"""
Implementation details for :mod:`.mathtext`.
"""
import copy
from collections import namedtuple
import enum
import functools
import logging
import os
import re
import types
import unicodedata
import numpy as np
from pyparsing import (
Empty, Forward, Literal, NotAny, oneOf, OneOrMore, Optional,
ParseBaseException, ParseException, ParseExpression, ParseFatalException,
ParserElement, ParseResults, QuotedString, Regex, StringEnd, ZeroOrMore,
pyparsing_common)
import matplotlib as mpl
from . import _api, cbook
from ._mathtext_data import (
latex_to_bakoma, stix_glyph_fixes, stix_virtual_fonts, tex2uni)
from .font_manager import FontProperties, findfont, get_font
from .ft2font import FT2Image, KERNING_DEFAULT
ParserElement.enablePackrat()
_log = logging.getLogger("matplotlib.mathtext")
##############################################################################
# FONTS
@_api.delete_parameter("3.6", "math")
def get_unicode_index(symbol, math=False): # Publicly exported.
r"""
Return the integer index (from the Unicode table) of *symbol*.
Parameters
----------
symbol : str
A single (Unicode) character, a TeX command (e.g. r'\pi') or a Type1
symbol name (e.g. 'phi').
math : bool, default: False
If True (deprecated), replace ASCII hyphen-minus by Unicode minus.
"""
# 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.
# Remove this block when the 'math' parameter is deleted.
if math and 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 as err:
raise ValueError(
"'{}' is not a valid Unicode character or TeX/Type1 symbol"
.format(symbol)) from err
VectorParse = namedtuple("VectorParse", "width height depth glyphs rects",
module="matplotlib.mathtext")
VectorParse.__doc__ = r"""
The namedtuple type returned by ``MathTextParser("path").parse(...)``.
This tuple contains the global metrics (*width*, *height*, *depth*), a list of
*glyphs* (including their positions) and of *rect*\angles.
"""
RasterParse = namedtuple("RasterParse", "ox oy width height depth image",
module="matplotlib.mathtext")
RasterParse.__doc__ = r"""
The namedtuple type returned by ``MathTextParser("agg").parse(...)``.
This tuple contains the global metrics (*width*, *height*, *depth*), and a
raster *image*. The offsets *ox*, *oy* are always zero.
"""
class Output:
r"""
Result of `ship`\ping a box: lists of positioned glyphs and rectangles.
This class is not exposed to end users, but converted to a `VectorParse` or
a `RasterParse` by `.MathTextParser.parse`.
"""
def __init__(self, box):
self.box = box
self.glyphs = [] # (ox, oy, info)
self.rects = [] # (x1, y1, x2, y2)
def to_vector(self):
w, h, d = map(
np.ceil, [self.box.width, self.box.height, self.box.depth])
gs = [(info.font, info.fontsize, info.num, ox, h - oy + info.offset)
for ox, oy, info in self.glyphs]
rs = [(x1, h - y2, x2 - x1, y2 - y1)
for x1, y1, x2, y2 in self.rects]
return VectorParse(w, h + d, d, gs, rs)
def to_raster(self):
# Metrics y's and mathtext y's are oriented in opposite directions,
# hence the switch between ymin and ymax.
xmin = min([*[ox + info.metrics.xmin for ox, oy, info in self.glyphs],
*[x1 for x1, y1, x2, y2 in self.rects], 0]) - 1
ymin = min([*[oy - info.metrics.ymax for ox, oy, info in self.glyphs],
*[y1 for x1, y1, x2, y2 in self.rects], 0]) - 1
xmax = max([*[ox + info.metrics.xmax for ox, oy, info in self.glyphs],
*[x2 for x1, y1, x2, y2 in self.rects], 0]) + 1
ymax = max([*[oy - info.metrics.ymin for ox, oy, info in self.glyphs],
*[y2 for x1, y1, x2, y2 in self.rects], 0]) + 1
w = xmax - xmin
h = ymax - ymin - self.box.depth
d = ymax - ymin - self.box.height
image = FT2Image(np.ceil(w), np.ceil(h + max(d, 0)))
# Ideally, we could just use self.glyphs and self.rects here, shifting
# their coordinates by (-xmin, -ymin), but this yields slightly
# different results due to floating point slop; shipping twice is the
# old approach and keeps baseline images backcompat.
shifted = ship(self.box, (-xmin, -ymin))
for ox, oy, info in shifted.glyphs:
info.font.draw_glyph_to_bitmap(
image, ox, oy - info.metrics.iceberg, info.glyph,
antialiased=mpl.rcParams['text.antialiased'])
for x1, y1, x2, y2 in shifted.rects:
height = max(int(y2 - y1) - 1, 0)
if height == 0:
center = (y2 + y1) / 2
y = int(center - (height + 1) / 2)
else:
y = int(y1)
image.draw_rect_filled(int(x1), y, np.ceil(x2), y + height)
return RasterParse(0, 0, w, h + d, d, image)
class Fonts:
"""
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, load_glyph_flags):
"""
Parameters
----------
default_font_prop : `~.font_manager.FontProperties`
The default non-math font, or the base font for Unicode (generic)
font rendering.
load_glyph_flags : int
Flags passed to the glyph loader (e.g. ``FT_Load_Glyph`` and
``FT_Load_Char`` for FreeType-based fonts).
"""
self.default_font_prop = default_font_prop
self.load_glyph_flags = load_glyph_flags
def get_kern(self, font1, fontclass1, sym1, fontsize1,
font2, fontclass2, sym2, fontsize2, dpi):
"""
Get the kerning distance for font between *sym1* and *sym2*.
See `~.Fonts.get_metrics` for a detailed description of the parameters.
"""
return 0.
def get_metrics(self, font, font_class, sym, fontsize, dpi):
r"""
Parameters
----------
font : str
One of the TeX font names: "tt", "it", "rm", "cal", "sf", "bf",
"default", "regular", "bb", "frak", "scr". "default" and "regular"
are synonyms and use the non-math font.
font_class : str
One of the TeX font names (as for *font*), but **not** "bb",
"frak", or "scr". This is used to combine two font classes. The
only supported combination currently is ``get_metrics("frak", "bf",
...)``.
sym : str
A symbol in raw TeX form, e.g., "1", "x", or "\sigma".
fontsize : float
Font size in points.
dpi : float
Rendering dots-per-inch.
Returns
-------
object
The returned object has the following attributes (all floats,
except *slanted*):
- *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".)
- *slanted*: Whether the glyph should be considered as "slanted"
(currently used for kerning sub/superscripts).
"""
info = self._get_info(font, font_class, sym, fontsize, dpi)
return info.metrics
def render_glyph(
self, output, ox, oy, font, font_class, sym, fontsize, dpi):
"""
At position (*ox*, *oy*), draw the glyph specified by the remaining
parameters (see `get_metrics` for their detailed description).
"""
info = self._get_info(font, font_class, sym, fontsize, dpi)
output.glyphs.append((ox, oy, info))
def render_rect_filled(self, output, x1, y1, x2, y2):
"""
Draw a filled rectangle from (*x1*, *y1*) to (*x2*, *y2*).
"""
output.rects.append((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_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).
