Note
Click here to download the full example code
An introduction to writing mathematical expressions in Matplotlib.
You can use a subset TeX markup in any matplotlib text string by placing it inside a pair of dollar signs ($).
Note that you do not need to have TeX installed, since Matplotlib ships
its own TeX expression parser, layout engine, and fonts. The layout engine
is a fairly direct adaptation of the layout algorithms in Donald Knuth's
TeX, so the quality is quite good (matplotlib also provides a usetex
option for those who do want to call out to TeX to generate their text (see
Text rendering With LaTeX).
Any text element can use math text. You should use raw strings (precede the
quotes with an 'r'
), and surround the math text with dollar signs ($), as
in TeX. Regular text and mathtext can be interleaved within the same string.
Mathtext can use DejaVu Sans (default), DejaVu Serif, the Computer Modern fonts
(from (La)TeX), STIX fonts (with are designed
to blend well with Times), or a Unicode font that you provide. The mathtext
font can be selected with the customization variable mathtext.fontset
(see
Customizing Matplotlib with style sheets and rcParams)
Here is a simple example:
# plain text
plt.title('alpha > beta')
produces "alpha > beta".
Whereas this:
# math text
plt.title(r'$\alpha > \beta$')
produces "".
Note
Mathtext should be placed between a pair of dollar signs ($). To make it easy to display monetary values, e.g., "$100.00", if a single dollar sign is present in the entire string, it will be displayed verbatim as a dollar sign. This is a small change from regular TeX, where the dollar sign in non-math text would have to be escaped ('\$').
Note
While the syntax inside the pair of dollar signs ($) aims to be TeX-like, the text outside does not. In particular, characters such as:
# $ % & ~ _ ^ \ { } \( \) \[ \]
have special meaning outside of math mode in TeX. Therefore, these
characters will behave differently depending on the rcParam text.usetex
flag. See the usetex tutorial for more
information.
To make subscripts and superscripts, use the '_'
and '^'
symbols:
r'$\alpha_i > \beta_i$'
Some symbols automatically put their sub/superscripts under and over the operator. For example, to write the sum of from to , you could do:
r'$\sum_{i=0}^\infty x_i$'
Fractions, binomials, and stacked numbers can be created with the
\frac{}{}
, \binom{}{}
and \genfrac{}{}{}{}{}{}
commands,
respectively:
r'$\frac{3}{4} \binom{3}{4} \genfrac{}{}{0}{}{3}{4}$'
produces
Fractions can be arbitrarily nested:
r'$\frac{5 - \frac{1}{x}}{4}$'
produces
Note that special care needs to be taken to place parentheses and brackets around fractions. Doing things the obvious way produces brackets that are too small:
r'$(\frac{5 - \frac{1}{x}}{4})$'
The solution is to precede the bracket with \left
and \right
to inform
the parser that those brackets encompass the entire object.:
r'$\left(\frac{5 - \frac{1}{x}}{4}\right)$'
Radicals can be produced with the \sqrt[]{}
command. For example:
r'$\sqrt{2}$'
Any base can (optionally) be provided inside square brackets. Note that the base must be a simple expression, and can not contain layout commands such as fractions or sub/superscripts:
r'$\sqrt[3]{x}$'
The default font is italics for mathematical symbols.
Note
This default can be changed using the mathtext.default
rcParam. This is
useful, for example, to use the same font as regular non-math text for math
text, by setting it to regular
.
To change fonts, e.g., to write "sin" in a Roman font, enclose the text in a font command:
r'$s(t) = \mathcal{A}\mathrm{sin}(2 \omega t)$'
More conveniently, many commonly used function names that are typeset in a Roman font have shortcuts. So the expression above could be written as follows:
r'$s(t) = \mathcal{A}\sin(2 \omega t)$'
Here "s" and "t" are variable in italics font (default), "sin" is in Roman
font, and the amplitude "A" is in calligraphy font. Note in the example above
the calligraphy A
is squished into the sin
. You can use a spacing
command to add a little whitespace between them:
r's(t) = \mathcal{A}\/\sin(2 \omega t)'
The choices available with all fonts are:
Command Result \mathrm{Roman}
\mathit{Italic}
\mathtt{Typewriter}
\mathcal{CALLIGRAPHY}
When using the STIX fonts, you also have the choice of:
Command Result \mathbb{blackboard}
\mathrm{\mathbb{blackboard}}
\mathfrak{Fraktur}
\mathsf{sansserif}
\mathrm{\mathsf{sansserif}}
There are also three global "font sets" to choose from, which are
selected using the mathtext.fontset
parameter in matplotlibrc.
