diff --git "a/llava_next/lib/python3.10/site-packages/matplotlib/_mathtext.py" "b/llava_next/lib/python3.10/site-packages/matplotlib/_mathtext.py" new file mode 100644--- /dev/null +++ "b/llava_next/lib/python3.10/site-packages/matplotlib/_mathtext.py" @@ -0,0 +1,2861 @@ +""" +Implementation details for :mod:`.mathtext`. +""" + +from __future__ import annotations + +import abc +import copy +import enum +import functools +import logging +import os +import re +import types +import unicodedata +import string +import typing as T +from typing import NamedTuple + +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, Group) + +import matplotlib as mpl +from . import 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 FT2Font, FT2Image, KERNING_DEFAULT + +from packaging.version import parse as parse_version +from pyparsing import __version__ as pyparsing_version +if parse_version(pyparsing_version).major < 3: + from pyparsing import nestedExpr as nested_expr +else: + from pyparsing import nested_expr + +if T.TYPE_CHECKING: + from collections.abc import Iterable + from .ft2font import Glyph + +ParserElement.enablePackrat() +_log = logging.getLogger("matplotlib.mathtext") + + +############################################################################## +# FONTS + + +def get_unicode_index(symbol: str) -> int: # 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'). + """ + 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( + f"{symbol!r} is not a valid Unicode character or TeX/Type1 symbol" + ) from err + + +class VectorParse(NamedTuple): + """ + The namedtuple type returned by ``MathTextParser("path").parse(...)``. + + Attributes + ---------- + width, height, depth : float + The global metrics. + glyphs : list + The glyphs including their positions. + rect : list + The list of rectangles. + """ + width: float + height: float + depth: float + glyphs: list[tuple[FT2Font, float, int, float, float]] + rects: list[tuple[float, float, float, float]] + +VectorParse.__module__ = "matplotlib.mathtext" + + +class RasterParse(NamedTuple): + """ + The namedtuple type returned by ``MathTextParser("agg").parse(...)``. + + Attributes + ---------- + ox, oy : float + The offsets are always zero. + width, height, depth : float + The global metrics. + image : FT2Image + A raster image. + """ + ox: float + oy: float + width: float + height: float + depth: float + image: FT2Image + +RasterParse.__module__ = "matplotlib.mathtext" + + +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: Box): + self.box = box + self.glyphs: list[tuple[float, float, FontInfo]] = [] # (ox, oy, info) + self.rects: list[tuple[float, float, float, float]] = [] # (x1, y1, x2, y2) + + def to_vector(self) -> VectorParse: + 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, *, antialiased: bool) -> RasterParse: + # 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=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 FontMetrics(NamedTuple): + """ + Metrics of a font. + + Attributes + ---------- + advance : float + The advance distance (in points) of the glyph. + height : float + The height of the glyph in points. + width : float + The width of the glyph in points. + xmin, xmax, ymin, ymax : float + The ink rectangle of the glyph. + iceberg : float + The distance from the baseline to the top of the glyph. (This corresponds to + TeX's definition of "height".) + slanted : bool + Whether the glyph should be considered as "slanted" (currently used for kerning + sub/superscripts). + """ + advance: float + height: float + width: float + xmin: float + xmax: float + ymin: float + ymax: float + iceberg: float + slanted: bool + + +class FontInfo(NamedTuple): + font: FT2Font + fontsize: float + postscript_name: str + metrics: FontMetrics + num: int + glyph: Glyph + offset: float + + +class Fonts(abc.ABC): + """ + 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: FontProperties, load_glyph_flags: int): + """ + 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: str, fontclass1: str, sym1: str, fontsize1: float, + font2: str, fontclass2: str, sym2: str, fontsize2: float, + dpi: float) -> float: + """ + 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_font(self, font: str) -> FT2Font: + raise NotImplementedError + + def _get_info(self, font: str, font_class: str, sym: str, fontsize: float, + dpi: float) -> FontInfo: + raise NotImplementedError + + def get_metrics(self, font: str, font_class: str, sym: str, fontsize: float, + dpi: float) -> FontMetrics: + 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 + ------- + FontMetrics + """ + info = self._get_info(font, font_class, sym, fontsize, dpi) + return info.metrics + + def render_glyph(self, output: Output, ox: float, oy: float, font: str, + font_class: str, sym: str, fontsize: float, dpi: float) -> None: + """ + 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: Output, + x1: float, y1: float, x2: float, y2: float) -> None: + """ + Draw a filled rectangle from (*x1*, *y1*) to (*x2*, *y2*). + """ + output.rects.append((x1, y1, x2, y2)) + + def get_xheight(self, font: str, fontsize: float, dpi: float) -> float: + """ + Get the xheight for the given *font* and *fontsize*. + """ + raise NotImplementedError() + + def get_underline_thickness(self, font: str, fontsize: float, dpi: float) -> float: + """ + 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_sized_alternatives_for_symbol(self, fontname: str, + sym: str) -> list[tuple[str, str]]: + """ + 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, metaclass=abc.ABCMeta): + """ + A generic base class for all font setups that use Truetype fonts + (through FT2Font). + """ + + def __init__(self, default_font_prop: FontProperties, load_glyph_flags: int): + super().__init__(default_font_prop, load_glyph_flags) + # Per-instance cache. + self._get_info = functools.cache(self._get_info) # type: ignore[method-assign] + self._fonts = {} + self.fontmap: dict[str | int, str] = {} + + 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: str | int) -> FT2Font: + if font in self.fontmap: + basename = self.fontmap[font] + else: + # NOTE: An int is only passed by subclasses which have placed int keys into + # `self.fontmap`, so we must cast this to confirm it to typing. + basename = T.cast(str, 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 T.cast(FT2Font, cached_font) # FIXME: Not sure this is guaranteed. + + def _get_offset(self, font: FT2Font, glyph: Glyph, fontsize: float, + dpi: float) -> float: + if font.postscript_name == 'Cmex10': + return (glyph.height / 64 / 2) + (fontsize/3 * dpi/72) + return 0. + + def _get_glyph(self, fontname: str, font_class: str, + sym: str) -> tuple[FT2Font, int, bool]: + raise NotImplementedError + + # The return value of _get_info is cached per-instance. + def _get_info(self, fontname: str, font_class: str, sym: str, fontsize: float, + dpi: float) -> FontInfo: + 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 = FontMetrics( + 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 FontInfo( + font = font, + fontsize = fontsize, + postscript_name = font.postscript_name, + metrics = metrics, + num = num, + glyph = glyph, + offset = offset + ) + + def get_xheight(self, fontname: str, fontsize: float, dpi: float) -> float: + 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: str, fontsize: float, dpi: float) -> float: + # 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: str, fontclass1: str, sym1: str, fontsize1: float, + font2: str, fontclass2: str, sym2: str, fontsize2: float, + dpi: float) -> float: + 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, default_font_prop: FontProperties, load_glyph_flags: int): + self._stix_fallback = StixFonts(default_font_prop, load_glyph_flags) + + super().__init__(default_font_prop, load_glyph_flags) + 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: str, font_class: str, + sym: str) -> tuple[FT2Font, int, bool]: + 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: str, + sym: str) -> list[tuple[str, str]]: + 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 cannot 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, default_font_prop: FontProperties, load_glyph_flags: int): + # This must come first so the backend's owner is set correctly + fallback_rc = mpl.rcParams['mathtext.fallback'] + font_cls: type[TruetypeFonts] | None = { + 'stix': StixFonts, + 'stixsans': StixSansFonts, + 'cm': BakomaFonts + }.get(fallback_rc) + self._fallback_font = (font_cls(default_font_prop, load_glyph_flags) + if font_cls else None) + + super().__init__(default_font_prop, load_glyph_flags) + for texfont in "cal rm tt it bf sf bfit".