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Edit File: mathtext.py

r""" :mod:`~matplotlib.mathtext` is a module for parsing a subset of the TeX math syntax and drawing them to a matplotlib backend. For a tutorial of its usage see :doc:`/tutorials/text/mathtext`. This document is primarily concerned with implementation details. The module uses pyparsing_ to parse the TeX expression. .. _pyparsing: http://pyparsing.wikispaces.com/ The Bakoma distribution of the TeX Computer Modern fonts, and STIX fonts are supported. There is experimental support for using arbitrary fonts, but results may vary without proper tweaking and metrics for those fonts. """ from collections import namedtuple import functools from io import StringIO import logging import os import types import unicodedata import numpy as np from pyparsing import ( Combine, Empty, FollowedBy, Forward, Group, Literal, oneOf, OneOrMore, Optional, ParseBaseException, ParseFatalException, ParserElement, QuotedString, Regex, StringEnd, Suppress, ZeroOrMore) ParserElement.enablePackrat() from matplotlib import cbook, colors as mcolors, get_data_path, rcParams from matplotlib.afm import AFM from matplotlib.cbook import get_realpath_and_stat from matplotlib.ft2font import FT2Image, KERNING_DEFAULT, LOAD_NO_HINTING from matplotlib.font_manager import findfont, FontProperties, get_font from matplotlib._mathtext_data import (latex_to_bakoma, latex_to_standard, tex2uni, latex_to_cmex, stix_virtual_fonts) _log = logging.getLogger(__name__) ############################################################################## # FONTS def get_unicode_index(symbol, math=True): r""" Return the integer index (from the Unicode table) of *symbol*. Parameters ---------- symbol : str A single unicode character, a TeX command (e.g. r'\pi') or a Type1 symbol name (e.g. 'phi'). math : bool, default is True If False, always treat as a single unicode character. """ # for a non-math symbol, simply return its unicode index if not math: return ord(symbol) # From UTF #25: U+2212 minus sign is the preferred # representation of the unary and binary minus sign rather than # the ASCII-derived U+002D hyphen-minus, because minus sign is # unambiguous and because it is rendered with a more desirable # length, usually longer than a hyphen. if symbol == '-': return 0x2212 try: # This will succeed if symbol is a single unicode char return ord(symbol) except TypeError: pass try: # Is symbol a TeX symbol (i.e. \alpha) return tex2uni[symbol.strip("\\")] except KeyError: raise ValueError( "'{}' is not a valid Unicode character or TeX/Type1 symbol" .format(symbol)) unichr_safe = cbook.deprecated("3.0")(chr) class MathtextBackend(object): """ The base class for the mathtext backend-specific code. The purpose of :class:`MathtextBackend` subclasses is to interface between mathtext and a specific matplotlib graphics backend. Subclasses need to override the following: - :meth:`render_glyph` - :meth:`render_rect_filled` - :meth:`get_results` And optionally, if you need to use a FreeType hinting style: - :meth:`get_hinting_type` """ def __init__(self): self.width = 0 self.height = 0 self.depth = 0 def set_canvas_size(self, w, h, d): 'Dimension the drawing canvas' self.width = w self.height = h self.depth = d def render_glyph(self, ox, oy, info): """ Draw a glyph described by *info* to the reference point (*ox*, *oy*). """ raise NotImplementedError() def render_rect_filled(self, x1, y1, x2, y2): """ Draw a filled black rectangle from (*x1*, *y1*) to (*x2*, *y2*). """ raise NotImplementedError() def get_results(self, box): """ Return a backend-specific tuple to return to the backend after all processing is done. """ raise NotImplementedError() def get_hinting_type(self): """ Get the FreeType hinting type to use with this particular backend. """ return LOAD_NO_HINTING class MathtextBackendAgg(MathtextBackend): """ Render glyphs and rectangles to an FTImage buffer, which is later transferred to the Agg image by the Agg backend. """ def __init__(self): self.ox = 0 self.oy = 0 self.image = None self.mode = 'bbox' self.bbox = [0, 0, 0, 0] MathtextBackend.__init__(self) def _update_bbox(self, x1, y1, x2, y2): self.bbox = [min(self.bbox[0], x1), min(self.bbox[1], y1), max(self.bbox[2], x2), max(self.bbox[3], y2)] def set_canvas_size(self, w, h, d): MathtextBackend.set_canvas_size(self, w, h, d) if self.mode != 'bbox': self.image = FT2Image(np.ceil(w), np.ceil(h + max(d, 0))) def render_glyph(self, ox, oy, info): if self.mode == 'bbox': self._update_bbox(ox + info.metrics.xmin, oy - info.metrics.ymax, ox + info.metrics.xmax, oy - info.metrics.ymin) else: info.font.draw_glyph_to_bitmap( self.image, ox, oy - info.metrics.iceberg, info.glyph, antialiased=rcParams['text.antialiased']) def render_rect_filled(self, x1, y1, x2, y2): if self.mode == 'bbox': self._update_bbox(x1, y1, x2, y2) else: height = max(int(y2 - y1) - 1, 0) if height == 0: center = (y2 + y1) / 2.0 y = int(center - (height + 1) / 2.0) else: y = int(y1) self.image.draw_rect_filled(int(x1), y, np.ceil(x2), y + height) def get_results(self, box, used_characters): self.mode = 'bbox' orig_height = box.height orig_depth = box.depth ship(0, 0, box) bbox = self.bbox bbox = [bbox[0] - 1, bbox[1] - 1, bbox[2] + 1, bbox[3] + 1] self.mode = 'render' self.set_canvas_size( bbox[2] - bbox[0], (bbox[3] - bbox[1]) - orig_depth, (bbox[3] - bbox[1]) - orig_height) ship(-bbox[0], -bbox[1], box) result = (self.ox, self.oy, self.width, self.height + self.depth, self.depth, self.image, used_characters) self.image = None return result def get_hinting_type(self): from matplotlib.backends import backend_agg return backend_agg.get_hinting_flag() class MathtextBackendBitmap(MathtextBackendAgg): def get_results(self, box, used_characters): ox, oy, width, height, depth, image, characters = \ MathtextBackendAgg.get_results(self, box, used_characters) return image, depth class MathtextBackendPs(MathtextBackend): """ Store information to write a mathtext rendering to the PostScript backend. """ _PSResult = namedtuple( "_PSResult", "width height depth pswriter used_characters") def __init__(self): self.pswriter = StringIO() self.lastfont = None def render_glyph(self, ox, oy, info): oy = self.height - oy + info.offset postscript_name = info.postscript_name fontsize = info.fontsize symbol_name = info.symbol_name if (postscript_name, fontsize) != self.lastfont: ps = """/%(postscript_name)s findfont %(fontsize)s scalefont setfont """ % locals() self.lastfont = postscript_name, fontsize self.pswriter.write(ps) ps = """%(ox)f %(oy)f moveto /%(symbol_name)s glyphshow\n """ % locals() self.pswriter.write(ps) def render_rect_filled(self, x1, y1, x2, y2): ps = "%f %f %f %f rectfill\n" % ( x1, self.height - y2, x2 - x1, y2 - y1) self.pswriter.write(ps) def get_results(self, box, used_characters): ship(0, 0, box) return self._PSResult(self.width, self.height + self.depth, self.depth, self.pswriter, used_characters) class MathtextBackendPdf(MathtextBackend): """Store information to write a mathtext rendering to the PDF backend.""" _PDFResult = namedtuple( "_PDFResult", "width height depth glyphs rects used_characters") def __init__(self): self.glyphs = [] self.rects = [] def render_glyph(self, ox, oy, info): filename = info.font.fname oy = self.height - oy + info.offset self.glyphs.append( (ox, oy, filename, info.fontsize, info.num, info.symbol_name)) def render_rect_filled(self, x1, y1, x2, y2): self.rects.append((x1, self.height - y2, x2 - x1, y2 - y1)) def get_results(self, box, used_characters): ship(0, 0, box) return self._PDFResult(self.width, self.height + self.depth, self.depth, self.glyphs, self.rects, used_characters) class MathtextBackendSvg(MathtextBackend): """ Store information to write a mathtext rendering to the SVG backend. """ def __init__(self): self.svg_glyphs = [] self.svg_rects = [] def render_glyph(self, ox, oy, info): oy = self.height - oy + info.offset self.svg_glyphs.append( (info.font, info.fontsize, info.num, ox, oy, info.metrics)) def render_rect_filled(self, x1, y1, x2, y2): self.svg_rects.append( (x1, self.height - y1 + 1, x2 - x1, y2 - y1)) def get_results(self, box, used_characters): ship(0, 0, box) svg_elements = types.SimpleNamespace(svg_glyphs=self.svg_glyphs, svg_rects=self.svg_rects) return (self.width, self.height + self.depth, self.depth, svg_elements, used_characters) class MathtextBackendPath(MathtextBackend): """ Store information to write a mathtext rendering to the text path machinery. """ def __init__(self): self.glyphs = [] self.rects = [] def render_glyph(self, ox, oy, info): oy = self.height - oy + info.offset thetext = info.num self.glyphs.append( (info.font, info.fontsize, thetext, ox, oy)) def render_rect_filled(self, x1, y1, x2, y2): self.rects.append((x1, self.height - y2, x2 - x1, y2 - y1)) def get_results(self, box, used_characters): ship(0, 0, box) return (self.width, self.height + self.depth, self.depth, self.glyphs, self.rects) class MathtextBackendCairo(MathtextBackend): """ Store information to write a mathtext rendering to the Cairo backend. """ def __init__(self): self.glyphs = [] self.rects = [] def render_glyph(self, ox, oy, info): oy = oy - info.offset - self.height thetext = chr(info.num) self.glyphs.append( (info.font, info.fontsize, thetext, ox, oy)) def render_rect_filled(self, x1, y1, x2, y2): self.rects.append( (x1, y1 - self.height, x2 - x1, y2 - y1)) def get_results(self, box, used_characters): ship(0, 0, box) return (self.width, self.height + self.depth, self.depth, self.glyphs, self.rects) class Fonts(object): """ An abstract base class for a system of fonts to use for mathtext. The class must be able to take symbol keys and font file names and return the character metrics. It also delegates to a backend class to do the actual drawing. """ def __init__(self, default_font_prop, mathtext_backend): """ *default_font_prop*: A :class:`~matplotlib.font_manager.FontProperties` object to use for the default non-math font, or the base font for Unicode (generic) font rendering. *mathtext_backend*: A subclass of :class:`MathTextBackend` used to delegate the actual rendering. """ self.default_font_prop = default_font_prop self.mathtext_backend = mathtext_backend self.used_characters = {} def destroy(self): """ Fix any cyclical references before the object is about to be destroyed. """ self.used_characters = None def get_kern(self, font1, fontclass1, sym1, fontsize1, font2, fontclass2, sym2, fontsize2, dpi): """ Get the kerning distance for font between *sym1* and *sym2*. *fontX*: one of the TeX font names:: tt, it, rm, cal, sf, bf or default/regular (non-math) *fontclassX*: TODO *symX*: a symbol in raw TeX form. e.g., '1', 'x' or '\\sigma' *fontsizeX*: the fontsize in points *dpi*: the current dots-per-inch """ return 0. def