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/test/matrix/test_matrix.rb

http://github.com/ruby/ruby
Ruby | 815 lines | 709 code | 95 blank | 11 comment | 4 complexity | 8f05973b6776153ebbaf2b632d9fa0fc MD5 | raw file
Possible License(s): GPL-2.0, BSD-3-Clause, AGPL-3.0 
    

  1. # frozen_string_literal: false
    2. 

  2. require 'test/unit'
    3. 

  3. require 'matrix'
    4. 

  4. 

  5. class SubMatrix < Matrix
    6. 

  6. end
    7. 

  7. 

  8. class TestMatrix < Test::Unit::TestCase
    9. 

  9.   def setup
    10. 

  10.     @m1 = Matrix[[1,2,3], [4,5,6]]
    11. 

  11.     @m2 = Matrix[[1,2,3], [4,5,6]]
    12. 

  12.     @m3 = @m1.clone
    13. 

  13.     @m4 = Matrix[[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
    14. 

  14.     @n1 = Matrix[[2,3,4], [5,6,7]]
    15. 

  15.     @c1 = Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
    16. 

  16.     @e1 = Matrix.empty(2,0)
    17. 

  17.     @e2 = Matrix.empty(0,3)
    18. 

  18.     @a3  = Matrix[[4, 1, -3], [0, 3, 7], [11, -4, 2]]
    19. 

  19.     @a5  = Matrix[[2, 0, 9, 3, 9], [8, 7, 0, 1, 9], [7, 5, 6, 6, 5], [0, 7, 8, 3, 0], [7, 8, 2, 3, 1]]
    20. 

  20.     @b3  = Matrix[[-7, 7, -10], [9, -3, -2], [-1, 3, 9]]
    21. 

  21.     @rot = Matrix[[0, -1, 0], [1, 0, 0], [0, 0, -1]]
    22. 

  22.   end
    23. 

  23. 

  24.   def test_matrix
    25. 

  25.     assert_equal(1, @m1[0, 0])
    26. 

  26.     assert_equal(2, @m1[0, 1])
    27. 

  27.     assert_equal(3, @m1[0, 2])
    28. 

  28.     assert_equal(4, @m1[1, 0])
    29. 

  29.     assert_equal(5, @m1[1, 1])
    30. 

  30.     assert_equal(6, @m1[1, 2])
    31. 

  31.   end
    32. 

  32. 

  33.   def test_identity
    34. 

  34.     assert_same @m1, @m1
    35. 

  35.     assert_not_same @m1, @m2
    36. 

  36.     assert_not_same @m1, @m3
    37. 

  37.     assert_not_same @m1, @m4
    38. 

  38.     assert_not_same @m1, @n1
    39. 

  39.   end
    40. 

  40. 

  41.   def test_equality
    42. 

  42.     assert_equal @m1, @m1
    43. 

  43.     assert_equal @m1, @m2
    44. 

  44.     assert_equal @m1, @m3
    45. 

  45.     assert_equal @m1, @m4
    46. 

  46.     assert_not_equal @m1, @n1
    47. 

  47.   end
    48. 

  48. 

  49.   def test_hash_equality
    50. 

  50.     assert @m1.eql?(@m1)
    51. 

  51.     assert @m1.eql?(@m2)
    52. 

  52.     assert @m1.eql?(@m3)
    53. 

  53.     assert !@m1.eql?(@m4)
    54. 

  54.     assert !@m1.eql?(@n1)
    55. 

  55. 

  56.     hash = { @m1 => :value }
    57. 

  57.     assert hash.key?(@m1)
    58. 

  58.     assert hash.key?(@m2)
    59. 

  59.     assert hash.key?(@m3)
    60. 

  60.     assert !hash.key?(@m4)
    61. 

  61.     assert !hash.key?(@n1)
    62. 

  62.   end
    63. 

  63. 

  64.   def test_hash
    65. 

  65.     assert_equal @m1.hash, @m1.hash
    66. 

  66.     assert_equal @m1.hash, @m2.hash
    67. 

  67.     assert_equal @m1.hash, @m3.hash
    68. 

  68.   end
    69. 

  69. 

  70.   def test_uplus
    71. 

  71.     assert_equal(@m1, +@m1)
    72. 

  72.   end
    73. 

  73. 

  74.   def test_negate
    75. 

  75.     assert_equal(Matrix[[-1, -2, -3], [-4, -5, -6]], -@m1)
    76. 

  76.     assert_equal(@m1, -(-@m1))
    77. 

  77.   end
    78. 

  78. 

  79.   def test_rank
    80. 

  80.     [
    81. 

  81.       [[0]],
    82. 

  82.       [[0], [0]],
    83. 

  83.       [[0, 0], [0, 0]],
    84. 

  84.       [[0, 0], [0, 0], [0, 0]],
    85. 

  85.       [[0, 0, 0]],
    86. 

  86.       [[0, 0, 0], [0, 0, 0]],
    87. 

  87.       [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
    88. 

  88.       [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]],
    89. 

  89.     ].each do |rows|
    90. 

  90.       assert_equal 0, Matrix[*rows].rank
    91. 

  91.     end
    92. 

  92. 

  93.     [
    94. 

  94.       [[1], [0]],
    95. 

  95.       [[1, 0], [0, 0]],
    96. 

  96.       [[1, 0], [1, 0]],
    97. 

  97.       [[0, 0], [1, 0]],
    98. 

  98.       [[1, 0], [0, 0], [0, 0]],
    99. 

  99.       [[0, 0], [1, 0], [0, 0]],
    100. 

  100.       [[0, 0], [0, 0], [1, 0]],
    101. 

  101.       [[1, 0], [1, 0], [0, 0]],
    102. 

  102.       [[0, 0], [1, 0], [1, 0]],
    103. 

  103.       [[1, 0], [1, 0], [1, 0]],
    104. 

  104.       [[1, 0, 0]],
    105. 

  105.       [[1, 0, 0], [0, 0, 0]],
    106. 

  106.       [[0, 0, 0], [1, 0, 0]],
    107. 

  107.       [[1, 0, 0], [1, 0, 0]],
    108. 

  108.       [[1, 0, 0], [1, 0, 0]],
    109. 

  109.       [[1, 0, 0], [0, 0, 0], [0, 0, 0]],
    110. 

  110.       [[0, 0, 0], [1, 0, 0], [0, 0, 0]],
    111. 

  111.       [[0, 0, 0], [0, 0, 0], [1, 0, 0]],
    112. 

  112.       [[1, 0, 0], [1, 0, 0], [0, 0, 0]],
    113. 