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: str, font_class: str, + uniindex: int) -> tuple[str, int]: + return fontname, uniindex + + def _get_glyph(self, fontname: str, font_class: str, + sym: str) -> tuple[FT2Font, int, bool]: + 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.", 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.", + 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: str, + sym: str) -> list[tuple[str, str]]: + if self._fallback_font: + return self._fallback_font.get_sized_alternatives_for_symbol( + fontname, sym) + return [(fontname, sym)] + + +class DejaVuFonts(UnicodeFonts, metaclass=abc.ABCMeta): + _fontmap: dict[str | int, str] = {} + + def __init__(self, default_font_prop: FontProperties, load_glyph_flags: int): + # This must come first so the backend's owner is set correctly + if isinstance(self, DejaVuSerifFonts): + self._fallback_font = StixFonts(default_font_prop, load_glyph_flags) + else: + self._fallback_font = StixSansFonts(default_font_prop, load_glyph_flags) + self.bakoma = BakomaFonts(default_font_prop, load_glyph_flags) + TruetypeFonts.__init__(self, default_font_prop, load_glyph_flags) + # 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: str, font_class: str, + sym: str) -> tuple[FT2Font, int, bool]: + # 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', + 'bfit': 'DejaVu Serif:italic: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', + 'bfit': 'DejaVu Sans:italic: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: dict[str | int, str] = { + 'rm': 'STIXGeneral', + 'it': 'STIXGeneral:italic', + 'bf': 'STIXGeneral:weight=bold', + 'bfit': 'STIXGeneral:italic:bold', + 'nonunirm': 'STIXNonUnicode', + 'nonuniit': 'STIXNonUnicode:italic', + 'nonunibf': 'STIXNonUnicode:weight=bold', + 0: 'STIXGeneral', + 1: 'STIXSizeOneSym', + 2: 'STIXSizeTwoSym', + 3: 'STIXSizeThreeSym', + 4: 'STIXSizeFourSym', + 5: 'STIXSizeFiveSym', + } + _fallback_font = None + _sans = False + + def __init__(self, default_font_prop: FontProperties, load_glyph_flags: int): + TruetypeFonts.__init__(self, default_font_prop, load_glyph_flags) + for key, name in self._fontmap.items(): + fullpath = findfont(name) + self.fontmap[key] = fullpath + self.fontmap[name] = fullpath + + def _map_virtual_font(self, fontname: str, font_class: str, + uniindex: int) -> tuple[str, int]: + # Handle these "fonts" that are actually embedded in + # other fonts. + font_mapping = stix_virtual_fonts.get(fontname) + if (self._sans and font_mapping is None + and fontname not in ('regular', 'default')): + font_mapping = stix_virtual_fonts['sf'] + doing_sans_conversion = True + else: + doing_sans_conversion = False + + if isinstance(font_mapping, dict): + try: + mapping = font_mapping[font_class] + except KeyError: + mapping = font_mapping['rm'] + elif isinstance(font_mapping, list): + mapping = font_mapping + else: + mapping = None + + if mapping is not None: + # 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', 'bfit') and 0xe000 <= uniindex <= 0xf8ff: + fontname = 'nonuni' + fontname + + return fontname, uniindex + + @functools.cache + def get_sized_alternatives_for_symbol( # type: ignore[override] + self, + fontname: str, + sym: str) -> list[tuple[str, str]] | list[tuple[int, str]]: + 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: T.ClassVar[float] = 0.05 + + # Percentage of x-height that sub/superscripts drop below the baseline + subdrop: T.ClassVar[float] = 0.4 + + # Percentage of x-height that superscripts are raised from the baseline + sup1: T.ClassVar[float] = 0.7 + + # Percentage of x-height that subscripts drop below the baseline + sub1: T.ClassVar[float] = 0.3 + + # Percentage of x-height that subscripts drop below the baseline when a + # superscript is present + sub2: T.ClassVar[float] = 0.5 + + # Percentage of x-height that sub/superscripts are offset relative to the + # nucleus edge for non-slanted nuclei + delta: T.ClassVar[float] = 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: T.ClassVar[float] = 0.2 + + # Percentage of x-height that superscripts and subscripts are offset for + # integrals + delta_integral: T.ClassVar[float] = 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: ParserState) -> type[FontConstantsBase]: + 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) -> None: + self.size = 0 + + def __repr__(self) -> str: + return type(self).__name__ + + def get_kerning(self, next: Node | None) -> float: + return 0.0 + + def shrink(self) -> None: + """ + 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: Output, x: float, y: float) -> None: + """Render this node.""" + + +class Box(Node): + """A node with a physical location.""" + + def __init__(self, width: float, height: float, depth: float) -> None: + super().