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Your IP : 13.58.21.119
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 division
import os
from cStringIO import StringIO
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
from matplotlib.pyparsing import Combine, Group, Optional, Forward, \
Literal, OneOrMore, ZeroOrMore, ParseException, Empty, \
ParseResults, Suppress, oneOf, StringEnd, ParseFatalException, \
FollowedBy, Regex, ParserElement
# Enable packrat parsing
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
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.fonts_object = None
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 MathtextBackendBbox(MathtextBackend):
"""
A backend whose only purpose is to get a precise bounding box.
Only required for the Agg backend.
"""
def __init__(self, real_backend):
MathtextBackend.__init__(self)
self.bbox = [0, 0, 0, 0]
self.real_backend = real_backend
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 render_glyph(self, ox, oy, info):
self._update_bbox(ox + info.metrics.xmin,
oy - info.metrics.ymax,
ox + info.metrics.xmax,
oy - info.metrics.ymin)
def render_rect_filled(self, x1, y1, x2, y2):
self._update_bbox(x1, y1, x2, y2)
def get_results(self, box):
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._switch_to_real_backend()
self.fonts_object.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)
return self.fonts_object.get_results(box)
def get_hinting_type(self):
return self.real_backend.get_hinting_type()
def _switch_to_real_backend(self):
self.fonts_object.mathtext_backend = self.real_backend
self.real_backend.fonts_object = self.fonts_object
self.real_backend.ox = self.bbox[0]
self.real_backend.oy = self.bbox[1]
class MathtextBackendAggRender(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
MathtextBackend.__init__(self)
def set_canvas_size(self, w, h, d):
MathtextBackend.set_canvas_size(self, w, h, d)
self.image = FT2Image(ceil(w), ceil(h + d))
def render_glyph(self, ox, oy, info):
info.font.draw_glyph_to_bitmap(
self.image, ox, oy - info.metrics.iceberg, info.glyph)
def render_rect_filled(self, x1, y1, x2, y2):
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):
return (self.ox,
self.oy,
self.width,
self.height + self.depth,
self.depth,
self.image,
self.fonts_object.get_used_characters())
def get_hinting_type(self):
return LOAD_FORCE_AUTOHINT
def MathtextBackendAgg():
return MathtextBackendBbox(MathtextBackendAggRender())
class MathtextBackendBitmapRender(MathtextBackendAggRender):
def get_results(self, box):
return self.image, self.depth
def MathtextBackendBitmap():
"""
A backend to generate standalone mathtext images. No additional
matplotlib backend is required.
"""
return MathtextBackendBbox(MathtextBackendBitmapRender())
class MathtextBackendPs(MathtextBackend):
"""
Store information to write a mathtext rendering to the PostScript
backend.
"""
def __init__(self):
self.pswriter = StringIO()
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):
ship(0, -self.depth, box)
#print self.depth
return (self.width,
self.height + self.depth,
self.depth,
self.pswriter,
self.fonts_object.get_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):
ship(0, -self.depth, box)
return (self.width,
self.height + self.depth,
self.depth,
self.glyphs,
self.rects,
self.fonts_object.get_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
thetext = unichr(info.num)
self.svg_glyphs.append(
(info.font, info.fontsize, thetext, 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):
ship(0, -self.depth, 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,
self.fonts_object.get_used_characters())
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(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):
ship(0, -self.depth, 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
# Make these classes doubly-linked
self.mathtext_backend.fonts_object = self
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.
"""
return self.mathtext_backend.get_results(box)
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 self.charmap.iteritems()])
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(str(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:
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 + 256.0/64.0 * 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 self._fontmap.iteritems():
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
try:
cached_font = self._get_font(basename)
except RuntimeError:
pass
else:
symbol_name = cached_font.font.get_glyph_name(num)
num = cached_font.glyphmap[num]
elif len(sym) == 1:
slanted = (fontname == "it")
try:
cached_font = self._get_font(fontname)
except RuntimeError:
pass
else:
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', ']')]:
_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)
# Only characters in the "Letter" class should be italicized in 'it'
# mode. Greek capital letters should be Roman.
if found_symbol:
new_fontname = fontname
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
try:
cached_font = self._get_font(new_fontname)
except RuntimeError:
pass
else:
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'" %
(fontname, sym.encode('ascii', 'backslashreplace')),
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 : 'STIXSize1',
2 : 'STIXSize2',
3 : 'STIXSize3',
4 : 'STIXSize4',
5 : 'STIXSize5'
}
use_cmex = False
cm_fallback = False
_sans = False
def __init__(self, *args, **kwargs):
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
for key, name in self._fontmap.iteritems():
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):
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(uniindex)))
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')
default_font = AFM(file(filename, 'r'))
default_font.fname = filename
self.fonts['default'] = default_font
self.fonts['regular'] = default_font
self.pswriter = StringIO()
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")
cached_font = AFM(file(fname, 'r'))
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(unicode(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 = 4
# 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, (str, unicode, 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_FACTOR
self.glue_set *= GROW_FACTOR
class Hlist(List):
"""
A horizontal list of boxes.
"""
def __init__(self, elements, w=0., m='additional', do_kern=True):
List.__init__(self, elements)
if do_kern:
self.kern()
self.hpack()
def kern(self):
"""
Insert :class:`Kern` nodes between :class:`Char` nodes to set
kerning. The :class:`Char` nodes themselves determine the
amount of kerning they need (in :meth:`~Char.get_kerning`),
and this function just creates the linked list in the correct
way.