get_metrics(self, font, font_class, sym, fontsize, dpi, math=True): """ *font*: one of the TeX font names:: tt, it, rm, cal, sf, bf or default/regular (non-math) *font_class*: TODO *sym*: a symbol in raw TeX form. e.g., '1', 'x' or '\\sigma' *fontsize*: font size in points *dpi*: current dots-per-inch *math*: whether sym is a math character Returns an object with the following attributes: - *advance*: The advance distance (in points) of the glyph. - *height*: The height of the glyph in points. - *width*: The width of the glyph in points. - *xmin*, *xmax*, *ymin*, *ymax* - the ink rectangle of the glyph - *iceberg* - the distance from the baseline to the top of the glyph. This corresponds to TeX's definition of "height". """ info = self._get_info(font, font_class, sym, fontsize, dpi, math) return info.metrics def set_canvas_size(self, w, h, d): """ Set the size of the buffer used to render the math expression. Only really necessary for the bitmap backends. """ self.width, self.height, self.depth = np.ceil([w, h, d]) self.mathtext_backend.set_canvas_size( self.width, self.height, self.depth) def render_glyph(self, ox, oy, facename, font_class, sym, fontsize, dpi): """ Draw a glyph at - *ox*, *oy*: position - *facename*: One of the TeX face names - *font_class*: - *sym*: TeX symbol name or single character - *fontsize*: fontsize in points - *dpi*: The dpi to draw at. """ info = self._get_info(facename, font_class, sym, fontsize, dpi) realpath, stat_key = get_realpath_and_stat(info.font.fname) used_characters = self.used_characters.setdefault( stat_key, (realpath, set())) used_characters[1].add(info.num) self.mathtext_backend.render_glyph(ox, oy, info) def render_rect_filled(self, x1, y1, x2, y2): """ Draw a filled rectangle from (*x1*, *y1*) to (*x2*, *y2*). """ self.mathtext_backend.render_rect_filled(x1, y1, x2, y2) def get_xheight(self, font, fontsize, dpi): """ Get the xheight for the given *font* and *fontsize*. """ raise NotImplementedError() def get_underline_thickness(self, font, fontsize, dpi): """ Get the line thickness that matches the given font. Used as a base unit for drawing lines such as in a fraction or radical. """ raise NotImplementedError() def get_used_characters(self): """ Get the set of characters that were used in the math expression. Used by backends that need to subset fonts so they know which glyphs to include. """ return self.used_characters def get_results(self, box): """ Get the data needed by the backend to render the math expression. The return value is backend-specific. """ result = self.mathtext_backend.get_results( box, self.get_used_characters()) self.destroy() return result def get_sized_alternatives_for_symbol(self, fontname, sym): """ Override if your font provides multiple sizes of the same symbol. Should return a list of symbols matching *sym* in various sizes. The expression renderer will select the most appropriate size for a given situation from this list. """ return [(fontname, sym)] class TruetypeFonts(Fonts): """ A generic base class for all font setups that use Truetype fonts (through FT2Font). """ def __init__(self, default_font_prop, mathtext_backend): Fonts.__init__(self, default_font_prop, mathtext_backend) self.glyphd = {} self._fonts = {} filename = findfont(default_font_prop) default_font = get_font(filename) self._fonts['default'] = default_font self._fonts['regular'] = default_font def destroy(self): self.glyphd = None Fonts.destroy(self) def _get_font(self, font): if font in self.fontmap: basename = self.fontmap[font] else: basename = font cached_font = self._fonts.get(basename) if cached_font is None and os.path.exists(basename): cached_font = get_font(basename) self._fonts[basename] = cached_font self._fonts[cached_font.postscript_name] = cached_font self._fonts[cached_font.postscript_name.lower()] = cached_font return cached_font def _get_offset(self, font, glyph, fontsize, dpi): if font.postscript_name == 'Cmex10': return ((glyph.height/64.0/2.0) + (fontsize/3.0 * dpi/72.0)) return 0. def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True): key = fontname, font_class, sym, fontsize, dpi bunch = self.glyphd.get(key) if bunch is not None: return bunch font, num, symbol_name, fontsize, slanted = \ self._get_glyph(fontname, font_class, sym, fontsize, math) font.set_size(fontsize, dpi) glyph = font.load_char( num, flags=self.mathtext_backend.get_hinting_type()) xmin, ymin, xmax, ymax = [val/64.0 for val in glyph.bbox] offset = self._get_offset(font, glyph, fontsize, dpi) metrics = types.SimpleNamespace( advance = glyph.linearHoriAdvance/65536.0, height = glyph.height/64.0, width = glyph.width/64.0, xmin = xmin, xmax = xmax, ymin = ymin+offset, ymax = ymax+offset, # iceberg is the equivalent of TeX's "height" iceberg = glyph.horiBearingY/64.0 + offset, slanted = slanted ) result = self.glyphd[key] = types.SimpleNamespace( font = font, fontsize = fontsize, postscript_name = font.postscript_name, metrics = metrics, symbol_name = symbol_name, num = num, glyph = glyph, offset = offset ) return result def get_xheight(self, fontname, fontsize, dpi): font = self._get_font(fontname) font.set_size(fontsize, dpi) pclt = font.get_sfnt_table('pclt') if pclt is None: # Some fonts don't store the xHeight, so we do a poor man's xHeight metrics = self.get_metrics( fontname, rcParams['mathtext.default'], 'x', fontsize, dpi) return metrics.iceberg xHeight = (pclt['xHeight'] / 64.0) * (fontsize / 12.0) * (dpi / 100.0) return xHeight def get_underline_thickness(self, font, fontsize, dpi): # This function used to grab underline thickness from the font # metrics, but that information is just too un-reliable, so it # is now hardcoded. return ((0.75 / 12.0) * fontsize * dpi) / 72.0 def get_kern(self, font1, fontclass1, sym1, fontsize1, font2, fontclass2, sym2, fontsize2, dpi): if font1 == font2 and fontsize1 == fontsize2: info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi) info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi) font = info1.font return font.get_kerning(info1.num, info2.num, KERNING_DEFAULT) / 64 return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1, font2, fontclass2, sym2, fontsize2, dpi) class BakomaFonts(TruetypeFonts): """ Use the Bakoma TrueType fonts for rendering. Symbols are strewn about a number of font files, each of which has its own proprietary 8-bit encoding. """ _fontmap = { 'cal' : 'cmsy10', 'rm' : 'cmr10', 'tt' : 'cmtt10', 'it' : 'cmmi10', 'bf' : 'cmb10', 'sf' : 'cmss10', 'ex' : 'cmex10' } def __init__(self, *args, **kwargs): self._stix_fallback = StixFonts(*args, **kwargs) TruetypeFonts.__init__(self, *args, **kwargs) self.fontmap = {} for key, val in self._fontmap.items(): fullpath = findfont(val) self.fontmap[key] = fullpath self.fontmap[val] = fullpath _slanted_symbols = set(r"\int \oint".split()) def _get_glyph(self, fontname, font_class, sym, fontsize, math=True): symbol_name = None 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: gid = font.get_char_index(num) if gid != 0: symbol_name = font.get_glyph_name(gid) if symbol_name is None: return self._stix_fallback._get_glyph( fontname, font_class, sym, fontsize, math) return font, num, symbol_name, fontsize, slanted # The Bakoma fonts contain many pre-sized alternatives for the # delimiters. The AutoSizedChar class will use these alternatives # and select the best (closest sized) glyph. _size_alternatives = { '(' : [('rm', '('), ('ex', '\xa1'), ('ex', '\xb3'), ('ex', '\xb5'), ('ex', '\xc3')], ')' : [('rm', ')'), ('ex', '\xa2'), ('ex', '\xb4'), ('ex', '\xb6'), ('ex', '\x21')], '{' : [('cal', '{'), ('ex', '\xa9'), ('ex', '\x6e'), ('ex', '\xbd'), ('ex', '\x28')], '}' : [('cal', '}'), ('ex', '\xaa'), ('ex', '\x6f'), ('ex', '\xbe'), ('ex', '\x29')], # The fourth size of '[' is mysteriously missing from the BaKoMa # font, so I've omitted it for both '[' and ']' '[' : [('rm', '['), ('ex', '\xa3'), ('ex', '\x68'), ('ex', '\x22')], ']' : [('rm', ']'), ('ex', '\xa4'), ('ex', '\x69'), ('ex', '\x23')], r'\lfloor' : [('ex', '\xa5'), ('ex', '\x6a'), ('ex', '\xb9'), ('ex', '\x24')], r'\rfloor' : [('ex', '\xa6'), ('ex', '\x6b'), ('ex', '\xba'), ('ex', '\x25')], r'\lceil' : [('ex', '\xa7'), ('ex', '\x6c'), ('ex', '\xbb'), ('ex', '\x26')], r'\rceil' : [('ex', '\xa8'), ('ex', '\x6d'), ('ex', '\xbc'), ('ex', '\x27')], r'\langle' : [('ex', '\xad'), ('ex', '\x44'), ('ex', '\xbf'), ('ex', '\x2a')], r'\rangle' : [('ex', '\xae'), ('ex', '\x45'), ('ex', '\xc0'), ('ex', '\x2b')], r'\__sqrt__' : [('ex', '\x70'), ('ex', '\x71'), ('ex', '\x72'), ('ex', '\x73')], r'\backslash': [('ex', '\xb2'), ('ex', '\x2f'), ('ex', '\xc2'), ('ex', '\x2d')], r'/' : [('rm', '/'), ('ex', '\xb1'), ('ex', '\x2e'), ('ex', '\xcb'), ('ex', '\x2c')], r'\widehat' : [('rm', '\x5e'), ('ex', '\x62'), ('ex', '\x63'), ('ex', '\x64')], r'\widetilde': [('rm', '\x7e'), ('ex', '\x65'), ('ex', '\x66'), ('ex', '\x67')], r'<' : [('cal', 'h'), ('ex', 'D')], r'>' : [('cal', 'i'), ('ex', 'E')] } for alias, target in [(r'\leftparen', '('), (r'\rightparent', ')'), (r'\leftbrace', '{'), (r'\rightbrace', '}'), (r'\leftbracket', '['), (r'\rightbracket', ']'), (r'\{', '{'), (r'\}', '}'), (r'\[', '['), (r'\]', ']')]: _size_alternatives[alias] = _size_alternatives[target] def get_sized_alternatives_for_symbol(self, fontname, sym): return self._size_alternatives.get(sym, [(fontname, sym)]) class UnicodeFonts(TruetypeFonts): """ An abstract base class for handling Unicode fonts. While some reasonably complete Unicode fonts (such as DejaVu) may work in some situations, the only Unicode font I'm aware of with a complete set of math symbols is STIX. This class will "fallback" on the Bakoma fonts when a required symbol can not be found in the font. """ use_cmex = True def __init__(self, *args, **kwargs): # This must come first so the backend's owner is set correctly if rcParams['mathtext.fallback_to_cm']: self.cm_fallback = BakomaFonts(*args, **kwargs) else: self.cm_fallback = None TruetypeFonts.