"""
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
# Per-instance cache.
self._get_info = functools.lru_cache(None)(self._get_info)
self._fonts = {}
filename = findfont(self.default_font_prop)
default_font = get_font(filename)
self._fonts['default'] = default_font
self._fonts['regular'] = default_font
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):
cached_font = get_font(basename)
self._fonts[basename] = cached_font
self._fonts[cached_font.postscript_name] = cached_font
self._fonts[cached_font.postscript_name.lower()] = cached_font
return cached_font
def _get_offset(self, font, glyph, fontsize, dpi):
if font.postscript_name == 'Cmex10':
return (glyph.height / 64 / 2) + (fontsize/3 * dpi/72)
return 0.
# The return value of _get_info is cached per-instance.
def _get_info(self, fontname, font_class, sym, fontsize, dpi):
font, num, slanted = self._get_glyph(fontname, font_class, sym)
font.set_size(fontsize, dpi)
glyph = font.load_char(num, flags=self.load_glyph_flags)
xmin, ymin, xmax, ymax = [val/64.0 for val in glyph.bbox]
offset = self._get_offset(font, glyph, fontsize, dpi)
metrics = types.SimpleNamespace(
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
)
return types.SimpleNamespace(
font = font,
fontsize = fontsize,
postscript_name = font.postscript_name,
metrics = metrics,
num = num,
glyph = glyph,
offset = offset
)
def get_xheight(self, fontname, fontsize, dpi):
font = self._get_font(fontname)
font.set_size(fontsize, dpi)
pclt = 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(
fontname, mpl.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
return super().get_kern(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)
super().__init__(*args, **kwargs)
self.fontmap = {}
for key, val in self._fontmap.items():
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):
font = 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
font = self._get_font(basename)
elif len(sym) == 1:
slanted = (fontname == "it")
font = self._get_font(fontname)
if font is not None:
num = ord(sym)
if font is not None and font.get_char_index(num) != 0:
return font, num, slanted
else:
return self._stix_fallback._get_glyph(fontname, font_class, sym)
# 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 omitted 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 [(r'\leftparen', '('),
(r'\rightparent', ')'),
(r'\leftbrace', '{'),
(r'\rightbrace', '}'),
(r'\leftbracket', '['),
(r'\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.
"""
# Some glyphs are not present in the `cmr10` font, and must be brought in
# from `cmsy10`. Map the Unicode indices of those glyphs to the indices at
# which they are found in `cmsy10`.
_cmr10_substitutions = {
0x00D7: 0x00A3, # Multiplication sign.
0x2212: 0x00A1, # Minus sign.
}
def __init__(self, *args, **kwargs):
# This must come first so the backend's owner is set correctly
fallback_rc = mpl.rcParams['mathtext.fallback']
font_cls = {'stix': StixFonts,
'stixsans': StixSansFonts,
'cm': BakomaFonts
}.get(fallback_rc)
self._fallback_font = font_cls(*args, **kwargs) if font_cls else None
super().__init__(*args, **kwargs)
self.fontmap = {}
for texfont in "cal rm tt it bf sf".split():
prop = mpl.rcParams['mathtext.' + texfont]
font = findfont(prop)
self.fontmap[texfont] = font
prop = FontProperties('cmex10')
font = findfont(prop)
self.fontmap['ex'] = font
# include STIX sized alternatives for glyphs if fallback is STIX
if isinstance(self._fallback_font, StixFonts):
stixsizedaltfonts = {
0: 'STIXGeneral',
1: 'STIXSizeOneSym',
2: 'STIXSizeTwoSym',
3: 'STIXSizeThreeSym',
4: 'STIXSizeFourSym',
5: 'STIXSizeFiveSym'}
for size, name in stixsizedaltfonts.items():
fullpath = findfont(name)
self.fontmap[size] = fullpath
self.fontmap[name] = fullpath
_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):
try:
uniindex = get_unicode_index(sym)
found_symbol = True
except ValueError:
uniindex = ord('?')
found_symbol = False
_log.warning("No TeX to Unicode mapping for {!a}.".format(sym))
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' and uniindex < 0x10000:
char = chr(uniindex)
if (unicodedata.category(char)[0] != "L"
or unicodedata.name(char).startswith("GREEK CAPITAL")):
new_fontname = 'rm'
slanted = (new_fontname == 'it') or sym in self._slanted_symbols
found_symbol = False
font = self._get_font(new_fontname)
if font is not None:
if (uniindex in self._cmr10_substitutions
and font.family_name == "cmr10"):
font = get_font(
cbook._get_data_path("fonts/ttf/cmsy10.ttf"))
uniindex = self._cmr10_substitutions[uniindex]
glyphindex = font.get_char_index(uniindex)
if glyphindex != 0:
found_symbol = True
if not found_symbol:
if self._fallback_font:
if (fontname in ('it', 'regular')
and isinstance(self._fallback_font, StixFonts)):
fontname = 'rm'
g = self._fallback_font._get_glyph(fontname, font_class, sym)
family = g[0].family_name
if family in list(BakomaFonts._fontmap.values()):
family = "Computer Modern"
_log.info("Substituting symbol %s from %s", sym, family)
return g
else:
if (fontname in ('it', 'regular')
and isinstance(self, StixFonts)):
return self._get_glyph('rm', font_class, sym)
_log.warning("Font {!r} does not have a glyph for {!a} "
"[U+{:x}], substituting with a dummy "
"symbol.".format(new_fontname, sym, uniindex))
font = self._get_font('rm')
uniindex = 0xA4 # currency char, for lack of anything better
slanted = False
return font, uniindex, slanted
def get_sized_alternatives_for_symbol(self, fontname, sym):
if self._fallback_font:
return self._fallback_font.get_sized_alternatives_for_symbol(
fontname, sym)
return [(fontname, sym)]
class DejaVuFonts(UnicodeFonts):
def __init__(self, *args, **kwargs):
# This must come first so the backend's owner is set correctly
if isinstance(self, DejaVuSerifFonts):
self._fallback_font = StixFonts(*args, **kwargs)
else:
self._fallback_font = StixSansFonts(*args, **kwargs)
self.bakoma = BakomaFonts(*args, **kwargs)
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
# Include Stix sized alternatives for glyphs
self._fontmap.update({
1: 'STIXSizeOneSym',
2: 'STIXSizeTwoSym',
3: 'STIXSizeThreeSym',
4: 'STIXSizeFourSym',
5: 'STIXSizeFiveSym',
})
for key, name in self._fontmap.items():
fullpath = findfont(name)
self.fontmap[key] = fullpath
self.fontmap[name] = fullpath
def _get_glyph(self, fontname, font_class, sym):