"""
new_children = []
num_children = len(self.children)
if num_children:
for i in range(num_children):
elem = self.children[i]
if i < num_children - 1:
next = self.children[i + 1]
else:
next = None
new_children.append(elem)
kerning_distance = elem.get_kerning(next)
if kerning_distance != 0.:
kern = Kern(kerning_distance)
new_children.append(kern)
self.children = new_children
# This is a failed experiment to fake cross-font kerning.
# def get_kerning(self, next):
# if len(self.children) >= 2 and isinstance(self.children[-2], Char):
# if isinstance(next, Char):
# print "CASE A"
# return self.children[-2].get_kerning(next)
# elif isinstance(next, Hlist) and len(next.children) and isinstance(next.children[0], Char):
# print "CASE B"
# result = self.children[-2].get_kerning(next.children[0])
# print result
# return result
# return 0.0
def hpack(self, w=0., m='additional'):
"""
The main duty of :meth:`hpack` is to compute the dimensions of
the resulting boxes, and to adjust the glue if one of those
dimensions is pre-specified. The computed sizes normally
enclose all of the material inside the new box; but some items
may stick out if negative glue is used, if the box is
overfull, or if a ``\\vbox`` includes other boxes that have
been shifted left.
- *w*: specifies a width
- *m*: is either 'exactly' or 'additional'.
Thus, ``hpack(w, 'exactly')`` produces a box whose width is
exactly *w*, while ``hpack(w, 'additional')`` yields a box
whose width is the natural width plus *w*. The default values
produce a box with the natural width.
"""
# I don't know why these get reset in TeX. Shift_amount is pretty
# much useless if we do.
#self.shift_amount = 0.
h = 0.
d = 0.
x = 0.
total_stretch = [0.] * 4
total_shrink = [0.] * 4
for p in self.children:
if isinstance(p, Char):
x += p.width
h = max(h, p.height)
d = max(d, p.depth)
elif isinstance(p, Box):
x += p.width
if not isinf(p.height) and not isinf(p.depth):
s = getattr(p, 'shift_amount', 0.)
h = max(h, p.height - s)
d = max(d, p.depth + s)
elif isinstance(p, Glue):
glue_spec = p.glue_spec
x += glue_spec.width
total_stretch[glue_spec.stretch_order] += glue_spec.stretch
total_shrink[glue_spec.shrink_order] += glue_spec.shrink
elif isinstance(p, Kern):
x += p.width
self.height = h
self.depth = d
if m == 'additional':
w += x
self.width = w
x = w - x
if x == 0.:
self.glue_sign = 0
self.glue_order = 0
self.glue_ratio = 0.
return
if x > 0.:
self._set_glue(x, 1, total_stretch, "Overfull")
else:
self._set_glue(x, -1, total_shrink, "Underfull")
class Vlist(List):
"""
A vertical list of boxes.
"""
def __init__(self, elements, h=0., m='additional'):
List.__init__(self, elements)
self.vpack()
def vpack(self, h=0., m='additional', l=float(inf)):
"""
The main duty of :meth:`vpack` is to compute the dimensions of
the resulting boxes, and to adjust the glue if one of those
dimensions is pre-specified.
- *h*: specifies a height
- *m*: is either 'exactly' or 'additional'.
- *l*: a maximum height
Thus, ``vpack(h, 'exactly')`` produces a box whose height is
exactly *h*, while ``vpack(h, 'additional')`` yields a box
whose height is the natural height plus *h*. The default
values produce a box with the natural width.
"""
# I don't know why these get reset in TeX. Shift_amount is pretty
# much useless if we do.
# self.shift_amount = 0.
w = 0.
d = 0.
x = 0.
total_stretch = [0.] * 4
total_shrink = [0.] * 4
for p in self.children:
if isinstance(p, Box):
x += d + p.height
d = p.depth
if not isinf(p.width):
s = getattr(p, 'shift_amount', 0.)
w = max(w, p.width + s)
elif isinstance(p, Glue):
x += d
d = 0.
glue_spec = p.glue_spec
x += glue_spec.width
total_stretch[glue_spec.stretch_order] += glue_spec.stretch
total_shrink[glue_spec.shrink_order] += glue_spec.shrink
elif isinstance(p, Kern):
x += d + p.width
d = 0.
elif isinstance(p, Char):
raise RuntimeError("Internal mathtext error: Char node found in Vlist.")
self.width = w
if d > l:
x += d - l
self.depth = l
else:
self.depth = d
if m == 'additional':
h += x
self.height = h
x = h - x
if x == 0:
self.glue_sign = 0
self.glue_order = 0
self.glue_ratio = 0.
return
if x > 0.:
self._set_glue(x, 1, total_stretch, "Overfull")
else:
self._set_glue(x, -1, total_shrink, "Underfull")
class Rule(Box):
"""
A :class:`Rule` node stands for a solid black rectangle; it has
*width*, *depth*, and *height* fields just as in an
:class:`Hlist`. However, if any of these dimensions is inf, the
actual value will be determined by running the rule up to the
boundary of the innermost enclosing box. This is called a "running
dimension." The width is never running in an :class:`Hlist`; the
height and depth are never running in a :class:`Vlist`.
"""
def __init__(self, width, height, depth, state):
Box.__init__(self, width, height, depth)
self.font_output = state.font_output
def render(self, x, y, w, h):
self.font_output.render_rect_filled(x, y, x + w, y + h)
class Hrule(Rule):
"""
Convenience class to create a horizontal rule.
"""
def __init__(self, state):
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
height = depth = thickness * 0.5
Rule.__init__(self, inf, height, depth, state)
class Vrule(Rule):
"""
Convenience class to create a vertical rule.
"""
def __init__(self, state):
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
Rule.__init__(self, thickness, inf, inf, state)
class Glue(Node):
"""
Most of the information in this object is stored in the underlying
:class:`GlueSpec` class, which is shared between multiple glue objects. (This
is a memory optimization which probably doesn't matter anymore, but it's
easier to stick to what TeX does.)
"""
def __init__(self, glue_type, copy=False):
Node.__init__(self)
self.glue_subtype = 'normal'
if is_string_like(glue_type):
glue_spec = GlueSpec.factory(glue_type)
elif isinstance(glue_type, GlueSpec):
glue_spec = glue_type
else:
raise ArgumentError("glue_type must be a glue spec name or instance.")
if copy:
glue_spec = glue_spec.copy()
self.glue_spec = glue_spec
def shrink(self):
Node.shrink(self)
if self.size < NUM_SIZE_LEVELS:
if self.glue_spec.width != 0.:
self.glue_spec = self.glue_spec.copy()
self.glue_spec.width *= SHRINK_FACTOR
def grow(self):
Node.grow(self)
if self.glue_spec.width != 0.:
self.glue_spec = self.glue_spec.copy()
self.glue_spec.width *= GROW_FACTOR
class GlueSpec(object):
"""
See :class:`Glue`.
