Vehicle-cpp/hkpc/software/sympy/plotting/tests/test_plot.py

import os
from tempfile import TemporaryDirectory

from sympy.concrete.summations import Sum
from sympy.core.numbers import (I, oo, pi)
from sympy.core.relational import Ne
from sympy.core.symbol import Symbol
from sympy.functions.elementary.exponential import (LambertW, exp, exp_polar, log)
from sympy.functions.elementary.miscellaneous import (real_root, sqrt)
from sympy.functions.elementary.piecewise import Piecewise
from sympy.functions.elementary.trigonometric import (cos, sin)
from sympy.functions.special.hyper import meijerg
from sympy.integrals.integrals import Integral
from sympy.logic.boolalg import And
from sympy.core.singleton import S
from sympy.core.sympify import sympify
from sympy.external import import_module
from sympy.plotting.plot import (
    Plot, plot, plot_parametric, plot3d_parametric_line, plot3d,
    plot3d_parametric_surface)
from sympy.plotting.plot import (
    unset_show, plot_contour, PlotGrid, DefaultBackend, MatplotlibBackend,
    TextBackend, BaseBackend)
from sympy.testing.pytest import skip, raises, warns, warns_deprecated_sympy
from sympy.utilities import lambdify as lambdify_
from sympy.utilities.exceptions import ignore_warnings


unset_show()


matplotlib = import_module(
    'matplotlib', min_module_version='1.1.0', catch=(RuntimeError,))


class DummyBackendNotOk(BaseBackend):
    """ Used to verify if users can create their own backends.
    This backend is meant to raise NotImplementedError for methods `show`,
    `save`, `close`.
    """
    pass


class DummyBackendOk(BaseBackend):
    """ Used to verify if users can create their own backends.
    This backend is meant to pass all tests.
    """
    def show(self):
        pass

    def save(self):
        pass

    def close(self):
        pass


def test_plot_and_save_1():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    y = Symbol('y')

    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        ###
        # Examples from the 'introduction' notebook
        ###
        p = plot(x, legend=True, label='f1')
        p = plot(x*sin(x), x*cos(x), label='f2')
        p.extend(p)
        p[0].line_color = lambda a: a
        p[1].line_color = 'b'
        p.title = 'Big title'
        p.xlabel = 'the x axis'
        p[1].label = 'straight line'
        p.legend = True
        p.aspect_ratio = (1, 1)
        p.xlim = (-15, 20)
        filename = 'test_basic_options_and_colors.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p.extend(plot(x + 1))
        p.append(plot(x + 3, x**2)[1])
        filename = 'test_plot_extend_append.png'
        p.save(os.path.join(tmpdir, filename))

        p[2] = plot(x**2, (x, -2, 3))
        filename = 'test_plot_setitem.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot(sin(x), (x, -2*pi, 4*pi))
        filename = 'test_line_explicit.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot(sin(x))
        filename = 'test_line_default_range.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot((x**2, (x, -5, 5)), (x**3, (x, -3, 3)))
        filename = 'test_line_multiple_range.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        raises(ValueError, lambda: plot(x, y))

        #Piecewise plots
        p = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1))
        filename = 'test_plot_piecewise.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot(Piecewise((x, x < 1), (x**2, True)), (x, -3, 3))
        filename = 'test_plot_piecewise_2.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # test issue 7471
        p1 = plot(x)
        p2 = plot(3)
        p1.extend(p2)
        filename = 'test_horizontal_line.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # test issue 10925
        f = Piecewise((-1, x < -1), (x, And(-1 <= x, x < 0)), \
            (x**2, And(0 <= x, x < 1)), (x**3, x >= 1))
        p = plot(f, (x, -3, 3))
        filename = 'test_plot_piecewise_3.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()


def test_plot_and_save_2():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    y = Symbol('y')
    z = Symbol('z')