  113.       [[0, 0, 0], [1, 0, 0], [1, 0, 0]],
    114. 

  114.       [[1, 0, 0], [0, 0, 0], [1, 0, 0]],
    115. 

  115.       [[1, 0, 0], [1, 0, 0], [1, 0, 0]],
    116. 

  116.       [[1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]],
    117. 

  117.       [[1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]],
    118. 

  118.       [[1, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0]],
    119. 

  119.       [[1, 0, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0]],
    120. 

  120.       [[1, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, 0]],
    121. 

  121.       [[1, 0, 0], [1, 0, 0], [1, 0, 0], [0, 0, 0]],
    122. 

  122.       [[1, 0, 0], [0, 0, 0], [1, 0, 0], [1, 0, 0]],
    123. 

  123.       [[1, 0, 0], [1, 0, 0], [0, 0, 0], [1, 0, 0]],
    124. 

  124.       [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 0]],
    125. 

  125. 

  126.       [[1]],
    127. 

  127.       [[1], [1]],
    128. 

  128.       [[1, 1]],
    129. 

  129.       [[1, 1], [1, 1]],
    130. 

  130.       [[1, 1], [1, 1], [1, 1]],
    131. 

  131.       [[1, 1, 1]],
    132. 

  132.       [[1, 1, 1], [1, 1, 1]],
    133. 

  133.       [[1, 1, 1], [1, 1, 1], [1, 1, 1]],
    134. 

  134.       [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
    135. 

  135.     ].each do |rows|
    136. 

  136.       matrix = Matrix[*rows]
    137. 

  137.       assert_equal 1, matrix.rank
    138. 

  138.       assert_equal 1, matrix.transpose.rank
    139. 

  139.     end
    140. 

  140. 

  141.     [
    142. 

  142.       [[1, 0], [0, 1]],
    143. 

  143.       [[1, 0], [0, 1], [0, 0]],
    144. 

  144.       [[1, 0], [0, 1], [0, 1]],
    145. 

  145.       [[1, 0], [0, 1], [1, 1]],
    146. 

  146.       [[1, 0, 0], [0, 1, 0]],
    147. 

  147.       [[1, 0, 0], [0, 0, 1]],
    148. 

  148.       [[1, 0, 0], [0, 1, 0], [0, 0, 0]],
    149. 

  149.       [[1, 0, 0], [0, 0, 1], [0, 0, 0]],
    150. 

  150. 

  151.       [[1, 0, 0], [0, 0, 0], [0, 1, 0]],
    152. 

  152.       [[1, 0, 0], [0, 0, 0], [0, 0, 1]],
    153. 

  153. 

  154.       [[1, 0], [1, 1]],
    155. 

  155.       [[1, 2], [1, 1]],
    156. 

  156.       [[1, 2], [0, 1], [1, 1]],
    157. 

  157.     ].each do |rows|
    158. 

  158.       m = Matrix[*rows]
    159. 

  159.       assert_equal 2, m.rank
    160. 

  160.       assert_equal 2, m.transpose.rank
    161. 

  161.     end
    162. 

  162. 

  163.     [
    164. 

  164.       [[1, 0, 0], [0, 1, 0], [0, 0, 1]],
    165. 

  165.       [[1, 1, 0], [0, 1, 1], [1, 0, 1]],
    166. 

  166.       [[1, 1, 0], [0, 1, 1], [1, 0, 1]],
    167. 

  167.       [[1, 1, 0], [0, 1, 1], [1, 0, 1], [0, 0, 0]],
    168. 

  168.       [[1, 1, 0], [0, 1, 1], [1, 0, 1], [1, 1, 1]],
    169. 

  169.       [[1, 1, 1], [1, 1, 2], [1, 3, 1], [4, 1, 1]],
    170. 

  170.     ].each do |rows|
    171. 

  171.       m = Matrix[*rows]
    172. 

  172.       assert_equal 3, m.rank
    173. 

  173.       assert_equal 3, m.transpose.rank
    174. 

  174.     end
    175. 

  175.   end
    176. 

  176. 

  177.   def test_inverse
    178. 

  178.     assert_equal(Matrix.empty(0, 0), Matrix.empty.inverse)
    179. 

  179.     assert_equal(Matrix[[-1, 1], [0, -1]], Matrix[[-1, -1], [0, -1]].inverse)
    180. 

  180.     assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { @m1.inverse }
    181. 

  181.   end
    182. 

  182. 

  183.   def test_determinant
    184. 

  184.     assert_equal(0, Matrix[[0,0],[0,0]].determinant)
    185. 

  185.     assert_equal(45, Matrix[[7,6], [3,9]].determinant)
    186. 

  186.     assert_equal(-18, Matrix[[2,0,1],[0,-2,2],[1,2,3]].determinant)
    187. 

  187.     assert_equal(-7, Matrix[[0,0,1],[0,7,6],[1,3,9]].determinant)
    188. 

  188.     assert_equal(42, Matrix[[7,0,1,0,12],[8,1,1,9,1],[4,0,0,-7,17],[-1,0,0,-4,8],[10,1,1,8,6]].determinant)
    189. 

  189.   end
    190. 

  190. 

  191.   def test_new_matrix
    192. 

  192.     assert_raise(TypeError) { Matrix[Object.new] }
    193. 

  193.     o = Object.new
    194. 

  194.     def o.to_ary; [1,2,3]; end
    195. 

  195.     assert_equal(@m1, Matrix[o, [4,5,6]])
    196. 

  196.   end
    197. 

  197. 

  198.   def test_round
    199. 

  199.     a = Matrix[[1.0111, 2.32320, 3.04343], [4.81, 5.0, 6.997]]
    200. 

  200.     b = Matrix[[1.01, 2.32, 3.04], [4.81, 5.0, 7.0]]
    201. 

  201.     assert_equal(a.round(2), b)
    202. 

  202.   end
    203. 

  203. 

  204.   def test_rows
    205. 

  205.     assert_equal(@m1, Matrix.rows([[1, 2, 3], [4, 5, 6]]))
    206. 

  206.   end
    207. 

  207. 

  208.   def test_rows_copy
    209. 

  209.     rows1 = [[1], [1]]
    210. 

  210.     rows2 = [[1], [1]]
    211. 

  211. 

  212.     m1 = Matrix.rows(rows1, copy = false)
    213. 

  213.     m2 = Matrix.rows(rows2, copy = true)
    214. 

  214. 

  215.     rows1.uniq!
    216. 

  216.     rows2.uniq!
    217. 

  217. 

  218.     assert_equal([[1]],      m1.to_a)
    219. 

