""" Implementation details for :mod:`.mathtext`. """ from __future__ import annotations import abc import copy import enum import functools import itertools import logging import math import os import re import types import unicodedata import string import textwrap import typing as T from typing import NamedTuple import numpy as np from numpy.typing import NDArray from pyparsing import ( Empty, Forward, Literal, Group, NotAny, OneOrMore, Optional, ParseBaseException, ParseExpression, ParseFatalException, ParserElement, ParseResults, QuotedString, Regex, StringEnd, ZeroOrMore, pyparsing_common, nested_expr, one_of) 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, Kerning, LoadFlags if T.TYPE_CHECKING: from collections.abc import Iterable from .ft2font import CharacterCodeType, Glyph, GlyphIndexType ParserElement.enable_packrat() _log = logging.getLogger("matplotlib.mathtext") ############################################################################## # FONTS def get_unicode_index(symbol: str) -> CharacterCodeType: # 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, CharacterCodeType, GlyphIndexType, 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 : 2D array of uint8 A raster image. """ ox: float oy: float width: float height: float depth: float image: NDArray[np.uint8] 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]] = [] # (x, y, w, h) 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, info.glyph_index, ox, h - oy + info.offset) for ox, oy, info in self.glyphs] rs = [(bx, h - (by + bh), bw, bh) for bx, by, bw, bh in self.rects] # Output.rects has downwards ys, VectorParse.rects has upwards ys. 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], *[x for x, y, w, h in self.rects], 0]) - 1 ymin = min([*[oy - info.metrics.ymax for ox, oy, info in self.glyphs], *[y for x, y, w, h in self.rects], 0]) - 1 xmax = max([*[ox + info.metrics.xmax for ox, oy, info in self.glyphs], *[x + w for x, y, w, h in self.rects], 0]) + 1 ymax = max([*[oy - info.metrics.ymin for ox, oy, info in self.glyphs], *[y + h for x, y, w, h in self.rects], 0]) + 1 w = xmax - xmin h = ymax - ymin - self.box.depth d = ymax - ymin - self.box.height image = np.zeros((math.ceil(h + max(d, 0)), math.ceil(w)), np.uint8) # 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, int(ox), int(oy - info.metrics.iceberg), info.glyph, antialiased=antialiased) for x, y, bw, bh in shifted.rects: height = max(int(bh) - 1, 0) if height == 0: center = y + bh / 2 y = int(center - (height + 1) / 2) else: y = int(y) x1 = math.floor(x) x2 = math.ceil(x + bw) image[y:y+height+1, x1:x2+1] = 0xff 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: CharacterCodeType glyph_index: GlyphIndexType 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: LoadFlags): """ Parameters ---------- default_font_prop : `~.font_manager.FontProperties` The default non-math font, or the base font for Unicode (generic) font rendering. load_glyph_flags : `.ft2font.LoadFlags` 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", "normal", "bb", "frak", "scr". "default" and "regular" are synonyms and use the non-math font. "normal" denotes the normal 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, x: float, y: float, w: float, h: float) -> None: """ Draw a filled rectangle at (*x*, *y*) with size (*w*, *h*). """ output.rects.append((x, y, w, h)) def get_axis_height(self, font: str, fontsize: float, dpi: float) -> float: """ Get the axis height for the given *font* and *fontsize*. """ raise NotImplementedError() def get_quad(self, font: str, fontsize: float, dpi: float) -> float: """ Get the size of a quad for the given *font* and *fontsize*. """ raise NotImplementedError() 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)] def get_font_constants(self) -> type[FontConstantsBase]: return FontConstantsBase 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: LoadFlags): 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, 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) -> FT2Font: basename = self.fontmap.get(font, 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, CharacterCodeType, 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_index = font.get_char_index(num) glyph = font.load_glyph(glyph_index, flags=self.load_glyph_flags) xmin, ymin, xmax, ymax = (val / 64 for val in glyph.bbox) offset = self._get_offset(font, glyph, fontsize, dpi) metrics = FontMetrics( advance=glyph.linearHoriAdvance / 65536, height=glyph.height / 64, width=glyph.width / 64, xmin=xmin, xmax=xmax, ymin=ymin + offset, ymax=ymax + offset, # iceberg is the equivalent of TeX's "height" iceberg=glyph.horiBearingY / 64 + offset, slanted=slanted ) return FontInfo( font=font, fontsize=fontsize, postscript_name=font.postscript_name, metrics=metrics, num=num, glyph_index=glyph_index, glyph=glyph, offset=offset ) def get_axis_height(self, fontname: str, fontsize: float, dpi: float) -> float: consts = self.get_font_constants() if consts.axis_height is not None: return consts.axis_height * fontsize * dpi / 72 else: # The fraction line (if present) must be aligned with the minus sign. # Therefore, the height of the latter from the baseline is the axis height. metrics = self.get_metrics( fontname, mpl.rcParams['mathtext.default'], '\u2212', fontsize, dpi) return (metrics.ymax + metrics.ymin) / 2 def get_quad(self, fontname: str, fontsize: float, dpi: float) -> float: consts = self.get_font_constants() if consts.quad is not None: return consts.quad * fontsize * dpi / 72 else: # With no other option, we measure the size of an 'm'. metrics = self.get_metrics( fontname, mpl.rcParams['mathtext.default'], 'm', fontsize, dpi) return metrics.advance def get_xheight(self, fontname: str, fontsize: float, dpi: float) -> float: consts = self.get_font_constants() if consts.x_height is not None: return consts.x_height * fontsize * dpi / 72 else: # Some fonts report the wrong x-height, while some don't store it, so # we do a poor man's x-height. metrics = self.get_metrics( fontname, mpl.rcParams['mathtext.default'], 'x', fontsize, dpi) return metrics.iceberg 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) * fontsize * dpi) / 72 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.glyph_index, info2.glyph_index, 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 = { 'normal': 'cmmi10', 'cal': 'cmsy10', 'rm': 'cmr10', 'tt': 'cmtt10', 'it': 'cmti10', 'bf': 'cmb10', 'sf': 'cmss10', 'ex': 'cmex10', } def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlags): 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, CharacterCodeType, bool]: font = None if fontname in self.fontmap and sym in latex_to_bakoma: basename, num = latex_to_bakoma[sym] slanted = (basename in ("cmmi10", "cmti10")) or sym in self._slanted_symbols font = self._get_font(basename) elif len(sym) == 1: slanted = (fontname in ("it", "normal")) if fontname == "normal" and sym.isdigit(): # use digits from cmr (roman alphabet) instead of cmm (math alphabet), # same as LaTeX does. fontname = "rm" slanted = False 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 # Auto(Height|Width)Char classes will use these alternatives and select the best # (closest sized) glyph. _latex_sizes = ('big', 'Big', 'bigg', 'Bigg') _size_alternatives = { '(': [('rm', '('), *[('ex', fr'\__parenleft{s}__') for s in _latex_sizes]], ')': [('rm', ')'), *[('ex', fr'\__parenright{s}__') for s in _latex_sizes]], '{': [('ex', fr'\__braceleft{s}__') for s in _latex_sizes], '}': [('ex', fr'\__braceright{s}__') for s in _latex_sizes], '[': [('rm', '['), *[('ex', fr'\__bracketleft{s}__') for s in _latex_sizes]], ']': [('rm', ']'), *[('ex', fr'\__bracketright{s}__') for s in _latex_sizes]], '<': [('cal', r'\__angbracketleft__'), *[('ex', fr'\__angbracketleft{s}__') for s in _latex_sizes]], '>': [('cal', r'\__angbracketright__'), *[('ex', fr'\__angbracketright{s}__') for s in _latex_sizes]], r'\lfloor': [('ex', fr'\__floorleft{s}__') for s in _latex_sizes], r'\rfloor': [('ex', fr'\__floorright{s}__') for s in _latex_sizes], r'\lceil': [('ex', fr'\__ceilingleft{s}__') for s in _latex_sizes], r'\rceil': [('ex', fr'\__ceilingright{s}__') for s in _latex_sizes], r'\__sqrt__': [('ex', fr'\__radical{s}__') for s in _latex_sizes], r'\backslash': [('ex', fr'\__backslash{s}__') for s in _latex_sizes], r'/': [('rm', '/'), *[('ex', fr'\__slash{s}__') for s in _latex_sizes]], r'\widehat': [('rm', '\x5e'), ('ex', r'\__hatwide__'), ('ex', r'\__hatwider__'), ('ex', r'\__hatwidest__')], r'\widetilde': [('rm', '\x7e'), ('ex', r'\__tildewide__'), ('ex', r'\__tildewider__'), ('ex', r'\__tildewidest__')], } for alias, target in [(r'\leftparen', '('), (r'\rightparen', ')'), (r'\leftbrace', '{'), (r'\rightbrace', '}'), (r'\leftbracket', '['), (r'\rightbracket', ']'), (r'\langle', '<'), (r'\rangle', '>'), (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)]) def get_font_constants(self) -> type[FontConstantsBase]: return ComputerModernFontConstants 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: dict[CharacterCodeType, CharacterCodeType] = { 0x00D7: 0x00A3, # Multiplication sign. 0x2212: 0x00A1, # Minus sign. } def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlags): # 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] # type: ignore[index] 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: CharacterCodeType) -> tuple[str, CharacterCodeType]: return fontname, uniindex def _get_glyph(self, fontname: str, font_class: str, sym: str) -> tuple[FT2Font, CharacterCodeType, 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 == 'normal' and uniindex < 0x10000: # normal mathematics font char = chr(uniindex) if (unicodedata.category(char)[0] != "L" or unicodedata.name(char).startswith("GREEK CAPITAL")): new_fontname = 'rm' else: new_fontname = 'it' 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', 'normal') 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 BakomaFonts._fontmap.values(): family = "Computer Modern" _log.info("Substituting symbol %s from %s", sym, family) return g else: if (fontname in ('it', 'regular', 'normal') 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, str] = {} def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlags): # 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, CharacterCodeType, 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', } def get_font_constants(self) -> type[FontConstantsBase]: return DejaVuSerifFontConstants 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', } def get_font_constants(self) -> type[FontConstantsBase]: return DejaVuSansFontConstants 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', '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: LoadFlags): 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: CharacterCodeType) -> tuple[str, CharacterCodeType]: # 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', 'normal'): 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(self, fontname: str, sym: str) -> list[tuple[str, 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 = [(str(i), chr(uniindex)) for i in range(6) if self._get_font(str(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 def get_font_constants(self) -> type[FontConstantsBase]: if self._sans: return STIXSansFontConstants else: return STIXFontConstants 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 superscripts drop below the top of large box supdrop: T.ClassVar[float] = 0.4 # Percentage of x-height that subscripts drop below the bottom of large box 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 # Percentage of x-height the numerator is shifted up in display style. num1: T.ClassVar[float] = 1.4 # Percentage of x-height the numerator is shifted up in text, script and # scriptscript styles if there is a fraction line. num2: T.ClassVar[float] = 1.5 # Percentage of x-height the numerator is shifted up in text, script and # scriptscript styles if there is no fraction line. num3: T.ClassVar[float] = 1.3 # Percentage of x-height the denominator is shifted down in display style. denom1: T.ClassVar[float] = 1.3 # Percentage of x-height the denominator is shifted down in text, script # and scriptscript styles. denom2: T.ClassVar[float] = 1.1 # The height of a horizontal reference line used for positioning elements in a # formula, similar to a baseline, as a multiple of design size. axis_height: T.ClassVar[float | None] = None # The size of a quad space in LaTeX, as a multiple of design size. quad: T.ClassVar[float | None] = None # The size of x-height in font design units (i.e., divided by units-per-em). If not # provided, then this will be measured from the font itself. x_height: T.ClassVar[float | None] = None class ComputerModernFontConstants(FontConstantsBase): # Previously, the x-height of Computer Modern was obtained from the font # table. However, that x-height was greater than the the actual (rendered) # x-height by a factor of 1.771484375 (at font size 12, DPI 100 and hinting # type 32). Now that we're using the rendered x-height, some font constants # have been increased by the same factor to compensate. script_space = 0.132861328125 delta = 0.132861328125 delta_slanted = 0.3 delta_integral = 0.3 _x_height = 451470 # These all come from the cmsy10.tfm metrics, divided by the design xheight from # there, since we multiply these values by the scaled xheight later. supdrop = 404864 / _x_height subdrop = 52429 / _x_height sup1 = 432949 / _x_height sub1 = 157286 / _x_height sub2 = 259226 / _x_height num1 = 709370 / _x_height num2 = 412858 / _x_height num3 = 465286 / _x_height denom1 = 719272 / _x_height denom2 = 361592 / _x_height # These come from the cmsy10.tfm metrics, scaled so they are in multiples of design # size. axis_height = 262144 / 2**20 quad = 1048579 / 2**20 x_height = _x_height / 2**20 class STIXFontConstants(FontConstantsBase): script_space = 0.1 delta = 0.05 delta_slanted = 0.3 delta_integral = 0.3 _x_height = 450 x_height = _x_height / 1000 # These values are extracted from the TeX table of STIXGeneral.ttf using FontForge, # and then divided by design xheight, since we multiply these values by the scaled # xheight later. supdrop = 386 / _x_height subdrop = 50.0002 / _x_height sup1 = 413 / _x_height sub1 = 150 / _x_height sub2 = 309 / _x_height num1 = 747 / _x_height num2 = 424 / _x_height num3 = 474 / _x_height denom1 = 756 / _x_height denom2 = 375 / _x_height # These come from the same TeX table, scaled by Em size so they are in multiples of # design size. axis_height = 250 / 1000 quad = 1000 / 1000 class STIXSansFontConstants(STIXFontConstants): script_space = 0.05 delta_slanted = 0.6 delta_integral = 0.3 class DejaVuSerifFontConstants(FontConstantsBase): _x_height = 1063 x_height = _x_height / 2048 # These values are extracted from the TeX table of DejaVuSerif.ttf using FontForge, # and then divided by design xheight, since we multiply these values by the scaled # xheight later. supdrop = 790.527 / _x_height subdrop = 102.4 / _x_height sup1 = 845.824 / _x_height sub1 = 307.199 / _x_height sub2 = 632.832 / _x_height num1 = 1529.86 / _x_height num2 = 868.352 / _x_height num3 = 970.752 / _x_height denom1 = 1548.29 / _x_height denom2 = 768 / _x_height # These come from the same TeX table, scaled by Em size so they are in multiples of # design size. axis_height = 512 / 2048 class DejaVuSansFontConstants(FontConstantsBase): _x_height = 1120 x_height = _x_height / 2048 # These values are extracted from the TeX table of DejaVuSans.ttf using FontForge, # and then divided by design xheight, since we multiply these values by the scaled # xheight later. supdrop = 790.527 / _x_height subdrop = 102.4 / _x_height sup1 = 845.824 / _x_height sub1 = 307.199 / _x_height sub2 = 632.832 / _x_height num1 = 1529.86 / _x_height num2 = 868.352 / _x_height num3 = 970.752 / _x_height denom1 = 1548.29 / _x_height denom2 = 768 / _x_height # These come from the same TeX table, scaled by Em size so they are in multiples of # design size. axis_height = 512 / 2048 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.""" def is_char_node(self) -> bool: # TeX defines a `char_node` as one which represents a single character, # but also states that a `char_node` will never appear in a `Vlist` # (node134). Further, nuclei made of one `Char` and nuclei made of # multiple `Char`s have their superscripts and subscripts shifted by # the same amount. In order to make Mathtext behave similarly, just # check whether this node is a `Vlist` or has any `Vlist` descendants. return True 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, "\n" + textwrap.indent( "\n".join(map("{!r},".format, self.children)), " ") + "\n" if self.children else "" ) 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) self.is_phantom = False def is_char_node(self) -> bool: # See description in Node.is_char_node. return all(map(lambda node: node.is_char_node(), self.children)) 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 = [] for elem0, elem1 in itertools.zip_longest(self.children, self.children[1:]): new_children.append(elem0) kerning_distance = elem0.get_kerning(elem1) 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 is_char_node(self) -> bool: # See description in Node.is_char_node. return False 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 - h, w, 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, factor: float | None = None): alternatives = state.fontset.get_sized_alternatives_for_symbol(state.font, c) x_height = 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 * x_height if char.height + char.depth >= target_total - 0.2 * x_height: 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, 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) phantom: list[bool] = [] def render(node, *args): if not any(phantom): node.render(*args) 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 cur_g = 0 cur_glue = 0. glue_order = box.glue_order glue_sign = box.glue_sign base_line = cur_v left_edge = cur_h phantom.append(box.is_phantom) for p in box.children: if isinstance(p, Char): render(p, 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 render(p, 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 phantom.pop() def vlist_out(box: Vlist) -> None: nonlocal cur_v, cur_h 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 render(p, 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().set_parse_action(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 ('normal', '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 normal".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.set_name(key) # Set actions if hasattr(self, key): val.set_parse_action(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 = one_of(self._space_widths)("space") p.style_literal = one_of( [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").leave_whitespace() p.unknown_symbol = Regex(r"\\[A-Za-z]+")("name") p.font = csnames("font", self._fontnames) p.start_group = Optional(r"\math" + one_of(self._fontnames)("font")) + "{" p.end_group = Literal("}") p.delim = one_of(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.phantom = cmd(r"\phantom", p.optional_group("value")) p.llap = cmd(r"\llap", p.optional_group("value")) p.rlap = cmd(r"\rlap", p.optional_group("value")) 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.underline = cmd(r"\underline", 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('{', '\\', end_quote_char="}")) 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(one_of(["_", "^"]) - 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.phantom | p.llap | p.rlap | 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.underline | p.text | p.boldsymbol | p.substack | p.auto_delim ) 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('$', '\\', unquote_results=False) p.non_math = Regex(r"(?:(?:\\[$])|[^$])*").leave_whitespace() p.main = ( p.non_math + ZeroOrMore(p.math_string + p.non_math) + StringEnd() ) set_names_and_parse_actions() # for leaf definitions. self._expression = p.main self._math_expression = p.math # To add space to nucleus operators after sub/superscripts self._needs_space_after_subsuper = False def parse(self, s: str, fonts_object: Fonts, fontsize: float, dpi: float) -> Hlist: """ Parse expression *s* using the given *fonts_object* for output, at the given *fontsize* and *dpi*. Returns the parse tree of `Node` instances. """ self._state_stack = [ ParserState(fonts_object, 'default', 'rm', fontsize, dpi)] self._em_width_cache: dict[tuple[str, float, float], float] = {} try: result = self._expression.parse_string(s) except ParseBaseException as err: raise ValueError("\n" + err.explain(0)) from None self._state_stack = [] self._needs_space_after_subsuper = False # prevent operator spacing from leaking into a new expression self._em_width_cache = {} ParserElement.reset_cache() return T.cast(Hlist, result[0]) # Known return type from main. def get_state(self) -> ParserState: """Get the current `State` of the parser.""" return self._state_stack[-1] def pop_state(self) -> None: """Pop a `State` off of the stack.""" self._state_stack.pop() def