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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. 

""" 

 

import functools 

from io import StringIO 

import os 

import types 

import unicodedata 

import warnings 

 

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 _png, 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) 

 

#################### 

 

 

 

############################################################################## 

# FONTS 

 

def get_unicode_index(symbol, math=True): 

"""get_unicode_index(symbol, [bool]) -> integer 

 

Return the integer index (from the Unicode table) of symbol. *symbol* 

can be a single unicode character, a TeX command (i.e. r'\\pi'), or a 

Type1 symbol name (i.e. 'phi'). 

If math is False, the current symbol should be treated as a non-math symbol. 

""" 

# 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. 

""" 

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.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. 

""" 

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.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) / 64.0 

return Fonts.get_kern(self, font1, fontclass1, sym1, fontsize1, 

font2, fontclass2, sym2, fontsize2, dpi) 

 

class BakomaFonts(TruetypeFonts): 

""" 

Use the Bakoma TrueType fonts for rendering. 

 

Symbols are strewn about a number of font files, each of which has 

its own proprietary 8-bit encoding. 

""" 

_fontmap = { 'cal' : 'cmsy10', 

'rm' : 'cmr10', 

'tt' : 'cmtt10', 

'it' : 'cmmi10', 

'bf' : 'cmb10', 

'sf' : 'cmss10', 

'ex' : 'cmex10' 

} 

 

def __init__(self, *args, **kwargs): 

self._stix_fallback = StixFonts(*args, **kwargs) 

 

TruetypeFonts.__init__(self, *args, **kwargs) 

self.fontmap = {} 

for key, val in self._fontmap.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('?') 

warnings.warn( 

"No TeX to unicode mapping for {!a}.".format(sym), 

MathTextWarning) 

 

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': 

if uniindex < 0x10000: 

unistring = chr(uniindex) 

if (not unicodedata.category(unistring)[0] == "L" 

or unicodedata.name(unistring).startswith("GREEK CAPITAL")): 

new_fontname = 'rm' 

 

slanted = (new_fontname == 'it') or sym in self._slanted_symbols 

found_symbol = False 

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): 

warnings.warn( 

"Substituting with a symbol from Computer Modern.", 

MathTextWarning) 

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) 

warnings.warn( 

"Font {!r} does not have a glyph for {!a} [U+{:x}], " 

"substituting with a dummy symbol.".format( 

new_fontname, sym, uniindex), 

MathTextWarning) 

fontname = 'rm' 

new_fontname = fontname 

font = self._get_font(fontname) 

uniindex = 0xA4 # currency character, 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 

uniindex >= 0xe000 and 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: 

warnings.warn( 

"No TeX to built-in Postscript mapping for {!r}".format(sym), 

MathTextWarning) 

 

slanted = (fontname == 'it') 

font = self._get_font(fontname) 

 

if found_symbol: 

try: 

symbol_name = font.get_name_char(glyph) 

except KeyError: 

warnings.warn( 

"No glyph in standard Postscript font {!r} for {!r}" 

.format(font.get_fontname(), sym), 

MathTextWarning) 

found_symbol = False 

 

if not found_symbol: 

glyph = sym = '?' 

num = ord(glyph) 

symbol_name = font.get_name_char(glyph) 

 

offset = 0 

 

scale = 0.001 * fontsize 

 

xmin, ymin, xmax, ymax = [val * scale 

for val in font.get_bbox_char(glyph)] 

metrics = 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): 

warnings.warn( 

"%s %s: %r" % (error_type, self.__class__.__name__, self), 

MathTextWarning) 

 

def shrink(self): 

for child in self.children: 

child.shrink() 

Box.shrink(self) 

if self.size < NUM_SIZE_LEVELS: 

self.shift_amount *= SHRINK_FACTOR 

self.glue_set *= SHRINK_FACTOR 

 

def grow(self): 

for child in self.children: 

child.grow() 

Box.grow(self) 

self.shift_amount *= GROW_FACTOR 

self.glue_set *= GROW_FACTOR 

 

class Hlist(List): 

""" 

A horizontal list of boxes. 

""" 

def __init__(self, elements, w=0., m='additional', do_kern=True): 

List.__init__(self, elements) 

if do_kern: 

self.kern() 

self.hpack() 

 

def kern(self): 

""" 

Insert :class:`Kern` nodes between :class:`Char` nodes to set 

kerning. The :class:`Char` nodes themselves determine the 

amount of kerning they need (in :meth:`~Char.get_kerning`), 

and this function just creates the linked list in the correct 

way. 

