Plotting¶
Introduction¶
The plotting module allows you to make 2-dimensional and 3-dimensional plots.
Presently the plots are rendered using matplotlib
as a backend. It is
also possible to plot 2-dimensional plots using a TextBackend
if you don’t
have matplotlib
.
The plotting module has the following functions:
plot: Plots 2D line plots.
plot_parametric: Plots 2D parametric plots.
plot_implicit: Plots 2D implicit and region plots.
plot3d: Plots 3D plots of functions in two variables.
plot3d_parametric_line: Plots 3D line plots, defined by a parameter.
plot3d_parametric_surface: Plots 3D parametric surface plots.
The above functions are only for convenience and ease of use. It is possible to
plot any plot by passing the corresponding Series
class to Plot
as
argument.
Plot Class¶
- class sympy.plotting.plot.Plot(*args, title=None, xlabel=None, ylabel=None, zlabel=None, aspect_ratio='auto', xlim=None, ylim=None, axis_center='auto', axis=True, xscale='linear', yscale='linear', legend=False, autoscale=True, margin=0, annotations=None, markers=None, rectangles=None, fill=None, backend='default', size=None, **kwargs)[source]¶
The central class of the plotting module.
Explanation
For interactive work the function
plot
is better suited.This class permits the plotting of sympy expressions using numerous backends (matplotlib, textplot, the old pyglet module for sympy, Google charts api, etc).
The figure can contain an arbitrary number of plots of sympy expressions, lists of coordinates of points, etc. Plot has a private attribute _series that contains all data series to be plotted (expressions for lines or surfaces, lists of points, etc (all subclasses of BaseSeries)). Those data series are instances of classes not imported by
from sympy import *
.The customization of the figure is on two levels. Global options that concern the figure as a whole (eg title, xlabel, scale, etc) and per-data series options (eg name) and aesthetics (eg. color, point shape, line type, etc.).
The difference between options and aesthetics is that an aesthetic can be a function of the coordinates (or parameters in a parametric plot). The supported values for an aesthetic are: - None (the backend uses default values) - a constant - a function of one variable (the first coordinate or parameter) - a function of two variables (the first and second coordinate or parameters) - a function of three variables (only in nonparametric 3D plots) Their implementation depends on the backend so they may not work in some backends.
If the plot is parametric and the arity of the aesthetic function permits it the aesthetic is calculated over parameters and not over coordinates. If the arity does not permit calculation over parameters the calculation is done over coordinates.
Only cartesian coordinates are supported for the moment, but you can use the parametric plots to plot in polar, spherical and cylindrical coordinates.
The arguments for the constructor Plot must be subclasses of BaseSeries.
Any global option can be specified as a keyword argument.
The global options for a figure are:
title : str
xlabel : str
ylabel : str
zlabel : str
legend : bool
xscale : {‘linear’, ‘log’}
yscale : {‘linear’, ‘log’}
axis : bool
axis_center : tuple of two floats or {‘center’, ‘auto’}
xlim : tuple of two floats
ylim : tuple of two floats
aspect_ratio : tuple of two floats or {‘auto’}
autoscale : bool
margin : float in [0, 1]
backend : {‘default’, ‘matplotlib’, ‘text’} or a subclass of BaseBackend
size : optional tuple of two floats, (width, height); default: None
The per data series options and aesthetics are: There are none in the base series. See below for options for subclasses.
Some data series support additional aesthetics or options:
ListSeries, LineOver1DRangeSeries, Parametric2DLineSeries, Parametric3DLineSeries support the following:
Aesthetics:
- line_colorstring, or float, or function, optional
Specifies the color for the plot, which depends on the backend being used.
For example, if
MatplotlibBackend
is being used, then Matplotlib string colors are acceptable (“red”, “r”, “cyan”, “c”, …). Alternatively, we can use a float number \(0 < color < 1\) wrapped in a string (for example, \(line_color="0.5"\)) to specify grayscale colors. Alternatively, We can specify a function returning a single float value: this will be used to apply a color-loop (for example, \(line_color=lambda x: math.cos(x)\)).Note that by setting line_color, it would be applied simultaneously to all the series.
options:
label : str
steps : bool
integers_only : bool
SurfaceOver2DRangeSeries, ParametricSurfaceSeries support the following:
aesthetics:
surface_color : function which returns a float.
- append(arg)[source]¶
Adds an element from a plot’s series to an existing plot.
Examples
Consider two
Plot
objects,p1
andp2
. To add the second plot’s first series object to the first, use theappend
method, like so:>>> from sympy import symbols >>> from sympy.plotting import plot >>> x = symbols('x') >>> p1 = plot(x*x, show=False) >>> p2 = plot(x, show=False) >>> p1.append(p2[0]) >>> p1 Plot object containing: [0]: cartesian line: x**2 for x over (-10.0, 10.0) [1]: cartesian line: x for x over (-10.0, 10.0) >>> p1.show()
See also
- extend(arg)[source]¶
Adds all series from another plot.