  219.     assert_equal([[1], [1]], m2.to_a)
    220. 

  220.   end
    221. 

  221. 

  222.   def test_to_matrix
    223. 

  223.     assert @m1.equal? @m1.to_matrix
    224. 

  224.   end
    225. 

  225. 

  226.   def test_columns
    227. 

  227.     assert_equal(@m1, Matrix.columns([[1, 4], [2, 5], [3, 6]]))
    228. 

  228.   end
    229. 

  229. 

  230.   def test_diagonal
    231. 

  231.     assert_equal(Matrix.empty(0, 0), Matrix.diagonal( ))
    232. 

  232.     assert_equal(Matrix[[3,0,0],[0,2,0],[0,0,1]], Matrix.diagonal(3, 2, 1))
    233. 

  233.     assert_equal(Matrix[[4,0,0,0],[0,3,0,0],[0,0,2,0],[0,0,0,1]], Matrix.diagonal(4, 3, 2, 1))
    234. 

  234.   end
    235. 

  235. 

  236.   def test_scalar
    237. 

  237.     assert_equal(Matrix.empty(0, 0), Matrix.scalar(0, 1))
    238. 

  238.     assert_equal(Matrix[[2,0,0],[0,2,0],[0,0,2]], Matrix.scalar(3, 2))
    239. 

  239.     assert_equal(Matrix[[2,0,0,0],[0,2,0,0],[0,0,2,0],[0,0,0,2]], Matrix.scalar(4, 2))
    240. 

  240.   end
    241. 

  241. 

  242.   def test_identity2
    243. 

  243.     assert_equal(Matrix[[1,0,0],[0,1,0],[0,0,1]], Matrix.identity(3))
    244. 

  244.     assert_equal(Matrix[[1,0,0],[0,1,0],[0,0,1]], Matrix.unit(3))
    245. 

  245.     assert_equal(Matrix[[1,0,0],[0,1,0],[0,0,1]], Matrix.I(3))
    246. 

  246.     assert_equal(Matrix[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]], Matrix.identity(4))
    247. 

  247.   end
    248. 

  248. 

  249.   def test_zero
    250. 

  250.     assert_equal(Matrix[[0,0,0],[0,0,0],[0,0,0]], Matrix.zero(3))
    251. 

  251.     assert_equal(Matrix[[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]], Matrix.zero(4))
    252. 

  252.     assert_equal(Matrix[[0]], Matrix.zero(1))
    253. 

  253.   end
    254. 

  254. 

  255.   def test_row_vector
    256. 

  256.     assert_equal(Matrix[[1,2,3,4]], Matrix.row_vector([1,2,3,4]))
    257. 

  257.   end
    258. 

  258. 

  259.   def test_column_vector
    260. 

  260.     assert_equal(Matrix[[1],[2],[3],[4]], Matrix.column_vector([1,2,3,4]))
    261. 

  261.   end
    262. 

  262. 

  263.   def test_empty
    264. 

  264.     m = Matrix.empty(2, 0)
    265. 

  265.     assert_equal(Matrix[ [], [] ], m)
    266. 

  266.     n = Matrix.empty(0, 3)
    267. 

  267.     assert_equal(Matrix.columns([ [], [], [] ]), n)
    268. 

  268.     assert_equal(Matrix[[0, 0, 0], [0, 0, 0]], m * n)
    269. 

  269.   end
    270. 

  270. 

  271.   def test_row
    272. 

  272.     assert_equal(Vector[1, 2, 3], @m1.row(0))
    273. 

  273.     assert_equal(Vector[4, 5, 6], @m1.row(1))
    274. 

  274.     a = []; @m1.row(0) {|x| a << x }
    275. 

  275.     assert_equal([1, 2, 3], a)
    276. 

  276.   end
    277. 

  277. 

  278.   def test_column
    279. 

  279.     assert_equal(Vector[1, 4], @m1.column(0))
    280. 

  280.     assert_equal(Vector[2, 5], @m1.column(1))
    281. 

  281.     assert_equal(Vector[3, 6], @m1.column(2))
    282. 

  282.     a = []; @m1.column(0) {|x| a << x }
    283. 

  283.     assert_equal([1, 4], a)
    284. 

  284.   end
    285. 

  285. 

  286.   def test_collect
    287. 

  287.     m1 = Matrix.zero(2,2)
    288. 

  288.     m2 = Matrix.build(3,4){|row, col| 1}
    289. 

  289. 

  290.     assert_equal(Matrix[[5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5]], m2.collect{|e| e * 5})
    291. 

  291.     assert_equal(Matrix[[7, 0],[0, 7]], m1.collect(:diagonal){|e| e + 7})
    292. 

  292.     assert_equal(Matrix[[0, 5],[5, 0]], m1.collect(:off_diagonal){|e| e + 5})
    293. 

  293.     assert_equal(Matrix[[8, 1, 1, 1], [8, 8, 1, 1], [8, 8, 8, 1]], m2.collect(:lower){|e| e + 7})
    294. 

  294.     assert_equal(Matrix[[1, 1, 1, 1], [-11, 1, 1, 1], [-11, -11, 1, 1]], m2.collect(:strict_lower){|e| e - 12})
    295. 

  295.     assert_equal(Matrix[[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]], m2.collect(:strict_upper){|e| e ** 2})
    296. 

  296.     assert_equal(Matrix[[-1, -1, -1, -1], [1, -1, -1, -1], [1, 1, -1, -1]], m2.collect(:upper){|e| -e})
    297. 

  297.     assert_raise(ArgumentError) {m1.collect(:test){|e| e + 7}}
    298. 

  298.     assert_not_equal(m2, m2.collect {|e| e * 2 })
    299. 

  299.   end
    300. 

  300. 

  301.   def test_minor
    302. 

  302.     assert_equal(Matrix[[1, 2], [4, 5]], @m1.minor(0..1, 0..1))
    303. 

  303.     assert_equal(Matrix[[2], [5]], @m1.minor(0..1, 1..1))
    304. 

  304.     assert_equal(Matrix[[4, 5]], @m1.minor(1..1, 0..1))
    305. 

  305.     assert_equal(Matrix[[1, 2], [4, 5]], @m1.minor(0, 2, 0, 2))
    306. 

  306.     assert_equal(Matrix[[4, 5]], @m1.minor(1, 1, 0, 2))
    307. 

  307.     assert_equal(Matrix[[2], [5]], @m1.minor(0, 2, 1, 1))
    308. 

  308.     assert_raise(ArgumentError) { @m1.minor(0) }
    309. 

  309.   end
    310. 

  310. 

  311.   def test_first_minor
    312. 