# Override prime symbol to use Bakoma.
if sym == r'\prime':
return self.bakoma._get_glyph(fontname, font_class, sym)
else:
# check whether the glyph is available in the display font
uniindex = get_unicode_index(sym)
font = self._get_font('ex')
if font is not None:
glyphindex = font.get_char_index(uniindex)
if glyphindex != 0:
return super()._get_glyph('ex', font_class, sym)
# otherwise return regular glyph
return super()._get_glyph(fontname, font_class, sym)
class DejaVuSerifFonts(DejaVuFonts):
"""
A font handling class for the DejaVu Serif fonts
If a glyph is not found it will fallback to Stix Serif
"""
_fontmap = {
'rm': 'DejaVu Serif',
'it': 'DejaVu Serif:italic',
'bf': 'DejaVu Serif:weight=bold',
'sf': 'DejaVu Sans',
'tt': 'DejaVu Sans Mono',
'ex': 'DejaVu Serif Display',
0: 'DejaVu Serif',
}
class DejaVuSansFonts(DejaVuFonts):
"""
A font handling class for the DejaVu Sans fonts
If a glyph is not found it will fallback to Stix Sans
"""
_fontmap = {
'rm': 'DejaVu Sans',
'it': 'DejaVu Sans:italic',
'bf': 'DejaVu Sans:weight=bold',
'sf': 'DejaVu Sans',
'tt': 'DejaVu Sans Mono',
'ex': 'DejaVu Sans Display',
0: 'DejaVu Sans',
}
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',
}
_fallback_font = False
_sans = False
def __init__(self, *args, **kwargs):
TruetypeFonts.__init__(self, *args, **kwargs)
self.fontmap = {}
for key, name in self._fontmap.items():
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):
try:
mapping = mapping[font_class]
except KeyError:
mapping = mapping['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 range[0] <= 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 = mpl.rcParams['mathtext.default']
# Fix some incorrect glyphs.
if fontname in ('rm', 'it'):
uniindex = stix_glyph_fixes.get(uniindex, uniindex)
# Handle private use area glyphs
if fontname in ('it', 'rm', 'bf') and 0xe000 <= uniindex <= 0xf8ff:
fontname = 'nonuni' + fontname
return fontname, uniindex
@functools.lru_cache()
def get_sized_alternatives_for_symbol(self, fontname, sym):
fixes = {
'\\{': '{', '\\}': '}', '\\[': '[', '\\]': ']',
'<': '\N{MATHEMATICAL LEFT ANGLE BRACKET}',
'>': '\N{MATHEMATICAL RIGHT ANGLE BRACKET}',
}
sym = fixes.get(sym, sym)
try:
uniindex = get_unicode_index(sym)
except ValueError:
return [(fontname, sym)]
alternatives = [(i, chr(uniindex)) for i in range(6)
if self._get_font(i).get_char_index(uniindex) != 0]
# 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]
return alternatives
class StixSansFonts(StixFonts):
"""
A font handling class for the STIX fonts (that uses sans-serif
characters by default).
"""
_sans = True
##############################################################################
# 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())
# 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.
SHRINK_FACTOR = 0.7
# The number of different sizes of chars to use, beyond which they will not
# get any smaller
NUM_SIZE_LEVELS = 6
class FontConstantsBase:
"""
A set of constants that controls how certain things, such as sub-
and superscripts are laid out. These are all metrics that can't
be reliably retrieved from the font metrics in the font itself.
"""
# Percentage of x-height of additional horiz. space after sub/superscripts
script_space = 0.05
# Percentage of x-height that sub/superscripts drop below the baseline
subdrop = 0.4
# Percentage of x-height that superscripts are raised from the baseline
sup1 = 0.7
# Percentage of x-height that subscripts drop below the baseline
sub1 = 0.3
# Percentage of x-height that subscripts drop below the baseline when a
# superscript is present
sub2 = 0.5
# Percentage of x-height that sub/superscripts are offset relative to the
# nucleus edge for non-slanted nuclei
delta = 0.025
# Additional percentage of last character height above 2/3 of the
# x-height that superscripts are offset relative to the subscript
# for slanted nuclei
delta_slanted = 0.2
# Percentage of x-height that superscripts and subscripts are offset for
# integrals
delta_integral = 0.1
class ComputerModernFontConstants(FontConstantsBase):
script_space = 0.075
subdrop = 0.2
sup1 = 0.45
sub1 = 0.2
sub2 = 0.3
delta = 0.075
delta_slanted = 0.3
delta_integral = 0.3
class STIXFontConstants(FontConstantsBase):
script_space = 0.1
sup1 = 0.8
sub2 = 0.6
delta = 0.05
delta_slanted = 0.3
delta_integral = 0.3
class STIXSansFontConstants(FontConstantsBase):
script_space = 0.05
sup1 = 0.8
delta_slanted = 0.6
delta_integral = 0.3
class DejaVuSerifFontConstants(FontConstantsBase):
pass
class DejaVuSansFontConstants(FontConstantsBase):
pass
# Maps font family names to the FontConstantBase subclass to use
_font_constant_mapping = {
'DejaVu Sans': DejaVuSansFontConstants,
'DejaVu Sans Mono': DejaVuSansFontConstants,
'DejaVu Serif': DejaVuSerifFontConstants,
'cmb10': ComputerModernFontConstants,
'cmex10': ComputerModernFontConstants,
'cmmi10': ComputerModernFontConstants,
'cmr10': ComputerModernFontConstants,
'cmss10': ComputerModernFontConstants,
'cmsy10': ComputerModernFontConstants,
'cmtt10': ComputerModernFontConstants,
'STIXGeneral': STIXFontConstants,
'STIXNonUnicode': STIXFontConstants,
'STIXSizeFiveSym': STIXFontConstants,
'STIXSizeFourSym': STIXFontConstants,
'STIXSizeThreeSym': STIXFontConstants,
'STIXSizeTwoSym': STIXFontConstants,
'STIXSizeOneSym': STIXFontConstants,
# Map the fonts we used to ship, just for good measure
'Bitstream Vera Sans': DejaVuSansFontConstants,
'Bitstream Vera': DejaVuSansFontConstants,
}
def _get_font_constant_set(state):
constants = _font_constant_mapping.get(
state.fontset._get_font(state.font).family_name, FontConstantsBase)
# STIX sans isn't really its own fonts, just different code points
# in the STIX fonts, so we have to detect this one separately.
if (constants is STIXFontConstants and
isinstance(state.fontset, StixSansFonts)):
return STIXSansFontConstants
return constants
class Node:
"""A node in the TeX box model."""
def __init__(self):
self.size = 0
def __repr__(self):
return type(self).__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 render(self, output, x, y):
"""Render this node."""
class Box(Node):
"""A node with a physical location."""
def __init__(self, width, height, depth):
super().__init__()
self.width = width
self.height = height
self.depth = depth
def shrink(self):
super().shrink()
if self.size < NUM_SIZE_LEVELS:
self.width *= SHRINK_FACTOR
self.height *= SHRINK_FACTOR
self.depth *= SHRINK_FACTOR
def render(self, output, x1, y1, x2, y2):
pass
class Vbox(Box):
"""A box with only height (zero width)."""
def __init__(self, height, depth):
super().__init__(0., height, depth)
class Hbox(Box):
"""A box with only width (zero height and depth)."""
def __init__(self, width):
super().__init__(width, 0., 0.)
class Char(Node):
"""
A single character.
Unlike TeX, the font information and metrics are stored with each `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 model, and the advance (if different from width)
must be converted into a `Kern` node when the `Char` is added to its parent
`Hlist`.
"""
def __init__(self, c, state):
super().__init__()
self.c = c
self.fontset = state.fontset
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 __repr__(self):
return '`%s`' % self.c
def _update_metrics(self):
metrics = self._metrics = self.fontset.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.