"""
def __init__(self, width=0., stretch=0., stretch_order=0, shrink=0., shrink_order=0):
self.width = width
self.stretch = stretch
self.stretch_order = stretch_order
self.shrink = shrink
self.shrink_order = shrink_order
def copy(self):
return GlueSpec(
self.width,
self.stretch,
self.stretch_order,
self.shrink,
self.shrink_order)
def factory(cls, glue_type):
return cls._types[glue_type]
factory = classmethod(factory)
GlueSpec._types = {
'fil': GlueSpec(0., 1., 1, 0., 0),
'fill': GlueSpec(0., 1., 2, 0., 0),
'filll': GlueSpec(0., 1., 3, 0., 0),
'neg_fil': GlueSpec(0., 0., 0, 1., 1),
'neg_fill': GlueSpec(0., 0., 0, 1., 2),
'neg_filll': GlueSpec(0., 0., 0, 1., 3),
'empty': GlueSpec(0., 0., 0, 0., 0),
'ss': GlueSpec(0., 1., 1, -1., 1)
}
# Some convenient ways to get common kinds of glue
class Fil(Glue):
def __init__(self):
Glue.__init__(self, 'fil')
class Fill(Glue):
def __init__(self):
Glue.__init__(self, 'fill')
class Filll(Glue):
def __init__(self):
Glue.__init__(self, 'filll')
class NegFil(Glue):
def __init__(self):
Glue.__init__(self, 'neg_fil')
class NegFill(Glue):
def __init__(self):
Glue.__init__(self, 'neg_fill')
class NegFilll(Glue):
def __init__(self):
Glue.__init__(self, 'neg_filll')
class SsGlue(Glue):
def __init__(self):
Glue.__init__(self, 'ss')
class HCentered(Hlist):
"""
A convenience class to create an :class:`Hlist` whose contents are
centered within its enclosing box.
"""
def __init__(self, elements):
Hlist.__init__(self, [SsGlue()] + elements + [SsGlue()],
do_kern=False)
class VCentered(Hlist):
"""
A convenience class to create a :class:`Vlist` whose contents are
centered within its enclosing box.
"""
def __init__(self, elements):
Vlist.__init__(self, [SsGlue()] + elements + [SsGlue()])
class Kern(Node):
"""
A :class:`Kern` node has a width field to specify a (normally
negative) amount of spacing. This spacing correction appears in
horizontal lists between letters like A and V when the font
designer said that it looks better to move them closer together or
further apart. A kern node can also appear in a vertical list,
when its *width* denotes additional spacing in the vertical
direction.
"""
def __init__(self, width):
Node.__init__(self)
self.width = width
def __repr__(self):
return "k%.02f" % self.width
def shrink(self):
Node.shrink(self)
if self.size < NUM_SIZE_LEVELS:
self.width *= SHRINK_FACTOR
def grow(self):
Node.grow(self)
self.width *= GROW_FACTOR
class SubSuperCluster(Hlist):
"""
:class:`SubSuperCluster` is a sort of hack to get around that fact
that this code do a two-pass parse like TeX. This lets us store
enough information in the hlist itself, namely the nucleus, sub-
and super-script, such that if another script follows that needs
to be attached, it can be reconfigured on the fly.
"""
def __init__(self):
self.nucleus = None
self.sub = None
self.super = None
Hlist.__init__(self, [])
class AutoHeightChar(Hlist):
"""
:class:`AutoHeightChar` will create a character as close to the
given height and depth as possible. When using a font with
multiple height versions of some characters (such as the BaKoMa
fonts), the correct glyph will be selected, otherwise this will
always just return a scaled version of the glyph.
"""
def __init__(self, c, height, depth, state, always=False):
alternatives = state.font_output.get_sized_alternatives_for_symbol(
state.font, c)
state = state.copy()
target_total = height + depth
for fontname, sym in alternatives:
state.font = fontname
char = Char(sym, state)
if char.height + char.depth >= target_total:
break
factor = target_total / (char.height + char.depth)
state.fontsize *= factor
char = Char(sym, state)
shift = (depth - char.depth)
Hlist.__init__(self, [char])
self.shift_amount = shift
class AutoWidthChar(Hlist):
"""
:class:`AutoWidthChar` will create a character as close to the
given width as possible. When using a font with multiple width
versions of some characters (such as the BaKoMa fonts), the
correct glyph will be selected, otherwise this will always just
return a scaled version of the glyph.
"""
def __init__(self, c, width, state, always=False, char_class=Char):
alternatives = state.font_output.get_sized_alternatives_for_symbol(
state.font, c)
state = state.copy()
for fontname, sym in alternatives:
state.font = fontname
char = char_class(sym, state)
if char.width >= width:
break
factor = width / char.width
state.fontsize *= factor
char = char_class(sym, state)
Hlist.__init__(self, [char])
self.width = char.width
class Ship(object):
"""
Once the boxes have been set up, this sends them to output. Since
boxes can be inside of boxes inside of boxes, the main work of
:class:`Ship` is done by two mutually recursive routines,
:meth:`hlist_out` and :meth:`vlist_out`, which traverse the
:class:`Hlist` nodes and :class:`Vlist` nodes inside of horizontal
and vertical boxes. The global variables used in TeX to store
state as it processes have become member variables here.