__init__(self, *args, **kwargs) self.fontmap = {} for texfont in "cal rm tt it bf sf".split(): prop = rcParams['mathtext.' + texfont] font = findfont(prop) self.fontmap[texfont] = font prop = FontProperties('cmex10') font = findfont(prop) self.fontmap['ex'] = font _slanted_symbols = set(r"\int \oint".split()) def _map_virtual_font(self, fontname, font_class, uniindex): return fontname, uniindex def _get_glyph(self, fontname, font_class, sym, fontsize, math=True): found_symbol = False if self.use_cmex: uniindex = latex_to_cmex.get(sym) if uniindex is not None: fontname = 'ex' found_symbol = True if not found_symbol: try: uniindex = get_unicode_index(sym, math) found_symbol = True except ValueError: uniindex = ord('?') _log.warning( "No TeX to unicode mapping for {!a}.".format(sym)) fontname, uniindex = self._map_virtual_font( fontname, font_class, uniindex) new_fontname = fontname # Only characters in the "Letter" class should be italicized in 'it' # mode. Greek capital letters should be Roman. if found_symbol: if fontname == 'it' and uniindex < 0x10000: char = chr(uniindex) if (not 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: glyphindex = font.get_char_index(uniindex) if glyphindex != 0: found_symbol = True if not found_symbol: if self.cm_fallback: if isinstance(self.cm_fallback, BakomaFonts): _log.warning( "Substituting with a symbol from Computer Modern.") if (fontname in ('it', 'regular') and isinstance(self.cm_fallback, StixFonts)): return self.cm_fallback._get_glyph( 'rm', font_class, sym, fontsize) else: return self.cm_fallback._get_glyph( fontname, font_class, sym, fontsize) else: if (fontname in ('it', 'regular') and isinstance(self, StixFonts)): return self._get_glyph('rm', font_class, sym, fontsize) _log.warning("Font {!r} does not have a glyph for {!a} " "[U+{:x}], substituting with a dummy " "symbol.".format(new_fontname, sym, uniindex)) fontname = 'rm' font = self._get_font(fontname) uniindex = 0xA4 # currency char, for lack of anything better glyphindex = font.get_char_index(uniindex) slanted = False symbol_name = font.get_glyph_name(glyphindex) return font, uniindex, symbol_name, fontsize, slanted def get_sized_alternatives_for_symbol(self, fontname, sym): if self.cm_fallback: return self.cm_fallback.get_sized_alternatives_for_symbol( fontname, sym) return [(fontname, sym)] class DejaVuFonts(UnicodeFonts): use_cmex = False def __init__(self, *args, **kwargs): # This must come first so the backend's owner is set correctly if isinstance(self, DejaVuSerifFonts): self.cm_fallback = StixFonts(*args, **kwargs) else: self.cm_fallback = StixSansFonts(*args, **kwargs) self.bakoma = BakomaFonts(*args, **kwargs) TruetypeFonts.__init__(self, *args, **kwargs) self.fontmap = {} # Include Stix sized alternatives for glyphs self._fontmap.update({ 1 : 'STIXSizeOneSym', 2 : 'STIXSizeTwoSym', 3 : 'STIXSizeThreeSym', 4 : 'STIXSizeFourSym', 5 : 'STIXSizeFiveSym'}) for key, name in self._fontmap.items(): fullpath = findfont(name) self.fontmap[key] = fullpath self.fontmap[name] = fullpath def _get_glyph(self, fontname, font_class, sym, fontsize, math=True): # Override prime symbol to use Bakoma. if sym == r'\prime': return self.bakoma._get_glyph( fontname, font_class, sym, fontsize, math) 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, fontsize, math) # otherwise return regular glyph return super()._get_glyph( fontname, font_class, sym, fontsize, math) class DejaVuSerifFonts(DejaVuFonts): """ A font handling class for the DejaVu Serif fonts If a glyph is not found it will fallback to Stix Serif """ _fontmap = { 'rm' : 'DejaVu Serif', 'it' : 'DejaVu Serif:italic', 'bf' : 'DejaVu Serif:weight=bold', 'sf' : 'DejaVu Sans', 'tt' : 'DejaVu Sans Mono', 'ex' : 'DejaVu Serif Display', 0 : 'DejaVu Serif', } class DejaVuSansFonts(DejaVuFonts): """ A font handling class for the DejaVu Sans fonts If a glyph is not found it will fallback to Stix Sans """ _fontmap = { 'rm' : 'DejaVu Sans', 'it' : 'DejaVu Sans:italic', 'bf' : 'DejaVu Sans:weight=bold', 'sf' : 'DejaVu Sans', 'tt' : 'DejaVu Sans Mono', 'ex' : 'DejaVu Sans Display', 0 : 'DejaVu Sans', } class StixFonts(UnicodeFonts): """ A font handling class for the STIX fonts. In addition to what UnicodeFonts provides, this class: - supports "virtual fonts" which are complete alpha numeric character sets with different font styles at special Unicode code points, such as "Blackboard". - handles sized alternative characters for the STIXSizeX fonts. """ _fontmap = { 'rm' : 'STIXGeneral', 'it' : 'STIXGeneral:italic', 'bf' : 'STIXGeneral:weight=bold', 'nonunirm' : 'STIXNonUnicode', 'nonuniit' : 'STIXNonUnicode:italic', 'nonunibf' : 'STIXNonUnicode:weight=bold', 0 : 'STIXGeneral', 1 : 'STIXSizeOneSym', 2 : 'STIXSizeTwoSym', 3 : 'STIXSizeThreeSym', 4 : 'STIXSizeFourSym', 5 : 'STIXSizeFiveSym' } use_cmex = False cm_fallback = False _sans = False def __init__(self, *args, **kwargs): TruetypeFonts.__init__(self, *args, **kwargs) self.fontmap = {} for key, name in self._fontmap.items(): fullpath = findfont(name) self.fontmap[key] = fullpath self.fontmap[name] = fullpath def _map_virtual_font(self, fontname, font_class, uniindex): # Handle these "fonts" that are actually embedded in # other fonts. mapping = stix_virtual_fonts.get(fontname) if (self._sans and mapping is None and fontname not in ('regular', 'default')): mapping = stix_virtual_fonts['sf'] doing_sans_conversion = True else: doing_sans_conversion = False if mapping is not None: if isinstance(mapping, dict): try: mapping = mapping[font_class] except KeyError: mapping = mapping['rm'] # Binary search for the source glyph lo = 0 hi = len(mapping) while lo < hi: mid = (lo+hi)//2 range = mapping[mid] if uniindex < range[0]: hi = mid elif uniindex <= range[1]: break else: lo = mid + 1 if range[0] <= uniindex <= range[1]: uniindex = uniindex - range[0] + range[3] fontname = range[2] elif not doing_sans_conversion: # This will generate a dummy character uniindex = 0x1 fontname = rcParams['mathtext.default'] # Handle private use area glyphs if fontname in ('it', 'rm', 'bf') and 0xe000 <= uniindex <= 0xf8ff: fontname = 'nonuni' + fontname return fontname, uniindex _size_alternatives = {} def get_sized_alternatives_for_symbol(self, fontname, sym): fixes = {'\\{': '{', '\\}': '}', '\\[': '[', '\\]': ']'} sym = fixes.get(sym, sym) alternatives = self._size_alternatives.get(sym) if alternatives: return alternatives alternatives = [] try: uniindex = get_unicode_index(sym) except ValueError: return [(fontname, sym)] fix_ups = { ord('<'): 0x27e8, ord('>'): 0x27e9 } uniindex = fix_ups.get(uniindex, uniindex) for i in range(6): font = self._get_font(i) glyphindex = font.get_char_index(uniindex) if glyphindex != 0: alternatives.append((i, chr(uniindex))) # The largest size of the radical symbol in STIX has incorrect # metrics that cause it to be disconnected from the stem. if sym == r'\__sqrt__': alternatives = alternatives[:-1] self._size_alternatives[sym] = alternatives return alternatives class StixSansFonts(StixFonts): """ A font handling class for the STIX fonts (that uses sans-serif characters by default). """ _sans = True class StandardPsFonts(Fonts): """ Use the standard postscript fonts for rendering to backend_ps Unlike the other font classes, BakomaFont and UnicodeFont, this one requires the Ps backend. """ basepath = os.path.join(get_data_path(), 'fonts', 'afm') fontmap = { 'cal' : 'pzcmi8a', # Zapf Chancery 'rm' : 'pncr8a', # New Century Schoolbook 'tt' : 'pcrr8a', # Courier 'it' : 'pncri8a', # New Century Schoolbook Italic 'sf' : 'phvr8a', # Helvetica 'bf' : 'pncb8a', # New Century Schoolbook Bold None : 'psyr' # Symbol } def __init__(self, default_font_prop): Fonts.__init__(self, default_font_prop, MathtextBackendPs()) self.glyphd = {} self.fonts = {} filename = findfont(default_font_prop, fontext='afm', directory=self.basepath) if filename is None: filename = findfont('Helvetica', fontext='afm', directory=self.basepath) with open(filename, 'rb') as fd: default_font = AFM(fd) default_font.fname = filename self.fonts['default'] = default_font self.fonts['regular'] = default_font self.pswriter = StringIO() def _get_font(self, font): if font in self.fontmap: basename = self.fontmap[font] else: basename = font cached_font = self.fonts.get(basename) if cached_font is None: fname = os.path.join(self.basepath, basename + ".afm") with open(fname, 'rb') as fd: cached_font = AFM(fd) cached_font.fname = fname self.fonts[basename] = cached_font self.fonts[cached_font.get_fontname()] = cached_font return cached_font def _get_info(self, fontname, font_class, sym, fontsize, dpi, math=True): 'load the cmfont, metrics and glyph with caching' key = fontname, sym, fontsize, dpi tup = self.glyphd.get(key) if tup is not None: return tup # Only characters in the "Letter" class should really be italicized. # This class includes greek letters, so we're ok if (fontname == 'it' and (len(sym) > 1 or not unicodedata.category(sym).startswith("L"))): fontname = 'rm' found_symbol = False if sym in latex_to_standard: fontname, num = latex_to_standard[sym] glyph = chr(num) found_symbol = True elif len(sym) == 1: glyph = sym num = ord(glyph) found_symbol = True else: _log.warning( "No TeX to built-in Postscript mapping for {!r}".format(sym)) slanted = (fontname == 'it') font = self._get_font(fontname) if found_symbol: try: symbol_name = font.get_name_char(glyph) except KeyError: _log.warning( "No glyph in standard Postscript font {!r} for {!r}" .format(font.get_fontname(), sym)) found_symbol = False if not found_symbol: glyph = '?' num = ord(glyph) symbol_name = font.get_name_char(glyph) offset = 0 scale = 0.001 * fontsize xmin, ymin, xmax, ymax = [val * scale for val in font.get_bbox_char(glyph)] metrics = types.SimpleNamespace( advance = font.get_width_char(glyph) * scale, width = font.get_width_char(glyph) * scale, height = font.get_height_char(glyph) * scale, xmin = xmin, xmax = xmax, ymin = ymin+offset, ymax = ymax+offset, # iceberg is the equivalent of TeX's "height" iceberg = ymax + offset, slanted = slanted ) self.glyphd[key] = types.SimpleNamespace( font = font, fontsize = fontsize, postscript_name = font.get_fontname(), metrics = metrics, symbol_name = symbol_name, num = num, glyph = glyph, offset = offset ) return self.glyphd[key] def get_kern(self, font1, fontclass1, sym1, fontsize1, font2, fontclass2, sym2, fontsize2, dpi): if font1 == font2 and fontsize1 == fontsize2: info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi) info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi) font = info1.font return (font.get_kern_dist(info1.glyph, info2.glyph) * 0.001 * fontsize1) return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1, font2, fontclass2, sym2, fontsize2, dpi) def get_xheight(self, font, fontsize, dpi): font = self._get_font(font) return font.get_xheight() * 0.001 * fontsize def get_underline_thickness(self, font, fontsize, dpi): font = self._get_font(font) return font.get_underline_thickness() * 0.001 * fontsize ############################################################################## # TeX-LIKE BOX MODEL # The following is based directly on the document 'woven' from the # TeX82 source code. This information is also available in printed # form: # # Knuth, Donald E.. 1986. Computers and Typesetting, Volume B: # TeX: The Program. Addison-Wesley Professional. # # The most relevant "chapters" are: # Data structures for boxes and their friends # Shipping pages out (Ship class) # Packaging (hpack and vpack) # Data structures for math mode # Subroutines for math mode # Typesetting math formulas # # Many of the docstrings below refer to a numbered "node" in that # book, e.g., node123 # # Note that (as TeX) y increases downward, unlike many other parts of # matplotlib. # How much text shrinks when going to the next-smallest level. GROW_FACTOR # must be the inverse of SHRINK_FACTOR. SHRINK_FACTOR = 0.7 GROW_FACTOR = 1.0 / SHRINK_FACTOR # The number of different sizes of chars to use, beyond which they will not # get any smaller NUM_SIZE_LEVELS = 6 class FontConstantsBase(object): """ A set of constants that controls how certain things, such as sub- and superscripts are laid out. These are all metrics that can't be reliably retrieved from the font metrics in the font itself. """ # Percentage of x-height of additional horiz. space after sub/superscripts script_space = 0.05 # Percentage of x-height that sub/superscripts drop below the baseline subdrop = 0.4 # Percentage of x-height that superscripts are raised from the baseline sup1 = 0.7 # Percentage of x-height that subscripts drop below the baseline sub1 = 0.3 # Percentage of x-height that subscripts drop below the baseline when a # superscript is present sub2 = 0.5 # Percentage of x-height that sub/supercripts are offset relative to the # nucleus edge for non-slanted nuclei delta = 0.025 # Additional percentage of last character height above 2/3 of the # x-height that supercripts are offset relative to the subscript # for slanted nuclei delta_slanted = 0.2 # Percentage of x-height that supercripts and subscripts are offset for # integrals delta_integral = 0.1 class ComputerModernFontConstants(FontConstantsBase): script_space = 0.075 subdrop = 0.2 sup1 = 0.45 sub1 = 0.2 sub2 = 0.3 delta = 0.075 delta_slanted = 0.3 delta_integral = 0.3 class STIXFontConstants(FontConstantsBase): script_space = 0.1 sup1 = 0.8 sub2 = 0.6 delta = 0.05 delta_slanted = 0.3 delta_integral = 0.3 class STIXSansFontConstants(FontConstantsBase): script_space = 0.05 sup1 = 0.8 delta_slanted = 0.6 delta_integral = 0.3 class DejaVuSerifFontConstants(FontConstantsBase): pass class DejaVuSansFontConstants(FontConstantsBase): pass # Maps font family names to the FontConstantBase subclass to use _font_constant_mapping = { 'DejaVu Sans': DejaVuSansFontConstants, 'DejaVu Sans Mono': DejaVuSansFontConstants, 'DejaVu Serif': DejaVuSerifFontConstants, 'cmb10': ComputerModernFontConstants, 'cmex10': ComputerModernFontConstants, 'cmmi10': ComputerModernFontConstants, 'cmr10': ComputerModernFontConstants, 'cmss10': ComputerModernFontConstants, 'cmsy10': ComputerModernFontConstants, 'cmtt10': ComputerModernFontConstants, 'STIXGeneral': STIXFontConstants, 'STIXNonUnicode': STIXFontConstants, 'STIXSizeFiveSym': STIXFontConstants, 'STIXSizeFourSym': STIXFontConstants, 'STIXSizeThreeSym': STIXFontConstants, 'STIXSizeTwoSym': STIXFontConstants, 'STIXSizeOneSym': STIXFontConstants, # Map the fonts we used to ship, just for good measure 'Bitstream Vera Sans': DejaVuSansFontConstants, 'Bitstream Vera': DejaVuSansFontConstants, } def _get_font_constant_set(state): constants = _font_constant_mapping.get( state.font_output._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.font_output, StixSansFonts)): return STIXSansFontConstants return constants class MathTextWarning(Warning): pass class Node(object): """ A node in the TeX box model """ def __init__(self): self.size = 0 def __repr__(self): return self.__class__.__name__ def get_kerning(self, next): return 0.0 def shrink(self): """ Shrinks one level smaller. There are only three levels of sizes, after which things will no longer get smaller. """ self.size += 1 def grow(self): """ Grows one level larger. There is no limit to how big something can get. """ self.size -= 1 def render(self, x, y): pass class Box(Node): """ Represents any node with a physical location. """ def __init__(self, width, height, depth): Node.__init__(self) self.width = width self.height = height self.depth = depth def shrink(self): Node.shrink(self) if self.size < NUM_SIZE_LEVELS: self.width *= SHRINK_FACTOR self.height *= SHRINK_FACTOR self.depth *= SHRINK_FACTOR def grow(self): Node.grow(self) self.width *= GROW_FACTOR self.height *= GROW_FACTOR self.depth *= GROW_FACTOR def render(self, x1, y1, x2, y2): pass class Vbox(Box): """ A box with only height (zero width). """ def __init__(self, height, depth): Box.__init__(self, 0., height, depth) class Hbox(Box): """ A box with only width (zero height and depth). """ def __init__(self, width): Box.__init__(self, width, 0., 0.) class Char(Node): """ Represents a single character. Unlike TeX, the font information and metrics are stored with each :class:`Char` to make it easier to lookup the font metrics when needed. Note that TeX boxes have a width, height, and depth, unlike Type1 and Truetype which use a full bounding box and an advance in the x-direction. The metrics must be converted to the TeX way, and the advance (if different from width) must be converted into a :class:`Kern` node when the :class:`Char` is added to its parent :class:`Hlist`. """ def __init__(self, c, state, math=True): Node.__init__(self) self.c = c self.font_output = state.font_output self.font = state.font self.font_class = state.font_class self.fontsize = state.fontsize self.dpi = state.dpi self.math = math # The real width, height and depth will be set during the # pack phase, after we know the real fontsize self._update_metrics() def __repr__(self): return '`%s`' % self.c def _update_metrics(self): metrics = self._metrics = self.font_output.get_metrics( self.font, self.font_class, self.c, self.fontsize, self.dpi, self.math) if self.c == ' ': self.width = metrics.advance else: self.width = metrics.width self.height = metrics.iceberg self.depth = -(metrics.iceberg - metrics.height) def is_slanted(self): return self._metrics.slanted def get_kerning(self, next): """ Return the amount of kerning between this and the given character. Called when characters are strung together into :class:`Hlist` to create :class:`Kern` nodes. """ advance = self._metrics.advance - self.width kern = 0. if isinstance(next, Char): kern = self.font_output.get_kern( self.font, self.font_class, self.c, self.fontsize, next.font, next.font_class, next.c, next.fontsize, self.dpi) return advance + kern def render(self, x, y): """ Render the character to the canvas """ self.font_output.render_glyph( x, y, self.font, self.font_class, self.c, self.fontsize, self.dpi) def shrink(self): Node.shrink(self) if self.size < NUM_SIZE_LEVELS: self.fontsize *= SHRINK_FACTOR self.width *= SHRINK_FACTOR self.height *= SHRINK_FACTOR self.depth *= SHRINK_FACTOR def grow(self): Node.grow(self) self.fontsize *= GROW_FACTOR self.width *= GROW_FACTOR self.height *= GROW_FACTOR self.depth *= GROW_FACTOR class Accent(Char): """ The font metrics need to be dealt with differently for accents, since they are already offset correctly from the baseline in TrueType fonts. """ def _update_metrics(self): metrics = self._metrics = self.font_output.get_metrics( self.font, self.font_class, self.c, self.fontsize, self.dpi) self.width = metrics.xmax - metrics.xmin self.height = metrics.ymax - metrics.ymin self.depth = 0 def shrink(self): Char.shrink(self) self._update_metrics() def grow(self): Char.grow(self) self._update_metrics() def render(self, x, y): """ Render the character to the canvas. """ self.font_output.render_glyph( x - self._metrics.xmin, y + self._metrics.ymin, self.font, self.font_class, self.c, self.fontsize, self.dpi) class List(Box): """ A list of nodes (either horizontal or vertical). """ def __init__(self, elements): Box.__init__(self, 0., 0., 0.) self.shift_amount = 0. # An arbitrary offset self.children = elements # The child nodes of this list # The following parameters are set in the vpack and hpack functions self.glue_set = 0. # The glue setting of this list self.glue_sign = 0 # 0: normal, -1: shrinking, 1: stretching self.glue_order = 0 # The order of infinity (0 - 3) for the glue def __repr__(self): return '[%s <%.02f %.02f %.02f %.02f> %s]' % ( super().__repr__(), self.width, self.height, self.depth, self.shift_amount, ' '.join([repr(x) for x in self.children])) @staticmethod def _determine_order(totals): """ Determine the highest order of glue used by the members of this list. Helper function used by vpack and hpack. """ for i in range(len(totals))[::-1]: if totals[i] != 0: return i return 0 def _set_glue(self, x, sign, totals, error_type): o = self._determine_order(totals) self.glue_order = o self.glue_sign = sign if totals[o] != 0.: self.glue_set = x / totals[o] else: self.glue_sign = 0 self.glue_ratio = 0. if o == 0: if len(self.children): _log.warning("%s %s: %r", error_type, self.__class__.__name__, self) def shrink(self): for child in self.children: child.shrink() Box.shrink(self) if self.size < NUM_SIZE_LEVELS: self.shift_amount *= SHRINK_FACTOR self.glue_set *= SHRINK_FACTOR def grow(self): for child in self.children: child.grow() Box.grow(self) self.shift_amount *= GROW_FACTOR self.glue_set *= GROW_FACTOR class Hlist(List): """ A horizontal list of boxes. """ def __init__(self, elements, w=0., m='additional', do_kern=True): List.__init__(self, elements) if do_kern: self.kern() self.hpack() def kern(self): """ Insert :class:`Kern` nodes between :class:`Char` nodes to set kerning. The :class:`Char` nodes themselves determine the amount of kerning they need (in :meth:`~Char.get_kerning`), and this function just creates the linked list in the correct way. """ new_children = [] num_children = len(self.children) if num_children: for i in range(num_children): elem = self.children[i] if i < num_children - 1: next = self.children[i + 1] else: next = None new_children.append(elem) kerning_distance = elem.get_kerning(next) if kerning_distance != 0.: kern = Kern(kerning_distance) new_children.append(kern) self.children = new_children # This is a failed experiment to fake cross-font kerning. # def get_kerning(self, next): # if len(self.children) >= 2 and isinstance(self.children[-2], Char): # if isinstance(next, Char): # print "CASE A" # return self.children[-2].get_kerning(next) # elif (isinstance(next, Hlist) and len(next.children) # and isinstance(next.children[0], Char)): # print "CASE B" # result = self.children[-2].get_kerning(next.children[0]) # print result # return result # return 0.0 def hpack(self, w=0., m='additional'): """ The main duty of :meth:`hpack` is to compute the dimensions of the resulting boxes, and to adjust the glue if one of those dimensions is pre-specified. The computed sizes normally enclose all of the material inside the new box; but some items may stick out if negative glue is used, if the box is overfull, or if a ``\\vbox`` includes other boxes that have been shifted left. - *w*: specifies a width - *m*: is either 'exactly' or 'additional'. Thus, ``hpack(w, 'exactly')`` produces a box whose width is exactly *w*, while ``hpack(w, 'additional')`` yields a box whose width is the natural width plus *w*. The default values produce a box with the natural width. """ # I don't know why these get reset in TeX. Shift_amount is pretty # much useless if we do. # self.shift_amount = 0. h = 0. d = 0. x = 0. total_stretch = [0.] * 4 total_shrink = [0.] * 4 for p in self.children: if isinstance(p, Char): x += p.width h = max(h, p.height) d = max(d, p.depth) elif isinstance(p, Box): x += p.width if not 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, "Overfull") else: self._set_glue(x, -1, total_shrink, "Underfull") class Vlist(List): """ A vertical list of boxes. """ def __init__(self, elements, h=0., m='additional'): List.