    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        #parametric 2d plots.
        #Single plot with default range.
        p = plot_parametric(sin(x), cos(x))
        filename = 'test_parametric.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        #Single plot with range.
        p = plot_parametric(
            sin(x), cos(x), (x, -5, 5), legend=True, label='parametric_plot')
        filename = 'test_parametric_range.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        #Multiple plots with same range.
        p = plot_parametric((sin(x), cos(x)), (x, sin(x)))
        filename = 'test_parametric_multiple.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        #Multiple plots with different ranges.
        p = plot_parametric(
            (sin(x), cos(x), (x, -3, 3)), (x, sin(x), (x, -5, 5)))
        filename = 'test_parametric_multiple_ranges.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        #depth of recursion specified.
        p = plot_parametric(x, sin(x), depth=13)
        filename = 'test_recursion_depth.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        #No adaptive sampling.
        p = plot_parametric(cos(x), sin(x), adaptive=False, nb_of_points=500)
        filename = 'test_adaptive.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        #3d parametric plots
        p = plot3d_parametric_line(
            sin(x), cos(x), x, legend=True, label='3d_parametric_plot')
        filename = 'test_3d_line.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot3d_parametric_line(
            (sin(x), cos(x), x, (x, -5, 5)), (cos(x), sin(x), x, (x, -3, 3)))
        filename = 'test_3d_line_multiple.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot3d_parametric_line(sin(x), cos(x), x, nb_of_points=30)
        filename = 'test_3d_line_points.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # 3d surface single plot.
        p = plot3d(x * y)
        filename = 'test_surface.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Multiple 3D plots with same range.
        p = plot3d(-x * y, x * y, (x, -5, 5))
        filename = 'test_surface_multiple.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Multiple 3D plots with different ranges.
        p = plot3d(
            (x * y, (x, -3, 3), (y, -3, 3)), (-x * y, (x, -3, 3), (y, -3, 3)))
        filename = 'test_surface_multiple_ranges.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Single Parametric 3D plot
        p = plot3d_parametric_surface(sin(x + y), cos(x - y), x - y)
        filename = 'test_parametric_surface.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Multiple Parametric 3D plots.
        p = plot3d_parametric_surface(
            (x*sin(z), x*cos(z), z, (x, -5, 5), (z, -5, 5)),
            (sin(x + y), cos(x - y), x - y, (x, -5, 5), (y, -5, 5)))
        filename = 'test_parametric_surface.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Single Contour plot.
        p = plot_contour(sin(x)*sin(y), (x, -5, 5), (y, -5, 5))
        filename = 'test_contour_plot.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Multiple Contour plots with same range.
        p = plot_contour(x**2 + y**2, x**3 + y**3, (x, -5, 5), (y, -5, 5))
        filename = 'test_contour_plot.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # Multiple Contour plots with different range.
        p = plot_contour(
            (x**2 + y**2, (x, -5, 5), (y, -5, 5)),
            (x**3 + y**3, (x, -3, 3), (y, -3, 3)))
        filename = 'test_contour_plot.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()


def test_plot_and_save_3():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    y = Symbol('y')
    z = Symbol('z')

    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        ###
        # Examples from the 'colors' notebook
        ###

        p = plot(sin(x))
        p[0].line_color = lambda a: a
        filename = 'test_colors_line_arity1.png'
        p.save(os.path.join(tmpdir, filename))

        p[0].line_color = lambda a, b: b
        filename = 'test_colors_line_arity2.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot(x*sin(x), x*cos(x), (x, 0, 10))
        p[0].line_color = lambda a: a
        filename = 'test_colors_param_line_arity1.png'
        p.save(os.path.join(tmpdir, filename))

        p[0].line_color = lambda a, b: a
        filename = 'test_colors_param_line_arity1.png'
        p.save(os.path.join(tmpdir, filename))