Examples
Consider two
Plot
objects,p1
andp2
. To add the second plot to the first, use theextend
method, like so:>>> from sympy import symbols >>> from sympy.plotting import plot >>> x = symbols('x') >>> p1 = plot(x**2, show=False) >>> p2 = plot(x, -x, show=False) >>> p1.extend(p2) >>> p1 Plot object containing: [0]: cartesian line: x**2 for x over (-10.0, 10.0) [1]: cartesian line: x for x over (-10.0, 10.0) [2]: cartesian line: -x for x over (-10.0, 10.0) >>> p1.show()
Plotting Function Reference¶
- sympy.plotting.plot.plot(*args, show=True, **kwargs)[source]¶
Plots a function of a single variable as a curve.
- Parameters
args :
The first argument is the expression representing the function of single variable to be plotted.
The last argument is a 3-tuple denoting the range of the free variable. e.g.
(x, 0, 5)
Typical usage examples are in the followings:
- Plotting a single expression with a single range.
plot(expr, range, **kwargs)
- Plotting a single expression with the default range (-10, 10).
plot(expr, **kwargs)
- Plotting multiple expressions with a single range.
plot(expr1, expr2, ..., range, **kwargs)
- Plotting multiple expressions with multiple ranges.
plot((expr1, range1), (expr2, range2), ..., **kwargs)
It is best practice to specify range explicitly because default range may change in the future if a more advanced default range detection algorithm is implemented.
show : bool, optional
The default value is set to
True
. Set show toFalse
and the function will not display the plot. The returned instance of thePlot
class can then be used to save or display the plot by calling thesave()
andshow()
methods respectively.line_color : string, or float, or function, optional
Specifies the color for the plot. See
Plot
to see how to set color for the plots. Note that by settingline_color
, it would be applied simultaneously to all the series.title : str, optional
Title of the plot. It is set to the latex representation of the expression, if the plot has only one expression.
label : str, optional
The label of the expression in the plot. It will be used when called with
legend
. Default is the name of the expression. e.g.sin(x)
xlabel : str, optional
Label for the x-axis.
ylabel : str, optional
Label for the y-axis.
xscale : ‘linear’ or ‘log’, optional
Sets the scaling of the x-axis.
yscale : ‘linear’ or ‘log’, optional
Sets the scaling of the y-axis.
axis_center : (float, float), optional
Tuple of two floats denoting the coordinates of the center or {‘center’, ‘auto’}
xlim : (float, float), optional
Denotes the x-axis limits,
(min, max)`
.ylim : (float, float), optional
Denotes the y-axis limits,
(min, max)`
.annotations : list, optional
A list of dictionaries specifying the type of annotation required. The keys in the dictionary should be equivalent to the arguments of the matplotlib’s annotate() function.
markers : list, optional
A list of dictionaries specifying the type the markers required. The keys in the dictionary should be equivalent to the arguments of the matplotlib’s plot() function along with the marker related keyworded arguments.
rectangles : list, optional
A list of dictionaries specifying the dimensions of the rectangles to be plotted. The keys in the dictionary should be equivalent to the arguments of the matplotlib’s patches.Rectangle class.
fill : dict, optional
A dictionary specifying the type of color filling required in the plot. The keys in the dictionary should be equivalent to the arguments of the matplotlib’s fill_between() function.
adaptive : bool, optional
The default value is set to
True
. Set adaptive toFalse
and specifynb_of_points
if uniform sampling is required.The plotting uses an adaptive algorithm which samples recursively to accurately plot. The adaptive algorithm uses a random point near the midpoint of two points that has to be further sampled. Hence the same plots can appear slightly different.
depth : int, optional
Recursion depth of the adaptive algorithm. A depth of value
n
samples a maximum of \(2^{n}\) points.If the
adaptive
flag is set toFalse
, this will be ignored.nb_of_points : int, optional
Used when the
adaptive
is set toFalse
. The function is uniformly sampled atnb_of_points
number of points.If the
adaptive
flag is set toTrue
, this will be ignored.size : (float, float), optional
A tuple in the form (width, height) in inches to specify the size of the overall figure. The default value is set to
None
, meaning the size will be set by the default backend.
Examples
>>> from sympy import symbols >>> from sympy.plotting import plot >>> x = symbols('x')
Single Plot
>>> plot(x**2, (x, -5, 5)) Plot object containing: [0]: cartesian line: x**2 for x over (-5.0, 5.0)
Multiple plots with single range.
>>> plot(x, x**2, x**3, (x, -5, 5)) Plot object containing: [0]: cartesian line: x for x over (-5.0, 5.0) [1]: cartesian line: x**2 for x over (-5.0, 5.0) [2]: cartesian line: x**3 for x over (-5.0, 5.0)
Multiple plots with different ranges.