  312.     assert_equal(Matrix.empty(0, 0), Matrix[[1]].first_minor(0, 0))
    313. 

  313.     assert_equal(Matrix.empty(0, 2), Matrix[[1, 4, 2]].first_minor(0, 1))
    314. 

  314.     assert_equal(Matrix[[1, 3]], @m1.first_minor(1, 1))
    315. 

  315.     assert_equal(Matrix[[4, 6]], @m1.first_minor(0, 1))
    316. 

  316.     assert_equal(Matrix[[1, 2]], @m1.first_minor(1, 2))
    317. 

  317.     assert_raise(RuntimeError) { Matrix.empty(0, 0).first_minor(0, 0) }
    318. 

  318.     assert_raise(ArgumentError) { @m1.first_minor(4, 0) }
    319. 

  319.     assert_raise(ArgumentError) { @m1.first_minor(0, -1) }
    320. 

  320.     assert_raise(ArgumentError) { @m1.first_minor(-1, 4) }
    321. 

  321.   end
    322. 

  322. 

  323.   def test_cofactor
    324. 

  324.     assert_equal(1, Matrix[[1]].cofactor(0, 0))
    325. 

  325.     assert_equal(9, Matrix[[7,6],[3,9]].cofactor(0, 0))
    326. 

  326.     assert_equal(0, Matrix[[0,0],[0,0]].cofactor(0, 0))
    327. 

  327.     assert_equal(3, Matrix[[0,0,1],[0,7,6],[1,3,9]].cofactor(1, 0))
    328. 

  328.     assert_equal(-21, Matrix[[7,0,1,0,12],[8,1,1,9,1],[4,0,0,-7,17],[-1,0,0,-4,8],[10,1,1,8,6]].cofactor(2, 3))
    329. 

  329.     assert_raise(RuntimeError) { Matrix.empty(0, 0).cofactor(0, 0) }
    330. 

  330.     assert_raise(ArgumentError) { Matrix[[0,0],[0,0]].cofactor(-1, 4) }
    331. 

  331.     assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { Matrix[[2,0,1],[0,-2,2]].cofactor(0, 0) }
    332. 

  332.   end
    333. 

  333. 

  334.   def test_adjugate
    335. 

  335.     assert_equal(Matrix.empty, Matrix.empty.adjugate)
    336. 

  336.     assert_equal(Matrix[[1]], Matrix[[5]].adjugate)
    337. 

  337.     assert_equal(Matrix[[9,-6],[-3,7]], Matrix[[7,6],[3,9]].adjugate)
    338. 

  338.     assert_equal(Matrix[[45,3,-7],[6,-1,0],[-7,0,0]], Matrix[[0,0,1],[0,7,6],[1,3,9]].adjugate)
    339. 

  339.     assert_equal(Matrix.identity(5), (@a5.adjugate * @a5) / @a5.det)
    340. 

  340.     assert_equal(Matrix.I(3), Matrix.I(3).adjugate)
    341. 

  341.     assert_equal((@a3 * @b3).adjugate, @b3.adjugate * @a3.adjugate)
    342. 

  342.     assert_equal(4**(@a3.row_count-1) * @a3.adjugate, (4 * @a3).adjugate)
    343. 

  343.     assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { @m1.adjugate }
    344. 

  344.   end
    345. 

  345. 

  346.   def test_laplace_expansion
    347. 

  347.     assert_equal(1, Matrix[[1]].laplace_expansion(row: 0))
    348. 

  348.     assert_equal(45, Matrix[[7,6], [3,9]].laplace_expansion(row: 1))
    349. 

  349.     assert_equal(0, Matrix[[0,0],[0,0]].laplace_expansion(column: 0))
    350. 

  350.     assert_equal(-7, Matrix[[0,0,1],[0,7,6],[1,3,9]].laplace_expansion(column: 2))
    351. 

  351. 

  352.     assert_equal(Vector[3, -2], Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0))
    353. 

  353. 

  354.     assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { @m1.laplace_expansion(row: 1) }
    355. 

  355.     assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion() }
    356. 

  356.     assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(foo: 1) }
    357. 

  357.     assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(row: 1, column: 1) }
    358. 

  358.     assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(row: 2) }
    359. 

  359.     assert_raise(ArgumentError) { Matrix[[0,0,1],[0,7,6],[1,3,9]].laplace_expansion(column: -1) }
    360. 

  360. 

  361.     assert_raise(RuntimeError) { Matrix.empty(0, 0).laplace_expansion(row: 0) }
    362. 

  362.   end
    363. 

  363. 

  364.   def test_regular?
    365. 

  365.     assert(Matrix[[1, 0], [0, 1]].regular?)
    366. 

  366.     assert(Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].regular?)
    367. 

  367.     assert(!Matrix[[1, 0, 0], [0, 0, 1], [0, 0, 1]].regular?)
    368. 

  368.   end
    369. 

  369. 

  370.   def test_singular?
    371. 

  371.     assert(!Matrix[[1, 0], [0, 1]].singular?)
    372. 

  372.     assert(!Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].singular?)
    373. 

  373.     assert(Matrix[[1, 0, 0], [0, 0, 1], [0, 0, 1]].singular?)
    374. 

  374.   end
    375. 

  375. 

  376.   def test_square?
    377. 

  377.     assert(Matrix[[1, 0], [0, 1]].square?)
    378. 

  378.     assert(Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].square?)
    379. 

  379.     assert(Matrix[[1, 0, 0], [0, 0, 1], [0, 0, 1]].square?)
    380. 

  380.     assert(!Matrix[[1, 0, 0], [0, 1, 0]].square?)
    381. 

  381.   end
    382. 

  382. 

  383.   def test_mul
    384. 

  384.     assert_equal(Matrix[[2,4],[6,8]], Matrix[[2,4],[6,8]] * Matrix.I(2))
    385. 

  385.     assert_equal(Matrix[[4,8],[12,16]], Matrix[[2,4],[6,8]] * 2)
    386. 

  386.     assert_equal(Matrix[[4,8],[12,16]], 2 * Matrix[[2,4],[6,8]])
    387. 

  387.     assert_equal(Matrix[[14,32],[32,77]], @m1 * @m1.transpose)
    388. 

  388.     assert_equal(Matrix[[17,22,27],[22,29,36],[27,36,45]], @m1.transpose * @m1)
    389. 

  389.     assert_equal(Vector[14,32], @m1 * Vector[1,2,3])
    390. 

  390.     o = Object.new
    391. 

  391.     def o.coerce(m)
    392. 

  392.       [m, m.transpose]
    393. 

  393.     end
    394. 

