIMAG( T-ABI22 )*AIMAG( RTDISC )
+            T1 = HALF*( AD11+ABI22 )
+            RTDISC = SQRT( T1**2+AD12*AD21-AD11*AD22 )
+            TEMP = REAL( T1-ABI22 )*REAL( RTDISC ) +
+     $             AIMAG( T1-ABI22 )*AIMAG( RTDISC )
             IF( TEMP.LE.ZERO ) THEN
-               SHIFT = T + RTDISC
+               SHIFT = T1 + RTDISC
             ELSE
-               SHIFT = T - RTDISC
+               SHIFT = T1 - RTDISC
             END IF
          ELSE
 *
 *           Exceptional shift.  Chosen for no particularly good reason.
 *
-            ESHIFT = ESHIFT + CONJG( ( ASCALE*A( ILAST-1, ILAST ) ) /
-     $               ( BSCALE*B( ILAST-1, ILAST-1 ) ) )
+            ESHIFT = ESHIFT + CONJG( ( ASCALE*H( ILAST-1, ILAST ) ) /
+     $               ( BSCALE*T( ILAST-1, ILAST-1 ) ) )
             SHIFT = ESHIFT
          END IF
 *
@@ -611,46 +636,46 @@
 *
          DO 80 J = ILAST - 1, IFIRST + 1, -1
             ISTART = J
-            CTEMP = ASCALE*A( J, J ) - SHIFT*( BSCALE*B( J, J ) )
+            CTEMP = ASCALE*H( J, J ) - SHIFT*( BSCALE*T( J, J ) )
             TEMP = ABS1( CTEMP )
-            TEMP2 = ASCALE*ABS1( A( J+1, J ) )
+            TEMP2 = ASCALE*ABS1( H( J+1, J ) )
             TEMPR = MAX( TEMP, TEMP2 )
             IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
                TEMP = TEMP / TEMPR
                TEMP2 = TEMP2 / TEMPR
             END IF
-            IF( ABS1( A( J, J-1 ) )*TEMP2.LE.TEMP*ATOL )
+            IF( ABS1( H( J, J-1 ) )*TEMP2.LE.TEMP*ATOL )
      $         GO TO 90
    80    CONTINUE
 *
          ISTART = IFIRST
-         CTEMP = ASCALE*A( IFIRST, IFIRST ) -
-     $           SHIFT*( BSCALE*B( IFIRST, IFIRST ) )
+         CTEMP = ASCALE*H( IFIRST, IFIRST ) -
+     $           SHIFT*( BSCALE*T( IFIRST, IFIRST ) )
    90    CONTINUE
 *
 *        Do an implicit-shift QZ sweep.
 *
 *        Initial Q
 *
-         CTEMP2 = ASCALE*A( ISTART+1, ISTART )
+         CTEMP2 = ASCALE*H( ISTART+1, ISTART )
          CALL CLARTG( CTEMP, CTEMP2, C, S, CTEMP3 )
 *
 *        Sweep
 *
          DO 150 J = ISTART, ILAST - 1
             IF( J.GT.ISTART ) THEN
-               CTEMP = A( J, J-1 )
-               CALL CLARTG( CTEMP, A( J+1, J-1 ), C, S, A( J, J-1 ) )
-               A( J+1, J-1 ) = CZERO
+               CTEMP = H( J, J-1 )
+               CALL CLARTG( CTEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+               H( J+1, J-1 ) = CZERO
             END IF
 *
             DO 100 JC = J, ILASTM
-               CTEMP = C*A( J, JC ) + S*A( J+1, JC )
-               A( J+1, JC ) = -CONJG( S )*A( J, JC ) + C*A( J+1, JC )
-               A( J, JC ) = CTEMP
-               CTEMP2 = C*B( J, JC ) + S*B( J+1, JC )
-               B( J+1, JC ) = -CONJG( S )*B( J, JC ) + C*B( J+1, JC )
-               B( J, JC ) = CTEMP2
+               CTEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -CONJG( S )*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = CTEMP
+               CTEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -CONJG( S )*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = CTEMP2
   100       CONTINUE
             IF( ILQ ) THEN
                DO 110 JR = 1, N
@@ -660,19 +685,19 @@
   110          CONTINUE
             END IF
 *
-            CTEMP = B( J+1, J+1 )
-            CALL CLARTG( CTEMP, B( J+1, J ), C, S, B( J+1, J+1 ) )
-            B( J+1, J ) = CZERO
+            CTEMP = T( J+1, J+1 )
+            CALL CLARTG( CTEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = CZERO
 *
             DO 120 JR = IFRSTM, MIN( J+2, ILAST )
-               CTEMP = C*A( JR, J+1 ) + S*A( JR, J )
-               A( JR, J ) = -CONJG( S )*A( JR, J+1 ) + C*A( JR, J )
-               A( JR, J+1 ) = CTEMP
+               CTEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -CONJG( S )*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = CTEMP
   120       CONTINUE
             DO 130 JR = IFRSTM, J
-               CTEMP = C*B( JR, J+1 ) + S*B( JR, J )
-               B( JR, J ) = -CONJG( S )*B( JR, J+1 ) + C*B( JR, J )
-               B( JR, J+1 ) = CTEMP
+               CTEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -CONJG( S )*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = CTEMP
   130       CONTINUE
             IF( ILZ ) THEN
                DO 140 JR = 1, N
@@ -700,23 +725,23 @@
 *     Set Eigenvalues 1:ILO-1
 *
       DO 200 J = 1, ILO - 1
-         ABSB = ABS( B( J, J ) )
+         ABSB = ABS( T( J, J ) )
          IF( ABSB.GT.SAFMIN ) THEN
-            SIGNBC = CONJG( B( J, J ) / ABSB )
-            B( J, J ) = ABSB
+            SIGNBC = CONJG( T( J, J ) / ABSB )
+            T( J, J ) = ABSB
             IF( ILSCHR ) THEN
-               CALL CSCAL( J-1, SIGNBC, B( 1, J ), 1 )
-               CALL CSCAL( J, SIGNBC, A( 1, J ), 1 )
+               CALL CSCAL( J-1, SIGNBC, T( 1, J ), 1 )
+               CALL CSCAL( J, SIGNBC, H( 1, J ), 1 )
             ELSE
-               A( J, J ) = A( J, J )*SIGNBC
+               H( J, J ) = H( J, J )*SIGNBC
             END IF
             IF( ILZ )
      $         CALL CSCAL( N, SIGNBC, Z( 1, J ), 1 )
          ELSE
-            B( J, J ) = CZERO
+            T( J, J ) = CZERO
          END IF
-         ALPHA( J ) = A( J, J )
-         BETA( J ) = B( J, J )
+         ALPHA( J ) = H( J, J )
+         BETA( J ) = T( J, J )
   200 CONTINUE
 *
 *     Normal Termination
diff -uNr LAPACK.orig/SRC/clasr.f LAPACK/SRC/clasr.f
--- LAPACK.orig/SRC/clasr.f	Thu Nov  4 14:24:17 1999
+++ LAPACK/SRC/clasr.f	Fri May 25 16:12:37 2001
@@ -3,7 +3,7 @@
 *  -- LAPACK auxiliary routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1992
+*     May 3, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIRECT, PIVOT, SIDE
@@ -17,42 +17,77 @@
 *  Purpose
 *  =======
 *
-*  CLASR   performs the transformation
+*  CLASR applies a sequence of real plane rotations to a complex matrix
+*  A, from either the left or the right.
 *
-*     A := P*A,   when SIDE = 'L' or 'l'  (  Left-hand side )
+*  When SIDE = 'L', the transformation takes the form
 *
-*     A := A*P',  when SIDE = 'R' or 'r'  ( Right-hand side )
+*     A := P*A
 *
-*  where A is an m by n complex matrix and P is an orthogonal matrix,
-*  consisting of a sequence of plane rotations determined by the
-*  parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l'
-*  and z = n when SIDE = 'R' or 'r' ):
+*  and when SIDE = 'R', the transformation takes the form
 *
-*  When  DIRECT = 'F' or 'f'  ( Forward sequence ) then
-*
-*     P = P( z - 1 )*...*P( 2 )*P( 1 ),
-*
-*  and when DIRECT = 'B' or 'b'  ( Backward sequence ) then
-*
-*     P = P( 1 )*P( 2 )*...*P( z - 1 ),
-*
-*  where  P( k ) is a plane rotation matrix for the following planes:
-*
-*     when  PIVOT = 'V' or 'v'  ( Variable pivot ),
-*        the plane ( k, k + 1 )
-*
-*     when  PIVOT = 'T' or 't'  ( Top pivot ),
-*        the plane ( 1, k + 1 )
-*
-*     when  PIVOT = 'B' or 'b'  ( Bottom pivot ),
-*        the plane ( k, z )
-*
-*  c( k ) and s( k )  must contain the  cosine and sine that define the
-*  matrix  P( k ).  The two by two plane rotation part of the matrix
-*  P( k ), R( k ), is assumed to be of the form
-*
-*     R( k ) = (  c( k )  s( k ) ).
-*              ( -s( k )  c( k ) )
+*     A := A*P**T
+*
+*  where P is an orthogonal matrix consisting of a sequence of z plane
+*  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
+*  and P**T is the transpose of P.
+*  
+*  When DIRECT = 'F' (Forward sequence), then
+*  
+*     P = P(z-1) * ... * P(2) * P(1)
+*  
+*  and when DIRECT = 'B' (Backward sequence), then
+*  
+*     P = P(1) * P(2) * ... * P(z-1)
+*  
+*  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
+*  
+*     R(k) = (  c(k)  s(k) )
+*          = ( -s(k)  c(k) ).
+*  
+*  When PIVOT = 'V' (Variable pivot), the rotation is performed
+*  for the plane (k,k+1), i.e., P(k) has the form
+*  
+*     P(k) = (  1                                            )
+*            (       ...                                     )
+*            (              1                                )
+*            (                   c(k)  s(k)                  )
+*            (                  -s(k)  c(k)                  )
+*            (                                1              )
+*            (                                     ...       )
+*            (                                            1  )
+*  
+*  where R(k) appears as a rank-2 modification to the identity matrix in
+*  rows and columns k and k+1.
+*  
+*  When PIVOT = 'T' (Top pivot), the rotation is performed for the
+*  plane (1,k+1), so P(k) has the form
+*  
+*     P(k) = (  c(k)                    s(k)                 )
+*            (         1                                     )
+*            (              ...                              )
+*            (                     1                         )
+*            ( -s(k)                    c(k)                 )
+*            (                                 1             )
+*            (                                      ...      )
+*            (                                             1 )
+*  
+*  where R(k) appears in rows and columns 1 and k+1.
+*  
+*  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
+*  performed for the plane (k,z), giving P(k) the form
+*  
+*     P(k) = ( 1                                             )
+*            (      ...                                      )
+*            (             1                                 )
+*            (                  c(k)                    s(k) )
+*            (                         1                     )
+*            (                              ...              )
+*            (                                     1         )
+*            (                 -s(k)                    c(k) )
+*  
+*  where R(k) appears in rows and columns k and z.  The rotations are
+*  performed without ever forming P(k) explicitly.
 *
 *  Arguments
 *  =========
@@ -61,13 +96,13 @@
 *          Specifies whether the plane rotation matrix P is applied to
 *          A on the left or the right.
 *          = 'L':  Left, compute A := P*A
-*          = 'R':  Right, compute A:= A*P'
+*          = 'R':  Right, compute A:= A*P**T
 *
 *  DIRECT  (input) CHARACTER*1
 *          Specifies whether P is a forward or backward sequence of
 *          plane rotations.
-*          = 'F':  Forward, P = P( z - 1 )*...*P( 2 )*P( 1 )
-*          = 'B':  Backward, P = P( 1 )*P( 2 )*...*P( z - 1 )
+*          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
+*          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
 *
 *  PIVOT   (input) CHARACTER*1
 *          Specifies the plane for which P(k) is a plane rotation
@@ -84,18 +119,22 @@
 *          The number of columns of the matrix A.  If n <= 1, an
 *          immediate return is effected.
 *
-*  C, S    (input) REAL arrays, dimension
+*  C       (input) REAL array, dimension
+*                  (M-1) if SIDE = 'L'
+*                  (N-1) if SIDE = 'R'
+*          The cosines c(k) of the plane rotations.
+*
+*  S       (input) REAL array, dimension
 *                  (M-1) if SIDE = 'L'
 *                  (N-1) if SIDE = 'R'
-*          c(k) and s(k) contain the cosine and sine that define the
-*          matrix P(k).  The two by two plane rotation part of the
-*          matrix P(k), R(k), is assumed to be of the form
-*          R( k ) = (  c( k )  s( k ) ).
-*                   ( -s( k )  c( k ) )
+*          The sines s(k) of the plane rotations.  The 2-by-2 plane
+*          rotation part of the matrix P(k), R(k), has the form
+*          R(k) = (  c(k)  s(k) )
+*                 ( -s(k)  c(k) ).
 *
 *  A       (input/output) COMPLEX array, dimension (LDA,N)
-*          The m by n matrix A.  On exit, A is overwritten by P*A if
-*          SIDE = 'R' or by A*P' if SIDE = 'L'.
+*          The M-by-N matrix A.  On exit, A is overwritten by P*A if
+*          SIDE = 'R' or by A*P**T if SIDE = 'L'.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
diff -uNr LAPACK.orig/SRC/ctgevc.f LAPACK/SRC/ctgevc.f
--- LAPACK.orig/SRC/ctgevc.f	Thu Nov  4 14:26:09 1999
+++ LAPACK/SRC/ctgevc.f	Fri May 25 16:13:37 2001
@@ -1,19 +1,19 @@
-      SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
+      SUBROUTINE CTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
      $                   LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO )
 *
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 4, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          HOWMNY, SIDE
-      INTEGER            INFO, LDA, LDB, LDVL, LDVR, M, MM, N
+      INTEGER            INFO, LDP, LDS, LDVL, LDVR, M, MM, N
 *     ..
 *     .. Array Arguments ..
       LOGICAL            SELECT( * )
       REAL               RWORK( * )
-      COMPLEX            A( LDA, * ), B( LDB, * ), VL( LDVL, * ),
+      COMPLEX            P( LDP, * ), S( LDS, * ), VL( LDVL, * ),
      $                   VR( LDVR, * ), WORK( * )
 *     ..
 *
@@ -21,28 +21,30 @@
 *  Purpose
 *  =======
 *
-*  CTGEVC computes some or all of the right and/or left generalized
-*  eigenvectors of a pair of complex upper triangular matrices (A,B).
-*
-*  The right generalized eigenvector x and the left generalized
-*  eigenvector y of (A,B) corresponding to a generalized eigenvalue
-*  w are defined by:
-*
-*          (A - wB) * x = 0  and  y**H * (A - wB) = 0
-*
+*  CTGEVC computes some or all of the right and/or left eigenvectors of
+*  a pair of complex matrices (S,P), where S and P are upper triangular.
+*  Matrix pairs of this type are produced by the generalized Schur
+*  factorization of a complex matrix pair (A,B):
+*  
+*     A = Q*S*Z**H,  B = Q*P*Z**H
+*  
+*  as computed by CGGHRD + CHGEQZ.
+*  
+*  The right eigenvector x and the left eigenvector y of (S,P)
+*  corresponding to an eigenvalue w are defined by:
+*  
+*     S*x = w*P*x,  (y**H)*S = w*(y**H)*P,
+*  
 *  where y**H denotes the conjugate tranpose of y.
-*
-*  If an eigenvalue w is determined by zero diagonal elements of both A
-*  and B, a unit vector is returned as the corresponding eigenvector.
-*
-*  If all eigenvectors are requested, the routine may either return
-*  the matrices X and/or Y of right or left eigenvectors of (A,B), or
-*  the products Z*X and/or Q*Y, where Z and Q are input unitary
-*  matrices.  If (A,B) was obtained from the generalized Schur
-*  factorization of an original pair of matrices
-*     (A0,B0) = (Q*A*Z**H,Q*B*Z**H),
-*  then Z*X and Q*Y are the matrices of right or left eigenvectors of
-*  A.
+*  The eigenvalues are not input to this routine, but are computed
+*  directly from the diagonal elements of S and P.
+*  
+*  This routine returns the matrices X and/or Y of right and left
+*  eigenvectors of (S,P), or the products Z*X and/or Q*Y,
+*  where Z and Q are input matrices.
+*  If Q and Z are the unitary factors from the generalized Schur
+*  factorization of a matrix pair (A,B), then Z*X and Q*Y
+*  are the matrices of right and left eigenvectors of (A,B).
 *
 *  Arguments
 *  =========
@@ -54,66 +56,66 @@
 *
 *  HOWMNY  (input) CHARACTER*1
 *          = 'A': compute all right and/or left eigenvectors;
-*          = 'B': compute all right and/or left eigenvectors, and
-*                 backtransform them using the input matrices supplied
-*                 in VR and/or VL;
+*          = 'B': compute all right and/or left eigenvectors,
+*                 backtransformed by the matrices in VR and/or VL;
 *          = 'S': compute selected right and/or left eigenvectors,
 *                 specified by the logical array SELECT.
 *
 *  SELECT  (input) LOGICAL array, dimension (N)
 *          If HOWMNY='S', SELECT specifies the eigenvectors to be
-*          computed.
-*          If HOWMNY='A' or 'B', SELECT is not referenced.
-*          To select the eigenvector corresponding to the j-th
-*          eigenvalue, SELECT(j) must be set to .TRUE..
+*          computed.  The eigenvector corresponding to the j-th
+*          eigenvalue is computed if SELECT(j) = .TRUE..
+*          Not referenced if HOWMNY = 'A' or 'B'.
 *
 *  N       (input) INTEGER
-*          The order of the matrices A and B.  N >= 0.
-*
-*  A       (input) COMPLEX array, dimension (LDA,N)
-*          The upper triangular matrix A.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of array A.  LDA >= max(1,N).
+*          The order of the matrices S and P.  N >= 0.
 *
-*  B       (input) COMPLEX array, dimension (LDB,N)
-*          The upper triangular matrix B.  B must have real diagonal
-*          elements.
+*  S       (input) COMPLEX array, dimension (LDS,N)
+*          The upper triangular matrix S from a generalized Schur
+*          factorization, as computed by CHGEQZ.
+*
+*  LDS     (input) INTEGER
+*          The leading dimension of array S.  LDS >= max(1,N).
+*
+*  P       (input) COMPLEX array, dimension (LDP,N)
+*          The upper triangular matrix P from a generalized Schur
+*          factorization, as computed by CHGEQZ.  P must have real
+*          diagonal elements.
 *
-*  LDB     (input) INTEGER
-*          The leading dimension of array B.  LDB >= max(1,N).
+*  LDP     (input) INTEGER
+*          The leading dimension of array P.  LDP >= max(1,N).
 *
 *  VL      (input/output) COMPLEX array, dimension (LDVL,MM)
 *          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
 *          contain an N-by-N matrix Q (usually the unitary matrix Q
 *          of left Schur vectors returned by CHGEQZ).
 *          On exit, if SIDE = 'L' or 'B', VL contains:
-*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B);
+*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
 *          if HOWMNY = 'B', the matrix Q*Y;
-*          if HOWMNY = 'S', the left eigenvectors of (A,B) specified by
+*          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
 *                      SELECT, stored consecutively in the columns of
 *                      VL, in the same order as their eigenvalues.
-*          If SIDE = 'R', VL is not referenced.
+*          Not referenced if SIDE = 'R'.
 *
 *  LDVL    (input) INTEGER
-*          The leading dimension of array VL.
-*          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
+*          The leading dimension of array VL.  LDVL >= 1, and if
+*          SIDE = 'L' or 'l' or 'B' or 'b', LDVL >= N.
 *
 *  VR      (input/output) COMPLEX array, dimension (LDVR,MM)
 *          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
 *          contain an N-by-N matrix Q (usually the unitary matrix Z
 *          of right Schur vectors returned by CHGEQZ).
 *          On exit, if SIDE = 'R' or 'B', VR contains:
-*          if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B);
+*          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
 *          if HOWMNY = 'B', the matrix Z*X;
-*          if HOWMNY = 'S', the right eigenvectors of (A,B) specified by
+*          if HOWMNY = 'S', the right eigenvectors of (S,P) specified by
 *                      SELECT, stored consecutively in the columns of
 *                      VR, in the same order as their eigenvalues.
-*          If SIDE = 'L', VR is not referenced.
+*          Not referenced if SIDE = 'L'.
 *
 *  LDVR    (input) INTEGER
-*          The leading dimension of the array VR.
-*          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
+*          The leading dimension of the array VR.  LDVR >= 1, and if
+*          SIDE = 'R' or 'B', LDVR >= N.
 *
 *  MM      (input) INTEGER
 *          The number of columns in the arrays VL and/or VR. MM >= M.
@@ -180,7 +182,7 @@
          IHWMNY = 2
          ILALL = .FALSE.
          ILBACK = .FALSE.
-      ELSE IF( LSAME( HOWMNY, 'B' ) .OR. LSAME( HOWMNY, 'T' ) ) THEN
+      ELSE IF( LSAME( HOWMNY, 'B' ) ) THEN
          IHWMNY = 3
          ILALL = .TRUE.
          ILBACK = .TRUE.
@@ -211,9 +213,9 @@
          INFO = -2
       ELSE IF( N.LT.0 ) THEN
          INFO = -4
-      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+      ELSE IF( LDS.LT.MAX( 1, N ) ) THEN
          INFO = -6
-      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+      ELSE IF( LDP.LT.MAX( 1, N ) ) THEN
          INFO = -8
       END IF
       IF( INFO.NE.0 ) THEN
@@ -237,7 +239,7 @@
 *
       ILBBAD = .FALSE.
       DO 20 J = 1, N
-         IF( AIMAG( B( J, J ) ).NE.ZERO )
+         IF( AIMAG( P( J, J ) ).NE.ZERO )
      $      ILBBAD = .TRUE.
    20 CONTINUE
 *
@@ -275,19 +277,19 @@
 *     part of A and B to check for possible overflow in the triangular
 *     solver.
 *
-      ANORM = ABS1( A( 1, 1 ) )
-      BNORM = ABS1( B( 1, 1 ) )
+      ANORM = ABS1( S( 1, 1 ) )
+      BNORM = ABS1( P( 1, 1 ) )
       RWORK( 1 ) = ZERO
       RWORK( N+1 ) = ZERO
       DO 40 J = 2, N
          RWORK( J ) = ZERO
          RWORK( N+J ) = ZERO
          DO 30 I = 1, J - 1
-            RWORK( J ) = RWORK( J ) + ABS1( A( I, J ) )
-            RWORK( N+J ) = RWORK( N+J ) + ABS1( B( I, J ) )
+            RWORK( J ) = RWORK( J ) + ABS1( S( I, J ) )
+            RWORK( N+J ) = RWORK( N+J ) + ABS1( P( I, J ) )
    30    CONTINUE
-         ANORM = MAX( ANORM, RWORK( J )+ABS1( A( J, J ) ) )
-         BNORM = MAX( BNORM, RWORK( N+J )+ABS1( B( J, J ) ) )
+         ANORM = MAX( ANORM, RWORK( J )+ABS1( S( J, J ) ) )
+         BNORM = MAX( BNORM, RWORK( N+J )+ABS1( P( J, J ) ) )
    40 CONTINUE
 *
       ASCALE = ONE / MAX( ANORM, SAFMIN )
@@ -309,8 +311,8 @@
             IF( ILCOMP ) THEN
                IEIG = IEIG + 1
 *
-               IF( ABS1( A( JE, JE ) ).LE.SAFMIN .AND.
-     $             ABS( REAL( B( JE, JE ) ) ).LE.SAFMIN ) THEN
+               IF( ABS1( S( JE, JE ) ).LE.SAFMIN .AND.
+     $             ABS( REAL( P( JE, JE ) ) ).LE.SAFMIN ) THEN
 *
 *                 Singular matrix pencil -- return unit eigenvector
 *
@@ -326,10 +328,10 @@
 *                   H
 *                 y  ( a A - b B ) = 0
 *
-               TEMP = ONE / MAX( ABS1( A( JE, JE ) )*ASCALE,
-     $                ABS( REAL( B( JE, JE ) ) )*BSCALE, SAFMIN )
-               SALPHA = ( TEMP*A( JE, JE ) )*ASCALE
-               SBETA = ( TEMP*REAL( B( JE, JE ) ) )*BSCALE
+               TEMP = ONE / MAX( ABS1( S( JE, JE ) )*ASCALE,
+     $                ABS( REAL( P( JE, JE ) ) )*BSCALE, SAFMIN )
+               SALPHA = ( TEMP*S( JE, JE ) )*ASCALE
+               SBETA = ( TEMP*REAL( P( JE, JE ) ) )*BSCALE
                ACOEFF = SBETA*ASCALE
                BCOEFF = SALPHA*BSCALE
 *
@@ -380,7 +382,7 @@
 *
 *                 Compute
 *                       j-1
-*                 SUM = sum  conjg( a*A(k,j) - b*B(k,j) )*x(k)
+*                 SUM = sum  conjg( a*S(k,j) - b*P(k,j) )*x(k)
 *                       k=je
 *                 (Scale if necessary)
 *
@@ -396,16 +398,16 @@
                   SUMB = CZERO
 *
                   DO 80 JR = JE, J - 1
-                     SUMA = SUMA + CONJG( A( JR, J ) )*WORK( JR )
-                     SUMB = SUMB + CONJG( B( JR, J ) )*WORK( JR )
+                     SUMA = SUMA + CONJG( S( JR, J ) )*WORK( JR )
+                     SUMB = SUMB + CONJG( P( JR, J ) )*WORK( JR )
    80             CONTINUE
                   SUM = ACOEFF*SUMA - CONJG( BCOEFF )*SUMB
 *
-*                 Form x(j) = - SUM / conjg( a*A(j,j) - b*B(j,j) )
+*                 Form x(j) = - SUM / conjg( a*S(j,j) - b*P(j,j) )
 *
 *                 with scaling and perturbation of the denominator
 *
-                  D = CONJG( ACOEFF*A( J, J )-BCOEFF*B( J, J ) )
+                  D = CONJG( ACOEFF*S( J, J )-BCOEFF*P( J, J ) )
                   IF( ABS1( D ).LE.DMIN )
      $               D = CMPLX( DMIN )
 *
@@ -475,8 +477,8 @@
             IF( ILCOMP ) THEN
                IEIG = IEIG - 1
 *
-               IF( ABS1( A( JE, JE ) ).LE.SAFMIN .AND.
-     $             ABS( REAL( B( JE, JE ) ) ).LE.SAFMIN ) THEN
+               IF( ABS1( S( JE, JE ) ).LE.SAFMIN .AND.
+     $             ABS( REAL( P( JE, JE ) ) ).LE.SAFMIN ) THEN
 *
 *                 Singular matrix pencil -- return unit eigenvector
 *
@@ -492,10 +494,10 @@
 *
 *              ( a A - b B ) x  = 0
 *
-               TEMP = ONE / MAX( ABS1( A( JE, JE ) )*ASCALE,
-     $                ABS( REAL( B( JE, JE ) ) )*BSCALE, SAFMIN )
-               SALPHA = ( TEMP*A( JE, JE ) )*ASCALE
-               SBETA = ( TEMP*REAL( B( JE, JE ) ) )*BSCALE
+               TEMP = ONE / MAX( ABS1( S( JE, JE ) )*ASCALE,
+     $                ABS( REAL( P( JE, JE ) ) )*BSCALE, SAFMIN )
+               SALPHA = ( TEMP*S( JE, JE ) )*ASCALE
+               SBETA = ( TEMP*REAL( P( JE, JE ) ) )*BSCALE
                ACOEFF = SBETA*ASCALE
                BCOEFF = SALPHA*BSCALE
 *
@@ -542,7 +544,7 @@
 *              WORK(j+1:JE) contains x
 *
                DO 170 JR = 1, JE - 1
-                  WORK( JR ) = ACOEFF*A( JR, JE ) - BCOEFF*B( JR, JE )
+                  WORK( JR ) = ACOEFF*S( JR, JE ) - BCOEFF*P( JR, JE )
   170          CONTINUE
                WORK( JE ) = CONE
 *
@@ -551,7 +553,7 @@
 *                 Form x(j) := - w(j) / d
 *                 with scaling and perturbation of the denominator
 *
-                  D = ACOEFF*A( J, J ) - BCOEFF*B( J, J )
+                  D = ACOEFF*S( J, J ) - BCOEFF*P( J, J )
                   IF( ABS1( D ).LE.DMIN )
      $               D = CMPLX( DMIN )
 *
@@ -568,7 +570,7 @@
 *
                   IF( J.GT.1 ) THEN
 *
-*                    w = w + x(j)*(a A(*,j) - b B(*,j) ) with scaling
+*                    w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling
 *
                      IF( ABS1( WORK( J ) ).GT.ONE ) THEN
                         TEMP = ONE / ABS1( WORK( J ) )
@@ -583,8 +585,8 @@
                      CA = ACOEFF*WORK( J )
                      CB = BCOEFF*WORK( J )
                      DO 200 JR = 1, J - 1
-                        WORK( JR ) = WORK( JR ) + CA*A( JR, J ) -
-     $                               CB*B( JR, J )
+                        WORK( JR ) = WORK( JR ) + CA*S( JR, J ) -
+     $                               CB*P( JR, J )
   200                CONTINUE
                   END IF
   210          CONTINUE
diff -uNr LAPACK.orig/SRC/ctrevc.f LAPACK/SRC/ctrevc.f
--- LAPACK.orig/SRC/ctrevc.f	Thu Nov  4 14:24:23 1999
+++ LAPACK/SRC/ctrevc.f	Fri May 25 16:13:56 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 7, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          HOWMNY, SIDE
@@ -22,20 +22,23 @@
 *
 *  CTREVC computes some or all of the right and/or left eigenvectors of
 *  a complex upper triangular matrix T.
-*
+*  Matrices of this type are produced by the Schur factorization of
+*  a complex general matrix:  A = Q*T*Q**H, as computed by CHSEQR.
+*  
 *  The right eigenvector x and the left eigenvector y of T corresponding
 *  to an eigenvalue w are defined by:
-*
-*               T*x = w*x,     y'*T = w*y'
-*
-*  where y' denotes the conjugate transpose of the vector y.
-*
-*  If all eigenvectors are requested, the routine may either return the
-*  matrices X and/or Y of right or left eigenvectors of T, or the
-*  products Q*X and/or Q*Y, where Q is an input unitary
-*  matrix. If T was obtained from the Schur factorization of an
-*  original matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of
-*  right or left eigenvectors of A.
+*  
+*               T*x = w*x,     (y**H)*T = w*(y**H)
+*  
+*  where y**H denotes the conjugate transpose of the vector y.
+*  The eigenvalues are not input to this routine, but are read directly
+*  from the diagonal of T.
+*  
+*  This routine returns the matrices X and/or Y of right and left
+*  eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
+*  input matrix.  If Q is the unitary factor that reduces a matrix A to
+*  Schur form T, then Q*X and Q*Y are the matrices of right and left
+*  eigenvectors of A.
 *
 *  Arguments
 *  =========
@@ -48,17 +51,17 @@
 *  HOWMNY  (input) CHARACTER*1
 *          = 'A':  compute all right and/or left eigenvectors;
 *          = 'B':  compute all right and/or left eigenvectors,
-*                  and backtransform them using the input matrices
-*                  supplied in VR and/or VL;
+*                  backtransformed using the matrices supplied in
+*                  VR and/or VL;
 *          = 'S':  compute selected right and/or left eigenvectors,
-*                  specified by the logical array SELECT.
+*                  as indicated by the logical array SELECT.
 *
 *  SELECT  (input) LOGICAL array, dimension (N)
 *          If HOWMNY = 'S', SELECT specifies the eigenvectors to be
 *          computed.
-*          If HOWMNY = 'A' or 'B', SELECT is not referenced.
-*          To select the eigenvector corresponding to the j-th
-*          eigenvalue, SELECT(j) must be set to .TRUE..
+*          The eigenvector corresponding to the j-th eigenvalue is
+*          computed if SELECT(j) = .TRUE..
+*          Not referenced if HOWMNY = 'A' or 'B'.
 *
 *  N       (input) INTEGER
 *          The order of the matrix T. N >= 0.
@@ -76,19 +79,16 @@
 *          Schur vectors returned by CHSEQR).
 *          On exit, if SIDE = 'L' or 'B', VL contains:
 *          if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
-*                           VL is lower triangular. The i-th column
-*                           VL(i) of VL is the eigenvector corresponding
-*                           to T(i,i).
 *          if HOWMNY = 'B', the matrix Q*Y;
 *          if HOWMNY = 'S', the left eigenvectors of T specified by
 *                           SELECT, stored consecutively in the columns
 *                           of VL, in the same order as their
 *                           eigenvalues.
-*          If SIDE = 'R', VL is not referenced.
+*          Not referenced if SIDE = 'R'.
 *
 *  LDVL    (input) INTEGER
-*          The leading dimension of the array VL.  LDVL >= max(1,N) if
-*          SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
+*          The leading dimension of the array VL.  LDVL >= 1, and if
+*          SIDE = 'L' or 'B', LDVL >= N.
 *
 *  VR      (input/output) COMPLEX array, dimension (LDVR,MM)
 *          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
@@ -96,19 +96,16 @@
 *          Schur vectors returned by CHSEQR).
 *          On exit, if SIDE = 'R' or 'B', VR contains:
 *          if HOWMNY = 'A', the matrix X of right eigenvectors of T;
-*                           VR is upper triangular. The i-th column
-*                           VR(i) of VR is the eigenvector corresponding
-*                           to T(i,i).
 *          if HOWMNY = 'B', the matrix Q*X;
 *          if HOWMNY = 'S', the right eigenvectors of T specified by
 *                           SELECT, stored consecutively in the columns
 *                           of VR, in the same order as their
 *                           eigenvalues.
-*          If SIDE = 'L', VR is not referenced.
+*          Not referenced if SIDE = 'L'.
 *
 *  LDVR    (input) INTEGER
-*          The leading dimension of the array VR.  LDVR >= max(1,N) if
-*           SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
+*          The leading dimension of the array VR.  LDVR >= 1, and if
+*          SIDE = 'R' or 'B'; LDVR >= N.
 *
 *  MM      (input) INTEGER
 *          The number of columns in the arrays VL and/or VR. MM >= M.
diff -uNr LAPACK.orig/SRC/ctrsen.f LAPACK/SRC/ctrsen.f
--- LAPACK.orig/SRC/ctrsen.f	Thu Nov  4 14:24:24 1999
+++ LAPACK/SRC/ctrsen.f	Fri May 25 16:14:15 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     January 3, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, JOB
@@ -93,14 +93,13 @@
 *          If JOB = 'N' or 'E', SEP is not referenced.
 *
 *  WORK    (workspace/output) COMPLEX array, dimension (LWORK)
-*          If JOB = 'N', WORK is not referenced.  Otherwise,
-*          on exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK.
 *          If JOB = 'N', LWORK >= 1;
-*          if JOB = 'E', LWORK = M*(N-M);
-*          if JOB = 'V' or 'B', LWORK >= 2*M*(N-M).
+*          if JOB = 'E', LWORK = max(1,M*(N-M));
+*          if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)).
 *
 *          If LWORK = -1, then a workspace query is assumed; the routine
 *          only calculates the optimal size of the WORK array, returns
diff -uNr LAPACK.orig/SRC/ctrsyl.f LAPACK/SRC/ctrsyl.f
--- LAPACK.orig/SRC/ctrsyl.f	Thu Nov  4 14:24:24 1999
+++ LAPACK/SRC/ctrsyl.f	Fri May 25 16:14:25 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     January 9, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          TRANA, TRANB
@@ -119,11 +119,9 @@
       NOTRNB = LSAME( TRANB, 'N' )
 *
       INFO = 0
-      IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) .AND. .NOT.
-     $    LSAME( TRANA, 'C' ) ) THEN
+      IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'C' ) ) THEN
          INFO = -1
-      ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'T' ) .AND. .NOT.
-     $         LSAME( TRANB, 'C' ) ) THEN
+      ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'C' ) ) THEN
          INFO = -2
       ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
          INFO = -3
diff -uNr LAPACK.orig/SRC/dbdsqr.f LAPACK/SRC/dbdsqr.f
--- LAPACK.orig/SRC/dbdsqr.f	Thu Nov  4 14:24:42 1999
+++ LAPACK/SRC/dbdsqr.f	Fri May 25 15:59:00 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     April 25, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -18,14 +18,26 @@
 *  Purpose
 *  =======
 *
-*  DBDSQR computes the singular value decomposition (SVD) of a real
-*  N-by-N (upper or lower) bidiagonal matrix B:  B = Q * S * P' (P'
-*  denotes the transpose of P), where S is a diagonal matrix with
-*  non-negative diagonal elements (the singular values of B), and Q
-*  and P are orthogonal matrices.
+*  DBDSQR computes the singular values and, optionally, the right and/or
+*  left singular vectors from the singular value decomposition (SVD) of
+*  a real N-by-N (upper or lower) bidiagonal matrix B using the implicit
+*  zero-shift QR algorithm.  The SVD of B has the form
+* 
+*     B = Q * S * P**T
+* 
+*  where S is the diagonal matrix of singular values, Q is an orthogonal
+*  matrix of left singular vectors, and P is an orthogonal matrix of
+*  right singular vectors.  If left singular vectors are requested, this
+*  subroutine actually returns U*Q instead of Q, and, if right singular
+*  vectors are requested, this subroutine returns P**T*VT instead of
+*  P**T, for given real input matrices U and VT.  When U and VT are the
+*  orthogonal matrices that reduce a general matrix A to bidiagonal
+*  form:  A = U*B*VT, as computed by DGEBRD, then
 *
-*  The routine computes S, and optionally computes U * Q, P' * VT,
-*  or Q' * C, for given real input matrices U, VT, and C.
+*     A = (U*Q) * S * (P**T*VT)
+*
+*  is the SVD of A.  Optionally, the subroutine may also compute Q**T*C
+*  for a given real input matrix C.
 *
 *  See "Computing  Small Singular Values of Bidiagonal Matrices With
 *  Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
@@ -61,18 +73,17 @@
 *          order.
 *
 *  E       (input/output) DOUBLE PRECISION array, dimension (N)
-*          On entry, the elements of E contain the
-*          offdiagonal elements of the bidiagonal matrix whose SVD
-*          is desired. On normal exit (INFO = 0), E is destroyed.
-*          If the algorithm does not converge (INFO > 0), D and E
+*          On entry, the N-1 offdiagonal elements of the bidiagonal
+*          matrix B. 
+*          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E
 *          will contain the diagonal and superdiagonal elements of a
 *          bidiagonal matrix orthogonally equivalent to the one given
 *          as input. E(N) is used for workspace.
 *
 *  VT      (input/output) DOUBLE PRECISION array, dimension (LDVT, NCVT)
 *          On entry, an N-by-NCVT matrix VT.
-*          On exit, VT is overwritten by P' * VT.
-*          VT is not referenced if NCVT = 0.
+*          On exit, VT is overwritten by P**T * VT.
+*          Not referenced if NCVT = 0.
 *
 *  LDVT    (input) INTEGER
 *          The leading dimension of the array VT.
@@ -81,21 +92,22 @@
 *  U       (input/output) DOUBLE PRECISION array, dimension (LDU, N)
 *          On entry, an NRU-by-N matrix U.
 *          On exit, U is overwritten by U * Q.
-*          U is not referenced if NRU = 0.
+*          Not referenced if NRU = 0.
 *
 *  LDU     (input) INTEGER
 *          The leading dimension of the array U.  LDU >= max(1,NRU).
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC, NCC)
 *          On entry, an N-by-NCC matrix C.
-*          On exit, C is overwritten by Q' * C.
-*          C is not referenced if NCC = 0.
+*          On exit, C is overwritten by Q**T * C.
+*          Not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C.
 *          LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.
 *
-*  WORK    (workspace) DOUBLE PRECISION array, dimension (4*N)
+*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
+*          if NCVT = NRU = NCC = 0, (max(1, 4*N-4)) otherwise
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
diff -uNr LAPACK.orig/SRC/dgebd2.f LAPACK/SRC/dgebd2.f
--- LAPACK.orig/SRC/dgebd2.f	Thu Nov  4 14:24:42 1999
+++ LAPACK/SRC/dgebd2.f	Fri May 25 15:59:22 2001
@@ -3,7 +3,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     February 29, 1992
+*     May 7, 2001
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N
@@ -169,8 +169,9 @@
 *
 *           Apply H(i) to A(i:m,i+1:n) from the left
 *
-            CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAUQ( I ),
-     $                  A( I, I+1 ), LDA, WORK )
+            IF( I.LT.N )
+     $         CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAUQ( I ),
+     $                     A( I, I+1 ), LDA, WORK )
             A( I, I ) = D( I )
 *
             IF( I.LT.N ) THEN
@@ -207,8 +208,9 @@
 *
 *           Apply G(i) to A(i+1:m,i:n) from the right
 *
-            CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAUP( I ),
-     $                  A( MIN( I+1, M ), I ), LDA, WORK )
+            IF( I.LT.M )
+     $         CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
+     $                     TAUP( I ), A( MIN( I+1, M ), I ), LDA, WORK )
             A( I, I ) = D( I )
 *
             IF( I.LT.M ) THEN
diff -uNr LAPACK.orig/SRC/dgees.f LAPACK/SRC/dgees.f
--- LAPACK.orig/SRC/dgees.f	Thu Nov  4 14:24:43 1999
+++ LAPACK/SRC/dgees.f	Fri May 25 15:59:50 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVS, SORT
@@ -110,10 +111,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,3*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  BWORK   (workspace) LOGICAL array, dimension (N)
 *          Not referenced if SORT = 'N'.
@@ -138,12 +138,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            CURSL, LASTSL, LQUERY, LST2SL, SCALEA, WANTST,
-     $                   WANTVS
+      LOGICAL            CURSL, LASTSL, LST2SL, SCALEA, WANTST, WANTVS
       INTEGER            HSWORK, I, I1, I2, IBAL, ICOND, IERR, IEVAL,
      $                   IHI, ILO, INXT, IP, ITAU, IWRK, K, MAXB,
      $                   MAXWRK, MINWRK
@@ -154,8 +155,8 @@
       DOUBLE PRECISION   DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DCOPY, DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLACPY,
-     $                   DLASCL, DORGHR, DSWAP, DTRSEN, XERBLA
+      EXTERNAL           DCOPY, DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD,
+     $                   DLACPY, DLASCL, DORGHR, DSWAP, DTRSEN, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -171,7 +172,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVS = LSAME( JOBVS, 'V' )
       WANTST = LSAME( SORT, 'S' )
       IF( ( .NOT.WANTVS ) .AND. ( .NOT.LSAME( JOBVS, 'N' ) ) ) THEN
@@ -197,7 +197,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 2*N + N*ILAENV( 1, 'DGEHRD', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 3*N )
          IF( .NOT.WANTVS ) THEN
@@ -216,19 +216,18 @@
             MAXWRK = MAX( MAXWRK, N+HSWORK, 1 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGEES ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/dgeesx.f LAPACK/SRC/dgeesx.f
--- LAPACK.orig/SRC/dgeesx.f	Thu Nov  4 14:24:43 1999
+++ LAPACK/SRC/dgeesx.f	Fri May 25 16:00:13 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Do WS calculations if LWORK = -1 (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVS, SENSE, SORT
@@ -140,6 +141,10 @@
 *          N+2*SDIM*(N-SDIM) <= N+N*N/2.
 *          For good performance, LWORK must generally be larger.
 *
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
 *  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
 *          Not referenced if SENSE = 'N' or 'E'.
 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
@@ -171,6 +176,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
 *     ..
@@ -186,8 +193,8 @@
       DOUBLE PRECISION   DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DCOPY, DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLACPY,
-     $                   DLASCL, DORGHR, DSWAP, DTRSEN, XERBLA
+      EXTERNAL           DCOPY, DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD,
+     $                   DLACPY, DLASCL, DORGHR, DSWAP, DTRSEN, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -239,7 +246,7 @@
 *       in the code.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 2*N + N*ILAENV( 1, 'DGEHRD', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 3*N )
          IF( .NOT.WANTVS ) THEN
@@ -257,21 +264,25 @@
             HSWORK = MAX( K*( K+2 ), 2*N )
             MAXWRK = MAX( MAXWRK, N+HSWORK, 1 )
          END IF
+*
+*        Estimate the workspace needed by DTRSEN.