>>> plot((x**2, (x, -6, 6)), (x, (x, -5, 5))) Plot object containing: [0]: cartesian line: x**2 for x over (-6.0, 6.0) [1]: cartesian line: x for x over (-5.0, 5.0)
No adaptive sampling.
>>> plot(x**2, adaptive=False, nb_of_points=400) Plot object containing: [0]: cartesian line: x**2 for x over (-10.0, 10.0)
See also
- sympy.plotting.plot.plot_parametric(*args, show=True, **kwargs)[source]¶
Plots a 2D parametric curve.
- Parameters
args
Common specifications are:
- Plotting a single parametric curve with a range
plot_parametric((expr_x, expr_y), range)
- Plotting multiple parametric curves with the same range
plot_parametric((expr_x, expr_y), ..., range)
- Plotting multiple parametric curves with different ranges
plot_parametric((expr_x, expr_y, range), ...)
expr_x
is the expression representing \(x\) component of the parametric function.expr_y
is the expression representing \(y\) component of the parametric function.range
is a 3-tuple denoting the parameter symbol, start and stop. For example,(u, 0, 5)
.If the range is not specified, then a default range of (-10, 10) is used.
However, if the arguments are specified as
(expr_x, expr_y, range), ...
, you must specify the ranges for each expressions manually.Default range may change in the future if a more advanced algorithm is implemented.
adaptive : bool, optional
Specifies whether to use the adaptive sampling or not.
The default value is set to
True
. Set adaptive toFalse
and specifynb_of_points
if uniform sampling is required.depth : int, optional
The recursion depth of the adaptive algorithm. A depth of value \(n\) samples a maximum of \(2^n\) points.
nb_of_points : int, optional
Used when the
adaptive
flag is set toFalse
.Specifies the number of the points used for the uniform sampling.
line_color : string, or float, or function, optional
Specifies the color for the plot. See
Plot
to see how to set color for the plots. Note that by settingline_color
, it would be applied simultaneously to all the series.label : str, optional
The label of the expression in the plot. It will be used when called with
legend
. Default is the name of the expression. e.g.sin(x)
xlabel : str, optional
Label for the x-axis.
ylabel : str, optional
Label for the y-axis.
xscale : ‘linear’ or ‘log’, optional
Sets the scaling of the x-axis.
yscale : ‘linear’ or ‘log’, optional
Sets the scaling of the y-axis.
axis_center : (float, float), optional
Tuple of two floats denoting the coordinates of the center or {‘center’, ‘auto’}
xlim : (float, float), optional
Denotes the x-axis limits,
(min, max)`
.ylim : (float, float), optional
Denotes the y-axis limits,
(min, max)`
.size : (float, float), optional
A tuple in the form (width, height) in inches to specify the size of the overall figure. The default value is set to
None
, meaning the size will be set by the default backend.
Examples
>>> from sympy import symbols, cos, sin >>> from sympy.plotting import plot_parametric >>> u = symbols('u')
A parametric plot with a single expression:
>>> plot_parametric((cos(u), sin(u)), (u, -5, 5)) Plot object containing: [0]: parametric cartesian line: (cos(u), sin(u)) for u over (-5.0, 5.0)
A parametric plot with multiple expressions with the same range:
>>> plot_parametric((cos(u), sin(u)), (u, cos(u)), (u, -10, 10)) Plot object containing: [0]: parametric cartesian line: (cos(u), sin(u)) for u over (-10.0, 10.0) [1]: parametric cartesian line: (u, cos(u)) for u over (-10.0, 10.0)
A parametric plot with multiple expressions with different ranges for each curve:
>>> plot_parametric((cos(u), sin(u), (u, -5, 5)), ... (cos(u), u, (u, -5, 5))) Plot object containing: [0]: parametric cartesian line: (cos(u), sin(u)) for u over (-5.0, 5.0) [1]: parametric cartesian line: (cos(u), u) for u over (-5.0, 5.0)
Notes
The plotting uses an adaptive algorithm which samples recursively to accurately plot the curve. The adaptive algorithm uses a random point near the midpoint of two points that has to be further sampled. Hence, repeating the same plot command can give slightly different results because of the random sampling.
If there are multiple plots, then the same optional arguments are applied to all the plots drawn in the same canvas. If you want to set these options separately, you can index the returned
Plot
object and set it.For example, when you specify
line_color
once, it would be applied simultaneously to both series.>>> from sympy import pi >>> expr1 = (u, cos(2*pi*u)/2 + 1/2) >>> expr2 = (u, sin(2*pi*u)/2 + 1/2) >>> p = plot_parametric(expr1, expr2, (u, 0, 1), line_color='blue')
If you want to specify the line color for the specific series, you should index each item and apply the property manually.