__init__(self, elements) self.vpack() def vpack(self, h=0., m='additional', l=np.inf): """ The main duty of :meth:`vpack` is to compute the dimensions of the resulting boxes, and to adjust the glue if one of those dimensions is pre-specified. - *h*: specifies a height - *m*: is either 'exactly' or 'additional'. - *l*: a maximum height Thus, ``vpack(h, 'exactly')`` produces a box whose height is exactly *h*, while ``vpack(h, 'additional')`` yields a box whose height is the natural height plus *h*. The default values produce a box with the natural width. """ # I don't know why these get reset in TeX. Shift_amount is pretty # much useless if we do. # self.shift_amount = 0. w = 0. d = 0. x = 0. total_stretch = [0.] * 4 total_shrink = [0.] * 4 for p in self.children: if isinstance(p, Box): x += d + p.height d = p.depth if not 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, "Overfull") else: self._set_glue(x, -1, total_shrink, "Underfull") class Rule(Box): """ A :class:`Rule` node stands for a solid black rectangle; it has *width*, *depth*, and *height* fields just as in an :class:`Hlist`. However, if any of these dimensions is inf, the actual value will be determined by running the rule up to the boundary of the innermost enclosing box. This is called a "running dimension." The width is never running in an :class:`Hlist`; the height and depth are never running in a :class:`Vlist`. """ def __init__(self, width, height, depth, state): Box.__init__(self, width, height, depth) self.font_output = state.font_output def render(self, x, y, w, h): self.font_output.render_rect_filled(x, y, x + w, y + h) class Hrule(Rule): """ Convenience class to create a horizontal rule. """ def __init__(self, state, thickness=None): if thickness is None: thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) height = depth = thickness * 0.5 Rule.__init__(self, np.inf, height, depth, state) class Vrule(Rule): """ Convenience class to create a vertical rule. """ def __init__(self, state): thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) Rule.__init__(self, thickness, np.inf, np.inf, state) class Glue(Node): """ Most of the information in this object is stored in the underlying :class:`GlueSpec` class, which is shared between multiple glue objects. (This is a memory optimization which probably doesn't matter anymore, but it's easier to stick to what TeX does.) """ def __init__(self, glue_type, copy=False): Node.__init__(self) self.glue_subtype = 'normal' if isinstance(glue_type, str): glue_spec = GlueSpec.factory(glue_type) elif isinstance(glue_type, GlueSpec): glue_spec = glue_type else: raise ValueError("glue_type must be a glue spec name or instance") if copy: glue_spec = glue_spec.copy() self.glue_spec = glue_spec def shrink(self): Node.shrink(self) if self.size < NUM_SIZE_LEVELS: if self.glue_spec.width != 0.: self.glue_spec = self.glue_spec.copy() self.glue_spec.width *= SHRINK_FACTOR def grow(self): Node.grow(self) if self.glue_spec.width != 0.: self.glue_spec = self.glue_spec.copy() self.glue_spec.width *= GROW_FACTOR class GlueSpec(object): """ See :class:`Glue`. """ def __init__(self, width=0., stretch=0., stretch_order=0, shrink=0., shrink_order=0): self.width = width self.stretch = stretch self.stretch_order = stretch_order self.shrink = shrink self.shrink_order = shrink_order def copy(self): return GlueSpec( self.width, self.stretch, self.stretch_order, self.shrink, self.shrink_order) def factory(cls, glue_type): return cls._types[glue_type] factory = classmethod(factory) GlueSpec._types = { 'fil': GlueSpec(0., 1., 1, 0., 0), 'fill': GlueSpec(0., 1., 2, 0., 0), 'filll': GlueSpec(0., 1., 3, 0., 0), 'neg_fil': GlueSpec(0., 0., 0, 1., 1), 'neg_fill': GlueSpec(0., 0., 0, 1., 2), 'neg_filll': GlueSpec(0., 0., 0, 1., 3), 'empty': GlueSpec(0., 0., 0, 0., 0), 'ss': GlueSpec(0., 1., 1, -1., 1) } # Some convenient ways to get common kinds of glue class Fil(Glue): def __init__(self): Glue.__init__(self, 'fil') class Fill(Glue): def __init__(self): Glue.__init__(self, 'fill') class Filll(Glue): def __init__(self): Glue.__init__(self, 'filll') class NegFil(Glue): def __init__(self): Glue.__init__(self, 'neg_fil') class NegFill(Glue): def __init__(self): Glue.__init__(self, 'neg_fill') class NegFilll(Glue): def __init__(self): Glue.__init__(self, 'neg_filll') class SsGlue(Glue): def __init__(self): Glue.__init__(self, 'ss') class HCentered(Hlist): """ A convenience class to create an :class:`Hlist` whose contents are centered within its enclosing box. """ def __init__(self, elements): Hlist.__init__(self, [SsGlue()] + elements + [SsGlue()], do_kern=False) class VCentered(Hlist): """ A convenience class to create a :class:`Vlist` whose contents are centered within its enclosing box. """ def __init__(self, elements): Vlist.__init__(self, [SsGlue()] + elements + [SsGlue()]) class Kern(Node): """ A :class:`Kern` node has a width field to specify a (normally negative) amount of spacing. This spacing correction appears in horizontal lists between letters like A and V when the font designer said that it looks better to move them closer together or further apart. A kern node can also appear in a vertical list, when its *width* denotes additional spacing in the vertical direction. """ height = 0 depth = 0 def __init__(self, width): Node.__init__(self) self.width = width def __repr__(self): return "k%.02f" % self.width def shrink(self): Node.shrink(self) if self.size < NUM_SIZE_LEVELS: self.width *= SHRINK_FACTOR def grow(self): Node.grow(self) self.width *= GROW_FACTOR class SubSuperCluster(Hlist): """ :class:`SubSuperCluster` is a sort of hack to get around that fact that this code do a two-pass parse like TeX. This lets us store enough information in the hlist itself, namely the nucleus, sub- and super-script, such that if another script follows that needs to be attached, it can be reconfigured on the fly. """ def __init__(self): self.nucleus = None self.sub = None self.super = None Hlist.__init__(self, []) class AutoHeightChar(Hlist): """ :class:`AutoHeightChar` will create a character as close to the given height and depth as possible. When using a font with multiple height versions of some characters (such as the BaKoMa fonts), the correct glyph will be selected, otherwise this will always just return a scaled version of the glyph. """ def __init__(self, c, height, depth, state, always=False, factor=None): alternatives = state.font_output.get_sized_alternatives_for_symbol( state.font, c) xHeight = state.font_output.get_xheight( state.font, state.fontsize, state.dpi) state = state.copy() target_total = height + depth for fontname, sym in alternatives: state.font = fontname char = Char(sym, state) # Ensure that size 0 is chosen when the text is regular sized but # with descender glyphs by subtracting 0.2 * xHeight if char.height + char.depth >= target_total - 0.2 * xHeight: break shift = 0 if state.font != 0: if factor is None: factor = (target_total) / (char.height + char.depth) state.fontsize *= factor char = Char(sym, state) shift = (depth - char.depth) Hlist.__init__(self, [char]) self.shift_amount = shift class AutoWidthChar(Hlist): """ :class:`AutoWidthChar` will create a character as close to the given width as possible. When using a font with multiple width versions of some characters (such as the BaKoMa fonts), the correct glyph will be selected, otherwise this will always just return a scaled version of the glyph. """ def __init__(self, c, width, state, always=False, char_class=Char): alternatives = state.font_output.get_sized_alternatives_for_symbol( state.font, c) state = state.copy() for fontname, sym in alternatives: state.font = fontname char = char_class(sym, state) if char.width >= width: break factor = width / char.width state.fontsize *= factor char = char_class(sym, state) Hlist.__init__(self, [char]) self.width = char.width class Ship(object): """ Once the boxes have been set up, this sends them to output. Since boxes can be inside of boxes inside of boxes, the main work of :class:`Ship` is done by two mutually recursive routines, :meth:`hlist_out` and :meth:`vlist_out`, which traverse the :class:`Hlist` nodes and :class:`Vlist` nodes inside of horizontal and vertical boxes. The global variables used in TeX to store state as it processes have become member variables here. """ def __call__(self, ox, oy, box): self.max_push = 0 # Deepest nesting of push commands so far self.cur_s = 0 self.cur_v = 0. self.cur_h = 0. self.off_h = ox self.off_v = oy + box.height self.hlist_out(box) def clamp(value): if value < -1000000000.: return -1000000000. if value > 1000000000.: return 1000000000. return value clamp = staticmethod(clamp) def hlist_out(self, box): cur_g = 0 cur_glue = 0. glue_order = box.glue_order glue_sign = box.glue_sign base_line = self.cur_v left_edge = self.cur_h self.cur_s += 1 self.max_push = max(self.cur_s, self.max_push) clamp = self.clamp for p in box.children: if isinstance(p, Char): p.render(self.cur_h + self.off_h, self.cur_v + self.off_v) self.cur_h += p.width elif isinstance(p, Kern): self.cur_h += p.width elif isinstance(p, List): # node623 if len(p.children) == 0: self.cur_h += p.width else: edge = self.cur_h self.cur_v = base_line + p.shift_amount if isinstance(p, Hlist): self.hlist_out(p) else: # p.vpack(box.height + box.depth, 'exactly') self.vlist_out(p) self.cur_h = edge + p.width self.cur_v = base_line elif isinstance(p, Box): # node624 rule_height = p.height rule_depth = p.depth rule_width = p.width if 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: self.cur_v = base_line + rule_depth p.render(self.cur_h + self.off_h, self.cur_v + self.off_v, rule_width, rule_height) self.cur_v = base_line self.cur_h += rule_width elif isinstance(p, Glue): # node625 glue_spec = p.glue_spec rule_width = glue_spec.width - cur_g if glue_sign != 0: # normal if glue_sign == 1: # stretching if glue_spec.stretch_order == glue_order: cur_glue += glue_spec.stretch cur_g = round(clamp(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 self.cur_h += rule_width self.cur_s -= 1 def vlist_out(self, box): cur_g = 