+*
+         IF( WANTST ) THEN
+            MAXWRK = MAX( MAXWRK, N+( N*N+1 ) / 2 )
+         END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -16
       END IF
-      IF( LWORK.LT.MINWRK ) THEN
-         INFO = -16
-      END IF
-      IF( LIWORK.LT.1 ) THEN
-         INFO = -18
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGEESX', -INFO )
          RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/dgeev.f LAPACK/SRC/dgeev.f
--- LAPACK.orig/SRC/dgeev.f	Wed Dec  8 16:00:35 1999
+++ LAPACK/SRC/dgeev.f	Fri May 25 16:00:43 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     December 8, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -98,10 +99,9 @@
 *          if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N.  For good
 *          performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
@@ -114,11 +114,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
+      LOGICAL            SCALEA, WANTVL, WANTVR
       CHARACTER          SIDE
       INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, ITAU, IWRK, K,
      $                   MAXB, MAXWRK, MINWRK, NOUT
@@ -130,8 +132,9 @@
       DOUBLE PRECISION   DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLACPY, DLARTG,
-     $                   DLASCL, DORGHR, DROT, DSCAL, DTREVC, XERBLA
+      EXTERNAL           DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD, DLACPY,
+     $                   DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC,
+     $                   XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -148,7 +151,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVL = LSAME( JOBVL, 'V' )
       WANTVR = LSAME( JOBVR, 'V' )
       IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
@@ -176,7 +178,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 2*N + N*ILAENV( 1, 'DGEHRD', ' ', N, 1, N, 0 )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
             MINWRK = MAX( 1, 3*N )
@@ -197,19 +199,18 @@
             MAXWRK = MAX( MAXWRK, 4*N )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGEEV ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/dgeevx.f LAPACK/SRC/dgeevx.f
--- LAPACK.orig/SRC/dgeevx.f	Thu Nov  4 14:24:43 1999
+++ LAPACK/SRC/dgeevx.f	Fri May 25 16:01:05 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
@@ -179,10 +180,9 @@
 *          LWORK >= 3*N.  If SENSE = 'V' or 'B', LWORK >= N*(N+6).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (2*N-2)
 *          If SENSE = 'N' or 'E', not referenced.
@@ -198,12 +198,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
-     $                   WNTSNN, WNTSNV
+      LOGICAL            SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, WNTSNN,
+     $                   WNTSNV
       CHARACTER          JOB, SIDE
       INTEGER            HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXB,
      $                   MAXWRK, MINWRK, NOUT
@@ -215,9 +217,9 @@
       DOUBLE PRECISION   DUM( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLACPY, DLARTG,
-     $                   DLASCL, DORGHR, DROT, DSCAL, DTREVC, DTRSNA,
-     $                   XERBLA
+      EXTERNAL           DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD, DLACPY,
+     $                   DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC,
+     $                   DTRSNA, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -234,7 +236,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVL = LSAME( JOBVL, 'V' )
       WANTVR = LSAME( JOBVR, 'V' )
       WNTSNN = LSAME( SENSE, 'N' )
@@ -274,7 +275,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'DGEHRD', ' ', N, 1, N, 0 )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
             MINWRK = MAX( 1, 2*N )
@@ -308,19 +309,18 @@
             MAXWRK = MAX( MAXWRK, 3*N, 1 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -21
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -21
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGEEVX', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/dgegs.f LAPACK/SRC/dgegs.f
--- LAPACK.orig/SRC/dgegs.f	Thu Nov  4 14:24:43 1999
+++ LAPACK/SRC/dgegs.f	Fri May 25 16:01:53 2001
@@ -5,7 +5,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR
@@ -22,105 +22,75 @@
 *
 *  This routine is deprecated and has been replaced by routine DGGES.
 *
-*  DGEGS computes for a pair of N-by-N real nonsymmetric matrices A, B:
-*  the generalized eigenvalues (alphar +/- alphai*i, beta), the real
-*  Schur form (A, B), and optionally left and/or right Schur vectors
-*  (VSL and VSR).
-*
-*  (If only the generalized eigenvalues are needed, use the driver DGEGV
-*  instead.)
-*
-*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly
-*  speaking, a scalar w or a ratio  alpha/beta = w, such that  A - w*B
-*  is singular.  It is usually represented as the pair (alpha,beta),
-*  as there is a reasonable interpretation for beta=0, and even for
-*  both being zero.  A good beginning reference is the book, "Matrix
-*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
-*
-*  The (generalized) Schur form of a pair of matrices is the result of
-*  multiplying both matrices on the left by one orthogonal matrix and
-*  both on the right by another orthogonal matrix, these two orthogonal
-*  matrices being chosen so as to bring the pair of matrices into
-*  (real) Schur form.
-*
-*  A pair of matrices A, B is in generalized real Schur form if B is
-*  upper triangular with non-negative diagonal and A is block upper
-*  triangular with 1-by-1 and 2-by-2 blocks.  1-by-1 blocks correspond
-*  to real generalized eigenvalues, while 2-by-2 blocks of A will be
-*  "standardized" by making the corresponding elements of B have the
-*  form:
-*          [  a  0  ]
-*          [  0  b  ]
-*
-*  and the pair of corresponding 2-by-2 blocks in A and B will
-*  have a complex conjugate pair of generalized eigenvalues.
-*
-*  The left and right Schur vectors are the columns of VSL and VSR,
-*  respectively, where VSL and VSR are the orthogonal matrices
-*  which reduce A and B to Schur form:
-*
-*  Schur form of (A,B) = ( (VSL)**T A (VSR), (VSL)**T B (VSR) )
+*  DGEGS computes the eigenvalues, real Schur form, and, optionally,
+*  left and or/right Schur vectors of a real matrix pair (A,B).
+*  Given two square matrices A and B, the generalized real Schur
+*  factorization has the form
+*
+*    A = Q*S*Z**T,  B = Q*T*Z**T
+*
+*  where Q and Z are orthogonal matrices, T is upper triangular, and S
+*  is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
+*  blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
+*  of eigenvalues of (A,B).  The columns of Q are the left Schur vectors
+*  and the columns of Z are the right Schur vectors.
+*
+*  If only the eigenvalues of (A,B) are needed, the driver routine
+*  DGEGV should be used instead.  See DGEGV for a description of the
+*  eigenvalues of the generalized nonsymmetric eigenvalue problem
+*  (GNEP).
 *
 *  Arguments
 *  =========
 *
 *  JOBVSL  (input) CHARACTER*1
 *          = 'N':  do not compute the left Schur vectors;
-*          = 'V':  compute the left Schur vectors.
+*          = 'V':  compute the left Schur vectors (returned in VSL).
 *
 *  JOBVSR  (input) CHARACTER*1
 *          = 'N':  do not compute the right Schur vectors;
-*          = 'V':  compute the right Schur vectors.
+*          = 'V':  compute the right Schur vectors (returned in VSR).
 *
 *  N       (input) INTEGER
 *          The order of the matrices A, B, VSL, and VSR.  N >= 0.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
-*          On entry, the first of the pair of matrices whose generalized
-*          eigenvalues and (optionally) Schur vectors are to be
-*          computed.
-*          On exit, the generalized Schur form of A.
-*          Note: to avoid overflow, the Frobenius norm of the matrix
-*          A should be less than the overflow threshold.
+*          On entry, the matrix A.
+*          On exit, the upper quasi-triangular matrix S from the
+*          generalized real Schur factorization.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of A.  LDA >= max(1,N).
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
-*          On entry, the second of the pair of matrices whose
-*          generalized eigenvalues and (optionally) Schur vectors are
-*          to be computed.
-*          On exit, the generalized Schur form of B.
-*          Note: to avoid overflow, the Frobenius norm of the matrix
-*          B should be less than the overflow threshold.
+*          On entry, the matrix B.
+*          On exit, the upper triangular matrix T from the generalized
+*          real Schur factorization.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of B.  LDB >= max(1,N).
 *
 *  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
+*          The real parts of each scalar alpha defining an eigenvalue
+*          of GNEP.
+*
 *  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
-*  BETA    (output) DOUBLE PRECISION array, dimension (N)
-*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
-*          be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i,
-*          j=1,...,N  and  BETA(j),j=1,...,N  are the diagonals of the
-*          complex Schur form (A,B) that would result if the 2-by-2
-*          diagonal blocks of the real Schur form of (A,B) were further
-*          reduced to triangular form using 2-by-2 complex unitary
-*          transformations.  If ALPHAI(j) is zero, then the j-th
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th
 *          eigenvalue is real; if positive, then the j-th and (j+1)-st
-*          eigenvalues are a complex conjugate pair, with ALPHAI(j+1)
-*          negative.
+*          eigenvalues are a complex conjugate pair, with
+*          ALPHAI(j+1) = -ALPHAI(j).
 *
-*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
-*          may easily over- or underflow, and BETA(j) may even be zero.
-*          Thus, the user should avoid naively computing the ratio
-*          alpha/beta.  However, ALPHAR and ALPHAI will be always less
-*          than and usually comparable with norm(A) in magnitude, and
-*          BETA always less than and usually comparable with norm(B).
+*  BETA    (output) DOUBLE PRECISION array, dimension (N)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
 *
 *  VSL     (output) DOUBLE PRECISION array, dimension (LDVSL,N)
-*          If JOBVSL = 'V', VSL will contain the left Schur vectors.
-*          (See "Purpose", above.)
+*          If JOBVSL = 'V', the matrix of left Schur vectors Q.
 *          Not referenced if JOBVSL = 'N'.
 *
 *  LDVSL   (input) INTEGER
@@ -128,8 +98,7 @@
 *          if JOBVSL = 'V', LDVSL >= N.
 *
 *  VSR     (output) DOUBLE PRECISION array, dimension (LDVSR,N)
-*          If JOBVSR = 'V', VSR will contain the right Schur vectors.
-*          (See "Purpose", above.)
+*          If JOBVSR = 'V', the matrix of right Schur vectors Z.
 *          Not referenced if JOBVSR = 'N'.
 *
 *  LDVSR   (input) INTEGER
diff -uNr LAPACK.orig/SRC/dgegv.f LAPACK/SRC/dgegv.f
--- LAPACK.orig/SRC/dgegv.f	Thu Nov  4 14:25:43 1999
+++ LAPACK/SRC/dgegv.f	Fri May 25 16:02:16 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -21,23 +21,32 @@
 *
 *  This routine is deprecated and has been replaced by routine DGGEV.
 *
-*  DGEGV computes for a pair of n-by-n real nonsymmetric matrices A and
-*  B, the generalized eigenvalues (alphar +/- alphai*i, beta), and
-*  optionally, the left and/or right generalized eigenvectors (VL and
-*  VR).
-*
-*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly
-*  speaking, a scalar w or a ratio  alpha/beta = w, such that  A - w*B
-*  is singular.  It is usually represented as the pair (alpha,beta),
-*  as there is a reasonable interpretation for beta=0, and even for
-*  both being zero.  A good beginning reference is the book, "Matrix
-*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
-*
-*  A right generalized eigenvector corresponding to a generalized
-*  eigenvalue  w  for a pair of matrices (A,B) is a vector  r  such
-*  that  (A - w B) r = 0 .  A left generalized eigenvector is a vector
-*  l such that l**H * (A - w B) = 0, where l**H is the
-*  conjugate-transpose of l.
+*  DGEGV computes the eigenvalues and, optionally, the left and/or right
+*  eigenvectors of a real matrix pair (A,B).
+*  Given two square matrices A and B,
+*  the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
+*  eigenvalues lambda and corresponding (non-zero) eigenvectors x such
+*  that
+*
+*     A*x = lambda*B*x.
+*
+*  An alternate form is to find the eigenvalues mu and corresponding
+*  eigenvectors y such that
+*
+*     mu*A*y = B*y.
+*
+*  These two forms are equivalent with mu = 1/lambda and x = y if
+*  neither lambda nor mu is zero.  In order to deal with the case that
+*  lambda or mu is zero or small, two values alpha and beta are returned
+*  for each eigenvalue, such that lambda = alpha/beta and
+*  mu = beta/alpha.
+*
+*  The vectors x and y in the above equations are right eigenvectors of
+*  the matrix pair (A,B).  Vectors u and v satisfying
+*
+*     u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
+*
+*  are left eigenvectors of (A,B).
 *
 *  Note: this routine performs "full balancing" on A and B -- see
 *  "Further Details", below.
@@ -47,63 +56,75 @@
 *
 *  JOBVL   (input) CHARACTER*1
 *          = 'N':  do not compute the left generalized eigenvectors;
-*          = 'V':  compute the left generalized eigenvectors.
+*          = 'V':  compute the left generalized eigenvectors (returned
+*                  in VL).
 *
 *  JOBVR   (input) CHARACTER*1
 *          = 'N':  do not compute the right generalized eigenvectors;
-*          = 'V':  compute the right generalized eigenvectors.
+*          = 'V':  compute the right generalized eigenvectors (returned
+*                  in VR).
 *
 *  N       (input) INTEGER
 *          The order of the matrices A, B, VL, and VR.  N >= 0.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
-*          On entry, the first of the pair of matrices whose
-*          generalized eigenvalues and (optionally) generalized
-*          eigenvectors are to be computed.
-*          On exit, the contents will have been destroyed.  (For a
-*          description of the contents of A on exit, see "Further
-*          Details", below.)
+*          On entry, the matrix A.
+*          If JOBVL = 'V' or JOBVR = 'V', then on exit A
+*          contains the real Schur form of A from the generalized Schur
+*          factorization of the pair (A,B) after balancing.
+*          If no eigenvectors were computed, then only the diagonal
+*          blocks from the Schur form will be correct.  See DGGHRD and
+*          DHGEQZ for details.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of A.  LDA >= max(1,N).
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
-*          On entry, the second of the pair of matrices whose
-*          generalized eigenvalues and (optionally) generalized
-*          eigenvectors are to be computed.
-*          On exit, the contents will have been destroyed.  (For a
-*          description of the contents of B on exit, see "Further
-*          Details", below.)
+*          On entry, the matrix B.
+*          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
+*          upper triangular matrix obtained from B in the generalized
+*          Schur factorization of the pair (A,B) after balancing.
+*          If no eigenvectors were computed, then only those elements of
+*          B corresponding to the diagonal blocks from the Schur form of
+*          A will be correct.  See DGGHRD and DHGEQZ for details.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of B.  LDB >= max(1,N).
 *
 *  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
+*          The real parts of each scalar alpha defining an eigenvalue of
+*          GNEP.
+*
 *  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
-*  BETA    (output) DOUBLE PRECISION array, dimension (N)
-*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
-*          be the generalized eigenvalues.  If ALPHAI(j) is zero, then
-*          the j-th eigenvalue is real; if positive, then the j-th and
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th
+*          eigenvalue is real; if positive, then the j-th and
 *          (j+1)-st eigenvalues are a complex conjugate pair, with
-*          ALPHAI(j+1) negative.
+*          ALPHAI(j+1) = -ALPHAI(j).
 *
-*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
-*          may easily over- or underflow, and BETA(j) may even be zero.
-*          Thus, the user should avoid naively computing the ratio
-*          alpha/beta.  However, ALPHAR and ALPHAI will be always less
-*          than and usually comparable with norm(A) in magnitude, and
-*          BETA always less than and usually comparable with norm(B).
+*  BETA    (output) DOUBLE PRECISION array, dimension (N)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
 *
 *  VL      (output) DOUBLE PRECISION array, dimension (LDVL,N)
-*          If JOBVL = 'V', the left generalized eigenvectors.  (See
-*          "Purpose", above.)  Real eigenvectors take one column,
-*          complex take two columns, the first for the real part and
-*          the second for the imaginary part.  Complex eigenvectors
-*          correspond to an eigenvalue with positive imaginary part.
-*          Each eigenvector will be scaled so the largest component
-*          will have abs(real part) + abs(imag. part) = 1, *except*
-*          that for eigenvalues with alpha=beta=0, a zero vector will
-*          be returned as the corresponding eigenvector.
+*          If JOBVL = 'V', the left eigenvectors u(j) are stored
+*          in the columns of VL, in the same order as their eigenvalues.
+*          If the j-th eigenvalue is real, then u(j) = VL(:,j).
+*          If the j-th and (j+1)-st eigenvalues form a complex conjugate
+*          pair, then
+*             u(j) = VL(:,j) + i*VL(:,j+1)
+*          and
+*            u(j+1) = VL(:,j) - i*VL(:,j+1).
+*
+*          Each eigenvector is scaled so that its largest component has
+*          abs(real part) + abs(imag. part) = 1, except for eigenvectors
+*          corresponding to an eigenvalue with alpha = beta = 0, which
+*          are set to zero.
 *          Not referenced if JOBVL = 'N'.
 *
 *  LDVL    (input) INTEGER
@@ -111,15 +132,19 @@
 *          if JOBVL = 'V', LDVL >= N.
 *
 *  VR      (output) DOUBLE PRECISION array, dimension (LDVR,N)
-*          If JOBVR = 'V', the right generalized eigenvectors.  (See
-*          "Purpose", above.)  Real eigenvectors take one column,
-*          complex take two columns, the first for the real part and
-*          the second for the imaginary part.  Complex eigenvectors
-*          correspond to an eigenvalue with positive imaginary part.
-*          Each eigenvector will be scaled so the largest component
-*          will have abs(real part) + abs(imag. part) = 1, *except*
-*          that for eigenvalues with alpha=beta=0, a zero vector will
-*          be returned as the corresponding eigenvector.
+*          If JOBVR = 'V', the right eigenvectors x(j) are stored
+*          in the columns of VR, in the same order as their eigenvalues.
+*          If the j-th eigenvalue is real, then x(j) = VR(:,j).
+*          If the j-th and (j+1)-st eigenvalues form a complex conjugate
+*          pair, then
+*            x(j) = VR(:,j) + i*VR(:,j+1)
+*          and
+*            x(j+1) = VR(:,j) - i*VR(:,j+1).
+*
+*          Each eigenvector is scaled so that its largest component has
+*          abs(real part) + abs(imag. part) = 1, except for eigenvalues
+*          corresponding to an eigenvalue with alpha = beta = 0, which
+*          are set to zero.
 *          Not referenced if JOBVR = 'N'.
 *
 *  LDVR    (input) INTEGER
diff -uNr LAPACK.orig/SRC/dgelsd.f LAPACK/SRC/dgelsd.f
--- LAPACK.orig/SRC/dgelsd.f	Thu Nov  4 14:26:25 1999
+++ LAPACK/SRC/dgelsd.f	Fri May 25 16:03:10 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -61,9 +62,10 @@
 *          The number of right hand sides, i.e., the number of columns
 *          of the matrices B and X. NRHS >= 0.
 *
-*  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
+*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
-*          On exit, A has been destroyed.
+*          On exit, the first min(m,n) rows of A are overwritten with
+*          its right singular vectors, stored rowwise.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
@@ -95,23 +97,20 @@
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *
 *  LWORK   (input) INTEGER
-*          The dimension of the array WORK. LWORK must be at least 1.
+*          The dimension of the array WORK. LWORK >= 1.
 *          The exact minimum amount of workspace needed depends on M,
-*          N and NRHS. As long as LWORK is at least
-*              12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
-*          if M is greater than or equal to N or
-*              12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
-*          if M is less than N, the code will execute correctly.
+*          N and NRHS.
+*          If M >= N, LWORK >=  11*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS.
+*          If M < N, LWORK >=  11*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS.
 *          SMLSIZ is returned by ILAENV and is equal to the maximum
 *          size of the subproblems at the bottom of the computation
 *          tree (usually about 25), and
-*             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
+*              NLVL = INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (LIWORK)
 *          LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
@@ -135,14 +134,15 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE, TWO
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY
       INTEGER            IASCL, IBSCL, IE, IL, ITAU, ITAUP, ITAUQ,
      $                   LDWORK, MAXMN, MAXWRK, MINMN, MINWRK, MM,
-     $                   MNTHR, NLVL, NWORK, SMLSIZ, WLALSD
+     $                   MNTHR, NLVL, NWORK, SMLSIZ
       DOUBLE PRECISION   ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM
 *     ..
 *     .. External Subroutines ..
@@ -165,7 +165,6 @@
       MINMN = MIN( M, N )
       MAXMN = MAX( M, N )
       MNTHR = ILAENV( 6, 'DGELSD', ' ', M, N, NRHS, -1 )
-      LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
@@ -189,8 +188,8 @@
 *
       MINWRK = 1
       MINMN = MAX( 1, MINMN )
-      NLVL = MAX( INT( LOG( DBLE( MINMN ) / DBLE( SMLSIZ+1 ) ) /
-     $       LOG( TWO ) ) + 1, 0 )
+      NLVL = INT( LOG( DBLE( MINMN ) / DBLE( SMLSIZ+1 ) ) / LOG( TWO ) )
+     $        + 1
 *
       IF( INFO.EQ.0 ) THEN
          MAXWRK = 0
@@ -215,12 +214,11 @@
      $               ILAENV( 1, 'DORMBR', 'QLT', MM, NRHS, N, -1 ) )
             MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
      $               ILAENV( 1, 'DORMBR', 'PLN', N, NRHS, N, -1 ) )
-            WLALSD = 9*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS+(SMLSIZ+1)**2
-            MAXWRK = MAX( MAXWRK, 3*N+WLALSD )
-            MINWRK = MAX( 3*N+MM, 3*N+NRHS, 3*N+WLALSD )
+            MAXWRK = MAX( MAXWRK, 3*N+8*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS )
+            MINWRK = MAX( 3*N+MM, 3*N+NRHS,
+     $               3*N+8*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS )
          END IF
          IF( N.GT.M ) THEN
-            WLALSD = 9*M+2*M*SMLSIZ+8*M*NLVL+M*NRHS+(SMLSIZ+1)**2
             IF( N.GE.MNTHR ) THEN
 *
 *              Path 2a - underdetermined, with many more columns
@@ -240,7 +238,8 @@
                END IF
                MAXWRK = MAX( MAXWRK, M+NRHS*
      $                  ILAENV( 1, 'DORMLQ', 'LT', N, NRHS, M, -1 ) )
-               MAXWRK = MAX( MAXWRK, M*M+4*M+WLALSD )
+               MAXWRK = MAX( MAXWRK, M*M+4*M+8*M+2*M*SMLSIZ+8*M*NLVL+M*
+     $                  NRHS )
             ELSE
 *
 *              Path 2 - remaining underdetermined cases.
@@ -251,26 +250,26 @@
      $                  ILAENV( 1, 'DORMBR', 'QLT', M, NRHS, N, -1 ) )
                MAXWRK = MAX( MAXWRK, 3*M+M*
      $                  ILAENV( 1, 'DORMBR', 'PLN', N, NRHS, M, -1 ) )
-               MAXWRK = MAX( MAXWRK, 3*M+WLALSD )
+               MAXWRK = MAX( MAXWRK, 3*M+8*M+2*M*SMLSIZ+8*M*NLVL+M*
+     $                  NRHS )
             END IF
-            MINWRK = MAX( 3*M+NRHS, 3*M+M, 3*M+WLALSD )
+            MINWRK = MAX( 3*M+NRHS, 3*M+M,
+     $               3*M+8*M+2*M*SMLSIZ+8*M*NLVL+M*NRHS )
          END IF
          MINWRK = MIN( MINWRK, MAXWRK )
          WORK( 1 ) = MAXWRK
-         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-            INFO = -12
-         END IF
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
 *
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGELSD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         GO TO 10
       END IF
-*
-*     Quick return if possible.
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
          RANK = 0
          RETURN
diff -uNr LAPACK.orig/SRC/dgelss.f LAPACK/SRC/dgelss.f
--- LAPACK.orig/SRC/dgelss.f	Thu Nov  4 14:24:44 1999
+++ LAPACK/SRC/dgelss.f	Fri May 25 16:03:46 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     April 25, 2001 
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -86,10 +86,9 @@
 *          LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
@@ -156,7 +155,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 0
          MM = M
          IF( M.GE.N .AND. M.GE.MNTHR ) THEN
@@ -229,20 +228,18 @@
          END IF
          MAXWRK = MAX( MINWRK, MAXWRK )
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
+     $      INFO = -12
       END IF
 *
-      MINWRK = MAX( MINWRK, 1 )
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -12
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGELSS', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
          RETURN
       END IF
-*
-*     Quick return if possible
-*
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
          RANK = 0
          RETURN
@@ -491,8 +488,8 @@
             DO 40 I = 1, NRHS, CHUNK
                BL = MIN( NRHS-I+1, CHUNK )
                CALL DGEMM( 'T', 'N', M, BL, M, ONE, WORK( IL ), LDWORK,
-     $                     B( 1, I ), LDB, ZERO, WORK( IWORK ), N )
-               CALL DLACPY( 'G', M, BL, WORK( IWORK ), N, B( 1, I ),
+     $                     B( 1, I ), LDB, ZERO, WORK( IWORK ), M )
+               CALL DLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ),
      $                      LDB )
    40       CONTINUE
          ELSE
diff -uNr LAPACK.orig/SRC/dgesdd.f LAPACK/SRC/dgesdd.f
--- LAPACK.orig/SRC/dgesdd.f	Thu Nov 11 20:32:31 1999
+++ LAPACK/SRC/dgesdd.f	Fri May 25 16:07:58 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBZ
@@ -116,16 +117,20 @@
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK. LWORK >= 1.
 *          If JOBZ = 'N',
-*            LWORK >= 3*min(M,N) + max(max(M,N),6*min(M,N)).
+*            LWORK >= max(14*min(M,N)+4, 10*min(M,N)+2+
+*                     SMLSIZ*(SMLSIZ+8)) + max(M,N)
+*          where SMLSIZ is returned by ILAENV and is equal to the
+*          maximum size of the subproblems at the bottom of the
+*          computation tree (usually about 25).
 *          If JOBZ = 'O',
-*            LWORK >= 3*min(M,N)*min(M,N) + 
-*                     max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
+*            LWORK >= 5*min(M,N)*min(M,N) + max(M,N) + 9*min(M,N).
 *          If JOBZ = 'S' or 'A'
-*            LWORK >= 3*min(M,N)*min(M,N) +
-*                     max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)).
+*            LWORK >= 4*min(M,N)*min(M,N) + max(M,N) + 9*min(M,N).
 *          For good performance, LWORK should generally be larger.
-*          If LWORK < 0 but other input arguments are legal, WORK(1)
-*          returns the optimal LWORK.
+*
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (8*min(M,N))
 *
@@ -144,15 +149,17 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
-      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
+      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
-      INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IL,
+      LOGICAL            WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
+      INTEGER            BDSPAC, BDSPAN, BLK, CHUNK, I, IE, IERR, IL,
      $                   IR, ISCL, ITAU, ITAUP, ITAUQ, IU, IVT, LDWKVT,
      $                   LDWRKL, LDWRKR, LDWRKU, MAXWRK, MINMN, MINWRK,
-     $                   MNTHR, NWORK, WRKBL
+     $                   MNTHR, NWORK, SMLSIZ, WRKBL
       DOUBLE PRECISION   ANRM, BIGNUM, EPS, SMLNUM
 *     ..
 *     .. Local Arrays ..
@@ -168,7 +175,7 @@
       LOGICAL            LSAME
       INTEGER            ILAENV
       DOUBLE PRECISION   DLAMCH, DLANGE
-      EXTERNAL           DLAMCH, DLANGE, ILAENV, LSAME
+      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANGE
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          DBLE, INT, MAX, MIN, SQRT
@@ -187,7 +194,6 @@
       WNTQN = LSAME( JOBZ, 'N' )
       MINWRK = 1
       MAXWRK = 1
-      LQUERY = ( LWORK.EQ.-1 )
 *
       IF( .NOT.( WNTQA .OR. WNTQS .OR. WNTQO .OR. WNTQN ) ) THEN
          INFO = -1
@@ -206,6 +212,8 @@
          INFO = -10
       END IF
 *
+      SMLSIZ = ILAENV( 9, 'DGESDD', ' ', 0, 0, 0, 0 )
+*
 *     Compute workspace
 *      (Note: Comments in the code beginning "Workspace:" describe the
 *       minimal amount of workspace needed at that point in the code,
@@ -218,22 +226,19 @@
 *
 *           Compute space needed for DBDSDC
 *
-            IF( WNTQN ) THEN
-               BDSPAC = 7*N
-            ELSE
-               BDSPAC = 3*N*N + 4*N
-            END IF
+            BDSPAC = 3*N*N + 7*N
+            BDSPAN = MAX( 12*N+4, 8*N+2+SMLSIZ*( SMLSIZ+8 ) )
             IF( M.GE.MNTHR ) THEN
                IF( WNTQN ) THEN
 *
 *                 Path 1 (M much larger than N, JOBZ='N')
 *
-                  WRKBL = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1,
-     $                    -1 )
-                  WRKBL = MAX( WRKBL, 3*N+2*N*
-     $                    ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+N )
-                  MINWRK = BDSPAC + N
+                  MAXWRK = N + N*ILAENV( 1, 'DGEQRF', ' ', M, N, -1,
+     $                     -1 )
+                  MAXWRK = MAX( MAXWRK, 3*N+2*N*
+     $                     ILAENV( 1, 'DGEBRD', ' ', N, N, -1, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC )
+                  MINWRK = BDSPAC
                ELSE IF( WNTQO ) THEN
 *
 *                 Path 2 (M much larger than N, JOBZ='O')
@@ -247,9 +252,9 @@
      $                    ILAENV( 1, 'DORMBR', 'QLN', N, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N )
                   MAXWRK = WRKBL + 2*N*N
-                  MINWRK = BDSPAC + 2*N*N + 3*N
+                  MINWRK = BDSPAC + 2*N*N + 2*N
                ELSE IF( WNTQS ) THEN
 *
 *                 Path 3 (M much larger than N, JOBZ='S')
@@ -263,9 +268,9 @@
      $                    ILAENV( 1, 'DORMBR', 'QLN', N, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N )
                   MAXWRK = WRKBL + N*N
-                  MINWRK = BDSPAC + N*N + 3*N
+                  MINWRK = BDSPAC + N*N + 2*N
                ELSE IF( WNTQA ) THEN
 *
 *                 Path 4 (M much larger than N, JOBZ='A')
@@ -279,9 +284,9 @@
      $                    ILAENV( 1, 'DORMBR', 'QLN', N, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
-                  MAXWRK = WRKBL + N*N
-                  MINWRK = BDSPAC + N*N + 3*N
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N )
+                  MAXWRK = N*N + WRKBL
+                  MINWRK = BDSPAC + N*N + M + N
                END IF
             ELSE
 *
@@ -289,53 +294,47 @@
 *
                WRKBL = 3*N + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N, -1,
      $                 -1 )
-               IF( WNTQN ) THEN
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*N )
-                  MINWRK = 3*N + MAX( M, BDSPAC )
-               ELSE IF( WNTQO ) THEN
+               IF( WNTQO ) THEN
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'DORMBR', 'QLN', M, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N+M )
                   MAXWRK = WRKBL + M*N
-                  MINWRK = 3*N + MAX( M, N*N+BDSPAC )
+                  MINWRK = BDSPAC + N*N + 2*N + M
                ELSE IF( WNTQS ) THEN
-                  WRKBL = MAX( WRKBL, 3*N+N*
-     $                    ILAENV( 1, 'DORMBR', 'QLN', M, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*N+N*
-     $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*N )
-                  MINWRK = 3*N + MAX( M, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*N+N*
+     $                     ILAENV( 1, 'DORMBR', 'QLN', M, N, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*N+N*
+     $                     ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*N+M )
+                  MINWRK = BDSPAC + 2*N + M
                ELSE IF( WNTQA ) THEN
-                  WRKBL = MAX( WRKBL, 3*N+M*
-     $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*N+N*
-     $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
-                  MAXWRK = MAX( MAXWRK, BDSPAC+3*N )
-                  MINWRK = 3*N + MAX( M, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*N+M*
+     $                     ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*N+N*
+     $                     ILAENV( 1, 'DORMBR', 'PRT', N, N, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*N+M )
+                  MINWRK = BDSPAC + 2*N + M
                END IF
             END IF
          ELSE
 *
 *           Compute space needed for DBDSDC
 *
-            IF( WNTQN ) THEN
-               BDSPAC = 7*M
-            ELSE
-               BDSPAC = 3*M*M + 4*M
-            END IF
+            BDSPAC = 3*M*M + 7*M
+            BDSPAN = MAX( 12*M+4, 8*M+2+SMLSIZ*( SMLSIZ+8 ) )
             IF( N.GE.MNTHR ) THEN
                IF( WNTQN ) THEN
 *
 *                 Path 1t (N much larger than M, JOBZ='N')
 *
-                  WRKBL = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1,
-     $                    -1 )
-                  WRKBL = MAX( WRKBL, 3*M+2*M*
-     $                    ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+M )
-                  MINWRK = BDSPAC + M
+                  MAXWRK = M + M*ILAENV( 1, 'DGELQF', ' ', M, N, -1,
+     $                     -1 )
+                  MAXWRK = MAX( MAXWRK, 3*M+2*M*
+     $                     ILAENV( 1, 'DGEBRD', ' ', M, M, -1, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC )
+                  MINWRK = BDSPAC
                ELSE IF( WNTQO ) THEN
 *
 *                 Path 2t (N much larger than M, JOBZ='O')
@@ -349,9 +348,9 @@
      $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, M, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'DORMBR', 'PRT', M, M, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + 2*M*M
-                  MINWRK = BDSPAC + 2*M*M + 3*M
+                  MINWRK = BDSPAC + 2*M*M + 2*M
                ELSE IF( WNTQS ) THEN
 *
 *                 Path 3t (N much larger than M, JOBZ='S')
@@ -365,9 +364,9 @@
      $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, M, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'DORMBR', 'PRT', M, M, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + M*M
-                  MINWRK = BDSPAC + M*M + 3*M
+                  MINWRK = BDSPAC + M*M + 2*M
                ELSE IF( WNTQA ) THEN
 *
 *                 Path 4t (N much larger than M, JOBZ='A')
@@ -381,9 +380,9 @@
      $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, M, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'DORMBR', 'PRT', M, M, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + M*M
-                  MINWRK = BDSPAC + M*M + 3*M
+                  MINWRK = BDSPAC + M*M + M + N
                END IF
             ELSE
 *
@@ -391,52 +390,47 @@
 *
                WRKBL = 3*M + ( M+N )*ILAENV( 1, 'DGEBRD', ' ', M, N, -1,
      $                 -1 )
-               IF( WNTQN ) THEN
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*M )
-                  MINWRK = 3*M + MAX( N, BDSPAC )
-               ELSE IF( WNTQO ) THEN
+               IF( WNTQO ) THEN
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'DORMBR', 'PRT', M, N, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + M*N
-                  MINWRK = 3*M + MAX( N, M*M+BDSPAC )
+                  MINWRK = BDSPAC + M*M + 2*M + N
                ELSE IF( WNTQS ) THEN
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'DORMBR', 'PRT', M, N, M, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*M )
-                  MINWRK = 3*M + MAX( N, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*M+M*
+     $                     ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*M+M*
+     $                     ILAENV( 1, 'DORMBR', 'PRT', M, N, M, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*M )
+                  MINWRK = BDSPAC + 2*M + N
                ELSE IF( WNTQA ) THEN
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'DORMBR', 'PRT', N, N, M, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*M )
-                  MINWRK = 3*M + MAX( N, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*M+M*
+     $                     ILAENV( 1, 'DORMBR', 'QLN', M, M, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*M+N*
+     $                     ILAENV( 1, 'DORMBR', 'PRT', N, N, M, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*M )
+                  MINWRK = BDSPAC + 2*M + N
                END IF
             END IF
          END IF
+      END IF
+      IF( INFO.EQ.0 ) THEN
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -12
-      END IF
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGESDD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
-         IF( LWORK.GE.1 )
-     $      WORK( 1 ) = ONE
          RETURN
       END IF
 *
@@ -497,7 +491,7 @@
                NWORK = IE + N
 *
 *              Perform bidiagonal SVD, computing singular values only
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL DBDSDC( 'U', 'N', N, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
@@ -512,10 +506,10 @@
 *
 *              WORK(IR) is LDWRKR by N
 *
-               IF( LWORK.GE.LDA*N+N*N+3*N+BDSPAC ) THEN
+               IF( LWORK.GE.LDA*N+4*N*N+9*N ) THEN
                   LDWRKR = LDA
                ELSE
-                  LDWRKR = ( LWORK-N*N-3*N-BDSPAC ) / N
+                  LDWRKR = ( LWORK-4*N*N-9*N ) / N
                END IF
                ITAU = IR + LDWRKR*N
                NWORK = ITAU + N
@@ -557,7 +551,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in WORK(IU) and computing right
 *              singular vectors of bidiagonal matrix in VT
-*              (Workspace: need N+N*N+BDSPAC)
+*              (Workspace: need 2*N*N+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ), N,
      $                      VT, LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -633,7 +627,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagoal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need N*N+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
      $                      LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -681,7 +675,7 @@
                CALL DLACPY( 'L', M, N, A, LDA, U, LDU )
 *
 *              Generate Q in U
-*              (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+*              (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
                CALL DORGQR( M, M, N, U, LDU, WORK( ITAU ),
      $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
 *
@@ -703,7 +697,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in WORK(IU) and computing right
 *              singular vectors of bidiagonal matrix in VT
-*              (Workspace: need N+N*N+BDSPAC)
+*              (Workspace: need N*N+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ), N,
      $                      VT, LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -754,13 +748,13 @@
             IF( WNTQN ) THEN
 *
 *              Perform bidiagonal SVD, only computing singular values
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL DBDSDC( 'U', 'N', N, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
             ELSE IF( WNTQO ) THEN
                IU = NWORK
-               IF( LWORK.GE.M*N+3*N+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*N*N+9*N ) THEN
 *
 *                 WORK( IU ) is M by N
 *
@@ -785,7 +779,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in WORK(IU) and computing right
 *              singular vectors of bidiagonal matrix in VT
-*              (Workspace: need N+N*N+BDSPAC)
+*              (Workspace: need N*N+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ),
      $                      LDWRKU, VT, LDVT, DUM, IDUM, WORK( NWORK ),
@@ -798,7 +792,7 @@
      $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
 *
-               IF( LWORK.GE.M*N+3*N+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*N*N+9*N ) THEN
 *
 *                 Overwrite WORK(IU) by left singular vectors of A
 *                 (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
@@ -838,7 +832,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL DLASET( 'F', M, N, ZERO, ZERO, U, LDU )
                CALL DBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
@@ -855,12 +849,12 @@
                CALL DORMBR( 'P', 'R', 'T', N, N, N, A, LDA,
      $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
-            ELSE IF( WNTQA ) THEN
+            ELSE
 *
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL DLASET( 'F', M, M, ZERO, ZERO, U, LDU )
                CALL DBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
@@ -925,7 +919,7 @@
                NWORK = IE + M
 *
 *              Perform bidiagonal SVD, computing singular values only
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL DBDSDC( 'U', 'N', M, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
@@ -941,7 +935,7 @@
 *              IVT is M by M
 *
                IL = IVT + M*M
-               IF( LWORK.GE.M*N+M*M+3*M+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+4*M*M+9*M ) THEN
 *
 *                 WORK(IL) is M by N
 *
@@ -986,7 +980,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U, and computing right singular
 *              vectors of bidiagonal matrix in WORK(IVT)
-*              (Workspace: need M+M*M+BDSPAC)
+*              (Workspace: need 2*M*M+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU,
      $                      WORK( IVT ), M, DUM, IDUM, WORK( NWORK ),
@@ -1061,7 +1055,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need M*M+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU, VT,
      $                      LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -1108,7 +1102,7 @@
                CALL DLACPY( 'U', M, N, A, LDA, VT, LDVT )
 *
 *              Generate Q in VT
-*              (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+*              (Workspace: need M*M+M+N, prefer M*M+M+N*NB)
 *
                CALL DORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
      $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
@@ -1131,7 +1125,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in WORK(IVT)
-*              (Workspace: need M+M*M+BDSPAC)
+*              (Workspace: need M*M+BDSPAC)
 *
                CALL DBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU,
      $                      WORK( IVT ), LDWKVT, DUM, IDUM,
@@ -1182,14 +1176,14 @@
             IF( WNTQN ) THEN
 *
 *              Perform bidiagonal SVD, only computing singular values
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL DBDSDC( 'L', 'N', M, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
             ELSE IF( WNTQO ) THEN
                LDWKVT = M
                IVT = NWORK
-               IF( LWORK.GE.M*N+3*M+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*M*M+9*M ) THEN
 *
 *                 WORK( IVT ) is M by N
 *
@@ -1224,7 +1218,7 @@
      $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
 *
-               IF( LWORK.GE.M*N+3*M+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*M*M+9*M ) THEN
 *
 *                 Overwrite WORK(IVT) by left singular vectors of A
 *                 (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
@@ -1263,7 +1257,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL DLASET( 'F', M, N, ZERO, ZERO, VT, LDVT )
                CALL DBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU, VT,
@@ -1280,12 +1274,12 @@
                CALL DORMBR( 'P', 'R', 'T', M, N, M, A, LDA,
      $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
-            ELSE IF( WNTQA ) THEN
+            ELSE
 *
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL DLASET( 'F', N, N, ZERO, ZERO, VT, LDVT )
                CALL DBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU, VT,
@@ -1319,9 +1313,15 @@
          IF( ANRM.GT.BIGNUM )
      $      CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
      $                   IERR )
+         IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM )
+     $      CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1, WORK( 2 ),
+     $                   MINMN, IERR )
          IF( ANRM.LT.SMLNUM )
      $      CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
      $                   IERR )
+         IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM )
+     $      CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1, WORK( 2 ),
+     $                   MINMN, IERR )
       END IF
 *
 *     Return optimal workspace in WORK(1)
diff -uNr LAPACK.orig/SRC/dgesvd.f LAPACK/SRC/dgesvd.f
--- LAPACK.orig/SRC/dgesvd.f	Thu Nov  4 14:24:44 1999
+++ LAPACK/SRC/dgesvd.f	Fri May 25 16:08:25 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU, JOBVT
@@ -118,10 +119,9 @@
 *          LWORK >= MAX(3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit.
@@ -134,12 +134,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
-     $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
+      LOGICAL            WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS, WNTVA,
+     $                   WNTVAS, WNTVN, WNTVO, WNTVS
       INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IR, ISCL,
      $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
      $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
@@ -181,7 +183,7 @@
       WNTVO = LSAME( JOBVT, 'O' )
       WNTVN = LSAME( JOBVT, 'N' )
       MINWRK = 1
-      LQUERY = ( LWORK.EQ.-1 )
+      MAXWRK = 1
 *
       IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN
          INFO = -1
@@ -208,8 +210,7 @@
 *       NB refers to the optimal block size for the immediately
 *       following subroutine, as returned by ILAENV.)
 *
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) .AND. M.GT.0 .AND.
-     $    N.GT.0 ) THEN
+      IF( INFO.EQ.0 .AND. M.GT.0 .AND. N.GT.0 ) THEN
          IF( M.GE.N ) THEN
 *
 *           Compute space needed for DBDSQR
@@ -557,24 +558,22 @@
                MAXWRK = MAX( MAXWRK, MINWRK )
             END IF
          END IF
+      END IF
+      IF( INFO.EQ.0 ) THEN
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGESVD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
-         IF( LWORK.GE.1 )
-     $      WORK( 1 ) = ONE
          RETURN
       END IF
 *
diff -uNr LAPACK.orig/SRC/dggbak.f LAPACK/SRC/dggbak.f
--- LAPACK.orig/SRC/dggbak.f	Thu Nov  4 14:24:45 1999
+++ LAPACK/SRC/dggbak.f	Fri May 25 16:08:56 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     February 1, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB, SIDE
@@ -108,10 +108,15 @@
          INFO = -3
       ELSE IF( ILO.LT.1 ) THEN
          INFO = -4
-      ELSE IF( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) THEN
+      ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
+         INFO = -4
+      ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
+     $   THEN
+         INFO = -5
+      ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
          INFO = -5
       ELSE IF( M.LT.0 ) THEN
-         INFO = -6
+         INFO = -8
       ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
          INFO = -10
       END IF
diff -uNr LAPACK.orig/SRC/dggbal.f LAPACK/SRC/dggbal.f
--- LAPACK.orig/SRC/dggbal.f	Thu Nov  4 14:25:44 1999
+++ LAPACK/SRC/dggbal.f	Fri May 25 16:09:17 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     April 12, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB
@@ -141,7 +141,7 @@
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
-         INFO = -5
+         INFO = -6
       END IF
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGGBAL', -INFO )
@@ -188,8 +188,8 @@
       IF( L.NE.1 )
      $   GO TO 30
 *
-      RSCALE( 1 ) = 1
-      LSCALE( 1 ) = 1
+      RSCALE( 1 ) = ONE
+      LSCALE( 1 ) = ONE
       GO TO 190
 *
    30 CONTINUE
@@ -247,7 +247,7 @@
 *     Permute rows M and I
 *
   160 CONTINUE
-      LSCALE( M ) = I
+      LSCALE( M ) = DBLE( I )
       IF( I.EQ.M )
      $   GO TO 170
       CALL DSWAP( N-K+1, A( I, K ), LDA, A( M, K ), LDA )
@@ -256,7 +256,7 @@
 *     Permute columns M and J
 *
   170 CONTINUE
-      RSCALE( M ) = J
+      RSCALE( M ) = DBLE( J )
       IF( J.EQ.M )
      $   GO TO 180
       CALL DSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
@@ -424,7 +424,7 @@
       DO 360 I = ILO, IHI
          IRAB = IDAMAX( N-ILO+1, A( I, ILO ), LDA )
          RAB = ABS( A( I, IRAB+ILO-1 ) )
-         IRAB = IDAMAX( N-ILO+1, B( I, ILO ), LDA )
+         IRAB = IDAMAX( N-ILO+1, B( I, ILO ), LDB )
          RAB = MAX( RAB, ABS( B( I, IRAB+ILO-1 ) ) )
          LRAB = INT( LOG10( RAB+SFMIN ) / BASL+ONE )
          IR = LSCALE( I ) + SIGN( HALF, LSCALE( I ) )
diff -uNr LAPACK.orig/SRC/dgges.f LAPACK/SRC/dgges.f
--- LAPACK.orig/SRC/dgges.f	Thu Nov  4 14:26:18 1999
+++ LAPACK/SRC/dgges.f	Fri May 25 16:09:38 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SORT
@@ -158,10 +159,9 @@
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK.  LWORK >= 8*N+16.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  BWORK   (workspace) LOGICAL array, dimension (N)
 *          Not referenced if SORT = 'N'.