This method is called when characters are strung together into `Hlist`
to create `Kern` nodes.
"""
advance = self._metrics.advance - self.width
kern = 0.
if isinstance(next, Char):
kern = self.fontset.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, output, x, y):
self.fontset.render_glyph(
output, x, y,
self.font, self.font_class, self.c, self.fontsize, self.dpi)
def shrink(self):
super().shrink()
if self.size < NUM_SIZE_LEVELS:
self.fontsize *= SHRINK_FACTOR
self.width *= SHRINK_FACTOR
self.height *= SHRINK_FACTOR
self.depth *= SHRINK_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.fontset.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):
super().shrink()
self._update_metrics()
def render(self, output, x, y):
self.fontset.render_glyph(
output, 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):
super().__init__(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<w=%.02f h=%.02f d=%.02f s=%.02f>[%s]' % (
super().__repr__(),
self.width, self.height,
self.depth, self.shift_amount,
', '.join([repr(x) for x in self.children]))
def _set_glue(self, x, sign, totals, error_type):
self.glue_order = o = next(
# Highest order of glue used by the members of this list.
(i for i in range(len(totals))[::-1] if totals[i] != 0), 0)
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):
_log.warning("%s %s: %r",
error_type, type(self).__name__, self)
def shrink(self):
for child in self.children:
child.shrink()
super().shrink()
if self.size < NUM_SIZE_LEVELS:
self.shift_amount *= SHRINK_FACTOR
self.glue_set *= SHRINK_FACTOR
class Hlist(List):
"""A horizontal list of boxes."""
def __init__(self, elements, w=0., m='additional', do_kern=True):
super().__init__(elements)
if do_kern:
self.kern()
self.hpack(w=w, m=m)
def kern(self):
"""
Insert `Kern` nodes between `Char` nodes to set kerning.
The `Char` nodes themselves determine the amount of kerning they need
(in `~Char.get_kerning`), and this function just creates the correct
linked list.
"""
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'):
r"""
Compute the dimensions of the resulting boxes, and 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.
Parameters
----------
w : float, default: 0
A width.
m : {'exactly', 'additional'}, default: 'additional'
Whether to produce a box whose width is 'exactly' *w*; or a box
with the natural width of the contents, plus *w* ('additional').
Notes
-----
The defaults produce a box with the natural width of the contents.
"""
# 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 np.isinf(p.height) and not np.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, "Overful")
else:
self._set_glue(x, -1, total_shrink, "Underful")
class Vlist(List):
"""A vertical list of boxes."""
def __init__(self, elements, h=0., m='additional'):
super().__init__(elements)
self.vpack(h=h, m=m)
def vpack(self, h=0., m='additional', l=np.inf):
"""
Compute the dimensions of the resulting boxes, and to adjust the glue
if one of those dimensions is pre-specified.
Parameters
----------
h : float, default: 0
A height.
m : {'exactly', 'additional'}, default: 'additional'
Whether to produce a box whose height is 'exactly' *h*; or a box
with the natural height of the contents, plus *h* ('additional').
l : float, default: np.inf
The maximum height.
Notes
-----
The defaults produce a box with the natural height of the contents.
"""
# 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 np.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, "Overful")
else:
self._set_glue(x, -1, total_shrink, "Underful")
class Rule(Box):
"""
A solid black rectangle.
It has *width*, *depth*, and *height* fields just as in an `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 `Hlist`; the height and depth are never running in a `Vlist`.
"""
def __init__(self, width, height, depth, state):
super().__init__(width, height, depth)
self.fontset = state.fontset
def render(self, output, x, y, w, h):
self.fontset.render_rect_filled(output, x, y, x + w, y + h)
class Hrule(Rule):
"""Convenience class to create a horizontal rule."""
def __init__(self, state, thickness=None):
if thickness is None:
thickness = state.get_current_underline_thickness()
height = depth = thickness * 0.5
super().__init__(np.inf, height, depth, state)
class Vrule(Rule):
"""Convenience class to create a vertical rule."""
def __init__(self, state):
thickness = state.get_current_underline_thickness()
super().__init__(thickness, np.inf, np.inf, state)
_GlueSpec = namedtuple(
"_GlueSpec", "width stretch stretch_order shrink shrink_order")
_GlueSpec._named = {
'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),
}
class Glue(Node):
"""
Most of the information in this object is stored in the underlying
``_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):
super().__init__()
if isinstance(glue_type, str):
glue_spec = _GlueSpec._named[glue_type]
elif isinstance(glue_type, _GlueSpec):
glue_spec = glue_type
else:
raise ValueError("glue_type must be a glue spec name or instance")
self.glue_spec = glue_spec
def shrink(self):
super().shrink()
if self.size < NUM_SIZE_LEVELS:
g = self.glue_spec
self.glue_spec = g._replace(width=g.width * SHRINK_FACTOR)
class HCentered(Hlist):
"""
A convenience class to create an `Hlist` whose contents are
centered within its enclosing box.
"""
def __init__(self, elements):
super().__init__([Glue('ss'), *elements, Glue('ss')], do_kern=False)
class VCentered(Vlist):
"""
A convenience class to create a `Vlist` whose contents are
centered within its enclosing box.
"""
def __init__(self, elements):
super().__init__([Glue('ss'), *elements, Glue('ss')])
class Kern(Node):
"""
A `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.
"""
height = 0
depth = 0
def __init__(self, width):
super().__init__()
self.width = width
def __repr__(self):
return "k%.02f" % self.width
def shrink(self):
super().shrink()
if self.size < NUM_SIZE_LEVELS:
self.width *= SHRINK_FACTOR
class AutoHeightChar(Hlist):
"""
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, factor=None):
alternatives = state.fontset.get_sized_alternatives_for_symbol(
state.font, c)
xHeight = state.fontset.get_xheight(
state.font, state.fontsize, state.dpi)
state = state.copy()
target_total = height + depth
for fontname, sym in alternatives:
state.font = fontname
char = Char(sym, state)
# Ensure that size 0 is chosen when the text is regular sized but
# with descender glyphs by subtracting 0.2 * xHeight
if char.height + char.depth >= target_total - 0.2 * xHeight:
break
shift = 0
if state.font != 0 or len(alternatives) == 1:
if factor is None:
factor = target_total / (char.height + char.depth)
state.fontsize *= factor
char = Char(sym, state)
shift = (depth - char.depth)
super().__init__([char])
self.shift_amount = shift
class AutoWidthChar(Hlist):
"""
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.fontset.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)
super().__init__([char])
self.width = char.width
def ship(box, xy=(0, 0)):
"""
Ship out *box* at offset *xy*, converting it to an `Output`.
Since boxes can be inside of boxes inside of boxes, the main work of `ship`
is done by two mutually recursive routines, `hlist_out` and `vlist_out`,
which traverse the `Hlist` nodes and `Vlist` nodes inside of horizontal
and vertical boxes. The global variables used in TeX to store state as it
processes have become local variables here.