0 cur_glue = 0. glue_order = box.glue_order glue_sign = box.glue_sign self.cur_s += 1 self.max_push = max(self.max_push, self.cur_s) left_edge = self.cur_h self.cur_v -= box.height top_edge = self.cur_v clamp = self.clamp for p in box.children: if isinstance(p, Kern): self.cur_v += p.width elif isinstance(p, List): if len(p.children) == 0: self.cur_v += p.height + p.depth else: self.cur_v += p.height self.cur_h = left_edge + p.shift_amount save_v = self.cur_v p.width = box.width if isinstance(p, Hlist): self.hlist_out(p) else: self.vlist_out(p) self.cur_v = save_v + p.depth self.cur_h = left_edge elif isinstance(p, Box): rule_height = p.height rule_depth = p.depth rule_width = p.width if np.isinf(rule_width): rule_width = box.width rule_height += rule_depth if rule_height > 0 and rule_depth > 0: self.cur_v += rule_height p.render(self.cur_h + self.off_h, self.cur_v + self.off_v, rule_width, rule_height) elif isinstance(p, Glue): glue_spec = p.glue_spec rule_height = glue_spec.width - cur_g if glue_sign != 0: # normal if glue_sign == 1: # stretching if glue_spec.stretch_order == glue_order: cur_glue += glue_spec.stretch cur_g = round(clamp(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 self.cur_v += rule_height elif isinstance(p, Char): raise RuntimeError( "Internal mathtext error: Char node found in vlist") self.cur_s -= 1 ship = Ship() ############################################################################## # PARSER def Error(msg): """ Helper class to raise parser errors. """ def raise_error(s, loc, toks): raise ParseFatalException(s, loc, msg) empty = Empty() empty.setParseAction(raise_error) return empty class Parser(object): """ This is the pyparsing-based parser for math expressions. It actually parses full strings *containing* math expressions, in that raw text may also appear outside of pairs of ``$``. The grammar is based directly on that in TeX, though it cuts a few corners. """ _math_style_dict = dict(displaystyle=0, textstyle=1, scriptstyle=2, scriptscriptstyle=3) _binary_operators = set(''' + * - \\pm \\sqcap \\rhd \\mp \\sqcup \\unlhd \\times \\vee \\unrhd \\div \\wedge \\oplus \\ast \\setminus \\ominus \\star \\wr \\otimes \\circ \\diamond \\oslash \\bullet \\bigtriangleup \\odot \\cdot \\bigtriangledown \\bigcirc \\cap \\triangleleft \\dagger \\cup \\triangleright \\ddagger \\uplus \\lhd \\amalg'''.split()) _relation_symbols = set(''' = < > : \\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 \\dotplus \\doteqdot'''.split()) _arrow_symbols = set(''' \\leftarrow \\longleftarrow \\uparrow \\Leftarrow \\Longleftarrow \\Uparrow \\rightarrow \\longrightarrow \\downarrow \\Rightarrow \\Longrightarrow \\Downarrow \\leftrightarrow \\longleftrightarrow \\updownarrow \\Leftrightarrow \\Longleftrightarrow \\Updownarrow \\mapsto \\longmapsto \\nearrow \\hookleftarrow \\hookrightarrow \\searrow \\leftharpoonup \\rightharpoonup \\swarrow \\leftharpoondown \\rightharpoondown \\nwarrow \\rightleftharpoons \\leadsto'''.split()) _spaced_symbols = _binary_operators | _relation_symbols | _arrow_symbols _punctuation_symbols = set(r', ; . ! \ldotp \cdotp'.split()) _overunder_symbols = set(r''' \sum \prod \coprod \bigcap \bigcup \bigsqcup \bigvee \bigwedge \bigodot \bigotimes \bigoplus \biguplus '''.split()) _overunder_functions = set( "lim liminf limsup sup max min".split()) _dropsub_symbols = set(r'''\int \oint'''.split()) _fontnames = set( "rm cal it tt sf bf default bb frak circled scr regular".split()) _function_names = set(""" arccos csc ker min arcsin deg lg Pr arctan det lim sec arg dim liminf sin cos exp limsup sinh cosh gcd ln sup cot hom log tan coth inf max tanh""".split()) _ambi_delim = set(""" | \\| / \\backslash \\uparrow \\downarrow \\updownarrow \\Uparrow \\Downarrow \\Updownarrow . \\vert \\Vert \\\\|""".split()) _left_delim = set(r"( [ \{ < \lfloor \langle \lceil".split()) _right_delim = set(r") ] \} > \rfloor \rangle \rceil".split()) def __init__(self): p = types.SimpleNamespace() # All forward declarations are here p.accent = Forward() p.ambi_delim = Forward() p.apostrophe = Forward() p.auto_delim = Forward() p.binom = Forward() p.bslash = Forward() p.c_over_c = Forward() p.customspace = Forward() p.end_group = Forward() p.float_literal = Forward() p.font = Forward() p.frac = Forward() p.dfrac = Forward() p.function = Forward() p.genfrac = Forward() p.group = Forward() p.int_literal = Forward() p.latexfont = Forward() p.lbracket = Forward() p.left_delim = Forward() p.lbrace = Forward() p.main = Forward() p.math = Forward() p.math_string = Forward() p.non_math = Forward() p.operatorname = Forward() p.overline = Forward() p.placeable = Forward() p.rbrace = Forward() p.rbracket = Forward() p.required_group = Forward() p.right_delim = Forward() p.right_delim_safe = Forward() p.simple = Forward() p.simple_group = Forward() p.single_symbol = Forward() p.snowflake = Forward() p.space = Forward() p.sqrt = Forward() p.stackrel = Forward() p.start_group = Forward() p.subsuper = Forward() p.subsuperop = Forward() p.symbol = Forward() p.symbol_name = Forward() p.token = Forward() p.unknown_symbol = Forward() # Set names on everything -- very useful for debugging for key, val in vars(p).items(): if not key.startswith('_'): val.setName(key) p.float_literal <<= Regex(r"[-+]?([0-9]+\.?[0-9]*|\.[0-9]+)") p.int_literal <<= Regex("[-+]?[0-9]+") p.lbrace <<= Literal('{').suppress() p.rbrace <<= Literal('}').suppress() p.lbracket <<= Literal('[').suppress() p.rbracket <<= Literal(']').suppress() p.bslash <<= Literal('\\') p.space <<= oneOf(list(self._space_widths)) p.customspace <<= ( Suppress(Literal(r'\hspace')) - ((p.lbrace + p.float_literal + p.rbrace) | Error(r"Expected \hspace{n}")) ) unicode_range = "\U00000080-\U0001ffff" p.single_symbol <<= Regex( r"([a-zA-Z0-9 +\-*/<>=:,.;!\?&'@()\[\]|%s])|(\\[%%${}\[\]_|])" % unicode_range) p.snowflake <<= Suppress(p.bslash) + oneOf(self._snowflake) p.symbol_name <<= ( Combine(p.bslash + oneOf(list(tex2uni))) + FollowedBy(Regex("[^A-Za-z]").leaveWhitespace() | StringEnd()) ) p.symbol <<= (p.single_symbol | p.symbol_name).leaveWhitespace() p.apostrophe <<= Regex("'+") p.c_over_c <<= ( Suppress(p.bslash) + oneOf(list(self._char_over_chars)) ) p.accent <<= Group( Suppress(p.bslash) + oneOf([*self._accent_map, *self._wide_accents]) - p.placeable ) p.function <<= ( Suppress(p.bslash) + oneOf(list(self._function_names)) ) p.start_group <<= Optional(p.latexfont) + p.lbrace p.end_group <<= p.rbrace.copy() p.simple_group <<= Group(p.lbrace + ZeroOrMore(p.token) + p.rbrace) p.required_group<<= Group(p.lbrace + OneOrMore(p.token) + p.rbrace) p.group <<= Group( p.start_group + ZeroOrMore(p.token) + p.end_group ) p.font <<= Suppress(p.bslash) + oneOf(list(self._fontnames)) p.latexfont <<= ( Suppress(p.bslash) + oneOf(['math' + x for x in self._fontnames]) ) p.frac <<= Group( Suppress(Literal(r"\frac")) - ((p.required_group + p.required_group) | Error(r"Expected \frac{num}{den}")) ) p.dfrac <<= Group( Suppress(Literal(r"\dfrac")) - ((p.required_group + p.required_group) | Error(r"Expected \dfrac{num}{den}")) ) p.stackrel <<= Group( Suppress(Literal(r"\stackrel")) - ((p.required_group + p.required_group) | Error(r"Expected \stackrel{num}{den}")) ) p.binom <<= Group( Suppress(Literal(r"\binom")) - ((p.required_group + p.required_group) | Error(r"Expected \binom{num}{den}")) ) p.ambi_delim <<= oneOf(list(self._ambi_delim)) p.left_delim <<= oneOf(list(self._left_delim)) p.right_delim <<= oneOf(list(self._right_delim)) p.right_delim_safe <<= oneOf([*(self._right_delim - {'}'}), r'\}']) p.genfrac <<= Group( Suppress(Literal(r"\genfrac")) - (( (p.lbrace + Optional(p.ambi_delim | p.left_delim, default='') + p.rbrace) + (p.lbrace + Optional(p.ambi_delim | p.right_delim_safe, default='') + p.rbrace) + (p.lbrace + p.float_literal + p.rbrace) + p.simple_group + p.required_group + p.required_group) | Error("Expected " r"\genfrac{ldelim}{rdelim}{rulesize}{style}{num}{den}")) ) p.sqrt <<= Group( Suppress(Literal(r"\sqrt")) - ((Optional(p.lbracket + p.int_literal + p.rbracket, default=None) + p.required_group) | Error("Expected \\sqrt{value}")) ) p.overline <<= Group( Suppress(Literal(r"\overline")) - (p.required_group | Error("Expected \\overline{value}")) ) p.unknown_symbol<<= Combine(p.bslash + Regex("[A-Za-z]*")) p.operatorname <<= Group( Suppress(Literal(r"\operatorname")) - ((p.lbrace + ZeroOrMore(p.simple | p.unknown_symbol) + p.rbrace) | Error("Expected \\operatorname{value}")) ) p.placeable <<= ( p.snowflake # Must be before accent so named symbols that are # prefixed with an accent name work | p.accent # Must be before symbol as all accents are symbols | p.symbol # Must be third to catch all named symbols and single # chars not in a group | p.c_over_c | p.function | p.group | p.frac | p.dfrac | p.stackrel | p.binom | p.genfrac | p.sqrt | p.overline | p.operatorname ) p.simple <<= ( p.space | p.customspace | p.font | p.subsuper ) p.subsuperop <<= oneOf(["_", "^"]) p.subsuper <<= Group( (Optional(p.placeable) + OneOrMore(p.subsuperop - p.placeable) + Optional(p.apostrophe)) | (p.placeable + Optional(p.apostrophe)) | p.apostrophe ) p.token <<= ( p.simple | p.auto_delim | p.unknown_symbol # Must be last ) p.auto_delim <<= ( Suppress(Literal(r"\left")) - ((p.left_delim | p.ambi_delim) | Error("Expected a delimiter")) + Group(ZeroOrMore(p.simple | p.auto_delim)) + Suppress(Literal(r"\right")) - ((p.right_delim | p.ambi_delim) | Error("Expected a delimiter")) ) 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 actions for key, val in vars(p).items(): if not key.startswith('_'): if hasattr(self, key): val.setParseAction(getattr(self, key)) self._expression = p.main self._math_expression = p.math def parse(self, s, fonts_object, fontsize, dpi): """ Parse expression *s* using the given *fonts_object* for output, at the given *fontsize* and *dpi*. Returns the parse tree of :class:`Node` instances. """ self._state_stack = [ self.State(fonts_object, 'default', 'rm', fontsize, dpi)] self._em_width_cache = {} try: result = self._expression.parseString(s) except ParseBaseException as err: raise ValueError("\n".join(["", err.line, " " * (err.column - 1) + "^", str(err)])) self._state_stack = None self._em_width_cache = {} self._expression.resetCache() return result[0] # The state of the parser is maintained in a stack. Upon # entering and leaving a group { } or math/non-math, the stack # is pushed and popped accordingly. The current state always # exists in the top element of the stack. class State(object): """ Stores the state of the parser. States are pushed and popped from a stack as necessary, and the "current" state is always at the top of the stack. """ def __init__(self, font_output, font, font_class, fontsize, dpi): self.font_output = font_output self._font = font