@@ -184,12 +184,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
-     $                   LQUERY, LST2SL, WANTST
+     $                   LST2SL, WANTST
       INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
      $                   ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK,
      $                   MINWRK
@@ -245,7 +247,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -272,7 +273,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MINWRK = 7*( N+1 ) + 16
          MAXWRK = 7*( N+1 ) + N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) +
      $            16
@@ -281,19 +282,18 @@
      $               ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 ) )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -19
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -19
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGGES ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/dggesx.f LAPACK/SRC/dggesx.f
--- LAPACK.orig/SRC/dggesx.f	Thu Nov  4 14:26:18 1999
+++ LAPACK/SRC/dggesx.f	Fri May 25 16:09:56 2001
@@ -7,6 +7,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Do WS calculations if LWORK = -1 (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SENSE, SORT
@@ -185,6 +186,10 @@
 *          If SENSE = 'E', 'V', or 'B',
 *          LWORK >= MAX( 8*(N+1)+16, 2*SDIM*(N-SDIM) ).
 *
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
 *  IWORK   (workspace) INTEGER array, dimension (LIWORK)
 *          Not referenced if SENSE = 'N'.
 *
@@ -227,6 +232,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
 *     ..
@@ -330,7 +337,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
+      IF( INFO.EQ.0 ) THEN
          MINWRK = 8*( N+1 ) + 16
          MAXWRK = 7*( N+1 ) + N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 ) +
      $            16
@@ -338,7 +345,15 @@
             MAXWRK = MAX( MAXWRK, 8*( N+1 )+N*
      $               ILAENV( 1, 'DORGQR', ' ', N, 1, N, -1 )+16 )
          END IF
+*
+*        Estimate the workspace needed by DTGSEN.
+*
+         IF( WANTST ) THEN
+            MAXWRK = MAX( MAXWRK, 2*N+( N*N+1 ) / 2 )
+         END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -22
       END IF
       IF( .NOT.WANTSN ) THEN
          LIWMIN = 1
@@ -346,21 +361,19 @@
          LIWMIN = N + 6
       END IF
       IWORK( 1 ) = LIWMIN
-*
-      IF( INFO.EQ.0 .AND. LWORK.LT.MINWRK ) THEN
-         INFO = -22
-      ELSE IF( INFO.EQ.0 .AND. IJOB.GE.1 ) THEN
+      IF( INFO.EQ.0 .AND. IJOB.GE.1 ) THEN
          IF( LIWORK.LT.LIWMIN )
      $      INFO = -24
       END IF
 *
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGGESX', -INFO )
          RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/dggev.f LAPACK/SRC/dggev.f
--- LAPACK.orig/SRC/dggev.f	Thu Nov  4 14:26:18 1999
+++ LAPACK/SRC/dggev.f	Fri May 25 16:10:14 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -123,10 +124,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,8*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
@@ -141,11 +141,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
+      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR
       CHARACTER          CHTEMP
       INTEGER            ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
      $                   IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, MAXWRK,
@@ -157,8 +159,9 @@
       LOGICAL            LDUMMA( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLACPY,
-     $                   DLASCL, DLASET, DORGQR, DORMQR, DTGEVC, XERBLA
+      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
+     $                   DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGEVC,
+     $                   XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -199,7 +202,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -225,24 +227,22 @@
 *       computed assuming ILO = 1 and IHI = N, the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 7*N + N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 8*N )
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -16
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -16
+*     Quick returns
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGGEV ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/dggevx.f LAPACK/SRC/dggevx.f
--- LAPACK.orig/SRC/dggevx.f	Thu Nov  4 14:26:18 1999
+++ LAPACK/SRC/dggevx.f	Fri May 25 16:11:31 2001
@@ -7,6 +7,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
@@ -212,10 +213,9 @@
 *          If SENSE = 'E', LWORK >= 12*N.
 *          If SENSE = 'V' or 'B', LWORK >= 2*N*N+12*N+16.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (N+6)
 *          If SENSE = 'E', IWORK is not referenced.
@@ -262,12 +262,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       DOUBLE PRECISION   ZERO, ONE
       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY, PAIR,
-     $                   WANTSB, WANTSE, WANTSN, WANTSV
+      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, PAIR, WANTSB,
+     $                   WANTSE, WANTSN, WANTSV
       CHARACTER          CHTEMP
       INTEGER            I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
      $                   ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK,
@@ -279,9 +281,9 @@
       LOGICAL            LDUMMA( 1 )
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLACPY,
-     $                   DLASCL, DLASET, DORGQR, DORMQR, DTGEVC, DTGSNA,
-     $                   XERBLA
+      EXTERNAL           DGEQRF, DGGBAK, DGGBAL, DGGHRD, DHGEQZ, DLABAD,
+     $                   DLACPY, DLASCL, DLASET, DORGQR, DORMQR, DTGEVC,
+     $                   DTGSNA, XERBLA
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -327,7 +329,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC,
      $    'S' ) .OR. LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) )
      $     THEN
@@ -360,7 +361,7 @@
 *       computed assuming ILO = 1 and IHI = N, the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 5*N + N*ILAENV( 1, 'DGEQRF', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 6*N )
          IF( WANTSE ) THEN
@@ -370,24 +371,20 @@
             MAXWRK = MAX( MAXWRK, 2*N*N+12*N+16 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -26
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -26
-      END IF
+*     Quick returns
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'DGGEVX', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV )
+     $   RETURN
       IF( N.EQ.0 )
      $   RETURN
-*
 *
 *     Get machine constants
 *
diff -uNr LAPACK.orig/SRC/dgghrd.f LAPACK/SRC/dgghrd.f
--- LAPACK.orig/SRC/dgghrd.f	Thu Nov  4 14:25:43 1999
+++ LAPACK/SRC/dgghrd.f	Fri May 25 16:11:50 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ
@@ -20,16 +20,32 @@
 *
 *  DGGHRD reduces a pair of real matrices (A,B) to generalized upper
 *  Hessenberg form using orthogonal transformations, where A is a
-*  general matrix and B is upper triangular:  Q' * A * Z = H and
-*  Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular,
-*  and Q and Z are orthogonal, and ' means transpose.
+*  general matrix and B is upper triangular.  The form of the
+*  generalized eigenvalue problem is
+*     A*x = lambda*B*x,
+*  and B is typically made upper triangular by computing its QR
+*  factorization and moving the orthogonal matrix Q to the left side
+*  of the equation.
+*
+*  This subroutine simultaneously reduces A to a Hessenberg matrix H:
+*     Q**T*A*Z = H
+*  and transforms B to another upper triangular matrix T:
+*     Q**T*B*Z = T
+*  in order to reduce the problem to its standard form
+*     H*y = lambda*T*y
+*  where y = Z**T*x.
 *
 *  The orthogonal matrices Q and Z are determined as products of Givens
 *  rotations.  They may either be formed explicitly, or they may be
 *  postmultiplied into input matrices Q1 and Z1, so that
 *
-*       Q1 * A * Z1' = (Q1*Q) * H * (Z1*Z)'
-*       Q1 * B * Z1' = (Q1*Q) * T * (Z1*Z)'
+*       Q1 * A * Z1**T = (Q1*Q) * H * (Z1*Z)**T
+*
+*       Q1 * B * Z1**T = (Q1*Q) * T * (Z1*Z)**T
+*
+*  If Q1 is the orthogonal matrix from the QR factorization of B in the
+*  original equation A*x = lambda*B*x, then DGGHRD reduces the original
+*  problem to generalized Hessenberg form.
 *
 *  Arguments
 *  =========
@@ -53,10 +69,11 @@
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
-*          It is assumed that A is already upper triangular in rows and
-*          columns 1:ILO-1 and IHI+1:N.  ILO and IHI are normally set
-*          by a previous call to DGGBAL; otherwise they should be set
-*          to 1 and N respectively.
+*          ILO and IHI mark the rows and columns of A which are to be
+*          reduced.  It is assumed that A is already upper triangular
+*          in rows and columns 1:ILO-1 and IHI+1:N.  ILO and IHI are
+*          normally set by a previous call to SGGBAL; otherwise they
+*          should be set to 1 and N respectively.
 *          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
@@ -70,33 +87,28 @@
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
 *          On entry, the N-by-N upper triangular matrix B.
-*          On exit, the upper triangular matrix T = Q' B Z.  The
+*          On exit, the upper triangular matrix T = Q**T B Z.  The
 *          elements below the diagonal are set to zero.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of the array B.  LDB >= max(1,N).
 *
 *  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
-*          If COMPQ='N':  Q is not referenced.
-*          If COMPQ='I':  on entry, Q need not be set, and on exit it
-*                         contains the orthogonal matrix Q, where Q'
-*                         is the product of the Givens transformations
-*                         which are applied to A and B on the left.
-*          If COMPQ='V':  on entry, Q must contain an orthogonal matrix
-*                         Q1, and on exit this is overwritten by Q1*Q.
+*          On entry, if COMPQ = 'V', the orthogonal matrix Q1,
+*          typically from the QR factorization of B.
+*          On exit, if COMPQ='I', the orthogonal matrix Q, and if
+*          COMPQ = 'V', the product Q1*Q.
+*          Not referenced if COMPQ='N'.
 *
 *  LDQ     (input) INTEGER
 *          The leading dimension of the array Q.
 *          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
 *
 *  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
-*          If COMPZ='N':  Z is not referenced.
-*          If COMPZ='I':  on entry, Z need not be set, and on exit it
-*                         contains the orthogonal matrix Z, which is
-*                         the product of the Givens transformations
-*                         which are applied to A and B on the right.
-*          If COMPZ='V':  on entry, Z must contain an orthogonal matrix
-*                         Z1, and on exit this is overwritten by Z1*Z.
+*          On entry, if COMPZ = 'V', the orthogonal matrix Z1.
+*          On exit, if COMPZ='I', the orthogonal matrix Z, and if
+*          COMPZ = 'V', the product Z1*Z.
+*          Not referenced if COMPZ='N'.
 *
 *  LDZ     (input) INTEGER
 *          The leading dimension of the array Z.
diff -uNr LAPACK.orig/SRC/dhgeqz.f LAPACK/SRC/dhgeqz.f
--- LAPACK.orig/SRC/dhgeqz.f	Thu Nov  4 14:24:45 1999
+++ LAPACK/SRC/dhgeqz.f	Fri May 25 16:12:11 2001
@@ -1,56 +1,75 @@
-      SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB,
+      SUBROUTINE DHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
      $                   ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
      $                   LWORK, INFO )
 *
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 3, 2001 
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ, JOB
-      INTEGER            IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
+      INTEGER            IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N
 *     ..
 *     .. Array Arguments ..
-      DOUBLE PRECISION   A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
-     $                   B( LDB, * ), BETA( * ), Q( LDQ, * ), WORK( * ),
-     $                   Z( LDZ, * )
+      DOUBLE PRECISION   ALPHAI( * ), ALPHAR( * ), BETA( * ),
+     $                   H( LDH, * ), Q( LDQ, * ), T( LDT, * ),
+     $                   WORK( * ), Z( LDZ, * )
 *     ..
 *
 *  Purpose
 *  =======
 *
-*  DHGEQZ implements a single-/double-shift version of the QZ method for
-*  finding the generalized eigenvalues
-*
-*  w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j)   of the equation
-*
-*       det( A - w(i) B ) = 0
-*
-*  In addition, the pair A,B may be reduced to generalized Schur form:
-*  B is upper triangular, and A is block upper triangular, where the
-*  diagonal blocks are either 1-by-1 or 2-by-2, the 2-by-2 blocks having
-*  complex generalized eigenvalues (see the description of the argument
-*  JOB.)
-*
-*  If JOB='S', then the pair (A,B) is simultaneously reduced to Schur
-*  form by applying one orthogonal tranformation (usually called Q) on
-*  the left and another (usually called Z) on the right.  The 2-by-2
-*  upper-triangular diagonal blocks of B corresponding to 2-by-2 blocks
-*  of A will be reduced to positive diagonal matrices.  (I.e.,
-*  if A(j+1,j) is non-zero, then B(j+1,j)=B(j,j+1)=0 and B(j,j) and
-*  B(j+1,j+1) will be positive.)
-*
-*  If JOB='E', then at each iteration, the same transformations
-*  are computed, but they are only applied to those parts of A and B
-*  which are needed to compute ALPHAR, ALPHAI, and BETAR.
-*
-*  If JOB='S' and COMPQ and COMPZ are 'V' or 'I', then the orthogonal
-*  transformations used to reduce (A,B) are accumulated into the arrays
-*  Q and Z s.t.:
-*
-*       Q(in) A(in) Z(in)* = Q(out) A(out) Z(out)*
-*       Q(in) B(in) Z(in)* = Q(out) B(out) Z(out)*
+*  DHGEQZ computes the eigenvalues of a real matrix pair (H,T),
+*  where H is an upper Hessenberg matrix and T is upper triangular,
+*  using the double-shift QZ method.
+*  Matrix pairs of this type are produced by the reduction to
+*  generalized upper Hessenberg form of a real matrix pair (A,B):
+*
+*     A = Q1*H*Z1**T,  B = Q1*T*Z1**T,
+*
+*  as computed by DGGHRD.
+*
+*  If JOB='S', then the Hessenberg-triangular pair (H,T) is
+*  also reduced to generalized Schur form,
+*  
+*     H = Q*S*Z**T,  T = Q*P*Z**T,
+*  
+*  where Q and Z are orthogonal matrices, P is an upper triangular
+*  matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2
+*  diagonal blocks.
+*
+*  The 1-by-1 blocks correspond to real eigenvalues of the matrix pair
+*  (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of
+*  eigenvalues.
+*
+*  Additionally, the 2-by-2 upper triangular diagonal blocks of P
+*  corresponding to 2-by-2 blocks of S are reduced to positive diagonal
+*  form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0,
+*  P(j,j) > 0, and P(j+1,j+1) > 0.
+*
+*  Optionally, the orthogonal matrix Q from the generalized Schur
+*  factorization may be postmultiplied into an input matrix Q1, and the
+*  orthogonal matrix Z may be postmultiplied into an input matrix Z1.
+*  If Q1 and Z1 are the orthogonal matrices from DGGHRD that reduced
+*  the matrix pair (A,B) to generalized upper Hessenberg form, then the
+*  output matrices Q1*Q and Z1*Z are the orthogonal factors from the
+*  generalized Schur factorization of (A,B):
+*
+*     A = (Q1*Q)*S*(Z1*Z)**T,  B = (Q1*Q)*P*(Z1*Z)**T.
+*  
+*  To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently,
+*  of (A,B)) are computed as a pair of values (alpha,beta), where alpha is
+*  complex and beta real.
+*  If beta is nonzero, lambda = alpha / beta is an eigenvalue of the
+*  generalized nonsymmetric eigenvalue problem (GNEP)
+*     A*x = lambda*B*x
+*  and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the
+*  alternate form of the GNEP
+*     mu*A*y = B*y.
+*  Real eigenvalues can be read directly from the generalized Schur
+*  form: 
+*    alpha = S(i,i), beta = P(i,i).
 *
 *  Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
 *       Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
@@ -60,114 +79,98 @@
 *  =========
 *
 *  JOB     (input) CHARACTER*1
-*          = 'E': compute only ALPHAR, ALPHAI, and BETA.  A and B will
-*                 not necessarily be put into generalized Schur form.
-*          = 'S': put A and B into generalized Schur form, as well
-*                 as computing ALPHAR, ALPHAI, and BETA.
+*          = 'E': Compute eigenvalues only;
+*          = 'S': Compute eigenvalues and the Schur form. 
 *
 *  COMPQ   (input) CHARACTER*1
-*          = 'N': do not modify Q.
-*          = 'V': multiply the array Q on the right by the transpose of
-*                 the orthogonal tranformation that is applied to the
-*                 left side of A and B to reduce them to Schur form.
-*          = 'I': like COMPQ='V', except that Q will be initialized to
-*                 the identity first.
+*          = 'N': Left Schur vectors (Q) are not computed;
+*          = 'I': Q is initialized to the unit matrix and the matrix Q
+*                 of left Schur vectors of (H,T) is returned;
+*          = 'V': Q must contain an orthogonal matrix Q1 on entry and
+*                 the product Q1*Q is returned.
 *
 *  COMPZ   (input) CHARACTER*1
-*          = 'N': do not modify Z.
-*          = 'V': multiply the array Z on the right by the orthogonal
-*                 tranformation that is applied to the right side of
-*                 A and B to reduce them to Schur form.
-*          = 'I': like COMPZ='V', except that Z will be initialized to
-*                 the identity first.
+*          = 'N': Right Schur vectors (Z) are not computed;
+*          = 'I': Z is initialized to the unit matrix and the matrix Z
+*                 of right Schur vectors of (H,T) is returned;
+*          = 'V': Z must contain an orthogonal matrix Z1 on entry and
+*                 the product Z1*Z is returned.
 *
 *  N       (input) INTEGER
-*          The order of the matrices A, B, Q, and Z.  N >= 0.
+*          The order of the matrices H, T, Q, and Z.  N >= 0.
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
-*          It is assumed that A is already upper triangular in rows and
-*          columns 1:ILO-1 and IHI+1:N.
-*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
-*
-*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
-*          On entry, the N-by-N upper Hessenberg matrix A.  Elements
-*          below the subdiagonal must be zero.
-*          If JOB='S', then on exit A and B will have been
-*             simultaneously reduced to generalized Schur form.
-*          If JOB='E', then on exit A will have been destroyed.
-*             The diagonal blocks will be correct, but the off-diagonal
-*             portion will be meaningless.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max( 1, N ).
-*
-*  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
-*          On entry, the N-by-N upper triangular matrix B.  Elements
-*          below the diagonal must be zero.  2-by-2 blocks in B
-*          corresponding to 2-by-2 blocks in A will be reduced to
-*          positive diagonal form.  (I.e., if A(j+1,j) is non-zero,
-*          then B(j+1,j)=B(j,j+1)=0 and B(j,j) and B(j+1,j+1) will be
-*          positive.)
-*          If JOB='S', then on exit A and B will have been
-*             simultaneously reduced to Schur form.
-*          If JOB='E', then on exit B will have been destroyed.
-*             Elements corresponding to diagonal blocks of A will be
-*             correct, but the off-diagonal portion will be meaningless.
+*          ILO and IHI mark the rows and columns of H which are in
+*          Hessenberg form.  It is assumed that A is already upper
+*          triangular in rows and columns 1:ILO-1 and IHI+1:N.
+*          If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.
+*
+*  H       (input/output) DOUBLE PRECISION array, dimension (LDH, N)
+*          On entry, the N-by-N upper Hessenberg matrix H.
+*          On exit, if JOB = 'S', H contains the upper quasi-triangular
+*          matrix S from the generalized Schur factorization;
+*          2-by-2 diagonal blocks (corresponding to complex conjugate
+*          pairs of eigenvalues) are returned in standard form, with
+*          H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0.
+*          If JOB = 'E', the diagonal blocks of H match those of S, but
+*          the rest of H is unspecified.
+*
+*  LDH     (input) INTEGER
+*          The leading dimension of the array H.  LDH >= max( 1, N ).
+*
+*  T       (input/output) DOUBLE PRECISION array, dimension (LDT, N)
+*          On entry, the N-by-N upper triangular matrix T.
+*          On exit, if JOB = 'S', T contains the upper triangular
+*          matrix P from the generalized Schur factorization;
+*          2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S
+*          are reduced to positive diagonal form, i.e., if H(j+1,j) is
+*          non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and
+*          T(j+1,j+1) > 0.
+*          If JOB = 'E', the diagonal blocks of T match those of P, but
+*          the rest of T is unspecified.
 *
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max( 1, N ).
+*  LDT     (input) INTEGER
+*          The leading dimension of the array T.  LDT >= max( 1, N ).
 *
 *  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
-*          ALPHAR(1:N) will be set to real parts of the diagonal
-*          elements of A that would result from reducing A and B to
-*          Schur form and then further reducing them both to triangular
-*          form using unitary transformations s.t. the diagonal of B
-*          was non-negative real.  Thus, if A(j,j) is in a 1-by-1 block
-*          (i.e., A(j+1,j)=A(j,j+1)=0), then ALPHAR(j)=A(j,j).
-*          Note that the (real or complex) values
-*          (ALPHAR(j) + i*ALPHAI(j))/BETA(j), j=1,...,N, are the
-*          generalized eigenvalues of the matrix pencil A - wB.
+*          The real parts of each scalar alpha defining an eigenvalue
+*          of GNEP.
 *
 *  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
-*          ALPHAI(1:N) will be set to imaginary parts of the diagonal
-*          elements of A that would result from reducing A and B to
-*          Schur form and then further reducing them both to triangular
-*          form using unitary transformations s.t. the diagonal of B
-*          was non-negative real.  Thus, if A(j,j) is in a 1-by-1 block
-*          (i.e., A(j+1,j)=A(j,j+1)=0), then ALPHAR(j)=0.
-*          Note that the (real or complex) values
-*          (ALPHAR(j) + i*ALPHAI(j))/BETA(j), j=1,...,N, are the
-*          generalized eigenvalues of the matrix pencil A - wB.
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.
+*          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
+*          positive, then the j-th and (j+1)-st eigenvalues are a
+*          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
 *
 *  BETA    (output) DOUBLE PRECISION array, dimension (N)
-*          BETA(1:N) will be set to the (real) diagonal elements of B
-*          that would result from reducing A and B to Schur form and
-*          then further reducing them both to triangular form using
-*          unitary transformations s.t. the diagonal of B was
-*          non-negative real.  Thus, if A(j,j) is in a 1-by-1 block
-*          (i.e., A(j+1,j)=A(j,j+1)=0), then BETA(j)=B(j,j).
-*          Note that the (real or complex) values
-*          (ALPHAR(j) + i*ALPHAI(j))/BETA(j), j=1,...,N, are the
-*          generalized eigenvalues of the matrix pencil A - wB.
-*          (Note that BETA(1:N) will always be non-negative, and no
-*          BETAI is necessary.)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
 *
 *  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
-*          If COMPQ='N', then Q will not be referenced.
-*          If COMPQ='V' or 'I', then the transpose of the orthogonal
-*             transformations which are applied to A and B on the left
-*             will be applied to the array Q on the right.
+*          On entry, if COMPZ = 'V', the orthogonal matrix Q1 used in
+*          the reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the orthogonal matrix of left Schur
+*          vectors of (H,T), and if COMPZ = 'V', the orthogonal matrix
+*          of left Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
 *
 *  LDQ     (input) INTEGER
 *          The leading dimension of the array Q.  LDQ >= 1.
 *          If COMPQ='V' or 'I', then LDQ >= N.
 *
 *  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N)
-*          If COMPZ='N', then Z will not be referenced.
-*          If COMPZ='V' or 'I', then the orthogonal transformations
-*             which are applied to A and B on the right will be applied
-*             to the array Z on the right.
+*          On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in
+*          the reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the orthogonal matrix of
+*          right Schur vectors of (H,T), and if COMPZ = 'V', the
+*          orthogonal matrix of right Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
 *
 *  LDZ     (input) INTEGER
 *          The leading dimension of the array Z.  LDZ >= 1.
@@ -187,13 +190,12 @@
 *  INFO    (output) INTEGER
 *          = 0: successful exit
 *          < 0: if INFO = -i, the i-th argument had an illegal value
-*          = 1,...,N: the QZ iteration did not converge.  (A,B) is not
+*          = 1,...,N: the QZ iteration did not converge.  (H,T) is not
 *                     in Schur form, but ALPHAR(i), ALPHAI(i), and
 *                     BETA(i), i=INFO+1,...,N should be correct.
-*          = N+1,...,2*N: the shift calculation failed.  (A,B) is not
+*          = N+1,...,2*N: the shift calculation failed.  (H,T) is not
 *                     in Schur form, but ALPHAR(i), ALPHAI(i), and
 *                     BETA(i), i=INFO-N+1,...,N should be correct.
-*          > 2*N:     various "impossible" errors.
 *
 *  Further Details
 *  ===============
@@ -225,7 +227,7 @@
      $                   B1R, B22, B2A, B2I, B2R, BN, BNORM, BSCALE,
      $                   BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
      $                   CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
-     $                   SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T,
+     $                   SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
      $                   TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
      $                   U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
      $                   WR2
@@ -302,9 +304,9 @@
          INFO = -5
       ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN
          INFO = -6
-      ELSE IF( LDA.LT.N ) THEN
+      ELSE IF( LDH.LT.N ) THEN
          INFO = -8
-      ELSE IF( LDB.LT.N ) THEN
+      ELSE IF( LDT.LT.N ) THEN
          INFO = -10
       ELSE IF( LDQ.LT.1 .OR. ( ILQ .AND. LDQ.LT.N ) ) THEN
          INFO = -15
@@ -340,8 +342,8 @@
       SAFMIN = DLAMCH( 'S' )
       SAFMAX = ONE / SAFMIN
       ULP = DLAMCH( 'E' )*DLAMCH( 'B' )
-      ANORM = DLANHS( 'F', IN, A( ILO, ILO ), LDA, WORK )
-      BNORM = DLANHS( 'F', IN, B( ILO, ILO ), LDB, WORK )
+      ANORM = DLANHS( 'F', IN, H( ILO, ILO ), LDH, WORK )
+      BNORM = DLANHS( 'F', IN, T( ILO, ILO ), LDT, WORK )
       ATOL = MAX( SAFMIN, ULP*ANORM )
       BTOL = MAX( SAFMIN, ULP*BNORM )
       ASCALE = ONE / MAX( SAFMIN, ANORM )
@@ -350,15 +352,15 @@
 *     Set Eigenvalues IHI+1:N
 *
       DO 30 J = IHI + 1, N
-         IF( B( J, J ).LT.ZERO ) THEN
+         IF( T( J, J ).LT.ZERO ) THEN
             IF( ILSCHR ) THEN
                DO 10 JR = 1, J
-                  A( JR, J ) = -A( JR, J )
-                  B( JR, J ) = -B( JR, J )
+                  H( JR, J ) = -H( JR, J )
+                  T( JR, J ) = -T( JR, J )
    10          CONTINUE
             ELSE
-               A( J, J ) = -A( J, J )
-               B( J, J ) = -B( J, J )
+               H( J, J ) = -H( J, J )
+               T( J, J ) = -T( J, J )
             END IF
             IF( ILZ ) THEN
                DO 20 JR = 1, N
@@ -366,9 +368,9 @@
    20          CONTINUE
             END IF
          END IF
-         ALPHAR( J ) = A( J, J )
+         ALPHAR( J ) = H( J, J )
          ALPHAI( J ) = ZERO
-         BETA( J ) = B( J, J )
+         BETA( J ) = T( J, J )
    30 CONTINUE
 *
 *     If IHI < ILO, skip QZ steps
@@ -408,8 +410,8 @@
 *        Split the matrix if possible.
 *
 *        Two tests:
-*           1: A(j,j-1)=0  or  j=ILO
-*           2: B(j,j)=0
+*           1: H(j,j-1)=0  or  j=ILO
+*           2: T(j,j)=0
 *
          IF( ILAST.EQ.ILO ) THEN
 *
@@ -417,14 +419,14 @@
 *
             GO TO 80
          ELSE
-            IF( ABS( A( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
-               A( ILAST, ILAST-1 ) = ZERO
+            IF( ABS( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+               H( ILAST, ILAST-1 ) = ZERO
                GO TO 80
             END IF
          END IF
 *
-         IF( ABS( B( ILAST, ILAST ) ).LE.BTOL ) THEN
-            B( ILAST, ILAST ) = ZERO
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+            T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
 *
@@ -432,36 +434,36 @@
 *
          DO 60 J = ILAST - 1, ILO, -1
 *
-*           Test 1: for A(j,j-1)=0 or j=ILO
+*           Test 1: for H(j,j-1)=0 or j=ILO
 *
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS( A( J, J-1 ) ).LE.ATOL ) THEN
-                  A( J, J-1 ) = ZERO
+               IF( ABS( H( J, J-1 ) ).LE.ATOL ) THEN
+                  H( J, J-1 ) = ZERO
                   ILAZRO = .TRUE.
                ELSE
                   ILAZRO = .FALSE.
                END IF
             END IF
 *
-*           Test 2: for B(j,j)=0
+*           Test 2: for T(j,j)=0
 *
-            IF( ABS( B( J, J ) ).LT.BTOL ) THEN
-               B( J, J ) = ZERO
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+               T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
 *
                ILAZR2 = .FALSE.
                IF( .NOT.ILAZRO ) THEN
-                  TEMP = ABS( A( J, J-1 ) )
-                  TEMP2 = ABS( A( J, J ) )
+                  TEMP = ABS( H( J, J-1 ) )
+                  TEMP2 = ABS( H( J, J ) )
                   TEMPR = MAX( TEMP, TEMP2 )
                   IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
                      TEMP = TEMP / TEMPR
                      TEMP2 = TEMP2 / TEMPR
                   END IF
-                  IF( TEMP*( ASCALE*ABS( A( J+1, J ) ) ).LE.TEMP2*
+                  IF( TEMP*( ASCALE*ABS( H( J+1, J ) ) ).LE.TEMP2*
      $                ( ASCALE*ATOL ) )ILAZR2 = .TRUE.
                END IF
 *
@@ -473,21 +475,21 @@
 *
                IF( ILAZRO .OR. ILAZR2 ) THEN
                   DO 40 JCH = J, ILAST - 1
-                     TEMP = A( JCH, JCH )
-                     CALL DLARTG( TEMP, A( JCH+1, JCH ), C, S,
-     $                            A( JCH, JCH ) )
-                     A( JCH+1, JCH ) = ZERO
-                     CALL DROT( ILASTM-JCH, A( JCH, JCH+1 ), LDA,
-     $                          A( JCH+1, JCH+1 ), LDA, C, S )
-                     CALL DROT( ILASTM-JCH, B( JCH, JCH+1 ), LDB,
-     $                          B( JCH+1, JCH+1 ), LDB, C, S )
+                     TEMP = H( JCH, JCH )
+                     CALL DLARTG( TEMP, H( JCH+1, JCH ), C, S,
+     $                            H( JCH, JCH ) )
+                     H( JCH+1, JCH ) = ZERO
+                     CALL DROT( ILASTM-JCH, H( JCH, JCH+1 ), LDH,
+     $                          H( JCH+1, JCH+1 ), LDH, C, S )
+                     CALL DROT( ILASTM-JCH, T( JCH, JCH+1 ), LDT,
+     $                          T( JCH+1, JCH+1 ), LDT, C, S )
                      IF( ILQ )
      $                  CALL DROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
      $                             C, S )
                      IF( ILAZR2 )
-     $                  A( JCH, JCH-1 ) = A( JCH, JCH-1 )*C
+     $                  H( JCH, JCH-1 ) = H( JCH, JCH-1 )*C
                      ILAZR2 = .FALSE.
-                     IF( ABS( B( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
+                     IF( ABS( T( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
                         IF( JCH+1.GE.ILAST ) THEN
                            GO TO 80
                         ELSE
@@ -495,35 +497,35 @@
                            GO TO 110
                         END IF
                      END IF
-                     B( JCH+1, JCH+1 ) = ZERO
+                     T( JCH+1, JCH+1 ) = ZERO
    40             CONTINUE
                   GO TO 70
                ELSE
 *
-*                 Only test 2 passed -- chase the zero to B(ILAST,ILAST)
-*                 Then process as in the case B(ILAST,ILAST)=0
+*                 Only test 2 passed -- chase the zero to T(ILAST,ILAST)
+*                 Then process as in the case T(ILAST,ILAST)=0
 *
                   DO 50 JCH = J, ILAST - 1
-                     TEMP = B( JCH, JCH+1 )
-                     CALL DLARTG( TEMP, B( JCH+1, JCH+1 ), C, S,
-     $                            B( JCH, JCH+1 ) )
-                     B( JCH+1, JCH+1 ) = ZERO
+                     TEMP = T( JCH, JCH+1 )
+                     CALL DLARTG( TEMP, T( JCH+1, JCH+1 ), C, S,
+     $                            T( JCH, JCH+1 ) )
+                     T( JCH+1, JCH+1 ) = ZERO
                      IF( JCH.LT.ILASTM-1 )
-     $                  CALL DROT( ILASTM-JCH-1, B( JCH, JCH+2 ), LDB,
-     $                             B( JCH+1, JCH+2 ), LDB, C, S )
-                     CALL DROT( ILASTM-JCH+2, A( JCH, JCH-1 ), LDA,
-     $                          A( JCH+1, JCH-1 ), LDA, C, S )
+     $                  CALL DROT( ILASTM-JCH-1, T( JCH, JCH+2 ), LDT,
+     $                             T( JCH+1, JCH+2 ), LDT, C, S )
+                     CALL DROT( ILASTM-JCH+2, H( JCH, JCH-1 ), LDH,
+     $                          H( JCH+1, JCH-1 ), LDH, C, S )
                      IF( ILQ )
      $                  CALL DROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
      $                             C, S )
-                     TEMP = A( JCH+1, JCH )
-                     CALL DLARTG( TEMP, A( JCH+1, JCH-1 ), C, S,
-     $                            A( JCH+1, JCH ) )
-                     A( JCH+1, JCH-1 ) = ZERO
-                     CALL DROT( JCH+1-IFRSTM, A( IFRSTM, JCH ), 1,
-     $                          A( IFRSTM, JCH-1 ), 1, C, S )
-                     CALL DROT( JCH-IFRSTM, B( IFRSTM, JCH ), 1,
-     $                          B( IFRSTM, JCH-1 ), 1, C, S )
+                     TEMP = H( JCH+1, JCH )
+                     CALL DLARTG( TEMP, H( JCH+1, JCH-1 ), C, S,
+     $                            H( JCH+1, JCH ) )
+                     H( JCH+1, JCH-1 ) = ZERO
+                     CALL DROT( JCH+1-IFRSTM, H( IFRSTM, JCH ), 1,
+     $                          H( IFRSTM, JCH-1 ), 1, C, S )
+                     CALL DROT( JCH-IFRSTM, T( IFRSTM, JCH ), 1,
+     $                          T( IFRSTM, JCH-1 ), 1, C, S )
                      IF( ILZ )
      $                  CALL DROT( N, Z( 1, JCH ), 1, Z( 1, JCH-1 ), 1,
      $                             C, S )
@@ -547,34 +549,34 @@
          INFO = N + 1
          GO TO 420
 *
-*        B(ILAST,ILAST)=0 -- clear A(ILAST,ILAST-1) to split off a
+*        T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a
 *        1x1 block.
 *
    70    CONTINUE
-         TEMP = A( ILAST, ILAST )
-         CALL DLARTG( TEMP, A( ILAST, ILAST-1 ), C, S,
-     $                A( ILAST, ILAST ) )
-         A( ILAST, ILAST-1 ) = ZERO
-         CALL DROT( ILAST-IFRSTM, A( IFRSTM, ILAST ), 1,
-     $              A( IFRSTM, ILAST-1 ), 1, C, S )
-         CALL DROT( ILAST-IFRSTM, B( IFRSTM, ILAST ), 1,
-     $              B( IFRSTM, ILAST-1 ), 1, C, S )
+         TEMP = H( ILAST, ILAST )
+         CALL DLARTG( TEMP, H( ILAST, ILAST-1 ), C, S,
+     $                H( ILAST, ILAST ) )
+         H( ILAST, ILAST-1 ) = ZERO
+         CALL DROT( ILAST-IFRSTM, H( IFRSTM, ILAST ), 1,
+     $              H( IFRSTM, ILAST-1 ), 1, C, S )
+         CALL DROT( ILAST-IFRSTM, T( IFRSTM, ILAST ), 1,
+     $              T( IFRSTM, ILAST-1 ), 1, C, S )
          IF( ILZ )
      $      CALL DROT( N, Z( 1, ILAST ), 1, Z( 1, ILAST-1 ), 1, C, S )
 *
-*        A(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI,
+*        H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI,
 *                              and BETA
 *
    80    CONTINUE
-         IF( B( ILAST, ILAST ).LT.ZERO ) THEN
+         IF( T( ILAST, ILAST ).LT.ZERO ) THEN
             IF( ILSCHR ) THEN
                DO 90 J = IFRSTM, ILAST
-                  A( J, ILAST ) = -A( J, ILAST )
-                  B( J, ILAST ) = -B( J, ILAST )
+                  H( J, ILAST ) = -H( J, ILAST )
+                  T( J, ILAST ) = -T( J, ILAST )
    90          CONTINUE
             ELSE
-               A( ILAST, ILAST ) = -A( ILAST, ILAST )
-               B( ILAST, ILAST ) = -B( ILAST, ILAST )
+               H( ILAST, ILAST ) = -H( ILAST, ILAST )
+               T( ILAST, ILAST ) = -T( ILAST, ILAST )
             END IF
             IF( ILZ ) THEN
                DO 100 J = 1, N
@@ -582,9 +584,9 @@
   100          CONTINUE
             END IF
          END IF
-         ALPHAR( ILAST ) = A( ILAST, ILAST )
+         ALPHAR( ILAST ) = H( ILAST, ILAST )
          ALPHAI( ILAST ) = ZERO
-         BETA( ILAST ) = B( ILAST, ILAST )
+         BETA( ILAST ) = T( ILAST, ILAST )
 *
 *        Go to next block -- exit if finished.
 *
@@ -617,7 +619,7 @@
 *        Compute single shifts.
 *
 *        At this point, IFIRST < ILAST, and the diagonal elements of
-*        B(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
+*        T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
 *        magnitude)
 *
          IF( ( IITER / 10 )*10.EQ.IITER ) THEN
@@ -625,10 +627,10 @@
 *           Exceptional shift.  Chosen for no particularly good reason.
 *           (Single shift only.)
 *
-            IF( ( DBLE( MAXIT )*SAFMIN )*ABS( A( ILAST-1, ILAST ) ).LT.
-     $          ABS( B( ILAST-1, ILAST-1 ) ) ) THEN
-               ESHIFT = ESHIFT + A( ILAST-1, ILAST ) /
-     $                  B( ILAST-1, ILAST-1 )
+            IF( ( DBLE( MAXIT )*SAFMIN )*ABS( H( ILAST-1, ILAST ) ).LT.
+     $          ABS( T( ILAST-1, ILAST-1 ) ) ) THEN
+               ESHIFT = ESHIFT + H( ILAST-1, ILAST ) /
+     $                  T( ILAST-1, ILAST-1 )
             ELSE
                ESHIFT = ESHIFT + ONE / ( SAFMIN*DBLE( MAXIT ) )
             END IF
@@ -641,8 +643,8 @@
 *           bottom-right 2x2 block of A and B. The first eigenvalue
 *           returned by DLAG2 is the Wilkinson shift (AEP p.512),
 *
-            CALL DLAG2( A( ILAST-1, ILAST-1 ), LDA,
-     $                  B( ILAST-1, ILAST-1 ), LDB, SAFMIN*SAFETY, S1,
+            CALL DLAG2( H( ILAST-1, ILAST-1 ), LDH,
+     $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
      $                  S2, WR, WR2, WI )
 *
             TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) )
@@ -669,14 +671,14 @@
 *
          DO 120 J = ILAST - 1, IFIRST + 1, -1
             ISTART = J
-            TEMP = ABS( S1*A( J, J-1 ) )
-            TEMP2 = ABS( S1*A( J, J )-WR*B( J, J ) )
+            TEMP = ABS( S1*H( J, J-1 ) )
+            TEMP2 = ABS( S1*H( J, J )-WR*T( J, J ) )
             TEMPR = MAX( TEMP, TEMP2 )
             IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
                TEMP = TEMP / TEMPR
                TEMP2 = TEMP2 / TEMPR
             END IF
-            IF( ABS( ( ASCALE*A( J+1, J ) )*TEMP ).LE.( ASCALE*ATOL )*
+            IF( ABS( ( ASCALE*H( J+1, J ) )*TEMP ).LE.( ASCALE*ATOL )*
      $          TEMP2 )GO TO 130
   120    CONTINUE
 *
@@ -687,26 +689,26 @@
 *
 *        Initial Q
 *
-         TEMP = S1*A( ISTART, ISTART ) - WR*B( ISTART, ISTART )
-         TEMP2 = S1*A( ISTART+1, ISTART )
+         TEMP = S1*H( ISTART, ISTART ) - WR*T( ISTART, ISTART )
+         TEMP2 = S1*H( ISTART+1, ISTART )
          CALL DLARTG( TEMP, TEMP2, C, S, TEMPR )
 *
 *        Sweep
 *
          DO 190 J = ISTART, ILAST - 1
             IF( J.GT.ISTART ) THEN
-               TEMP = A( J, J-1 )
-               CALL DLARTG( TEMP, A( J+1, J-1 ), C, S, A( J, J-1 ) )
-               A( J+1, J-1 ) = ZERO
+               TEMP = H( J, J-1 )
+               CALL DLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+               H( J+1, J-1 ) = ZERO
             END IF
 *
             DO 140 JC = J, ILASTM
-               TEMP = C*A( J, JC ) + S*A( J+1, JC )
-               A( J+1, JC ) = -S*A( J, JC ) + C*A( J+1, JC )
-               A( J, JC ) = TEMP
-               TEMP2 = C*B( J, JC ) + S*B( J+1, JC )
-               B( J+1, JC ) = -S*B( J, JC ) + C*B( J+1, JC )
-               B( J, JC ) = TEMP2
+               TEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = TEMP
+               TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = TEMP2
   140       CONTINUE
             IF( ILQ ) THEN
                DO 150 JR = 1, N
@@ -716,19 +718,19 @@
   150          CONTINUE
             END IF
 *
-            TEMP = B( J+1, J+1 )
-            CALL DLARTG( TEMP, B( J+1, J ), C, S, B( J+1, J+1 ) )
-            B( J+1, J ) = ZERO
+            TEMP = T( J+1, J+1 )
+            CALL DLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = ZERO
 *
             DO 160 JR = IFRSTM, MIN( J+2, ILAST )
-               TEMP = C*A( JR, J+1 ) + S*A( JR, J )
-               A( JR, J ) = -S*A( JR, J+1 ) + C*A( JR, J )
-               A( JR, J+1 ) = TEMP
+               TEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = TEMP
   160       CONTINUE
             DO 170 JR = IFRSTM, J
-               TEMP = C*B( JR, J+1 ) + S*B( JR, J )
-               B( JR, J ) = -S*B( JR, J+1 ) + C*B( JR, J )
-               B( JR, J+1 ) = TEMP
+               TEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = TEMP
   170       CONTINUE
             IF( ILZ ) THEN
                DO 180 JR = 1, N
@@ -759,8 +761,8 @@
 *                   B = (         )  with B11 non-negative.