>>> p[0].line_color = 'red' >>> p.show()
See also
- sympy.plotting.plot.plot3d(*args, show=True, **kwargs)[source]¶
Plots a 3D surface plot.
Usage
Single plot
plot3d(expr, range_x, range_y, **kwargs)
If the ranges are not specified, then a default range of (-10, 10) is used.
Multiple plot with the same range.
plot3d(expr1, expr2, range_x, range_y, **kwargs)
If the ranges are not specified, then a default range of (-10, 10) is used.
Multiple plots with different ranges.
plot3d((expr1, range_x, range_y), (expr2, range_x, range_y), ..., **kwargs)
Ranges have to be specified for every expression.
Default range may change in the future if a more advanced default range detection algorithm is implemented.
Arguments
expr
: Expression representing the function along x.range_x
: (x, 0, 5), A 3-tuple denoting the range of the x variable.range_y
: (y, 0, 5), A 3-tuple denoting the range of the yvariable.
Keyword Arguments
Arguments for
SurfaceOver2DRangeSeries
class:nb_of_points_x
: int. The x range is sampled uniformly atnb_of_points_x
of points.nb_of_points_y
: int. The y range is sampled uniformly atnb_of_points_y
of points.Aesthetics:
surface_color
: Function which returns a float. Specifies the color for the surface of the plot. Seesympy.plotting.Plot
for more details.If there are multiple plots, then the same series arguments are applied to all the plots. If you want to set these options separately, you can index the returned
Plot
object and set it.Arguments for
Plot
class:title
: str. Title of the plot.size
: (float, float), optional A tuple in the form (width, height) in inches to specify the size of the overall figure. The default value is set toNone
, meaning the size will be set by the default backend.Examples
>>> from sympy import symbols >>> from sympy.plotting import plot3d >>> x, y = symbols('x y')
Single plot
>>> plot3d(x*y, (x, -5, 5), (y, -5, 5)) Plot object containing: [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
Multiple plots with same range
>>> plot3d(x*y, -x*y, (x, -5, 5), (y, -5, 5)) Plot object containing: [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0) [1]: cartesian surface: -x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
Multiple plots with different ranges.
>>> plot3d((x**2 + y**2, (x, -5, 5), (y, -5, 5)), ... (x*y, (x, -3, 3), (y, -3, 3))) Plot object containing: [0]: cartesian surface: x**2 + y**2 for x over (-5.0, 5.0) and y over (-5.0, 5.0) [1]: cartesian surface: x*y for x over (-3.0, 3.0) and y over (-3.0, 3.0)
See also
- sympy.plotting.plot.plot3d_parametric_line(*args, show=True, **kwargs)[source]¶
Plots a 3D parametric line plot.
Usage
Single plot:
plot3d_parametric_line(expr_x, expr_y, expr_z, range, **kwargs)
If the range is not specified, then a default range of (-10, 10) is used.
Multiple plots.
plot3d_parametric_line((expr_x, expr_y, expr_z, range), ..., **kwargs)
Ranges have to be specified for every expression.
Default range may change in the future if a more advanced default range detection algorithm is implemented.
Arguments
expr_x
: Expression representing the function along x.expr_y
: Expression representing the function along y.expr_z
: Expression representing the function along z.range
:(u, 0, 5)
, A 3-tuple denoting the range of the parameter variable.Keyword Arguments
Arguments for
Parametric3DLineSeries
class.nb_of_points
: The range is uniformly sampled atnb_of_points
number of points.Aesthetics:
line_color
: string, or float, or function, optionalSpecifies the color for the plot. See
Plot
to see how to set color for the plots. Note that by settingline_color
, it would be applied simultaneously to all the series.label
: strThe label to the plot. It will be used when called with
legend=True
to denote the function with the given label in the plot.
If there are multiple plots, then the same series arguments are applied to all the plots. If you want to set these options separately, you can index the returned
Plot
object and set it.Arguments for
Plot
class.title
: str. Title of the plot.size
(float, float), optionalA tuple in the form (width, height) in inches to specify the size of the overall figure. The default value is set to
None
, meaning the size will be set by the default backend.
Examples
>>> from sympy import symbols, cos, sin >>> from sympy.plotting import plot3d_parametric_line >>> u = symbols('u')
Single plot.
>>> plot3d_parametric_line(cos(u), sin(u), u, (u, -5, 5)) Plot object containing: [0]: 3D parametric cartesian line: (cos(u), sin(u), u) for u over (-5.0, 5.0)
Multiple plots.
>>> plot3d_parametric_line((cos(u), sin(u), u, (u, -5, 5)), ... (sin(u), u**2, u, (u, -5, 5))) Plot object containing: [0]: 3D parametric cartesian line: (cos(u), sin(u), u) for u over (-5.0, 5.0) [1]: 3D parametric cartesian line: (sin(u), u**2, u) for u over (-5.0, 5.0)
See also
- sympy.plotting.plot.plot3d_parametric_surface(*args, show=True, **kwargs)[source]¶
Plots a 3D parametric surface plot.