__init__() + self.width = width + self.height = height + self.depth = depth + + def shrink(self) -> None: + super().shrink() + if self.size < NUM_SIZE_LEVELS: + self.width *= SHRINK_FACTOR + self.height *= SHRINK_FACTOR + self.depth *= SHRINK_FACTOR + + def render(self, output: Output, # type: ignore[override] + x1: float, y1: float, x2: float, y2: float) -> None: + pass + + +class Vbox(Box): + """A box with only height (zero width).""" + + def __init__(self, height: float, depth: float): + super().__init__(0., height, depth) + + +class Hbox(Box): + """A box with only width (zero height and depth).""" + + def __init__(self, width: float): + 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: str, state: ParserState): + 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) -> str: + return '`%s`' % self.c + + def _update_metrics(self) -> None: + 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) -> bool: + return self._metrics.slanted + + def get_kerning(self, next: Node | None) -> float: + """ + 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: Output, x: float, y: float) -> None: + self.fontset.render_glyph( + output, x, y, + self.font, self.font_class, self.c, self.fontsize, self.dpi) + + def shrink(self) -> None: + 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) -> None: + 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) -> None: + super().shrink() + self._update_metrics() + + def render(self, output: Output, x: float, y: float) -> None: + 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: T.Sequence[Node]): + 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) -> str: + return '{}[{}]'.format( + super().__repr__(), + self.width, self.height, + self.depth, self.shift_amount, + ', '.join([repr(x) for x in self.children])) + + def _set_glue(self, x: float, sign: int, totals: list[float], + error_type: str) -> None: + 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) -> None: + 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: T.Sequence[Node], w: float = 0.0, + m: T.Literal['additional', 'exactly'] = 'additional', + do_kern: bool = True): + super().__init__(elements) + if do_kern: + self.kern() + self.hpack(w=w, m=m) + + def kern(self) -> None: + """ + 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 + + def hpack(self, w: float = 0.0, + m: T.Literal['additional', 'exactly'] = 'additional') -> None: + 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: T.Sequence[Node], h: float = 0.0, + m: T.Literal['additional', 'exactly'] = 'additional'): + super().__init__(elements) + self.vpack(h=h, m=m) + + def vpack(self, h: float = 0.0, + m: T.Literal['additional', 'exactly'] = 'additional', + l: float = np.inf) -> None: + """ + 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: float, height: float, depth: float, state: ParserState): + super().__init__(width, height, depth) + self.fontset = state.fontset + + def render(self, output: Output, # type: ignore[override] + x: float, y: float, w: float, h: float) -> None: + 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: ParserState, thickness: float | None = 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: ParserState): + thickness = state.get_current_underline_thickness() + super().__init__(thickness, np.inf, np.inf, state) + + +class _GlueSpec(NamedTuple): + width: float + stretch: float + stretch_order: int + shrink: float + shrink_order: int + + +_GlueSpec._named = { # type: ignore[attr-defined] + '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: _GlueSpec | T.Literal["fil", "fill", "filll", + "neg_fil", "neg_fill", "neg_filll", + "empty", "ss"]): + super().__init__() + if isinstance(glue_type, str): + glue_spec = _GlueSpec._named[glue_type] # type: ignore[attr-defined] + 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) -> None: + 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: list[Node]): + 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: list[Node]): + 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: float): + super().