 *                       (  0  B22 )
 *
-            CALL DLASV2( B( ILAST-1, ILAST-1 ), B( ILAST-1, ILAST ),
-     $                   B( ILAST, ILAST ), B22, B11, SR, CR, SL, CL )
+            CALL DLASV2( T( ILAST-1, ILAST-1 ), T( ILAST-1, ILAST ),
+     $                   T( ILAST, ILAST ), B22, B11, SR, CR, SL, CL )
 *
             IF( B11.LT.ZERO ) THEN
                CR = -CR
@@ -769,17 +771,17 @@
                B22 = -B22
             END IF
 *
-            CALL DROT( ILASTM+1-IFIRST, A( ILAST-1, ILAST-1 ), LDA,
-     $                 A( ILAST, ILAST-1 ), LDA, CL, SL )
-            CALL DROT( ILAST+1-IFRSTM, A( IFRSTM, ILAST-1 ), 1,
-     $                 A( IFRSTM, ILAST ), 1, CR, SR )
+            CALL DROT( ILASTM+1-IFIRST, H( ILAST-1, ILAST-1 ), LDH,
+     $                 H( ILAST, ILAST-1 ), LDH, CL, SL )
+            CALL DROT( ILAST+1-IFRSTM, H( IFRSTM, ILAST-1 ), 1,
+     $                 H( IFRSTM, ILAST ), 1, CR, SR )
 *
             IF( ILAST.LT.ILASTM )
-     $         CALL DROT( ILASTM-ILAST, B( ILAST-1, ILAST+1 ), LDB,
-     $                    B( ILAST, ILAST+1 ), LDA, CL, SL )
+     $         CALL DROT( ILASTM-ILAST, T( ILAST-1, ILAST+1 ), LDT,
+     $                    T( ILAST, ILAST+1 ), LDH, CL, SL )
             IF( IFRSTM.LT.ILAST-1 )
-     $         CALL DROT( IFIRST-IFRSTM, B( IFRSTM, ILAST-1 ), 1,
-     $                    B( IFRSTM, ILAST ), 1, CR, SR )
+     $         CALL DROT( IFIRST-IFRSTM, T( IFRSTM, ILAST-1 ), 1,
+     $                    T( IFRSTM, ILAST ), 1, CR, SR )
 *
             IF( ILQ )
      $         CALL DROT( N, Q( 1, ILAST-1 ), 1, Q( 1, ILAST ), 1, CL,
@@ -788,17 +790,17 @@
      $         CALL DROT( N, Z( 1, ILAST-1 ), 1, Z( 1, ILAST ), 1, CR,
      $                    SR )
 *
-            B( ILAST-1, ILAST-1 ) = B11
-            B( ILAST-1, ILAST ) = ZERO
-            B( ILAST, ILAST-1 ) = ZERO
-            B( ILAST, ILAST ) = B22
+            T( ILAST-1, ILAST-1 ) = B11
+            T( ILAST-1, ILAST ) = ZERO
+            T( ILAST, ILAST-1 ) = ZERO
+            T( ILAST, ILAST ) = B22
 *
 *           If B22 is negative, negate column ILAST
 *
             IF( B22.LT.ZERO ) THEN
                DO 210 J = IFRSTM, ILAST
-                  A( J, ILAST ) = -A( J, ILAST )
-                  B( J, ILAST ) = -B( J, ILAST )
+                  H( J, ILAST ) = -H( J, ILAST )
+                  T( J, ILAST ) = -T( J, ILAST )
   210          CONTINUE
 *
                IF( ILZ ) THEN
@@ -812,8 +814,8 @@
 *
 *           Recompute shift
 *
-            CALL DLAG2( A( ILAST-1, ILAST-1 ), LDA,
-     $                  B( ILAST-1, ILAST-1 ), LDB, SAFMIN*SAFETY, S1,
+            CALL DLAG2( H( ILAST-1, ILAST-1 ), LDH,
+     $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
      $                  TEMP, WR, TEMP2, WI )
 *
 *           If standardization has perturbed the shift onto real line,
@@ -825,10 +827,10 @@
 *
 *           Do EISPACK (QZVAL) computation of alpha and beta
 *
-            A11 = A( ILAST-1, ILAST-1 )
-            A21 = A( ILAST, ILAST-1 )
-            A12 = A( ILAST-1, ILAST )
-            A22 = A( ILAST, ILAST )
+            A11 = H( ILAST-1, ILAST-1 )
+            A21 = H( ILAST, ILAST-1 )
+            A12 = H( ILAST-1, ILAST )
+            A22 = H( ILAST, ILAST )
 *
 *           Compute complex Givens rotation on right
 *           (Assume some element of C = (sA - wB) > unfl )
@@ -845,10 +847,10 @@
 *
             IF( ABS( C11R )+ABS( C11I )+ABS( C12 ).GT.ABS( C21 )+
      $          ABS( C22R )+ABS( C22I ) ) THEN
-               T = DLAPY3( C12, C11R, C11I )
-               CZ = C12 / T
-               SZR = -C11R / T
-               SZI = -C11I / T
+               T1 = DLAPY3( C12, C11R, C11I )
+               CZ = C12 / T1
+               SZR = -C11R / T1
+               SZI = -C11I / T1
             ELSE
                CZ = DLAPY2( C22R, C22I )
                IF( CZ.LE.SAFMIN ) THEN
@@ -858,10 +860,10 @@
                ELSE
                   TEMPR = C22R / CZ
                   TEMPI = C22I / CZ
-                  T = DLAPY2( CZ, C21 )
-                  CZ = CZ / T
-                  SZR = -C21*TEMPR / T
-                  SZI = C21*TEMPI / T
+                  T1 = DLAPY2( CZ, C21 )
+                  CZ = CZ / T1
+                  SZR = -C21*TEMPR / T1
+                  SZI = C21*TEMPI / T1
                END IF
             END IF
 *
@@ -895,10 +897,10 @@
                   SQI = TEMPI*A2R - TEMPR*A2I
                END IF
             END IF
-            T = DLAPY3( CQ, SQR, SQI )
-            CQ = CQ / T
-            SQR = SQR / T
-            SQI = SQI / T
+            T1 = DLAPY3( CQ, SQR, SQI )
+            CQ = CQ / T1
+            SQR = SQR / T1
+            SQI = SQI / T1
 *
 *           Compute diagonal elements of QBZ
 *
@@ -950,26 +952,26 @@
 *
 *           We assume that the block is at least 3x3
 *
-            AD11 = ( ASCALE*A( ILAST-1, ILAST-1 ) ) /
-     $             ( BSCALE*B( ILAST-1, ILAST-1 ) )
-            AD21 = ( ASCALE*A( ILAST, ILAST-1 ) ) /
-     $             ( BSCALE*B( ILAST-1, ILAST-1 ) )
-            AD12 = ( ASCALE*A( ILAST-1, ILAST ) ) /
-     $             ( BSCALE*B( ILAST, ILAST ) )
-            AD22 = ( ASCALE*A( ILAST, ILAST ) ) /
-     $             ( BSCALE*B( ILAST, ILAST ) )
-            U12 = B( ILAST-1, ILAST ) / B( ILAST, ILAST )
-            AD11L = ( ASCALE*A( IFIRST, IFIRST ) ) /
-     $              ( BSCALE*B( IFIRST, IFIRST ) )
-            AD21L = ( ASCALE*A( IFIRST+1, IFIRST ) ) /
-     $              ( BSCALE*B( IFIRST, IFIRST ) )
-            AD12L = ( ASCALE*A( IFIRST, IFIRST+1 ) ) /
-     $              ( BSCALE*B( IFIRST+1, IFIRST+1 ) )
-            AD22L = ( ASCALE*A( IFIRST+1, IFIRST+1 ) ) /
-     $              ( BSCALE*B( IFIRST+1, IFIRST+1 ) )
-            AD32L = ( ASCALE*A( IFIRST+2, IFIRST+1 ) ) /
-     $              ( BSCALE*B( IFIRST+1, IFIRST+1 ) )
-            U12L = B( IFIRST, IFIRST+1 ) / B( IFIRST+1, IFIRST+1 )
+            AD11 = ( ASCALE*H( ILAST-1, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD21 = ( ASCALE*H( ILAST, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD12 = ( ASCALE*H( ILAST-1, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            AD22 = ( ASCALE*H( ILAST, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            U12 = T( ILAST-1, ILAST ) / T( ILAST, ILAST )
+            AD11L = ( ASCALE*H( IFIRST, IFIRST ) ) /
+     $              ( BSCALE*T( IFIRST, IFIRST ) )
+            AD21L = ( ASCALE*H( IFIRST+1, IFIRST ) ) /
+     $              ( BSCALE*T( IFIRST, IFIRST ) )
+            AD12L = ( ASCALE*H( IFIRST, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            AD22L = ( ASCALE*H( IFIRST+1, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            AD32L = ( ASCALE*H( IFIRST+2, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            U12L = T( IFIRST, IFIRST+1 ) / T( IFIRST+1, IFIRST+1 )
 *
             V( 1 ) = ( AD11-AD11L )*( AD22-AD11L ) - AD12*AD21 +
      $               AD21*U12*AD11L + ( AD12L-AD11L*U12L )*AD21L
@@ -991,27 +993,27 @@
 *              Zero (j-1)st column of A
 *
                IF( J.GT.ISTART ) THEN
-                  V( 1 ) = A( J, J-1 )
-                  V( 2 ) = A( J+1, J-1 )
-                  V( 3 ) = A( J+2, J-1 )
+                  V( 1 ) = H( J, J-1 )
+                  V( 2 ) = H( J+1, J-1 )
+                  V( 3 ) = H( J+2, J-1 )
 *
-                  CALL DLARFG( 3, A( J, J-1 ), V( 2 ), 1, TAU )
+                  CALL DLARFG( 3, H( J, J-1 ), V( 2 ), 1, TAU )
                   V( 1 ) = ONE
-                  A( J+1, J-1 ) = ZERO
-                  A( J+2, J-1 ) = ZERO
+                  H( J+1, J-1 ) = ZERO
+                  H( J+2, J-1 ) = ZERO
                END IF
 *
                DO 230 JC = J, ILASTM
-                  TEMP = TAU*( A( J, JC )+V( 2 )*A( J+1, JC )+V( 3 )*
-     $                   A( J+2, JC ) )
-                  A( J, JC ) = A( J, JC ) - TEMP
-                  A( J+1, JC ) = A( J+1, JC ) - TEMP*V( 2 )
-                  A( J+2, JC ) = A( J+2, JC ) - TEMP*V( 3 )
-                  TEMP2 = TAU*( B( J, JC )+V( 2 )*B( J+1, JC )+V( 3 )*
-     $                    B( J+2, JC ) )
-                  B( J, JC ) = B( J, JC ) - TEMP2
-                  B( J+1, JC ) = B( J+1, JC ) - TEMP2*V( 2 )
-                  B( J+2, JC ) = B( J+2, JC ) - TEMP2*V( 3 )
+                  TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
+     $                   H( J+2, JC ) )
+                  H( J, JC ) = H( J, JC ) - TEMP
+                  H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
+                  H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
+                  TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
+     $                    T( J+2, JC ) )
+                  T( J, JC ) = T( J, JC ) - TEMP2
+                  T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
+                  T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
   230          CONTINUE
                IF( ILQ ) THEN
                   DO 240 JR = 1, N
@@ -1028,27 +1030,27 @@
 *              Swap rows to pivot
 *
                ILPIVT = .FALSE.
-               TEMP = MAX( ABS( B( J+1, J+1 ) ), ABS( B( J+1, J+2 ) ) )
-               TEMP2 = MAX( ABS( B( J+2, J+1 ) ), ABS( B( J+2, J+2 ) ) )
+               TEMP = MAX( ABS( T( J+1, J+1 ) ), ABS( T( J+1, J+2 ) ) )
+               TEMP2 = MAX( ABS( T( J+2, J+1 ) ), ABS( T( J+2, J+2 ) ) )
                IF( MAX( TEMP, TEMP2 ).LT.SAFMIN ) THEN
                   SCALE = ZERO
                   U1 = ONE
                   U2 = ZERO
                   GO TO 250
                ELSE IF( TEMP.GE.TEMP2 ) THEN
-                  W11 = B( J+1, J+1 )
-                  W21 = B( J+2, J+1 )
-                  W12 = B( J+1, J+2 )
-                  W22 = B( J+2, J+2 )
-                  U1 = B( J+1, J )
-                  U2 = B( J+2, J )
+                  W11 = T( J+1, J+1 )
+                  W21 = T( J+2, J+1 )
+                  W12 = T( J+1, J+2 )
+                  W22 = T( J+2, J+2 )
+                  U1 = T( J+1, J )
+                  U2 = T( J+2, J )
                ELSE
-                  W21 = B( J+1, J+1 )
-                  W11 = B( J+2, J+1 )
-                  W22 = B( J+1, J+2 )
-                  W12 = B( J+2, J+2 )
-                  U2 = B( J+1, J )
-                  U1 = B( J+2, J )
+                  W21 = T( J+1, J+1 )
+                  W11 = T( J+2, J+1 )
+                  W22 = T( J+1, J+2 )
+                  W12 = T( J+2, J+2 )
+                  U2 = T( J+1, J )
+                  U1 = T( J+2, J )
                END IF
 *
 *              Swap columns if nec.
@@ -1098,9 +1100,9 @@
 *
 *              Compute Householder Vector
 *
-               T = SQRT( SCALE**2+U1**2+U2**2 )
-               TAU = ONE + SCALE / T
-               VS = -ONE / ( SCALE+T )
+               T1 = SQRT( SCALE**2+U1**2+U2**2 )
+               TAU = ONE + SCALE / T1
+               VS = -ONE / ( SCALE+T1 )
                V( 1 ) = ONE
                V( 2 ) = VS*U1
                V( 3 ) = VS*U2
@@ -1108,18 +1110,18 @@
 *              Apply transformations from the right.
 *
                DO 260 JR = IFRSTM, MIN( J+3, ILAST )
-                  TEMP = TAU*( A( JR, J )+V( 2 )*A( JR, J+1 )+V( 3 )*
-     $                   A( JR, J+2 ) )
-                  A( JR, J ) = A( JR, J ) - TEMP
-                  A( JR, J+1 ) = A( JR, J+1 ) - TEMP*V( 2 )
-                  A( JR, J+2 ) = A( JR, J+2 ) - TEMP*V( 3 )
+                  TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
+     $                   H( JR, J+2 ) )
+                  H( JR, J ) = H( JR, J ) - TEMP
+                  H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
+                  H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
   260          CONTINUE
                DO 270 JR = IFRSTM, J + 2
-                  TEMP = TAU*( B( JR, J )+V( 2 )*B( JR, J+1 )+V( 3 )*
-     $                   B( JR, J+2 ) )
-                  B( JR, J ) = B( JR, J ) - TEMP
-                  B( JR, J+1 ) = B( JR, J+1 ) - TEMP*V( 2 )
-                  B( JR, J+2 ) = B( JR, J+2 ) - TEMP*V( 3 )
+                  TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
+     $                   T( JR, J+2 ) )
+                  T( JR, J ) = T( JR, J ) - TEMP
+                  T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
+                  T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
   270          CONTINUE
                IF( ILZ ) THEN
                   DO 280 JR = 1, N
@@ -1130,8 +1132,8 @@
                      Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
   280             CONTINUE
                END IF
-               B( J+1, J ) = ZERO
-               B( J+2, J ) = ZERO
+               T( J+1, J ) = ZERO
+               T( J+2, J ) = ZERO
   290       CONTINUE
 *
 *           Last elements: Use Givens rotations
@@ -1139,17 +1141,17 @@
 *           Rotations from the left
 *
             J = ILAST - 1
-            TEMP = A( J, J-1 )
-            CALL DLARTG( TEMP, A( J+1, J-1 ), C, S, A( J, J-1 ) )
-            A( J+1, J-1 ) = ZERO
+            TEMP = H( J, J-1 )
+            CALL DLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+            H( J+1, J-1 ) = ZERO
 *
             DO 300 JC = J, ILASTM
-               TEMP = C*A( J, JC ) + S*A( J+1, JC )
-               A( J+1, JC ) = -S*A( J, JC ) + C*A( J+1, JC )
-               A( J, JC ) = TEMP
-               TEMP2 = C*B( J, JC ) + S*B( J+1, JC )
-               B( J+1, JC ) = -S*B( J, JC ) + C*B( J+1, JC )
-               B( J, JC ) = TEMP2
+               TEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = TEMP
+               TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = TEMP2
   300       CONTINUE
             IF( ILQ ) THEN
                DO 310 JR = 1, N
@@ -1161,19 +1163,19 @@
 *
 *           Rotations from the right.
 *
-            TEMP = B( J+1, J+1 )
-            CALL DLARTG( TEMP, B( J+1, J ), C, S, B( J+1, J+1 ) )
-            B( J+1, J ) = ZERO
+            TEMP = T( J+1, J+1 )
+            CALL DLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = ZERO
 *
             DO 320 JR = IFRSTM, ILAST
-               TEMP = C*A( JR, J+1 ) + S*A( JR, J )
-               A( JR, J ) = -S*A( JR, J+1 ) + C*A( JR, J )
-               A( JR, J+1 ) = TEMP
+               TEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = TEMP
   320       CONTINUE
             DO 330 JR = IFRSTM, ILAST - 1
-               TEMP = C*B( JR, J+1 ) + S*B( JR, J )
-               B( JR, J ) = -S*B( JR, J+1 ) + C*B( JR, J )
-               B( JR, J+1 ) = TEMP
+               TEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = TEMP
   330       CONTINUE
             IF( ILZ ) THEN
                DO 340 JR = 1, N
@@ -1207,15 +1209,15 @@
 *     Set Eigenvalues 1:ILO-1
 *
       DO 410 J = 1, ILO - 1
-         IF( B( J, J ).LT.ZERO ) THEN
+         IF( T( J, J ).LT.ZERO ) THEN
             IF( ILSCHR ) THEN
                DO 390 JR = 1, J
-                  A( JR, J ) = -A( JR, J )
-                  B( JR, J ) = -B( JR, J )
+                  H( JR, J ) = -H( JR, J )
+                  T( JR, J ) = -T( JR, J )
   390          CONTINUE
             ELSE
-               A( J, J ) = -A( J, J )
-               B( J, J ) = -B( J, J )
+               H( J, J ) = -H( J, J )
+               T( J, J ) = -T( J, J )
             END IF
             IF( ILZ ) THEN
                DO 400 JR = 1, N
@@ -1223,9 +1225,9 @@
   400          CONTINUE
             END IF
          END IF
-         ALPHAR( J ) = A( J, J )
+         ALPHAR( J ) = H( J, J )
          ALPHAI( J ) = ZERO
-         BETA( J ) = B( J, J )
+         BETA( J ) = T( J, J )
   410 CONTINUE
 *
 *     Normal Termination
diff -uNr LAPACK.orig/SRC/dlasr.f LAPACK/SRC/dlasr.f
--- LAPACK.orig/SRC/dlasr.f	Thu Nov  4 14:24:50 1999
+++ LAPACK/SRC/dlasr.f	Fri May 25 16:12:31 2001
@@ -3,7 +3,7 @@
 *  -- LAPACK auxiliary routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1992
+*     May 3, 2001 
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIRECT, PIVOT, SIDE
@@ -16,44 +16,77 @@
 *  Purpose
 *  =======
 *
-*  DLASR   performs the transformation
-*
-*     A := P*A,   when SIDE = 'L' or 'l'  (  Left-hand side )
-*
-*     A := A*P',  when SIDE = 'R' or 'r'  ( Right-hand side )
-*
-*  where A is an m by n real matrix and P is an orthogonal matrix,
-*  consisting of a sequence of plane rotations determined by the
-*  parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l'
-*  and z = n when SIDE = 'R' or 'r' ):
-*
-*  When  DIRECT = 'F' or 'f'  ( Forward sequence ) then
-*
-*     P = P( z - 1 )*...*P( 2 )*P( 1 ),
-*
-*  and when DIRECT = 'B' or 'b'  ( Backward sequence ) then
-*
-*     P = P( 1 )*P( 2 )*...*P( z - 1 ),
-*
-*  where  P( k ) is a plane rotation matrix for the following planes:
-*
-*     when  PIVOT = 'V' or 'v'  ( Variable pivot ),
-*        the plane ( k, k + 1 )
-*
-*     when  PIVOT = 'T' or 't'  ( Top pivot ),
-*        the plane ( 1, k + 1 )
-*
-*     when  PIVOT = 'B' or 'b'  ( Bottom pivot ),
-*        the plane ( k, z )
-*
-*  c( k ) and s( k )  must contain the  cosine and sine that define the
-*  matrix  P( k ).  The two by two plane rotation part of the matrix
-*  P( k ), R( k ), is assumed to be of the form
-*
-*     R( k ) = (  c( k )  s( k ) ).
-*              ( -s( k )  c( k ) )
-*
-*  This version vectorises across rows of the array A when SIDE = 'L'.
+*  DLASR applies a sequence of plane rotations to a real matrix A,
+*  from either the left or the right.
+*  
+*  When SIDE = 'L', the transformation takes the form
+*  
+*     A := P*A
+*  
+*  and when SIDE = 'R', the transformation takes the form
+*  
+*     A := A*P**T
+*  
+*  where P is an orthogonal matrix consisting of a sequence of z plane
+*  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
+*  and P**T is the transpose of P.
+*  
+*  When DIRECT = 'F' (Forward sequence), then
+*  
+*     P = P(z-1) * ... * P(2) * P(1)
+*  
+*  and when DIRECT = 'B' (Backward sequence), then
+*  
+*     P = P(1) * P(2) * ... * P(z-1)
+*  
+*  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
+*  
+*     R(k) = (  c(k)  s(k) )
+*          = ( -s(k)  c(k) ).
+*  
+*  When PIVOT = 'V' (Variable pivot), the rotation is performed
+*  for the plane (k,k+1), i.e., P(k) has the form
+*  
+*     P(k) = (  1                                            )
+*            (       ...                                     )
+*            (              1                                )
+*            (                   c(k)  s(k)                  )
+*            (                  -s(k)  c(k)                  )
+*            (                                1              )
+*            (                                     ...       )
+*            (                                            1  )
+*  
+*  where R(k) appears as a rank-2 modification to the identity matrix in
+*  rows and columns k and k+1.
+*  
+*  When PIVOT = 'T' (Top pivot), the rotation is performed for the
+*  plane (1,k+1), so P(k) has the form
+*  
+*     P(k) = (  c(k)                    s(k)                 )
+*            (         1                                     )
+*            (              ...                              )
+*            (                     1                         )
+*            ( -s(k)                    c(k)                 )
+*            (                                 1             )
+*            (                                      ...      )
+*            (                                             1 )
+*  
+*  where R(k) appears in rows and columns 1 and k+1.
+*  
+*  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
+*  performed for the plane (k,z), giving P(k) the form
+*  
+*     P(k) = ( 1                                             )
+*            (      ...                                      )
+*            (             1                                 )
+*            (                  c(k)                    s(k) )
+*            (                         1                     )
+*            (                              ...              )
+*            (                                     1         )
+*            (                 -s(k)                    c(k) )
+*  
+*  where R(k) appears in rows and columns k and z.  The rotations are
+*  performed without ever forming P(k) explicitly.
 *
 *  Arguments
 *  =========
@@ -62,13 +95,13 @@
 *          Specifies whether the plane rotation matrix P is applied to
 *          A on the left or the right.
 *          = 'L':  Left, compute A := P*A
-*          = 'R':  Right, compute A:= A*P'
+*          = 'R':  Right, compute A:= A*P**T
 *
 *  DIRECT  (input) CHARACTER*1
 *          Specifies whether P is a forward or backward sequence of
 *          plane rotations.
-*          = 'F':  Forward, P = P( z - 1 )*...*P( 2 )*P( 1 )
-*          = 'B':  Backward, P = P( 1 )*P( 2 )*...*P( z - 1 )
+*          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
+*          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
 *
 *  PIVOT   (input) CHARACTER*1
 *          Specifies the plane for which P(k) is a plane rotation
@@ -85,18 +118,22 @@
 *          The number of columns of the matrix A.  If n <= 1, an
 *          immediate return is effected.
 *
-*  C, S    (input) DOUBLE PRECISION arrays, dimension
+*  C       (input) DOUBLE PRECISION array, dimension
+*                  (M-1) if SIDE = 'L'
+*                  (N-1) if SIDE = 'R'
+*          The cosines c(k) of the plane rotations.
+*
+*  S       (input) DOUBLE PRECISION array, dimension
 *                  (M-1) if SIDE = 'L'
 *                  (N-1) if SIDE = 'R'
-*          c(k) and s(k) contain the cosine and sine that define the
-*          matrix P(k).  The two by two plane rotation part of the
-*          matrix P(k), R(k), is assumed to be of the form
-*          R( k ) = (  c( k )  s( k ) ).
-*                   ( -s( k )  c( k ) )
+*          The sines s(k) of the plane rotations.  The 2-by-2 plane
+*          rotation part of the matrix P(k), R(k), has the form
+*          R(k) = (  c(k)  s(k) )
+*                 ( -s(k)  c(k) ).
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-*          The m by n matrix A.  On exit, A is overwritten by P*A if
-*          SIDE = 'R' or by A*P' if SIDE = 'L'.
+*          The M-by-N matrix A.  On exit, A is overwritten by P*A if
+*          SIDE = 'R' or by A*P**T if SIDE = 'L'.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
diff -uNr LAPACK.orig/SRC/dsbgst.f LAPACK/SRC/dsbgst.f
--- LAPACK.orig/SRC/dsbgst.f	Thu Nov  4 14:23:31 1999
+++ LAPACK/SRC/dsbgst.f	Fri May 25 16:12:50 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     January 9, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO, VECT
@@ -125,7 +125,7 @@
          INFO = -3
       ELSE IF( KA.LT.0 ) THEN
          INFO = -4
-      ELSE IF( KB.LT.0 ) THEN
+      ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
          INFO = -5
       ELSE IF( LDAB.LT.KA+1 ) THEN
          INFO = -7
diff -uNr LAPACK.orig/SRC/dstebz.f LAPACK/SRC/dstebz.f
--- LAPACK.orig/SRC/dstebz.f	Thu Nov  4 14:24:57 1999
+++ LAPACK/SRC/dstebz.f	Fri May 25 16:13:23 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-18-00:  Increase FUDGE factor for T3E (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          ORDER, RANGE
@@ -175,7 +176,7 @@
       PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
      $                   HALF = 1.0D0 / TWO )
       DOUBLE PRECISION   FUDGE, RELFAC
-      PARAMETER          ( FUDGE = 2.0D0, RELFAC = 2.0D0 )
+      PARAMETER          ( FUDGE = 2.1D0, RELFAC = 2.0D0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            NCNVRG, TOOFEW
diff -uNr LAPACK.orig/SRC/dtgevc.f LAPACK/SRC/dtgevc.f
--- LAPACK.orig/SRC/dtgevc.f	Thu Nov  4 14:26:09 1999
+++ LAPACK/SRC/dtgevc.f	Fri May 25 16:13:33 2001
@@ -1,18 +1,18 @@
-      SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
+      SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
      $                   LDVL, VR, LDVR, MM, M, WORK, INFO )
 *
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 4, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          HOWMNY, SIDE
-      INTEGER            INFO, LDA, LDB, LDVL, LDVR, M, MM, N
+      INTEGER            INFO, LDP, LDS, LDVL, LDVR, M, MM, N
 *     ..
 *     .. Array Arguments ..
       LOGICAL            SELECT( * )
-      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), VL( LDVL, * ),
+      DOUBLE PRECISION   P( LDP, * ), S( LDS, * ), VL( LDVL, * ),
      $                   VR( LDVR, * ), WORK( * )
 *     ..
 *
@@ -20,35 +20,31 @@
 *  Purpose
 *  =======
 *
-*  DTGEVC computes some or all of the right and/or left generalized
-*  eigenvectors of a pair of real upper triangular matrices (A,B).
-*
-*  The right generalized eigenvector x and the left generalized
-*  eigenvector y of (A,B) corresponding to a generalized eigenvalue
-*  w are defined by:
-*
-*          (A - wB) * x = 0  and  y**H * (A - wB) = 0
-*
+*  DTGEVC computes some or all of the right and/or left eigenvectors of
+*  a pair of real matrices (S,P), where S is a quasi-triangular matrix
+*  and P is upper triangular.  Matrix pairs of this type are produced by
+*  the generalized Schur factorization of a matrix pair (A,B):
+*
+*     A = Q*S*Z**T,  B = Q*P*Z**T
+*
+*  as computed by DGGHRD + DHGEQZ.
+*
+*  The right eigenvector x and the left eigenvector y of (S,P)
+*  corresponding to an eigenvalue w are defined by:
+*  
+*     S*x = w*P*x,  (y**H)*S = w*(y**H)*P,
+*  
 *  where y**H denotes the conjugate tranpose of y.
-*
-*  If an eigenvalue w is determined by zero diagonal elements of both A
-*  and B, a unit vector is returned as the corresponding eigenvector.
-*
-*  If all eigenvectors are requested, the routine may either return
-*  the matrices X and/or Y of right or left eigenvectors of (A,B), or
-*  the products Z*X and/or Q*Y, where Z and Q are input orthogonal
-*  matrices.  If (A,B) was obtained from the generalized real-Schur
-*  factorization of an original pair of matrices
-*     (A0,B0) = (Q*A*Z**H,Q*B*Z**H),
-*  then Z*X and Q*Y are the matrices of right or left eigenvectors of
-*  A.
-*
-*  A must be block upper triangular, with 1-by-1 and 2-by-2 diagonal
-*  blocks.  Corresponding to each 2-by-2 diagonal block is a complex
-*  conjugate pair of eigenvalues and eigenvectors; only one
-*  eigenvector of the pair is computed, namely the one corresponding
-*  to the eigenvalue with positive imaginary part.
-*
+*  The eigenvalues are not input to this routine, but are computed
+*  directly from the diagonal blocks of S and P.
+*  
+*  This routine returns the matrices X and/or Y of right and left
+*  eigenvectors of (S,P), or the products Z*X and/or Q*Y,
+*  where Z and Q are input matrices.
+*  If Q and Z are the orthogonal factors from the generalized Schur
+*  factorization of a matrix pair (A,B), then Z*X and Q*Y
+*  are the matrices of right and left eigenvectors of (A,B).
+* 
 *  Arguments
 *  =========
 *
@@ -59,78 +55,84 @@
 *
 *  HOWMNY  (input) CHARACTER*1
 *          = 'A': compute all right and/or left eigenvectors;
-*          = 'B': compute all right and/or left eigenvectors, and
-*                 backtransform them using the input matrices supplied
-*                 in VR and/or VL;
+*          = 'B': compute all right and/or left eigenvectors,
+*                 backtransformed by the matrices in VR and/or VL;
 *          = 'S': compute selected right and/or left eigenvectors,
 *                 specified by the logical array SELECT.
 *
 *  SELECT  (input) LOGICAL array, dimension (N)
 *          If HOWMNY='S', SELECT specifies the eigenvectors to be
-*          computed.
-*          If HOWMNY='A' or 'B', SELECT is not referenced.
-*          To select the real eigenvector corresponding to the real
-*          eigenvalue w(j), SELECT(j) must be set to .TRUE.  To select
-*          the complex eigenvector corresponding to a complex conjugate
-*          pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must
-*          be set to .TRUE..
+*          computed.  If w(j) is a real eigenvalue, the corresponding
+*          real eigenvector is computed if SELECT(j) is .TRUE..
+*          If w(j) and w(j+1) are the real and imaginary parts of a
+*          complex eigenvalue, the corresponding complex eigenvector
+*          is computed if either SELECT(j) or SELECT(j+1) is .TRUE.,
+*          and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is
+*          set to .FALSE..
+*          Not referenced if HOWMNY = 'A' or 'B'.
 *
 *  N       (input) INTEGER
-*          The order of the matrices A and B.  N >= 0.
+*          The order of the matrices S and P.  N >= 0.
 *
-*  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
-*          The upper quasi-triangular matrix A.
+*  S       (input) DOUBLE PRECISION array, dimension (LDS,N)
+*          The upper quasi-triangular matrix S from a generalized Schur
+*          factorization, as computed by DHGEQZ.
+*
+*  LDS     (input) INTEGER
+*          The leading dimension of array S.  LDS >= max(1,N).
+*
+*  P       (input) DOUBLE PRECISION array, dimension (LDP,N)
+*          The upper triangular matrix P from a generalized Schur
+*          factorization, as computed by DHGEQZ.
+*          2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks
+*          of S must be in positive diagonal form.
 *
-*  LDA     (input) INTEGER
-*          The leading dimension of array A.  LDA >= max(1, N).
-*
-*  B       (input) DOUBLE PRECISION array, dimension (LDB,N)
-*          The upper triangular matrix B.  If A has a 2-by-2 diagonal
-*          block, then the corresponding 2-by-2 block of B must be
-*          diagonal with positive elements.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of array B.  LDB >= max(1,N).
+*  LDP     (input) INTEGER
+*          The leading dimension of array P.  LDP >= max(1,N).
 *
 *  VL      (input/output) DOUBLE PRECISION array, dimension (LDVL,MM)
 *          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
 *          contain an N-by-N matrix Q (usually the orthogonal matrix Q
 *          of left Schur vectors returned by DHGEQZ).
 *          On exit, if SIDE = 'L' or 'B', VL contains:
-*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B);
+*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
 *          if HOWMNY = 'B', the matrix Q*Y;
-*          if HOWMNY = 'S', the left eigenvectors of (A,B) specified by
+*          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
 *                      SELECT, stored consecutively in the columns of
 *                      VL, in the same order as their eigenvalues.
-*          If SIDE = 'R', VL is not referenced.
 *
 *          A complex eigenvector corresponding to a complex eigenvalue
 *          is stored in two consecutive columns, the first holding the
 *          real part, and the second the imaginary part.
 *
+*          Not referenced if SIDE = 'R'.
+*
 *  LDVL    (input) INTEGER
-*          The leading dimension of array VL.
-*          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
+*          The leading dimension of array VL.  LDVL >= 1, and if
+*          SIDE = 'L' or 'B', LDVL >= N.
 *
 *  VR      (input/output) DOUBLE PRECISION array, dimension (LDVR,MM)
 *          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
-*          contain an N-by-N matrix Q (usually the orthogonal matrix Z
+*          contain an N-by-N matrix Z (usually the orthogonal matrix Z
 *          of right Schur vectors returned by DHGEQZ).
+*
 *          On exit, if SIDE = 'R' or 'B', VR contains:
-*          if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B);
-*          if HOWMNY = 'B', the matrix Z*X;
-*          if HOWMNY = 'S', the right eigenvectors of (A,B) specified by
-*                      SELECT, stored consecutively in the columns of
-*                      VR, in the same order as their eigenvalues.
-*          If SIDE = 'L', VR is not referenced.
+*          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
+*          if HOWMNY = 'B' or 'b', the matrix Z*X;
+*          if HOWMNY = 'S' or 's', the right eigenvectors of (S,P)
+*                      specified by SELECT, stored consecutively in the
+*                      columns of VR, in the same order as their
+*                      eigenvalues.
 *
 *          A complex eigenvector corresponding to a complex eigenvalue
 *          is stored in two consecutive columns, the first holding the
 *          real part and the second the imaginary part.
+*          
+*          Not referenced if SIDE = 'L'.
 *
 *  LDVR    (input) INTEGER
-*          The leading dimension of the array VR.
-*          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
+*          The leading dimension of the array VR.  LDVR >= 1, and if
+*          SIDE = 'R' or 'B', LDVR >= N.
 *
 *  MM      (input) INTEGER
 *          The number of columns in the arrays VL and/or VR. MM >= M.
@@ -199,7 +201,7 @@
 *  partial sums.  Since FORTRAN arrays are stored columnwise, this has
 *  the advantage that at each step, the elements of C that are accessed
 *  are adjacent to one another, whereas with the rowwise method, the
-*  elements accessed at a step are spaced LDA (and LDB) words apart.
+*  elements accessed at a step are spaced LDS (and LDP) words apart.
 *
 *  When finding left eigenvectors, the matrix in question is the
 *  transpose of the one in storage, so the rowwise method then
@@ -226,8 +228,8 @@
      $                   XSCALE
 *     ..
 *     .. Local Arrays ..
-      DOUBLE PRECISION   BDIAG( 2 ), SUM( 2, 2 ), SUMA( 2, 2 ),
-     $                   SUMB( 2, 2 )
+      DOUBLE PRECISION   BDIAG( 2 ), SUM( 2, 2 ), SUMS( 2, 2 ),
+     $                   SUMP( 2, 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -235,7 +237,7 @@
       EXTERNAL           LSAME, DLAMCH
 *     ..
 *     .. External Subroutines ..
-      EXTERNAL           DGEMV, DLACPY, DLAG2, DLALN2, XERBLA
+      EXTERNAL           DGEMV, DLABAD, DLACPY, DLAG2, DLALN2, XERBLA
 *     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, MAX, MIN
@@ -252,7 +254,7 @@
          IHWMNY = 2
          ILALL = .FALSE.
          ILBACK = .FALSE.
-      ELSE IF( LSAME( HOWMNY, 'B' ) .OR. LSAME( HOWMNY, 'T' ) ) THEN
+      ELSE IF( LSAME( HOWMNY, 'B' ) ) THEN
          IHWMNY = 3
          ILALL = .TRUE.
          ILBACK = .TRUE.
@@ -284,9 +286,9 @@
          INFO = -2
       ELSE IF( N.LT.0 ) THEN
          INFO = -4
-      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+      ELSE IF( LDS.LT.MAX( 1, N ) ) THEN
          INFO = -6
-      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+      ELSE IF( LDP.LT.MAX( 1, N ) ) THEN
          INFO = -8
       END IF
       IF( INFO.NE.0 ) THEN
@@ -305,7 +307,7 @@
                GO TO 10
             END IF
             IF( J.LT.N ) THEN
-               IF( A( J+1, J ).NE.ZERO )
+               IF( S( J+1, J ).NE.ZERO )
      $            ILCPLX = .TRUE.
             END IF
             IF( ILCPLX ) THEN
@@ -325,11 +327,11 @@
       ILABAD = .FALSE.
       ILBBAD = .FALSE.
       DO 20 J = 1, N - 1
-         IF( A( J+1, J ).NE.ZERO ) THEN
-            IF( B( J, J ).EQ.ZERO .OR. B( J+1, J+1 ).EQ.ZERO .OR.
-     $          B( J, J+1 ).NE.ZERO )ILBBAD = .TRUE.
+         IF( S( J+1, J ).NE.ZERO ) THEN
+            IF( P( J, J ).EQ.ZERO .OR. P( J+1, J+1 ).EQ.ZERO .OR.
+     $          P( J, J+1 ).NE.ZERO )ILBBAD = .TRUE.
             IF( J.LT.N-1 ) THEN
-               IF( A( J+2, J+1 ).NE.ZERO )
+               IF( S( J+2, J+1 ).NE.ZERO )
      $            ILABAD = .TRUE.
             END IF
          END IF
@@ -372,30 +374,30 @@
 *     blocks) of A and B to check for possible overflow in the
 *     triangular solver.
 *
-      ANORM = ABS( A( 1, 1 ) )
+      ANORM = ABS( S( 1, 1 ) )
       IF( N.GT.1 )
-     $   ANORM = ANORM + ABS( A( 2, 1 ) )
-      BNORM = ABS( B( 1, 1 ) )
+     $   ANORM = ANORM + ABS( S( 2, 1 ) )
+      BNORM = ABS( P( 1, 1 ) )
       WORK( 1 ) = ZERO
       WORK( N+1 ) = ZERO
 *
       DO 50 J = 2, N
          TEMP = ZERO
          TEMP2 = ZERO
-         IF( A( J, J-1 ).EQ.ZERO ) THEN
+         IF( S( J, J-1 ).EQ.ZERO ) THEN
             IEND = J - 1
          ELSE
             IEND = J - 2
          END IF
          DO 30 I = 1, IEND
-            TEMP = TEMP + ABS( A( I, J ) )
-            TEMP2 = TEMP2 + ABS( B( I, J ) )
+            TEMP = TEMP + ABS( S( I, J ) )
+            TEMP2 = TEMP2 + ABS( P( I, J ) )
    30    CONTINUE
          WORK( J ) = TEMP
          WORK( N+J ) = TEMP2
          DO 40 I = IEND + 1, MIN( J+1, N )
-            TEMP = TEMP + ABS( A( I, J ) )
-            TEMP2 = TEMP2 + ABS( B( I, J ) )
+            TEMP = TEMP + ABS( S( I, J ) )
+            TEMP2 = TEMP2 + ABS( P( I, J ) )
    40    CONTINUE
          ANORM = MAX( ANORM, TEMP )
          BNORM = MAX( BNORM, TEMP2 )
@@ -425,7 +427,7 @@
             END IF
             NW = 1
             IF( JE.LT.N ) THEN
-               IF( A( JE+1, JE ).NE.ZERO ) THEN
+               IF( S( JE+1, JE ).NE.ZERO ) THEN
                   ILCPLX = .TRUE.
                   NW = 2
                END IF
@@ -444,8 +446,8 @@
 *           (c) complex eigenvalue.
 *
             IF( .NOT.ILCPLX ) THEN
-               IF( ABS( A( JE, JE ) ).LE.SAFMIN .AND.
-     $             ABS( B( JE, JE ) ).LE.SAFMIN ) THEN
+               IF( ABS( S( JE, JE ) ).LE.SAFMIN .AND.
+     $             ABS( P( JE, JE ) ).LE.SAFMIN ) THEN
 *
 *                 Singular matrix pencil -- return unit eigenvector
 *
@@ -472,10 +474,10 @@
 *
 *              Real eigenvalue
 *
-               TEMP = ONE / MAX( ABS( A( JE, JE ) )*ASCALE,
-     $                ABS( B( JE, JE ) )*BSCALE, SAFMIN )
-               SALFAR = ( TEMP*A( JE, JE ) )*ASCALE
-               SBETA = ( TEMP*B( JE, JE ) )*BSCALE
+               TEMP = ONE / MAX( ABS( S( JE, JE ) )*ASCALE,
+     $                ABS( P( JE, JE ) )*BSCALE, SAFMIN )
+               SALFAR = ( TEMP*S( JE, JE ) )*ASCALE
+               SBETA = ( TEMP*P( JE, JE ) )*BSCALE
                ACOEF = SBETA*ASCALE
                BCOEFR = SALFAR*BSCALE
                BCOEFI = ZERO
@@ -517,7 +519,7 @@
 *
 *              Complex eigenvalue
 *
-               CALL DLAG2( A( JE, JE ), LDA, B( JE, JE ), LDB,
+               CALL DLAG2( S( JE, JE ), LDS, P( JE, JE ), LDP,
      $                     SAFMIN*SAFETY, ACOEF, TEMP, BCOEFR, TEMP2,
      $                     BCOEFI )
                BCOEFI = -BCOEFI
@@ -549,9 +551,9 @@
 *
 *              Compute first two components of eigenvector
 *
-               TEMP = ACOEF*A( JE+1, JE )
-               TEMP2R = ACOEF*A( JE, JE ) - BCOEFR*B( JE, JE )
-               TEMP2I = -BCOEFI*B( JE, JE )
+               TEMP = ACOEF*S( JE+1, JE )
+               TEMP2R = ACOEF*S( JE, JE ) - BCOEFR*P( JE, JE )
+               TEMP2I = -BCOEFI*P( JE, JE )
                IF( ABS( TEMP ).GT.ABS( TEMP2R )+ABS( TEMP2I ) ) THEN
                   WORK( 2*N+JE ) = ONE
                   WORK( 3*N+JE ) = ZERO
@@ -560,10 +562,10 @@
                ELSE
                   WORK( 2*N+JE+1 ) = ONE
                   WORK( 3*N+JE+1 ) = ZERO
-                  TEMP = ACOEF*A( JE, JE+1 )
-                  WORK( 2*N+JE ) = ( BCOEFR*B( JE+1, JE+1 )-ACOEF*
-     $                             A( JE+1, JE+1 ) ) / TEMP
-                  WORK( 3*N+JE ) = BCOEFI*B( JE+1, JE+1 ) / TEMP
+                  TEMP = ACOEF*S( JE, JE+1 )
+                  WORK( 2*N+JE ) = ( BCOEFR*P( JE+1, JE+1 )-ACOEF*
+     $                             S( JE+1, JE+1 ) ) / TEMP
+                  WORK( 3*N+JE ) = BCOEFI*P( JE+1, JE+1 ) / TEMP
                END IF
                XMAX = MAX( ABS( WORK( 2*N+JE ) )+ABS( WORK( 3*N+JE ) ),
      $                ABS( WORK( 2*N+JE+1 ) )+ABS( WORK( 3*N+JE+1 ) ) )
@@ -586,11 +588,11 @@
                END IF
 *
                NA = 1
-               BDIAG( 1 ) = B( J, J )
+               BDIAG( 1 ) = P( J, J )
                IF( J.LT.N ) THEN
-                  IF( A( J+1, J ).NE.ZERO ) THEN
+                  IF( S( J+1, J ).NE.ZERO ) THEN
                      IL2BY2 = .TRUE.
-                     BDIAG( 2 ) = B( J+1, J+1 )
+                     BDIAG( 2 ) = P( J+1, J+1 )
                      NA = 2
                   END IF
                END IF
@@ -616,13 +618,13 @@
 *              Compute dot products
 *
 *                    j-1
-*              SUM = sum  conjg( a*A(k,j) - b*B(k,j) )*x(k)
+*              SUM = sum  conjg( a*S(k,j) - b*P(k,j) )*x(k)
 *                    k=je
 *
 *              To reduce the op count, this is done as
 *
 *              _        j-1                  _        j-1
-*              a*conjg( sum  A(k,j)*x(k) ) - b*conjg( sum  B(k,j)*x(k) )
+*              a*conjg( sum  S(k,j)*x(k) ) - b*conjg( sum  P(k,j)*x(k) )
 *                       k=je                          k=je
 *
 *              which may cause underflow problems if A or B are close
@@ -659,15 +661,15 @@
 *$PL$ CMCHAR='*'
 *
                   DO 110 JA = 1, NA
-                     SUMA( JA, JW ) = ZERO
-                     SUMB( JA, JW ) = ZERO
+                     SUMS( JA, JW ) = ZERO
+                     SUMP( JA, JW ) = ZERO
 *
                      DO 100 JR = JE, J - 1
-                        SUMA( JA, JW ) = SUMA( JA, JW ) +
-     $                                   A( JR, J+JA-1 )*
+                        SUMS( JA, JW ) = SUMS( JA, JW ) +
+     $                                   S( JR, J+JA-1 )*
      $                                   WORK( ( JW+1 )*N+JR )
-                        SUMB( JA, JW ) = SUMB( JA, JW ) +
-     $                                   B( JR, J+JA-1 )*
+                        SUMP( JA, JW ) = SUMP( JA, JW ) +
+     $                                   P( JR, J+JA-1 )*
      $                                   WORK( ( JW+1 )*N+JR )
   100                CONTINUE
   110             CONTINUE
@@ -687,15 +689,15 @@
 *
                DO 130 JA = 1, NA
                   IF( ILCPLX ) THEN
-                     SUM( JA, 1 ) = -ACOEF*SUMA( JA, 1 ) +
-     $                              BCOEFR*SUMB( JA, 1 ) -
-     $                              BCOEFI*SUMB( JA, 2 )
-                     SUM( JA, 2 ) = -ACOEF*SUMA( JA, 2 ) +
-     $                              BCOEFR*SUMB( JA, 2 ) +
-     $                              BCOEFI*SUMB( JA, 1 )
+                     SUM( JA, 1 ) = -ACOEF*SUMS( JA, 1 ) +
+     $                              BCOEFR*SUMP( JA, 1 ) -
+     $                              BCOEFI*SUMP( JA, 2 )
+                     SUM( JA, 2 ) = -ACOEF*SUMS( JA, 2 ) +
+     $                              BCOEFR*SUMP( JA, 2 ) +
+     $                              BCOEFI*SUMP( JA, 1 )
                   ELSE
-                     SUM( JA, 1 ) = -ACOEF*SUMA( JA, 1 ) +
-     $                              BCOEFR*SUMB( JA, 1 )
+                     SUM( JA, 1 ) = -ACOEF*SUMS( JA, 1 ) +
+     $                              BCOEFR*SUMP( JA, 1 )
                   END IF
   130          CONTINUE
 *
@@ -703,7 +705,7 @@
 *              Solve  ( a A - b B )  y = SUM(,)
 *              with scaling and perturbation of the denominator
 *
-               CALL DLALN2( .TRUE., NA, NW, DMIN, ACOEF, A( J, J ), LDA,
+               CALL DLALN2( .TRUE., NA, NW, DMIN, ACOEF, S( J, J ), LDS,
      $                      BDIAG( 1 ), BDIAG( 2 ), SUM, 2, BCOEFR,
      $                      BCOEFI, WORK( 2*N+J ), N, SCALE, TEMP,
      $                      IINFO )
@@ -790,7 +792,7 @@
             END IF
             NW = 1
             IF( JE.GT.1 ) THEN
-               IF( A( JE, JE-1 ).NE.ZERO ) THEN
+               IF( S( JE, JE-1 ).NE.ZERO ) THEN
                   ILCPLX = .TRUE.