Explanation
Single plot.
plot3d_parametric_surface(expr_x, expr_y, expr_z, range_u, range_v, **kwargs)
If the ranges is not specified, then a default range of (-10, 10) is used.
Multiple plots.
plot3d_parametric_surface((expr_x, expr_y, expr_z, range_u, range_v), ..., **kwargs)
Ranges have to be specified for every expression.
Default range may change in the future if a more advanced default range detection algorithm is implemented.
Arguments
expr_x
: Expression representing the function alongx
.expr_y
: Expression representing the function alongy
.expr_z
: Expression representing the function alongz
.range_u
:(u, 0, 5)
, A 3-tuple denoting the range of theu
variable.range_v
:(v, 0, 5)
, A 3-tuple denoting the range of the v variable.Keyword Arguments
Arguments for
ParametricSurfaceSeries
class:nb_of_points_u
: int. Theu
range is sampled uniformly atnb_of_points_v
of pointsnb_of_points_y
: int. Thev
range is sampled uniformly atnb_of_points_y
of pointsAesthetics:
surface_color
: Function which returns a float. Specifies the color for the surface of the plot. Seesympy.plotting.Plot
for more details.If there are multiple plots, then the same series arguments are applied for all the plots. If you want to set these options separately, you can index the returned
Plot
object and set it.Arguments for
Plot
class:title
: str. Title of the plot.size
: (float, float), optional A tuple in the form (width, height) in inches to specify the size of the overall figure. The default value is set toNone
, meaning the size will be set by the default backend.Examples
>>> from sympy import symbols, cos, sin >>> from sympy.plotting import plot3d_parametric_surface >>> u, v = symbols('u v')
Single plot.
>>> plot3d_parametric_surface(cos(u + v), sin(u - v), u - v, ... (u, -5, 5), (v, -5, 5)) Plot object containing: [0]: parametric cartesian surface: (cos(u + v), sin(u - v), u - v) for u over (-5.0, 5.0) and v over (-5.0, 5.0)
See also
- sympy.plotting.plot_implicit.plot_implicit(expr, x_var=None, y_var=None, adaptive=True, depth=0, points=300, line_color='blue', show=True, **kwargs)[source]¶
A plot function to plot implicit equations / inequalities.
Arguments
expr
: The equation / inequality that is to be plotted.x_var
(optional) : symbol to plot on x-axis or tuple giving symbol and range as(symbol, xmin, xmax)
y_var
(optional) : symbol to plot on y-axis or tuple giving symbol and range as(symbol, ymin, ymax)
If neither
x_var
nory_var
are given then the free symbols in the expression will be assigned in the order they are sorted.The following keyword arguments can also be used:
adaptive
Boolean. The default value is set to True. It has to beset to False if you want to use a mesh grid.
depth
integer. The depth of recursion for adaptive mesh grid.Default value is 0. Takes value in the range (0, 4).
points
integer. The number of points if adaptive mesh grid is notused. Default value is 300.
show
Boolean. Default value is True. If set to False, the plot willnot be shown. See
Plot
for further information.
title
string. The title for the plot.xlabel
string. The label for the x-axisylabel
string. The label for the y-axis
Aesthetics options:
line_color
: float or string. Specifies the color for the plot.See
Plot
to see how to set color for the plots. Default value is “Blue”
plot_implicit, by default, uses interval arithmetic to plot functions. If the expression cannot be plotted using interval arithmetic, it defaults to a generating a contour using a mesh grid of fixed number of points. By setting adaptive to False, you can force plot_implicit to use the mesh grid. The mesh grid method can be effective when adaptive plotting using interval arithmetic, fails to plot with small line width.
Examples
Plot expressions:
>>> from sympy import plot_implicit, symbols, Eq, And >>> x, y = symbols('x y')
Without any ranges for the symbols in the expression:
>>> p1 = plot_implicit(Eq(x**2 + y**2, 5))
With the range for the symbols:
>>> p2 = plot_implicit( ... Eq(x**2 + y**2, 3), (x, -3, 3), (y, -3, 3))
With depth of recursion as argument:
>>> p3 = plot_implicit( ... Eq(x**2 + y**2, 5), (x, -4, 4), (y, -4, 4), depth = 2)
Using mesh grid and not using adaptive meshing:
>>> p4 = plot_implicit( ... Eq(x**2 + y**2, 5), (x, -5, 5), (y, -2, 2), ... adaptive=False)
Using mesh grid without using adaptive meshing with number of points specified:
>>> p5 = plot_implicit( ... Eq(x**2 + y**2, 5), (x, -5, 5), (y, -2, 2), ... adaptive=False, points=400)
Plotting regions:
>>> p6 = plot_implicit(y > x**2)
Plotting Using boolean conjunctions:
>>> p7 = plot_implicit(And(y > x, y > -x))
When plotting an expression with a single variable (y - 1, for example), specify the x or the y variable explicitly:
>>> p8 = plot_implicit(y - 1, y_var=y) >>> p9 = plot_implicit(x - 1, x_var=x)
PlotGrid Class¶
- class sympy.plotting.plot.PlotGrid(nrows, ncolumns, *args, show=True, size=None, **kwargs)[source]¶
This class helps to plot subplots from already created sympy plots in a single figure.