""" 

new_children = [] 

num_children = len(self.children) 

if num_children: 

for i in range(num_children): 

elem = self.children[i] 

if i < num_children - 1: 

next = self.children[i + 1] 

else: 

next = None 

 

new_children.append(elem) 

kerning_distance = elem.get_kerning(next) 

if kerning_distance != 0.: 

kern = Kern(kerning_distance) 

new_children.append(kern) 

self.children = new_children 

 

# This is a failed experiment to fake cross-font kerning. 

# def get_kerning(self, next): 

# if len(self.children) >= 2 and isinstance(self.children[-2], Char): 

# if isinstance(next, Char): 

# print "CASE A" 

# return self.children[-2].get_kerning(next) 

# elif isinstance(next, Hlist) and len(next.children) and isinstance(next.children[0], Char): 

# print "CASE B" 

# result = self.children[-2].get_kerning(next.children[0]) 

# print result 

# return result 

# return 0.0 

 

def hpack(self, w=0., m='additional'): 

""" 

The main duty of :meth:`hpack` is to compute the dimensions of 

the resulting boxes, and to adjust the glue if one of those 

dimensions is pre-specified. The computed sizes normally 

enclose all of the material inside the new box; but some items 

may stick out if negative glue is used, if the box is 

overfull, or if a ``\\vbox`` includes other boxes that have 

been shifted left. 

 

- *w*: specifies a width 

 

- *m*: is either 'exactly' or 'additional'. 

 

Thus, ``hpack(w, 'exactly')`` produces a box whose width is 

exactly *w*, while ``hpack(w, 'additional')`` yields a box 

whose width is the natural width plus *w*. The default values 

produce a box with the natural width. 

""" 

# I don't know why these get reset in TeX. Shift_amount is pretty 

# much useless if we do. 

#self.shift_amount = 0. 

h = 0. 

d = 0. 

x = 0. 

total_stretch = [0.] * 4 

total_shrink = [0.] * 4 

for p in self.children: 

if isinstance(p, Char): 

x += p.width 

h = max(h, p.height) 

d = max(d, p.depth) 

elif isinstance(p, Box): 

x += p.width 

if not 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 = np.round(clamp(float(box.glue_set) * cur_glue)) 

elif glue_spec.shrink_order == glue_order: 

cur_glue += glue_spec.shrink 

cur_g = np.round(clamp(float(box.glue_set) * cur_glue)) 

rule_width += cur_g 

self.cur_h += rule_width 

self.cur_s -= 1 

 

def vlist_out(self, box): 

cur_g = 0 

cur_glue = 0. 

glue_order = box.glue_order 

glue_sign = box.glue_sign 

self.cur_s += 1 

self.max_push = max(self.max_push, self.cur_s) 

left_edge = self.cur_h 

self.cur_v -= box.height 

top_edge = self.cur_v 

clamp = self.clamp 

 

for p in box.children: 

if isinstance(p, Kern): 

self.cur_v += p.width 

elif isinstance(p, List): 

if len(p.children) == 0: 

self.cur_v += p.height + p.depth 

else: 

self.cur_v += p.height 

self.cur_h = left_edge + p.shift_amount 

save_v = self.cur_v 

p.width = box.width 

if isinstance(p, Hlist): 

self.hlist_out(p) 

else: 

self.vlist_out(p) 

self.cur_v = save_v + p.depth 

self.cur_h = left_edge 

elif isinstance(p, Box): 

rule_height = p.height 

rule_depth = p.depth 

rule_width = p.width 

if 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 = np.round(clamp(float(box.glue_set) * cur_glue)) 

elif glue_spec.shrink_order == glue_order: # shrinking 

cur_glue += glue_spec.shrink 

cur_g = np.round(clamp(float(box.glue_set) * cur_glue)) 

rule_height += cur_g 

self.cur_v += rule_height 

elif isinstance(p, Char): 

raise RuntimeError("Internal mathtext error: Char node found in vlist") 

self.cur_s -= 1 

 

 

ship = Ship() 

 

############################################################################## 

# PARSER 

 

def Error(msg): 

""" 

Helper class to raise parser errors. 

