/lib/matplotlib/mathtext.py

r"""
:mod:`~matplotlib.mathtext` is a module for parsing a subset of the
TeX math syntax and drawing them to a matplotlib backend.

For a tutorial of its usage see :ref:`mathtext-tutorial`.  This
document is primarily concerned with implementation details.

The module uses pyparsing_ to parse the TeX expression.

.. _pyparsing: http://pyparsing.wikispaces.com/

The Bakoma distribution of the TeX Computer Modern fonts, and STIX
fonts are supported.  There is experimental support for using
arbitrary fonts, but results may vary without proper tweaking and
metrics for those fonts.

If you find TeX expressions that don't parse or render properly,
please email mdroe@stsci.edu, but please check KNOWN ISSUES below first.
"""
from __future__ import (absolute_import, division, print_function,
                        unicode_literals)

import six

import os, sys
if six.PY3:
    unichr = chr
from math import ceil
try:
    set
except NameError:
    from sets import Set as set
import unicodedata
from warnings import warn

from numpy import inf, isinf
import numpy as np

import pyparsing
from pyparsing import Combine, Group, Optional, Forward, \
     Literal, OneOrMore, ZeroOrMore, ParseException, Empty, \
     ParseResults, Suppress, oneOf, StringEnd, ParseFatalException, \
     FollowedBy, Regex, ParserElement, QuotedString, ParseBaseException

# Enable packrat parsing
if (six.PY3 and
    [int(x) for x in pyparsing.__version__.split('.')] < [2, 0, 0]):
    warn("Due to a bug in pyparsing <= 2.0.0 on Python 3.x, packrat parsing "
         "has been disabled.  Mathtext rendering will be much slower as a "
         "result.  Install pyparsing 2.0.0 or later to improve performance.")
else:
    ParserElement.enablePackrat()

from matplotlib.afm import AFM
from matplotlib.cbook import Bunch, get_realpath_and_stat, \
    is_string_like, maxdict
from matplotlib.ft2font import FT2Font, FT2Image, KERNING_DEFAULT, LOAD_FORCE_AUTOHINT, LOAD_NO_HINTING
from matplotlib.font_manager import findfont, FontProperties
from matplotlib._mathtext_data import latex_to_bakoma, \
        latex_to_standard, tex2uni, latex_to_cmex, stix_virtual_fonts
from matplotlib import get_data_path, rcParams

import matplotlib.colors as mcolors
import matplotlib._png as _png
####################



##############################################################################
# FONTS

def get_unicode_index(symbol):
    """get_unicode_index(symbol) -> integer

Return the integer index (from the Unicode table) of symbol.  *symbol*
can be a single unicode character, a TeX command (i.e. r'\pi'), or a
Type1 symbol name (i.e. 'phi').
"""
    # From UTF #25: U+2212 minus sign is the preferred
    # representation of the unary and binary minus sign rather than
    # the ASCII-derived U+002D hyphen-minus, because minus sign is
    # unambiguous and because it is rendered with a more desirable
    # length, usually longer than a hyphen.
    if symbol == '-':
        return 0x2212
    try:# This will succeed if symbol is a single unicode char
        return ord(symbol)
    except TypeError:
        pass
    try:# Is symbol a TeX symbol (i.e. \alpha)
        return tex2uni[symbol.strip("\\")]
    except KeyError:
        message = """'%(symbol)s' is not a valid Unicode character or
TeX/Type1 symbol"""%locals()
        raise ValueError(message)

def unichr_safe(index):
    """Return the Unicode character corresponding to the index,
or the replacement character if this is a narrow build of Python
and the requested character is outside the BMP."""
    try:
        return unichr(index)
    except ValueError:
        return unichr(0xFFFD)

class MathtextBackend(object):
    """
    The base class for the mathtext backend-specific code.  The
    purpose of :class:`MathtextBackend` subclasses is to interface
    between mathtext and a specific matplotlib graphics backend.

    Subclasses need to override the following:

      - :meth:`render_glyph`
      - :meth:`render_filled_rect`
      - :meth:`get_results`

    And optionally, if you need to use a Freetype hinting style:

      - :meth:`get_hinting_type`
    """
    def __init__(self):
        self.width = 0
        self.height = 0
        self.depth = 0

    def set_canvas_size(self, w, h, d):
        'Dimension the drawing canvas'
        self.width  = w
        self.height = h
        self.depth  = d

    def render_glyph(self, ox, oy, info):
        """
        Draw a glyph described by *info* to the reference point (*ox*,
        *oy*).
        """
        raise NotImplementedError()

    def render_filled_rect(self, x1, y1, x2, y2):
        """
        Draw a filled black rectangle from (*x1*, *y1*) to (*x2*, *y2*).
        """
        raise NotImplementedError()

    def get_results(self, box):
        """
        Return a backend-specific tuple to return to the backend after
        all processing is done.
        """
        raise NotImplementedError()

    def get_hinting_type(self):
        """
        Get the Freetype hinting type to use with this particular
        backend.
        """
        return LOAD_NO_HINTING

class MathtextBackendAgg(MathtextBackend):
    """
    Render glyphs and rectangles to an FTImage buffer, which is later
    transferred to the Agg image by the Agg backend.
    """
    def __init__(self):
        self.ox = 0
        self.oy = 0
        self.image = None
        self.mode = 'bbox'
        self.bbox = [0, 0, 0, 0]
        MathtextBackend.__init__(self)

    def _update_bbox(self, x1, y1, x2, y2):
        self.bbox = [min(self.bbox[0], x1),
                     min(self.bbox[1], y1),
                     max(self.bbox[2], x2),
                     max(self.bbox[3], y2)]

    def set_canvas_size(self, w, h, d):
        MathtextBackend.set_canvas_size(self, w, h, d)
        if self.mode != 'bbox':
            self.image = FT2Image(ceil(w), ceil(h + d))