cm
: Computer Modern (TeX)
stix
: STIX (designed to blend well with Times)
stixsans
: STIX sans-serif
Additionally, you can use \mathdefault{...}
or its alias
\mathregular{...}
to use the font used for regular text outside of
mathtext. There are a number of limitations to this approach, most notably
that far fewer symbols will be available, but it can be useful to make math
expressions blend well with other text in the plot.
mathtext also provides a way to use custom fonts for math. This method is
fairly tricky to use, and should be considered an experimental feature for
patient users only. By setting the rcParam mathtext.fontset
to custom
,
you can then set the following parameters, which control which font file to use
for a particular set of math characters.
Parameter Corresponds to mathtext.it
\mathit{}
or default italicmathtext.rm
\mathrm{}
Roman (upright)mathtext.tt
\mathtt{}
Typewriter (monospace)mathtext.bf
\mathbf{}
bold italicmathtext.cal
\mathcal{}
calligraphicmathtext.sf
\mathsf{}
sans-serif
Each parameter should be set to a fontconfig font descriptor (as defined in the yet-to-be-written font chapter).
The fonts used should have a Unicode mapping in order to find any
non-Latin characters, such as Greek. If you want to use a math symbol
that is not contained in your custom fonts, you can set the rcParam
mathtext.fallback_to_cm
to True
which will cause the mathtext system
to use characters from the default Computer Modern fonts whenever a particular
character can not be found in the custom font.
Note that the math glyphs specified in Unicode have evolved over time, and many fonts may not have glyphs in the correct place for mathtext.
An accent command may precede any symbol to add an accent above it. There are long and short forms for some of them.
Command Result \acute a
or\'a
\bar a
\breve a
\ddot a
or\''a
\dot a
or\.a
\grave a
or\`a
\hat a
or\^a
\tilde a
or\~a
\vec a
\overline{abc}
In addition, there are two special accents that automatically adjust to the width of the symbols below:
Command Result \widehat{xyz}
\widetilde{xyz}
Care should be taken when putting accents on lower-case i's and j's. Note that
in the following \imath
is used to avoid the extra dot over the i:
r"$\hat i\ \ \hat \imath$"
You can also use a large number of the TeX symbols, as in \infty
,
\leftarrow
, \sum
, \int
.
Lower-case Greek
α \alpha
β \beta
χ \chi
δ \delta
ϝ \digamma
ε \epsilon
η \eta
γ \gamma
ι \iota
κ \kappa
λ \lambda
μ \mu
ν \nu
ω \omega
ϕ \phi
π \pi
ψ \psi
ρ \rho
σ \sigma
τ \tau
θ \theta
υ \upsilon
ε \varepsilon
ϰ \varkappa
φ \varphi
ϖ \varpi
ϱ \varrho
ς \varsigma
ϑ \vartheta