"""
def __call__(self, ox, oy, box):
self.max_push = 0 # Deepest nesting of push commands so far
self.cur_s = 0
self.cur_v = 0.
self.cur_h = 0.
self.off_h = ox
self.off_v = oy + box.height
self.hlist_out(box)
def clamp(value):
if value < -1000000000.:
return -1000000000.
if value > 1000000000.:
return 1000000000.
return value
clamp = staticmethod(clamp)
def hlist_out(self, box):
cur_g = 0
cur_glue = 0.
glue_order = box.glue_order
glue_sign = box.glue_sign
base_line = self.cur_v
left_edge = self.cur_h
self.cur_s += 1
self.max_push = max(self.cur_s, self.max_push)
clamp = self.clamp
for p in box.children:
if isinstance(p, Char):
p.render(self.cur_h + self.off_h, self.cur_v + self.off_v)
self.cur_h += p.width
elif isinstance(p, Kern):
self.cur_h += p.width
elif isinstance(p, List):
# node623
if len(p.children) == 0:
self.cur_h += p.width
else:
edge = self.cur_h
self.cur_v = base_line + p.shift_amount
if isinstance(p, Hlist):
self.hlist_out(p)
else:
# p.vpack(box.height + box.depth, 'exactly')
self.vlist_out(p)
self.cur_h = edge + p.width
self.cur_v = base_line
elif isinstance(p, Box):
# node624
rule_height = p.height
rule_depth = p.depth
rule_width = p.width
if isinf(rule_height):
rule_height = box.height
if isinf(rule_depth):
rule_depth = box.depth
if rule_height > 0 and rule_width > 0:
self.cur_v = baseline + rule_depth
p.render(self.cur_h + self.off_h,
self.cur_v + self.off_v,
rule_width, rule_height)
self.cur_v = baseline
self.cur_h += rule_width
elif isinstance(p, Glue):
# node625
glue_spec = p.glue_spec
rule_width = glue_spec.width - cur_g
if glue_sign != 0: # normal
if glue_sign == 1: # stretching
if glue_spec.stretch_order == glue_order:
cur_glue += glue_spec.stretch
cur_g = round(clamp(float(box.glue_set) * cur_glue))
elif glue_spec.shrink_order == glue_order:
cur_glue += glue_spec.shrink
cur_g = round(clamp(float(box.glue_set) * cur_glue))
rule_width += cur_g
self.cur_h += rule_width
self.cur_s -= 1
def vlist_out(self, box):
cur_g = 0
cur_glue = 0.
glue_order = box.glue_order
glue_sign = box.glue_sign
self.cur_s += 1
self.max_push = max(self.max_push, self.cur_s)
left_edge = self.cur_h
self.cur_v -= box.height
top_edge = self.cur_v
clamp = self.clamp
for p in box.children:
if isinstance(p, Kern):
self.cur_v += p.width
elif isinstance(p, List):
if len(p.children) == 0:
self.cur_v += p.height + p.depth
else:
self.cur_v += p.height
self.cur_h = left_edge + p.shift_amount
save_v = self.cur_v
p.width = box.width
if isinstance(p, Hlist):
self.hlist_out(p)
else:
self.vlist_out(p)
self.cur_v = save_v + p.depth
self.cur_h = left_edge
elif isinstance(p, Box):
rule_height = p.height
rule_depth = p.depth
rule_width = p.width
if isinf(rule_width):
rule_width = box.width
rule_height += rule_depth
if rule_height > 0 and rule_depth > 0:
self.cur_v += rule_height
p.render(self.cur_h + self.off_h,
self.cur_v + self.off_v,
rule_width, rule_height)
elif isinstance(p, Glue):
glue_spec = p.glue_spec
rule_height = glue_spec.width - cur_g
if glue_sign != 0: # normal
if glue_sign == 1: # stretching
if glue_spec.stretch_order == glue_order:
cur_glue += glue_spec.stretch
cur_g = round(clamp(float(box.glue_set) * cur_glue))
elif glue_spec.shrink_order == glue_order: # shrinking
cur_glue += glue_spec.shrink
cur_g = round(clamp(float(box.glue_set) * cur_glue))
rule_height += cur_g
self.cur_v += rule_height
elif isinstance(p, Char):
raise RuntimeError("Internal mathtext error: Char node found in vlist")
self.cur_s -= 1
ship = Ship()
##############################################################################
# PARSER
def Error(msg):
"""
Helper class to raise parser errors.
"""
def raise_error(s, loc, toks):
raise ParseFatalException(msg + "\n" + s)
empty = Empty()
empty.setParseAction(raise_error)
return empty
class Parser(object):
"""
This is the pyparsing-based parser for math expressions. It
actually parses full strings *containing* math expressions, in
that raw text may also appear outside of pairs of ``$``.
The grammar is based directly on that in TeX, though it cuts a few
corners.