"""
ox, oy = xy
cur_v = 0.
cur_h = 0.
off_h = ox
off_v = oy + box.height
output = Output(box)
def clamp(value):
return -1e9 if value < -1e9 else +1e9 if value > +1e9 else value
def hlist_out(box):
nonlocal cur_v, cur_h, off_h, off_v
cur_g = 0
cur_glue = 0.
glue_order = box.glue_order
glue_sign = box.glue_sign
base_line = cur_v
left_edge = cur_h
for p in box.children:
if isinstance(p, Char):
p.render(output, cur_h + off_h, cur_v + off_v)
cur_h += p.width
elif isinstance(p, Kern):
cur_h += p.width
elif isinstance(p, List):
# node623
if len(p.children) == 0:
cur_h += p.width
else:
edge = cur_h
cur_v = base_line + p.shift_amount
if isinstance(p, Hlist):
hlist_out(p)
else:
# p.vpack(box.height + box.depth, 'exactly')
vlist_out(p)
cur_h = edge + p.width
cur_v = base_line
elif isinstance(p, Box):
# node624
rule_height = p.height
rule_depth = p.depth
rule_width = p.width
if np.isinf(rule_height):
rule_height = box.height
if np.isinf(rule_depth):
rule_depth = box.depth
if rule_height > 0 and rule_width > 0:
cur_v = base_line + rule_depth
p.render(output,
cur_h + off_h, cur_v + off_v,
rule_width, rule_height)
cur_v = base_line
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(box.glue_set * cur_glue))
elif glue_spec.shrink_order == glue_order:
cur_glue += glue_spec.shrink
cur_g = round(clamp(box.glue_set * cur_glue))
rule_width += cur_g
cur_h += rule_width
def vlist_out(box):
nonlocal cur_v, cur_h, off_h, off_v
cur_g = 0
cur_glue = 0.
glue_order = box.glue_order
glue_sign = box.glue_sign
left_edge = cur_h
cur_v -= box.height
top_edge = cur_v
for p in box.children:
if isinstance(p, Kern):
cur_v += p.width
elif isinstance(p, List):
if len(p.children) == 0:
cur_v += p.height + p.depth
else:
cur_v += p.height
cur_h = left_edge + p.shift_amount
save_v = cur_v
p.width = box.width
if isinstance(p, Hlist):
hlist_out(p)
else:
vlist_out(p)
cur_v = save_v + p.depth
cur_h = left_edge
elif isinstance(p, Box):
rule_height = p.height
rule_depth = p.depth
rule_width = p.width
if np.isinf(rule_width):
rule_width = box.width
rule_height += rule_depth
if rule_height > 0 and rule_depth > 0:
cur_v += rule_height
p.render(output,
cur_h + off_h, cur_v + 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(box.glue_set * cur_glue))
elif glue_spec.shrink_order == glue_order: # shrinking
cur_glue += glue_spec.shrink
cur_g = round(clamp(box.glue_set * cur_glue))
rule_height += cur_g
cur_v += rule_height
elif isinstance(p, Char):
raise RuntimeError(
"Internal mathtext error: Char node found in vlist")
hlist_out(box)
return output
##############################################################################
# PARSER
def Error(msg):
"""Helper class to raise parser errors."""
def raise_error(s, loc, toks):
raise ParseFatalException(s, loc, msg)
return Empty().setParseAction(raise_error)
class ParserState:
"""
Parser state.
States are pushed and popped from a stack as necessary, and the "current"
state is always at the top of the stack.
Upon entering and leaving a group { } or math/non-math, the stack is pushed
and popped accordingly.
"""
def __init__(self, fontset, font, font_class, fontsize, dpi):
self.fontset = fontset
self._font = font
self.font_class = font_class
self.fontsize = fontsize
self.dpi = dpi
def copy(self):
return copy.copy(self)
@property
def font(self):
return self._font
@font.setter
def font(self, name):
if name in ('rm', 'it', 'bf'):
self.font_class = name
self._font = name
def get_current_underline_thickness(self):
"""Return the underline thickness for this state."""
return self.fontset.get_underline_thickness(
self.font, self.fontsize, self.dpi)
def cmd(expr, args):
r"""
Helper to define TeX commands.
``cmd("\cmd", args)`` is equivalent to
``"\cmd" - (args | Error("Expected \cmd{arg}{...}"))`` where the names in
the error message are taken from element names in *args*. If *expr*
already includes arguments (e.g. "\cmd{arg}{...}"), then they are stripped
when constructing the parse element, but kept (and *expr* is used as is) in
the error message.
"""
def names(elt):
if isinstance(elt, ParseExpression):
for expr in elt.exprs:
yield from names(expr)
elif elt.resultsName:
yield elt.resultsName
csname = expr.split("{", 1)[0]
err = (csname + "".join("{%s}" % name for name in names(args))
if expr == csname else expr)
return csname - (args | Error(f"Expected {err}"))
class Parser:
"""
A pyparsing-based parser for strings containing math expressions.
Raw text may also appear outside of pairs of ``$``.
The grammar is based directly on that in TeX, though it cuts a few corners.
"""
class _MathStyle(enum.Enum):
DISPLAYSTYLE = 0
TEXTSTYLE = 1
SCRIPTSTYLE = 2
SCRIPTSCRIPTSTYLE = 3
_binary_operators = set(
'+ * - \N{MINUS SIGN}'
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
\dotplus \dotminus'''.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 \doteqdot'''.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("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 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())
_ambi_delims = set(r"""
| \| / \backslash \uparrow \downarrow \updownarrow \Uparrow
\Downarrow \Updownarrow . \vert \Vert""".split())
_left_delims = set(r"( [ \{ < \lfloor \langle \lceil".split())
_right_delims = set(r") ] \} > \rfloor \rangle \rceil".split())
_delims = _left_delims | _right_delims | _ambi_delims
def __init__(self):
p = types.SimpleNamespace()
def set_names_and_parse_actions():
for key, val in vars(p).items():
if not key.startswith('_'):
# Set names on everything -- very useful for debugging
val.setName(key)
# Set actions
if hasattr(self, key):
val.setParseAction(getattr(self, key))
# Root definitions.
# In TeX parlance, a csname is a control sequence name (a "\foo").
def csnames(group, names):
ends_with_alpha = []
ends_with_nonalpha = []
for name in names:
if name[-1].isalpha():
ends_with_alpha.append(name)
else:
ends_with_nonalpha.append(name)
return Regex(r"\\(?P<{}>(?:{})(?![A-Za-z]){})".format(
group,
"|".join(map(re.escape, ends_with_alpha)),
"".join(f"|{s}" for s in map(re.escape, ends_with_nonalpha)),
))
p.float_literal = Regex(r"[-+]?([0-9]+\.?[0-9]*|\.[0-9]+)")
p.space = oneOf(self._space_widths)("space")
p.style_literal = oneOf(
[str(e.value) for e in self._MathStyle])("style_literal")
p.symbol = Regex(
r"[a-zA-Z0-9 +\-*/<>=:,.;!\?&'@()\[\]|\U00000080-\U0001ffff]"
r"|\\[%${}\[\]_|]"
+ r"|\\(?:{})(?![A-Za-z])".format(
"|".join(map(re.escape, tex2uni)))
)("sym").leaveWhitespace()
p.unknown_symbol = Regex(r"\\[A-Za-z]*")("name")
p.font = csnames("font", self._fontnames)
p.start_group = (
Optional(r"\math" + oneOf(self._fontnames)("font")) + "{")
p.end_group = Literal("}")
p.delim = oneOf(self._delims)
set_names_and_parse_actions() # for root definitions.