ξ \xi
ζ \zeta
Upper-case Greek
Δ \Delta
Γ \Gamma
Λ \Lambda
Ω \Omega
Φ \Phi
Π \Pi
Ψ \Psi
Σ \Sigma
Θ \Theta
Υ \Upsilon
Ξ \Xi
℧ \mho
∇ \nabla
Hebrew
ℵ \aleph
ℶ \beth
ℸ \daleth
ℷ \gimel
Delimiters
/ /
[ [
⇓ \Downarrow
⇑ \Uparrow
‖ \Vert
\backslash
↓ \downarrow
⟨ \langle
⌈ \lceil
⌊ \lfloor
⌞ \llcorner
⌟ \lrcorner
⟩ \rangle
⌉ \rceil
⌋ \rfloor
⌜ \ulcorner
↑ \uparrow
⌝ \urcorner
\vert
{ \{
\|
} \}
] ]
|
Big symbols
⋂ \bigcap
⋃ \bigcup
⨀ \bigodot
⨁ \bigoplus
⨂ \bigotimes
⨄ \biguplus
⋁ \bigvee
⋀ \bigwedge
∐ \coprod
∫ \int
∮ \oint
∏ \prod
∑ \sum
Standard function names
Pr \Pr
arccos \arccos
arcsin \arcsin
arctan \arctan
arg \arg
cos \cos
cosh \cosh
cot \cot
coth \coth
csc \csc
deg \deg
det \det
dim \dim
exp \exp
gcd \gcd
hom \hom
inf \inf
ker \ker
lg \lg
lim \lim
liminf \liminf
limsup \limsup
ln \ln
log \log
max \max
min \min
sec \sec
sin \sin
sinh \sinh
sup \sup
tan \tan
tanh \tanh
Binary operation and relation symbols
≎ \Bumpeq
⋒ \Cap
⋓ \Cup
≑ \Doteq
⨝ \Join
⋐ \Subset
⋑ \Supset
⊩ \Vdash
⊪ \Vvdash
≈ \approx
≊ \approxeq
∗ \ast
≍ \asymp
϶ \backepsilon
∽ \backsim
⋍ \backsimeq
⊼ \barwedge
∵ \because
≬ \between
○ \bigcirc
▽ \bigtriangledown
△ \bigtriangleup
◀ \blacktriangleleft
▶ \blacktriangleright
⊥ \bot
⋈ \bowtie
⊡ \boxdot
⊟ \boxminus
⊞ \boxplus
⊠ \boxtimes
∙ \bullet
≏ \bumpeq
∩ \cap
⋅ \cdot
∘ \circ
≗ \circeq
≔ \coloneq
≅ \cong
∪ \cup
⋞ \curlyeqprec
⋟ \curlyeqsucc
⋎ \curlyvee
⋏ \curlywedge
† \dag
⊣ \dashv
‡ \ddag
⋄ \diamond
÷ \div
⋇ \divideontimes
≐ \doteq
≑ \doteqdot
∔ \dotplus
⌆ \doublebarwedge
≖ \eqcirc
≕ \eqcolon
≂ \eqsim
⪖ \eqslantgtr
⪕ \eqslantless
≡ \equiv
≒ \fallingdotseq
⌢ \frown
≥ \geq
≧ \geqq
⩾ \geqslant
≫ \gg
⋙ \ggg
⪺ \gnapprox
≩ \gneqq
⋧ \gnsim
⪆ \gtrapprox
⋗ \gtrdot
⋛ \gtreqless
⪌ \gtreqqless
≷ \gtrless
≳ \gtrsim
∈ \in
⊺ \intercal
⋋ \leftthreetimes
≤ \leq
≦ \leqq
⩽ \leqslant
⪅ \lessapprox
⋖ \lessdot
⋚ \lesseqgtr
⪋ \lesseqqgtr
≶ \lessgtr
≲ \lesssim
≪ \ll
⋘ \lll
⪹ \lnapprox
≨ \lneqq
⋦ \lnsim
⋉ \ltimes
∣ \mid
⊧ \models
∓ \mp
⊯ \nVDash
⊮ \nVdash
≉ \napprox
≇ \ncong
≠ \ne
≠ \neq
≠ \neq
≢ \nequiv
≱ \ngeq
≯ \ngtr
∋ \ni
≰ \nleq
≮ \nless
∤ \nmid
∉ \notin
∦ \nparallel
⊀ \nprec
≁ \nsim
⊄ \nsubset
⊈ \nsubseteq
⊁ \nsucc
⊅ \nsupset
⊉ \nsupseteq
⋪ \ntriangleleft
⋬ \ntrianglelefteq
⋫ \ntriangleright
⋭ \ntrianglerighteq
⊭ \nvDash
⊬ \nvdash
⊙ \odot
⊖ \ominus
⊕ \oplus
⊘ \oslash
⊗ \otimes
∥ \parallel
⟂ \perp
⋔ \pitchfork
± \pm
≺ \prec
⪷ \precapprox
≼ \preccurlyeq
≼ \preceq
⪹ \precnapprox
⋨ \precnsim
≾ \precsim
∝ \propto
⋌ \rightthreetimes
≓ \risingdotseq
⋊ \rtimes
∼ \sim
≃ \simeq
∕ \slash
⌣ \smile
⊓ \sqcap
⊔ \sqcup
⊏ \sqsubset
⊏ \sqsubset
⊑ \sqsubseteq
⊐ \sqsupset
⊐ \sqsupset
⊒ \sqsupseteq