""" 

def raise_error(s, loc, toks): 

raise ParseFatalException(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( 

r"lim liminf limsup sup max min".split()) 

 

_dropsub_symbols = set(r'''\int \oint'''.split()) 

 

_fontnames = set("rm cal it tt sf bf default bb frak circled scr regular".split()) 

 

_function_names = set(""" 

arccos csc ker min arcsin deg lg Pr arctan det lim sec arg dim 

liminf sin cos exp limsup sinh cosh gcd ln sup cot hom log tan 

coth inf max tanh""".split()) 

 

_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(r"Expected \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 # this needs to 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) 

 

def _get_font(self): 

return self._font 

def _set_font(self, name): 

if name in ('rm', 'it', 'bf'): 

self.font_class = name 

self._font = name 

font = property(_get_font, _set_font) 

 

def get_state(self): 

""" 

Get the current :class:`State` of the parser. 

""" 

return self._state_stack[-1] 

 

def pop_state(self): 

""" 

Pop a :class:`State` off of the stack. 

""" 

self._state_stack.pop() 

 

def push_state(self): 

""" 

Push a new :class:`State` onto the stack which is just a copy 

of the current state. 

""" 

self._state_stack.append(self.get_state().copy()) 

 

def 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'\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-shrinked 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) 

 

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'] 

fontset_class = self._font_type_mapping.get(fontset.lower()) 

if fontset_class is not None: 

font_output = fontset_class(prop, backend) 

else: 

raise ValueError( 

"mathtext.fontset must be either 'cm', 'dejavuserif', " 

"'dejavusans', 'stix', 'stixsans', or 'custom'") 

 

fontsize = prop.get_size_in_points() 

 

# This is a class variable so we don't rebuild the parser 

# with each request. 

if self._parser is None: 

self.__class__._parser = Parser() 

 

box = self._parser.parse(s, font_output, fontsize, dpi) 

font_output.set_canvas_size(box.width, box.height, box.depth) 

return font_output.get_results(box) 

 

def to_mask(self, texstr, dpi=120, fontsize=14): 

""" 

*texstr* 

A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$' 

 

*dpi* 

The dots-per-inch to render the text 

 

*fontsize* 

The font size in points 

 

Returns a tuple (*array*, *depth*) 

 

- *array* is an NxM uint8 alpha ubyte mask array of 

rasterized tex. 

 

- depth is the offset of the baseline from the bottom of the 

image in pixels. 

""" 

assert self._output == "bitmap" 

prop = FontProperties(size=fontsize) 

ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop) 

 

x = ftimage.as_array() 

return x, depth 

 

def to_rgba(self, texstr, color='black', dpi=120, fontsize=14): 

""" 

*texstr* 

A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$' 

 

*color* 

Any matplotlib color argument 

 

*dpi* 

The dots-per-inch to render the text 

 

*fontsize* 

The font size in points 

 

Returns a tuple (*array*, *depth*) 

 

- *array* is an NxM uint8 alpha ubyte mask array of 

rasterized tex. 

 

- depth is the offset of the baseline from the bottom of the 

image in pixels. 

""" 

x, depth = self.to_mask(texstr, dpi=dpi, fontsize=fontsize) 

 

r, g, b, 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): 

""" 

Writes a tex expression to a PNG file. 

 

Returns the offset of the baseline from the bottom of the 

image in pixels. 

 

*filename* 

A writable filename or fileobject 

 

*texstr* 

A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$' 

 

*color* 

A valid matplotlib color argument 

 

*dpi* 

The dots-per-inch to render the text 

 

*fontsize* 

The font size in points 

 

Returns the offset of the baseline from the bottom of the 

image in pixels. 

""" 

rgba, depth = self.to_rgba(texstr, color=color, dpi=dpi, fontsize=fontsize) 

_png.write_png(rgba, filename) 

return depth 

 

def get_depth(self, texstr, dpi=120, fontsize=14): 

""" 

Returns the offset of the baseline from the bottom of the 

image in pixels. 

 

*texstr* 

A valid mathtext string, e.g., r'IQ: $\\sigma_i=15$' 

 

*dpi* 

The dots-per-inch to render the text 

 

*fontsize* 

The font size in points 

""" 

assert self._output=="bitmap" 

prop = FontProperties(size=fontsize) 

ftimage, depth = self.parse(texstr, dpi=dpi, prop=prop) 

return depth 

 

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