  394.     assert_equal(Matrix[[14,32],[32,77]], @m1 * o)
    395. 

  395.   end
    396. 

  396. 

  397.   def test_add
    398. 

  398.     assert_equal(Matrix[[6,0],[-4,12]], Matrix.scalar(2,5) + Matrix[[1,0],[-4,7]])
    399. 

  399.     assert_equal(Matrix[[3,5,7],[9,11,13]], @m1 + @n1)
    400. 

  400.     assert_equal(Matrix[[3,5,7],[9,11,13]], @n1 + @m1)
    401. 

  401.     assert_equal(Matrix[[2],[4],[6]], Matrix[[1],[2],[3]] + Vector[1,2,3])
    402. 

  402.     assert_raise(Matrix::ErrOperationNotDefined) { @m1 + 1 }
    403. 

  403.     o = Object.new
    404. 

  404.     def o.coerce(m)
    405. 

  405.       [m, m]
    406. 

  406.     end
    407. 

  407.     assert_equal(Matrix[[2,4,6],[8,10,12]], @m1 + o)
    408. 

  408.   end
    409. 

  409. 

  410.   def test_sub
    411. 

  411.     assert_equal(Matrix[[4,0],[4,-2]], Matrix.scalar(2,5) - Matrix[[1,0],[-4,7]])
    412. 

  412.     assert_equal(Matrix[[-1,-1,-1],[-1,-1,-1]], @m1 - @n1)
    413. 

  413.     assert_equal(Matrix[[1,1,1],[1,1,1]], @n1 - @m1)
    414. 

  414.     assert_equal(Matrix[[0],[0],[0]], Matrix[[1],[2],[3]] - Vector[1,2,3])
    415. 

  415.     assert_raise(Matrix::ErrOperationNotDefined) { @m1 - 1 }
    416. 

  416.     o = Object.new
    417. 

  417.     def o.coerce(m)
    418. 

  418.       [m, m]
    419. 

  419.     end
    420. 

  420.     assert_equal(Matrix[[0,0,0],[0,0,0]], @m1 - o)
    421. 

  421.   end
    422. 

  422. 

  423.   def test_div
    424. 

  424.     assert_equal(Matrix[[0,1,1],[2,2,3]], @m1 / 2)
    425. 

  425.     assert_equal(Matrix[[1,1],[1,1]], Matrix[[2,2],[2,2]] / Matrix.scalar(2,2))
    426. 

  426.     o = Object.new
    427. 

  427.     def o.coerce(m)
    428. 

  428.       [m, Matrix.scalar(2,2)]
    429. 

  429.     end
    430. 

  430.     assert_equal(Matrix[[1,1],[1,1]], Matrix[[2,2],[2,2]] / o)
    431. 

  431.   end
    432. 

  432. 

  433.   def test_hadamard_product
    434. 

  434.     assert_equal(Matrix[[1,4], [9,16]], Matrix[[1,2], [3,4]].hadamard_product(Matrix[[1,2], [3,4]]))
    435. 

  435.     assert_equal(Matrix[[2, 6, 12], [20, 30, 42]], @m1.hadamard_product(@n1))
    436. 

  436.     o = Object.new
    437. 

  437.     def o.to_matrix
    438. 

  438.       Matrix[[1, 2, 3], [-1, 0, 1]]
    439. 

  439.     end
    440. 

  440.     assert_equal(Matrix[[1, 4, 9], [-4, 0, 6]], @m1.hadamard_product(o))
    441. 

  441.     e = Matrix.empty(3, 0)
    442. 

  442.     assert_equal(e, e.hadamard_product(e))
    443. 

  443.     e = Matrix.empty(0, 3)
    444. 

  444.     assert_equal(e, e.hadamard_product(e))
    445. 

  445.   end
    446. 

  446. 

  447.   def test_exp
    448. 

  448.     assert_equal(Matrix[[67,96],[48,99]], Matrix[[7,6],[3,9]] ** 2)
    449. 

  449.     assert_equal(Matrix.I(5), Matrix.I(5) ** -1)
    450. 

  450.     assert_raise(Matrix::ErrOperationNotDefined) { Matrix.I(5) ** Object.new }
    451. 

  451.   end
    452. 

  452. 

  453.   def test_det
    454. 

  454.     assert_equal(Matrix.instance_method(:determinant), Matrix.instance_method(:det))
    455. 

  455.   end
    456. 

  456. 

  457.   def test_rank2
    458. 

  458.     assert_equal(2, Matrix[[7,6],[3,9]].rank)
    459. 

  459.     assert_equal(0, Matrix[[0,0],[0,0]].rank)
    460. 

  460.     assert_equal(3, Matrix[[0,0,1],[0,7,6],[1,3,9]].rank)
    461. 

  461.     assert_equal(1, Matrix[[0,1],[0,1],[0,1]].rank)
    462. 

  462.     assert_equal(2, @m1.rank)
    463. 

  463.   end
    464. 

  464. 

  465.   def test_trace
    466. 

  466.     assert_equal(1+5+9, Matrix[[1,2,3],[4,5,6],[7,8,9]].trace)
    467. 

  467.   end
    468. 

  468. 

  469.   def test_transpose
    470. 

  470.     assert_equal(Matrix[[1,4],[2,5],[3,6]], @m1.transpose)
    471. 

  471.   end
    472. 

  472. 

  473.   def test_conjugate
    474. 

  474.     assert_equal(Matrix[[Complex(1,-2), Complex(0,-1), 0], [1, 2, 3]], @c1.conjugate)
    475. 

  475.   end
    476. 

  476. 

  477.   def test_eigensystem
    478. 

  478.     m = Matrix[[1, 2], [3, 4]]
    479. 

  479.     v, d, v_inv = m.eigensystem
    480. 

  480.     assert(d.diagonal?)
    481. 

  481.     assert_equal(v.inv, v_inv)
    482. 

  482.     assert_equal((v * d * v_inv).round(5), m)
    483. 

  483.   end
    484. 

  484. 

  485.   def test_imaginary
    486. 

  486.     assert_equal(Matrix[[2, 1, 0], [0, 0, 0]], @c1.imaginary)
    487. 

  487.   end
    488. 

  488. 

  489.   def test_lup
    490. 

  490.     m = Matrix[[1, 2], [3, 4]]
    491. 

  491.     l, u, p = m.lup
    492. 

  492.     assert(l.lower_triangular?)
    493. 

  493.     assert(u.upper_triangular?)
    494. 

  494.     assert(p.permutation?)
    495. 

  495.     assert(l * u == p * m)
    496. 