    def render_glyph(self, ox, oy, info):
        if self.mode == 'bbox':
            self._update_bbox(ox + info.metrics.xmin,
                              oy - info.metrics.ymax,
                              ox + info.metrics.xmax,
                              oy - info.metrics.ymin)
        else:
            info.font.draw_glyph_to_bitmap(
                self.image, ox, oy - info.metrics.iceberg, info.glyph,
                antialiased=rcParams['text.antialiased'])

    def render_rect_filled(self, x1, y1, x2, y2):
        if self.mode == 'bbox':
            self._update_bbox(x1, y1, x2, y2)
        else:
            height = max(int(y2 - y1) - 1, 0)
            if height == 0:
                center = (y2 + y1) / 2.0
                y = int(center - (height + 1) / 2.0)
            else:
                y = int(y1)
            self.image.draw_rect_filled(int(x1), y, ceil(x2), y + height)

    def get_results(self, box, used_characters):
        self.mode = 'bbox'
        orig_height = box.height
        orig_depth  = box.depth
        ship(0, 0, box)
        bbox = self.bbox
        bbox = [bbox[0] - 1, bbox[1] - 1, bbox[2] + 1, bbox[3] + 1]
        self.mode = 'render'
        self.set_canvas_size(
            bbox[2] - bbox[0],
            (bbox[3] - bbox[1]) - orig_depth,
            (bbox[3] - bbox[1]) - orig_height)
        ship(-bbox[0], -bbox[1], box)
        result = (self.ox,
                  self.oy,
                  self.width,
                  self.height + self.depth,
                  self.depth,
                  self.image,
                  used_characters)
        self.image = None
        return result

    def get_hinting_type(self):
        from matplotlib.backends import backend_agg
        return backend_agg.get_hinting_flag()

class MathtextBackendBitmap(MathtextBackendAgg):
    def get_results(self, box, used_characters):
        ox, oy, width, height, depth, image, characters = \
            MathtextBackendAgg.get_results(self, box, used_characters)
        return image, depth

class MathtextBackendPs(MathtextBackend):
    """
    Store information to write a mathtext rendering to the PostScript
    backend.
    """
    def __init__(self):
        self.pswriter = six.moves.cStringIO()
        self.lastfont = None

    def render_glyph(self, ox, oy, info):
        oy = self.height - oy + info.offset
        postscript_name = info.postscript_name
        fontsize        = info.fontsize
        symbol_name     = info.symbol_name

        if (postscript_name, fontsize) != self.lastfont:
            ps = """/%(postscript_name)s findfont
%(fontsize)s scalefont
setfont
""" % locals()
            self.lastfont = postscript_name, fontsize
            self.pswriter.write(ps)

        ps = """%(ox)f %(oy)f moveto
/%(symbol_name)s glyphshow\n
""" % locals()
        self.pswriter.write(ps)

    def render_rect_filled(self, x1, y1, x2, y2):
        ps = "%f %f %f %f rectfill\n" % (x1, self.height - y2, x2 - x1, y2 - y1)
        self.pswriter.write(ps)

    def get_results(self, box, used_characters):
        ship(0, 0, box)
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.pswriter,
                used_characters)

class MathtextBackendPdf(MathtextBackend):
    """
    Store information to write a mathtext rendering to the PDF
    backend.
    """
    def __init__(self):
        self.glyphs = []
        self.rects = []

    def render_glyph(self, ox, oy, info):
        filename = info.font.fname
        oy = self.height - oy + info.offset
        self.glyphs.append(
            (ox, oy, filename, info.fontsize,
             info.num, info.symbol_name))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.rects.append((x1, self.height - y2, x2 - x1, y2 - y1))

    def get_results(self, box, used_characters):
        ship(0, 0, box)
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.glyphs,
                self.rects,
                used_characters)

class MathtextBackendSvg(MathtextBackend):
    """
    Store information to write a mathtext rendering to the SVG
    backend.
    """
    def __init__(self):
        self.svg_glyphs = []
        self.svg_rects = []

    def render_glyph(self, ox, oy, info):
        oy = self.height - oy + info.offset

        self.svg_glyphs.append(
            (info.font, info.fontsize, info.num, ox, oy, info.metrics))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.svg_rects.append(
            (x1, self.height - y1 + 1, x2 - x1, y2 - y1))

    def get_results(self, box, used_characters):
        ship(0, 0, box)
        svg_elements = Bunch(svg_glyphs = self.svg_glyphs,
                             svg_rects = self.svg_rects)
        return (self.width,
                self.height + self.depth,
                self.depth,
                svg_elements,
                used_characters)

class MathtextBackendPath(MathtextBackend):
    """
    Store information to write a mathtext rendering to the text path
    machinery.
    """

    def __init__(self):
        self.glyphs = []
        self.rects = []

    def render_glyph(self, ox, oy, info):
        oy = self.height - oy + info.offset
        thetext = info.num
        self.glyphs.append(
            (info.font, info.fontsize, thetext, ox, oy))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.rects.append(
            (x1, self.height-y2 , x2 - x1, y2 - y1))

    def get_results(self, box, used_characters):
        ship(0, 0, box)
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.glyphs,
                self.rects)

class MathtextBackendCairo(MathtextBackend):
    """
    Store information to write a mathtext rendering to the Cairo
    backend.
    """

    def __init__(self):
        self.glyphs = []
        self.rects = []

    def render_glyph(self, ox, oy, info):
        oy = oy - info.offset - self.height
        thetext = unichr_safe(info.num)
        self.glyphs.append(
            (info.font, info.fontsize, thetext, ox, oy))

    def render_rect_filled(self, x1, y1, x2, y2):
        self.rects.append(
            (x1, y1 - self.height, x2 - x1, y2 - y1))

    def get_results(self, box, used_characters):
        ship(0, 0, box)
        return (self.width,
                self.height + self.depth,
                self.depth,
                self.glyphs,
                self.rects)

class Fonts(object):
    """
    An abstract base class for a system of fonts to use for mathtext.