Examples
>>> from sympy import symbols >>> from sympy.plotting import plot, plot3d, PlotGrid >>> x, y = symbols('x, y') >>> p1 = plot(x, x**2, x**3, (x, -5, 5)) >>> p2 = plot((x**2, (x, -6, 6)), (x, (x, -5, 5))) >>> p3 = plot(x**3, (x, -5, 5)) >>> p4 = plot3d(x*y, (x, -5, 5), (y, -5, 5))
Plotting vertically in a single line:
>>> PlotGrid(2, 1 , p1, p2) PlotGrid object containing: Plot[0]:Plot object containing: [0]: cartesian line: x for x over (-5.0, 5.0) [1]: cartesian line: x**2 for x over (-5.0, 5.0) [2]: cartesian line: x**3 for x over (-5.0, 5.0) Plot[1]:Plot object containing: [0]: cartesian line: x**2 for x over (-6.0, 6.0) [1]: cartesian line: x for x over (-5.0, 5.0)
Plotting horizontally in a single line:
>>> PlotGrid(1, 3 , p2, p3, p4) PlotGrid object containing: Plot[0]:Plot object containing: [0]: cartesian line: x**2 for x over (-6.0, 6.0) [1]: cartesian line: x for x over (-5.0, 5.0) Plot[1]:Plot object containing: [0]: cartesian line: x**3 for x over (-5.0, 5.0) Plot[2]:Plot object containing: [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
Plotting in a grid form:
>>> PlotGrid(2, 2, p1, p2 ,p3, p4) PlotGrid object containing: Plot[0]:Plot object containing: [0]: cartesian line: x for x over (-5.0, 5.0) [1]: cartesian line: x**2 for x over (-5.0, 5.0) [2]: cartesian line: x**3 for x over (-5.0, 5.0) Plot[1]:Plot object containing: [0]: cartesian line: x**2 for x over (-6.0, 6.0) [1]: cartesian line: x for x over (-5.0, 5.0) Plot[2]:Plot object containing: [0]: cartesian line: x**3 for x over (-5.0, 5.0) Plot[3]:Plot object containing: [0]: cartesian surface: x*y for x over (-5.0, 5.0) and y over (-5.0, 5.0)
Series Classes¶
- class sympy.plotting.plot.BaseSeries[source]¶
Base class for the data objects containing stuff to be plotted.
Explanation
The backend should check if it supports the data series that it’s given. (eg TextBackend supports only LineOver1DRange). It’s the backend responsibility to know how to use the class of data series that it’s given.
Some data series classes are grouped (using a class attribute like is_2Dline) according to the api they present (based only on convention). The backend is not obliged to use that api (eg. The LineOver1DRange belongs to the is_2Dline group and presents the get_points method, but the TextBackend does not use the get_points method).
- class sympy.plotting.plot.Line2DBaseSeries[source]¶
A base class for 2D lines.
adding the label, steps and only_integers options
making is_2Dline true
defining get_segments and get_color_array
- class sympy.plotting.plot.LineOver1DRangeSeries(expr, var_start_end, **kwargs)[source]¶
Representation for a line consisting of a SymPy expression over a range.
- get_points()[source]¶
Return lists of coordinates for plotting. Depending on the \(adaptive\) option, this function will either use an adaptive algorithm or it will uniformly sample the expression over the provided range.
- Returns
x: list
List of x-coordinates
- y: list
List of y-coordinates
Explanation
The adaptive sampling is done by recursively checking if three points are almost collinear. If they are not collinear, then more points are added between those points.
References
- R637
Adaptive polygonal approximation of parametric curves, Luiz Henrique de Figueiredo.
- class sympy.plotting.plot.Parametric2DLineSeries(expr_x, expr_y, var_start_end, **kwargs)[source]¶
Representation for a line consisting of two parametric sympy expressions over a range.
- get_points()[source]¶
Return lists of coordinates for plotting. Depending on the \(adaptive\) option, this function will either use an adaptive algorithm or it will uniformly sample the expression over the provided range.
- Returns
x: list
List of x-coordinates
- y: list
List of y-coordinates
Explanation
The adaptive sampling is done by recursively checking if three points are almost collinear. If they are not collinear, then more points are added between those points.