  496.     assert_equal(m.lup.solve([2, 5]), Vector[1, Rational(1,2)])
    497. 

  497.   end
    498. 

  498. 

  499.   def test_real
    500. 

  500.     assert_equal(Matrix[[1, 0, 0], [1, 2, 3]], @c1.real)
    501. 

  501.   end
    502. 

  502. 

  503.   def test_rect
    504. 

  504.     assert_equal([Matrix[[1, 0, 0], [1, 2, 3]], Matrix[[2, 1, 0], [0, 0, 0]]], @c1.rect)
    505. 

  505.   end
    506. 

  506. 

  507.   def test_row_vectors
    508. 

  508.     assert_equal([Vector[1,2,3], Vector[4,5,6]], @m1.row_vectors)
    509. 

  509.   end
    510. 

  510. 

  511.   def test_column_vectors
    512. 

  512.     assert_equal([Vector[1,4], Vector[2,5], Vector[3,6]], @m1.column_vectors)
    513. 

  513.   end
    514. 

  514. 

  515.   def test_to_s
    516. 

  516.     assert_equal("Matrix[[1, 2, 3], [4, 5, 6]]", @m1.to_s)
    517. 

  517.     assert_equal("Matrix.empty(0, 0)", Matrix[].to_s)
    518. 

  518.     assert_equal("Matrix.empty(1, 0)", Matrix[[]].to_s)
    519. 

  519.   end
    520. 

  520. 

  521.   def test_inspect
    522. 

  522.     assert_equal("Matrix[[1, 2, 3], [4, 5, 6]]", @m1.inspect)
    523. 

  523.     assert_equal("Matrix.empty(0, 0)", Matrix[].inspect)
    524. 

  524.     assert_equal("Matrix.empty(1, 0)", Matrix[[]].inspect)
    525. 

  525.   end
    526. 

  526. 

  527.   def test_scalar_add
    528. 

  528.     s1 = @m1.coerce(1).first
    529. 

  529.     assert_equal(Matrix[[1]], (s1 + 0) * Matrix[[1]])
    530. 

  530.     assert_raise(Matrix::ErrOperationNotDefined) { s1 + Vector[0] }
    531. 

  531.     assert_raise(Matrix::ErrOperationNotDefined) { s1 + Matrix[[0]] }
    532. 

  532.     o = Object.new
    533. 

  533.     def o.coerce(x)
    534. 

  534.       [1, 1]
    535. 

  535.     end
    536. 

  536.     assert_equal(2, s1 + o)
    537. 

  537.   end
    538. 

  538. 

  539.   def test_scalar_sub
    540. 

  540.     s1 = @m1.coerce(1).first
    541. 

  541.     assert_equal(Matrix[[1]], (s1 - 0) * Matrix[[1]])
    542. 

  542.     assert_raise(Matrix::ErrOperationNotDefined) { s1 - Vector[0] }
    543. 

  543.     assert_raise(Matrix::ErrOperationNotDefined) { s1 - Matrix[[0]] }
    544. 

  544.     o = Object.new
    545. 

  545.     def o.coerce(x)
    546. 

  546.       [1, 1]
    547. 

  547.     end
    548. 

  548.     assert_equal(0, s1 - o)
    549. 

  549.   end
    550. 

  550. 

  551.   def test_scalar_mul
    552. 

  552.     s1 = @m1.coerce(1).first
    553. 

  553.     assert_equal(Matrix[[1]], (s1 * 1) * Matrix[[1]])
    554. 

  554.     assert_equal(Vector[2], s1 * Vector[2])
    555. 

  555.     assert_equal(Matrix[[2]], s1 * Matrix[[2]])
    556. 

  556.     o = Object.new
    557. 

  557.     def o.coerce(x)
    558. 

  558.       [1, 1]
    559. 

  559.     end
    560. 

  560.     assert_equal(1, s1 * o)
    561. 

  561.   end
    562. 

  562. 

  563.   def test_scalar_div
    564. 

  564.     s1 = @m1.coerce(1).first
    565. 

  565.     assert_equal(Matrix[[1]], (s1 / 1) * Matrix[[1]])
    566. 

  566.     assert_raise(Matrix::ErrOperationNotDefined) { s1 / Vector[0] }
    567. 

  567.     assert_equal(Matrix[[Rational(1,2)]], s1 / Matrix[[2]])
    568. 

  568.     o = Object.new
    569. 

  569.     def o.coerce(x)
    570. 

  570.       [1, 1]
    571. 

  571.     end
    572. 

  572.     assert_equal(1, s1 / o)
    573. 

  573.   end
    574. 

  574. 

  575.   def test_scalar_pow
    576. 

  576.     s1 = @m1.coerce(1).first
    577. 

  577.     assert_equal(Matrix[[1]], (s1 ** 1) * Matrix[[1]])
    578. 

  578.     assert_raise(Matrix::ErrOperationNotDefined) { s1 ** Vector[0] }
    579. 

  579.     assert_raise(Matrix::ErrOperationNotImplemented) { s1 ** Matrix[[1]] }
    580. 

  580.     o = Object.new
    581. 

  581.     def o.coerce(x)
    582. 

  582.       [1, 1]
    583. 

  583.     end
    584. 

  584.     assert_equal(1, s1 ** o)
    585. 

  585.   end
    586. 

  586. 

  587.   def test_abs
    588. 

  588.     s1 = @a3.abs
    589. 

  589.     assert_equal(s1, Matrix[[4, 1, 3], [0, 3, 7], [11, 4, 2]])
    590. 

  590.   end
    591. 

  591. 

  592.   def test_hstack
    593. 

  593.     assert_equal Matrix[[1,2,3,2,3,4,1,2,3], [4,5,6,5,6,7,4,5,6]],
    594. 

  594.       @m1.hstack(@n1, @m1)
    595. 

  595.     # Error checking:
    596. 

  596.     assert_raise(TypeError) { @m1.hstack(42) }
    597. 

  597.     assert_raise(TypeError) { Matrix.hstack(42, @m1) }
    598. 

  598.     assert_raise(Matrix::ErrDimensionMismatch) { @m1.hstack(Matrix.identity(3)) }
    599. 

  599.     assert_raise(Matrix::ErrDimensionMismatch) { @e1.hstack(@e2) }
    600. 

  600.     # Corner cases:
    601. 

  601.     assert_equal @m1, @m1.hstack
    602. 

  602.     assert_equal @e1, @e1.hstack(@e1)
    603. 

  603.     assert_equal Matrix.empty(0,6), @e2.hstack(@e2)
    604. 

  604.     assert_equal SubMatrix, SubMatrix.hstack(@e1).class
    605. 