# Mutually recursive definitions. (Minimizing the number of Forward
# elements is important for speed.)
p.accent = Forward()
p.auto_delim = Forward()
p.binom = Forward()
p.customspace = Forward()
p.frac = Forward()
p.dfrac = Forward()
p.function = Forward()
p.genfrac = Forward()
p.group = Forward()
p.operatorname = Forward()
p.overline = Forward()
p.overset = Forward()
p.placeable = Forward()
p.required_group = Forward()
p.simple = Forward()
p.optional_group = Forward()
p.sqrt = Forward()
p.subsuper = Forward()
p.token = Forward()
p.underset = Forward()
set_names_and_parse_actions() # for mutually recursive definitions.
p.customspace <<= cmd(r"\hspace", "{" + p.float_literal("space") + "}")
p.accent <<= (
csnames("accent", [*self._accent_map, *self._wide_accents])
- p.placeable("sym"))
p.function <<= csnames("name", self._function_names)
p.operatorname <<= cmd(
r"\operatorname",
"{" + ZeroOrMore(p.simple | p.unknown_symbol)("name") + "}")
p.group <<= p.start_group + ZeroOrMore(p.token)("group") + p.end_group
p.optional_group <<= "{" + ZeroOrMore(p.token)("group") + "}"
p.required_group <<= "{" + OneOrMore(p.token)("group") + "}"
p.frac <<= cmd(
r"\frac", p.required_group("num") + p.required_group("den"))
p.dfrac <<= cmd(
r"\dfrac", p.required_group("num") + p.required_group("den"))
p.binom <<= cmd(
r"\binom", p.required_group("num") + p.required_group("den"))
p.genfrac <<= cmd(
r"\genfrac",
"{" + Optional(p.delim)("ldelim") + "}"
+ "{" + Optional(p.delim)("rdelim") + "}"
+ "{" + p.float_literal("rulesize") + "}"
+ "{" + Optional(p.style_literal)("style") + "}"
+ p.required_group("num")
+ p.required_group("den"))
p.sqrt <<= cmd(
r"\sqrt{value}",
Optional("[" + OneOrMore(NotAny("]") + p.token)("root") + "]")
+ p.required_group("value"))
p.overline <<= cmd(r"\overline", p.required_group("body"))
p.overset <<= cmd(
r"\overset",
p.optional_group("annotation") + p.optional_group("body"))
p.underset <<= cmd(
r"\underset",
p.optional_group("annotation") + p.optional_group("body"))
p.placeable <<= (
p.accent # Must be before symbol as all accents are symbols
| p.symbol # Must be second to catch all named symbols and single
# chars not in a group
| p.function
| p.operatorname
| p.group
| p.frac
| p.dfrac
| p.binom
| p.genfrac
| p.overset
| p.underset
| p.sqrt
| p.overline
)
p.simple <<= (
p.space
| p.customspace
| p.font
| p.subsuper
)
p.subsuper <<= (
(Optional(p.placeable)("nucleus")
+ OneOrMore(oneOf(["_", "^"]) - p.placeable)("subsuper")
+ Regex("'*")("apostrophes"))
| Regex("'+")("apostrophes")
| (p.placeable("nucleus") + Regex("'*")("apostrophes"))
)
p.token <<= (
p.simple
| p.auto_delim
| p.unknown_symbol # Must be last
)
p.auto_delim <<= (
r"\left" - (p.delim("left") | Error("Expected a delimiter"))
+ ZeroOrMore(p.simple | p.auto_delim)("mid")
+ r"\right" - (p.delim("right") | Error("Expected a delimiter"))
)
# Leaf definitions.
p.math = OneOrMore(p.token)
p.math_string = QuotedString('$', '\\', unquoteResults=False)
p.non_math = Regex(r"(?:(?:\\[$])|[^$])*").leaveWhitespace()
p.main = (
p.non_math + ZeroOrMore(p.math_string + p.non_math) + StringEnd()
)
set_names_and_parse_actions() # for leaf definitions.
self._expression = p.main
self._math_expression = p.math
# To add space to nucleus operators after sub/superscripts
self._in_subscript_or_superscript = False
def parse(self, s, fonts_object, fontsize, dpi):
"""
Parse expression *s* using the given *fonts_object* for
output, at the given *fontsize* and *dpi*.
Returns the parse tree of `Node` instances.
"""
self._state_stack = [
ParserState(fonts_object, 'default', 'rm', fontsize, dpi)]
self._em_width_cache = {}
try:
result = self._expression.parseString(s)
except ParseBaseException as err:
# explain becomes a plain method on pyparsing 3 (err.explain(0)).
raise ValueError("\n" + ParseException.explain(err, 0)) from None
self._state_stack = None
self._in_subscript_or_superscript = False
# prevent operator spacing from leaking into a new expression
self._em_width_cache = {}
self._expression.resetCache()
return result[0]
def get_state(self):
"""Get the current `State` of the parser."""
return self._state_stack[-1]
def pop_state(self):
"""Pop a `State` off of the stack."""
self._state_stack.pop()
def push_state(self):
"""Push a new `State` onto the stack, copying the current state."""
self._state_stack.append(self.get_state().copy())
def main(self, s, loc, toks):
return [Hlist(toks)]
def math_string(self, s, loc, toks):
return self._math_expression.parseString(toks[0][1:-1])
def math(self, s, loc, toks):
hlist = Hlist(toks)
self.pop_state()
return [hlist]
def non_math(self, s, loc, toks):
s = toks[0].replace(r'\$', '$')
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 = mpl.rcParams['mathtext.default']
return [hlist]
float_literal = staticmethod(pyparsing_common.convertToFloat)
def _make_space(self, percentage):
# In TeX, an em (the unit usually used to measure horizontal lengths)
# is not the width of the character 'm'; it is the same in different
# font styles (e.g. roman or italic). Mathtext, however, uses 'm' in
# the italic style so that horizontal spaces don't depend on the
# current font style.
state = self.get_state()
key = (state.font, state.fontsize, state.dpi)
width = self._em_width_cache.get(key)
if width is None:
metrics = state.fontset.get_metrics(
'it', mpl.rcParams['mathtext.default'], 'm',
state.fontsize, state.dpi)
width = metrics.advance
self._em_width_cache[key] = width
return Kern(width * percentage)
_space_widths = {
r'\,': 0.16667, # 3/18 em = 3 mu
r'\thinspace': 0.16667, # 3/18 em = 3 mu
r'\/': 0.16667, # 3/18 em = 3 mu
r'\>': 0.22222, # 4/18 em = 4 mu
r'\:': 0.22222, # 4/18 em = 4 mu
r'\;': 0.27778, # 5/18 em = 5 mu
r'\ ': 0.33333, # 6/18 em = 6 mu
r'~': 0.33333, # 6/18 em = 6 mu, nonbreakable
r'\enspace': 0.5, # 9/18 em = 9 mu
r'\quad': 1, # 1 em = 18 mu
r'\qquad': 2, # 2 em = 36 mu
r'\!': -0.16667, # -3/18 em = -3 mu
}
def space(self, s, loc, toks):
num = self._space_widths[toks["space"]]
box = self._make_space(num)
return [box]
def customspace(self, s, loc, toks):
return [self._make_space(toks["space"])]
def symbol(self, s, loc, toks):
c = toks["sym"]
if c == "-":
# "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." (https://www.unicode.org/reports/tr25/)
c = "\N{MINUS SIGN}"
try:
char = Char(c, self.get_state())
except ValueError as err:
raise ParseFatalException(s, loc,
"Unknown symbol: %s" % c) from err
if c in self._spaced_symbols:
# iterate until we find previous character, needed for cases
# such as ${ -2}$, $ -2$, or $ -2$.
prev_char = next((c for c in s[:loc][::-1] if c != ' '), '')
# Binary operators at start of string should not be spaced
if (c in self._binary_operators and
(len(s[:loc].split()) == 0 or prev_char == '{' or
prev_char in self._left_delims)):
return [char]
else:
return [Hlist([self._make_space(0.2),
char,
self._make_space(0.2)],
do_kern=True)]
elif c in self._punctuation_symbols:
prev_char = next((c for c in s[:loc][::-1] if c != ' '), '')
next_char = next((c for c in s[loc + 1:] if c != ' '), '')
# Do not space commas between brackets
if c == ',':
if prev_char == '{' and next_char == '}':
return [char]
# Do not space dots as decimal separators
if c == '.' and prev_char.isdigit() and next_char.isdigit():
return [char]
else:
return [Hlist([char, self._make_space(0.2)], do_kern=True)]
return [char]
def unknown_symbol(self, s, loc, toks):
raise ParseFatalException(s, loc, f"Unknown symbol: {toks['name']}")
_accent_map = {
r'hat': r'\circumflexaccent',
r'breve': r'\combiningbreve',
r'bar': r'\combiningoverline',
r'grave': r'\combininggraveaccent',
r'acute': r'\combiningacuteaccent',
r'tilde': r'\combiningtilde',
r'dot': r'\combiningdotabove',
r'ddot': r'\combiningdiaeresis',
r'dddot': r'\combiningthreedotsabove',
r'ddddot': r'\combiningfourdotsabove',
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',
r'mathring': r'\circ',
}
_wide_accents = set(r"widehat widetilde widebar".split())
def accent(self, s, loc, toks):
state = self.get_state()
thickness = state.get_current_underline_thickness()
accent = toks["accent"]
sym = toks["sym"]
if accent in self._wide_accents:
accent_box = AutoWidthChar(
'\\' + accent, sym.width, state, char_class=Accent)
else:
accent_box = Accent(self._accent_map[accent], state)
if accent == 'mathring':
accent_box.shrink()
accent_box.shrink()
centered = HCentered([Hbox(sym.width / 4.0), accent_box])
centered.hpack(sym.width, 'exactly')
return Vlist([
centered,
Vbox(0., thickness * 2.0),
Hlist([sym])
])
def function(self, s, loc, toks):
hlist = self.operatorname(s, loc, toks)
hlist.function_name = toks["name"]
return hlist
def operatorname(self, s, loc, toks):
self.push_state()
state = self.get_state()
state.font = 'rm'
hlist_list = []
# Change the font of Chars, but leave Kerns alone
name = toks["name"]
for c in name:
if isinstance(c, Char):
c.font = 'rm'
c._update_metrics()
hlist_list.append(c)
elif isinstance(c, str):
hlist_list.append(Char(c, state))
else:
hlist_list.append(c)
next_char_loc = loc + len(name) + 1
if isinstance(name, ParseResults):
next_char_loc += len('operatorname{}')
next_char = next((c for c in s[next_char_loc:] if c != ' '), '')
delimiters = self._delims | {'^', '_'}
if (next_char not in delimiters and
name not in self._overunder_functions):
# Add thin space except when followed by parenthesis, bracket, etc.
hlist_list += [self._make_space(self._space_widths[r'\,'])]
self.pop_state()
# if followed by a super/subscript, set flag to true
# This flag tells subsuper to add space after this operator
if next_char in {'^', '_'}:
self._in_subscript_or_superscript = True
else:
self._in_subscript_or_superscript = False
return Hlist(hlist_list)
def start_group(self, s, loc, toks):
self.push_state()
# Deal with LaTeX-style font tokens
if toks.get("font"):
self.get_state().font = toks.get("font")
return []
def group(self, s, loc, toks):
grp = Hlist(toks.get("group", []))
return [grp]
def required_group(self, s, loc, toks):
return Hlist(toks.get("group", []))
optional_group = required_group
def end_group(self, s, loc, toks):
self.pop_state()
return []
def font(self, s, loc, toks):
self.get_state().font = toks["font"]
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 is_between_brackets(self, s, loc):
return False
def subsuper(self, s, loc, toks):
nucleus = toks.get("nucleus", Hbox(0))
subsuper = toks.get("subsuper", [])
napostrophes = len(toks.get("apostrophes", []))
if not subsuper and not napostrophes:
return nucleus
sub = super = None
while subsuper:
op, arg, *subsuper = subsuper
if op == '_':
if sub is not None:
raise ParseFatalException("Double subscript")
sub = arg
else:
if super is not None:
raise ParseFatalException("Double superscript")
super = arg
state = self.get_state()
rule_thickness = state.fontset.get_underline_thickness(
state.font, state.fontsize, state.dpi)
xHeight = state.fontset.get_xheight(
state.font, state.fontsize, state.dpi)
if napostrophes:
if super is None:
super = Hlist([])
for i in range(napostrophes):
super.children.extend(self.symbol(s, loc, {"sym": "\\prime"}))
# kern() and hpack() needed to get the metrics right after
# extending
super.kern()
super.hpack()
# Handle over/under symbols, such as sum or prod
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)
vgap = rule_thickness * 3.0
if super is not None:
hlist = HCentered([super])
hlist.hpack(width, 'exactly')
vlist.extend([hlist, Vbox(0, vgap)])
hlist = HCentered([nucleus])
hlist.hpack(width, 'exactly')
vlist.append(hlist)
if sub is not None:
hlist = HCentered([sub])
hlist.hpack(width, 'exactly')
vlist.extend([Vbox(0, vgap), hlist])
shift = hlist.height + vgap + nucleus.depth
vlist = Vlist(vlist)
vlist.shift_amount = shift
result = Hlist([vlist])
return [result]
# We remove kerning on the last character for consistency (otherwise
# it will compute kerning based on non-shrunk characters and may put
# them too close together when superscripted)
# We change the width of the last character to match the advance to
# consider some fonts with weird metrics: e.g. stix's f has a width of
# 7.75 and a kerning of -4.0 for an advance of 3.72, and we want to put
# the superscript at the advance
last_char = nucleus
if isinstance(nucleus, Hlist):
new_children = nucleus.children
if len(new_children):
# remove last kern
if (isinstance(new_children[-1], Kern) and
hasattr(new_children[-2], '_metrics')):
new_children = new_children[:-1]
last_char = new_children[-1]
if hasattr(last_char, '_metrics'):
last_char.width = last_char._metrics.advance
# create new Hlist without kerning
nucleus = Hlist(new_children, do_kern=False)
else:
if isinstance(nucleus, Char):
last_char.width = last_char._metrics.advance
nucleus = Hlist([nucleus])
# Handle regular sub/superscripts
constants = _get_font_constant_set(state)
lc_height = last_char.height
lc_baseline = 0
if self.is_dropsub(last_char):
lc_baseline = last_char.depth
# Compute kerning for sub and super
superkern = constants.delta * xHeight
subkern = constants.delta * xHeight
if self.is_slanted(last_char):
superkern += constants.delta * xHeight
superkern += (constants.delta_slanted *
(lc_height - xHeight * 2. / 3.))