__init__() + self.width = width + + def __repr__(self) -> str: + return "k%.02f" % self.width + + def shrink(self) -> None: + 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: str, height: float, depth: float, state: ParserState, + always: bool = False, factor: float | None = 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 = 0.0 + 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: str, width: float, state: ParserState, always: bool = False, + char_class: type[Char] = 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: Box, xy: tuple[float, float] = (0, 0)) -> Output: + """ + 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: float) -> float: + return -1e9 if value < -1e9 else +1e9 if value > +1e9 else value + + def hlist_out(box: Hlist) -> None: + 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) + elif isinstance(p, Vlist): + # p.vpack(box.height + box.depth, 'exactly') + vlist_out(p) + else: + assert False, "unreachable code" + 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: Vlist) -> None: + 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) + elif isinstance(p, Vlist): + vlist_out(p) + else: + assert False, "unreachable code" + 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") + + assert isinstance(box, Hlist) + hlist_out(box) + return output + + +############################################################################## +# PARSER + + +def Error(msg: str) -> ParserElement: + """Helper class to raise parser errors.""" + def raise_error(s: str, loc: int, toks: ParseResults) -> T.Any: + 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: Fonts, font: str, font_class: str, fontsize: float, + dpi: float): + self.fontset = fontset + self._font = font + self.font_class = font_class + self.fontsize = fontsize + self.dpi = dpi + + def copy(self) -> ParserState: + return copy.copy(self) + + @property + def font(self) -> str: + return self._font + + @font.setter + def font(self, name: str) -> None: + if name in ('rm', 'it', 'bf', 'bfit'): + self.font_class = name + self._font = name + + def get_current_underline_thickness(self) -> float: + """Return the underline thickness for this state.""" + return self.fontset.get_underline_thickness( + self.font, self.fontsize, self.dpi) + + +def cmd(expr: str, args: ParserElement) -> ParserElement: + 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: ParserElement) -> T.Generator[str, None, None]: + 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 \Cap + \Cup \barwedge \boxdot + \boxminus \boxplus \boxtimes + \curlyvee \curlywedge \divideontimes + \doublebarwedge \leftthreetimes \rightthreetimes + \slash \veebar \barvee + \cupdot \intercal \amalg + \circledcirc \circleddash \circledast + \boxbar \obar \merge + \minuscolon \dotsminusdots + '''.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 \leqq + \geqq \lneqq \gneqq \lessgtr + \leqslant \geqslant \eqgtr \eqless + \eqslantless \eqslantgtr \lesseqgtr \backsim + \backsimeq \lesssim \gtrsim \precsim + \precnsim \gnsim \lnsim \succsim + \succnsim \nsim \lesseqqgtr \gtreqqless + \gtreqless \subseteqq \supseteqq \subsetneqq + \supsetneqq \lessapprox \approxeq \gtrapprox + \precapprox \succapprox \precnapprox \succnapprox + \npreccurlyeq \nsucccurlyeq \nsqsubseteq \nsqsupseteq + \sqsubsetneq \sqsupsetneq \nlesssim \ngtrsim + \nlessgtr \ngtrless \lnapprox \gnapprox + \napprox \approxeq \approxident \lll + \ggg \nparallel \Vdash \Vvdash + \nVdash \nvdash \vDash \nvDash + \nVDash \oequal \simneqq \triangle + \triangleq \triangleeq \triangleleft + \triangleright \ntriangleleft \ntriangleright + \trianglelefteq \ntrianglelefteq \trianglerighteq + \ntrianglerighteq \blacktriangleleft \blacktriangleright + \equalparallel \measuredrightangle \varlrtriangle + \Doteq \Bumpeq \Subset \Supset + \backepsilon \because \therefore \bot + \top \bumpeq \circeq \coloneq + \curlyeqprec \curlyeqsucc \eqcirc \eqcolon + \eqsim \fallingdotseq \gtrdot \gtrless + \ltimes \rtimes \lessdot \ne + \ncong \nequiv \ngeq \ngtr + \nleq \nless \nmid \notin + \nprec \nsubset \nsubseteq \nsucc + \nsupset \nsupseteq \pitchfork \preccurlyeq + \risingdotseq \subsetneq \succcurlyeq \supsetneq + \varpropto \vartriangleleft \scurel + \vartriangleright \rightangle \equal \backcong + \eqdef \wedgeq \questeq \between + \veeeq \disin \varisins \isins + \isindot \varisinobar \isinobar \isinvb + \isinE \nisd \varnis \nis + \varniobar \niobar \bagmember \ratio + \Equiv \stareq \measeq \arceq + \rightassert \rightModels \smallin \smallowns + \notsmallowns \nsimeq'''.split()) + + _arrow_symbols = set(r""" + \leftarrow \longleftarrow \uparrow \Leftarrow \Longleftarrow + \Uparrow \rightarrow \longrightarrow \downarrow \Rightarrow + \Longrightarrow \Downarrow \leftrightarrow \updownarrow + \longleftrightarrow \updownarrow \Leftrightarrow + \Longleftrightarrow \Updownarrow \mapsto \longmapsto \nearrow + \hookleftarrow \hookrightarrow \searrow \leftharpoonup + \rightharpoonup \swarrow \leftharpoondown \rightharpoondown + \nwarrow \rightleftharpoons \leadsto \dashrightarrow + \dashleftarrow \leftleftarrows \leftrightarrows \Lleftarrow + \Rrightarrow \twoheadleftarrow \leftarrowtail \looparrowleft + \leftrightharpoons \curvearrowleft \circlearrowleft \Lsh + \upuparrows \upharpoonleft \downharpoonleft \multimap + \leftrightsquigarrow \rightrightarrows \rightleftarrows + \rightrightarrows \rightleftarrows \twoheadrightarrow + \rightarrowtail \looparrowright \rightleftharpoons + \curvearrowright \circlearrowright \Rsh \downdownarrows + \upharpoonright \downharpoonright \rightsquigarrow \nleftarrow + \nrightarrow \nLeftarrow \nRightarrow \nleftrightarrow + \nLeftrightarrow \to \Swarrow \Searrow \Nwarrow \Nearrow + \leftsquigarrow \overleftarrow \overleftrightarrow \cwopencirclearrow + \downzigzagarrow \cupleftarrow \rightzigzagarrow \twoheaddownarrow + \updownarrowbar \twoheaduparrow \rightarrowbar \updownarrows + \barleftarrow \mapsfrom \mapsdown \mapsup \Ldsh \Rdsh + """.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 \iint \oiint \iiint \oiiint \iiiint'.split()) + + _fontnames = set("rm cal it tt sf bf bfit " + "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 \lbrace \leftbrace \lbrack \leftparen \lgroup + """.split()) + _right_delims = set(r""" + ) ] \} > \rfloor \rangle \rceil \rbrace \rightbrace \rbrack \rightparen \rgroup + """.split()) + _delims = _left_delims | _right_delims | _ambi_delims + + _small_greek = set([unicodedata.name(chr(i)).split()[-1].lower() for i in + range(ord('\N{GREEK SMALL LETTER ALPHA}'), + ord('\N{GREEK SMALL LETTER OMEGA}') + 1)]) + _latin_alphabets = set(string.ascii_letters) + + def __init__(self) -> None: + p = types.SimpleNamespace() + + def set_names_and_parse_actions() -> None: + for key, val in vars(p).items(): + if not key.startswith('_'): + # Set names on (almost) everything -- very useful for debugging + # token, placeable, and auto_delim are forward references which + # are left without names to ensure useful error messages + if key not in ("token", "placeable", "auto_delim"): + 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: str, names: Iterable[str]) -> Regex: + 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<{group}>(?:{alpha})(?![A-Za-z]){additional}{nonalpha})".format( + group=group, + alpha="|".join(map(re.escape, ends_with_alpha)), + additional="|" if ends_with_nonalpha else "", + nonalpha="|".join(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) + + # Mutually recursive definitions. (Minimizing the number of Forward + # elements is important for speed.) + p.auto_delim = Forward() + p.placeable = Forward() + p.named_placeable = Forward() + p.required_group = Forward() + p.optional_group = Forward() + p.token = Forward() + + # Workaround for placable being part of a cycle of definitions + # calling `p.placeable("name")` results in a copy, so not guaranteed + # to get the definition added after it is used. + # ref https://github.com/matplotlib/matplotlib/issues/25204 + # xref https://github.com/pyparsing/pyparsing/issues/95 + p.named_placeable <<= p.placeable + + set_names_and_parse_actions() # for mutually recursive definitions. + + p.optional_group <<= "{" + ZeroOrMore(p.token)("group") + "}" + p.required_group <<= "{" + OneOrMore(p.token)("group") + "}" + + p.customspace = cmd(r"\hspace", "{" + p.float_literal("space") + "}") + + p.accent = ( + csnames("accent", [*self._accent_map, *self._wide_accents]) + - p.named_placeable("sym")) + + p.function = csnames("name", self._function_names) + + p.group = p.start_group + ZeroOrMore(p.token)("group") + p.end_group + p.unclosed_group = (p.start_group + ZeroOrMore(p.token)("group") + StringEnd()) + + 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.text = cmd(r"\text", QuotedString('{', '\\', endQuoteChar="}")) + + p.substack = cmd(r"\substack", + nested_expr(opener="{", closer="}", + content=Group(OneOrMore(p.token)) + + ZeroOrMore(Literal("\\\\").suppress()))("parts")) + + p.subsuper = ( + (Optional(p.placeable)("nucleus") + + OneOrMore(oneOf(["_", "^"]) - p.placeable)("subsuper") + + Regex("'*")("apostrophes")) + | Regex("'+")("apostrophes") + | (p.named_placeable("nucleus") + Regex("'*")("apostrophes")) + ) + + p.simple = p.space | p.customspace | p.font | p.subsuper + + p.token <<= ( + p.simple + | p.auto_delim + | p.unclosed_group + | p.unknown_symbol # Must be last + ) + + p.operatorname = cmd(r"\operatorname", "{" + ZeroOrMore(p.simple)("name") + "}") + + p.boldsymbol = cmd( + r"\boldsymbol", "{" + ZeroOrMore(p.simple)("value") + "}") + + 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.text + | p.boldsymbol + | p.substack + ) + + mdelim = r"\middle" - (p.delim("mdelim") | Error("Expected a delimiter")) + p.auto_delim <<= ( + r"\left" - (p.delim("left") | Error("Expected a delimiter")) + + ZeroOrMore(p.simple | p.auto_delim | mdelim)("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: str, fonts_object: Fonts, fontsize: float, dpi: float) -> Hlist: + """ + 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: dict[tuple[str, float, float], float] = {} + 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 = [] + self._in_subscript_or_superscript = False + # prevent operator spacing from leaking into a new expression + self._em_width_cache = {} + ParserElement.resetCache() + return T.cast(Hlist, result[0]) # Known return type from main. + + def get_state(self) -> ParserState: + """Get the current `State` of the parser.""" + return self._state_stack[-1] + + def pop_state(self) -> None: + """Pop a `State` off of the stack.""" + self._state_stack.pop() + + def push_state(self) -> None: + """Push a new `State` onto the stack, copying the current state.""" + self._state_stack.append(self.get_state().copy()) + + def main(self, toks: ParseResults) -> list[Hlist]: + return [Hlist(toks.asList())] + + def math_string(self, toks: ParseResults) -> ParseResults: + return self._math_expression.parseString(toks[0][1:-1], parseAll=True) + + def math(self, toks: ParseResults) -> T.Any: + hlist = Hlist(toks.asList()) + self.pop_state() + return [hlist] + + def non_math(self, toks: ParseResults) -> T.Any: + 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 text(self, toks: ParseResults) -> T.Any: + self.push_state() + state = self.get_state() + state.font = 'rm' + hlist = Hlist([Char(c, state) for c in toks[1]]) + self.pop_state() + return [hlist] + + def _make_space(self, percentage: float) -> Kern: + # 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, toks: ParseResults) -> T.Any: + num = self._space_widths[toks["space"]] + box = self._make_space(num) + return [box] + + def customspace(self, toks: ParseResults) -> T.Any: + return [self._make_space(toks["space"])] + + def symbol(self, s: str, loc: int, + toks: ParseResults | dict[str, str]) -> T.Any: + 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 + # Also, operators in sub- or superscripts should not be spaced + if (self._in_subscript_or_superscript or ( + 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: str, loc: int, toks: ParseResults) -> T.Any: + 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, toks: ParseResults) -> T.Any: + state = self.get_state() + thickness = state.get_current_underline_thickness() + accent = toks["accent"] + sym = toks["sym"] + accent_box: Node + 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: str, loc: int, toks: ParseResults) -> T.Any: + hlist = self.operatorname(s, loc, toks) + hlist.function_name = toks["name"] + return hlist + + def operatorname(self, s: str, loc: int, toks: ParseResults) -> T.Any: + self.push_state() + state = self.get_state() + state.font = 'rm' + hlist_list: list[Node] = [] + # 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, toks: ParseResults) -> T.Any: + self.push_state() + # Deal with LaTeX-style font tokens + if toks.get("font"): + self.get_state().font = toks.get("font") + return [] + + def group(self, toks: ParseResults) -> T.Any: + grp = Hlist(toks.get("group", [])) + return [grp] + + def required_group(self, toks: ParseResults) -> T.Any: + return Hlist(toks.get("group", [])) + + optional_group = required_group + + def end_group(self) -> T.Any: + self.pop_state() + return [] + + def unclosed_group(self, s: str, loc: int, toks: ParseResults) -> T.Any: + raise ParseFatalException(s, len(s), "Expected '}'") + + def font(self, toks: ParseResults) -> T.Any: + self.get_state().font = toks["font"] + return [] + + def is_overunder(self, nucleus: Node) -> bool: + 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: Node) -> bool: + if isinstance(nucleus, Char): + return nucleus.c in self._dropsub_symbols + return False + + def is_slanted(self, nucleus: Node) -> bool: + if isinstance(nucleus, Char): + return nucleus.is_slanted() + return False + + def subsuper(self, s: str, loc: int, toks: ParseResults) -> T.Any: + 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 + vlt = Vlist(vlist) + vlt.shift_amount = shift + result = Hlist([vlt]) + 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 + + x: List + if super is None: + # node757 + # Note: One of super or sub must be a Node if we're in this function, but + # mypy can't know this, since it can't interpret pyparsing expressions, + # hence the cast. + x = Hlist([Kern(subkern), T.cast(Node, 