References
- R638
Adaptive polygonal approximation of parametric curves, Luiz Henrique de Figueiredo.
- class sympy.plotting.plot.Line3DBaseSeries[source]¶
A base class for 3D lines.
Most of the stuff is derived from Line2DBaseSeries.
- class sympy.plotting.plot.Parametric3DLineSeries(expr_x, expr_y, expr_z, var_start_end, **kwargs)[source]¶
Representation for a 3D line consisting of three parametric sympy expressions and a range.
- class sympy.plotting.plot.SurfaceOver2DRangeSeries(expr, var_start_end_x, var_start_end_y, **kwargs)[source]¶
Representation for a 3D surface consisting of a sympy expression and 2D range.
Backends¶
- class sympy.plotting.plot.BaseBackend(parent)[source]¶
Base class for all backends. A backend represents the plotting library, which implements the necessary functionalities in order to use SymPy plotting functions.
How the plotting module works:
- Whenever a plotting function is called, the provided expressions are
processed and a list of instances of the \(BaseSeries\) class is created, containing the necessary information to plot the expressions (eg the expression, ranges, series name, …). Eventually, these objects will generate the numerical data to be plotted.
- A Plot object is instantiated, which stores the list of series and the
main attributes of the plot (eg axis labels, title, …).
- When the “show” command is executed, a new backend is instantiated,
which loops through each series object to generate and plot the numerical data. The backend is also going to set the axis labels, title, …, according to the values stored in the Plot instance.
The backend should check if it supports the data series that it’s given (eg TextBackend supports only LineOver1DRange).
It’s the backend responsibility to know how to use the class of data series that it’s given. Note that the current implementation of the \(*Series\) classes is “matplotlib-centric”: the numerical data returned by the \(get_points\) and \(get_meshes\) methods is meant to be used directly by Matplotlib. Therefore, the new backend will have to pre-process the numerical data to make it compatible with the chosen plotting library. Keep in mind that future SymPy versions may improve the \(*Series\) classes in order to return numerical data “non-matplotlib-centric”, hence if you code a new backend you have the responsibility to check if its working on each SymPy release.
Please, explore the \(MatplotlibBackend\) source code to understand how a backend should be coded.
See also
- class sympy.plotting.plot.MatplotlibBackend(parent)[source]¶
This class implements the functionalities to use Matplotlib with SymPy plotting functions.
Pyglet Plotting¶
This is the documentation for the old plotting module that uses pyglet. This module has some limitations and is not actively developed anymore. For an alternative you can look at the new plotting module.
The pyglet plotting module can do nice 2D and 3D plots that can be
controlled by console commands as well as keyboard and mouse, with
the only dependency being pyglet
.
Here is the simplest usage:
>>> from sympy import var
>>> from sympy.plotting.pygletplot import PygletPlot as Plot
>>> var('x y z')
>>> Plot(x*y**3-y*x**3)
To see lots of plotting examples, see examples/pyglet_plotting.py
and try running
it in interactive mode (python -i plotting.py):
$ python -i examples/pyglet_plotting.py
And type for instance example(7)
or example(11)
.
See also the Plotting Module wiki page for screenshots.
Plot Window Controls¶
Camera |
Keys |
---|---|
Sensitivity Modifier |
SHIFT |
Zoom |
R and F, Page Up and Down, Numpad + and - |
Rotate View X,Y axis |
Arrow Keys, A,S,D,W, Numpad 4,6,8,2 |
Rotate View Z axis |
Q and E, Numpad 7 and 9 |
Rotate Ordinate Z axis |
Z and C, Numpad 1 and 3 |
View XY |
F1 |
View XZ |
F2 |
View YZ |
F3 |
View Perspective |
F4 |
Reset |
X, Numpad 5 |
Axes |
Keys |
---|---|
Toggle Visible |
F5 |
Toggle Colors |
F6 |
Window |
Keys |
---|---|
Close |
ESCAPE |
Screenshot |
F8 |
The mouse can be used to rotate, zoom, and translate by dragging the left, middle, and right mouse buttons respectively.
Coordinate Modes¶
Plot
supports several curvilinear coordinate modes, and they are independent
for each plotted function. You can specify a coordinate mode explicitly with
the ‘mode’ named argument, but it can be automatically determined for cartesian
or parametric plots, and therefore must only be specified for polar,
cylindrical, and spherical modes.
Specifically, Plot(function arguments)
and Plot.__setitem__(i, function
arguments)
(accessed using array-index syntax on the Plot
instance) will
interpret your arguments as a cartesian plot if you provide one function and a
parametric plot if you provide two or three functions. Similarly, the arguments
will be interpreted as a curve is one variable is used, and a surface if two
are used.