if self.is_dropsub(last_char):
subkern = (3 * constants.delta -
constants.delta_integral) * lc_height
superkern = (3 * constants.delta +
constants.delta_integral) * lc_height
else:
subkern = 0
if super is None:
# node757
x = Hlist([Kern(subkern), sub])
x.shrink()
if self.is_dropsub(last_char):
shift_down = lc_baseline + constants.subdrop * xHeight
else:
shift_down = constants.sub1 * xHeight
x.shift_amount = shift_down
else:
x = Hlist([Kern(superkern), super])
x.shrink()
if self.is_dropsub(last_char):
shift_up = lc_height - constants.subdrop * xHeight
else:
shift_up = constants.sup1 * xHeight
if sub is None:
x.shift_amount = -shift_up
else: # Both sub and superscript
y = Hlist([Kern(subkern), sub])
y.shrink()
if self.is_dropsub(last_char):
shift_down = lc_baseline + constants.subdrop * xHeight
else:
shift_down = constants.sub2 * xHeight
# If sub and superscript collide, move super up
clr = (2.0 * rule_thickness -
((shift_up - x.depth) - (y.height - shift_down)))
if clr > 0.:
shift_up += clr
x = Vlist([
x,
Kern((shift_up - x.depth) - (y.height - shift_down)),
y])
x.shift_amount = shift_down
if not self.is_dropsub(last_char):
x.width += constants.script_space * xHeight
# Do we need to add a space after the nucleus?
# To find out, check the flag set by operatorname
spaced_nucleus = [nucleus, x]
if self._in_subscript_or_superscript:
spaced_nucleus += [self._make_space(self._space_widths[r'\,'])]
self._in_subscript_or_superscript = False
result = Hlist(spaced_nucleus)
return [result]
def _genfrac(self, ldelim, rdelim, rule, style, num, den):
state = self.get_state()
thickness = state.get_current_underline_thickness()
for _ in range(style.value):
num.shrink()
den.shrink()
cnum = HCentered([num])
cden = HCentered([den])
width = max(num.width, den.width)
cnum.hpack(width, 'exactly')
cden.hpack(width, 'exactly')
vlist = Vlist([cnum, # numerator
Vbox(0, thickness * 2.0), # space
Hrule(state, rule), # rule
Vbox(0, thickness * 2.0), # space
cden # denominator
])
# Shift so the fraction line sits in the middle of the
# equals sign
metrics = state.fontset.get_metrics(
state.font, mpl.rcParams['mathtext.default'],
'=', state.fontsize, state.dpi)
shift = (cden.height -
((metrics.ymax + metrics.ymin) / 2 -
thickness * 3.0))
vlist.shift_amount = shift
result = [Hlist([vlist, Hbox(thickness * 2.)])]
if ldelim or rdelim:
if ldelim == '':
ldelim = '.'
if rdelim == '':
rdelim = '.'
return self._auto_sized_delimiter(ldelim, result, rdelim)
return result
def style_literal(self, s, loc, toks):
return self._MathStyle(int(toks["style_literal"]))
def genfrac(self, s, loc, toks):
return self._genfrac(
toks.get("ldelim", ""), toks.get("rdelim", ""),
toks["rulesize"], toks.get("style", self._MathStyle.TEXTSTYLE),
toks["num"], toks["den"])
def frac(self, s, loc, toks):
return self._genfrac(
"", "", self.get_state().get_current_underline_thickness(),
self._MathStyle.TEXTSTYLE, toks["num"], toks["den"])
def dfrac(self, s, loc, toks):
return self._genfrac(
"", "", self.get_state().get_current_underline_thickness(),
self._MathStyle.DISPLAYSTYLE, toks["num"], toks["den"])
def binom(self, s, loc, toks):
return self._genfrac(
"(", ")", 0,
self._MathStyle.TEXTSTYLE, toks["num"], toks["den"])
def _genset(self, s, loc, toks):
annotation = toks["annotation"]
body = toks["body"]
thickness = self.get_state().get_current_underline_thickness()
annotation.shrink()
cannotation = HCentered([annotation])
cbody = HCentered([body])
width = max(cannotation.width, cbody.width)
cannotation.hpack(width, 'exactly')
cbody.hpack(width, 'exactly')
vgap = thickness * 3
if s[loc + 1] == "u": # \underset
vlist = Vlist([cbody, # body
Vbox(0, vgap), # space
cannotation # annotation
])
# Shift so the body sits in the same vertical position
vlist.shift_amount = cbody.depth + cannotation.height + vgap
else: # \overset
vlist = Vlist([cannotation, # annotation
Vbox(0, vgap), # space
cbody # body
])
# To add horizontal gap between symbols: wrap the Vlist into
# an Hlist and extend it with an Hbox(0, horizontal_gap)
return vlist
overset = underset = _genset
def sqrt(self, s, loc, toks):
root = toks.get("root")
body = toks["value"]
state = self.get_state()
thickness = state.get_current_underline_thickness()
# 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(2 * thickness), body, Hbox(2 * thickness)])
rightside = Vlist([Hrule(state), Glue('fill'), padded_body])
# Stretch the glue between the hrule and the body
rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
'exactly', depth)
# Add the root and shift it upward so it is above the tick.
# The value of 0.6 is a hard-coded hack ;)
if not root:
root = Box(check.width * 0.5, 0., 0.)
else:
root = Hlist(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 overline(self, s, loc, toks):
body = toks["body"]
state = self.get_state()
thickness = state.get_current_underline_thickness()
height = body.height - body.shift_amount + thickness * 3.0
depth = body.depth + body.shift_amount
# Place overline above body
rightside = Vlist([Hrule(state), Glue('fill'), Hlist([body])])
# Stretch the glue between the hrule and the body
rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0),
'exactly', depth)
hlist = Hlist([rightside])
return [hlist]
def _auto_sized_delimiter(self, front, middle, back):
state = self.get_state()
if len(middle):
height = max(x.height for x in middle)
depth = max(x.depth for x in middle)
factor = None
else:
height = 0
depth = 0
factor = 1.0
parts = []
# \left. and \right. aren't supposed to produce any symbols
if front != '.':
parts.append(
AutoHeightChar(front, height, depth, state, factor=factor))
parts.extend(middle)
if back != '.':
parts.append(
AutoHeightChar(back, height, depth, state, factor=factor))
hlist = Hlist(parts)
return hlist
def auto_delim(self, s, loc, toks):
return self._auto_sized_delimiter(
toks["left"],
# if "mid" in toks ... can be removed when requiring pyparsing 3.
toks["mid"].asList() if "mid" in toks else [],
toks["right"])