        p[0].line_color = lambda a, b: b
        filename = 'test_colors_param_line_arity2b.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot3d_parametric_line(sin(x) + 0.1*sin(x)*cos(7*x),
                cos(x) + 0.1*cos(x)*cos(7*x),
            0.1*sin(7*x),
            (x, 0, 2*pi))
        p[0].line_color = lambdify_(x, sin(4*x))
        filename = 'test_colors_3d_line_arity1.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].line_color = lambda a, b: b
        filename = 'test_colors_3d_line_arity2.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].line_color = lambda a, b, c: c
        filename = 'test_colors_3d_line_arity3.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot3d(sin(x)*y, (x, 0, 6*pi), (y, -5, 5))
        p[0].surface_color = lambda a: a
        filename = 'test_colors_surface_arity1.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].surface_color = lambda a, b: b
        filename = 'test_colors_surface_arity2.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].surface_color = lambda a, b, c: c
        filename = 'test_colors_surface_arity3a.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].surface_color = lambdify_((x, y, z), sqrt((x - 3*pi)**2 + y**2))
        filename = 'test_colors_surface_arity3b.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot3d_parametric_surface(x * cos(4 * y), x * sin(4 * y), y,
                (x, -1, 1), (y, -1, 1))
        p[0].surface_color = lambda a: a
        filename = 'test_colors_param_surf_arity1.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].surface_color = lambda a, b: a*b
        filename = 'test_colors_param_surf_arity2.png'
        p.save(os.path.join(tmpdir, filename))
        p[0].surface_color = lambdify_((x, y, z), sqrt(x**2 + y**2 + z**2))
        filename = 'test_colors_param_surf_arity3.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()


def test_plot_and_save_4():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    y = Symbol('y')

    ###
    # Examples from the 'advanced' notebook
    ###

    # XXX: This raises the warning "The evaluation of the expression is
    # problematic. We are trying a failback method that may still work. Please
    # report this as a bug." It has to use the fallback because using evalf()
    # is the only way to evaluate the integral. We should perhaps just remove
    # that warning.
    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        with warns(
            UserWarning,
            match="The evaluation of the expression is problematic",
            test_stacklevel=False,
        ):
            i = Integral(log((sin(x)**2 + 1)*sqrt(x**2 + 1)), (x, 0, y))
            p = plot(i, (y, 1, 5))
            filename = 'test_advanced_integral.png'
            p.save(os.path.join(tmpdir, filename))
            p._backend.close()


def test_plot_and_save_5():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    y = Symbol('y')

    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        s = Sum(1/x**y, (x, 1, oo))
        p = plot(s, (y, 2, 10))
        filename = 'test_advanced_inf_sum.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p = plot(Sum(1/x, (x, 1, y)), (y, 2, 10), show=False)
        p[0].only_integers = True
        p[0].steps = True
        filename = 'test_advanced_fin_sum.png'

        # XXX: This should be fixed in experimental_lambdify or by using
        # ordinary lambdify so that it doesn't warn. The error results from
        # passing an array of values as the integration limit.
        #
        # UserWarning: The evaluation of the expression is problematic. We are
        # trying a failback method that may still work. Please report this as a
        # bug.
        with ignore_warnings(UserWarning):
            p.save(os.path.join(tmpdir, filename))

        p._backend.close()


def test_plot_and_save_6():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')

    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        filename = 'test.png'
        ###
        # Test expressions that can not be translated to np and generate complex
        # results.
        ###
        p = plot(sin(x) + I*cos(x))
        p.save(os.path.join(tmpdir, filename))

        with ignore_warnings(RuntimeWarning):
            p = plot(sqrt(sqrt(-x)))
            p.save(os.path.join(tmpdir, filename))

        p = plot(LambertW(x))
        p.save(os.path.join(tmpdir, filename))
        p = plot(sqrt(LambertW(x)))
        p.save(os.path.join(tmpdir, filename))