    The class must be able to take symbol keys and font file names and
    return the character metrics.  It also delegates to a backend class
    to do the actual drawing.
    """

    def __init__(self, default_font_prop, mathtext_backend):
        """
        *default_font_prop*: A
        :class:`~matplotlib.font_manager.FontProperties` object to use
        for the default non-math font, or the base font for Unicode
        (generic) font rendering.

        *mathtext_backend*: A subclass of :class:`MathTextBackend`
        used to delegate the actual rendering.
        """
        self.default_font_prop = default_font_prop
        self.mathtext_backend = mathtext_backend
        self.used_characters = {}

    def destroy(self):
        """
        Fix any cyclical references before the object is about
        to be destroyed.
        """
        self.used_characters = None

    def get_kern(self, font1, fontclass1, sym1, fontsize1,
                 font2, fontclass2, sym2, fontsize2, dpi):
        """
        Get the kerning distance for font between *sym1* and *sym2*.

        *fontX*: one of the TeX font names::

          tt, it, rm, cal, sf, bf or default/regular (non-math)

        *fontclassX*: TODO

        *symX*: a symbol in raw TeX form. e.g., '1', 'x' or '\sigma'

        *fontsizeX*: the fontsize in points

        *dpi*: the current dots-per-inch
        """
        return 0.

    def get_metrics(self, font, font_class, sym, fontsize, dpi):
        """
        *font*: one of the TeX font names::

          tt, it, rm, cal, sf, bf or default/regular (non-math)

        *font_class*: TODO

        *sym*:  a symbol in raw TeX form. e.g., '1', 'x' or '\sigma'

        *fontsize*: font size in points

        *dpi*: current dots-per-inch

        Returns an object with the following attributes:

          - *advance*: The advance distance (in points) of the glyph.

          - *height*: The height of the glyph in points.

          - *width*: The width of the glyph in points.

          - *xmin*, *xmax*, *ymin*, *ymax* - the ink rectangle of the glyph

          - *iceberg* - the distance from the baseline to the top of
            the glyph.  This corresponds to TeX's definition of
            "height".
        """
        info = self._get_info(font, font_class, sym, fontsize, dpi)
        return info.metrics

    def set_canvas_size(self, w, h, d):
        """
        Set the size of the buffer used to render the math expression.
        Only really necessary for the bitmap backends.
        """
        self.width, self.height, self.depth = ceil(w), ceil(h), ceil(d)
        self.mathtext_backend.set_canvas_size(self.width, self.height, self.depth)

    def render_glyph(self, ox, oy, facename, font_class, sym, fontsize, dpi):
        """
        Draw a glyph at

          - *ox*, *oy*: position

          - *facename*: One of the TeX face names

          - *font_class*:

          - *sym*: TeX symbol name or single character

          - *fontsize*: fontsize in points

          - *dpi*: The dpi to draw at.
        """
        info = self._get_info(facename, font_class, sym, fontsize, dpi)
        realpath, stat_key = get_realpath_and_stat(info.font.fname)
        used_characters = self.used_characters.setdefault(
            stat_key, (realpath, set()))
        used_characters[1].add(info.num)
        self.mathtext_backend.render_glyph(ox, oy, info)

    def render_rect_filled(self, x1, y1, x2, y2):
        """
        Draw a filled rectangle from (*x1*, *y1*) to (*x2*, *y2*).
        """
        self.mathtext_backend.render_rect_filled(x1, y1, x2, y2)

    def get_xheight(self, font, fontsize, dpi):
        """
        Get the xheight for the given *font* and *fontsize*.
        """
        raise NotImplementedError()

    def get_underline_thickness(self, font, fontsize, dpi):
        """
        Get the line thickness that matches the given font.  Used as a
        base unit for drawing lines such as in a fraction or radical.
        """
        raise NotImplementedError()

    def get_used_characters(self):
        """
        Get the set of characters that were used in the math
        expression.  Used by backends that need to subset fonts so
        they know which glyphs to include.
        """
        return self.used_characters

    def get_results(self, box):
        """
        Get the data needed by the backend to render the math
        expression.  The return value is backend-specific.
        """
        result = self.mathtext_backend.get_results(box, self.get_used_characters())
        self.destroy()
        return result

    def get_sized_alternatives_for_symbol(self, fontname, sym):
        """
        Override if your font provides multiple sizes of the same
        symbol.  Should return a list of symbols matching *sym* in
        various sizes.  The expression renderer will select the most
        appropriate size for a given situation from this list.
        """
        return [(fontname, sym)]

class TruetypeFonts(Fonts):
    """
    A generic base class for all font setups that use Truetype fonts
    (through FT2Font).
    """
    class CachedFont:
        def __init__(self, font):
            self.font     = font
            self.charmap  = font.get_charmap()
            self.glyphmap = dict(
                [(glyphind, ccode) for ccode, glyphind in six.iteritems(self.charmap)])

        def __repr__(self):
            return repr(self.font)

    def __init__(self, default_font_prop, mathtext_backend):
        Fonts.__init__(self, default_font_prop, mathtext_backend)
        self.glyphd = {}
        self._fonts = {}

        filename = findfont(default_font_prop)
        default_font = self.CachedFont(FT2Font(filename))
        self._fonts['default'] = default_font
        self._fonts['regular'] = default_font

    def destroy(self):
        self.glyphd = None
        Fonts.destroy(self)

    def _get_font(self, font):
        if font in self.fontmap:
            basename = self.fontmap[font]
        else:
            basename = font

        cached_font = self._fonts.get(basename)
        if cached_font is None and os.path.exists(basename):
            font = FT2Font(basename)
            cached_font = self.CachedFont(font)
            self._fonts[basename] = cached_font
            self._fonts[font.postscript_name] = cached_font
            self._fonts[font.postscript_name.lower()] = cached_font
        return cached_font

    def _get_offset(self, cached_font, glyph, fontsize, dpi):
        if cached_font.font.postscript_name == 'Cmex10':
            return ((glyph.height/64.0/2.0) + (fontsize/3.0 * dpi/72.0))
        return 0.