                   NW = 2
                END IF
@@ -809,8 +811,8 @@
 *           (c) complex eigenvalue.
 *
             IF( .NOT.ILCPLX ) THEN
-               IF( ABS( A( JE, JE ) ).LE.SAFMIN .AND.
-     $             ABS( B( JE, JE ) ).LE.SAFMIN ) THEN
+               IF( ABS( S( JE, JE ) ).LE.SAFMIN .AND.
+     $             ABS( P( JE, JE ) ).LE.SAFMIN ) THEN
 *
 *                 Singular matrix pencil -- unit eigenvector
 *
@@ -839,10 +841,10 @@
 *
 *              Real eigenvalue
 *
-               TEMP = ONE / MAX( ABS( A( JE, JE ) )*ASCALE,
-     $                ABS( B( JE, JE ) )*BSCALE, SAFMIN )
-               SALFAR = ( TEMP*A( JE, JE ) )*ASCALE
-               SBETA = ( TEMP*B( JE, JE ) )*BSCALE
+               TEMP = ONE / MAX( ABS( S( JE, JE ) )*ASCALE,
+     $                ABS( P( JE, JE ) )*BSCALE, SAFMIN )
+               SALFAR = ( TEMP*S( JE, JE ) )*ASCALE
+               SBETA = ( TEMP*P( JE, JE ) )*BSCALE
                ACOEF = SBETA*ASCALE
                BCOEFR = SALFAR*BSCALE
                BCOEFI = ZERO
@@ -885,14 +887,14 @@
 *              (See "Further Details", above.)
 *
                DO 260 JR = 1, JE - 1
-                  WORK( 2*N+JR ) = BCOEFR*B( JR, JE ) -
-     $                             ACOEF*A( JR, JE )
+                  WORK( 2*N+JR ) = BCOEFR*P( JR, JE ) -
+     $                             ACOEF*S( JR, JE )
   260          CONTINUE
             ELSE
 *
 *              Complex eigenvalue
 *
-               CALL DLAG2( A( JE-1, JE-1 ), LDA, B( JE-1, JE-1 ), LDB,
+               CALL DLAG2( S( JE-1, JE-1 ), LDS, P( JE-1, JE-1 ), LDP,
      $                     SAFMIN*SAFETY, ACOEF, TEMP, BCOEFR, TEMP2,
      $                     BCOEFI )
                IF( BCOEFI.EQ.ZERO ) THEN
@@ -924,9 +926,9 @@
 *              Compute first two components of eigenvector
 *              and contribution to sums
 *
-               TEMP = ACOEF*A( JE, JE-1 )
-               TEMP2R = ACOEF*A( JE, JE ) - BCOEFR*B( JE, JE )
-               TEMP2I = -BCOEFI*B( JE, JE )
+               TEMP = ACOEF*S( JE, JE-1 )
+               TEMP2R = ACOEF*S( JE, JE ) - BCOEFR*P( JE, JE )
+               TEMP2I = -BCOEFI*P( JE, JE )
                IF( ABS( TEMP ).GE.ABS( TEMP2R )+ABS( TEMP2I ) ) THEN
                   WORK( 2*N+JE ) = ONE
                   WORK( 3*N+JE ) = ZERO
@@ -935,10 +937,10 @@
                ELSE
                   WORK( 2*N+JE-1 ) = ONE
                   WORK( 3*N+JE-1 ) = ZERO
-                  TEMP = ACOEF*A( JE-1, JE )
-                  WORK( 2*N+JE ) = ( BCOEFR*B( JE-1, JE-1 )-ACOEF*
-     $                             A( JE-1, JE-1 ) ) / TEMP
-                  WORK( 3*N+JE ) = BCOEFI*B( JE-1, JE-1 ) / TEMP
+                  TEMP = ACOEF*S( JE-1, JE )
+                  WORK( 2*N+JE ) = ( BCOEFR*P( JE-1, JE-1 )-ACOEF*
+     $                             S( JE-1, JE-1 ) ) / TEMP
+                  WORK( 3*N+JE ) = BCOEFI*P( JE-1, JE-1 ) / TEMP
                END IF
 *
                XMAX = MAX( ABS( WORK( 2*N+JE ) )+ABS( WORK( 3*N+JE ) ),
@@ -958,12 +960,12 @@
                CRE2B = BCOEFR*WORK( 2*N+JE ) - BCOEFI*WORK( 3*N+JE )
                CIM2B = BCOEFI*WORK( 2*N+JE ) + BCOEFR*WORK( 3*N+JE )
                DO 270 JR = 1, JE - 2
-                  WORK( 2*N+JR ) = -CREALA*A( JR, JE-1 ) +
-     $                             CREALB*B( JR, JE-1 ) -
-     $                             CRE2A*A( JR, JE ) + CRE2B*B( JR, JE )
-                  WORK( 3*N+JR ) = -CIMAGA*A( JR, JE-1 ) +
-     $                             CIMAGB*B( JR, JE-1 ) -
-     $                             CIM2A*A( JR, JE ) + CIM2B*B( JR, JE )
+                  WORK( 2*N+JR ) = -CREALA*S( JR, JE-1 ) +
+     $                             CREALB*P( JR, JE-1 ) -
+     $                             CRE2A*S( JR, JE ) + CRE2B*P( JR, JE )
+                  WORK( 3*N+JR ) = -CIMAGA*S( JR, JE-1 ) +
+     $                             CIMAGB*P( JR, JE-1 ) -
+     $                             CIM2A*S( JR, JE ) + CIM2B*P( JR, JE )
   270          CONTINUE
             END IF
 *
@@ -978,23 +980,23 @@
 *              next iteration to process it (when it will be j:j+1)
 *
                IF( .NOT.IL2BY2 .AND. J.GT.1 ) THEN
-                  IF( A( J, J-1 ).NE.ZERO ) THEN
+                  IF( S( J, J-1 ).NE.ZERO ) THEN
                      IL2BY2 = .TRUE.
                      GO TO 370
                   END IF
                END IF
-               BDIAG( 1 ) = B( J, J )
+               BDIAG( 1 ) = P( J, J )
                IF( IL2BY2 ) THEN
                   NA = 2
-                  BDIAG( 2 ) = B( J+1, J+1 )
+                  BDIAG( 2 ) = P( J+1, J+1 )
                ELSE
                   NA = 1
                END IF
 *
 *              Compute x(j) (and x(j+1), if 2-by-2 block)
 *
-               CALL DLALN2( .FALSE., NA, NW, DMIN, ACOEF, A( J, J ),
-     $                      LDA, BDIAG( 1 ), BDIAG( 2 ), WORK( 2*N+J ),
+               CALL DLALN2( .FALSE., NA, NW, DMIN, ACOEF, S( J, J ),
+     $                      LDS, BDIAG( 1 ), BDIAG( 2 ), WORK( 2*N+J ),
      $                      N, BCOEFR, BCOEFI, SUM, 2, SCALE, TEMP,
      $                      IINFO )
                IF( SCALE.LT.ONE ) THEN
@@ -1014,7 +1016,7 @@
   300             CONTINUE
   310          CONTINUE
 *
-*              w = w + x(j)*(a A(*,j) - b B(*,j) ) with scaling
+*              w = w + x(j)*(a S(*,j) - b P(*,j) ) with scaling
 *
                IF( J.GT.1 ) THEN
 *
@@ -1052,19 +1054,19 @@
      $                           BCOEFR*WORK( 3*N+J+JA-1 )
                         DO 340 JR = 1, J - 1
                            WORK( 2*N+JR ) = WORK( 2*N+JR ) -
-     $                                      CREALA*A( JR, J+JA-1 ) +
-     $                                      CREALB*B( JR, J+JA-1 )
+     $                                      CREALA*S( JR, J+JA-1 ) +
+     $                                      CREALB*P( JR, J+JA-1 )
                            WORK( 3*N+JR ) = WORK( 3*N+JR ) -
-     $                                      CIMAGA*A( JR, J+JA-1 ) +
-     $                                      CIMAGB*B( JR, J+JA-1 )
+     $                                      CIMAGA*S( JR, J+JA-1 ) +
+     $                                      CIMAGB*P( JR, J+JA-1 )
   340                   CONTINUE
                      ELSE
                         CREALA = ACOEF*WORK( 2*N+J+JA-1 )
                         CREALB = BCOEFR*WORK( 2*N+J+JA-1 )
                         DO 350 JR = 1, J - 1
                            WORK( 2*N+JR ) = WORK( 2*N+JR ) -
-     $                                      CREALA*A( JR, J+JA-1 ) +
-     $                                      CREALB*B( JR, J+JA-1 )
+     $                                      CREALA*S( JR, J+JA-1 ) +
+     $                                      CREALB*P( JR, J+JA-1 )
   350                   CONTINUE
                      END IF
   360             CONTINUE
diff -uNr LAPACK.orig/SRC/dtrevc.f LAPACK/SRC/dtrevc.f
--- LAPACK.orig/SRC/dtrevc.f	Thu Nov  4 14:24:59 1999
+++ LAPACK/SRC/dtrevc.f	Fri May 25 16:13:52 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 7, 2001 
 *
 *     .. Scalar Arguments ..
       CHARACTER          HOWMNY, SIDE
@@ -21,28 +21,23 @@
 *
 *  DTREVC computes some or all of the right and/or left eigenvectors of
 *  a real upper quasi-triangular matrix T.
-*
+*  Matrices of this type are produced by the Schur factorization of
+*  a real general matrix:  A = Q*T*Q**T, as computed by DHSEQR.
+*  
 *  The right eigenvector x and the left eigenvector y of T corresponding
 *  to an eigenvalue w are defined by:
-*
-*               T*x = w*x,     y'*T = w*y'
-*
-*  where y' denotes the conjugate transpose of the vector y.
-*
-*  If all eigenvectors are requested, the routine may either return the
-*  matrices X and/or Y of right or left eigenvectors of T, or the
-*  products Q*X and/or Q*Y, where Q is an input orthogonal
-*  matrix. If T was obtained from the real-Schur factorization of an
-*  original matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of
-*  right or left eigenvectors of A.
-*
-*  T must be in Schur canonical form (as returned by DHSEQR), that is,
-*  block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
-*  2-by-2 diagonal block has its diagonal elements equal and its
-*  off-diagonal elements of opposite sign.  Corresponding to each 2-by-2
-*  diagonal block is a complex conjugate pair of eigenvalues and
-*  eigenvectors; only one eigenvector of the pair is computed, namely
-*  the one corresponding to the eigenvalue with positive imaginary part.
+*  
+*     T*x = w*x,     (y**H)*T = w*(y**H)
+*  
+*  where y**H denotes the conjugate transpose of y.
+*  The eigenvalues are not input to this routine, but are read directly
+*  from the diagonal blocks of T.
+*  
+*  This routine returns the matrices X and/or Y of right and left
+*  eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
+*  input matrix.  If Q is the orthogonal factor that reduces a matrix
+*  A to Schur form T, then Q*X and Q*Y are the matrices of right and
+*  left eigenvectors of A.
 *
 *  Arguments
 *  =========
@@ -55,21 +50,21 @@
 *  HOWMNY  (input) CHARACTER*1
 *          = 'A':  compute all right and/or left eigenvectors;
 *          = 'B':  compute all right and/or left eigenvectors,
-*                  and backtransform them using the input matrices
-*                  supplied in VR and/or VL;
+*                  backtransformed by the matrices in VR and/or VL;
 *          = 'S':  compute selected right and/or left eigenvectors,
-*                  specified by the logical array SELECT.
+*                  as indicated by the logical array SELECT.
 *
 *  SELECT  (input/output) LOGICAL array, dimension (N)
 *          If HOWMNY = 'S', SELECT specifies the eigenvectors to be
 *          computed.
-*          If HOWMNY = 'A' or 'B', SELECT is not referenced.
-*          To select the real eigenvector corresponding to a real
-*          eigenvalue w(j), SELECT(j) must be set to .TRUE..  To select
-*          the complex eigenvector corresponding to a complex conjugate
-*          pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must be
-*          set to .TRUE.; then on exit SELECT(j) is .TRUE. and
-*          SELECT(j+1) is .FALSE..
+*          If w(j) is a real eigenvalue, the corresponding real
+*          eigenvector is computed if SELECT(j) is .TRUE..
+*          If w(j) and w(j+1) are the real and imaginary parts of a
+*          complex eigenvalue, the corresponding complex eigenvector is
+*          computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
+*          on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
+*          .FALSE..
+*          Not referenced if HOWMNY = 'A' or 'B'.
 *
 *  N       (input) INTEGER
 *          The order of the matrix T. N >= 0.
@@ -86,15 +81,6 @@
 *          of Schur vectors returned by DHSEQR).
 *          On exit, if SIDE = 'L' or 'B', VL contains:
 *          if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
-*                           VL has the same quasi-lower triangular form
-*                           as T'. If T(i,i) is a real eigenvalue, then
-*                           the i-th column VL(i) of VL  is its
-*                           corresponding eigenvector. If T(i:i+1,i:i+1)
-*                           is a 2-by-2 block whose eigenvalues are
-*                           complex-conjugate eigenvalues of T, then
-*                           VL(i)+sqrt(-1)*VL(i+1) is the complex
-*                           eigenvector corresponding to the eigenvalue
-*                           with positive real part.
 *          if HOWMNY = 'B', the matrix Q*Y;
 *          if HOWMNY = 'S', the left eigenvectors of T specified by
 *                           SELECT, stored consecutively in the columns
@@ -103,11 +89,11 @@
 *          A complex eigenvector corresponding to a complex eigenvalue
 *          is stored in two consecutive columns, the first holding the
 *          real part, and the second the imaginary part.
-*          If SIDE = 'R', VL is not referenced.
+*          Not referenced if SIDE = 'R'.
 *
 *  LDVL    (input) INTEGER
-*          The leading dimension of the array VL.  LDVL >= max(1,N) if
-*          SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
+*          The leading dimension of the array VL.  LDVL >= 1, and if
+*          SIDE = 'L' or 'B', LDVL >= N.
 *
 *  VR      (input/output) DOUBLE PRECISION array, dimension (LDVR,MM)
 *          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
@@ -115,15 +101,6 @@
 *          of Schur vectors returned by DHSEQR).
 *          On exit, if SIDE = 'R' or 'B', VR contains:
 *          if HOWMNY = 'A', the matrix X of right eigenvectors of T;
-*                           VR has the same quasi-upper triangular form
-*                           as T. If T(i,i) is a real eigenvalue, then
-*                           the i-th column VR(i) of VR  is its
-*                           corresponding eigenvector. If T(i:i+1,i:i+1)
-*                           is a 2-by-2 block whose eigenvalues are
-*                           complex-conjugate eigenvalues of T, then
-*                           VR(i)+sqrt(-1)*VR(i+1) is the complex
-*                           eigenvector corresponding to the eigenvalue
-*                           with positive real part.
 *          if HOWMNY = 'B', the matrix Q*X;
 *          if HOWMNY = 'S', the right eigenvectors of T specified by
 *                           SELECT, stored consecutively in the columns
@@ -132,11 +109,11 @@
 *          A complex eigenvector corresponding to a complex eigenvalue
 *          is stored in two consecutive columns, the first holding the
 *          real part and the second the imaginary part.
-*          If SIDE = 'L', VR is not referenced.
+*          Not referenced if SIDE = 'L'.
 *
 *  LDVR    (input) INTEGER
-*          The leading dimension of the array VR.  LDVR >= max(1,N) if
-*          SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
+*          The leading dimension of the array VR.  LDVR >= 1, and if
+*          SIDE = 'R' or 'B', LDVR >= N.
 *
 *  MM      (input) INTEGER
 *          The number of columns in the arrays VL and/or VR. MM >= M.
diff -uNr LAPACK.orig/SRC/dtrsen.f LAPACK/SRC/dtrsen.f
--- LAPACK.orig/SRC/dtrsen.f	Thu Nov  4 14:24:59 1999
+++ LAPACK/SRC/dtrsen.f	Fri May 25 16:14:10 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     January 3, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, JOB
@@ -118,8 +118,8 @@
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK.
 *          If JOB = 'N', LWORK >= max(1,N);
-*          if JOB = 'E', LWORK >= M*(N-M);
-*          if JOB = 'V' or 'B', LWORK >= 2*M*(N-M).
+*          if JOB = 'E', LWORK >= max(1,M*(N-M));
+*          if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)).
 *
 *          If LWORK = -1, then a workspace query is assumed; the routine
 *          only calculates the optimal size of the WORK array, returns
@@ -127,12 +127,12 @@
 *          message related to LWORK is issued by XERBLA.
 *
 *  IWORK   (workspace) INTEGER array, dimension (LIWORK)
-*          IF JOB = 'N' or 'E', IWORK is not referenced.
+*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
 *
 *  LIWORK  (input) INTEGER
 *          The dimension of the array IWORK.
 *          If JOB = 'N' or 'E', LIWORK >= 1;
-*          if JOB = 'V' or 'B', LIWORK >= M*(N-M).
+*          if JOB = 'V' or 'B', LIWORK >= max(1,M*(N-M)).
 *
 *          If LIWORK = -1, then a workspace query is assumed; the
 *          routine only calculates the optimal size of the IWORK array,
diff -uNr LAPACK.orig/SRC/sbdsqr.f LAPACK/SRC/sbdsqr.f
--- LAPACK.orig/SRC/sbdsqr.f	Thu Nov  4 14:25:42 1999
+++ LAPACK/SRC/sbdsqr.f	Fri May 25 15:58:54 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     April 25, 2001 
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -18,14 +18,26 @@
 *  Purpose
 *  =======
 *
-*  SBDSQR computes the singular value decomposition (SVD) of a real
-*  N-by-N (upper or lower) bidiagonal matrix B:  B = Q * S * P' (P'
-*  denotes the transpose of P), where S is a diagonal matrix with
-*  non-negative diagonal elements (the singular values of B), and Q
-*  and P are orthogonal matrices.
-*
-*  The routine computes S, and optionally computes U * Q, P' * VT,
-*  or Q' * C, for given real input matrices U, VT, and C.
+*  SBDSQR computes the singular values and, optionally, the right and/or
+*  left singular vectors from the singular value decomposition (SVD) of
+*  a real N-by-N (upper or lower) bidiagonal matrix B using the implicit
+*  zero-shift QR algorithm.  The SVD of B has the form
+*  
+*     B = Q * S * P**T
+*  
+*  where S is the diagonal matrix of singular values, Q is an orthogonal
+*  matrix of left singular vectors, and P is an orthogonal matrix of
+*  right singular vectors.  If left singular vectors are requested, this
+*  subroutine actually returns U*Q instead of Q, and, if right singular
+*  vectors are requested, this subroutine returns P**T*VT instead of
+*  P**T, for given real input matrices U and VT.  When U and VT are the
+*  orthogonal matrices that reduce a general matrix A to bidiagonal
+*  form:  A = U*B*VT, as computed by SGEBRD, then
+* 
+*     A = (U*Q) * S * (P**T*VT)
+* 
+*  is the SVD of A.  Optionally, the subroutine may also compute Q**T*C
+*  for a given real input matrix C.
 *
 *  See "Computing  Small Singular Values of Bidiagonal Matrices With
 *  Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
@@ -61,18 +73,17 @@
 *          order.
 *
 *  E       (input/output) REAL array, dimension (N)
-*          On entry, the elements of E contain the
-*          offdiagonal elements of the bidiagonal matrix whose SVD
-*          is desired. On normal exit (INFO = 0), E is destroyed.
-*          If the algorithm does not converge (INFO > 0), D and E
+*          On entry, the N-1 offdiagonal elements of the bidiagonal
+*          matrix B.
+*          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E
 *          will contain the diagonal and superdiagonal elements of a
 *          bidiagonal matrix orthogonally equivalent to the one given
 *          as input. E(N) is used for workspace.
 *
 *  VT      (input/output) REAL array, dimension (LDVT, NCVT)
 *          On entry, an N-by-NCVT matrix VT.
-*          On exit, VT is overwritten by P' * VT.
-*          VT is not referenced if NCVT = 0.
+*          On exit, VT is overwritten by P**T * VT.
+*          Not referenced if NCVT = 0.
 *
 *  LDVT    (input) INTEGER
 *          The leading dimension of the array VT.
@@ -81,21 +92,22 @@
 *  U       (input/output) REAL array, dimension (LDU, N)
 *          On entry, an NRU-by-N matrix U.
 *          On exit, U is overwritten by U * Q.
-*          U is not referenced if NRU = 0.
+*          Not referenced if NRU = 0.
 *
 *  LDU     (input) INTEGER
 *          The leading dimension of the array U.  LDU >= max(1,NRU).
 *
 *  C       (input/output) REAL array, dimension (LDC, NCC)
 *          On entry, an N-by-NCC matrix C.
-*          On exit, C is overwritten by Q' * C.
-*          C is not referenced if NCC = 0.
+*          On exit, C is overwritten by Q**T * C.
+*          Not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C.
 *          LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0.
 *
-*  WORK    (workspace) REAL array, dimension (4*N)
+*  WORK    (workspace) REAL array, dimension (2*N)
+*          if NCVT = NRU = NCC = 0, (max(1, 4*N-4)) otherwise
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
diff -uNr LAPACK.orig/SRC/sgebd2.f LAPACK/SRC/sgebd2.f
--- LAPACK.orig/SRC/sgebd2.f	Thu Nov  4 14:23:33 1999
+++ LAPACK/SRC/sgebd2.f	Fri May 25 15:59:24 2001
@@ -3,7 +3,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     February 29, 1992
+*     May 7, 2001
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N
@@ -169,8 +169,9 @@
 *
 *           Apply H(i) to A(i:m,i+1:n) from the left
 *
-            CALL SLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAUQ( I ),
-     $                  A( I, I+1 ), LDA, WORK )
+            IF( I.LT.N )
+     $         CALL SLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAUQ( I ),
+     $                     A( I, I+1 ), LDA, WORK )
             A( I, I ) = D( I )
 *
             IF( I.LT.N ) THEN
@@ -207,8 +208,9 @@
 *
 *           Apply G(i) to A(i+1:m,i:n) from the right
 *
-            CALL SLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAUP( I ),
-     $                  A( MIN( I+1, M ), I ), LDA, WORK )
+            IF( I.LT.M )
+     $         CALL SLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
+     $                     TAUP( I ), A( MIN( I+1, M ), I ), LDA, WORK )
             A( I, I ) = D( I )
 *
             IF( I.LT.M ) THEN
diff -uNr LAPACK.orig/SRC/sgees.f LAPACK/SRC/sgees.f
--- LAPACK.orig/SRC/sgees.f	Thu Nov  4 14:23:33 1999
+++ LAPACK/SRC/sgees.f	Fri May 25 15:59:45 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVS, SORT
@@ -110,10 +111,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,3*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  BWORK   (workspace) LOGICAL array, dimension (N)
 *          Not referenced if SORT = 'N'.
@@ -138,12 +138,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            CURSL, LASTSL, LQUERY, LST2SL, SCALEA, WANTST,
-     $                   WANTVS
+      LOGICAL            CURSL, LASTSL, LST2SL, SCALEA, WANTST, WANTVS
       INTEGER            HSWORK, I, I1, I2, IBAL, ICOND, IERR, IEVAL,
      $                   IHI, ILO, INXT, IP, ITAU, IWRK, K, MAXB,
      $                   MAXWRK, MINWRK
@@ -171,7 +172,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVS = LSAME( JOBVS, 'V' )
       WANTST = LSAME( SORT, 'S' )
       IF( ( .NOT.WANTVS ) .AND. ( .NOT.LSAME( JOBVS, 'N' ) ) ) THEN
@@ -197,7 +197,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 2*N + N*ILAENV( 1, 'SGEHRD', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 3*N )
          IF( .NOT.WANTVS ) THEN
@@ -216,19 +216,17 @@
             MAXWRK = MAX( MAXWRK, N+HSWORK, 1 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGEES ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/sgeesx.f LAPACK/SRC/sgeesx.f
--- LAPACK.orig/SRC/sgeesx.f	Thu Nov  4 14:23:34 1999
+++ LAPACK/SRC/sgeesx.f	Fri May 25 16:00:09 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999 
+*     8-15-00:  Do WS calculations if LWORK = -1 (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVS, SENSE, SORT
@@ -140,6 +141,10 @@
 *          N+2*SDIM*(N-SDIM) <= N+N*N/2.
 *          For good performance, LWORK must generally be larger.
 *
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
 *  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
 *          Not referenced if SENSE = 'N' or 'E'.
 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
@@ -171,6 +176,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
@@ -239,7 +246,7 @@
 *       in the code.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 2*N + N*ILAENV( 1, 'SGEHRD', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 3*N )
          IF( .NOT.WANTVS ) THEN
@@ -257,21 +264,24 @@
             HSWORK = MAX( K*( K+2 ), 2*N )
             MAXWRK = MAX( MAXWRK, N+HSWORK, 1 )
          END IF
+*
+*        Estimate the workspace needed by STRSEN.
+*
+         IF( WANTST ) THEN
+            MAXWRK = MAX( MAXWRK, N+(N*N+1)/2 )
+         END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -16
       END IF
-      IF( LWORK.LT.MINWRK ) THEN
-         INFO = -16
-      END IF
-      IF( LIWORK.LT.1 ) THEN
-         INFO = -18
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGEESX', -INFO )
          RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/sgeev.f LAPACK/SRC/sgeev.f
--- LAPACK.orig/SRC/sgeev.f	Wed Dec  8 16:00:09 1999
+++ LAPACK/SRC/sgeev.f	Fri May 25 16:00:38 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     December 8, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -98,10 +99,9 @@
 *          if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N.  For good
 *          performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
@@ -114,11 +114,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR
+      LOGICAL            SCALEA, WANTVL, WANTVR
       CHARACTER          SIDE
       INTEGER            HSWORK, I, IBAL, IERR, IHI, ILO, ITAU, IWRK, K,
      $                   MAXB, MAXWRK, MINWRK, NOUT
@@ -149,7 +151,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVL = LSAME( JOBVL, 'V' )
       WANTVR = LSAME( JOBVR, 'V' )
       IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
@@ -177,7 +178,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 2*N + N*ILAENV( 1, 'SGEHRD', ' ', N, 1, N, 0 )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
             MINWRK = MAX( 1, 3*N )
@@ -198,19 +199,17 @@
             MAXWRK = MAX( MAXWRK, 4*N )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGEEV ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/sgeevx.f LAPACK/SRC/sgeevx.f
--- LAPACK.orig/SRC/sgeevx.f	Thu Nov  4 14:23:34 1999
+++ LAPACK/SRC/sgeevx.f	Fri May 25 16:00:59 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
@@ -179,10 +180,9 @@
 *          LWORK >= 3*N.  If SENSE = 'V' or 'B', LWORK >= N*(N+6).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (2*N-2)
 *          If SENSE = 'N' or 'E', not referenced.
@@ -198,12 +198,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
-     $                   WNTSNN, WNTSNV
+      LOGICAL            SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE, WNTSNN,
+     $                   WNTSNV
       CHARACTER          JOB, SIDE
       INTEGER            HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXB,
      $                   MAXWRK, MINWRK, NOUT
@@ -234,7 +236,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       WANTVL = LSAME( JOBVL, 'V' )
       WANTVR = LSAME( JOBVR, 'V' )
       WNTSNN = LSAME( SENSE, 'N' )
@@ -273,7 +274,7 @@
 *       the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = N + N*ILAENV( 1, 'SGEHRD', ' ', N, 1, N, 0 )
          IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
             MINWRK = MAX( 1, 2*N )
@@ -307,19 +308,17 @@
             MAXWRK = MAX( MAXWRK, 3*N, 1 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -21
       END IF
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -21
-      END IF
+*
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGEEVX', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/sgegs.f LAPACK/SRC/sgegs.f
--- LAPACK.orig/SRC/sgegs.f	Thu Nov  4 14:23:34 1999
+++ LAPACK/SRC/sgegs.f	Fri May 25 16:01:48 2001
@@ -5,7 +5,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR
@@ -22,105 +22,75 @@
 *
 *  This routine is deprecated and has been replaced by routine SGGES.
 *
-*  SGEGS computes for a pair of N-by-N real nonsymmetric matrices A, B:
-*  the generalized eigenvalues (alphar +/- alphai*i, beta), the real
-*  Schur form (A, B), and optionally left and/or right Schur vectors
-*  (VSL and VSR).
-*
-*  (If only the generalized eigenvalues are needed, use the driver SGEGV
-*  instead.)
-*
-*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly
-*  speaking, a scalar w or a ratio  alpha/beta = w, such that  A - w*B
-*  is singular.  It is usually represented as the pair (alpha,beta),
-*  as there is a reasonable interpretation for beta=0, and even for
-*  both being zero.  A good beginning reference is the book, "Matrix
-*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
-*
-*  The (generalized) Schur form of a pair of matrices is the result of
-*  multiplying both matrices on the left by one orthogonal matrix and
-*  both on the right by another orthogonal matrix, these two orthogonal
-*  matrices being chosen so as to bring the pair of matrices into
-*  (real) Schur form.
-*
-*  A pair of matrices A, B is in generalized real Schur form if B is
-*  upper triangular with non-negative diagonal and A is block upper
-*  triangular with 1-by-1 and 2-by-2 blocks.  1-by-1 blocks correspond
-*  to real generalized eigenvalues, while 2-by-2 blocks of A will be
-*  "standardized" by making the corresponding elements of B have the
-*  form:
-*          [  a  0  ]
-*          [  0  b  ]
-*
-*  and the pair of corresponding 2-by-2 blocks in A and B will
-*  have a complex conjugate pair of generalized eigenvalues.
-*
-*  The left and right Schur vectors are the columns of VSL and VSR,
-*  respectively, where VSL and VSR are the orthogonal matrices
-*  which reduce A and B to Schur form:
-*
-*  Schur form of (A,B) = ( (VSL)**T A (VSR), (VSL)**T B (VSR) )
+*  SGEGS computes the eigenvalues, real Schur form, and, optionally,
+*  left and or/right Schur vectors of a real matrix pair (A,B).
+*  Given two square matrices A and B, the generalized real Schur
+*  factorization has the form
+*  
+*    A = Q*S*Z**T,  B = Q*T*Z**T
+*
+*  where Q and Z are orthogonal matrices, T is upper triangular, and S
+*  is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
+*  blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
+*  of eigenvalues of (A,B).  The columns of Q are the left Schur vectors
+*  and the columns of Z are the right Schur vectors.
+*  
+*  If only the eigenvalues of (A,B) are needed, the driver routine
+*  SGEGV should be used instead.  See SGEGV for a description of the
+*  eigenvalues of the generalized nonsymmetric eigenvalue problem
+*  (GNEP).
 *
 *  Arguments
 *  =========
 *
 *  JOBVSL  (input) CHARACTER*1
 *          = 'N':  do not compute the left Schur vectors;
-*          = 'V':  compute the left Schur vectors.
+*          = 'V':  compute the left Schur vectors (returned in VSL).
 *
 *  JOBVSR  (input) CHARACTER*1
 *          = 'N':  do not compute the right Schur vectors;
-*          = 'V':  compute the right Schur vectors.
+*          = 'V':  compute the right Schur vectors (returned in VSR).
 *
 *  N       (input) INTEGER
 *          The order of the matrices A, B, VSL, and VSR.  N >= 0.
 *
 *  A       (input/output) REAL array, dimension (LDA, N)
-*          On entry, the first of the pair of matrices whose generalized
-*          eigenvalues and (optionally) Schur vectors are to be
-*          computed.
-*          On exit, the generalized Schur form of A.
-*          Note: to avoid overflow, the Frobenius norm of the matrix
-*          A should be less than the overflow threshold.
+*          On entry, the matrix A.
+*          On exit, the upper quasi-triangular matrix S from the
+*          generalized real Schur factorization.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of A.  LDA >= max(1,N).
 *
 *  B       (input/output) REAL array, dimension (LDB, N)
-*          On entry, the second of the pair of matrices whose
-*          generalized eigenvalues and (optionally) Schur vectors are
-*          to be computed.
-*          On exit, the generalized Schur form of B.
-*          Note: to avoid overflow, the Frobenius norm of the matrix
-*          B should be less than the overflow threshold.
+*          On entry, the matrix B.
+*          On exit, the upper triangular matrix T from the generalized
+*          real Schur factorization.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of B.  LDB >= max(1,N).
 *
 *  ALPHAR  (output) REAL array, dimension (N)
+*          The real parts of each scalar alpha defining an eigenvalue
+*          of GNEP.
+*
 *  ALPHAI  (output) REAL array, dimension (N)
-*  BETA    (output) REAL array, dimension (N)
-*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
-*          be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i,
-*          j=1,...,N  and  BETA(j),j=1,...,N  are the diagonals of the
-*          complex Schur form (A,B) that would result if the 2-by-2
-*          diagonal blocks of the real Schur form of (A,B) were further
-*          reduced to triangular form using 2-by-2 complex unitary
-*          transformations.  If ALPHAI(j) is zero, then the j-th
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th
 *          eigenvalue is real; if positive, then the j-th and (j+1)-st
-*          eigenvalues are a complex conjugate pair, with ALPHAI(j+1)
-*          negative.
+*          eigenvalues are a complex conjugate pair, with
+*          ALPHAI(j+1) = -ALPHAI(j).
 *
-*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
-*          may easily over- or underflow, and BETA(j) may even be zero.
-*          Thus, the user should avoid naively computing the ratio
-*          alpha/beta.  However, ALPHAR and ALPHAI will be always less
-*          than and usually comparable with norm(A) in magnitude, and
-*          BETA always less than and usually comparable with norm(B).
+*  BETA    (output) REAL array, dimension (N)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
 *
 *  VSL     (output) REAL array, dimension (LDVSL,N)
-*          If JOBVSL = 'V', VSL will contain the left Schur vectors.
-*          (See "Purpose", above.)
+*          If JOBVSL = 'V', the matrix of left Schur vectors Q.
 *          Not referenced if JOBVSL = 'N'.
 *
 *  LDVSL   (input) INTEGER
@@ -128,8 +98,7 @@
 *          if JOBVSL = 'V', LDVSL >= N.
 *
 *  VSR     (output) REAL array, dimension (LDVSR,N)
-*          If JOBVSR = 'V', VSR will contain the right Schur vectors.
-*          (See "Purpose", above.)
+*          If JOBVSR = 'V', the matrix of right Schur vectors Z.
 *          Not referenced if JOBVSR = 'N'.
 *
 *  LDVSR   (input) INTEGER
diff -uNr LAPACK.orig/SRC/sgegv.f LAPACK/SRC/sgegv.f
--- LAPACK.orig/SRC/sgegv.f	Thu Nov  4 14:25:42 1999
+++ LAPACK/SRC/sgegv.f	Fri May 25 16:02:12 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -21,23 +21,32 @@
 *
 *  This routine is deprecated and has been replaced by routine SGGEV.
 *
-*  SGEGV computes for a pair of n-by-n real nonsymmetric matrices A and
-*  B, the generalized eigenvalues (alphar +/- alphai*i, beta), and
-*  optionally, the left and/or right generalized eigenvectors (VL and
-*  VR).
-*
-*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly
-*  speaking, a scalar w or a ratio  alpha/beta = w, such that  A - w*B
-*  is singular.  It is usually represented as the pair (alpha,beta),
-*  as there is a reasonable interpretation for beta=0, and even for
-*  both being zero.  A good beginning reference is the book, "Matrix
-*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
-*
-*  A right generalized eigenvector corresponding to a generalized
-*  eigenvalue  w  for a pair of matrices (A,B) is a vector  r  such
-*  that  (A - w B) r = 0 .  A left generalized eigenvector is a vector
-*  l such that l**H * (A - w B) = 0, where l**H is the
-*  conjugate-transpose of l.
+*  SGEGV computes the eigenvalues and, optionally, the left and/or right
+*  eigenvectors of a real matrix pair (A,B).
+*  Given two square matrices A and B,
+*  the generalized nonsymmetric eigenvalue problem (GNEP) is to find the
+*  eigenvalues lambda and corresponding (non-zero) eigenvectors x such
+*  that
+*
+*     A*x = lambda*B*x.
+*
+*  An alternate form is to find the eigenvalues mu and corresponding
+*  eigenvectors y such that
+*
+*     mu*A*y = B*y.
+*
+*  These two forms are equivalent with mu = 1/lambda and x = y if
+*  neither lambda nor mu is zero.  In order to deal with the case that
+*  lambda or mu is zero or small, two values alpha and beta are returned
+*  for each eigenvalue, such that lambda = alpha/beta and
+*  mu = beta/alpha.
+*
+*  The vectors x and y in the above equations are right eigenvectors of
+*  the matrix pair (A,B).  Vectors u and v satisfying
+*
+*     u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B
+*
+*  are left eigenvectors of (A,B).
 *
 *  Note: this routine performs "full balancing" on A and B -- see
 *  "Further Details", below.
@@ -47,63 +56,75 @@
 *
 *  JOBVL   (input) CHARACTER*1
 *          = 'N':  do not compute the left generalized eigenvectors;
-*          = 'V':  compute the left generalized eigenvectors.
+*          = 'V':  compute the left generalized eigenvectors (returned
+*                  in VL).
 *
 *  JOBVR   (input) CHARACTER*1
 *          = 'N':  do not compute the right generalized eigenvectors;
-*          = 'V':  compute the right generalized eigenvectors.
+*          = 'V':  compute the right generalized eigenvectors (returned
+*                  in VR).
 *
 *  N       (input) INTEGER
 *          The order of the matrices A, B, VL, and VR.  N >= 0.
 *
 *  A       (input/output) REAL array, dimension (LDA, N)
-*          On entry, the first of the pair of matrices whose
-*          generalized eigenvalues and (optionally) generalized
-*          eigenvectors are to be computed.
-*          On exit, the contents will have been destroyed.  (For a
-*          description of the contents of A on exit, see "Further
-*          Details", below.)
+*          On entry, the matrix A.
+*          If JOBVL = 'V' or JOBVR = 'V', then on exit A
+*          contains the real Schur form of A from the generalized Schur
+*          factorization of the pair (A,B) after balancing.
+*          If no eigenvectors were computed, then only the diagonal
+*          blocks from the Schur form will be correct.  See SGGHRD and
+*          SHGEQZ for details.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of A.  LDA >= max(1,N).
 *
 *  B       (input/output) REAL array, dimension (LDB, N)
-*          On entry, the second of the pair of matrices whose
-*          generalized eigenvalues and (optionally) generalized
-*          eigenvectors are to be computed.
-*          On exit, the contents will have been destroyed.  (For a
-*          description of the contents of B on exit, see "Further
-*          Details", below.)
+*          On entry, the matrix B.
+*          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the
+*          upper triangular matrix obtained from B in the generalized
+*          Schur factorization of the pair (A,B) after balancing.
+*          If no eigenvectors were computed, then only those elements of
+*          B corresponding to the diagonal blocks from the Schur form of
+*          A will be correct.  See SGGHRD and SHGEQZ for details.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of B.  LDB >= max(1,N).
 *
 *  ALPHAR  (output) REAL array, dimension (N)
+*          The real parts of each scalar alpha defining an eigenvalue of
+*          GNEP.
+*
 *  ALPHAI  (output) REAL array, dimension (N)
-*  BETA    (output) REAL array, dimension (N)
-*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
-*          be the generalized eigenvalues.  If ALPHAI(j) is zero, then
-*          the j-th eigenvalue is real; if positive, then the j-th and
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th
+*          eigenvalue is real; if positive, then the j-th and
 *          (j+1)-st eigenvalues are a complex conjugate pair, with
-*          ALPHAI(j+1) negative.
+*          ALPHAI(j+1) = -ALPHAI(j).
 *
-*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
-*          may easily over- or underflow, and BETA(j) may even be zero.
-*          Thus, the user should avoid naively computing the ratio
-*          alpha/beta.  However, ALPHAR and ALPHAI will be always less
-*          than and usually comparable with norm(A) in magnitude, and
-*          BETA always less than and usually comparable with norm(B).
+*  BETA    (output) REAL array, dimension (N)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
 *
 *  VL      (output) REAL array, dimension (LDVL,N)
-*          If JOBVL = 'V', the left generalized eigenvectors.  (See
-*          "Purpose", above.)  Real eigenvectors take one column,
-*          complex take two columns, the first for the real part and
-*          the second for the imaginary part.  Complex eigenvectors
-*          correspond to an eigenvalue with positive imaginary part.
-*          Each eigenvector will be scaled so the largest component
-*          will have abs(real part) + abs(imag. part) = 1, *except*
-*          that for eigenvalues with alpha=beta=0, a zero vector will
-*          be returned as the corresponding eigenvector.
+*          If JOBVL = 'V', the left eigenvectors u(j) are stored
+*          in the columns of VL, in the same order as their eigenvalues.
+*          If the j-th eigenvalue is real, then u(j) = VL(:,j).
+*          If the j-th and (j+1)-st eigenvalues form a complex conjugate
+*          pair, then
+*             u(j) = VL(:,j) + i*VL(:,j+1)
+*          and
+*            u(j+1) = VL(:,j) - i*VL(:,j+1).
+*
+*          Each eigenvector is scaled so that its largest component has
+*          abs(real part) + abs(imag. part) = 1, except for eigenvectors
+*          corresponding to an eigenvalue with alpha = beta = 0, which
+*          are set to zero.
 *          Not referenced if JOBVL = 'N'.
 *
 *  LDVL    (input) INTEGER
@@ -111,15 +132,19 @@
 *          if JOBVL = 'V', LDVL >= N.
 *
 *  VR      (output) REAL array, dimension (LDVR,N)
-*          If JOBVR = 'V', the right generalized eigenvectors.  (See
-*          "Purpose", above.)  Real eigenvectors take one column,
-*          complex take two columns, the first for the real part and
-*          the second for the imaginary part.  Complex eigenvectors
-*          correspond to an eigenvalue with positive imaginary part.
-*          Each eigenvector will be scaled so the largest component
-*          will have abs(real part) + abs(imag. part) = 1, *except*
-*          that for eigenvalues with alpha=beta=0, a zero vector will
-*          be returned as the corresponding eigenvector.
+*          If JOBVR = 'V', the right eigenvectors x(j) are stored
+*          in the columns of VR, in the same order as their eigenvalues.
+*          If the j-th eigenvalue is real, then x(j) = VR(:,j).
+*          If the j-th and (j+1)-st eigenvalues form a complex conjugate
+*          pair, then
+*            x(j) = VR(:,j) + i*VR(:,j+1)
+*          and
+*            x(j+1) = VR(:,j) - i*VR(:,j+1).
+*
+*          Each eigenvector is scaled so that its largest component has
+*          abs(real part) + abs(imag. part) = 1, except for eigenvalues
+*          corresponding to an eigenvalue with alpha = beta = 0, which
+*          are set to zero.
 *          Not referenced if JOBVR = 'N'.
 *
 *  LDVR    (input) INTEGER
diff -uNr LAPACK.orig/SRC/sgelsd.f LAPACK/SRC/sgelsd.f
--- LAPACK.orig/SRC/sgelsd.f	Thu Nov  4 14:26:24 1999
+++ LAPACK/SRC/sgelsd.f	Fri May 25 16:03:05 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -61,9 +62,10 @@
 *          The number of right hand sides, i.e., the number of columns
 *          of the matrices B and X. NRHS >= 0.
 *
-*  A       (input) REAL array, dimension (LDA,N)
+*  A       (input/output) REAL array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
-*          On exit, A has been destroyed.
+*          On exit, the first min(m,n) rows of A are overwritten with
+*          its right singular vectors, stored rowwise.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
@@ -95,24 +97,20 @@
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *
 *  LWORK   (input) INTEGER
-*          The dimension of the array WORK. LWORK must be at least 1.
+*          The dimension of the array WORK. LWORK >= 1.