        #Characteristic function of a StudentT distribution with nu=10
        x1 = 5 * x**2 * exp_polar(-I*pi)/2
        m1 = meijerg(((1 / 2,), ()), ((5, 0, 1 / 2), ()), x1)
        x2 = 5*x**2 * exp_polar(I*pi)/2
        m2 = meijerg(((1/2,), ()), ((5, 0, 1/2), ()), x2)
        expr = (m1 + m2) / (48 * pi)
        p = plot(expr, (x, 1e-6, 1e-2))
        p.save(os.path.join(tmpdir, filename))


def test_plotgrid_and_save():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    y = Symbol('y')

    with TemporaryDirectory(prefix='sympy_') as tmpdir:
        p1 = plot(x)
        p2 = plot_parametric((sin(x), cos(x)), (x, sin(x)), show=False)
        p3 = plot_parametric(
            cos(x), sin(x), adaptive=False, nb_of_points=500, show=False)
        p4 = plot3d_parametric_line(sin(x), cos(x), x, show=False)
        # symmetric grid
        p = PlotGrid(2, 2, p1, p2, p3, p4)
        filename = 'test_grid1.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        # grid size greater than the number of subplots
        p = PlotGrid(3, 4, p1, p2, p3, p4)
        filename = 'test_grid2.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()

        p5 = plot(cos(x),(x, -pi, pi), show=False)
        p5[0].line_color = lambda a: a
        p6 = plot(Piecewise((1, x > 0), (0, True)), (x, -1, 1), show=False)
        p7 = plot_contour(
            (x**2 + y**2, (x, -5, 5), (y, -5, 5)),
            (x**3 + y**3, (x, -3, 3), (y, -3, 3)), show=False)
        # unsymmetric grid (subplots in one line)
        p = PlotGrid(1, 3, p5, p6, p7)
        filename = 'test_grid3.png'
        p.save(os.path.join(tmpdir, filename))
        p._backend.close()


def test_append_issue_7140():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    p1 = plot(x)
    p2 = plot(x**2)
    plot(x + 2)

    # append a series
    p2.append(p1[0])
    assert len(p2._series) == 2

    with raises(TypeError):
        p1.append(p2)

    with raises(TypeError):
        p1.append(p2._series)


def test_issue_15265():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    eqn = sin(x)

    p = plot(eqn, xlim=(-S.Pi, S.Pi), ylim=(-1, 1))
    p._backend.close()

    p = plot(eqn, xlim=(-1, 1), ylim=(-S.Pi, S.Pi))
    p._backend.close()

    p = plot(eqn, xlim=(-1, 1), ylim=(sympify('-3.14'), sympify('3.14')))
    p._backend.close()

    p = plot(eqn, xlim=(sympify('-3.14'), sympify('3.14')), ylim=(-1, 1))
    p._backend.close()

    raises(ValueError,
        lambda: plot(eqn, xlim=(-S.ImaginaryUnit, 1), ylim=(-1, 1)))

    raises(ValueError,
        lambda: plot(eqn, xlim=(-1, 1), ylim=(-1, S.ImaginaryUnit)))

    raises(ValueError,
        lambda: plot(eqn, xlim=(S.NegativeInfinity, 1), ylim=(-1, 1)))

    raises(ValueError,
        lambda: plot(eqn, xlim=(-1, 1), ylim=(-1, S.Infinity)))


def test_empty_Plot():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    # No exception showing an empty plot
    plot()
    p = Plot()
    p.show()


def test_issue_17405():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    f = x**0.3 - 10*x**3 + x**2
    p = plot(f, (x, -10, 10), show=False)
    # Random number of segments, probably more than 100, but we want to see
    # that there are segments generated, as opposed to when the bug was present