    def _get_info(self, fontname, font_class, sym, fontsize, dpi):
        key = fontname, font_class, sym, fontsize, dpi
        bunch = self.glyphd.get(key)
        if bunch is not None:
            return bunch

        cached_font, num, symbol_name, fontsize, slanted = \
            self._get_glyph(fontname, font_class, sym, fontsize)

        font = cached_font.font
        font.set_size(fontsize, dpi)
        glyph = font.load_char(
            num,
            flags=self.mathtext_backend.get_hinting_type())

        xmin, ymin, xmax, ymax = [val/64.0 for val in glyph.bbox]
        offset = self._get_offset(cached_font, glyph, fontsize, dpi)
        metrics = Bunch(
            advance = glyph.linearHoriAdvance/65536.0,
            height  = glyph.height/64.0,
            width   = glyph.width/64.0,
            xmin    = xmin,
            xmax    = xmax,
            ymin    = ymin+offset,
            ymax    = ymax+offset,
            # iceberg is the equivalent of TeX's "height"
            iceberg = glyph.horiBearingY/64.0 + offset,
            slanted = slanted
            )

        result = self.glyphd[key] = Bunch(
            font            = font,
            fontsize        = fontsize,
            postscript_name = font.postscript_name,
            metrics         = metrics,
            symbol_name     = symbol_name,
            num             = num,
            glyph           = glyph,
            offset          = offset
            )
        return result

    def get_xheight(self, font, fontsize, dpi):
        cached_font = self._get_font(font)
        cached_font.font.set_size(fontsize, dpi)
        pclt = cached_font.font.get_sfnt_table('pclt')
        if pclt is None:
            # Some fonts don't store the xHeight, so we do a poor man's xHeight
            metrics = self.get_metrics(font, rcParams['mathtext.default'], 'x', fontsize, dpi)
            return metrics.iceberg
        xHeight = (pclt['xHeight'] / 64.0) * (fontsize / 12.0) * (dpi / 100.0)
        return xHeight

    def get_underline_thickness(self, font, fontsize, dpi):
        # This function used to grab underline thickness from the font
        # metrics, but that information is just too un-reliable, so it
        # is now hardcoded.
        return ((0.75 / 12.0) * fontsize * dpi) / 72.0

    def get_kern(self, font1, fontclass1, sym1, fontsize1,
                 font2, fontclass2, sym2, fontsize2, dpi):
        if font1 == font2 and fontsize1 == fontsize2:
            info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
            info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
            font = info1.font
            return font.get_kerning(info1.num, info2.num, KERNING_DEFAULT) / 64.0
        return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1,
                              font2, fontclass2, sym2, fontsize2, dpi)

class BakomaFonts(TruetypeFonts):
    """
    Use the Bakoma TrueType fonts for rendering.

    Symbols are strewn about a number of font files, each of which has
    its own proprietary 8-bit encoding.
    """
    _fontmap = { 'cal' : 'cmsy10',
                 'rm'  : 'cmr10',
                 'tt'  : 'cmtt10',
                 'it'  : 'cmmi10',
                 'bf'  : 'cmb10',
                 'sf'  : 'cmss10',
                 'ex'  : 'cmex10'
                 }

    def __init__(self, *args, **kwargs):
        self._stix_fallback = StixFonts(*args, **kwargs)

        TruetypeFonts.__init__(self, *args, **kwargs)
        self.fontmap = {}
        for key, val in six.iteritems(self._fontmap):
            fullpath = findfont(val)
            self.fontmap[key] = fullpath
            self.fontmap[val] = fullpath


    _slanted_symbols = set(r"\int \oint".split())

    def _get_glyph(self, fontname, font_class, sym, fontsize):
        symbol_name = None
        if fontname in self.fontmap and sym in latex_to_bakoma:
            basename, num = latex_to_bakoma[sym]
            slanted = (basename == "cmmi10") or sym in self._slanted_symbols
            cached_font = self._get_font(basename)
            if cached_font is not None:
                symbol_name = cached_font.font.get_glyph_name(num)
                num = cached_font.glyphmap[num]
        elif len(sym) == 1:
            slanted = (fontname == "it")
            cached_font = self._get_font(fontname)
            if cached_font is not None:
                num = ord(sym)
                gid = cached_font.charmap.get(num)
                if gid is not None:
                    symbol_name = cached_font.font.get_glyph_name(
                        cached_font.charmap[num])

        if symbol_name is None:
            return self._stix_fallback._get_glyph(
                fontname, font_class, sym, fontsize)