self.font_class = font_class self.fontsize = fontsize self.dpi = dpi def copy(self): return Parser.State( self.font_output, self.font, self.font_class, self.fontsize, self.dpi) @property def font(self): return self._font @font.setter def font(self, name): if name == "circled": cbook.warn_deprecated( "3.1", name="\\mathcircled", obj_type="mathtext command", alternative="unicode characters (e.g. '\\N{CIRCLED LATIN " "CAPITAL LETTER A}' or '\\u24b6')") if name in ('rm', 'it', 'bf'): self.font_class = name self._font = name def get_state(self): """ Get the current :class:`State` of the parser. """ return self._state_stack[-1] def pop_state(self): """ Pop a :class:`State` off of the stack. """ self._state_stack.pop() def push_state(self): """ Push a new :class:`State` onto the stack which is just a copy of the current state. """ self._state_stack.append(self.get_state().copy()) def main(self, s, loc, toks): return [Hlist(toks)] def math_string(self, s, loc, toks): return self._math_expression.parseString(toks[0][1:-1]) def math(self, s, loc, toks): hlist = Hlist(toks) self.pop_state() return [hlist] def non_math(self, s, loc, toks): s = toks[0].replace(r'\$', '$') symbols = [Char(c, self.get_state(), math=False) for c in s] hlist = Hlist(symbols) # We're going into math now, so set font to 'it' self.push_state() self.get_state().font = rcParams['mathtext.default'] return [hlist] def _make_space(self, percentage): # All spaces are relative to em width state = self.get_state() key = (state.font, state.fontsize, state.dpi) width = self._em_width_cache.get(key) if width is None: metrics = state.font_output.get_metrics( state.font, rcParams['mathtext.default'], 'm', state.fontsize, state.dpi) width = metrics.advance self._em_width_cache[key] = width return Kern(width * percentage) _space_widths = { r'\,' : 0.16667, # 3/18 em = 3 mu r'\thinspace' : 0.16667, # 3/18 em = 3 mu r'\/' : 0.16667, # 3/18 em = 3 mu r'\>' : 0.22222, # 4/18 em = 4 mu r'\:' : 0.22222, # 4/18 em = 4 mu r'\;' : 0.27778, # 5/18 em = 5 mu r'\ ' : 0.33333, # 6/18 em = 6 mu r'~' : 0.33333, # 6/18 em = 6 mu, nonbreakable r'\enspace' : 0.5, # 9/18 em = 9 mu r'\quad' : 1, # 1 em = 18 mu r'\qquad' : 2, # 2 em = 36 mu r'\!' : -0.16667, # -3/18 em = -3 mu } def space(self, s, loc, toks): assert len(toks)==1 num = self._space_widths[toks[0]] box = self._make_space(num) return [box] def customspace(self, s, loc, toks): return [self._make_space(float(toks[0]))] def symbol(self, s, loc, toks): c = toks[0] try: char = Char(c, self.get_state()) except ValueError: raise ParseFatalException(s, loc, "Unknown symbol: %s" % c) if c in self._spaced_symbols: # iterate until we find previous character, needed for cases # such as ${ -2}$, $ -2$, or $ -2$. prev_char = next((c for c in s[:loc][::-1] if c != ' '), '') # Binary operators at start of string should not be spaced if (c in self._binary_operators and (len(s[:loc].split()) == 0 or prev_char == '{' or prev_char in self._left_delim)): 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: # Do not space commas between brackets if c == ',': prev_char = next((c for c in s[:loc][::-1] if c != ' '), '') next_char = next((c for c in s[loc + 1:] if c != ' '), '') if prev_char == '{' and next_char == '}': return [char] # Do not space dots as decimal separators if c == '.' and s[loc - 1].isdigit() and s[loc + 1].isdigit(): return [char] else: return [Hlist([char, self._make_space(0.2)], do_kern = True)] return [char] snowflake = symbol def unknown_symbol(self, s, loc, toks): c = toks[0] raise ParseFatalException(s, loc, "Unknown symbol: %s" % c) _char_over_chars = { # The first 2 entries in the tuple are (font, char, sizescale) for # the two symbols under and over. The third element is the space # (in multiples of underline height) r'AA': (('it', 'A', 1.0), (None, '\\circ', 0.5), 0.0), } def c_over_c(self, s, loc, toks): sym = toks[0] state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) under_desc, over_desc, space = \ self._char_over_chars.get(sym, (None, None, 0.0)) if under_desc is None: raise ParseFatalException("Error parsing symbol") over_state = state.copy() if over_desc[0] is not None: over_state.font = over_desc[0] over_state.fontsize *= over_desc[2] over = Accent(over_desc[1], over_state) under_state = state.copy() if under_desc[0] is not None: under_state.font = under_desc[0] under_state.fontsize *= under_desc[2] under = Char(under_desc[1], under_state) width = max(over.width, under.width) over_centered = HCentered([over]) over_centered.hpack(width, 'exactly') under_centered = HCentered([under]) under_centered.hpack(width, 'exactly') return Vlist([ over_centered, Vbox(0., thickness * space), under_centered ]) _accent_map = { r'hat' : r'\circumflexaccent', r'breve' : r'\combiningbreve', r'bar' : r'\combiningoverline', r'grave' : r'\combininggraveaccent', r'acute' : r'\combiningacuteaccent', r'tilde' : r'\combiningtilde', r'dot' : r'\combiningdotabove', r'ddot' : r'\combiningdiaeresis', 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()) # make a lambda and call it to get the namespace right _snowflake = (lambda am: [p for p in tex2uni if any(p.startswith(a) and a != p for a in am)] ) (set(_accent_map)) def accent(self, s, loc, toks): assert len(toks)==1 state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) if len(toks[0]) != 2: raise ParseFatalException("Error parsing accent") accent, sym = toks[0] if accent in self._wide_accents: accent_box = AutoWidthChar( '\\' + accent, sym.width, state, char_class=Accent) else: accent_box = Accent(self._accent_map[accent], state) if accent == 'mathring': accent_box.shrink() accent_box.shrink() centered = HCentered([Hbox(sym.width / 4.0), accent_box]) centered.hpack(sym.width, 'exactly') return Vlist([ centered, Vbox(0., thickness * 2.0), Hlist([sym]) ]) def function(self, s, loc, toks): self.push_state() state = self.get_state() state.font = 'rm' hlist = Hlist([Char(c, state) for c in toks[0]]) self.pop_state() hlist.function_name = toks[0] return hlist def operatorname(self, s, loc, toks): self.push_state() state = self.get_state() state.font = 'rm' # Change the font of Chars, but leave Kerns alone for c in toks[0]: if isinstance(c, Char): c.font = 'rm' c._update_metrics() self.pop_state() return Hlist(toks[0]) def start_group(self, s, loc, toks): self.push_state() # Deal with LaTeX-style font tokens if len(toks): self.get_state().font = toks[0][4:] return [] def group(self, s, loc, toks): grp = Hlist(toks[0]) return [grp] required_group = simple_group = group def end_group(self, s, loc, toks): self.pop_state() return [] def font(self, s, loc, toks): assert len(toks)==1 name = toks[0] self.get_state().font = name return [] def is_overunder(self, nucleus): if isinstance(nucleus, Char): return nucleus.c in self._overunder_symbols elif isinstance(nucleus, Hlist) and hasattr(nucleus, 'function_name'): return nucleus.function_name in self._overunder_functions return False def is_dropsub(self, nucleus): if isinstance(nucleus, Char): return nucleus.c in self._dropsub_symbols return False def is_slanted(self, nucleus): if isinstance(nucleus, Char): return nucleus.is_slanted() return False def is_between_brackets(self, s, loc): return False def subsuper(self, s, loc, toks): assert len(toks)==1 nucleus = None sub = None super = None # Pick all of the apostrophes out, including first apostrophes that # have been parsed as characters napostrophes = 0 new_toks = [] for tok in toks[0]: if isinstance(tok, str) and tok not in ('^', '_'): napostrophes += len(tok) elif isinstance(tok, Char) and tok.c == "'": napostrophes += 1 else: new_toks.append(tok) toks = new_toks if len(toks) == 0: assert napostrophes nucleus = Hbox(0.0) elif len(toks) == 1: if not napostrophes: return toks[0] # .asList() else: nucleus = toks[0] elif len(toks) in (2, 3): # single subscript or superscript nucleus = toks[0] if len(toks) == 3 else Hbox(0.0) op, next = toks[-2:] if op == '_': sub = next else: super = next elif len(toks) in (4, 5): # subscript and superscript nucleus = toks[0] if len(toks) == 5 else Hbox(0.0) op1, next1, op2, next2 = toks[-4:] if op1 == op2: if op1 == '_': raise ParseFatalException("Double subscript") else: raise ParseFatalException("Double superscript") if op1 == '_': sub = next1 super = next2 else: super = next1 sub = next2 else: raise ParseFatalException( "Subscript/superscript sequence is too long. " "Use braces { } to remove ambiguity.") state = self.get_state() rule_thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) xHeight = state.font_output.get_xheight( state.font, state.fontsize, state.dpi) if napostrophes: if super is None: super = Hlist([]) for i in range(napostrophes): super.children.extend(self.symbol(s, loc, ['\\prime'])) # kern() and hpack() needed to get the metrics right after # extending super.kern() super.hpack() # Handle over/under symbols, such as sum or integral if self.is_overunder(nucleus): vlist = [] shift = 0. width = nucleus.width if super is not None: super.shrink() width = max(width, super.width) if sub is not None: sub.shrink() width = max(width, sub.width) if super is not None: hlist = HCentered([super]) hlist.hpack(width, 'exactly') vlist.extend([hlist, Kern(rule_thickness * 3.0)]) hlist = HCentered([nucleus]) hlist.hpack(width, 'exactly') vlist.append(hlist) if sub is not None: hlist = HCentered([sub]) hlist.hpack(width, 'exactly') vlist.extend([Kern(rule_thickness * 3.0), hlist]) shift = hlist.height vlist = Vlist(vlist) vlist.shift_amount = shift + nucleus.depth result = Hlist([vlist]) return [result] # We remove kerning on the last character for consistency (otherwise # it will compute kerning based on non-shrunk characters and may put # them too close together when superscripted) # We change the width of the last character to match the advance to # consider some fonts with weird metrics: e.g. stix's f has a width of # 7.75 and a kerning of -4.0 for an advance of 3.72, and we want to put # the superscript at the advance last_char = nucleus if isinstance(nucleus, Hlist): new_children = nucleus.children if len(new_children): # remove last kern if (isinstance(new_children[-1], Kern) and hasattr(new_children[-2], '_metrics')): new_children = new_children[:-1] last_char = new_children[-1] if hasattr(last_char, '_metrics'): last_char.width = last_char._metrics.advance # create new Hlist without kerning nucleus = Hlist(new_children, do_kern=False) else: if isinstance(nucleus, Char): last_char.width = last_char._metrics.advance nucleus = Hlist([nucleus]) # Handle regular sub/superscripts constants = _get_font_constant_set(state) lc_height = last_char.height lc_baseline = 0 if self.is_dropsub(last_char): lc_baseline = last_char.depth # Compute kerning for sub and super superkern = constants.delta * xHeight subkern = constants.delta * xHeight if