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: str, rdelim: str, rule: float | None, style: _MathStyle, + num: Hlist, den: Hlist) -> T.Any: + 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, + T.cast(list[T.Union[Box, Char, str]], + result), + rdelim) + return result + + def style_literal(self, toks: ParseResults) -> T.Any: + return self._MathStyle(int(toks["style_literal"])) + + def genfrac(self, toks: ParseResults) -> T.Any: + return self._genfrac( + toks.get("ldelim", ""), toks.get("rdelim", ""), + toks["rulesize"], toks.get("style", self._MathStyle.TEXTSTYLE), + toks["num"], toks["den"]) + + def frac(self, toks: ParseResults) -> T.Any: + return self._genfrac( + "", "", self.get_state().get_current_underline_thickness(), + self._MathStyle.TEXTSTYLE, toks["num"], toks["den"]) + + def dfrac(self, toks: ParseResults) -> T.Any: + return self._genfrac( + "", "", self.get_state().get_current_underline_thickness(), + self._MathStyle.DISPLAYSTYLE, toks["num"], toks["den"]) + + def binom(self, toks: ParseResults) -> T.Any: + return self._genfrac( + "(", ")", 0, + self._MathStyle.TEXTSTYLE, toks["num"], toks["den"]) + + def _genset(self, s: str, loc: int, toks: ParseResults) -> T.Any: + annotation = toks["annotation"] + body = toks["body"] + thickness = self.get_state().get_current_underline_thickness() + + annotation.shrink() + centered_annotation = HCentered([annotation]) + centered_body = HCentered([body]) + width = max(centered_annotation.width, centered_body.width) + centered_annotation.hpack(width, 'exactly') + centered_body.hpack(width, 'exactly') + + vgap = thickness * 3 + if s[loc + 1] == "u": # \underset + vlist = Vlist([ + centered_body, # body + Vbox(0, vgap), # space + centered_annotation # annotation + ]) + # Shift so the body sits in the same vertical position + vlist.shift_amount = centered_body.depth + centered_annotation.height + vgap + else: # \overset + vlist = Vlist([ + centered_annotation, # annotation + Vbox(0, vgap), # space + centered_body # 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, toks: ParseResults) -> T.Any: + 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, toks: ParseResults) -> T.Any: + 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: str, + middle: list[Box | Char | str], + back: str) -> T.Any: + state = self.get_state() + if len(middle): + height = max([x.height for x in middle if not isinstance(x, str)]) + depth = max([x.depth for x in middle if not isinstance(x, str)]) + factor = None + for idx, el in enumerate(middle): + if el == r'\middle': + c = T.cast(str, middle[idx + 1]) # Should be one of p.delims. + if c != '.': + middle[idx + 1] = AutoHeightChar( + c, height, depth, state, factor=factor) + else: + middle.remove(c) + del middle[idx] + # There should only be \middle and its delimiter as str, which have + # just been removed. + middle_part = T.cast(list[T.Union[Box, Char]], middle) + else: + height = 0 + depth = 0 + factor = 1.0 + middle_part = [] + + parts: list[Node] = [] + # \left. and \right. aren't supposed to produce any symbols + if front != '.': + parts.append( + AutoHeightChar(front, height, depth, state, factor=factor)) + parts.extend(middle_part) + if back != '.': + parts.append( + AutoHeightChar(back, height, depth, state, factor=factor)) + hlist = Hlist(parts) + return hlist + + def auto_delim(self, toks: ParseResults) -> T.Any: + 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"]) + + def boldsymbol(self, toks: ParseResults) -> T.Any: + self.push_state() + state = self.get_state() + hlist: list[Node] = [] + name = toks["value"] + for c in name: + if isinstance(c, Hlist): + k = c.children[1] + if isinstance(k, Char): + k.font = "bf" + k._update_metrics() + hlist.append(c) + elif isinstance(c, Char): + c.font = "bf" + if (c.c in self._latin_alphabets or + c.c[1:] in self._small_greek): + c.font = "bfit" + c._update_metrics() + c._update_metrics() + hlist.append(c) + else: + hlist.append(c) + self.pop_state() + + return Hlist(hlist) + + def substack(self, toks: ParseResults) -> T.Any: + parts = toks["parts"] + state = self.get_state() + thickness = state.get_current_underline_thickness() + + hlist = [Hlist(k) for k in parts[0]] + max_width = max(map(lambda c: c.width, hlist)) + + vlist = [] + for sub in hlist: + cp = HCentered([sub]) + cp.hpack(max_width, 'exactly') + vlist.append(cp) + + stack = [val + for pair in zip(vlist, [Vbox(0, thickness * 2)] * len(vlist)) + for val in pair] + del stack[-1] + vlt = Vlist(stack) + result = [Hlist([vlt])] + return result