Supported mode names by number of variables:
1 (curves): parametric, cartesian, polar
2 (surfaces): parametric, cartesian, cylindrical, spherical
>>> Plot(1, 'mode=spherical; color=zfade4')
Note that function parameters are given as option strings of the form “key1=value1; key2 = value2” (spaces are truncated). Keyword arguments given directly to plot apply to the plot itself.
Specifying Intervals for Variables¶
The basic format for variable intervals is [var, min, max, steps]. However, the syntax is quite flexible, and arguments not specified are taken from the defaults for the current coordinate mode:
>>> Plot(x**2) # implies [x,-5,5,100]
>>> Plot(x**2, [], []) # [x,-1,1,40], [y,-1,1,40]
>>> Plot(x**2-y**2, [100], [100]) # [x,-1,1,100], [y,-1,1,100]
>>> Plot(x**2, [x,-13,13,100])
>>> Plot(x**2, [-13,13]) # [x,-13,13,100]
>>> Plot(x**2, [x,-13,13]) # [x,-13,13,100]
>>> Plot(1*x, [], [x], 'mode=cylindrical') # [unbound_theta,0,2*Pi,40], [x,-1,1,20]
Using the Interactive Interface¶
>>> p = Plot(visible=False)
>>> f = x**2
>>> p[1] = f
>>> p[2] = f.diff(x)
>>> p[3] = f.diff(x).diff(x)
>>> p
[1]: x**2, 'mode=cartesian'
[2]: 2*x, 'mode=cartesian'
[3]: 2, 'mode=cartesian'
>>> p.show()
>>> p.clear()
>>> p
<blank plot>
>>> p[1] = x**2+y**2
>>> p[1].style = 'solid'
>>> p[2] = -x**2-y**2
>>> p[2].style = 'wireframe'
>>> p[1].color = z, (0.4,0.4,0.9), (0.9,0.4,0.4)
>>> p[1].style = 'both'
>>> p[2].style = 'both'
>>> p.close()
Using Custom Color Functions¶
The following code plots a saddle and color it by the magnitude of its gradient:
>>> fz = x**2-y**2
>>> Fx, Fy, Fz = fz.diff(x), fz.diff(y), 0
>>> p[1] = fz, 'style=solid'
>>> p[1].color = (Fx**2 + Fy**2 + Fz**2)**(0.5)
The coloring algorithm works like this:
Evaluate the color function(s) across the curve or surface.
Find the minimum and maximum value of each component.
Scale each component to the color gradient.
When not specified explicitly, the default color gradient is f(0.0)=(0.4,0.4,0.4) -> f(1.0)=(0.9,0.9,0.9). In our case, everything is gray-scale because we have applied the default color gradient uniformly for each color component. When defining a color scheme in this way, you might want to supply a color gradient as well:
>>> p[1].color = (Fx**2 + Fy**2 + Fz**2)**(0.5), (0.1,0.1,0.9), (0.9,0.1,0.1)
Here’s a color gradient with four steps:
>>> gradient = [ 0.0, (0.1,0.1,0.9), 0.3, (0.1,0.9,0.1),
... 0.7, (0.9,0.9,0.1), 1.0, (1.0,0.0,0.0) ]
>>> p[1].color = (Fx**2 + Fy**2 + Fz**2)**(0.5), gradient
The other way to specify a color scheme is to give a separate function for each component r, g, b. With this syntax, the default color scheme is defined:
>>> p[1].color = z,y,x, (0.4,0.4,0.4), (0.9,0.9,0.9)
This maps z->red, y->green, and x->blue. In some cases, you might prefer to use the following alternative syntax:
>>> p[1].color = z,(0.4,0.9), y,(0.4,0.9), x,(0.4,0.9)
You can still use multi-step gradients with three-function color schemes.
Plotting Geometric Entities¶
The plotting module is capable of plotting some 2D geometric entities like line, circle and ellipse. The following example plots a circle centred at origin and of radius 2 units.
>>> from sympy import *
>>> x,y = symbols('x y')
>>> plot_implicit(Eq(x**2+y**2, 4))
Similarly, plot_implicit()
may be used to plot any 2-D geometric structure from
its implicit equation.
Plotting polygons (Polygon, RegularPolygon, Triangle) are not supported directly.
Plotting with ASCII art¶
- sympy.plotting.textplot.textplot(expr, a, b, W=55, H=21)[source]¶
Print a crude ASCII art plot of the SymPy expression ‘expr’ (which should contain a single symbol, e.g. x or something else) over the interval [a, b].
Examples
>>> from sympy import Symbol, sin >>> from sympy.plotting import textplot >>> t = Symbol('t') >>> textplot(sin(t)*t, 0, 15) 14 | ... | . | . | . | . | ... | / . . | / | / . | . . . 1.5 |----.......-------------------------------------------- |.... \ . . | \ / . | .. / . | \ / . | .... | . | . . | | . . -11 |_______________________________________________________ 0 7.5 15