        return cached_font, num, symbol_name, fontsize, slanted

    # The Bakoma fonts contain many pre-sized alternatives for the
    # delimiters.  The AutoSizedChar class will use these alternatives
    # and select the best (closest sized) glyph.
    _size_alternatives = {
        '('          : [('rm', '('), ('ex', '\xa1'), ('ex', '\xb3'),
                        ('ex', '\xb5'), ('ex', '\xc3')],
        ')'          : [('rm', ')'), ('ex', '\xa2'), ('ex', '\xb4'),
                        ('ex', '\xb6'), ('ex', '\x21')],
        '{'          : [('cal', '{'), ('ex', '\xa9'), ('ex', '\x6e'),
                        ('ex', '\xbd'), ('ex', '\x28')],
        '}'          : [('cal', '}'), ('ex', '\xaa'), ('ex', '\x6f'),
                        ('ex', '\xbe'), ('ex', '\x29')],
        # The fourth size of '[' is mysteriously missing from the BaKoMa
        # font, so I've ommitted it for both '[' and ']'
        '['          : [('rm', '['), ('ex', '\xa3'), ('ex', '\x68'),
                        ('ex', '\x22')],
        ']'          : [('rm', ']'), ('ex', '\xa4'), ('ex', '\x69'),
                        ('ex', '\x23')],
        r'\lfloor'   : [('ex', '\xa5'), ('ex', '\x6a'),
                        ('ex', '\xb9'), ('ex', '\x24')],
        r'\rfloor'   : [('ex', '\xa6'), ('ex', '\x6b'),
                        ('ex', '\xba'), ('ex', '\x25')],
        r'\lceil'    : [('ex', '\xa7'), ('ex', '\x6c'),
                        ('ex', '\xbb'), ('ex', '\x26')],
        r'\rceil'    : [('ex', '\xa8'), ('ex', '\x6d'),
                        ('ex', '\xbc'), ('ex', '\x27')],
        r'\langle'   : [('ex', '\xad'), ('ex', '\x44'),
                        ('ex', '\xbf'), ('ex', '\x2a')],
        r'\rangle'   : [('ex', '\xae'), ('ex', '\x45'),
                        ('ex', '\xc0'), ('ex', '\x2b')],
        r'\__sqrt__' : [('ex', '\x70'), ('ex', '\x71'),
                        ('ex', '\x72'), ('ex', '\x73')],
        r'\backslash': [('ex', '\xb2'), ('ex', '\x2f'),
                        ('ex', '\xc2'), ('ex', '\x2d')],
        r'/'         : [('rm', '/'), ('ex', '\xb1'), ('ex', '\x2e'),
                        ('ex', '\xcb'), ('ex', '\x2c')],
        r'\widehat'  : [('rm', '\x5e'), ('ex', '\x62'), ('ex', '\x63'),
                        ('ex', '\x64')],
        r'\widetilde': [('rm', '\x7e'), ('ex', '\x65'), ('ex', '\x66'),
                        ('ex', '\x67')],
        r'<'         : [('cal', 'h'), ('ex', 'D')],
        r'>'         : [('cal', 'i'), ('ex', 'E')]
        }

    for alias, target in [('\leftparen', '('),
                          ('\rightparent', ')'),
                          ('\leftbrace', '{'),
                          ('\rightbrace', '}'),
                          ('\leftbracket', '['),
                          ('\rightbracket', ']'),
                          (r'\{', '{'),
                          (r'\}', '}'),
                          (r'\[', '['),
                          (r'\]', ']')]:
        _size_alternatives[alias] = _size_alternatives[target]

    def get_sized_alternatives_for_symbol(self, fontname, sym):
        return self._size_alternatives.get(sym, [(fontname, sym)])

class UnicodeFonts(TruetypeFonts):
    """
    An abstract base class for handling Unicode fonts.

    While some reasonably complete Unicode fonts (such as DejaVu) may
    work in some situations, the only Unicode font I'm aware of with a
    complete set of math symbols is STIX.

    This class will "fallback" on the Bakoma fonts when a required
    symbol can not be found in the font.
    """
    use_cmex = True

    def __init__(self, *args, **kwargs):
        # This must come first so the backend's owner is set correctly
        if rcParams['mathtext.fallback_to_cm']:
            self.cm_fallback = BakomaFonts(*args, **kwargs)
        else:
            self.cm_fallback = None
        TruetypeFonts.__init__(self, *args, **kwargs)
        self.fontmap = {}
        for texfont in "cal rm tt it bf sf".split():
            prop = rcParams['mathtext.' + texfont]
            font = findfont(prop)
            self.fontmap[texfont] = font
        prop = FontProperties('cmex10')
        font = findfont(prop)
        self.fontmap['ex'] = font

    _slanted_symbols = set(r"\int \oint".split())

    def _map_virtual_font(self, fontname, font_class, uniindex):
        return fontname, uniindex

    def _get_glyph(self, fontname, font_class, sym, fontsize):
        found_symbol = False

        if self.use_cmex:
            uniindex = latex_to_cmex.get(sym)
            if uniindex is not None:
                fontname = 'ex'
                found_symbol = True

        if not found_symbol:
            try:
                uniindex = get_unicode_index(sym)
                found_symbol = True
            except ValueError:
                uniindex = ord('?')
                warn("No TeX to unicode mapping for '%s'" %
                     sym.encode('ascii', 'backslashreplace'),
                     MathTextWarning)

        fontname, uniindex = self._map_virtual_font(
            fontname, font_class, uniindex)

        new_fontname = fontname

        # Only characters in the "Letter" class should be italicized in 'it'
        # mode.  Greek capital letters should be Roman.
        if found_symbol:
            if fontname == 'it':
                if uniindex < 0x10000:
                    unistring = unichr(uniindex)
                    if (not unicodedata.category(unistring)[0] == "L"
                        or unicodedata.name(unistring).startswith("GREEK CAPITAL")):
                        new_fontname = 'rm'

            slanted = (new_fontname == 'it') or sym in self._slanted_symbols
            found_symbol = False
            cached_font = self._get_font(new_fontname)
            if cached_font is not None:
                try:
                    glyphindex = cached_font.charmap[uniindex]
                    found_symbol = True
                except KeyError:
                    pass

        if not found_symbol:
            if self.cm_fallback:
                warn("Substituting with a symbol from Computer Modern.",
                     MathTextWarning)
                return self.cm_fallback._get_glyph(
                    fontname, 'it', sym, fontsize)
            else:
                if fontname in ('it', 'regular') and isinstance(self, StixFonts):
                    return self._get_glyph('rm', font_class, sym, fontsize)
                warn("Font '%s' does not have a glyph for '%s' [U%x]" %
                     (new_fontname, sym.encode('ascii', 'backslashreplace'), uniindex),
                     MathTextWarning)
                warn("Substituting with a dummy symbol.", MathTextWarning)
                fontname = 'rm'
                new_fontname = fontname
                cached_font = self._get_font(fontname)
                uniindex = 0xA4 # currency character, for lack of anything better
                glyphindex = cached_font.charmap[uniindex]
                slanted = False

        symbol_name = cached_font.font.get_glyph_name(glyphindex)
        return cached_font, uniindex, symbol_name, fontsize, slanted

    def get_sized_alternatives_for_symbol(self, fontname, sym):
        if self.cm_fallback:
            return self.cm_fallback.get_sized_alternatives_for_symbol(
                fontname, sym)
        return [(fontname, sym)]

class StixFonts(UnicodeFonts):
    """
    A font handling class for the STIX fonts.