push_state(self) -> None: """Push a new `State` onto the stack, copying the current state.""" self._state_stack.append(self.get_state().copy()) def main(self, toks: ParseResults) -> list[Hlist]: return [Hlist(toks.as_list())] def math_string(self, toks: ParseResults) -> ParseResults: return self._math_expression.parse_string(toks[0][1:-1], parse_all=True) def math(self, toks: ParseResults) -> T.Any: hlist = Hlist(toks.as_list()) self.pop_state() return [hlist] def non_math(self, toks: ParseResults) -> T.Any: s = toks[0].replace(r'\$', '$') symbols = [Char(c, self.get_state()) for c in s] hlist = Hlist(symbols) # We're going into math now, so set font to 'normal' self.push_state() self.get_state().font = mpl.rcParams['mathtext.default'] return [hlist] float_literal = staticmethod(pyparsing_common.convert_to_float) 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 normal style so that horizontal spaces don't depend on the # current font style. # TODO: this should be read from the font file state = self.get_state() key = (state.font, state.fontsize, state.dpi) width = self._em_width_cache.get(key) if width is None: width = state.fontset.get_quad('normal', state.fontsize, state.dpi) 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 $=-2$, ${ -2}$, $ -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._needs_space_after_subsuper or ( c in self._binary_operators and ( len(s[:loc].split()) == 0 or prev_char in { '{', *self._left_delims, *self._relation_symbols}))): 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']}") def phantom(self, toks: ParseResults) -> T.Any: toks["value"].is_phantom = True return toks["value"] def llap(self, toks: ParseResults) -> T.Any: return [Hlist([Kern(-toks["value"].width), toks["value"]])] def rlap(self, toks: ParseResults) -> T.Any: return [Hlist([toks["value"], Kern(-toks["value"].width)])] _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) centered = HCentered([accent_box]) 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: # 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 sub/superscript, set flag to true to tell subsuper # to add space after this operator. self._needs_space_after_subsuper = next_char in {'^', '_'} 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) x_height = 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 optional_spacing = ([self._make_space(self._space_widths[r'\,'])] if self._needs_space_after_subsuper else []) self._needs_space_after_subsuper = False result = Hlist([vlt, *optional_spacing]) 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 isinstance(new_children[-2], Char)): new_children = new_children[:-1] last_char = new_children[-1] if isinstance(last_char, Char): 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 consts = state.fontset.get_font_constants() lc_height = last_char.height lc_baseline = 0.0 if self.is_dropsub(last_char): lc_baseline = last_char.depth # Compute kerning for sub and super superkern = consts.delta * x_height subkern = consts.delta * x_height if self.is_slanted(last_char): superkern += consts.delta * x_height superkern += consts.delta_slanted * (lc_height - x_height * 2 / 3) if self.is_dropsub(last_char): subkern = (3 * consts.delta - consts.delta_integral) * lc_height superkern = (3 * consts.delta + consts.delta_integral) * lc_height else: subkern = 0 # Set the minimum shifts for the superscript and subscript (node756). if nucleus.is_char_node(): shift_up = 0.0 shift_down = 0.0 else: shrunk_x_height = state.fontset.get_xheight( state.font, state.fontsize * SHRINK_FACTOR, state.dpi) shift_up = nucleus.height - consts.supdrop * shrunk_x_height shift_down = nucleus.depth + consts.subdrop * shrunk_x_height x: List if super is None: # Align subscript without superscript (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 + consts.subdrop * x_height else: shift_down = max(shift_down, consts.sub1 * x_height, x.height - x_height * 4 / 5) x.shift_amount = shift_down else: # Align superscript (node758). x = Hlist([Kern(superkern), super]) x.shrink() if self.is_dropsub(last_char): shift_up = lc_height - consts.subdrop * x_height else: shift_up = max(shift_up, consts.sup1 * x_height, x.depth + x_height / 4) if