  605.     # From Vectors:
    606. 

  606.     assert_equal Matrix[[1, 3],[2, 4]], Matrix.hstack(Vector[1,2], Vector[3, 4])
    607. 

  607.   end
    608. 

  608. 

  609.   def test_vstack
    610. 

  610.     assert_equal Matrix[[1,2,3], [4,5,6], [2,3,4], [5,6,7], [1,2,3], [4,5,6]],
    611. 

  611.       @m1.vstack(@n1, @m1)
    612. 

  612.     # Error checking:
    613. 

  613.     assert_raise(TypeError) { @m1.vstack(42) }
    614. 

  614.     assert_raise(TypeError) { Matrix.vstack(42, @m1) }
    615. 

  615.     assert_raise(Matrix::ErrDimensionMismatch) { @m1.vstack(Matrix.identity(2)) }
    616. 

  616.     assert_raise(Matrix::ErrDimensionMismatch) { @e1.vstack(@e2) }
    617. 

  617.     # Corner cases:
    618. 

  618.     assert_equal @m1, @m1.vstack
    619. 

  619.     assert_equal Matrix.empty(4,0), @e1.vstack(@e1)
    620. 

  620.     assert_equal @e2, @e2.vstack(@e2)
    621. 

  621.     assert_equal SubMatrix, SubMatrix.vstack(@e1).class
    622. 

  622.     # From Vectors:
    623. 

  623.     assert_equal Matrix[[1],[2],[3]], Matrix.vstack(Vector[1,2], Vector[3])
    624. 

  624.   end
    625. 

  625. 

  626.   def test_combine
    627. 

  627.     x = Matrix[[6, 6], [4, 4]]
    628. 

  628.     y = Matrix[[1, 2], [3, 4]]
    629. 

  629.     assert_equal Matrix[[5, 4], [1, 0]], Matrix.combine(x, y) {|a, b| a - b}
    630. 

  630.     assert_equal Matrix[[5, 4], [1, 0]], x.combine(y) {|a, b| a - b}
    631. 

  631.     # Without block
    632. 

  632.     assert_equal Matrix[[5, 4], [1, 0]], Matrix.combine(x, y).each {|a, b| a - b}
    633. 

  633.     # With vectors
    634. 

  634.     assert_equal Matrix[[111], [222]], Matrix.combine(Matrix[[1], [2]], Vector[10,20], Vector[100,200], &:sum)
    635. 

  635.     # Basic checks
    636. 

  636.     assert_raise(Matrix::ErrDimensionMismatch) { @m1.combine(x) { raise } }
    637. 

  637.     # Edge cases
    638. 

  638.     assert_equal Matrix.empty, Matrix.combine{ raise }
    639. 

  639.     assert_equal Matrix.empty(3,0), Matrix.combine(Matrix.empty(3,0), Matrix.empty(3,0)) { raise }
    640. 

  640.     assert_equal Matrix.empty(0,3), Matrix.combine(Matrix.empty(0,3), Matrix.empty(0,3)) { raise }
    641. 

  641.   end
    642. 

  642. 

  643.   def test_set_element
    644. 

  644.     src = Matrix[
    645. 

  645.       [1, 2, 3, 4],
    646. 

  646.       [5, 6, 7, 8],
    647. 

  647.       [9, 10, 11, 12],
    648. 

  648.     ]
    649. 

  649.     rows = {
    650. 

  650.       range:   [1..2, 1...3, 1..-1, -2..2, 1.., 1..., -2.., -2...],
    651. 

  651.       int:     [2, -1],
    652. 

  652.       invalid: [-4, 4, -4..2, 2..-4, 0...0, 2..0, -4..],
    653. 

  653.     }
    654. 

  654.     columns = {
    655. 

  655.       range:   [2..3, 2...4, 2..-1, -2..3, 2.., 2..., -2..., -2..],
    656. 

  656.       int:     [3, -1],
    657. 

  657.       invalid: [-5, 5, -5..2, 2..-5, 0...0, -5..],
    658. 

  658.     }
    659. 

  659.     values = {
    660. 

  660.       element: 42,
    661. 

  661.       matrix:  Matrix[[20, 21], [22, 23]],
    662. 

  662.       vector:  Vector[30, 31],
    663. 

  663.       row:     Matrix[[60, 61]],
    664. 

  664.       column:  Matrix[[50], [51]],
    665. 

  665.       mismatched_matrix: Matrix.identity(3),
    666. 

  666.       mismatched_vector: Vector[0, 1, 2, 3],
    667. 

  667.     }
    668. 

  668.     solutions = {
    669. 

  669.       [:int, :int] => {
    670. 

  670.         element: Matrix[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 42]],
    671. 

  671.       },
    672. 

  672.       [:range , :int] => {
    673. 

  673.         element: Matrix[[1, 2, 3, 4], [5, 6, 7, 42], [9, 10, 11, 42]],
    674. 

  674.         column:  Matrix[[1, 2, 3, 4], [5, 6, 7, 50], [9, 10, 11, 51]],
    675. 

  675.         vector:  Matrix[[1, 2, 3, 4], [5, 6, 7, 30], [9, 10, 11, 31]],
    676. 

  676.       },
    677. 

  677.       [:int, :range] => {
    678. 

  678.         element: Matrix[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 42, 42]],
    679. 

  679.         row:     Matrix[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 60, 61]],
    680. 

  680.         vector:  Matrix[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 30, 31]],
    681. 

  681.       },
    682. 

  682.       [:range , :range] => {
    683. 

  683.         element: Matrix[[1, 2, 3, 4], [5, 6, 42, 42], [9, 10, 42, 42]],
    684. 

  684.         matrix:  Matrix[[1, 2, 3, 4], [5, 6, 20, 21], [9, 10, 22, 23]],
    685. 

  685.       },
    686. 

  686.     }
    687. 

  687.     solutions.default = Hash.new(IndexError)
    688. 

  688. 

  689.     rows.each do |row_style, row_arguments|
    690. 

  690.       row_arguments.each do |row_argument|
    691. 

  691.         columns.each do |column_style, column_arguments|
    692. 

  692.           column_arguments.each do |column_argument|
    693. 

  693.             values.each do |value_type, value|
    694. 

  694.               expected = solutions[[row_style, column_style]][value_type] || Matrix::ErrDimensionMismatch
    695. 

  695. 

  696.               result = src.clone
    697. 

  697.               begin
    698. 

  698.                 result[row_argument, column_argument] = value
    699. 

  699.                 assert_equal expected, result,
    700. 