    In addition to what UnicodeFonts provides, this class:

    - supports "virtual fonts" which are complete alpha numeric
      character sets with different font styles at special Unicode
      code points, such as "Blackboard".

    - handles sized alternative characters for the STIXSizeX fonts.
    """
    _fontmap = { 'rm'  : 'STIXGeneral',
                 'it'  : 'STIXGeneral:italic',
                 'bf'  : 'STIXGeneral:weight=bold',
                 'nonunirm' : 'STIXNonUnicode',
                 'nonuniit' : 'STIXNonUnicode:italic',
                 'nonunibf' : 'STIXNonUnicode:weight=bold',

                 0 : 'STIXGeneral',
                 1 : 'STIXSizeOneSym',
                 2 : 'STIXSizeTwoSym',
                 3 : 'STIXSizeThreeSym',
                 4 : 'STIXSizeFourSym',
                 5 : 'STIXSizeFiveSym'
                 }
    use_cmex = False
    cm_fallback = False
    _sans = False

    def __init__(self, *args, **kwargs):
        TruetypeFonts.__init__(self, *args, **kwargs)
        self.fontmap = {}
        for key, name in six.iteritems(self._fontmap):
            fullpath = findfont(name)
            self.fontmap[key] = fullpath
            self.fontmap[name] = fullpath

    def _map_virtual_font(self, fontname, font_class, uniindex):
        # Handle these "fonts" that are actually embedded in
        # other fonts.
        mapping = stix_virtual_fonts.get(fontname)
        if (self._sans and mapping is None and
            fontname not in ('regular', 'default')):
            mapping = stix_virtual_fonts['sf']
            doing_sans_conversion = True
        else:
            doing_sans_conversion = False

        if mapping is not None:
            if isinstance(mapping, dict):
                mapping = mapping.get(font_class, 'rm')

            # Binary search for the source glyph
            lo = 0
            hi = len(mapping)
            while lo < hi:
                mid = (lo+hi)//2
                range = mapping[mid]
                if uniindex < range[0]:
                    hi = mid
                elif uniindex <= range[1]:
                    break
                else:
                    lo = mid + 1

            if uniindex >= range[0] and uniindex <= range[1]:
                uniindex = uniindex - range[0] + range[3]
                fontname = range[2]
            elif not doing_sans_conversion:
                # This will generate a dummy character
                uniindex = 0x1
                fontname = rcParams['mathtext.default']

        # Handle private use area glyphs
        if (fontname in ('it', 'rm', 'bf') and
            uniindex >= 0xe000 and uniindex <= 0xf8ff):
            fontname = 'nonuni' + fontname

        return fontname, uniindex

    _size_alternatives = {}
    def get_sized_alternatives_for_symbol(self, fontname, sym):
        fixes = {'\{': '{', '\}': '}', '\[': '[', '\]': ']'}
        sym = fixes.get(sym, sym)

        alternatives = self._size_alternatives.get(sym)
        if alternatives:
            return alternatives

        alternatives = []
        try:
            uniindex = get_unicode_index(sym)
        except ValueError:
            return [(fontname, sym)]

        fix_ups = {
            ord('<'): 0x27e8,
            ord('>'): 0x27e9 }

        uniindex = fix_ups.get(uniindex, uniindex)

        for i in range(6):
            cached_font = self._get_font(i)
            glyphindex = cached_font.charmap.get(uniindex)
            if glyphindex is not None:
                alternatives.append((i, unichr_safe(uniindex)))

        # The largest size of the radical symbol in STIX has incorrect
        # metrics that cause it to be disconnected from the stem.
        if sym == r'\__sqrt__':
            alternatives = alternatives[:-1]

        self._size_alternatives[sym] = alternatives
        return alternatives

class StixSansFonts(StixFonts):
    """
    A font handling class for the STIX fonts (that uses sans-serif
    characters by default).
    """
    _sans = True

class StandardPsFonts(Fonts):
    """
    Use the standard postscript fonts for rendering to backend_ps

    Unlike the other font classes, BakomaFont and UnicodeFont, this
    one requires the Ps backend.
    """
    basepath = os.path.join( get_data_path(), 'fonts', 'afm' )

    fontmap = { 'cal' : 'pzcmi8a',  # Zapf Chancery
                'rm'  : 'pncr8a',   # New Century Schoolbook
                'tt'  : 'pcrr8a',   # Courier
                'it'  : 'pncri8a',  # New Century Schoolbook Italic
                'sf'  : 'phvr8a',   # Helvetica
                'bf'  : 'pncb8a',   # New Century Schoolbook Bold
                None  : 'psyr'      # Symbol
                }

    def __init__(self, default_font_prop):
        Fonts.__init__(self, default_font_prop, MathtextBackendPs())
        self.glyphd = {}
        self.fonts = {}

        filename = findfont(default_font_prop, fontext='afm',
                            directory=self.basepath)
        if filename is None:
            filename = findfont('Helvetica', fontext='afm',
                                directory=self.basepath)
        with open(filename, 'r') as fd:
            default_font = AFM(fd)
        default_font.fname = filename

        self.fonts['default'] = default_font
        self.fonts['regular'] = default_font
        self.pswriter = six.moves.cStringIO()

    def _get_font(self, font):
        if font in self.fontmap:
            basename = self.fontmap[font]
        else:
            basename = font

