======== Plotting ======== .. module:: sympy.plotting.plot Introduction ------------ The plotting module allows you to make 2-dimensional and 3-dimensional plots. Presently the plots are rendered using :external:mod:`matplotlib` as a backend. It is also possible to plot 2-dimensional plots using a :class:`~.TextBackend` if you do not have :external:mod:`matplotlib`. The plotting module has the following functions: * :func:`~.plot`: Plots 2D line plots. * :func:`~.plot_parametric`: Plots 2D parametric plots. * :func:`~.plot_implicit`: Plots 2D implicit and region plots. * :func:`~.plot3d`: Plots 3D plots of functions in two variables. * :func:`~.plot3d_parametric_line`: Plots 3D line plots, defined by a parameter. * :func:`~.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 :class:`~.Plot` as argument. Plot Class ---------- .. autoclass:: sympy.plotting.plot::Plot :members: Plotting Function Reference --------------------------- .. autofunction:: plot .. autofunction:: plot_parametric .. autofunction:: plot3d .. autofunction:: plot3d_parametric_line .. autofunction:: plot3d_parametric_surface .. autofunction:: sympy.plotting.plot_implicit::plot_implicit PlotGrid Class -------------- .. autoclass:: sympy.plotting.plot::PlotGrid :members: Series Classes -------------- .. autoclass:: sympy.plotting.plot::BaseSeries :members: .. autoclass:: sympy.plotting.plot::Line2DBaseSeries :members: .. autoclass:: sympy.plotting.plot::LineOver1DRangeSeries :members: .. autoclass:: sympy.plotting.plot::Parametric2DLineSeries :members: .. autoclass:: sympy.plotting.plot::Line3DBaseSeries :members: .. autoclass:: sympy.plotting.plot::Parametric3DLineSeries :members: .. autoclass:: sympy.plotting.plot::SurfaceBaseSeries :members: .. autoclass:: sympy.plotting.plot::SurfaceOver2DRangeSeries :members: .. autoclass:: sympy.plotting.plot::ParametricSurfaceSeries :members: .. autoclass:: sympy.plotting.plot_implicit::ImplicitSeries :members: Backends -------- .. autoclass:: sympy.plotting.plot::BaseBackend :members: .. autoclass:: sympy.plotting.plot::MatplotlibBackend :members: .. autoclass:: sympy.plotting.plot::TextBackend :members: Pyglet Plotting --------------- .. module:: sympy.plotting.pygletplot 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 >>> 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 $f(0.0)=(0.4,0.4,0.4) \rightarrow f(1.0)=(0.9,0.9,0.9)$. 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. .. _plot_geom: 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, :func:`~.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 ----------------------- .. autofunction:: sympy.plotting.textplot::textplot