"""
_binary_operators = set(r'''
+ *
\pm \sqcap \rhd
\mp \sqcup \unlhd
\times \vee \unrhd
\div \wedge \oplus
\ast \setminus \ominus
\star \wr \otimes
\circ \diamond \oslash
\bullet \bigtriangleup \odot
\cdot \bigtriangledown \bigcirc
\cap \triangleleft \dagger
\cup \triangleright \ddagger
\uplus \lhd \amalg'''.split())
_relation_symbols = set(r'''
= < > :
\leq \geq \equiv \models
\prec \succ \sim \perp
\preceq \succeq \simeq \mid
\ll \gg \asymp \parallel
\subset \supset \approx \bowtie
\subseteq \supseteq \cong \Join
\sqsubset \sqsupset \neq \smile
\sqsubseteq \sqsupseteq \doteq \frown
\in \ni \propto
\vdash \dashv \dots'''.split())
_arrow_symbols = set(r'''
\leftarrow \longleftarrow \uparrow
\Leftarrow \Longleftarrow \Uparrow
\rightarrow \longrightarrow \downarrow
\Rightarrow \Longrightarrow \Downarrow
\leftrightarrow \longleftrightarrow \updownarrow
\Leftrightarrow \Longleftrightarrow \Updownarrow
\mapsto \longmapsto \nearrow
\hookleftarrow \hookrightarrow \searrow
\leftharpoonup \rightharpoonup \swarrow
\leftharpoondown \rightharpoondown \nwarrow
\rightleftharpoons \leadsto'''.split())
_spaced_symbols = _binary_operators | _relation_symbols | _arrow_symbols
_punctuation_symbols = set(r', ; . ! \ldotp \cdotp'.split())
_overunder_symbols = set(r'''
\sum \prod \coprod \bigcap \bigcup \bigsqcup \bigvee
\bigwedge \bigodot \bigotimes \bigoplus \biguplus
'''.split())
_overunder_functions = set(
r"lim liminf limsup sup max min".split())
_dropsub_symbols = set(r'''\int \oint'''.split())
_fontnames = set("rm cal it tt sf bf default bb frak circled scr regular".split())
_function_names = set("""
arccos csc ker min arcsin deg lg Pr arctan det lim sec arg dim
liminf sin cos exp limsup sinh cosh gcd ln sup cot hom log tan
coth inf max tanh""".split())
_ambiDelim = set(r"""
| \| / \backslash \uparrow \downarrow \updownarrow \Uparrow
\Downarrow \Updownarrow .""".split())
_leftDelim = set(r"( [ { < \lfloor \langle \lceil".split())
_rightDelim = set(r") ] } > \rfloor \rangle \rceil".split())
def __init__(self):
# All forward declarations are here
font = Forward().setParseAction(self.font).setName("font")
latexfont = Forward()
subsuper = Forward().setParseAction(self.subsuperscript).setName("subsuper")
placeable = Forward().setName("placeable")
simple = Forward().setName("simple")
autoDelim = Forward().setParseAction(self.auto_sized_delimiter)
self._expression = Forward().setParseAction(self.finish).setName("finish")
float = Regex(r"[-+]?([0-9]+\.?[0-9]*|\.[0-9]+)")
lbrace = Literal('{').suppress()
rbrace = Literal('}').suppress()
start_group = (Optional(latexfont) - lbrace)
start_group.setParseAction(self.start_group)
end_group = rbrace.copy()
end_group.setParseAction(self.end_group)
bslash = Literal('\\')
accent = oneOf(self._accent_map.keys() +
list(self._wide_accents))
function = oneOf(list(self._function_names))
fontname = oneOf(list(self._fontnames))
latex2efont = oneOf(['math' + x for x in self._fontnames])
space =(FollowedBy(bslash)
+ oneOf([r'\ ',
r'\/',
r'\,',
r'\;',
r'\quad',
r'\qquad',
r'\!'])
).setParseAction(self.space).setName('space')
customspace =(Literal(r'\hspace')
- (( lbrace
- float
- rbrace
) | Error(r"Expected \hspace{n}"))
).setParseAction(self.customspace).setName('customspace')
unicode_range = u"\U00000080-\U0001ffff"
symbol =(Regex(UR"([a-zA-Z0-9 +\-*/<>=:,.;!'@()\[\]|%s])|(\\[%%${}\[\]_|])" % unicode_range)
| (Combine(
bslash
+ oneOf(tex2uni.keys())
) + FollowedBy(Regex("[^a-zA-Z]")))
).setParseAction(self.symbol).leaveWhitespace()
c_over_c =(Suppress(bslash)
+ oneOf(self._char_over_chars.keys())
).setParseAction(self.char_over_chars)
accent = Group(
Suppress(bslash)
+ accent
- placeable
).setParseAction(self.accent).setName("accent")
function =(Suppress(bslash)
+ function
).setParseAction(self.function).setName("function")
group = Group(
start_group
+ ZeroOrMore(
autoDelim
^ simple)
- end_group
).setParseAction(self.group).setName("group")
font <<(Suppress(bslash)
+ fontname)
latexfont <<(Suppress(bslash)
+ latex2efont)
frac = Group(
Suppress(Literal(r"\frac"))
+ ((group + group)
| Error(r"Expected \frac{num}{den}"))
).setParseAction(self.frac).setName("frac")
sqrt = Group(
Suppress(Literal(r"\sqrt"))
+ Optional(
Suppress(Literal("["))
- Regex("[0-9]+")
- Suppress(Literal("]")),
default = None
)
+ (group | Error("Expected \sqrt{value}"))
).setParseAction(self.sqrt).setName("sqrt")
placeable <<(function
^ (c_over_c | symbol)
^ accent
^ group
^ frac
^ sqrt
)
simple <<(space
| customspace
| font
| subsuper
)
subsuperop = oneOf(["_", "^"])
subsuper << Group(
( Optional(placeable)
+ OneOrMore(
subsuperop
- placeable
)
)
| placeable
)
ambiDelim = oneOf(list(self._ambiDelim))
leftDelim = oneOf(list(self._leftDelim))
rightDelim = oneOf(list(self._rightDelim))
autoDelim <<(Suppress(Literal(r"\left"))
+ ((leftDelim | ambiDelim) | Error("Expected a delimiter"))
+ Group(
autoDelim
^ OneOrMore(simple))
+ Suppress(Literal(r"\right"))
+ ((rightDelim | ambiDelim) | Error("Expected a delimiter"))
)
math = OneOrMore(
autoDelim
^ simple
).setParseAction(self.math).setName("math")
math_delim = ~bslash + Literal('$')
non_math = Regex(r"(?:(?:\\[$])|[^$])*"
).setParseAction(self.non_math).setName("non_math").leaveWhitespace()
self._expression << (
non_math
+ ZeroOrMore(
Suppress(math_delim)
+ Optional(math)
+ (Suppress(math_delim)
| Error("Expected end of math '$'"))
+ non_math
)
) + StringEnd()
self.clear()
def clear(self):
"""
Clear any state before parsing.
"""
self._expr = None
self._state_stack = None
self._em_width_cache = {}
def parse(self, s, fonts_object, fontsize, dpi):
"""
Parse expression *s* using the given *fonts_object* for
output, at the given *fontsize* and *dpi*.
Returns the parse tree of :class:`Node` instances.
"""
self._state_stack = [self.State(fonts_object, 'default', 'rm', fontsize, dpi)]
try:
self._expression.parseString(s)
except ParseException, err:
raise ValueError("\n".join([
"",
err.line,
" " * (err.column - 1) + "^",
str(err)]))
return self._expr
# The state of the parser is maintained in a stack. Upon
# entering and leaving a group { } or math/non-math, the stack
# is pushed and popped accordingly. The current state always
# exists in the top element of the stack.
class State(object):
"""
Stores the state of the parser.