        cached_font = self.fonts.get(basename)
        if cached_font is None:
            fname = os.path.join(self.basepath, basename + ".afm")
            with open(fname, 'r') as fd:
                cached_font = AFM(fd)
            cached_font.fname = fname
            self.fonts[basename] = cached_font
            self.fonts[cached_font.get_fontname()] = cached_font
        return cached_font

    def _get_info (self, fontname, font_class, sym, fontsize, dpi):
        'load the cmfont, metrics and glyph with caching'
        key = fontname, sym, fontsize, dpi
        tup = self.glyphd.get(key)

        if tup is not None:
            return tup

        # Only characters in the "Letter" class should really be italicized.
        # This class includes greek letters, so we're ok
        if (fontname == 'it' and
            (len(sym) > 1 or
             not unicodedata.category(six.text_type(sym)).startswith("L"))):
            fontname = 'rm'

        found_symbol = False

        if sym in latex_to_standard:
            fontname, num = latex_to_standard[sym]
            glyph = chr(num)
            found_symbol = True
        elif len(sym) == 1:
            glyph = sym
            num = ord(glyph)
            found_symbol = True
        else:
            warn("No TeX to built-in Postscript mapping for '%s'" % sym,
                 MathTextWarning)

        slanted = (fontname == 'it')
        font = self._get_font(fontname)

        if found_symbol:
            try:
                symbol_name = font.get_name_char(glyph)
            except KeyError:
                warn("No glyph in standard Postscript font '%s' for '%s'" %
                     (font.postscript_name, sym),
                     MathTextWarning)
                found_symbol = False

        if not found_symbol:
            glyph = sym = '?'
            num = ord(glyph)
            symbol_name = font.get_name_char(glyph)

        offset = 0

        scale = 0.001 * fontsize

        xmin, ymin, xmax, ymax = [val * scale
                                  for val in font.get_bbox_char(glyph)]
        metrics = Bunch(
            advance  = font.get_width_char(glyph) * scale,
            width    = font.get_width_char(glyph) * scale,
            height   = font.get_height_char(glyph) * scale,
            xmin = xmin,
            xmax = xmax,
            ymin = ymin+offset,
            ymax = ymax+offset,
            # iceberg is the equivalent of TeX's "height"
            iceberg = ymax + offset,
            slanted = slanted
            )

        self.glyphd[key] = Bunch(
            font            = font,
            fontsize        = fontsize,
            postscript_name = font.get_fontname(),
            metrics         = metrics,
            symbol_name     = symbol_name,
            num             = num,
            glyph           = glyph,
            offset          = offset
            )

        return self.glyphd[key]

    def get_kern(self, font1, fontclass1, sym1, fontsize1,
                 font2, fontclass2, sym2, fontsize2, dpi):
        if font1 == font2 and fontsize1 == fontsize2:
            info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
            info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
            font = info1.font
            return (font.get_kern_dist(info1.glyph, info2.glyph)
                    * 0.001 * fontsize1)
        return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1,
                              font2, fontclass2, sym2, fontsize2, dpi)

    def get_xheight(self, font, fontsize, dpi):
        cached_font = self._get_font(font)
        return cached_font.get_xheight() * 0.001 * fontsize

    def get_underline_thickness(self, font, fontsize, dpi):
        cached_font = self._get_font(font)
        return cached_font.get_underline_thickness() * 0.001 * fontsize

##############################################################################
# TeX-LIKE BOX MODEL

# The following is based directly on the document 'woven' from the
# TeX82 source code.  This information is also available in printed
# form:
#
#    Knuth, Donald E.. 1986.  Computers and Typesetting, Volume B:
#    TeX: The Program.  Addison-Wesley Professional.
#
# The most relevant "chapters" are:
#    Data structures for boxes and their friends
#    Shipping pages out (Ship class)
#    Packaging (hpack and vpack)
#    Data structures for math mode
#    Subroutines for math mode
#    Typesetting math formulas
#
# Many of the docstrings below refer to a numbered "node" in that
# book, e.g., node123
#
# Note that (as TeX) y increases downward, unlike many other parts of
# matplotlib.

# How much text shrinks when going to the next-smallest level.  GROW_FACTOR
# must be the inverse of SHRINK_FACTOR.
SHRINK_FACTOR   = 0.7
GROW_FACTOR     = 1.0 / SHRINK_FACTOR
# The number of different sizes of chars to use, beyond which they will not
# get any smaller
NUM_SIZE_LEVELS = 6
# Percentage of x-height of additional horiz. space after sub/superscripts
SCRIPT_SPACE    = 0.2
# Percentage of x-height that sub/superscripts drop below the baseline
SUBDROP         = 0.3
# Percentage of x-height that superscripts drop below the baseline
SUP1            = 0.5
# Percentage of x-height that subscripts drop below the baseline
SUB1            = 0.0
# Percentage of x-height that superscripts are offset relative to the subscript
DELTA           = 0.18

class MathTextWarning(Warning):
    pass

class Node(object):
    """
    A node in the TeX box model
    """
    def __init__(self):
        self.size = 0

    def __repr__(self):
        return self.__internal_repr__()

    def __internal_repr__(self):
        return self.__class__.__name__

    def get_kerning(self, next):
        return 0.0

    def shrink(self):
        """
        Shrinks one level smaller.  There are only three levels of
        sizes, after which things will no longer get smaller.
        """
        self.size += 1

    def grow(self):
        """
        Grows one level larger.  There is no limit to how big
        something can get.
        """
        self.size -= 1

    def render(self, x, y):
        pass

class Box(Node):
    """
    Represents any node with a physical location.
    """
    def __init__(self, width, height, depth):
        Node.__init__(self)
        self.width  = width
        self.height = height
        self.depth  = depth

    def shrink(self):
        Node.shrink(self)
        if self.size < NUM_SIZE_LEVELS:
            self.width  *= SHRINK_FACTOR
            self.height *= SHRINK_FACTOR
            self.depth  *= SHRINK_FACTOR

    def grow(self):
        Node.grow(self)
        self.width  *= GROW_FACTOR
        self.height *= GROW_FACTOR
        self.depth  *= GROW_FACTOR

    def render(self, x1, y1, x2, y2):
        pass

class Vbox(Box):
    """
    A box with only height (zero width).
    """
    def __init__(self, height, depth):
        Box.__init__(self, 0., height, depth)

class Hbox(Box):
    """
    A box with only width (zero height and depth).
    """
    def __init__(self, width):
        Box.__init__(self, width, 0., 0.)