⋆ \star
⊂ \subset
⊆ \subseteq
⫅ \subseteqq
⊊ \subsetneq
⫋ \subsetneqq
≻ \succ
⪸ \succapprox
≽ \succcurlyeq
≽ \succeq
⪺ \succnapprox
⋩ \succnsim
≿ \succsim
⊃ \supset
⊇ \supseteq
⫆ \supseteqq
⊋ \supsetneq
⫌ \supsetneqq
∴ \therefore
× \times
⊤ \top
◁ \triangleleft
⊴ \trianglelefteq
≜ \triangleq
▷ \triangleright
⊵ \trianglerighteq
⊎ \uplus
⊨ \vDash
∝ \varpropto
⊲ \vartriangleleft
⊳ \vartriangleright
⊢ \vdash
∨ \vee
⊻ \veebar
∧ \wedge
≀ \wr
Arrow symbols
⇓ \Downarrow
⇐ \Leftarrow
⇔ \Leftrightarrow
⇚ \Lleftarrow
⟸ \Longleftarrow
⟺ \Longleftrightarrow
⟹ \Longrightarrow
↰ \Lsh
⇗ \Nearrow
⇖ \Nwarrow
⇒ \Rightarrow
⇛ \Rrightarrow
↱ \Rsh
⇘ \Searrow
⇙ \Swarrow
⇑ \Uparrow
⇕ \Updownarrow
↺ \circlearrowleft
↻ \circlearrowright
↶ \curvearrowleft
↷ \curvearrowright
⤎ \dashleftarrow
⤏ \dashrightarrow
↓ \downarrow
⇊ \downdownarrows
⇃ \downharpoonleft
⇂ \downharpoonright
↩ \hookleftarrow
↪ \hookrightarrow
⇝ \leadsto
← \leftarrow
↢ \leftarrowtail
↽ \leftharpoondown
↼ \leftharpoonup
⇇ \leftleftarrows
↔ \leftrightarrow
⇆ \leftrightarrows
⇋ \leftrightharpoons
↭ \leftrightsquigarrow
↜ \leftsquigarrow
⟵ \longleftarrow
⟷ \longleftrightarrow
⟼ \longmapsto
⟶ \longrightarrow
↫ \looparrowleft
↬ \looparrowright
↦ \mapsto
⊸ \multimap
⇍ \nLeftarrow
⇎ \nLeftrightarrow
⇏ \nRightarrow
↗ \nearrow
↚ \nleftarrow
↮ \nleftrightarrow
↛ \nrightarrow
↖ \nwarrow
→ \rightarrow
↣ \rightarrowtail
⇁ \rightharpoondown
⇀ \rightharpoonup
⇄ \rightleftarrows
⇄ \rightleftarrows
⇌ \rightleftharpoons
⇌ \rightleftharpoons
⇉ \rightrightarrows
⇉ \rightrightarrows
↝ \rightsquigarrow
↘ \searrow
↙ \swarrow
→ \to
↞ \twoheadleftarrow
↠ \twoheadrightarrow
↑ \uparrow
↕ \updownarrow
↕ \updownarrow
↿ \upharpoonleft
↾ \upharpoonright
⇈ \upuparrows
Miscellaneous symbols
$ \$
Å \AA
Ⅎ \Finv
⅁ \Game
ℑ \Im
¶ \P
ℜ \Re
§ \S
∠ \angle
‵ \backprime
★ \bigstar
■ \blacksquare
▴ \blacktriangle
▾ \blacktriangledown
⋯ \cdots
✓ \checkmark
® \circledR
Ⓢ \circledS
♣ \clubsuit
∁ \complement
© \copyright
⋱ \ddots
♢ \diamondsuit
ℓ \ell
∅ \emptyset
ð \eth
∃ \exists
♭ \flat
∀ \forall
ħ \hbar
♡ \heartsuit
ℏ \hslash
∭ \iiint
∬ \iint
ı \imath
∞ \infty
ȷ \jmath
… \ldots
∡ \measuredangle
♮ \natural
¬ \neg
∄ \nexists
∰ \oiiint
∂ \partial
′ \prime
♯ \sharp
♠ \spadesuit
∢ \sphericalangle
ß \ss
▿ \triangledown
∅ \varnothing
▵ \vartriangle
⋮ \vdots
℘ \wp
¥ \yen
If a particular symbol does not have a name (as is true of many of the more obscure symbols in the STIX fonts), Unicode characters can also be used:
ur'$\u23ce$'
Here is an example illustrating many of these features in context.
Keywords: matplotlib code example, codex, python plot, pyplot Gallery generated by Sphinx-Gallery