self.is_slanted(last_char): superkern += constants.delta * xHeight superkern += (constants.delta_slanted * (lc_height - xHeight * 2. / 3.)) if self.is_dropsub(last_char): subkern = (3 * constants.delta - constants.delta_integral) * lc_height superkern = (3 * constants.delta + constants.delta_integral) * lc_height else: subkern = 0 if super is None: # node757 x = Hlist([Kern(subkern), sub]) x.shrink() if self.is_dropsub(last_char): shift_down = lc_baseline + constants.subdrop * xHeight else: shift_down = constants.sub1 * xHeight x.shift_amount = shift_down else: x = Hlist([Kern(superkern), super]) x.shrink() if self.is_dropsub(last_char): shift_up = lc_height - constants.subdrop * xHeight else: shift_up = constants.sup1 * xHeight if sub is None: x.shift_amount = -shift_up else: # Both sub and superscript y = Hlist([Kern(subkern), sub]) y.shrink() if self.is_dropsub(last_char): shift_down = lc_baseline + constants.subdrop * xHeight else: shift_down = constants.sub2 * xHeight # If sub and superscript collide, move super up clr = (2.0 * rule_thickness - ((shift_up - x.depth) - (y.height - shift_down))) if clr > 0.: shift_up += clr x = Vlist([ x, Kern((shift_up - x.depth) - (y.height - shift_down)), y]) x.shift_amount = shift_down if not self.is_dropsub(last_char): x.width += constants.script_space * xHeight result = Hlist([nucleus, x]) return [result] def _genfrac(self, ldelim, rdelim, rule, style, num, den): state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) rule = float(rule) # If style != displaystyle == 0, shrink the num and den if style != self._math_style_dict['displaystyle']: 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.font_output.get_metrics( state.font, rcParams['mathtext.default'], '=', state.fontsize, state.dpi) shift = (cden.height - ((metrics.ymax + metrics.ymin) / 2 - thickness * 3.0)) vlist.shift_amount = shift result = [Hlist([vlist, Hbox(thickness * 2.)])] if ldelim or rdelim: if ldelim == '': ldelim = '.' if rdelim == '': rdelim = '.' return self._auto_sized_delimiter(ldelim, result, rdelim) return result def genfrac(self, s, loc, toks): assert len(toks) == 1 assert len(toks[0]) == 6 return self._genfrac(*tuple(toks[0])) def frac(self, s, loc, toks): assert len(toks) == 1 assert len(toks[0]) == 2 state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) num, den = toks[0] return self._genfrac('', '', thickness, self._math_style_dict['textstyle'], num, den) def dfrac(self, s, loc, toks): assert len(toks) == 1 assert len(toks[0]) == 2 state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) num, den = toks[0] return self._genfrac('', '', thickness, self._math_style_dict['displaystyle'], num, den) @cbook.deprecated("3.1", obj_type="mathtext command", alternative=r"\genfrac") def stackrel(self, s, loc, toks): assert len(toks) == 1 assert len(toks[0]) == 2 num, den = toks[0] return self._genfrac('', '', 0.0, self._math_style_dict['textstyle'], num, den) def binom(self, s, loc, toks): assert len(toks) == 1 assert len(toks[0]) == 2 num, den = toks[0] return self._genfrac('(', ')', 0.0, self._math_style_dict['textstyle'], num, den) def sqrt(self, s, loc, toks): root, body = toks[0] state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) # Determine the height of the body, and add a little extra to # the height so it doesn't seem cramped height = body.height - body.shift_amount + thickness * 5.0 depth = body.depth + body.shift_amount check = AutoHeightChar(r'\__sqrt__', height, depth, state, always=True) height = check.height - check.shift_amount depth = check.depth + check.shift_amount # Put a little extra space to the left and right of the body padded_body = Hlist([Hbox(thickness * 2.0), body, Hbox(thickness * 2.0)]) rightside = Vlist([Hrule(state), Fill(), padded_body]) # Stretch the glue between the hrule and the body rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0), '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 root is None: root = Box(check.width * 0.5, 0., 0.) else: root = Hlist([Char(x, state) for x in root]) root.shrink() root.shrink() root_vlist = Vlist([Hlist([root])]) root_vlist.shift_amount = -height * 0.6 hlist = Hlist([root_vlist, # Root # Negative kerning to put root over tick Kern(-check.width * 0.5), check, # Check rightside]) # Body return [hlist] def overline(self, s, loc, toks): assert len(toks)==1 assert len(toks[0])==1 body = toks[0][0] state = self.get_state() thickness = state.font_output.get_underline_thickness( state.font, state.fontsize, state.dpi) height = body.height - body.shift_amount + thickness * 3.0 depth = body.depth + body.shift_amount # Place overline above body rightside = Vlist([Hrule(state), Fill(), Hlist([body])]) # Stretch the glue between the hrule and the body rightside.vpack(height + (state.fontsize * state.dpi) / (100.0 * 12.0), 'exactly', depth) hlist = Hlist([rightside]) return [hlist] def _auto_sized_delimiter(self, front, middle, back): state = self.get_state() if len(middle): height = max(x.height for x in middle) depth = max(x.depth for x in middle) factor = None else: height = 0 depth = 0 factor = 1.0 parts = [] # \left. and \right. aren't supposed to produce any symbols if front != '.': parts.append( AutoHeightChar(front, height, depth, state, factor=factor)) parts.extend(middle) if back != '.': parts.append( AutoHeightChar(back, height, depth, state, factor=factor)) hlist = Hlist(parts) return hlist def auto_delim(self, s, loc, toks): front, middle, back = toks return self._auto_sized_delimiter(front, middle.asList(), back) ############################################################################## # MAIN class MathTextParser(object): _parser = None _backend_mapping = { 'bitmap': MathtextBackendBitmap, 'agg' : MathtextBackendAgg, 'ps' : MathtextBackendPs, 'pdf' : MathtextBackendPdf, 'svg' : MathtextBackendSvg, 'path' : MathtextBackendPath, 'cairo' : MathtextBackendCairo, 'macosx': MathtextBackendAgg, } _font_type_mapping = { 'cm' : BakomaFonts, 'dejavuserif' : DejaVuSerifFonts, 'dejavusans' : DejaVuSansFonts, 'stix' : StixFonts, 'stixsans' : StixSansFonts, 'custom' : UnicodeFonts } def __init__(self, output): """ Create a MathTextParser for the given backend *output*. """ self._output = output.lower() @functools.lru_cache(50) def parse(self, s, dpi = 72, prop = None): """ Parse the given math expression *s* at the given *dpi*. If *prop* is provided, it is a :class:`~matplotlib.font_manager.FontProperties` object specifying the "default" font to use in the math expression, used for all non-math text. The results are cached, so multiple calls to :meth:`parse` with the same expression should be fast. """ if prop is None: prop = FontProperties() if self._output == 'ps' and rcParams['ps.useafm']: font_output = StandardPsFonts(prop) else: backend = self._backend_mapping[self._output]() fontset = rcParams['mathtext.fontset'].lower() cbook._check_in_list(self._font_type_mapping, fontset=fontset) fontset_class = self._font_type_mapping[fontset] font_output = fontset_class(prop, backend) fontsize = prop.get_size_in_points() # This is a class variable so we don't rebuild the parser # with each request. if self._parser is None: self.__class__._parser = Parser() box = self._parser.parse(s, font_output, fontsize, dpi) font_output.set_canvas_size(box.width, box.height, box.depth) return font_output.get_results(box) def to_mask(self, texstr, dpi=120, fontsize=14): r""" Parameters ---------- texstr : str A valid mathtext string, e.g., r'IQ: $\sigma_i=15$'. dpi : float The dots-per-inch setting used to render the text. fontsize : int The font size in points Returns ------- array : 2D uint8 alpha Mask array of rasterized tex. depth : int Offset of the baseline from the bottom of the image, in pixels. """ assert self._output == "bitmap" prop = FontProperties(size=fontsize) ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop) x = ftimage.as_array() return x, depth def to_rgba(self, texstr, color='black', dpi=120, fontsize=14): r""" Parameters ---------- texstr : str A valid mathtext string, e.g., r'IQ: $\sigma_i=15$'. color : color The text color. dpi : float The dots-per-inch setting used to render the text. fontsize : int The font size in points. Returns ------- array : (M, N, 4) array RGBA color values of rasterized tex, colorized with *color*. depth : int Offset of the baseline from the bottom of the image, in pixels. """ x, depth = self.to_mask(texstr, dpi=dpi, fontsize=fontsize) r, g, b, a = mcolors.to_rgba(color) RGBA = np.zeros((x.shape[0], x.shape[1], 4), dtype=np.uint8) RGBA[:, :, 0] = 255 * r RGBA[:, :, 1] = 255 * g RGBA[:, :, 2] = 255 * b RGBA[:, :, 3] = x return RGBA, depth def to_png(self, filename, texstr, color='black', dpi=120, fontsize=14): r""" Render a tex expression to a PNG file. Parameters ---------- filename A writable filename or fileobject. texstr : str A valid mathtext string, e.g., r'IQ: $\sigma_i=15$'. color : color The text color. dpi : float The dots-per-inch setting used to render the text. fontsize : int The font size in points. Returns ------- depth : int Offset of the baseline from the bottom of the image, in pixels. """ from matplotlib import _png rgba, depth = self.to_rgba( texstr, color=color, dpi=dpi, fontsize=fontsize) _png.write_png(rgba, filename) return depth def get_depth(self, texstr, dpi=120, fontsize=14): r""" Parameters ---------- texstr : str A valid mathtext string, e.g., r'IQ: $\sigma_i=15$'. dpi : float The dots-per-inch setting used to render the text. Returns ------- depth : int Offset of the baseline from the bottom of the image, in pixels. """ assert self._output=="bitmap" prop = FontProperties(size=fontsize) ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop) return depth def math_to_image(s, filename_or_obj, prop=None, dpi=None, format=None): """ Given a math expression, renders it in a closely-clipped bounding box to an image file. *s* A math expression. The math portion should be enclosed in dollar signs. *filename_or_obj* A filepath or writable file-like object to write the image data to. *prop* If provided, a FontProperties() object describing the size and style of the text. *dpi* Override the output dpi, otherwise use the default associated with the output format. *format* The output format, e.g., 'svg', 'pdf', 'ps' or 'png'. If not provided, will be deduced from the filename. """ from matplotlib import figure # backend_agg supports all of the core output formats from matplotlib.backends import backend_agg if prop is None: prop = FontProperties() parser = MathTextParser('path') width, height, depth, _, _ = parser.parse(s, dpi=72, prop=prop) fig = figure.Figure(figsize=(width / 72.0, height / 72.0)) fig.text(0, depth/height, s, fontproperties=prop) backend_agg.FigureCanvasAgg(fig) fig.savefig(filename_or_obj, dpi=dpi, format=format) return depth