class Char(Node):
    """
    Represents a single character.  Unlike TeX, the font information
    and metrics are stored with each :class:`Char` to make it easier
    to lookup the font metrics when needed.  Note that TeX boxes have
    a width, height, and depth, unlike Type1 and Truetype which use a
    full bounding box and an advance in the x-direction.  The metrics
    must be converted to the TeX way, and the advance (if different
    from width) must be converted into a :class:`Kern` node when the
    :class:`Char` is added to its parent :class:`Hlist`.
    """
    def __init__(self, c, state):
        Node.__init__(self)
        self.c = c
        self.font_output = state.font_output
        assert isinstance(state.font, (six.string_types, int))
        self.font = state.font
        self.font_class = state.font_class
        self.fontsize = state.fontsize
        self.dpi = state.dpi
        # The real width, height and depth will be set during the
        # pack phase, after we know the real fontsize
        self._update_metrics()

    def __internal_repr__(self):
        return '`%s`' % self.c

    def _update_metrics(self):
        metrics = self._metrics = self.font_output.get_metrics(
            self.font, self.font_class, self.c, self.fontsize, self.dpi)
        if self.c == ' ':
            self.width = metrics.advance
        else:
            self.width = metrics.width
        self.height = metrics.iceberg
        self.depth = -(metrics.iceberg - metrics.height)

    def is_slanted(self):
        return self._metrics.slanted

    def get_kerning(self, next):
        """
        Return the amount of kerning between this and the given
        character.  Called when characters are strung together into
        :class:`Hlist` to create :class:`Kern` nodes.
        """
        advance = self._metrics.advance - self.width
        kern = 0.
        if isinstance(next, Char):
            kern = self.font_output.get_kern(
                self.font, self.font_class, self.c, self.fontsize,
                next.font, next.font_class, next.c, next.fontsize,
                self.dpi)
        return advance + kern

    def render(self, x, y):
        """
        Render the character to the canvas
        """
        self.font_output.render_glyph(
            x, y,
            self.font, self.font_class, self.c, self.fontsize, self.dpi)

    def shrink(self):
        Node.shrink(self)
        if self.size < NUM_SIZE_LEVELS:
            self.fontsize *= SHRINK_FACTOR
            self.width    *= SHRINK_FACTOR
            self.height   *= SHRINK_FACTOR
            self.depth    *= SHRINK_FACTOR

    def grow(self):
        Node.grow(self)
        self.fontsize *= GROW_FACTOR
        self.width    *= GROW_FACTOR
        self.height   *= GROW_FACTOR
        self.depth    *= GROW_FACTOR

class Accent(Char):
    """
    The font metrics need to be dealt with differently for accents,
    since they are already offset correctly from the baseline in
    TrueType fonts.
    """
    def _update_metrics(self):
        metrics = self._metrics = self.font_output.get_metrics(
            self.font, self.font_class, self.c, self.fontsize, self.dpi)
        self.width = metrics.xmax - metrics.xmin
        self.height = metrics.ymax - metrics.ymin
        self.depth = 0

    def shrink(self):
        Char.shrink(self)
        self._update_metrics()

    def grow(self):
        Char.grow(self)
        self._update_metrics()

    def render(self, x, y):
        """
        Render the character to the canvas.
        """
        self.font_output.render_glyph(
            x - self._metrics.xmin, y + self._metrics.ymin,
            self.font, self.font_class, self.c, self.fontsize, self.dpi)

class List(Box):
    """
    A list of nodes (either horizontal or vertical).
    """
    def __init__(self, elements):
        Box.__init__(self, 0., 0., 0.)
        self.shift_amount = 0.   # An arbitrary offset
        self.children     = elements # The child nodes of this list
        # The following parameters are set in the vpack and hpack functions
        self.glue_set     = 0.   # The glue setting of this list
        self.glue_sign    = 0    # 0: normal, -1: shrinking, 1: stretching
        self.glue_order   = 0    # The order of infinity (0 - 3) for the glue

    def __repr__(self):
        return '[%s <%.02f %.02f %.02f %.02f> %s]' % (
            self.__internal_repr__(),
            self.width, self.height,
            self.depth, self.shift_amount,
            ' '.join([repr(x) for x in self.children]))

    def _determine_order(self, totals):
        """
        A helper function to determine the highest order of glue
        used by the members of this list.  Used by vpack and hpack.
        """
        o = 0
        for i in range(len(totals) - 1, 0, -1):
            if totals[i] != 0.0:
                o = i
                break
        return o

    def _set_glue(self, x, sign, totals, error_type):
        o = self._determine_order(totals)
        self.glue_order = o
        self.glue_sign = sign
        if totals[o] != 0.:
            self.glue_set = x / totals[o]
        else:
            self.glue_sign = 0
            self.glue_ratio = 0.
        if o == 0:
            if len(self.children):
                warn("%s %s: %r" % (error_type, self.__class__.__name__, self),
                     MathTextWarning)

    def shrink(self):
        for child in self.children:
            child.shrink()
        Box.shrink(self)
        if self.size < NUM_SIZE_LEVELS:
            self.shift_amount *= SHRINK_FACTOR
            self.glue_set     *= SHRINK_FACTOR

    def grow(self):
        for child in self.children:
            child.grow()
        Box.grow(self)
        self.shift_amount *= GROW_FAC