 *          The exact minimum amount of workspace needed depends on M,
-*          N and NRHS. As long as LWORK is at least
-*              12*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2,
-*          if M is greater than or equal to N or
-*              12*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS + (SMLSIZ+1)**2,
-*          if M is less than N, the code will execute correctly.
+*          N and NRHS.
+*          If M >= N, LWORK >=  11*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS.
+*          If M < N, LWORK >=  11*M + 2*M*SMLSIZ + 8*M*NLVL + M*NRHS.
 *          SMLSIZ is returned by ILAENV and is equal to the maximum
 *          size of the subproblems at the bottom of the computation
 *          tree (usually about 25), and
-*             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
+*              NLVL = INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
-*
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (LIWORK)
 *          LIWORK >= 3 * MINMN * NLVL + 11 * MINMN,
@@ -136,14 +134,15 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE, TWO
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY
       INTEGER            IASCL, IBSCL, IE, IL, ITAU, ITAUP, ITAUQ,
      $                   LDWORK, MAXMN, MAXWRK, MINMN, MINWRK, MM,
-     $                   MNTHR, NLVL, NWORK, SMLSIZ, WLALSD
+     $                   MNTHR, NLVL, NWORK, SMLSIZ
       REAL               ANRM, BIGNUM, BNRM, EPS, SFMIN, SMLNUM
 *     ..
 *     .. External Subroutines ..
@@ -166,7 +165,6 @@
       MINMN = MIN( M, N )
       MAXMN = MAX( M, N )
       MNTHR = ILAENV( 6, 'SGELSD', ' ', M, N, NRHS, -1 )
-      LQUERY = ( LWORK.EQ.-1 )
       IF( M.LT.0 ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
@@ -190,8 +188,8 @@
 *
       MINWRK = 1
       MINMN = MAX( 1, MINMN )
-      NLVL = MAX( INT( LOG( REAL( MINMN ) / REAL( SMLSIZ+1 ) ) / 
-     $       LOG( TWO ) ) + 1, 0 )
+      NLVL = INT( LOG( REAL( MINMN ) / REAL( SMLSIZ+1 ) ) / 
+     $       LOG( TWO ) ) + 1
 *
       IF( INFO.EQ.0 ) THEN
          MAXWRK = 0
@@ -216,12 +214,11 @@
      $               ILAENV( 1, 'SORMBR', 'QLT', MM, NRHS, N, -1 ) )
             MAXWRK = MAX( MAXWRK, 3*N+( N-1 )*
      $               ILAENV( 1, 'SORMBR', 'PLN', N, NRHS, N, -1 ) )
-            WLALSD = 9*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS+(SMLSIZ+1)**2
-            MAXWRK = MAX( MAXWRK, 3*N+WLALSD )
-            MINWRK = MAX( 3*N+MM, 3*N+NRHS, 3*N+WLALSD )
+            MAXWRK = MAX( MAXWRK, 3*N+8*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS )
+            MINWRK = MAX( 3*N+MM, 3*N+NRHS,
+     $               3*N+8*N+2*N*SMLSIZ+8*N*NLVL+N*NRHS )
          END IF
          IF( N.GT.M ) THEN
-            WLALSD = 9*M+2*M*SMLSIZ+8*M*NLVL+M*NRHS+(SMLSIZ+1)**2
             IF( N.GE.MNTHR ) THEN
 *
 *              Path 2a - underdetermined, with many more columns
@@ -241,7 +238,8 @@
                END IF
                MAXWRK = MAX( MAXWRK, M+NRHS*
      $                  ILAENV( 1, 'SORMLQ', 'LT', N, NRHS, M, -1 ) )
-               MAXWRK = MAX( MAXWRK, M*M+4*M+WLALSD )
+               MAXWRK = MAX( MAXWRK, M*M+4*M+8*M+2*M*SMLSIZ+8*M*NLVL+M*
+     $                  NRHS )
             ELSE
 *
 *              Path 2 - remaining underdetermined cases.
@@ -252,26 +250,25 @@
      $                  ILAENV( 1, 'SORMBR', 'QLT', M, NRHS, N, -1 ) )
                MAXWRK = MAX( MAXWRK, 3*M+M*
      $                  ILAENV( 1, 'SORMBR', 'PLN', N, NRHS, M, -1 ) )
-               MAXWRK = MAX( MAXWRK, 3*M+WLALSD )
+               MAXWRK = MAX( MAXWRK, 3*M+8*M+2*M*SMLSIZ+8*M*NLVL+M*
+     $                  NRHS )
             END IF
-            MINWRK = MAX( 3*M+NRHS, 3*M+M, 3*M+WLALSD )
+            MINWRK = MAX( 3*M+NRHS, 3*M+M,
+     $               3*M+8*M+2*M*SMLSIZ+8*M*NLVL+M*NRHS )
          END IF
          MINWRK = MIN( MINWRK, MAXWRK )
          WORK( 1 ) = MAXWRK
-         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-            INFO = -12
-         END IF
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
 *
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGELSD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         GO TO 10
       END IF
-*
-*     Quick return if possible.
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
          RANK = 0
          RETURN
diff -uNr LAPACK.orig/SRC/sgelss.f LAPACK/SRC/sgelss.f
--- LAPACK.orig/SRC/sgelss.f	Thu Nov  4 14:23:34 1999
+++ LAPACK/SRC/sgelss.f	Fri May 25 16:03:41 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     April 25, 2001 
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
@@ -86,10 +86,9 @@
 *          LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS )
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
@@ -156,7 +155,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 0
          MM = M
          IF( M.GE.N .AND. M.GE.MNTHR ) THEN
@@ -229,20 +228,18 @@
          END IF
          MAXWRK = MAX( MINWRK, MAXWRK )
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
+     $      INFO = -12
       END IF
 *
-      MINWRK = MAX( MINWRK, 1 )
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -12
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGELSS', -INFO )
          RETURN
       ELSE IF( LQUERY ) THEN
          RETURN
       END IF
-*
-*     Quick return if possible
-*
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
          RANK = 0
          RETURN
@@ -491,8 +488,8 @@
             DO 40 I = 1, NRHS, CHUNK
                BL = MIN( NRHS-I+1, CHUNK )
                CALL SGEMM( 'T', 'N', M, BL, M, ONE, WORK( IL ), LDWORK,
-     $                     B( 1, I ), LDB, ZERO, WORK( IWORK ), N )
-               CALL SLACPY( 'G', M, BL, WORK( IWORK ), N, B( 1, I ),
+     $                     B( 1, I ), LDB, ZERO, WORK( IWORK ), M )
+               CALL SLACPY( 'G', M, BL, WORK( IWORK ), M, B( 1, I ),
      $                      LDB )
    40       CONTINUE
          ELSE
diff -uNr LAPACK.orig/SRC/sgesdd.f LAPACK/SRC/sgesdd.f
--- LAPACK.orig/SRC/sgesdd.f	Thu Nov 11 20:32:10 1999
+++ LAPACK/SRC/sgesdd.f	Fri May 25 16:07:52 2001
@@ -1,10 +1,11 @@
-      SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
-     $                   LWORK, IWORK, INFO )
+      SUBROUTINE SGESDD( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
+     $                   WORK, LWORK, IWORK, INFO )
 *
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBZ
@@ -116,16 +117,20 @@
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK. LWORK >= 1.
 *          If JOBZ = 'N',
-*            LWORK >= 3*min(M,N) + max(max(M,N),6*min(M,N)).
+*            LWORK >= max(14*min(M,N)+4, 10*min(M,N)+2+
+*                     SMLSIZ*(SMLSIZ+8)) + max(M,N)
+*          where SMLSIZ is returned by ILAENV and is equal to the
+*          maximum size of the subproblems at the bottom of the
+*          computation tree (usually about 25).
 *          If JOBZ = 'O',
-*            LWORK >= 3*min(M,N)*min(M,N) + 
-*                     max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
+*            LWORK >= 5*min(M,N)*min(M,N) + max(M,N) + 9*min(M,N).
 *          If JOBZ = 'S' or 'A'
-*            LWORK >= 3*min(M,N)*min(M,N) +
-*                     max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)).
+*            LWORK >= 4*min(M,N)*min(M,N) + max(M,N) + 9*min(M,N).
 *          For good performance, LWORK should generally be larger.
-*          If LWORK < 0 but other input arguments are legal, WORK(1)
-*          returns the optimal LWORK.
+*
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (8*min(M,N))
 *
@@ -144,15 +149,17 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
-      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
+      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
-      INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IL,
+      LOGICAL            WNTQA, WNTQAS, WNTQN, WNTQO, WNTQS
+      INTEGER            BDSPAC, BDSPAN, BLK, CHUNK, I, IE, IERR, IL,
      $                   IR, ISCL, ITAU, ITAUP, ITAUQ, IU, IVT, LDWKVT,
      $                   LDWRKL, LDWRKR, LDWRKU, MAXWRK, MINMN, MINWRK,
-     $                   MNTHR, NWORK, WRKBL
+     $                   MNTHR, NWORK, SMLSIZ, WRKBL
       REAL               ANRM, BIGNUM, EPS, SMLNUM
 *     ..
 *     .. Local Arrays ..
@@ -168,10 +175,10 @@
       LOGICAL            LSAME
       INTEGER            ILAENV
       REAL               SLAMCH, SLANGE
-      EXTERNAL           ILAENV, LSAME, SLAMCH, SLANGE
+      EXTERNAL           SLAMCH, SLANGE, ILAENV, LSAME
 *     ..
 *     .. Intrinsic Functions ..
-      INTRINSIC          INT, MAX, MIN, REAL, SQRT
+      INTRINSIC          REAL, INT, MAX, MIN, SQRT
 *     ..
 *     .. Executable Statements ..
 *
@@ -179,7 +186,7 @@
 *
       INFO = 0
       MINMN = MIN( M, N )
-      MNTHR = INT( MINMN*11.0E0 / 6.0E0 )
+      MNTHR = INT( MINMN*11.0 / 6.0 )
       WNTQA = LSAME( JOBZ, 'A' )
       WNTQS = LSAME( JOBZ, 'S' )
       WNTQAS = WNTQA .OR. WNTQS
@@ -187,7 +194,6 @@
       WNTQN = LSAME( JOBZ, 'N' )
       MINWRK = 1
       MAXWRK = 1
-      LQUERY = ( LWORK.EQ.-1 )
 *
       IF( .NOT.( WNTQA .OR. WNTQS .OR. WNTQO .OR. WNTQN ) ) THEN
          INFO = -1
@@ -206,6 +212,8 @@
          INFO = -10
       END IF
 *
+      SMLSIZ = ILAENV( 9, 'SGESDD', ' ', 0, 0, 0, 0 )
+*
 *     Compute workspace
 *      (Note: Comments in the code beginning "Workspace:" describe the
 *       minimal amount of workspace needed at that point in the code,
@@ -218,22 +226,19 @@
 *
 *           Compute space needed for SBDSDC
 *
-            IF( WNTQN ) THEN
-               BDSPAC = 7*N
-            ELSE
-               BDSPAC = 3*N*N + 4*N
-            END IF
+            BDSPAC = 3*N*N + 7*N
+            BDSPAN = MAX( 12*N+4, 8*N+2+SMLSIZ*( SMLSIZ+8 ) )
             IF( M.GE.MNTHR ) THEN
                IF( WNTQN ) THEN
 *
 *                 Path 1 (M much larger than N, JOBZ='N')
 *
-                  WRKBL = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1,
-     $                    -1 )
-                  WRKBL = MAX( WRKBL, 3*N+2*N*
-     $                    ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+N )
-                  MINWRK = BDSPAC + N
+                  MAXWRK = N + N*ILAENV( 1, 'SGEQRF', ' ', M, N, -1,
+     $                     -1 )
+                  MAXWRK = MAX( MAXWRK, 3*N+2*N*
+     $                     ILAENV( 1, 'SGEBRD', ' ', N, N, -1, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC )
+                  MINWRK = BDSPAC
                ELSE IF( WNTQO ) THEN
 *
 *                 Path 2 (M much larger than N, JOBZ='O')
@@ -247,9 +252,9 @@
      $                    ILAENV( 1, 'SORMBR', 'QLN', N, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N )
                   MAXWRK = WRKBL + 2*N*N
-                  MINWRK = BDSPAC + 2*N*N + 3*N
+                  MINWRK = BDSPAC + 2*N*N + 2*N
                ELSE IF( WNTQS ) THEN
 *
 *                 Path 3 (M much larger than N, JOBZ='S')
@@ -263,9 +268,9 @@
      $                    ILAENV( 1, 'SORMBR', 'QLN', N, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N )
                   MAXWRK = WRKBL + N*N
-                  MINWRK = BDSPAC + N*N + 3*N
+                  MINWRK = BDSPAC + N*N + 2*N
                ELSE IF( WNTQA ) THEN
 *
 *                 Path 4 (M much larger than N, JOBZ='A')
@@ -279,9 +284,9 @@
      $                    ILAENV( 1, 'SORMBR', 'QLN', N, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
-                  MAXWRK = WRKBL + N*N
-                  MINWRK = BDSPAC + N*N + 3*N
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N )
+                  MAXWRK = N*N + WRKBL
+                  MINWRK = BDSPAC + N*N + M + N
                END IF
             ELSE
 *
@@ -289,53 +294,47 @@
 *
                WRKBL = 3*N + ( M+N )*ILAENV( 1, 'SGEBRD', ' ', M, N, -1,
      $                 -1 )
-               IF( WNTQN ) THEN
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*N )
-                  MINWRK = 3*N + MAX( M, BDSPAC )
-               ELSE IF( WNTQO ) THEN
+               IF( WNTQO ) THEN
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'SORMBR', 'QLN', M, N, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*N+N*
      $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*N )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*N+M )
                   MAXWRK = WRKBL + M*N
-                  MINWRK = 3*N + MAX( M, N*N+BDSPAC )
+                  MINWRK = BDSPAC + N*N + 2*N + M
                ELSE IF( WNTQS ) THEN
-                  WRKBL = MAX( WRKBL, 3*N+N*
-     $                    ILAENV( 1, 'SORMBR', 'QLN', M, N, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*N+N*
-     $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*N )
-                  MINWRK = 3*N + MAX( M, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*N+N*
+     $                     ILAENV( 1, 'SORMBR', 'QLN', M, N, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*N+N*
+     $                     ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*N+M )
+                  MINWRK = BDSPAC + 2*N + M
                ELSE IF( WNTQA ) THEN
-                  WRKBL = MAX( WRKBL, 3*N+M*
-     $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*N+N*
-     $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
-                  MAXWRK = MAX( MAXWRK, BDSPAC+3*N )
-                  MINWRK = 3*N + MAX( M, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*N+M*
+     $                     ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*N+N*
+     $                     ILAENV( 1, 'SORMBR', 'PRT', N, N, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*N+M )
+                  MINWRK = BDSPAC + 2*N + M
                END IF
             END IF
          ELSE
 *
 *           Compute space needed for SBDSDC
 *
-            IF( WNTQN ) THEN
-               BDSPAC = 7*M
-            ELSE
-               BDSPAC = 3*M*M + 4*M
-            END IF
+            BDSPAC = 3*M*M + 7*M
+            BDSPAN = MAX( 12*M+4, 8*M+2+SMLSIZ*( SMLSIZ+8 ) )
             IF( N.GE.MNTHR ) THEN
                IF( WNTQN ) THEN
 *
 *                 Path 1t (N much larger than M, JOBZ='N')
 *
-                  WRKBL = M + M*ILAENV( 1, 'SGELQF', ' ', M, N, -1,
-     $                    -1 )
-                  WRKBL = MAX( WRKBL, 3*M+2*M*
-     $                    ILAENV( 1, 'SGEBRD', ' ', M, M, -1, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+M )
-                  MINWRK = BDSPAC + M
+                  MAXWRK = M + M*ILAENV( 1, 'SGELQF', ' ', M, N, -1,
+     $                     -1 )
+                  MAXWRK = MAX( MAXWRK, 3*M+2*M*
+     $                     ILAENV( 1, 'SGEBRD', ' ', M, M, -1, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC )
+                  MINWRK = BDSPAC
                ELSE IF( WNTQO ) THEN
 *
 *                 Path 2t (N much larger than M, JOBZ='O')
@@ -349,9 +348,9 @@
      $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, M, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'SORMBR', 'PRT', M, M, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + 2*M*M
-                  MINWRK = BDSPAC + 2*M*M + 3*M
+                  MINWRK = BDSPAC + 2*M*M + 2*M
                ELSE IF( WNTQS ) THEN
 *
 *                 Path 3t (N much larger than M, JOBZ='S')
@@ -365,9 +364,9 @@
      $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, M, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'SORMBR', 'PRT', M, M, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + M*M
-                  MINWRK = BDSPAC + M*M + 3*M
+                  MINWRK = BDSPAC + M*M + 2*M
                ELSE IF( WNTQA ) THEN
 *
 *                 Path 4t (N much larger than M, JOBZ='A')
@@ -381,9 +380,9 @@
      $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, M, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'SORMBR', 'PRT', M, M, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + M*M
-                  MINWRK = BDSPAC + M*M + 3*M
+                  MINWRK = BDSPAC + M*M + M + N
                END IF
             ELSE
 *
@@ -391,52 +390,46 @@
 *
                WRKBL = 3*M + ( M+N )*ILAENV( 1, 'SGEBRD', ' ', M, N, -1,
      $                 -1 )
-               IF( WNTQN ) THEN
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*M )
-                  MINWRK = 3*M + MAX( N, BDSPAC )
-               ELSE IF( WNTQO ) THEN
+               IF( WNTQO ) THEN
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
                   WRKBL = MAX( WRKBL, 3*M+M*
      $                    ILAENV( 1, 'SORMBR', 'PRT', M, N, M, -1 ) )
-                  WRKBL = MAX( WRKBL, BDSPAC+3*M )
+                  WRKBL = MAX( WRKBL, BDSPAC+2*M )
                   MAXWRK = WRKBL + M*N
-                  MINWRK = 3*M + MAX( N, M*M+BDSPAC )
+                  MINWRK = BDSPAC + M*M + 2*M + N
                ELSE IF( WNTQS ) THEN
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'SORMBR', 'PRT', M, N, M, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*M )
-                  MINWRK = 3*M + MAX( N, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*M+M*
+     $                     ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*M+M*
+     $                     ILAENV( 1, 'SORMBR', 'PRT', M, N, M, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*M )
+                  MINWRK = BDSPAC + 2*M + N
                ELSE IF( WNTQA ) THEN
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
-                  WRKBL = MAX( WRKBL, 3*M+M*
-     $                    ILAENV( 1, 'SORMBR', 'PRT', N, N, M, -1 ) )
-                  MAXWRK = MAX( WRKBL, BDSPAC+3*M )
-                  MINWRK = 3*M + MAX( N, BDSPAC )
+                  MAXWRK = MAX( MAXWRK, 3*M+M*
+     $                     ILAENV( 1, 'SORMBR', 'QLN', M, M, N, -1 ) )
+                  MAXWRK = MAX( MAXWRK, 3*M+N*
+     $                     ILAENV( 1, 'SORMBR', 'PRT', N, N, M, -1 ) )
+                  MAXWRK = MAX( MAXWRK, BDSPAC+2*M )
+                  MINWRK = BDSPAC + 2*M + N
                END IF
             END IF
          END IF
+      END IF
+      IF( INFO.EQ.0 ) THEN
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -12
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -12
-      END IF
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGESDD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
-         IF( LWORK.GE.1 )
-     $      WORK( 1 ) = ONE
          RETURN
       END IF
 *
@@ -497,7 +490,7 @@
                NWORK = IE + N
 *
 *              Perform bidiagonal SVD, computing singular values only
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', N, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
@@ -512,10 +505,10 @@
 *
 *              WORK(IR) is LDWRKR by N
 *
-               IF( LWORK.GE.LDA*N+N*N+3*N+BDSPAC ) THEN
+               IF( LWORK.GE.LDA*N+4*N*N+9*N ) THEN
                   LDWRKR = LDA
                ELSE
-                  LDWRKR = ( LWORK-N*N-3*N-BDSPAC ) / N
+                  LDWRKR = ( LWORK-4*N*N-9*N ) / N
                END IF
                ITAU = IR + LDWRKR*N
                NWORK = ITAU + N
@@ -557,7 +550,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in WORK(IU) and computing right
 *              singular vectors of bidiagonal matrix in VT
-*              (Workspace: need N+N*N+BDSPAC)
+*              (Workspace: need 2*N*N+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ), N,
      $                      VT, LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -633,7 +626,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagoal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need N*N+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
      $                      LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -681,7 +674,7 @@
                CALL SLACPY( 'L', M, N, A, LDA, U, LDU )
 *
 *              Generate Q in U
-*              (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
+*              (Workspace: need N*N+N+M, prefer N*N+N+M*NB)
                CALL SORGQR( M, M, N, U, LDU, WORK( ITAU ),
      $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
 *
@@ -703,7 +696,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in WORK(IU) and computing right
 *              singular vectors of bidiagonal matrix in VT
-*              (Workspace: need N+N*N+BDSPAC)
+*              (Workspace: need N*N+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ), N,
      $                      VT, LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -754,13 +747,13 @@
             IF( WNTQN ) THEN
 *
 *              Perform bidiagonal SVD, only computing singular values
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', N, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
             ELSE IF( WNTQO ) THEN
                IU = NWORK
-               IF( LWORK.GE.M*N+3*N+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*N*N+9*N ) THEN
 *
 *                 WORK( IU ) is M by N
 *
@@ -785,7 +778,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in WORK(IU) and computing right
 *              singular vectors of bidiagonal matrix in VT
-*              (Workspace: need N+N*N+BDSPAC)
+*              (Workspace: need N*N+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), WORK( IU ),
      $                      LDWRKU, VT, LDVT, DUM, IDUM, WORK( NWORK ),
@@ -798,7 +791,7 @@
      $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
 *
-               IF( LWORK.GE.M*N+3*N+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*N*N+9*N ) THEN
 *
 *                 Overwrite WORK(IU) by left singular vectors of A
 *                 (Workspace: need N*N+2*N, prefer N*N+N+N*NB)
@@ -838,7 +831,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL SLASET( 'F', M, N, ZERO, ZERO, U, LDU )
                CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
@@ -855,12 +848,12 @@
                CALL SORMBR( 'P', 'R', 'T', N, N, N, A, LDA,
      $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
-            ELSE IF( WNTQA ) THEN
+            ELSE
 *
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need N+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL SLASET( 'F', M, M, ZERO, ZERO, U, LDU )
                CALL SBDSDC( 'U', 'I', N, S, WORK( IE ), U, LDU, VT,
@@ -925,7 +918,7 @@
                NWORK = IE + M
 *
 *              Perform bidiagonal SVD, computing singular values only
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL SBDSDC( 'U', 'N', M, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
@@ -941,7 +934,7 @@
 *              IVT is M by M
 *
                IL = IVT + M*M
-               IF( LWORK.GE.M*N+M*M+3*M+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+4*M*M+9*M ) THEN
 *
 *                 WORK(IL) is M by N
 *
@@ -986,7 +979,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U, and computing right singular
 *              vectors of bidiagonal matrix in WORK(IVT)
-*              (Workspace: need M+M*M+BDSPAC)
+*              (Workspace: need 2*M*M+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU,
      $                      WORK( IVT ), M, DUM, IDUM, WORK( NWORK ),
@@ -1061,7 +1054,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need M*M+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU, VT,
      $                      LDVT, DUM, IDUM, WORK( NWORK ), IWORK,
@@ -1108,7 +1101,7 @@
                CALL SLACPY( 'U', M, N, A, LDA, VT, LDVT )
 *
 *              Generate Q in VT
-*              (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
+*              (Workspace: need M*M+M+N, prefer M*M+M+N*NB)
 *
                CALL SORGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
      $                      WORK( NWORK ), LWORK-NWORK+1, IERR )
@@ -1131,7 +1124,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in WORK(IVT)
-*              (Workspace: need M+M*M+BDSPAC)
+*              (Workspace: need M*M+BDSPAC)
 *
                CALL SBDSDC( 'U', 'I', M, S, WORK( IE ), U, LDU,
      $                      WORK( IVT ), LDWKVT, DUM, IDUM,
@@ -1182,14 +1175,14 @@
             IF( WNTQN ) THEN
 *
 *              Perform bidiagonal SVD, only computing singular values
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAN)
 *
                CALL SBDSDC( 'L', 'N', M, S, WORK( IE ), DUM, 1, DUM, 1,
      $                      DUM, IDUM, WORK( NWORK ), IWORK, INFO )
             ELSE IF( WNTQO ) THEN
                LDWKVT = M
                IVT = NWORK
-               IF( LWORK.GE.M*N+3*M+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*M*M+9*M ) THEN
 *
 *                 WORK( IVT ) is M by N
 *
@@ -1224,7 +1217,7 @@
      $                      WORK( ITAUQ ), U, LDU, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
 *
-               IF( LWORK.GE.M*N+3*M+BDSPAC ) THEN
+               IF( LWORK.GE.M*N+3*M*M+9*M ) THEN
 *
 *                 Overwrite WORK(IVT) by left singular vectors of A
 *                 (Workspace: need M*M+2*M, prefer M*M+M+M*NB)
@@ -1263,7 +1256,7 @@
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL SLASET( 'F', M, N, ZERO, ZERO, VT, LDVT )
                CALL SBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU, VT,
@@ -1280,12 +1273,12 @@
                CALL SORMBR( 'P', 'R', 'T', M, N, M, A, LDA,
      $                      WORK( ITAUP ), VT, LDVT, WORK( NWORK ),
      $                      LWORK-NWORK+1, IERR )
-            ELSE IF( WNTQA ) THEN
+            ELSE
 *
 *              Perform bidiagonal SVD, computing left singular vectors
 *              of bidiagonal matrix in U and computing right singular
 *              vectors of bidiagonal matrix in VT
-*              (Workspace: need M+BDSPAC)
+*              (Workspace: need BDSPAC)
 *
                CALL SLASET( 'F', N, N, ZERO, ZERO, VT, LDVT )
                CALL SBDSDC( 'L', 'I', M, S, WORK( IE ), U, LDU, VT,
@@ -1319,9 +1312,15 @@
          IF( ANRM.GT.BIGNUM )
      $      CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
      $                   IERR )
+         IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM )
+     $      CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1, WORK( 2 ),
+     $                   MINMN, IERR )
          IF( ANRM.LT.SMLNUM )
      $      CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
      $                   IERR )
+         IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM )
+     $      CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1, WORK( 2 ),
+     $                   MINMN, IERR )
       END IF
 *
 *     Return optimal workspace in WORK(1)
diff -uNr LAPACK.orig/SRC/sgesvd.f LAPACK/SRC/sgesvd.f
--- LAPACK.orig/SRC/sgesvd.f	Thu Nov  4 14:23:35 1999
+++ LAPACK/SRC/sgesvd.f	Fri May 25 16:08:20 2001
@@ -4,7 +4,8 @@
 *  -- LAPACK driver routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1999
+*     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU, JOBVT
@@ -118,10 +119,9 @@
 *          LWORK >= MAX(3*MIN(M,N)+MAX(M,N),5*MIN(M,N)).
 *          For good performance, LWORK should generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit.
@@ -134,12 +134,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
-     $                   WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS
+      LOGICAL            WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS, WNTVA,
+     $                   WNTVAS, WNTVN, WNTVO, WNTVS
       INTEGER            BDSPAC, BLK, CHUNK, I, IE, IERR, IR, ISCL,
      $                   ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU,
      $                   MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU,
@@ -181,7 +183,7 @@
       WNTVO = LSAME( JOBVT, 'O' )
       WNTVN = LSAME( JOBVT, 'N' )
       MINWRK = 1
-      LQUERY = ( LWORK.EQ.-1 )
+      MAXWRK = 1
 *
       IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN
          INFO = -1
@@ -208,8 +210,7 @@
 *       NB refers to the optimal block size for the immediately
 *       following subroutine, as returned by ILAENV.)
 *
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) .AND. M.GT.0 .AND.
-     $   N.GT.0 ) THEN
+      IF( INFO.EQ.0 .AND. M.GT.0 .AND. N.GT.0 ) THEN
          IF( M.GE.N ) THEN
 *
 *           Compute space needed for SBDSQR
@@ -557,24 +558,21 @@
                MAXWRK = MAX( MAXWRK, MINWRK )
             END IF
          END IF
+      END IF
+      IF( INFO.EQ.0 ) THEN
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -13
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -13
-      END IF
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGESVD', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
-         IF( LWORK.GE.1 )
-     $      WORK( 1 ) = ONE
          RETURN
       END IF
 *
diff -uNr LAPACK.orig/SRC/sggbak.f LAPACK/SRC/sggbak.f
--- LAPACK.orig/SRC/sggbak.f	Thu Nov  4 14:23:36 1999
+++ LAPACK/SRC/sggbak.f	Fri May 25 16:08:51 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     February 1, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB, SIDE
@@ -108,10 +108,15 @@
          INFO = -3
       ELSE IF( ILO.LT.1 ) THEN
          INFO = -4
-      ELSE IF( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) THEN
+      ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
+         INFO = -4
+      ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
+     $   THEN
+         INFO = -5
+      ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
          INFO = -5
       ELSE IF( M.LT.0 ) THEN
-         INFO = -6
+         INFO = -8
       ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
          INFO = -10
       END IF
diff -uNr LAPACK.orig/SRC/sggbal.f LAPACK/SRC/sggbal.f
--- LAPACK.orig/SRC/sggbal.f	Thu Nov  4 14:25:42 1999
+++ LAPACK/SRC/sggbal.f	Fri May 25 16:09:11 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     April 12, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOB
@@ -141,7 +141,7 @@
       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
          INFO = -4
       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
-         INFO = -5
+         INFO = -6
       END IF
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGGBAL', -INFO )
@@ -188,8 +188,8 @@
       IF( L.NE.1 )
      $   GO TO 30
 *
-      RSCALE( 1 ) = 1
-      LSCALE( 1 ) = 1
+      RSCALE( 1 ) = ONE
+      LSCALE( 1 ) = ONE
       GO TO 190
 *
    30 CONTINUE
@@ -247,7 +247,7 @@
 *     Permute rows M and I
 *
   160 CONTINUE
-      LSCALE( M ) = I
+      LSCALE( M ) = REAL( I )
       IF( I.EQ.M )
      $   GO TO 170
       CALL SSWAP( N-K+1, A( I, K ), LDA, A( M, K ), LDA )
@@ -256,7 +256,7 @@
 *     Permute columns M and J
 *
   170 CONTINUE
-      RSCALE( M ) = J
+      RSCALE( M ) = REAL( J )
       IF( J.EQ.M )
      $   GO TO 180
       CALL SSWAP( L, A( 1, J ), 1, A( 1, M ), 1 )
@@ -424,7 +424,7 @@
       DO 360 I = ILO, IHI
          IRAB = ISAMAX( N-ILO+1, A( I, ILO ), LDA )
          RAB = ABS( A( I, IRAB+ILO-1 ) )
-         IRAB = ISAMAX( N-ILO+1, B( I, ILO ), LDA )
+         IRAB = ISAMAX( N-ILO+1, B( I, ILO ), LDB )
          RAB = MAX( RAB, ABS( B( I, IRAB+ILO-1 ) ) )
          LRAB = INT( LOG10( RAB+SFMIN ) / BASL+ONE )
          IR = LSCALE( I ) + SIGN( HALF, LSCALE( I ) )
diff -uNr LAPACK.orig/SRC/sgges.f LAPACK/SRC/sgges.f
--- LAPACK.orig/SRC/sgges.f	Thu Nov  4 14:26:20 1999
+++ LAPACK/SRC/sgges.f	Fri May 25 16:09:33 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SORT
@@ -158,10 +159,9 @@
 *  LWORK   (input) INTEGER
 *          The dimension of the array WORK.  LWORK >= 8*N+16.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  BWORK   (workspace) LOGICAL array, dimension (N)
 *          Not referenced if SORT = 'N'.
@@ -184,12 +184,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
-     $                   LQUERY, LST2SL, WANTST
+     $                   LST2SL, WANTST
       INTEGER            I, ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT,
      $                   ILO, IP, IRIGHT, IROWS, ITAU, IWRK, MAXWRK,
      $                   MINWRK
@@ -245,7 +247,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -272,7 +273,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MINWRK = 7*( N+1 ) + 16
          MAXWRK = 7*( N+1 ) + N*ILAENV( 1, 'SGEQRF', ' ', N, 1, N, 0 ) +
      $            16
@@ -281,19 +282,17 @@
      $               ILAENV( 1, 'SORGQR', ' ', N, 1, N, -1 ) )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -19
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -19
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGGES ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/sggesx.f LAPACK/SRC/sggesx.f
--- LAPACK.orig/SRC/sggesx.f	Thu Nov  4 14:26:20 1999
+++ LAPACK/SRC/sggesx.f	Fri May 25 16:09:52 2001
@@ -7,6 +7,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Do WS calculations if LWORK = -1 (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVSL, JOBVSR, SENSE, SORT
@@ -185,6 +186,10 @@
 *          If SENSE = 'E', 'V', or 'B',
 *          LWORK >= MAX( 8*(N+1)+16, 2*SDIM*(N-SDIM) ).
 *
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
+*
 *  IWORK   (workspace) INTEGER array, dimension (LIWORK)
 *          Not referenced if SENSE = 'N'.
 *
@@ -227,6 +232,8 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
 *     ..
@@ -330,7 +337,7 @@
 *       following subroutine, as returned by ILAENV.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN
+      IF( INFO.EQ.0 ) THEN
          MINWRK = 8*( N+1 ) + 16
          MAXWRK = 7*( N+1 ) + N*ILAENV( 1, 'SGEQRF', ' ', N, 1, N, 0 ) +
      $            16
@@ -338,7 +345,15 @@
             MAXWRK = MAX( MAXWRK, 8*( N+1 )+N*
      $               ILAENV( 1, 'SORGQR', ' ', N, 1, N, -1 )+16 )
          END IF
+*
+*        Estimate the workspace needed by STGSEN.
+*
+         IF( WANTST ) THEN
+            MAXWRK = MAX( MAXWRK, 2*N+(N*N+1)/2 )
+         END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -22
       END IF
       IF( .NOT.WANTSN ) THEN
          LIWMIN = 1
@@ -346,21 +361,18 @@
          LIWMIN = N + 6
       END IF
       IWORK( 1 ) = LIWMIN
-*
-      IF( INFO.EQ.0 .AND. LWORK.LT.MINWRK ) THEN
-         INFO = -22
-      ELSE IF( INFO.EQ.0 .AND. IJOB.GE.1 ) THEN
+      IF( INFO.EQ.0 .AND. IJOB.GE.1 ) THEN
          IF( LIWORK.LT.LIWMIN )
      $      INFO = -24
       END IF
 *
+*     Quick returns
+*
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGGESX', -INFO )
          RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 ) THEN
          SDIM = 0
          RETURN
diff -uNr LAPACK.orig/SRC/sggev.f LAPACK/SRC/sggev.f
--- LAPACK.orig/SRC/sggev.f	Thu Nov  4 14:26:20 1999
+++ LAPACK/SRC/sggev.f	Fri May 25 16:10:10 2001
@@ -5,6 +5,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBVL, JOBVR
@@ -123,10 +124,9 @@
 *          The dimension of the array WORK.  LWORK >= max(1,8*N).
 *          For good performance, LWORK must generally be larger.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  INFO    (output) INTEGER
 *          = 0:  successful exit
@@ -141,11 +141,13 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
+      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR
       CHARACTER          CHTEMP
       INTEGER            ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
      $                   IN, IRIGHT, IROWS, ITAU, IWRK, JC, JR, MAXWRK,
@@ -200,7 +202,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( IJOBVL.LE.0 ) THEN
          INFO = -1
       ELSE IF( IJOBVR.LE.0 ) THEN
@@ -226,24 +227,21 @@
 *       computed assuming ILO = 1 and IHI = N, the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 7*N + N*ILAENV( 1, 'SGEQRF', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 8*N )
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -16
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY )
-     $   INFO = -16
+*     Quick returns
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGGEV ', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
 *
diff -uNr LAPACK.orig/SRC/sggevx.f LAPACK/SRC/sggevx.f
--- LAPACK.orig/SRC/sggevx.f	Thu Nov  4 14:26:20 1999
+++ LAPACK/SRC/sggevx.f	Fri May 25 16:11:25 2001
@@ -7,6 +7,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-15-00:  Improve consistency of WS calculations (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          BALANC, JOBVL, JOBVR, SENSE
@@ -212,10 +213,9 @@
 *          If SENSE = 'E', LWORK >= 12*N.
 *          If SENSE = 'V' or 'B', LWORK >= 2*N*N+12*N+16.
 *
-*          If LWORK = -1, then a workspace query is assumed; the routine
-*          only calculates the optimal size of the WORK array, returns
-*          this value as the first entry of the WORK array, and no error
-*          message related to LWORK is issued by XERBLA.
+*          If LWORK = -1, a workspace query is assumed.  The optimal
+*          size for the WORK array is calculated and stored in WORK(1),
+*          and no other work except argument checking is performed.
 *
 *  IWORK   (workspace) INTEGER array, dimension (N+6)
 *          If SENSE = 'E', IWORK is not referenced.
@@ -262,12 +262,14 @@
 *  =====================================================================
 *
 *     .. Parameters ..
+      INTEGER            LQUERV
+      PARAMETER          ( LQUERV = -1 )
       REAL               ZERO, ONE
       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
 *     ..
 *     .. Local Scalars ..
-      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY, PAIR,
-     $                   WANTSB, WANTSE, WANTSN, WANTSV
+      LOGICAL            ILASCL, ILBSCL, ILV, ILVL, ILVR, PAIR, WANTSB,
+     $                   WANTSE, WANTSN, WANTSV
       CHARACTER          CHTEMP
       INTEGER            I, ICOLS, IERR, IJOBVL, IJOBVR, IN, IROWS,
      $                   ITAU, IWRK, IWRK1, J, JC, JR, M, MAXWRK,
@@ -327,7 +329,6 @@
 *     Test the input arguments
 *
       INFO = 0
-      LQUERY = ( LWORK.EQ.-1 )
       IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC,
      $    'S' ) .OR. LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) )
      $     THEN
@@ -360,7 +361,7 @@
 *       computed assuming ILO = 1 and IHI = N, the worst case.)
 *
       MINWRK = 1
-      IF( INFO.EQ.0 .AND. ( LWORK.GE.1 .OR. LQUERY ) ) THEN
+      IF( INFO.EQ.0 ) THEN
          MAXWRK = 5*N + N*ILAENV( 1, 'SGEQRF', ' ', N, 1, N, 0 )
          MINWRK = MAX( 1, 6*N )
          IF( WANTSE ) THEN
@@ -370,24 +371,19 @@
             MAXWRK = MAX( MAXWRK, 2*N*N+12*N+16 )
          END IF
          WORK( 1 ) = MAXWRK
+         IF( LWORK.LT.MINWRK .AND. LWORK.NE.LQUERV )
+     $      INFO = -26
       END IF
 *
-      IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
-         INFO = -26
-      END IF
+*     Quick returns
 *
       IF( INFO.NE.0 ) THEN
          CALL XERBLA( 'SGGEVX', -INFO )
          RETURN
-      ELSE IF( LQUERY ) THEN
-         RETURN
       END IF
-*
-*     Quick return if possible
-*
+      IF( LWORK.EQ.LQUERV ) RETURN
       IF( N.EQ.0 )
      $   RETURN
-*
 *
 *     Get machine constants
 *
diff -uNr LAPACK.orig/SRC/sgghrd.f LAPACK/SRC/sgghrd.f
--- LAPACK.orig/SRC/sgghrd.f	Thu Nov  4 14:25:44 1999
+++ LAPACK/SRC/sgghrd.f	Fri May 25 16:11:45 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     September 30, 1994
+*     April 26, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ
@@ -20,16 +20,32 @@
 *
 *  SGGHRD reduces a pair of real matrices (A,B) to generalized upper
 *  Hessenberg form using orthogonal transformations, where A is a
-*  general matrix and B is upper triangular:  Q' * A * Z = H and
-*  Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular,
-*  and Q and Z are orthogonal, and ' means transpose.
+*  general matrix and B is upper triangular.  The form of the
+*  generalized eigenvalue problem is
+*     A*x = lambda*B*x,
+*  and B is typically made upper triangular by computing its QR
+*  factorization and moving the orthogonal matrix Q to the left side
+*  of the equation.
+*
+*  This subroutine simultaneously reduces A to a Hessenberg matrix H:
+*     Q**T*A*Z = H
+*  and transforms B to another upper triangular matrix T:
+*     Q**T*B*Z = T
+*  in order to reduce the problem to its standard form
+*     H*y = lambda*T*y
+*  where y = Z**T*x.
 *
 *  The orthogonal matrices Q and Z are determined as products of Givens
 *  rotations.  They may either be formed explicitly, or they may be
-*  postmultiplied into input matrices Q1 and Z1, so that 
+*  postmultiplied into input matrices Q1 and Z1, so that
 *
-*       Q1 * A * Z1' = (Q1*Q) * H * (Z1*Z)'
-*       Q1 * B * Z1' = (Q1*Q) * T * (Z1*Z)'
+*       Q1 * A * Z1**T = (Q1*Q) * H * (Z1*Z)**T
+*
+*       Q1 * B * Z1**T = (Q1*Q) * T * (Z1*Z)**T
+*
+*  If Q1 is the orthogonal matrix from the QR factorization of B in the
+*  original equation A*x = lambda*B*x, then SGGHRD reduces the original
+*  problem to generalized Hessenberg form.
 *
 *  Arguments
 *  =========
@@ -53,10 +69,11 @@
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
-*          It is assumed that A is already upper triangular in rows and
-*          columns 1:ILO-1 and IHI+1:N.  ILO and IHI are normally set
-*          by a previous call to SGGBAL; otherwise they should be set
-*          to 1 and N respectively.
+*          ILO and IHI mark the rows and columns of A which are to be
+*          reduced.  It is assumed that A is already upper triangular
+*          in rows and columns 1:ILO-1 and IHI+1:N.  ILO and IHI are
+*          normally set by a previous call to SGGBAL; otherwise they
+*          should be set to 1 and N respectively.
 *          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
 *
 *  A       (input/output) REAL array, dimension (LDA, N)
@@ -70,33 +87,28 @@
 *
 *  B       (input/output) REAL array, dimension (LDB, N)
 *          On entry, the N-by-N upper triangular matrix B.
-*          On exit, the upper triangular matrix T = Q' B Z.  The
+*          On exit, the upper triangular matrix T = Q**T B Z.  The
 *          elements below the diagonal are set to zero.
 *
 *  LDB     (input) INTEGER
 *          The leading dimension of the array B.  LDB >= max(1,N).
 *
 *  Q       (input/output) REAL array, dimension (LDQ, N)
-*          If COMPQ='N':  Q is not referenced.
-*          If COMPQ='I':  on entry, Q need not be set, and on exit it
-*                         contains the orthogonal matrix Q, where Q'
-*                         is the product of the Givens transformations
-*                         which are applied to A and B on the left.
-*          If COMPQ='V':  on entry, Q must contain an orthogonal matrix
-*                         Q1, and on exit this is overwritten by Q1*Q.
+*          On entry, if COMPQ = 'V', the orthogonal matrix Q1,
+*          typically from the QR factorization of B.
+*          On exit, if COMPQ='I', the orthogonal matrix Q, and if
+*          COMPQ = 'V', the product Q1*Q.
+*          Not referenced if COMPQ='N'.
 *
 *  LDQ     (input) INTEGER
 *          The leading dimension of the array Q.
 *          LDQ >= N if COMPQ='V' or 'I'; LDQ >= 1 otherwise.
 *
 *  Z       (input/output) REAL array, dimension (LDZ, N)
-*          If COMPZ='N':  Z is not referenced.
-*          If COMPZ='I':  on entry, Z need not be set, and on exit it 
-*                         contains the orthogonal matrix Z, which is
-*                         the product of the Givens transformations
-*                         which are applied to A and B on the right.
-*          If COMPZ='V':  on entry, Z must contain an orthogonal matrix
-*                         Z1, and on exit this is overwritten by Z1*Z.
+*          On entry, if COMPZ = 'V', the orthogonal matrix Z1.
+*          On exit, if COMPZ='I', the orthogonal matrix Z, and if
+*          COMPZ = 'V', the product Z1*Z.
+*          Not referenced if COMPZ='N'.
 *
 *  LDZ     (input) INTEGER
 *          The leading dimension of the array Z.
diff -uNr LAPACK.orig/SRC/shgeqz.f LAPACK/SRC/shgeqz.f
--- LAPACK.orig/SRC/shgeqz.f	Thu Nov  4 14:23:36 1999
+++ LAPACK/SRC/shgeqz.f	Fri May 25 16:12:05 2001
@@ -1,56 +1,75 @@
-      SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB,
+      SUBROUTINE SHGEQZ( JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT,
      $                   ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDZ, WORK,
      $                   LWORK, INFO )
 *
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 3, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          COMPQ, COMPZ, JOB
-      INTEGER            IHI, ILO, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
+      INTEGER            IHI, ILO, INFO, LDH, LDQ, LDT, LDZ, LWORK, N
 *     ..
 *     .. Array Arguments ..