  700.                   "m[#{row_argument.inspect}][#{column_argument.inspect}] = #{value.inspect} failed"
    701. 

  701.               rescue Exception => e
    702. 

  702.                 raise if e.class != expected
    703. 

  703.               end
    704. 

  704.             end
    705. 

  705.           end
    706. 

  706.         end
    707. 

  707.       end
    708. 

  708.     end
    709. 

  709.   end
    710. 

  710. 

  711.   def test_map!
    712. 

  712.     m1 = Matrix.zero(2,2)
    713. 

  713.     m2 = Matrix.build(3,4){|row, col| 1}
    714. 

  714.     m3 = Matrix.zero(3,5).freeze
    715. 

  715.     m4 = Matrix.empty.freeze
    716. 

  716. 

  717.     assert_equal Matrix[[5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5, 5]], m2.map!{|e| e * 5}
    718. 

  718.     assert_equal Matrix[[7, 0],[0, 7]], m1.map!(:diagonal){|e| e + 7}
    719. 

  719.     assert_equal Matrix[[7, 5],[5, 7]], m1.map!(:off_diagonal){|e| e + 5}
    720. 

  720.     assert_equal Matrix[[12, 5, 5, 5], [12, 12, 5, 5], [12, 12, 12, 5]], m2.map!(:lower){|e| e + 7}
    721. 

  721.     assert_equal Matrix[[12, 5, 5, 5], [0, 12, 5, 5], [0, 0, 12, 5]], m2.map!(:strict_lower){|e| e - 12}
    722. 

  722.     assert_equal Matrix[[12, 25, 25, 25], [0, 12, 25, 25], [0, 0, 12, 25]], m2.map!(:strict_upper){|e| e ** 2}
    723. 

  723.     assert_equal Matrix[[-12, -25, -25, -25], [0, -12, -25, -25], [0, 0, -12, -25]], m2.map!(:upper){|e| -e}
    724. 

  724.     assert_equal m1, m1.map!{|e| e ** 2 }
    725. 

  725.     assert_equal m2, m2.map!(:lower){ |e| e - 3 }
    726. 

  726.     assert_raise(ArgumentError) {m1.map!(:test){|e| e + 7}}
    727. 

  727.     assert_raise(FrozenError) { m3.map!{|e| e * 2} }
    728. 

  728.     assert_raise(FrozenError) { m4.map!{} }
    729. 

  729.   end
    730. 

  730. 

  731.   def test_freeze
    732. 

  732.     m = Matrix[[1, 2, 3],[4, 5, 6]]
    733. 

  733.     f = m.freeze
    734. 

  734.     assert_equal true, f.frozen?
    735. 

  735.     assert m.equal?(f)
    736. 

  736.     assert m.equal?(f.freeze)
    737. 

  737.     assert_raise(FrozenError){ m[0, 1] = 56 }
    738. 

  738.     assert_equal m.dup, m
    739. 

  739.   end
    740. 

  740. 

  741.   def test_clone
    742. 

  742.     a = Matrix[[4]]
    743. 

  743.     def a.foo
    744. 

  744.       42
    745. 

  745.     end
    746. 

  746. 

  747.     m = a.clone
    748. 

  748.     m[0, 0] = 2
    749. 

  749.     assert_equal a, m * 2
    750. 

  750.     assert_equal 42, m.foo
    751. 

  751. 

  752.     a.freeze
    753. 

  753.     m = a.clone
    754. 

  754.     assert m.frozen?
    755. 

  755.     assert_equal 42, m.foo
    756. 

  756.   end
    757. 

  757. 

  758.   def test_dup
    759. 

  759.     a = Matrix[[4]]
    760. 

  760.     def a.foo
    761. 

  761.       42
    762. 

  762.     end
    763. 

  763.     a.freeze
    764. 

  764. 

  765.     m = a.dup
    766. 

  766.     m[0, 0] = 2
    767. 

  767.     assert_equal a, m * 2
    768. 

  768.     assert !m.respond_to?(:foo)
    769. 

  769.   end
    770. 

  770. 

  771.   def test_eigenvalues_and_eigenvectors_symmetric
    772. 

  772.     m = Matrix[
    773. 

  773.       [8, 1],
    774. 

  774.       [1, 8]
    775. 

  775.     ]
    776. 

  776.     values = m.eigensystem.eigenvalues
    777. 

  777.     assert_in_epsilon(7.0, values[0])
    778. 

  778.     assert_in_epsilon(9.0, values[1])
    779. 

  779.     vectors = m.eigensystem.eigenvectors
    780. 

  780.     assert_in_epsilon(-vectors[0][0], vectors[0][1])
    781. 

  781.     assert_in_epsilon(vectors[1][0], vectors[1][1])
    782. 

  782.   end
    783. 

  783. 

  784.   def test_eigenvalues_and_eigenvectors_nonsymmetric
    785. 

  785.     m = Matrix[
    786. 

  786.       [8, 1],
    787. 

  787.       [4, 5]
    788. 

  788.     ]
    789. 

  789.     values = m.eigensystem.eigenvalues
    790. 

  790.     assert_in_epsilon(9.0, values[0])
    791. 

  791.     assert_in_epsilon(4.0, values[1])
    792. 

  792.     vectors = m.eigensystem.eigenvectors
    793. 

  793.     assert_in_epsilon(vectors[0][0], vectors[0][1])
    794. 

  794.     assert_in_epsilon(-4 * vectors[1][0], vectors[1][1])
    795. 

  795.   end
    796. 

  796. 

  797.   def test_unitary?
    798. 

  798.     assert_equal true, @rot.unitary?
    799. 

  799.     assert_equal true, ((0+1i) * @rot).unitary?
    800. 

  800.     assert_equal false, @a3.unitary?
    801. 

  801.     assert_raise(Matrix::ErrDimensionMismatch) { @m1.unitary? }
    802. 

  802.   end
    803. 

  803. 

  804.   def test_orthogonal
    805. 

  805.     assert_equal true, @rot.orthogonal?
    806. 

  806.     assert_equal false, ((0+1i) * @rot).orthogonal?
    807. 

  807.     assert_equal false, @a3.orthogonal?
    808. 

  808.     assert_raise(Matrix::ErrDimensionMismatch) { @m1.orthogonal? }
    809. 

  809.   end
    810. 

  810. 

  811.   def test_adjoint
    812. 

  812.     assert_equal(Matrix[[(1-2i), 1], [(0-1i), 2], [0, 3]], @c1.adjoint)
    813. 

  813.     assert_equal(Matrix.empty(0,2), @e1.adjoint)
    814. 

  814.   end
    815. 

  815. end
    816. 

  816.