States are pushed and popped from a stack as necessary, and
the "current" state is always at the top of the stack.
"""
def __init__(self, font_output, font, font_class, fontsize, dpi):
self.font_output = font_output
self._font = font
self.font_class = font_class
self.fontsize = fontsize
self.dpi = dpi
def copy(self):
return Parser.State(
self.font_output,
self.font,
self.font_class,
self.fontsize,
self.dpi)
def _get_font(self):
return self._font
def _set_font(self, name):
if name in ('rm', 'it', 'bf'):
self.font_class = name
self._font = name
font = property(_get_font, _set_font)
def get_state(self):
"""
Get the current :class:`State` of the parser.
"""
return self._state_stack[-1]
def pop_state(self):
"""
Pop a :class:`State` off of the stack.
"""
self._state_stack.pop()
def push_state(self):
"""
Push a new :class:`State` onto the stack which is just a copy
of the current state.
"""
self._state_stack.append(self.get_state().copy())
def finish(self, s, loc, toks):
#~ print "finish", toks
self._expr = Hlist(toks)
return [self._expr]
def math(self, s, loc, toks):
#~ print "math", toks
hlist = Hlist(toks)
self.pop_state()
return [hlist]
def non_math(self, s, loc, toks):
#~ print "non_math", toks
s = toks[0].replace(r'\$', '$')
symbols = [Char(c, self.get_state()) for c in s]
hlist = Hlist(symbols)
# We're going into math now, so set font to 'it'
self.push_state()
self.get_state().font = rcParams['mathtext.default']
return [hlist]
def _make_space(self, percentage):
# All spaces are relative to em width
state = self.get_state()
key = (state.font, state.fontsize, state.dpi)
width = self._em_width_cache.get(key)
if width is None:
metrics = state.font_output.get_metrics(
state.font, rcParams['mathtext.default'], 'm', state.fontsize, state.dpi)
width = metrics.advance
self._em_width_cache[key] = width
return Kern(width * percentage)
_space_widths = { r'\ ' : 0.3,
r'\,' : 0.4,
r'\;' : 0.8,
r'\quad' : 1.6,
r'\qquad' : 3.2,
r'\!' : -0.4,
r'\/' : 0.4 }
def space(self, s, loc, toks):
assert(len(toks)==1)
num = self._space_widths[toks[0]]
box = self._make_space(num)
return [box]
def customspace(self, s, loc, toks):
return [self._make_space(float(toks[1]))]
def symbol(self, s, loc, toks):
# print "symbol", toks
c = toks[0]
try:
char = Char(c, self.get_state())
except ValueError:
raise ParseFatalException("Unknown symbol: %s" % c)
if c in self._spaced_symbols:
return [Hlist( [self._make_space(0.2),
char,
self._make_space(0.2)] ,
do_kern = False)]
elif c in self._punctuation_symbols:
return [Hlist( [char,
self._make_space(0.2)] ,
do_kern = False)]
return [char]
_char_over_chars = {
# The first 2 entires in the tuple are (font, char, sizescale) for
# the two symbols under and over. The third element is the space
# (in multiples of underline height)
r'AA' : ( ('rm', 'A', 1.0), (None, '\circ', 0.5), 0.0),
}
def char_over_chars(self, s, loc, toks):
sym = toks[0]
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
under_desc, over_desc, space = \
self._char_over_chars.get(sym, (None, None, 0.0))
if under_desc is None:
raise ParseFatalException("Error parsing symbol")
over_state = state.copy()
if over_desc[0] is not None:
over_state.font = over_desc[0]
over_state.fontsize *= over_desc[2]
over = Accent(over_desc[1], over_state)
under_state = state.copy()
if under_desc[0] is not None:
under_state.font = under_desc[0]
under_state.fontsize *= under_desc[2]
under = Char(under_desc[1], under_state)
width = max(over.width, under.width)
over_centered = HCentered([over])
over_centered.hpack(width, 'exactly')
under_centered = HCentered([under])
under_centered.hpack(width, 'exactly')
return Vlist([
over_centered,
Vbox(0., thickness * space),
under_centered
])
_accent_map = {
r'hat' : r'\circumflexaccent',
r'breve' : r'\combiningbreve',
r'bar' : r'\combiningoverline',
r'grave' : r'\combininggraveaccent',
r'acute' : r'\combiningacuteaccent',
r'ddot' : r'\combiningdiaeresis',
r'tilde' : r'\combiningtilde',
r'dot' : r'\combiningdotabove',
r'vec' : r'\combiningrightarrowabove',
r'"' : r'\combiningdiaeresis',
r"`" : r'\combininggraveaccent',
r"'" : r'\combiningacuteaccent',
r'~' : r'\combiningtilde',
r'.' : r'\combiningdotabove',
r'^' : r'\circumflexaccent',
r'overrightarrow' : r'\rightarrow',
r'overleftarrow' : r'\leftarrow'
}
_wide_accents = set(r"widehat widetilde".split())
def accent(self, s, loc, toks):
assert(len(toks)==1)
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
if len(toks[0]) != 2:
raise ParseFatalException("Error parsing accent")
accent, sym = toks[0]
if accent in self._wide_accents:
accent = AutoWidthChar(
'\\' + accent, sym.width, state, char_class=Accent)
else:
accent = Accent(self._accent_map[accent], state)
centered = HCentered([accent])
centered.hpack(sym.width, 'exactly')
return Vlist([
centered,
Vbox(0., thickness * 2.0),
Hlist([sym])
])
def function(self, s, loc, toks):
#~ print "function", toks
self.push_state()
state = self.get_state()
state.font = 'rm'
hlist = Hlist([Char(c, state) for c in toks[0]])
self.pop_state()
hlist.function_name = toks[0]
return hlist
def start_group(self, s, loc, toks):
self.push_state()
# Deal with LaTeX-style font tokens
if len(toks):
self.get_state().font = toks[0][4:]
return []
def group(self, s, loc, toks):
grp = Hlist(toks[0])
return [grp]
def end_group(self, s, loc, toks):
self.pop_state()