-      REAL               A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
-     $                   B( LDB, * ), BETA( * ), Q( LDQ, * ), WORK( * ),
-     $                   Z( LDZ, * )
+      REAL               ALPHAI( * ), ALPHAR( * ), BETA( * ),
+     $                   H( LDH, * ), Q( LDQ, * ), T( LDT, * ),
+     $                   WORK( * ), Z( LDZ, * )
 *     ..
 *
 *  Purpose
 *  =======
 *
-*  SHGEQZ implements a single-/double-shift version of the QZ method for
-*  finding the generalized eigenvalues
-*
-*  w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j)   of the equation
-*
-*       det( A - w(i) B ) = 0
-*
-*  In addition, the pair A,B may be reduced to generalized Schur form:
-*  B is upper triangular, and A is block upper triangular, where the
-*  diagonal blocks are either 1-by-1 or 2-by-2, the 2-by-2 blocks having
-*  complex generalized eigenvalues (see the description of the argument
-*  JOB.)
-*
-*  If JOB='S', then the pair (A,B) is simultaneously reduced to Schur
-*  form by applying one orthogonal tranformation (usually called Q) on
-*  the left and another (usually called Z) on the right.  The 2-by-2
-*  upper-triangular diagonal blocks of B corresponding to 2-by-2 blocks
-*  of A will be reduced to positive diagonal matrices.  (I.e.,
-*  if A(j+1,j) is non-zero, then B(j+1,j)=B(j,j+1)=0 and B(j,j) and
-*  B(j+1,j+1) will be positive.)
-*
-*  If JOB='E', then at each iteration, the same transformations
-*  are computed, but they are only applied to those parts of A and B
-*  which are needed to compute ALPHAR, ALPHAI, and BETAR.
-*
-*  If JOB='S' and COMPQ and COMPZ are 'V' or 'I', then the orthogonal
-*  transformations used to reduce (A,B) are accumulated into the arrays
-*  Q and Z s.t.:
-*
-*       Q(in) A(in) Z(in)* = Q(out) A(out) Z(out)*
-*       Q(in) B(in) Z(in)* = Q(out) B(out) Z(out)*
+*  SHGEQZ computes the eigenvalues of a real matrix pair (H,T),
+*  where H is an upper Hessenberg matrix and T is upper triangular,
+*  using the double-shift QZ method.
+*  Matrix pairs of this type are produced by the reduction to
+*  generalized upper Hessenberg form of a real matrix pair (A,B):
+*
+*     A = Q1*H*Z1**T,  B = Q1*T*Z1**T,
+*
+*  as computed by SGGHRD.
+*
+*  If JOB='S', then the Hessenberg-triangular pair (H,T) is
+*  also reduced to generalized Schur form,
+*  
+*     H = Q*S*Z**T,  T = Q*P*Z**T,
+*  
+*  where Q and Z are orthogonal matrices, P is an upper triangular
+*  matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2
+*  diagonal blocks.
+*
+*  The 1-by-1 blocks correspond to real eigenvalues of the matrix pair
+*  (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of
+*  eigenvalues.
+*
+*  Additionally, the 2-by-2 upper triangular diagonal blocks of P
+*  corresponding to 2-by-2 blocks of S are reduced to positive diagonal
+*  form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0,
+*  P(j,j) > 0, and P(j+1,j+1) > 0.
+*
+*  Optionally, the orthogonal matrix Q from the generalized Schur
+*  factorization may be postmultiplied into an input matrix Q1, and the
+*  orthogonal matrix Z may be postmultiplied into an input matrix Z1.
+*  If Q1 and Z1 are the orthogonal matrices from SGGHRD that reduced
+*  the matrix pair (A,B) to generalized upper Hessenberg form, then the
+*  output matrices Q1*Q and Z1*Z are the orthogonal factors from the
+*  generalized Schur factorization of (A,B):
+*
+*     A = (Q1*Q)*S*(Z1*Z)**T,  B = (Q1*Q)*P*(Z1*Z)**T.
+*  
+*  To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently,
+*  of (A,B)) are computed as a pair of values (alpha,beta), where alpha is
+*  complex and beta real.
+*  If beta is nonzero, lambda = alpha / beta is an eigenvalue of the
+*  generalized nonsymmetric eigenvalue problem (GNEP)
+*     A*x = lambda*B*x
+*  and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the
+*  alternate form of the GNEP
+*     mu*A*y = B*y.
+*  Real eigenvalues can be read directly from the generalized Schur
+*  form: 
+*    alpha = S(i,i), beta = P(i,i).
 *
 *  Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix
 *       Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973),
@@ -60,114 +79,98 @@
 *  =========
 *
 *  JOB     (input) CHARACTER*1
-*          = 'E': compute only ALPHAR, ALPHAI, and BETA.  A and B will
-*                 not necessarily be put into generalized Schur form.
-*          = 'S': put A and B into generalized Schur form, as well
-*                 as computing ALPHAR, ALPHAI, and BETA.
+*          = 'E': Compute eigenvalues only;
+*          = 'S': Compute eigenvalues and the Schur form. 
 *
 *  COMPQ   (input) CHARACTER*1
-*          = 'N': do not modify Q.
-*          = 'V': multiply the array Q on the right by the transpose of
-*                 the orthogonal tranformation that is applied to the
-*                 left side of A and B to reduce them to Schur form.
-*          = 'I': like COMPQ='V', except that Q will be initialized to
-*                 the identity first.
+*          = 'N': Left Schur vectors (Q) are not computed;
+*          = 'I': Q is initialized to the unit matrix and the matrix Q
+*                 of left Schur vectors of (H,T) is returned;
+*          = 'V': Q must contain an orthogonal matrix Q1 on entry and
+*                 the product Q1*Q is returned.
 *
 *  COMPZ   (input) CHARACTER*1
-*          = 'N': do not modify Z.
-*          = 'V': multiply the array Z on the right by the orthogonal
-*                 tranformation that is applied to the right side of
-*                 A and B to reduce them to Schur form.
-*          = 'I': like COMPZ='V', except that Z will be initialized to
-*                 the identity first.
+*          = 'N': Right Schur vectors (Z) are not computed;
+*          = 'I': Z is initialized to the unit matrix and the matrix Z
+*                 of right Schur vectors of (H,T) is returned;
+*          = 'V': Z must contain an orthogonal matrix Z1 on entry and
+*                 the product Z1*Z is returned.
 *
 *  N       (input) INTEGER
-*          The order of the matrices A, B, Q, and Z.  N >= 0.
+*          The order of the matrices H, T, Q, and Z.  N >= 0.
 *
 *  ILO     (input) INTEGER
 *  IHI     (input) INTEGER
-*          It is assumed that A is already upper triangular in rows and
-*          columns 1:ILO-1 and IHI+1:N.
-*          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
-*
-*  A       (input/output) REAL array, dimension (LDA, N)
-*          On entry, the N-by-N upper Hessenberg matrix A.  Elements
-*          below the subdiagonal must be zero.
-*          If JOB='S', then on exit A and B will have been
-*             simultaneously reduced to generalized Schur form.
-*          If JOB='E', then on exit A will have been destroyed.
-*             The diagonal blocks will be correct, but the off-diagonal
-*             portion will be meaningless.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max( 1, N ).
-*
-*  B       (input/output) REAL array, dimension (LDB, N)
-*          On entry, the N-by-N upper triangular matrix B.  Elements
-*          below the diagonal must be zero.  2-by-2 blocks in B
-*          corresponding to 2-by-2 blocks in A will be reduced to
-*          positive diagonal form.  (I.e., if A(j+1,j) is non-zero,
-*          then B(j+1,j)=B(j,j+1)=0 and B(j,j) and B(j+1,j+1) will be
-*          positive.)
-*          If JOB='S', then on exit A and B will have been
-*             simultaneously reduced to Schur form.
-*          If JOB='E', then on exit B will have been destroyed.
-*             Elements corresponding to diagonal blocks of A will be
-*             correct, but the off-diagonal portion will be meaningless.
+*          ILO and IHI mark the rows and columns of H which are in
+*          Hessenberg form.  It is assumed that A is already upper
+*          triangular in rows and columns 1:ILO-1 and IHI+1:N.
+*          If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0.
+*
+*  H       (input/output) REAL array, dimension (LDH, N)
+*          On entry, the N-by-N upper Hessenberg matrix H.
+*          On exit, if JOB = 'S', H contains the upper quasi-triangular
+*          matrix S from the generalized Schur factorization;
+*          2-by-2 diagonal blocks (corresponding to complex conjugate
+*          pairs of eigenvalues) are returned in standard form, with
+*          H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0.
+*          If JOB = 'E', the diagonal blocks of H match those of S, but
+*          the rest of H is unspecified.
+*
+*  LDH     (input) INTEGER
+*          The leading dimension of the array H.  LDH >= max( 1, N ).
+*
+*  T       (input/output) REAL array, dimension (LDT, N)
+*          On entry, the N-by-N upper triangular matrix T.
+*          On exit, if JOB = 'S', T contains the upper triangular
+*          matrix P from the generalized Schur factorization;
+*          2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S
+*          are reduced to positive diagonal form, i.e., if H(j+1,j) is
+*          non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and
+*          T(j+1,j+1) > 0.
+*          If JOB = 'E', the diagonal blocks of T match those of P, but
+*          the rest of T is unspecified.
 *
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max( 1, N ).
+*  LDT     (input) INTEGER
+*          The leading dimension of the array T.  LDT >= max( 1, N ).
 *
 *  ALPHAR  (output) REAL array, dimension (N)
-*          ALPHAR(1:N) will be set to real parts of the diagonal
-*          elements of A that would result from reducing A and B to
-*          Schur form and then further reducing them both to triangular
-*          form using unitary transformations s.t. the diagonal of B
-*          was non-negative real.  Thus, if A(j,j) is in a 1-by-1 block
-*          (i.e., A(j+1,j)=A(j,j+1)=0), then ALPHAR(j)=A(j,j).
-*          Note that the (real or complex) values
-*          (ALPHAR(j) + i*ALPHAI(j))/BETA(j), j=1,...,N, are the
-*          generalized eigenvalues of the matrix pencil A - wB.
+*          The real parts of each scalar alpha defining an eigenvalue
+*          of GNEP.
 *
 *  ALPHAI  (output) REAL array, dimension (N)
-*          ALPHAI(1:N) will be set to imaginary parts of the diagonal
-*          elements of A that would result from reducing A and B to
-*          Schur form and then further reducing them both to triangular
-*          form using unitary transformations s.t. the diagonal of B
-*          was non-negative real.  Thus, if A(j,j) is in a 1-by-1 block
-*          (i.e., A(j+1,j)=A(j,j+1)=0), then ALPHAR(j)=0.
-*          Note that the (real or complex) values
-*          (ALPHAR(j) + i*ALPHAI(j))/BETA(j), j=1,...,N, are the
-*          generalized eigenvalues of the matrix pencil A - wB.
+*          The imaginary parts of each scalar alpha defining an
+*          eigenvalue of GNEP.
+*          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
+*          positive, then the j-th and (j+1)-st eigenvalues are a
+*          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
 *
 *  BETA    (output) REAL array, dimension (N)
-*          BETA(1:N) will be set to the (real) diagonal elements of B
-*          that would result from reducing A and B to Schur form and
-*          then further reducing them both to triangular form using
-*          unitary transformations s.t. the diagonal of B was
-*          non-negative real.  Thus, if A(j,j) is in a 1-by-1 block
-*          (i.e., A(j+1,j)=A(j,j+1)=0), then BETA(j)=B(j,j).
-*          Note that the (real or complex) values
-*          (ALPHAR(j) + i*ALPHAI(j))/BETA(j), j=1,...,N, are the
-*          generalized eigenvalues of the matrix pencil A - wB.
-*          (Note that BETA(1:N) will always be non-negative, and no
-*          BETAI is necessary.)
+*          The scalars beta that define the eigenvalues of GNEP.
+*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
+*          beta = BETA(j) represent the j-th eigenvalue of the matrix
+*          pair (A,B), in one of the forms lambda = alpha/beta or
+*          mu = beta/alpha.  Since either lambda or mu may overflow,
+*          they should not, in general, be computed.
 *
 *  Q       (input/output) REAL array, dimension (LDQ, N)
-*          If COMPQ='N', then Q will not be referenced.
-*          If COMPQ='V' or 'I', then the transpose of the orthogonal
-*             transformations which are applied to A and B on the left
-*             will be applied to the array Q on the right.
+*          On entry, if COMPZ = 'V', the orthogonal matrix Q1 used in
+*          the reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the orthogonal matrix of left Schur
+*          vectors of (H,T), and if COMPZ = 'V', the orthogonal matrix
+*          of left Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
 *
 *  LDQ     (input) INTEGER
 *          The leading dimension of the array Q.  LDQ >= 1.
 *          If COMPQ='V' or 'I', then LDQ >= N.
 *
 *  Z       (input/output) REAL array, dimension (LDZ, N)
-*          If COMPZ='N', then Z will not be referenced.
-*          If COMPZ='V' or 'I', then the orthogonal transformations
-*             which are applied to A and B on the right will be applied
-*             to the array Z on the right.
+*          On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in
+*          the reduction of (A,B) to generalized Hessenberg form.
+*          On exit, if COMPZ = 'I', the orthogonal matrix of
+*          right Schur vectors of (H,T), and if COMPZ = 'V', the
+*          orthogonal matrix of right Schur vectors of (A,B).
+*          Not referenced if COMPZ = 'N'.
 *
 *  LDZ     (input) INTEGER
 *          The leading dimension of the array Z.  LDZ >= 1.
@@ -187,13 +190,12 @@
 *  INFO    (output) INTEGER
 *          = 0: successful exit
 *          < 0: if INFO = -i, the i-th argument had an illegal value
-*          = 1,...,N: the QZ iteration did not converge.  (A,B) is not
+*          = 1,...,N: the QZ iteration did not converge.  (H,T) is not
 *                     in Schur form, but ALPHAR(i), ALPHAI(i), and
 *                     BETA(i), i=INFO+1,...,N should be correct.
-*          = N+1,...,2*N: the shift calculation failed.  (A,B) is not
+*          = N+1,...,2*N: the shift calculation failed.  (H,T) is not
 *                     in Schur form, but ALPHAR(i), ALPHAI(i), and
 *                     BETA(i), i=INFO-N+1,...,N should be correct.
-*          > 2*N:     various "impossible" errors.
 *
 *  Further Details
 *  ===============
@@ -225,7 +227,7 @@
      $                   B1R, B22, B2A, B2I, B2R, BN, BNORM, BSCALE,
      $                   BTOL, C, C11I, C11R, C12, C21, C22I, C22R, CL,
      $                   CQ, CR, CZ, ESHIFT, S, S1, S1INV, S2, SAFMAX,
-     $                   SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T,
+     $                   SAFMIN, SCALE, SL, SQI, SQR, SR, SZI, SZR, T1,
      $                   TAU, TEMP, TEMP2, TEMPI, TEMPR, U1, U12, U12L,
      $                   U2, ULP, VS, W11, W12, W21, W22, WABS, WI, WR,
      $                   WR2
@@ -302,9 +304,9 @@
          INFO = -5
       ELSE IF( IHI.GT.N .OR. IHI.LT.ILO-1 ) THEN
          INFO = -6
-      ELSE IF( LDA.LT.N ) THEN
+      ELSE IF( LDH.LT.N ) THEN
          INFO = -8
-      ELSE IF( LDB.LT.N ) THEN
+      ELSE IF( LDT.LT.N ) THEN
          INFO = -10
       ELSE IF( LDQ.LT.1 .OR. ( ILQ .AND. LDQ.LT.N ) ) THEN
          INFO = -15
@@ -340,8 +342,8 @@
       SAFMIN = SLAMCH( 'S' )
       SAFMAX = ONE / SAFMIN
       ULP = SLAMCH( 'E' )*SLAMCH( 'B' )
-      ANORM = SLANHS( 'F', IN, A( ILO, ILO ), LDA, WORK )
-      BNORM = SLANHS( 'F', IN, B( ILO, ILO ), LDB, WORK )
+      ANORM = SLANHS( 'F', IN, H( ILO, ILO ), LDH, WORK )
+      BNORM = SLANHS( 'F', IN, T( ILO, ILO ), LDT, WORK )
       ATOL = MAX( SAFMIN, ULP*ANORM )
       BTOL = MAX( SAFMIN, ULP*BNORM )
       ASCALE = ONE / MAX( SAFMIN, ANORM )
@@ -350,15 +352,15 @@
 *     Set Eigenvalues IHI+1:N
 *
       DO 30 J = IHI + 1, N
-         IF( B( J, J ).LT.ZERO ) THEN
+         IF( T( J, J ).LT.ZERO ) THEN
             IF( ILSCHR ) THEN
                DO 10 JR = 1, J
-                  A( JR, J ) = -A( JR, J )
-                  B( JR, J ) = -B( JR, J )
+                  H( JR, J ) = -H( JR, J )
+                  T( JR, J ) = -T( JR, J )
    10          CONTINUE
             ELSE
-               A( J, J ) = -A( J, J )
-               B( J, J ) = -B( J, J )
+               H( J, J ) = -H( J, J )
+               T( J, J ) = -T( J, J )
             END IF
             IF( ILZ ) THEN
                DO 20 JR = 1, N
@@ -366,9 +368,9 @@
    20          CONTINUE
             END IF
          END IF
-         ALPHAR( J ) = A( J, J )
+         ALPHAR( J ) = H( J, J )
          ALPHAI( J ) = ZERO
-         BETA( J ) = B( J, J )
+         BETA( J ) = T( J, J )
    30 CONTINUE
 *
 *     If IHI < ILO, skip QZ steps
@@ -408,8 +410,8 @@
 *        Split the matrix if possible.
 *
 *        Two tests:
-*           1: A(j,j-1)=0  or  j=ILO
-*           2: B(j,j)=0
+*           1: H(j,j-1)=0  or  j=ILO
+*           2: T(j,j)=0
 *
          IF( ILAST.EQ.ILO ) THEN
 *
@@ -417,14 +419,14 @@
 *
             GO TO 80
          ELSE
-            IF( ABS( A( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
-               A( ILAST, ILAST-1 ) = ZERO
+            IF( ABS( H( ILAST, ILAST-1 ) ).LE.ATOL ) THEN
+               H( ILAST, ILAST-1 ) = ZERO
                GO TO 80
             END IF
          END IF
 *
-         IF( ABS( B( ILAST, ILAST ) ).LE.BTOL ) THEN
-            B( ILAST, ILAST ) = ZERO
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
+            T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
 *
@@ -432,36 +434,36 @@
 *
          DO 60 J = ILAST - 1, ILO, -1
 *
-*           Test 1: for A(j,j-1)=0 or j=ILO
+*           Test 1: for H(j,j-1)=0 or j=ILO
 *
             IF( J.EQ.ILO ) THEN
                ILAZRO = .TRUE.
             ELSE
-               IF( ABS( A( J, J-1 ) ).LE.ATOL ) THEN
-                  A( J, J-1 ) = ZERO
+               IF( ABS( H( J, J-1 ) ).LE.ATOL ) THEN
+                  H( J, J-1 ) = ZERO
                   ILAZRO = .TRUE.
                ELSE
                   ILAZRO = .FALSE.
                END IF
             END IF
 *
-*           Test 2: for B(j,j)=0
+*           Test 2: for T(j,j)=0
 *
-            IF( ABS( B( J, J ) ).LT.BTOL ) THEN
-               B( J, J ) = ZERO
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
+               T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A
 *
                ILAZR2 = .FALSE.
                IF( .NOT.ILAZRO ) THEN
-                  TEMP = ABS( A( J, J-1 ) )
-                  TEMP2 = ABS( A( J, J ) )
+                  TEMP = ABS( H( J, J-1 ) )
+                  TEMP2 = ABS( H( J, J ) )
                   TEMPR = MAX( TEMP, TEMP2 )
                   IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
                      TEMP = TEMP / TEMPR
                      TEMP2 = TEMP2 / TEMPR
                   END IF
-                  IF( TEMP*( ASCALE*ABS( A( J+1, J ) ) ).LE.TEMP2*
+                  IF( TEMP*( ASCALE*ABS( H( J+1, J ) ) ).LE.TEMP2*
      $                ( ASCALE*ATOL ) )ILAZR2 = .TRUE.
                END IF
 *
@@ -473,21 +475,21 @@
 *
                IF( ILAZRO .OR. ILAZR2 ) THEN
                   DO 40 JCH = J, ILAST - 1
-                     TEMP = A( JCH, JCH )
-                     CALL SLARTG( TEMP, A( JCH+1, JCH ), C, S,
-     $                            A( JCH, JCH ) )
-                     A( JCH+1, JCH ) = ZERO
-                     CALL SROT( ILASTM-JCH, A( JCH, JCH+1 ), LDA,
-     $                          A( JCH+1, JCH+1 ), LDA, C, S )
-                     CALL SROT( ILASTM-JCH, B( JCH, JCH+1 ), LDB,
-     $                          B( JCH+1, JCH+1 ), LDB, C, S )
+                     TEMP = H( JCH, JCH )
+                     CALL SLARTG( TEMP, H( JCH+1, JCH ), C, S,
+     $                            H( JCH, JCH ) )
+                     H( JCH+1, JCH ) = ZERO
+                     CALL SROT( ILASTM-JCH, H( JCH, JCH+1 ), LDH,
+     $                          H( JCH+1, JCH+1 ), LDH, C, S )
+                     CALL SROT( ILASTM-JCH, T( JCH, JCH+1 ), LDT,
+     $                          T( JCH+1, JCH+1 ), LDT, C, S )
                      IF( ILQ )
      $                  CALL SROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
      $                             C, S )
                      IF( ILAZR2 )
-     $                  A( JCH, JCH-1 ) = A( JCH, JCH-1 )*C
+     $                  H( JCH, JCH-1 ) = H( JCH, JCH-1 )*C
                      ILAZR2 = .FALSE.
-                     IF( ABS( B( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
+                     IF( ABS( T( JCH+1, JCH+1 ) ).GE.BTOL ) THEN
                         IF( JCH+1.GE.ILAST ) THEN
                            GO TO 80
                         ELSE
@@ -495,35 +497,35 @@
                            GO TO 110
                         END IF
                      END IF
-                     B( JCH+1, JCH+1 ) = ZERO
+                     T( JCH+1, JCH+1 ) = ZERO
    40             CONTINUE
                   GO TO 70
                ELSE
 *
-*                 Only test 2 passed -- chase the zero to B(ILAST,ILAST)
-*                 Then process as in the case B(ILAST,ILAST)=0
+*                 Only test 2 passed -- chase the zero to T(ILAST,ILAST)
+*                 Then process as in the case T(ILAST,ILAST)=0
 *
                   DO 50 JCH = J, ILAST - 1
-                     TEMP = B( JCH, JCH+1 )
-                     CALL SLARTG( TEMP, B( JCH+1, JCH+1 ), C, S,
-     $                            B( JCH, JCH+1 ) )
-                     B( JCH+1, JCH+1 ) = ZERO
+                     TEMP = T( JCH, JCH+1 )
+                     CALL SLARTG( TEMP, T( JCH+1, JCH+1 ), C, S,
+     $                            T( JCH, JCH+1 ) )
+                     T( JCH+1, JCH+1 ) = ZERO
                      IF( JCH.LT.ILASTM-1 )
-     $                  CALL SROT( ILASTM-JCH-1, B( JCH, JCH+2 ), LDB,
-     $                             B( JCH+1, JCH+2 ), LDB, C, S )
-                     CALL SROT( ILASTM-JCH+2, A( JCH, JCH-1 ), LDA,
-     $                          A( JCH+1, JCH-1 ), LDA, C, S )
+     $                  CALL SROT( ILASTM-JCH-1, T( JCH, JCH+2 ), LDT,
+     $                             T( JCH+1, JCH+2 ), LDT, C, S )
+                     CALL SROT( ILASTM-JCH+2, H( JCH, JCH-1 ), LDH,
+     $                          H( JCH+1, JCH-1 ), LDH, C, S )
                      IF( ILQ )
      $                  CALL SROT( N, Q( 1, JCH ), 1, Q( 1, JCH+1 ), 1,
      $                             C, S )
-                     TEMP = A( JCH+1, JCH )
-                     CALL SLARTG( TEMP, A( JCH+1, JCH-1 ), C, S,
-     $                            A( JCH+1, JCH ) )
-                     A( JCH+1, JCH-1 ) = ZERO
-                     CALL SROT( JCH+1-IFRSTM, A( IFRSTM, JCH ), 1,
-     $                          A( IFRSTM, JCH-1 ), 1, C, S )
-                     CALL SROT( JCH-IFRSTM, B( IFRSTM, JCH ), 1,
-     $                          B( IFRSTM, JCH-1 ), 1, C, S )
+                     TEMP = H( JCH+1, JCH )
+                     CALL SLARTG( TEMP, H( JCH+1, JCH-1 ), C, S,
+     $                            H( JCH+1, JCH ) )
+                     H( JCH+1, JCH-1 ) = ZERO
+                     CALL SROT( JCH+1-IFRSTM, H( IFRSTM, JCH ), 1,
+     $                          H( IFRSTM, JCH-1 ), 1, C, S )
+                     CALL SROT( JCH-IFRSTM, T( IFRSTM, JCH ), 1,
+     $                          T( IFRSTM, JCH-1 ), 1, C, S )
                      IF( ILZ )
      $                  CALL SROT( N, Z( 1, JCH ), 1, Z( 1, JCH-1 ), 1,
      $                             C, S )
@@ -547,34 +549,34 @@
          INFO = N + 1
          GO TO 420
 *
-*        B(ILAST,ILAST)=0 -- clear A(ILAST,ILAST-1) to split off a
+*        T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a
 *        1x1 block.
 *
    70    CONTINUE
-         TEMP = A( ILAST, ILAST )
-         CALL SLARTG( TEMP, A( ILAST, ILAST-1 ), C, S,
-     $                A( ILAST, ILAST ) )
-         A( ILAST, ILAST-1 ) = ZERO
-         CALL SROT( ILAST-IFRSTM, A( IFRSTM, ILAST ), 1,
-     $              A( IFRSTM, ILAST-1 ), 1, C, S )
-         CALL SROT( ILAST-IFRSTM, B( IFRSTM, ILAST ), 1,
-     $              B( IFRSTM, ILAST-1 ), 1, C, S )
+         TEMP = H( ILAST, ILAST )
+         CALL SLARTG( TEMP, H( ILAST, ILAST-1 ), C, S,
+     $                H( ILAST, ILAST ) )
+         H( ILAST, ILAST-1 ) = ZERO
+         CALL SROT( ILAST-IFRSTM, H( IFRSTM, ILAST ), 1,
+     $              H( IFRSTM, ILAST-1 ), 1, C, S )
+         CALL SROT( ILAST-IFRSTM, T( IFRSTM, ILAST ), 1,
+     $              T( IFRSTM, ILAST-1 ), 1, C, S )
          IF( ILZ )
      $      CALL SROT( N, Z( 1, ILAST ), 1, Z( 1, ILAST-1 ), 1, C, S )
 *
-*        A(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI,
+*        H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI,
 *                              and BETA
 *
    80    CONTINUE
-         IF( B( ILAST, ILAST ).LT.ZERO ) THEN
+         IF( T( ILAST, ILAST ).LT.ZERO ) THEN
             IF( ILSCHR ) THEN
                DO 90 J = IFRSTM, ILAST
-                  A( J, ILAST ) = -A( J, ILAST )
-                  B( J, ILAST ) = -B( J, ILAST )
+                  H( J, ILAST ) = -H( J, ILAST )
+                  T( J, ILAST ) = -T( J, ILAST )
    90          CONTINUE
             ELSE
-               A( ILAST, ILAST ) = -A( ILAST, ILAST )
-               B( ILAST, ILAST ) = -B( ILAST, ILAST )
+               H( ILAST, ILAST ) = -H( ILAST, ILAST )
+               T( ILAST, ILAST ) = -T( ILAST, ILAST )
             END IF
             IF( ILZ ) THEN
                DO 100 J = 1, N
@@ -582,9 +584,9 @@
   100          CONTINUE
             END IF
          END IF
-         ALPHAR( ILAST ) = A( ILAST, ILAST )
+         ALPHAR( ILAST ) = H( ILAST, ILAST )
          ALPHAI( ILAST ) = ZERO
-         BETA( ILAST ) = B( ILAST, ILAST )
+         BETA( ILAST ) = T( ILAST, ILAST )
 *
 *        Go to next block -- exit if finished.
 *
@@ -617,7 +619,7 @@
 *        Compute single shifts.
 *
 *        At this point, IFIRST < ILAST, and the diagonal elements of
-*        B(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
+*        T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in
 *        magnitude)
 *
          IF( ( IITER / 10 )*10.EQ.IITER ) THEN
@@ -625,10 +627,10 @@
 *           Exceptional shift.  Chosen for no particularly good reason.
 *           (Single shift only.)
 *
-            IF( ( REAL( MAXIT )*SAFMIN )*ABS( A( ILAST-1, ILAST ) ).LT.
-     $          ABS( B( ILAST-1, ILAST-1 ) ) ) THEN
-               ESHIFT = ESHIFT + A( ILAST-1, ILAST ) /
-     $                  B( ILAST-1, ILAST-1 )
+            IF( ( REAL( MAXIT )*SAFMIN )*ABS( H( ILAST-1, ILAST ) ).LT.
+     $          ABS( T( ILAST-1, ILAST-1 ) ) ) THEN
+               ESHIFT = ESHIFT + H( ILAST-1, ILAST ) /
+     $                  T( ILAST-1, ILAST-1 )
             ELSE
                ESHIFT = ESHIFT + ONE / ( SAFMIN*REAL( MAXIT ) )
             END IF
@@ -641,8 +643,8 @@
 *           bottom-right 2x2 block of A and B. The first eigenvalue
 *           returned by SLAG2 is the Wilkinson shift (AEP p.512),
 *
-            CALL SLAG2( A( ILAST-1, ILAST-1 ), LDA,
-     $                  B( ILAST-1, ILAST-1 ), LDB, SAFMIN*SAFETY, S1,
+            CALL SLAG2( H( ILAST-1, ILAST-1 ), LDH,
+     $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
      $                  S2, WR, WR2, WI )
 *
             TEMP = MAX( S1, SAFMIN*MAX( ONE, ABS( WR ), ABS( WI ) ) )
@@ -669,14 +671,14 @@
 *
          DO 120 J = ILAST - 1, IFIRST + 1, -1
             ISTART = J
-            TEMP = ABS( S1*A( J, J-1 ) )
-            TEMP2 = ABS( S1*A( J, J )-WR*B( J, J ) )
+            TEMP = ABS( S1*H( J, J-1 ) )
+            TEMP2 = ABS( S1*H( J, J )-WR*T( J, J ) )
             TEMPR = MAX( TEMP, TEMP2 )
             IF( TEMPR.LT.ONE .AND. TEMPR.NE.ZERO ) THEN
                TEMP = TEMP / TEMPR
                TEMP2 = TEMP2 / TEMPR
             END IF
-            IF( ABS( ( ASCALE*A( J+1, J ) )*TEMP ).LE.( ASCALE*ATOL )*
+            IF( ABS( ( ASCALE*H( J+1, J ) )*TEMP ).LE.( ASCALE*ATOL )*
      $          TEMP2 )GO TO 130
   120    CONTINUE
 *
@@ -687,26 +689,26 @@
 *
 *        Initial Q
 *
-         TEMP = S1*A( ISTART, ISTART ) - WR*B( ISTART, ISTART )
-         TEMP2 = S1*A( ISTART+1, ISTART )
+         TEMP = S1*H( ISTART, ISTART ) - WR*T( ISTART, ISTART )
+         TEMP2 = S1*H( ISTART+1, ISTART )
          CALL SLARTG( TEMP, TEMP2, C, S, TEMPR )
 *
 *        Sweep
 *
          DO 190 J = ISTART, ILAST - 1
             IF( J.GT.ISTART ) THEN
-               TEMP = A( J, J-1 )
-               CALL SLARTG( TEMP, A( J+1, J-1 ), C, S, A( J, J-1 ) )
-               A( J+1, J-1 ) = ZERO
+               TEMP = H( J, J-1 )
+               CALL SLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+               H( J+1, J-1 ) = ZERO
             END IF
 *
             DO 140 JC = J, ILASTM
-               TEMP = C*A( J, JC ) + S*A( J+1, JC )
-               A( J+1, JC ) = -S*A( J, JC ) + C*A( J+1, JC )
-               A( J, JC ) = TEMP
-               TEMP2 = C*B( J, JC ) + S*B( J+1, JC )
-               B( J+1, JC ) = -S*B( J, JC ) + C*B( J+1, JC )
-               B( J, JC ) = TEMP2
+               TEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = TEMP
+               TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = TEMP2
   140       CONTINUE
             IF( ILQ ) THEN
                DO 150 JR = 1, N
@@ -716,19 +718,19 @@
   150          CONTINUE
             END IF
 *
-            TEMP = B( J+1, J+1 )
-            CALL SLARTG( TEMP, B( J+1, J ), C, S, B( J+1, J+1 ) )
-            B( J+1, J ) = ZERO
+            TEMP = T( J+1, J+1 )
+            CALL SLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = ZERO
 *
             DO 160 JR = IFRSTM, MIN( J+2, ILAST )
-               TEMP = C*A( JR, J+1 ) + S*A( JR, J )
-               A( JR, J ) = -S*A( JR, J+1 ) + C*A( JR, J )
-               A( JR, J+1 ) = TEMP
+               TEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = TEMP
   160       CONTINUE
             DO 170 JR = IFRSTM, J
-               TEMP = C*B( JR, J+1 ) + S*B( JR, J )
-               B( JR, J ) = -S*B( JR, J+1 ) + C*B( JR, J )
-               B( JR, J+1 ) = TEMP
+               TEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = TEMP
   170       CONTINUE
             IF( ILZ ) THEN
                DO 180 JR = 1, N
@@ -759,8 +761,8 @@
 *                   B = (         )  with B11 non-negative.
 *                       (  0  B22 )
 *
-            CALL SLASV2( B( ILAST-1, ILAST-1 ), B( ILAST-1, ILAST ),
-     $                   B( ILAST, ILAST ), B22, B11, SR, CR, SL, CL )
+            CALL SLASV2( T( ILAST-1, ILAST-1 ), T( ILAST-1, ILAST ),
+     $                   T( ILAST, ILAST ), B22, B11, SR, CR, SL, CL )
 *
             IF( B11.LT.ZERO ) THEN
                CR = -CR
@@ -769,17 +771,17 @@
                B22 = -B22
             END IF
 *
-            CALL SROT( ILASTM+1-IFIRST, A( ILAST-1, ILAST-1 ), LDA,
-     $                 A( ILAST, ILAST-1 ), LDA, CL, SL )
-            CALL SROT( ILAST+1-IFRSTM, A( IFRSTM, ILAST-1 ), 1,
-     $                 A( IFRSTM, ILAST ), 1, CR, SR )
+            CALL SROT( ILASTM+1-IFIRST, H( ILAST-1, ILAST-1 ), LDH,
+     $                 H( ILAST, ILAST-1 ), LDH, CL, SL )
+            CALL SROT( ILAST+1-IFRSTM, H( IFRSTM, ILAST-1 ), 1,
+     $                 H( IFRSTM, ILAST ), 1, CR, SR )
 *
             IF( ILAST.LT.ILASTM )
-     $         CALL SROT( ILASTM-ILAST, B( ILAST-1, ILAST+1 ), LDB,
-     $                    B( ILAST, ILAST+1 ), LDA, CL, SL )
+     $         CALL SROT( ILASTM-ILAST, T( ILAST-1, ILAST+1 ), LDT,
+     $                    T( ILAST, ILAST+1 ), LDH, CL, SL )
             IF( IFRSTM.LT.ILAST-1 )
-     $         CALL SROT( IFIRST-IFRSTM, B( IFRSTM, ILAST-1 ), 1,
-     $                    B( IFRSTM, ILAST ), 1, CR, SR )
+     $         CALL SROT( IFIRST-IFRSTM, T( IFRSTM, ILAST-1 ), 1,
+     $                    T( IFRSTM, ILAST ), 1, CR, SR )
 *
             IF( ILQ )
      $         CALL SROT( N, Q( 1, ILAST-1 ), 1, Q( 1, ILAST ), 1, CL,
@@ -788,17 +790,17 @@
      $         CALL SROT( N, Z( 1, ILAST-1 ), 1, Z( 1, ILAST ), 1, CR,
      $                    SR )
 *
-            B( ILAST-1, ILAST-1 ) = B11
-            B( ILAST-1, ILAST ) = ZERO
-            B( ILAST, ILAST-1 ) = ZERO
-            B( ILAST, ILAST ) = B22
+            T( ILAST-1, ILAST-1 ) = B11
+            T( ILAST-1, ILAST ) = ZERO
+            T( ILAST, ILAST-1 ) = ZERO
+            T( ILAST, ILAST ) = B22
 *
 *           If B22 is negative, negate column ILAST
 *
             IF( B22.LT.ZERO ) THEN
                DO 210 J = IFRSTM, ILAST
-                  A( J, ILAST ) = -A( J, ILAST )
-                  B( J, ILAST ) = -B( J, ILAST )
+                  H( J, ILAST ) = -H( J, ILAST )
+                  T( J, ILAST ) = -T( J, ILAST )
   210          CONTINUE
 *
                IF( ILZ ) THEN
@@ -812,8 +814,8 @@
 *
 *           Recompute shift
 *
-            CALL SLAG2( A( ILAST-1, ILAST-1 ), LDA,
-     $                  B( ILAST-1, ILAST-1 ), LDB, SAFMIN*SAFETY, S1,
+            CALL SLAG2( H( ILAST-1, ILAST-1 ), LDH,
+     $                  T( ILAST-1, ILAST-1 ), LDT, SAFMIN*SAFETY, S1,
      $                  TEMP, WR, TEMP2, WI )
 *
 *           If standardization has perturbed the shift onto real line,
@@ -825,10 +827,10 @@
 *
 *           Do EISPACK (QZVAL) computation of alpha and beta
 *
-            A11 = A( ILAST-1, ILAST-1 )
-            A21 = A( ILAST, ILAST-1 )
-            A12 = A( ILAST-1, ILAST )
-            A22 = A( ILAST, ILAST )
+            A11 = H( ILAST-1, ILAST-1 )
+            A21 = H( ILAST, ILAST-1 )
+            A12 = H( ILAST-1, ILAST )
+            A22 = H( ILAST, ILAST )
 *
 *           Compute complex Givens rotation on right
 *           (Assume some element of C = (sA - wB) > unfl )
@@ -845,10 +847,10 @@
 *
             IF( ABS( C11R )+ABS( C11I )+ABS( C12 ).GT.ABS( C21 )+
      $          ABS( C22R )+ABS( C22I ) ) THEN
-               T = SLAPY3( C12, C11R, C11I )
-               CZ = C12 / T
-               SZR = -C11R / T
-               SZI = -C11I / T
+               T1 = SLAPY3( C12, C11R, C11I )
+               CZ = C12 / T1
+               SZR = -C11R / T1
+               SZI = -C11I / T1
             ELSE
                CZ = SLAPY2( C22R, C22I )
                IF( CZ.LE.SAFMIN ) THEN
@@ -858,10 +860,10 @@
                ELSE
                   TEMPR = C22R / CZ
                   TEMPI = C22I / CZ
-                  T = SLAPY2( CZ, C21 )
-                  CZ = CZ / T
-                  SZR = -C21*TEMPR / T
-                  SZI = C21*TEMPI / T
+                  T1 = SLAPY2( CZ, C21 )
+                  CZ = CZ / T1
+                  SZR = -C21*TEMPR / T1
+                  SZI = C21*TEMPI / T1
                END IF
             END IF
 *
@@ -895,10 +897,10 @@
                   SQI = TEMPI*A2R - TEMPR*A2I
                END IF
             END IF
-            T = SLAPY3( CQ, SQR, SQI )
-            CQ = CQ / T
-            SQR = SQR / T
-            SQI = SQI / T
+            T1 = SLAPY3( CQ, SQR, SQI )
+            CQ = CQ / T1
+            SQR = SQR / T1
+            SQI = SQI / T1
 *
 *           Compute diagonal elements of QBZ
 *
@@ -950,26 +952,26 @@
 *
 *           We assume that the block is at least 3x3
 *
-            AD11 = ( ASCALE*A( ILAST-1, ILAST-1 ) ) /
-     $             ( BSCALE*B( ILAST-1, ILAST-1 ) )
-            AD21 = ( ASCALE*A( ILAST, ILAST-1 ) ) /
-     $             ( BSCALE*B( ILAST-1, ILAST-1 ) )
-            AD12 = ( ASCALE*A( ILAST-1, ILAST ) ) /
-     $             ( BSCALE*B( ILAST, ILAST ) )
-            AD22 = ( ASCALE*A( ILAST, ILAST ) ) /
-     $             ( BSCALE*B( ILAST, ILAST ) )
-            U12 = B( ILAST-1, ILAST ) / B( ILAST, ILAST )
-            AD11L = ( ASCALE*A( IFIRST, IFIRST ) ) /
-     $              ( BSCALE*B( IFIRST, IFIRST ) )
-            AD21L = ( ASCALE*A( IFIRST+1, IFIRST ) ) /
-     $              ( BSCALE*B( IFIRST, IFIRST ) )
-            AD12L = ( ASCALE*A( IFIRST, IFIRST+1 ) ) /
-     $              ( BSCALE*B( IFIRST+1, IFIRST+1 ) )
-            AD22L = ( ASCALE*A( IFIRST+1, IFIRST+1 ) ) /
-     $              ( BSCALE*B( IFIRST+1, IFIRST+1 ) )
-            AD32L = ( ASCALE*A( IFIRST+2, IFIRST+1 ) ) /
-     $              ( BSCALE*B( IFIRST+1, IFIRST+1 ) )
-            U12L = B( IFIRST, IFIRST+1 ) / B( IFIRST+1, IFIRST+1 )
+            AD11 = ( ASCALE*H( ILAST-1, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD21 = ( ASCALE*H( ILAST, ILAST-1 ) ) /
+     $             ( BSCALE*T( ILAST-1, ILAST-1 ) )
+            AD12 = ( ASCALE*H( ILAST-1, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            AD22 = ( ASCALE*H( ILAST, ILAST ) ) /
+     $             ( BSCALE*T( ILAST, ILAST ) )
+            U12 = T( ILAST-1, ILAST ) / T( ILAST, ILAST )
+            AD11L = ( ASCALE*H( IFIRST, IFIRST ) ) /
+     $              ( BSCALE*T( IFIRST, IFIRST ) )
+            AD21L = ( ASCALE*H( IFIRST+1, IFIRST ) ) /
+     $              ( BSCALE*T( IFIRST, IFIRST ) )
+            AD12L = ( ASCALE*H( IFIRST, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            AD22L = ( ASCALE*H( IFIRST+1, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            AD32L = ( ASCALE*H( IFIRST+2, IFIRST+1 ) ) /
+     $              ( BSCALE*T( IFIRST+1, IFIRST+1 ) )
+            U12L = T( IFIRST, IFIRST+1 ) / T( IFIRST+1, IFIRST+1 )
 *
             V( 1 ) = ( AD11-AD11L )*( AD22-AD11L ) - AD12*AD21 +
      $               AD21*U12*AD11L + ( AD12L-AD11L*U12L )*AD21L
@@ -991,27 +993,27 @@
 *              Zero (j-1)st column of A
 *
                IF( J.GT.ISTART ) THEN
-                  V( 1 ) = A( J, J-1 )
-                  V( 2 ) = A( J+1, J-1 )
-                  V( 3 ) = A( J+2, J-1 )
+                  V( 1 ) = H( J, J-1 )
+                  V( 2 ) = H( J+1, J-1 )
+                  V( 3 ) = H( J+2, J-1 )
 *
-                  CALL SLARFG( 3, A( J, J-1 ), V( 2 ), 1, TAU )
+                  CALL SLARFG( 3, H( J, J-1 ), V( 2 ), 1, TAU )
                   V( 1 ) = ONE
-                  A( J+1, J-1 ) = ZERO
-                  A( J+2, J-1 ) = ZERO
+                  H( J+1, J-1 ) = ZERO
+                  H( J+2, J-1 ) = ZERO
                END IF
 *
                DO 230 JC = J, ILASTM
-                  TEMP = TAU*( A( J, JC )+V( 2 )*A( J+1, JC )+V( 3 )*
-     $                   A( J+2, JC ) )
-                  A( J, JC ) = A( J, JC ) - TEMP
-                  A( J+1, JC ) = A( J+1, JC ) - TEMP*V( 2 )
-                  A( J+2, JC ) = A( J+2, JC ) - TEMP*V( 3 )
-                  TEMP2 = TAU*( B( J, JC )+V( 2 )*B( J+1, JC )+V( 3 )*
-     $                    B( J+2, JC ) )
-                  B( J, JC ) = B( J, JC ) - TEMP2
-                  B( J+1, JC ) = B( J+1, JC ) - TEMP2*V( 2 )
-                  B( J+2, JC ) = B( J+2, JC ) - TEMP2*V( 3 )
+                  TEMP = TAU*( H( J, JC )+V( 2 )*H( J+1, JC )+V( 3 )*
+     $                   H( J+2, JC ) )
+                  H( J, JC ) = H( J, JC ) - TEMP
+                  H( J+1, JC ) = H( J+1, JC ) - TEMP*V( 2 )
+                  H( J+2, JC ) = H( J+2, JC ) - TEMP*V( 3 )
+                  TEMP2 = TAU*( T( J, JC )+V( 2 )*T( J+1, JC )+V( 3 )*
+     $                    T( J+2, JC ) )
+                  T( J, JC ) = T( J, JC ) - TEMP2
+                  T( J+1, JC ) = T( J+1, JC ) - TEMP2*V( 2 )
+                  T( J+2, JC ) = T( J+2, JC ) - TEMP2*V( 3 )
   230          CONTINUE
                IF( ILQ ) THEN
                   DO 240 JR = 1, N
@@ -1028,27 +1030,27 @@
 *              Swap rows to pivot
 *
                ILPIVT = .FALSE.