sub is None: x.shift_amount = -shift_up else: # Align subscript with superscript (node759). y = Hlist([Kern(subkern), sub]) y.shrink() if self.is_dropsub(last_char): shift_down = lc_baseline + consts.subdrop * x_height else: shift_down = max(shift_down, consts.sub2 * x_height) # If the subscript and superscript are too close to each other, # move the subscript down. clr = (4 * rule_thickness - ((shift_up - x.depth) - (y.height - shift_down))) if clr > 0.: shift_down += clr clr = x_height * 4 / 5 - shift_up + x.depth if clr > 0: shift_up += clr shift_down -= 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 += consts.script_space * x_height # Do we need to add a space after the nucleus? # To find out, check the flag set by operatorname optional_spacing = ([self._make_space(self._space_widths[r'\,'])] if self._needs_space_after_subsuper else []) self._needs_space_after_subsuper = False result = Hlist([nucleus, x, *optional_spacing]) 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() axis_height = state.fontset.get_axis_height( state.font, state.fontsize, state.dpi) consts = state.fontset.get_font_constants() x_height = state.fontset.get_xheight(state.font, state.fontsize, state.dpi) for _ in range(style.value): x_height *= SHRINK_FACTOR num.shrink() den.shrink() cnum = HCentered([num]) cden = HCentered([den]) width = max(num.width, den.width) cnum.hpack(width, 'exactly') cden.hpack(width, 'exactly') # Align the fraction with a fraction line (node743, node744 and node746). if rule: if style is self._MathStyle.DISPLAYSTYLE: num_shift_up = consts.num1 * x_height den_shift_down = consts.denom1 * x_height clr = 3 * rule # The minimum clearance. else: num_shift_up = consts.num2 * x_height den_shift_down = consts.denom2 * x_height clr = rule # The minimum clearance. delta = rule / 2 num_clr = max((num_shift_up - cnum.depth) - (axis_height + delta), clr) den_clr = max((axis_height - delta) - (cden.height - den_shift_down), clr) vlist = Vlist([cnum, # numerator Vbox(0, num_clr), # space Hrule(state, rule), # rule Vbox(0, den_clr), # space cden # denominator ]) vlist.shift_amount = cden.height + den_clr + delta - axis_height # Align the fraction without a fraction line (node743, node744 and node745). else: if style is self._MathStyle.DISPLAYSTYLE: num_shift_up = consts.num1 * x_height den_shift_down = consts.denom1 * x_height min_clr = 7 * thickness # The minimum clearance. else: num_shift_up = consts.num3 * x_height den_shift_down = consts.denom2 * x_height min_clr = 3 * thickness # The minimum clearance. def_clr = (num_shift_up - cnum.depth) - (cden.height - den_shift_down) clr = max(def_clr, min_clr) vlist = Vlist([cnum, # numerator Vbox(0, clr), # space cden # denominator ]) vlist.shift_amount = den_shift_down if def_clr < min_clr: vlist.shift_amount += (min_clr - def_clr) / 2 result: list[Box | Char | str] = [Hlist([ Hbox(thickness), vlist, Hbox(thickness) ])] if ldelim or rdelim: return self._auto_sized_delimiter(ldelim or ".", result, rdelim or ".") 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 + 5 * thickness depth = body.depth + body.shift_amount check = AutoHeightChar(r'\__sqrt__', height, depth, state) 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 * 12), '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(0.5 * check.width, 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 Kern(-0.5 * check.width), # Negative kerning to put root over tick 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 + 3 * thickness 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 * 12), 'exactly', depth) hlist = Hlist([rightside]) return [hlist] def underline(self, toks: ParseResults) -> T.Any: body = toks["body"] state = self.get_state() thickness = state.get_current_underline_thickness() # Place the underline below `body` (node735). vlist = Vlist([ Hlist([body]), Kern(3 * thickness), Hrule(state, thickness), ]) delta = vlist.height + vlist.depth + thickness vlist.height = body.height vlist.depth = delta - vlist.height return [Hlist([vlist])] 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[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"], toks["mid"].as_list(), 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