return []
def font(self, s, loc, toks):
assert(len(toks)==1)
name = toks[0]
self.get_state().font = name
return []
def is_overunder(self, nucleus):
if isinstance(nucleus, Char):
return nucleus.c in self._overunder_symbols
elif isinstance(nucleus, Hlist) and hasattr(nucleus, 'function_name'):
return nucleus.function_name in self._overunder_functions
return False
def is_dropsub(self, nucleus):
if isinstance(nucleus, Char):
return nucleus.c in self._dropsub_symbols
return False
def is_slanted(self, nucleus):
if isinstance(nucleus, Char):
return nucleus.is_slanted()
return False
def subsuperscript(self, s, loc, toks):
assert(len(toks)==1)
# print 'subsuperscript', toks
nucleus = None
sub = None
super = None
if len(toks[0]) == 1:
return toks[0].asList()
elif len(toks[0]) == 2:
op, next = toks[0]
nucleus = Hbox(0.0)
if op == '_':
sub = next
else:
super = next
elif len(toks[0]) == 3:
nucleus, op, next = toks[0]
if op == '_':
sub = next
else:
super = next
elif len(toks[0]) == 5:
nucleus, op1, next1, op2, next2 = toks[0]
if op1 == op2:
if op1 == '_':
raise ParseFatalException("Double subscript")
else:
raise ParseFatalException("Double superscript")
if op1 == '_':
sub = next1
super = next2
else:
super = next1
sub = next2
else:
raise ParseFatalException(
"Subscript/superscript sequence is too long. "
"Use braces { } to remove ambiguity.")
state = self.get_state()
rule_thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
xHeight = state.font_output.get_xheight(
state.font, state.fontsize, state.dpi)
# Handle over/under symbols, such as sum or integral
if self.is_overunder(nucleus):
vlist = []
shift = 0.
width = nucleus.width
if super is not None:
super.shrink()
width = max(width, super.width)
if sub is not None:
sub.shrink()
width = max(width, sub.width)
if super is not None:
hlist = HCentered([super])
hlist.hpack(width, 'exactly')
vlist.extend([hlist, Kern(rule_thickness * 3.0)])
hlist = HCentered([nucleus])
hlist.hpack(width, 'exactly')
vlist.append(hlist)
if sub is not None:
hlist = HCentered([sub])
hlist.hpack(width, 'exactly')
vlist.extend([Kern(rule_thickness * 3.0), hlist])
shift = hlist.height + hlist.depth + rule_thickness * 2.0
vlist = Vlist(vlist)
vlist.shift_amount = shift + nucleus.depth * 0.5
result = Hlist([vlist])
return [result]
# Handle regular sub/superscripts
shift_up = nucleus.height - SUBDROP * xHeight
if self.is_dropsub(nucleus):
shift_down = nucleus.depth + SUBDROP * xHeight
else:
shift_down = SUBDROP * xHeight
if super is None:
# node757
sub.shrink()
x = Hlist([sub])
# x.width += SCRIPT_SPACE * xHeight
shift_down = max(shift_down, SUB1)
clr = x.height - (abs(xHeight * 4.0) / 5.0)
shift_down = max(shift_down, clr)
x.shift_amount = shift_down
else:
super.shrink()
x = Hlist([super, Kern(SCRIPT_SPACE * xHeight)])
# x.width += SCRIPT_SPACE * xHeight
clr = SUP1 * xHeight
shift_up = max(shift_up, clr)
clr = x.depth + (abs(xHeight) / 4.0)
shift_up = max(shift_up, clr)
if sub is None:
x.shift_amount = -shift_up
else: # Both sub and superscript
sub.shrink()
y = Hlist([sub])
# y.width += SCRIPT_SPACE * xHeight
shift_down = max(shift_down, SUB1 * xHeight)
clr = (2.0 * rule_thickness -
((shift_up - x.depth) - (y.height - shift_down)))
if clr > 0.:
shift_up += clr
shift_down += clr
if self.is_slanted(nucleus):
x.shift_amount = DELTA * (shift_up + shift_down)
x = Vlist([x,
Kern((shift_up - x.depth) - (y.height - shift_down)),
y])
x.shift_amount = shift_down
result = Hlist([nucleus, x])
return [result]
def frac(self, s, loc, toks):
assert(len(toks)==1)
assert(len(toks[0])==2)
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
num, den = toks[0]
num.shrink()
den.shrink()
cnum = HCentered([num])
cden = HCentered([den])
width = max(num.width, den.width) + thickness * 10.
cnum.hpack(width, 'exactly')
cden.hpack(width, 'exactly')
vlist = Vlist([cnum, # numerator
Vbox(0, thickness * 2.0), # space
Hrule(state), # rule
Vbox(0, thickness * 4.0), # space
cden # denominator
])
# Shift so the fraction line sits in the middle of the
# equals sign
metrics = state.font_output.get_metrics(
state.font, rcParams['mathtext.default'], '=', state.fontsize, state.dpi)
shift = (cden.height -
((metrics.ymax + metrics.ymin) / 2 -
thickness * 3.0))
vlist.shift_amount = shift
hlist = Hlist([vlist, Hbox(thickness * 2.)])
return [hlist]
def sqrt(self, s, loc, toks):
#~ print "sqrt", toks
root, body = toks[0]
state = self.get_state()
thickness = state.font_output.get_underline_thickness(
state.font, state.fontsize, state.dpi)
# Determine the height of the body, and add a little extra to
# the height so it doesn't seem cramped
height = body.height - body.shift_amount + thickness * 5.0
depth = body.depth + body.shift_amount
check = AutoHeightChar(r'\__sqrt__', height, depth, state, always=True)
height = check.height - check.shift_amount
depth = check.depth + check.shift_amount
# Put a little extra space to the left and right of the body
padded_body = Hlist([Hbox(thickness * 2.0),
body,
Hbox(thickness * 2.0)])
rightside = Vlist([Hrule(state),
Fill(),
padded_body])
# Stretch the glue between the hrule and the body
rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
depth, 'exactly')
# Add the root and shift it upward so it is above the tick.
# The value of 0.6 is a hard-coded hack ;)
if root is None:
root = Box(check.width * 0.5, 0., 0.)