-               TEMP = MAX( ABS( B( J+1, J+1 ) ), ABS( B( J+1, J+2 ) ) )
-               TEMP2 = MAX( ABS( B( J+2, J+1 ) ), ABS( B( J+2, J+2 ) ) )
+               TEMP = MAX( ABS( T( J+1, J+1 ) ), ABS( T( J+1, J+2 ) ) )
+               TEMP2 = MAX( ABS( T( J+2, J+1 ) ), ABS( T( J+2, J+2 ) ) )
                IF( MAX( TEMP, TEMP2 ).LT.SAFMIN ) THEN
                   SCALE = ZERO
                   U1 = ONE
                   U2 = ZERO
                   GO TO 250
                ELSE IF( TEMP.GE.TEMP2 ) THEN
-                  W11 = B( J+1, J+1 )
-                  W21 = B( J+2, J+1 )
-                  W12 = B( J+1, J+2 )
-                  W22 = B( J+2, J+2 )
-                  U1 = B( J+1, J )
-                  U2 = B( J+2, J )
+                  W11 = T( J+1, J+1 )
+                  W21 = T( J+2, J+1 )
+                  W12 = T( J+1, J+2 )
+                  W22 = T( J+2, J+2 )
+                  U1 = T( J+1, J )
+                  U2 = T( J+2, J )
                ELSE
-                  W21 = B( J+1, J+1 )
-                  W11 = B( J+2, J+1 )
-                  W22 = B( J+1, J+2 )
-                  W12 = B( J+2, J+2 )
-                  U2 = B( J+1, J )
-                  U1 = B( J+2, J )
+                  W21 = T( J+1, J+1 )
+                  W11 = T( J+2, J+1 )
+                  W22 = T( J+1, J+2 )
+                  W12 = T( J+2, J+2 )
+                  U2 = T( J+1, J )
+                  U1 = T( J+2, J )
                END IF
 *
 *              Swap columns if nec.
@@ -1098,9 +1100,9 @@
 *
 *              Compute Householder Vector
 *
-               T = SQRT( SCALE**2+U1**2+U2**2 )
-               TAU = ONE + SCALE / T
-               VS = -ONE / ( SCALE+T )
+               T1 = SQRT( SCALE**2+U1**2+U2**2 )
+               TAU = ONE + SCALE / T1
+               VS = -ONE / ( SCALE+T1 )
                V( 1 ) = ONE
                V( 2 ) = VS*U1
                V( 3 ) = VS*U2
@@ -1108,18 +1110,18 @@
 *              Apply transformations from the right.
 *
                DO 260 JR = IFRSTM, MIN( J+3, ILAST )
-                  TEMP = TAU*( A( JR, J )+V( 2 )*A( JR, J+1 )+V( 3 )*
-     $                   A( JR, J+2 ) )
-                  A( JR, J ) = A( JR, J ) - TEMP
-                  A( JR, J+1 ) = A( JR, J+1 ) - TEMP*V( 2 )
-                  A( JR, J+2 ) = A( JR, J+2 ) - TEMP*V( 3 )
+                  TEMP = TAU*( H( JR, J )+V( 2 )*H( JR, J+1 )+V( 3 )*
+     $                   H( JR, J+2 ) )
+                  H( JR, J ) = H( JR, J ) - TEMP
+                  H( JR, J+1 ) = H( JR, J+1 ) - TEMP*V( 2 )
+                  H( JR, J+2 ) = H( JR, J+2 ) - TEMP*V( 3 )
   260          CONTINUE
                DO 270 JR = IFRSTM, J + 2
-                  TEMP = TAU*( B( JR, J )+V( 2 )*B( JR, J+1 )+V( 3 )*
-     $                   B( JR, J+2 ) )
-                  B( JR, J ) = B( JR, J ) - TEMP
-                  B( JR, J+1 ) = B( JR, J+1 ) - TEMP*V( 2 )
-                  B( JR, J+2 ) = B( JR, J+2 ) - TEMP*V( 3 )
+                  TEMP = TAU*( T( JR, J )+V( 2 )*T( JR, J+1 )+V( 3 )*
+     $                   T( JR, J+2 ) )
+                  T( JR, J ) = T( JR, J ) - TEMP
+                  T( JR, J+1 ) = T( JR, J+1 ) - TEMP*V( 2 )
+                  T( JR, J+2 ) = T( JR, J+2 ) - TEMP*V( 3 )
   270          CONTINUE
                IF( ILZ ) THEN
                   DO 280 JR = 1, N
@@ -1130,8 +1132,8 @@
                      Z( JR, J+2 ) = Z( JR, J+2 ) - TEMP*V( 3 )
   280             CONTINUE
                END IF
-               B( J+1, J ) = ZERO
-               B( J+2, J ) = ZERO
+               T( J+1, J ) = ZERO
+               T( J+2, J ) = ZERO
   290       CONTINUE
 *
 *           Last elements: Use Givens rotations
@@ -1139,17 +1141,17 @@
 *           Rotations from the left
 *
             J = ILAST - 1
-            TEMP = A( J, J-1 )
-            CALL SLARTG( TEMP, A( J+1, J-1 ), C, S, A( J, J-1 ) )
-            A( J+1, J-1 ) = ZERO
+            TEMP = H( J, J-1 )
+            CALL SLARTG( TEMP, H( J+1, J-1 ), C, S, H( J, J-1 ) )
+            H( J+1, J-1 ) = ZERO
 *
             DO 300 JC = J, ILASTM
-               TEMP = C*A( J, JC ) + S*A( J+1, JC )
-               A( J+1, JC ) = -S*A( J, JC ) + C*A( J+1, JC )
-               A( J, JC ) = TEMP
-               TEMP2 = C*B( J, JC ) + S*B( J+1, JC )
-               B( J+1, JC ) = -S*B( J, JC ) + C*B( J+1, JC )
-               B( J, JC ) = TEMP2
+               TEMP = C*H( J, JC ) + S*H( J+1, JC )
+               H( J+1, JC ) = -S*H( J, JC ) + C*H( J+1, JC )
+               H( J, JC ) = TEMP
+               TEMP2 = C*T( J, JC ) + S*T( J+1, JC )
+               T( J+1, JC ) = -S*T( J, JC ) + C*T( J+1, JC )
+               T( J, JC ) = TEMP2
   300       CONTINUE
             IF( ILQ ) THEN
                DO 310 JR = 1, N
@@ -1161,19 +1163,19 @@
 *
 *           Rotations from the right.
 *
-            TEMP = B( J+1, J+1 )
-            CALL SLARTG( TEMP, B( J+1, J ), C, S, B( J+1, J+1 ) )
-            B( J+1, J ) = ZERO
+            TEMP = T( J+1, J+1 )
+            CALL SLARTG( TEMP, T( J+1, J ), C, S, T( J+1, J+1 ) )
+            T( J+1, J ) = ZERO
 *
             DO 320 JR = IFRSTM, ILAST
-               TEMP = C*A( JR, J+1 ) + S*A( JR, J )
-               A( JR, J ) = -S*A( JR, J+1 ) + C*A( JR, J )
-               A( JR, J+1 ) = TEMP
+               TEMP = C*H( JR, J+1 ) + S*H( JR, J )
+               H( JR, J ) = -S*H( JR, J+1 ) + C*H( JR, J )
+               H( JR, J+1 ) = TEMP
   320       CONTINUE
             DO 330 JR = IFRSTM, ILAST - 1
-               TEMP = C*B( JR, J+1 ) + S*B( JR, J )
-               B( JR, J ) = -S*B( JR, J+1 ) + C*B( JR, J )
-               B( JR, J+1 ) = TEMP
+               TEMP = C*T( JR, J+1 ) + S*T( JR, J )
+               T( JR, J ) = -S*T( JR, J+1 ) + C*T( JR, J )
+               T( JR, J+1 ) = TEMP
   330       CONTINUE
             IF( ILZ ) THEN
                DO 340 JR = 1, N
@@ -1207,15 +1209,15 @@
 *     Set Eigenvalues 1:ILO-1
 *
       DO 410 J = 1, ILO - 1
-         IF( B( J, J ).LT.ZERO ) THEN
+         IF( T( J, J ).LT.ZERO ) THEN
             IF( ILSCHR ) THEN
                DO 390 JR = 1, J
-                  A( JR, J ) = -A( JR, J )
-                  B( JR, J ) = -B( JR, J )
+                  H( JR, J ) = -H( JR, J )
+                  T( JR, J ) = -T( JR, J )
   390          CONTINUE
             ELSE
-               A( J, J ) = -A( J, J )
-               B( J, J ) = -B( J, J )
+               H( J, J ) = -H( J, J )
+               T( J, J ) = -T( J, J )
             END IF
             IF( ILZ ) THEN
                DO 400 JR = 1, N
@@ -1223,9 +1225,9 @@
   400          CONTINUE
             END IF
          END IF
-         ALPHAR( J ) = A( J, J )
+         ALPHAR( J ) = H( J, J )
          ALPHAI( J ) = ZERO
-         BETA( J ) = B( J, J )
+         BETA( J ) = T( J, J )
   410 CONTINUE
 *
 *     Normal Termination
diff -uNr LAPACK.orig/SRC/slasr.f LAPACK/SRC/slasr.f
--- LAPACK.orig/SRC/slasr.f	Thu Nov  4 14:23:40 1999
+++ LAPACK/SRC/slasr.f	Fri May 25 16:12:26 2001
@@ -3,7 +3,7 @@
 *  -- LAPACK auxiliary routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     October 31, 1992
+*     May 3, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          DIRECT, PIVOT, SIDE
@@ -16,44 +16,77 @@
 *  Purpose
 *  =======
 *
-*  SLASR   performs the transformation
-*
-*     A := P*A,   when SIDE = 'L' or 'l'  (  Left-hand side )
-*
-*     A := A*P',  when SIDE = 'R' or 'r'  ( Right-hand side )
-*
-*  where A is an m by n real matrix and P is an orthogonal matrix,
-*  consisting of a sequence of plane rotations determined by the
-*  parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l'
-*  and z = n when SIDE = 'R' or 'r' ):
-*
-*  When  DIRECT = 'F' or 'f'  ( Forward sequence ) then
-*
-*     P = P( z - 1 )*...*P( 2 )*P( 1 ),
-*
-*  and when DIRECT = 'B' or 'b'  ( Backward sequence ) then
-*
-*     P = P( 1 )*P( 2 )*...*P( z - 1 ),
-*
-*  where  P( k ) is a plane rotation matrix for the following planes:
-*
-*     when  PIVOT = 'V' or 'v'  ( Variable pivot ),
-*        the plane ( k, k + 1 )
-*
-*     when  PIVOT = 'T' or 't'  ( Top pivot ),
-*        the plane ( 1, k + 1 )
-*
-*     when  PIVOT = 'B' or 'b'  ( Bottom pivot ),
-*        the plane ( k, z )
-*
-*  c( k ) and s( k )  must contain the  cosine and sine that define the
-*  matrix  P( k ).  The two by two plane rotation part of the matrix
-*  P( k ), R( k ), is assumed to be of the form
-*
-*     R( k ) = (  c( k )  s( k ) ).
-*              ( -s( k )  c( k ) )
-*
-*  This version vectorises across rows of the array A when SIDE = 'L'.
+*  SLASR applies a sequence of plane rotations to a real matrix A,
+*  from either the left or the right.
+*  
+*  When SIDE = 'L', the transformation takes the form
+*  
+*     A := P*A
+*  
+*  and when SIDE = 'R', the transformation takes the form
+*  
+*     A := A*P**T
+*  
+*  where P is an orthogonal matrix consisting of a sequence of z plane
+*  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
+*  and P**T is the transpose of P.
+*  
+*  When DIRECT = 'F' (Forward sequence), then
+*  
+*     P = P(z-1) * ... * P(2) * P(1)
+*  
+*  and when DIRECT = 'B' (Backward sequence), then
+*  
+*     P = P(1) * P(2) * ... * P(z-1)
+*  
+*  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
+*  
+*     R(k) = (  c(k)  s(k) )
+*          = ( -s(k)  c(k) ).
+*  
+*  When PIVOT = 'V' (Variable pivot), the rotation is performed
+*  for the plane (k,k+1), i.e., P(k) has the form
+*  
+*     P(k) = (  1                                            )
+*            (       ...                                     )
+*            (              1                                )
+*            (                   c(k)  s(k)                  )
+*            (                  -s(k)  c(k)                  )
+*            (                                1              )
+*            (                                     ...       )
+*            (                                            1  )
+*  
+*  where R(k) appears as a rank-2 modification to the identity matrix in
+*  rows and columns k and k+1.
+*  
+*  When PIVOT = 'T' (Top pivot), the rotation is performed for the
+*  plane (1,k+1), so P(k) has the form
+*  
+*     P(k) = (  c(k)                    s(k)                 )
+*            (         1                                     )
+*            (              ...                              )
+*            (                     1                         )
+*            ( -s(k)                    c(k)                 )
+*            (                                 1             )
+*            (                                      ...      )
+*            (                                             1 )
+*  
+*  where R(k) appears in rows and columns 1 and k+1.
+*  
+*  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
+*  performed for the plane (k,z), giving P(k) the form
+*  
+*     P(k) = ( 1                                             )
+*            (      ...                                      )
+*            (             1                                 )
+*            (                  c(k)                    s(k) )
+*            (                         1                     )
+*            (                              ...              )
+*            (                                     1         )
+*            (                 -s(k)                    c(k) )
+*  
+*  where R(k) appears in rows and columns k and z.  The rotations are
+*  performed without ever forming P(k) explicitly.
 *
 *  Arguments
 *  =========
@@ -62,13 +95,13 @@
 *          Specifies whether the plane rotation matrix P is applied to
 *          A on the left or the right.
 *          = 'L':  Left, compute A := P*A
-*          = 'R':  Right, compute A:= A*P'
+*          = 'R':  Right, compute A:= A*P**T
 *
 *  DIRECT  (input) CHARACTER*1
 *          Specifies whether P is a forward or backward sequence of
 *          plane rotations.
-*          = 'F':  Forward, P = P( z - 1 )*...*P( 2 )*P( 1 )
-*          = 'B':  Backward, P = P( 1 )*P( 2 )*...*P( z - 1 )
+*          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
+*          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
 *
 *  PIVOT   (input) CHARACTER*1
 *          Specifies the plane for which P(k) is a plane rotation
@@ -85,18 +118,22 @@
 *          The number of columns of the matrix A.  If n <= 1, an
 *          immediate return is effected.
 *
-*  C, S    (input) REAL arrays, dimension
+*  C       (input) REAL array, dimension
+*                  (M-1) if SIDE = 'L'
+*                  (N-1) if SIDE = 'R'
+*          The cosines c(k) of the plane rotations.
+*
+*  S       (input) REAL array, dimension
 *                  (M-1) if SIDE = 'L'
 *                  (N-1) if SIDE = 'R'
-*          c(k) and s(k) contain the cosine and sine that define the
-*          matrix P(k).  The two by two plane rotation part of the
-*          matrix P(k), R(k), is assumed to be of the form
-*          R( k ) = (  c( k )  s( k ) ).
-*                   ( -s( k )  c( k ) )
+*          The sines s(k) of the plane rotations.  The 2-by-2 plane
+*          rotation part of the matrix P(k), R(k), has the form
+*          R(k) = (  c(k)  s(k) )
+*                 ( -s(k)  c(k) ).
 *
 *  A       (input/output) REAL array, dimension (LDA,N)
-*          The m by n matrix A.  On exit, A is overwritten by P*A if
-*          SIDE = 'R' or by A*P' if SIDE = 'L'.
+*          The M-by-N matrix A.  On exit, A is overwritten by P*A if
+*          SIDE = 'R' or by A*P**T if SIDE = 'L'.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,M).
diff -uNr LAPACK.orig/SRC/ssbgst.f LAPACK/SRC/ssbgst.f
--- LAPACK.orig/SRC/ssbgst.f	Thu Nov  4 14:23:32 1999
+++ LAPACK/SRC/ssbgst.f	Fri May 25 16:12:46 2001
@@ -4,7 +4,7 @@
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     January 9, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO, VECT
@@ -125,7 +125,7 @@
          INFO = -3
       ELSE IF( KA.LT.0 ) THEN
          INFO = -4
-      ELSE IF( KB.LT.0 ) THEN
+      ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
          INFO = -5
       ELSE IF( LDAB.LT.KA+1 ) THEN
          INFO = -7
diff -uNr LAPACK.orig/SRC/sstebz.f LAPACK/SRC/sstebz.f
--- LAPACK.orig/SRC/sstebz.f	Thu Nov  4 14:24:00 1999
+++ LAPACK/SRC/sstebz.f	Fri May 25 16:13:18 2001
@@ -6,6 +6,7 @@
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
 *     June 30, 1999
+*     8-18-00:  Increase FUDGE factor for T3E (eca)
 *
 *     .. Scalar Arguments ..
       CHARACTER          ORDER, RANGE
@@ -175,7 +176,7 @@
       PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0,
      $                   HALF = 1.0E0 / TWO )
       REAL               FUDGE, RELFAC
-      PARAMETER          ( FUDGE = 2.0E0, RELFAC = 2.0E0 )
+      PARAMETER          ( FUDGE = 2.1E0, RELFAC = 2.0E0 )
 *     ..
 *     .. Local Scalars ..
       LOGICAL            NCNVRG, TOOFEW
diff -uNr LAPACK.orig/SRC/stgevc.f LAPACK/SRC/stgevc.f
--- LAPACK.orig/SRC/stgevc.f	Thu Nov  4 14:26:09 1999
+++ LAPACK/SRC/stgevc.f	Fri May 25 16:13:28 2001
@@ -1,18 +1,18 @@
-      SUBROUTINE STGEVC( SIDE, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
+      SUBROUTINE STGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
      $                   LDVL, VR, LDVR, MM, M, WORK, INFO )
 *
 *  -- LAPACK routine (version 3.0) --
 *     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
 *     Courant Institute, Argonne National Lab, and Rice University
-*     June 30, 1999
+*     May 4, 2001
 *
 *     .. Scalar Arguments ..
       CHARACTER          HOWMNY, SIDE
-      INTEGER            INFO, LDA, LDB, LDVL, LDVR, M, MM, N
+      INTEGER            INFO, LDP, LDS, LDVL, LDVR, M, MM, N
 *     ..
 *     .. Array Arguments ..
       LOGICAL            SELECT( * )
-      REAL               A( LDA, * ), B( LDB, * ), VL( LDVL, * ),
+      REAL               P( LDP, * ), S( LDS, * ), VL( LDVL, * ),
      $                   VR( LDVR, * ), WORK( * )
 *     ..
 *
@@ -20,34 +20,30 @@
 *  Purpose
 *  =======
 *
-*  STGEVC computes some or all of the right and/or left generalized
-*  eigenvectors of a pair of real upper triangular matrices (A,B).
-*
-*  The right generalized eigenvector x and the left generalized 
-*  eigenvector y of (A,B) corresponding to a generalized eigenvalue
-*  w are defined by:
-*
-*          (A - wB) * x = 0  and  y**H * (A - wB) = 0
-*
+*  STGEVC computes some or all of the right and/or left eigenvectors of
+*  a pair of real matrices (S,P), where S is a quasi-triangular matrix
+*  and P is upper triangular.  Matrix pairs of this type are produced by
+*  the generalized Schur factorization of a matrix pair (A,B):
+*
+*     A = Q*S*Z**T,  B = Q*P*Z**T
+*
+*  as computed by SGGHRD + SHGEQZ.
+*
+*  The right eigenvector x and the left eigenvector y of (S,P)
+*  corresponding to an eigenvalue w are defined by:
+*  
+*     S*x = w*P*x,  (y**H)*S = w*(y**H)*P,
+*  
 *  where y**H denotes the conjugate tranpose of y.
-*
-*  If an eigenvalue w is determined by zero diagonal elements of both A
-*  and B, a unit vector is returned as the corresponding eigenvector.
-*
-*  If all eigenvectors are requested, the routine may either return
-*  the matrices X and/or Y of right or left eigenvectors of (A,B), or
-*  the products Z*X and/or Q*Y, where Z and Q are input orthogonal
-*  matrices.  If (A,B) was obtained from the generalized real-Schur
-*  factorization of an original pair of matrices
-*     (A0,B0) = (Q*A*Z**H,Q*B*Z**H),
-*  then Z*X and Q*Y are the matrices of right or left eigenvectors of
-*  A.
-*
-*  A must be block upper triangular, with 1-by-1 and 2-by-2 diagonal
-*  blocks.  Corresponding to each 2-by-2 diagonal block is a complex
-*  conjugate pair of eigenvalues and eigenvectors; only one
-*  eigenvector of the pair is computed, namely the one corresponding
-*  to the eigenvalue with positive imaginary part.
+*  The eigenvalues are not input to this routine, but are computed
+*  directly from the diagonal blocks of S and P.
+*  
+*  This routine returns the matrices X and/or Y of right and left
+*  eigenvectors of (S,P), or the products Z*X and/or Q*Y,
+*  where Z and Q are input matrices.
+*  If Q and Z are the orthogonal factors from the generalized Schur
+*  factorization of a matrix pair (A,B), then Z*X and Q*Y
+*  are the matrices of right and left eigenvectors of (A,B).
 * 
 *  Arguments
 *  =========
@@ -59,78 +55,84 @@
 *
 *  HOWMNY  (input) CHARACTER*1
 *          = 'A': compute all right and/or left eigenvectors;
-*          = 'B': compute all right and/or left eigenvectors, and
-*                 backtransform them using the input matrices supplied
-*                 in VR and/or VL; 
+*          = 'B': compute all right and/or left eigenvectors,
+*                 backtransformed by the matrices in VR and/or VL;
 *          = 'S': compute selected right and/or left eigenvectors,
 *                 specified by the logical array SELECT.
 *
 *  SELECT  (input) LOGICAL array, dimension (N)
 *          If HOWMNY='S', SELECT specifies the eigenvectors to be
-*          computed.
-*          If HOWMNY='A' or 'B', SELECT is not referenced.
-*          To select the real eigenvector corresponding to the real
-*          eigenvalue w(j), SELECT(j) must be set to .TRUE.  To select
-*          the complex eigenvector corresponding to a complex conjugate
-*          pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must
-*          be set to .TRUE..
+*          computed.  If w(j) is a real eigenvalue, the corresponding
+*          real eigenvector is computed if SELECT(j) is .TRUE..
+*          If w(j) and w(j+1) are the real and imaginary parts of a
+*          complex eigenvalue, the corresponding complex eigenvector
+*          is computed if either SELECT(j) or SELECT(j+1) is .TRUE.,
+*          and on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is
+*          set to .FALSE..
+*          Not referenced if HOWMNY = 'A' or 'B'.
 *
 *  N       (input) INTEGER
-*          The order of the matrices A and B.  N >= 0.
+*          The order of the matrices S and P.  N >= 0.
 *
-*  A       (input) REAL array, dimension (LDA,N)
-*          The upper quasi-triangular matrix A.
+*  S       (input) REAL array, dimension (LDS,N)
+*          The upper quasi-triangular matrix S from a generalized Schur
+*          factorization, as computed by SHGEQZ.
+*
+*  LDS     (input) INTEGER
+*          The leading dimension of array S.  LDS >= max(1,N).
+*
+*  P       (input) REAL array, dimension (LDP,N)
+*          The upper triangular matrix P from a generalized Schur
+*          factorization, as computed by SHGEQZ.
+*          2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks
+*          of S must be in positive diagonal form.
 *
-*  LDA     (input) INTEGER
-*          The leading dimension of array A.  LDA >= max(1, N).
-*
-*  B       (input) REAL array, dimension (LDB,N)
-*          The upper triangular matrix B.  If A has a 2-by-2 diagonal
-*          block, then the corresponding 2-by-2 block of B must be
-*          diagonal with positive elements.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of array B.  LDB >= max(1,N).
+*  LDP     (input) INTEGER
+*          The leading dimension of array P.  LDP >= max(1,N).
 *
 *  VL      (input/output) REAL array, dimension (LDVL,MM)
 *          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
 *          contain an N-by-N matrix Q (usually the orthogonal matrix Q
 *          of left Schur vectors returned by SHGEQZ).
 *          On exit, if SIDE = 'L' or 'B', VL contains:
-*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (A,B);
+*          if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
 *          if HOWMNY = 'B', the matrix Q*Y;
-*          if HOWMNY = 'S', the left eigenvectors of (A,B) specified by
+*          if HOWMNY = 'S', the left eigenvectors of (S,P) specified by
 *                      SELECT, stored consecutively in the columns of
 *                      VL, in the same order as their eigenvalues.
-*          If SIDE = 'R', VL is not referenced.
 *
 *          A complex eigenvector corresponding to a complex eigenvalue
 *          is stored in two consecutive columns, the first holding the
 *          real part, and the second the imaginary part.
 *
+*          Not referenced if SIDE = 'R'.
+*
 *  LDVL    (input) INTEGER
-*          The leading dimension of array VL.
-*          LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
+*          The leading dimension of array VL.  LDVL >= 1, and if
+*          SIDE = 'L' or 'B', LDVL >= N.
 *
 *  VR      (input/output) REAL array, dimension (LDVR,MM)
 *          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
-*          contain an N-by-N matrix Q (usually the orthogonal matrix Z
+*          contain an N-by-N matrix Z (usually the orthogonal matrix Z
 *          of right Schur vectors returned by SHGEQZ).
+*
 *          On exit, if SIDE = 'R' or 'B', VR contains:
-*          if HOWMNY = 'A', the matrix X of right eigenvectors of (A,B);
-*          if HOWMNY = 'B', the matrix Z*X;
-*          if HOWMNY = 'S', the right eigenvectors of (A,B) specified by
-*                      SELECT, stored consecutively in the columns of
-*                      VR, in the same order as their eigenvalues.
-*          If SIDE = 'L', VR is not referenced.
+*          if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
+*          if HOWMNY = 'B' or 'b', the matrix Z*X;
+*          if HOWMNY = 'S' or 's', the right eigenvectors of (S,P)
+*                      specified by SELECT, stored consecutively in the
+*                      columns of VR, in the same order as their
+*                      eigenvalues.
 *
 *          A complex eigenvector corresponding to a complex eigenvalue
 *          is stored in two consecutive columns, the first holding the
 *          real part and the second the imaginary part.
+*          
+*          Not referenced if SIDE = 'L'.
 *
 *  LDVR    (input) INTEGER
-*          The leading dimension of the array VR.
-*          LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
+*          The leading dimension of the array VR.  LDVR >= 1, and if
+*          SIDE = 'R' or 'B', LDVR >= N.
 *
 *  MM      (input) INTEGER
 *          The number of columns in the arrays VL and/or VR. MM >= M.
@@ -199,7 +201,7 @@
 *  partial sums.  Since FORTRAN arrays are stored columnwise, this has
 *  the advantage that at each step, the elements of C that are accessed
 *  are adjacent to one another, whereas with the rowwise method, the
-*  elements accessed at a step are spaced LDA (and LDB) words apart.
+*  elements accessed at a step are spaced LDS (and LDP) words apart.
 *
 *  When finding left eigenvectors, the matrix in question is the
 *  transpose of the one in storage, so the rowwise method then
@@ -226,8 +228,8 @@
      $                   XSCALE
 *     ..
 *     .. Local Arrays ..
-      REAL               BDIAG( 2 ), SUM( 2, 2 ), SUMA( 2, 2 ),
-     $                   SUMB( 2, 2 )
+      REAL               BDIAG( 2 ), SUM( 2, 2 ), SUMS( 2, 2 ),
+     $                   SUMP( 2, 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
@@ -252,7 +254,7 @@
          IHWMNY = 2
          ILALL = .FALSE.
          ILBACK = .FALSE.
-      ELSE IF( LSAME( HOWMNY, 'B' ) .OR. LSAME( HOWMNY, 'T' ) ) THEN
+      ELSE IF( LSAME( HOWMNY, 'B' ) ) THEN
          IHWMNY = 3
          ILALL = .TRUE.
          ILBACK = .TRUE.
@@ -284,9 +286,9 @@
          INFO = -2
       ELSE IF( N.LT.0 ) THEN
          INFO = -4
-      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+      ELSE IF( LDS.LT.MAX( 1, N ) ) THEN
          INFO = -6
-      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+      ELSE IF( LDP.LT.MAX( 1, N ) ) THEN
          INFO = -8
       END IF
       IF( INFO.NE.0 ) THEN
@@ -305,7 +307,7 @@
                GO TO 10
             END IF
             IF( J.LT.N ) THEN
-               IF( A( J+1, J ).NE.ZERO )
+               IF( S( J+1, J ).NE.ZERO )
      $            ILCPLX = .TRUE.
             END IF
             IF( ILCPLX ) THEN
@@ -325,11 +327,11 @@
       ILABAD = .FALSE.
       ILBBAD = .FALSE.
       DO 20 J = 1, N - 1
-         IF( A( J+1, J ).NE.ZERO ) THEN
-            IF( B( J, J ).EQ.ZERO .OR. B( J+1, J+1 ).EQ.ZERO .OR.
-     $          B( J, J+1 ).NE.ZERO )ILBBAD = .TRUE.
+         IF( S( J+1, J ).NE.ZERO ) THEN
+            IF( P( J, J ).EQ.ZERO .OR. P( J+1, J+1 ).EQ.ZERO .OR.
+     $          P( J, J+1 ).NE.ZERO )ILBBAD = .TRUE.
             IF( J.LT.N-1 ) THEN
-               IF( A( J+2, J+1 ).NE.ZERO )
+               IF( S( J+2, J+1 ).NE.ZERO )
      $            ILABAD = .TRUE.
             END IF
          END IF
@@ -372,30 +374,30 @@
 *     blocks) of A and B to check for possible overflow in the
 *     triangular solver.
 *
-      ANORM = ABS( A( 1, 1 ) )
+      ANORM = ABS( S( 1, 1 ) )
       IF( N.GT.1 )
-     $   ANORM = ANORM + ABS( A( 2, 1 ) )
-      BNORM = ABS( B( 1, 1 ) )
+     $   ANORM = ANORM + ABS( S( 2, 1 ) )
+      BNORM = ABS( P( 1, 1 ) )
       WORK( 1 ) = ZERO
       WORK( N+1 ) = ZERO
 *
       DO 50 J = 2, N
          TEMP = ZERO
          TEMP2 = ZERO
-         IF( A( J, J-1 ).EQ.ZERO ) THEN
+         IF( S( J, J-1 ).EQ.ZERO ) THEN
             IEND = J - 1
          ELSE
             IEND = J - 2
          END IF
          DO 30 I = 1, IEND
-            TEMP = TEMP + ABS( A( I, J ) )
-            TEMP2 = TEMP2 + ABS( B( I, J ) )
+            TEMP = TEMP + ABS( S( I, J ) )
+            TEMP2 = TEMP2 + ABS( P( I, J ) )
    30    CONTINUE
          WORK( J ) = TEMP
          WORK( N+J ) = TEMP2
          DO 40 I = IEND + 1, MIN( J+1, N )
-            TEMP = TEMP + ABS( A( I, J ) )
-            TEMP2 = TEMP2 + ABS( B( I, J ) )
+            TEMP = TEMP + ABS( S( I, J ) )
+            TEMP2 = TEMP2 + ABS( P( I, J ) )
    40    CONTINUE
          ANORM = MAX( ANORM, TEMP )
          BNORM = MAX( BNORM, TEMP2 )
@@ -425,7 +427,7 @@
             END IF
             NW = 1
             IF( JE.LT.N ) THEN
-               IF( A( JE+1, JE ).NE.ZERO ) THEN
+               IF( S( JE+1, JE ).NE.ZERO ) THEN
                   ILCPLX = .TRUE.
                   NW = 2
                END IF
@@ -444,8 +446,8 @@
 *           (c) complex eigenvalue.
 *
             IF( .NOT.ILCPLX ) THEN
-               IF( ABS( A( JE, JE ) ).LE.SAFMIN .AND.
-     $             ABS( B( JE, JE ) ).LE.SAFMIN ) THEN
+               IF( ABS( S( JE, JE ) ).LE.SAFMIN .AND.
+     $             ABS( P( JE, JE ) ).LE.SAFMIN ) THEN
 *
 *                 Singular matrix pencil -- return unit eigenvector
 *
@@ -472,10 +474,10 @@
 *
 *              Real eigenvalue
 *
-               TEMP = ONE / MAX( ABS( A( JE, JE ) )*ASCALE,
-     $                ABS( B( JE, JE ) )*BSCALE, SAFMIN )
-               SALFAR = ( TEMP*A( JE, JE ) )*ASCALE
-               SBETA = ( TEMP*B( JE, JE ) )*BSCALE
+               TEMP = ONE / MAX( ABS( S( JE, JE ) )*ASCALE,
+     $                ABS( P( JE, JE ) )*BSCALE, SAFMIN )
+               SALFAR = ( TEMP*S( JE, JE ) )*ASCALE
+               SBETA = ( TEMP*P( JE, JE ) )*BSCALE
                ACOEF = SBETA*ASCALE
                BCOEFR = SALFAR*BSCALE
                BCOEFI = ZERO
@@ -517,7 +519,7 @@
 *
 *              Complex eigenvalue
 *
-               CALL SLAG2( A( JE, JE ), LDA, B( JE, JE ), LDB,
+               CALL SLAG2( S( JE, JE ), LDS, P( JE, JE ), LDP,
      $                     SAFMIN*SAFETY, ACOEF, TEMP, BCOEFR, TEMP2,
      $                     BCOEFI )
                BCOEFI = -BCOEFI
@@ -549,9 +551,9 @@
 *
 *              Compute first two components of eigenvector
 *
-               TEMP = ACOEF*A( JE+1, JE )
-               TEMP2R = ACOEF*A( JE, JE ) - BCOEFR*B( JE, JE )
-               TEMP2I = -BCOEFI*B( JE, JE )
+               TEMP = ACOEF*S( JE+1, JE )
+               TEMP2R = ACOEF*S( JE, JE ) - BCOEFR*P( JE, JE )
+               TEMP2I = -BCOEFI*P( JE, JE )
                IF( ABS( TEMP ).GT.ABS( TEMP2R )+ABS( TEMP2I ) ) THEN
                   WORK( 2*N+JE ) = ONE
                   WORK( 3*N+JE ) = ZERO
@@ -560,10 +562,10 @@
                ELSE
                   WORK( 2*N+JE+1 ) = ONE
                   WORK( 3*N+JE+1 ) = ZERO
-                  TEMP = ACOEF*A( JE, JE+1 )
-                  WORK( 2*N+JE ) = ( BCOEFR*B( JE+1, JE+1 )-ACOEF*
-     $                             A( JE+1, JE+1 ) ) / TEMP
-                  WORK( 3*N+JE ) = BCOEFI*B( JE+1, JE+1 ) / TEMP
+                  TEMP = ACOEF*S( JE, JE+1 )
+                  WORK( 2*N+JE ) = ( BCOEFR*P( JE+1, JE+1 )-ACOEF*
+     $                             S( JE+1, JE+1 ) ) / TEMP
+                  WORK( 3*N+JE ) = BCOEFI*P( JE+1, JE+1 ) / TEMP
                END IF
                XMAX = MAX( ABS( WORK( 2*N+JE ) )+ABS( WORK( 3*N+JE ) ),
      $                ABS( WORK( 2*N+JE+1 ) )+ABS( WORK( 3*N+JE+1 ) ) )
@@ -586,11 +588,11 @@
                END IF
 *
                NA = 1
-               BDIAG( 1 ) = B( J, J )
+               BDIAG( 1 ) = P( J, J )
                IF( J.LT.N ) THEN
-                  IF( A( J+1, J ).NE.ZERO ) THEN
+                  IF( S( J+1, J ).NE.ZERO ) THEN
                      IL2BY2 = .TRUE.
-                     BDIAG( 2 ) = B( J+1, J+1 )
+                     BDIAG( 2 ) = P( J+1, J+1 )
                      NA = 2
                   END IF
                END IF
@@ -616,13 +618,13 @@
 *              Compute dot products
 *
 *                    j-1
-*              SUM = sum  conjg( a*A(k,j) - b*B(k,j) )*x(k)
+*              SUM = sum  conjg( a*S(k,j) - b*P(k,j) )*x(k)
 *                    k=je
 *
 *              To reduce the op count, this is done as
 *
 *              _        j-1                  _        j-1
-*              a*conjg( sum  A(k,j)*x(k) ) - b*conjg( sum  B(k,j)*x(k) )
+*              a*conjg( sum  S(k,j)*x(k) ) - b*conjg( sum  P(k,j)*x(k) )
 *                       k=je                          k=je
 *
 *              which may cause underflow problems if A or B are close
@@ -659,15 +661,15 @@
 *$PL$ CMCHAR='*'
 *
                   DO 110 JA = 1, NA
-                     SUMA( JA, JW ) = ZERO
-                     SUMB( JA, JW ) = ZERO
+                     SUMS( JA, JW ) = ZERO
+                     SUMP( JA, JW ) = ZERO
 *
                      DO 100 JR = JE, J - 1
-                        SUMA( JA, JW ) = SUMA( JA, JW ) +
-     $                                   A( JR, J+JA-1 )*
+                        SUMS( JA, JW ) = SUMS( JA, JW ) +
+     $                                   S( JR, J+JA-1 )*
      $                                   WORK( ( JW+1 )*N+JR )
-                        SUMB( JA, JW ) = SUMB( JA, JW ) +
-     $                                   B( JR, J+JA-1 )*
+                        SUMP( JA, JW ) = SUMP( JA, JW ) +
+     $                                   P( JR, J+JA-1 )*
      $                                   WORK( ( JW+1 )*N+JR )
   100                CONTINUE
   110             CONTINUE
@@ -687,15 +689,15 @@
 *
                DO 130 JA = 1, NA
                   IF( ILCPLX ) THEN
-                     SUM( JA, 1 ) = -ACOEF*SUMA( JA, 1 ) +
-     $                              BCOEFR*SUMB( JA, 1 ) -
-     $                              BCOEFI*SUMB( JA, 2 )
-                     SUM( JA, 2 ) = -ACOEF*SUMA( JA, 2 ) +
-     $                              BCOEFR*SUMB( JA, 2 ) +
-     $                              BCOEFI*SUMB( JA, 1 )
+                     SUM( JA, 1 ) = -ACOEF*SUMS( JA, 1 ) +
+     $                              BCOEFR*SUMP( JA, 1 ) -
+     $                              BCOEFI*SUMP( JA, 2 )
+                     SUM( JA, 2 ) = -ACOEF*SUMS( JA, 2 ) +
+     $                              BCOEFR*SUMP( JA, 2 ) +
+     $                              BCOEFI*SUMP( JA, 1 )
                   ELSE
-                     SUM( JA, 1 ) = -ACOEF*SUMA( JA, 1 ) +
-     $                              BCOEFR*SUMB( JA, 1 )
+                     SUM( JA, 1 ) = -ACOEF*SUMS( JA, 1 ) +
+     $                              BCOEFR*SUMP( JA, 1 )
                   END IF
   130          CONTINUE
 *
@@ -703,7 +705,7 @@
 *              Solve  ( a A - b B )  y = SUM(,)
 *              with scaling and perturbation of the denominator
 *
-               CALL SLALN2( .TRUE., NA, NW, DMIN, ACOEF, A( J, J ), LDA,
+               CALL SLALN2( .TRUE., NA, NW, DMIN, ACOEF, S( J, J ), LDS,
      $                      BDIAG( 1 ), BDIAG( 2 ), SUM, 2, BCOEFR,
      $                      BCOEFI, WORK( 2*N+J ), N, SCALE, TEMP,
      $                      IINFO )
@@ -790,7 +792,7 @@
             END IF
             NW = 1
             IF( JE.GT.1 ) THEN
-               IF( A( JE, JE-1 ).NE.ZERO ) THEN
+               IF( S( JE, JE-1 ).NE.ZERO ) THEN
                   ILCPLX = .TRUE.
                   NW = 2
                END IF
@@ -809,8 +811,8 @@
 *           (c) complex eigenvalue.
 *
             IF( .NOT.ILCPLX ) THEN
-               IF( ABS( A( JE, JE ) ).LE.SAFMIN .AND.
-     $             ABS( B( JE, JE ) ).LE.SAFMIN ) THEN
+               IF( ABS( S( JE, JE ) ).LE.SAFMIN .AND.
+     $             ABS( P( JE, JE ) ).LE.SAFMIN ) THEN
 *
 *                 Singular matrix pencil -- unit eigenvector
 *
@@ -839,10 +841,10 @@
 *
 *              Real eigenvalue
 *
-               TEMP = ONE / MAX( ABS( A( JE, JE ) )*ASCALE,
-     $                ABS( B( JE, JE ) )*BSCALE, SAFMIN )
-               SALFAR = ( TEMP*A( JE, JE ) )*ASCALE
-               SBETA = ( TEMP*B( JE, JE ) )*BSCALE
+               TEMP = ONE / MAX( ABS( S( JE, JE ) )*ASCALE,
+     $                ABS( P( JE, JE ) )*BSCALE, SAFMIN )
+               SALFAR = ( TEMP*S( JE, JE ) )*ASCALE
+               SBETA = ( TEMP*P( JE, JE ) )*BSCALE
                ACOEF = SBETA*ASCALE
                BCOEFR = SALFAR*BSCALE
                BCOEFI = ZERO
@@ -885,14 +887,14 @@
 *              (See "Further Details", above.)
 *
                DO 260 JR = 1, JE - 1
-                  WORK( 2*N+JR ) = BCOEFR*B( JR, JE ) -
-     $                             ACOEF*A( JR, JE )
+                  WORK( 2*N+JR ) = BCOEFR*P( JR, JE ) -
+     $                             ACOEF*S( JR, JE )
   260          CONTINUE
             ELSE
 *
 *              Complex eigenvalue
 *
-               CALL SLAG2( A( JE-1, JE-1 ), LDA, B( JE-1, JE-1 ), LDB,
+               CALL SLAG2( S( JE-1, JE-1 ), LDS, P( JE-1, JE-1 ), LDP,
      $                     SAFMIN*SAFETY, ACOEF, TEMP, BCOEFR, TEMP2,
      $                     BCOEFI )
                IF( BCOEFI.EQ.ZERO ) THEN
@@ -924,9 +926,9 @@
 *              Compute first two components of eigenvector
 *              and contribution to sums
 *
-               TEMP = ACOEF*A( JE, JE-1 )
-               TEMP2R = ACOEF*A( JE, JE ) - BCOEFR*B( JE, JE )
-               TEMP2I = -BCOEFI*B( JE, JE )
+               TEMP = ACOEF*S( JE, JE-1 )
+               TEMP2R = ACOEF*S( JE, JE ) - BCOEFR*P( JE, JE )
+               TEMP2I = -BCOEFI*P( JE, JE )
                IF( ABS( TEMP ).GE.ABS( TEMP2R )+ABS( TEMP2I ) ) THEN
                   WORK( 2*N+JE ) = ONE
                   WORK( 3*N+JE ) = ZERO
@@ -935,10 +937,10 @@
                ELSE
                   WORK( 2*N+JE-1 ) = ONE
                   WORK( 3*N+JE-1 ) = ZERO
-                  TEMP = ACOEF*A( JE-1, JE )
-                  WORK( 2*N+JE ) = ( BCOEFR*B( JE-1, JE-1 )-ACOEF*
-     $                             A( JE-1, JE-1 ) ) / TEMP
-                  WORK( 3*N+JE ) = BCOEFI*B( JE-1, JE-1 ) / TEMP
+                  TEMP = ACOEF*S( JE-1, JE )
+                  WORK( 2*N+JE ) = ( BCOEFR*P( JE-1, JE-1 )-ACOEF*
+     $                             S( JE-1, JE-1 ) ) / TEMP
+                  WORK( 3*N+JE ) = BCOEFI*P( JE-1, JE-1 ) / TEMP
                END IF
 *
                XMAX = MAX( ABS( WORK( 2*N+JE ) )+ABS( WORK( 3*N+JE ) ),
@@ -958,12 +960,12 @@
                CRE2B = BCOEFR*WORK( 2*N+JE ) - BCOEFI*WORK( 3*N+JE )
                CIM2B = BCOEFI*WORK( 2*N+JE ) + BCOEFR*WORK( 3*N+JE )
                DO 270 JR = 1, JE - 2
-                  WORK( 2*N+JR ) = -CREALA*A( JR, JE-1 ) +
-     $                             CREALB*B( JR, JE-1 ) -
-     $                             CRE2A*A( JR, JE ) + CRE2B*B( JR, JE )
-                  WORK( 3*N+JR ) = -CIMAGA*A( JR, JE-1 ) +
-     $                             CIMAGB*B( JR, J