else:
root = Hlist([Char(x, state) for x in root])
root.shrink()
root.shrink()
root_vlist = Vlist([Hlist([root])])
root_vlist.shift_amount = -height * 0.6
hlist = Hlist([root_vlist, # Root
# Negative kerning to put root over tick
Kern(-check.width * 0.5),
check, # Check
rightside]) # Body
return [hlist]
def auto_sized_delimiter(self, s, loc, toks):
#~ print "auto_sized_delimiter", toks
front, middle, back = toks
state = self.get_state()
height = max([x.height for x in middle])
depth = max([x.depth for x in middle])
parts = []
# \left. and \right. aren't supposed to produce any symbols
if front != '.':
parts.append(AutoHeightChar(front, height, depth, state))
parts.extend(middle.asList())
if back != '.':
parts.append(AutoHeightChar(back, height, depth, state))
hlist = Hlist(parts)
return hlist
###
##############################################################################
# MAIN
class MathTextParser(object):
_parser = None
_backend_mapping = {
'bitmap': MathtextBackendBitmap,
'agg' : MathtextBackendAgg,
'ps' : MathtextBackendPs,
'pdf' : MathtextBackendPdf,
'svg' : MathtextBackendSvg,
'cairo' : MathtextBackendCairo,
'macosx': MathtextBackendAgg,
}
_font_type_mapping = {
'cm' : BakomaFonts,
'stix' : StixFonts,
'stixsans' : StixSansFonts,
'custom' : UnicodeFonts
}
def __init__(self, output):
"""
Create a MathTextParser for the given backend *output*.
"""
self._output = output.lower()
self._cache = maxdict(50)
def parse(self, s, dpi = 72, prop = None):
"""
Parse the given math expression *s* at the given *dpi*. If
*prop* is provided, it is a
:class:`~matplotlib.font_manager.FontProperties` object
specifying the "default" font to use in the math expression,
used for all non-math text.
The results are cached, so multiple calls to :meth:`parse`
with the same expression should be fast.
"""
if prop is None:
prop = FontProperties()
cacheKey = (s, dpi, hash(prop))
result = self._cache.get(cacheKey)
if result is not None:
return result
if self._output == 'ps' and rcParams['ps.useafm']:
font_output = StandardPsFonts(prop)
else:
backend = self._backend_mapping[self._output]()
fontset = rcParams['mathtext.fontset']
fontset_class = self._font_type_mapping.get(fontset.lower())
if fontset_class is not None:
font_output = fontset_class(prop, backend)
else:
raise ValueError(
"mathtext.fontset must be either 'cm', 'stix', "
"'stixsans', or 'custom'")
fontsize = prop.get_size_in_points()
# This is a class variable so we don't rebuild the parser
# with each request.
if self._parser is None:
self.__class__._parser = Parser()
box = self._parser.parse(s, font_output, fontsize, dpi)
font_output.set_canvas_size(box.width, box.height, box.depth)
result = font_output.get_results(box)
self._cache[cacheKey] = result
# Free up the transient data structures
self._parser.clear()
# Fix cyclical references
font_output.destroy()
font_output.mathtext_backend.fonts_object = None
font_output.mathtext_backend = None
return result
def to_mask(self, texstr, dpi=120, fontsize=14):
"""
*texstr*
A valid mathtext string, eg r'IQ: $\sigma_i=15$'
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
Returns a tuple (*array*, *depth*)
- *array* is an NxM uint8 alpha ubyte mask array of
rasterized tex.
- depth is the offset of the baseline from the bottom of the
image in pixels.
"""
assert(self._output=="bitmap")
prop = FontProperties(size=fontsize)
ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop)
x = ftimage.as_array()
return x, depth
def to_rgba(self, texstr, color='black', dpi=120, fontsize=14):
"""
*texstr*
A valid mathtext string, eg r'IQ: $\sigma_i=15$'
*color*
Any matplotlib color argument
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
Returns a tuple (*array*, *depth*)
- *array* is an NxM uint8 alpha ubyte mask array of
rasterized tex.
- depth is the offset of the baseline from the bottom of the
image in pixels.
"""
x, depth = self.to_mask(texstr, dpi=dpi, fontsize=fontsize)
r, g, b = mcolors.colorConverter.to_rgb(color)
RGBA = np.zeros((x.shape[0], x.shape[1], 4), dtype=np.uint8)
RGBA[:,:,0] = int(255*r)
RGBA[:,:,1] = int(255*g)
RGBA[:,:,2] = int(255*b)
RGBA[:,:,3] = x
return RGBA, depth
def to_png(self, filename, texstr, color='black', dpi=120, fontsize=14):
"""
Writes a tex expression to a PNG file.
Returns the offset of the baseline from the bottom of the
image in pixels.
*filename*
A writable filename or fileobject
*texstr*
A valid mathtext string, eg r'IQ: $\sigma_i=15$'
*color*
A valid matplotlib color argument
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
Returns the offset of the baseline from the bottom of the
image in pixels.
"""
rgba, depth = self.to_rgba(texstr, color=color, dpi=dpi, fontsize=fontsize)
numrows, numcols, tmp = rgba.shape
_png.write_png(rgba.tostring(), numcols, numrows, filename)
return depth
def get_depth(self, texstr, dpi=120, fontsize=14):
"""
Returns the offset of the baseline from the bottom of the
image in pixels.
*texstr*
A valid mathtext string, eg r'IQ: $\sigma_i=15$'
*dpi*
The dots-per-inch to render the text
*fontsize*
The font size in points
"""
assert(self._output=="bitmap")
prop = FontProperties(size=fontsize)
ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop)
return depth