    # RuntimeWarning: invalid value encountered in double_scalars
    with ignore_warnings(RuntimeWarning):
        assert len(p[0].get_data()[0]) >= 30


def test_logplot_PR_16796():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    p = plot(x, (x, .001, 100), xscale='log', show=False)
    # Random number of segments, probably more than 100, but we want to see
    # that there are segments generated, as opposed to when the bug was present
    assert len(p[0].get_data()[0]) >= 30
    assert p[0].end == 100.0
    assert p[0].start == .001


def test_issue_16572():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    p = plot(LambertW(x), show=False)
    # Random number of segments, probably more than 50, but we want to see
    # that there are segments generated, as opposed to when the bug was present
    assert len(p[0].get_data()[0]) >= 30


def test_issue_11865():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    k = Symbol('k', integer=True)
    f = Piecewise((-I*exp(I*pi*k)/k + I*exp(-I*pi*k)/k, Ne(k, 0)), (2*pi, True))
    p = plot(f, show=False)
    # Random number of segments, probably more than 100, but we want to see
    # that there are segments generated, as opposed to when the bug was present
    # and that there are no exceptions.
    assert len(p[0].get_data()[0]) >= 30


def test_issue_11461():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    p = plot(real_root((log(x/(x-2))), 3), show=False)
    # Random number of segments, probably more than 100, but we want to see
    # that there are segments generated, as opposed to when the bug was present
    # and that there are no exceptions.
    assert len(p[0].get_data()[0]) >= 30


def test_issue_11764():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    p = plot_parametric(cos(x), sin(x), (x, 0, 2 * pi), aspect_ratio=(1,1), show=False)
    assert p.aspect_ratio == (1, 1)
    # Random number of segments, probably more than 100, but we want to see
    # that there are segments generated, as opposed to when the bug was present
    assert len(p[0].get_data()[0]) >= 30


def test_issue_13516():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')

    pm = plot(sin(x), backend="matplotlib", show=False)
    assert pm.backend == MatplotlibBackend
    assert len(pm[0].get_data()[0]) >= 30

    pt = plot(sin(x), backend="text", show=False)
    assert pt.backend == TextBackend
    assert len(pt[0].get_data()[0]) >= 30

    pd = plot(sin(x), backend="default", show=False)
    assert pd.backend == DefaultBackend
    assert len(pd[0].get_data()[0]) >= 30

    p = plot(sin(x), show=False)
    assert p.backend == DefaultBackend
    assert len(p[0].get_data()[0]) >= 30


def test_plot_limits():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    p = plot(x, x**2, (x, -10, 10))
    backend = p._backend

    xmin, xmax = backend.ax[0].get_xlim()
    assert abs(xmin + 10) < 2
    assert abs(xmax - 10) < 2
    ymin, ymax = backend.ax[0].get_ylim()
    assert abs(ymin + 10) < 10
    assert abs(ymax - 100) < 10


def test_plot3d_parametric_line_limits():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')

    v1 = (2*cos(x), 2*sin(x), 2*x, (x, -5, 5))
    v2 = (sin(x), cos(x), x, (x, -5, 5))
    p = plot3d_parametric_line(v1, v2)
    backend = p._backend

    xmin, xmax = backend.ax[0].get_xlim()
    assert abs(xmin + 2) < 1e-2
    assert abs(xmax - 2) < 1e-2
    ymin, ymax = backend.ax[0].get_ylim()
    assert abs(ymin + 2) < 1e-2
    assert abs(ymax - 2) < 1e-2
    zmin, zmax = backend.ax[0].get_zlim()
    assert abs(zmin + 10) < 1e-2
    assert abs(zmax - 10) < 1e-2

    p = plot3d_parametric_line(v2, v1)
    backend = p._backend

    xmin, xmax = backend.ax[0].get_xlim()
    assert abs(xmin + 2) < 1e-2
    assert abs(xmax - 2) < 1e-2
    ymin, ymax = backend.ax[0].get_ylim()
    assert abs(ymin + 2) < 1e-2
    assert abs(ymax - 2) < 1e-2
    zmin, zmax = backend.ax[0].get_zlim()
    assert abs(zmin + 10) < 1e-2
    assert abs(zmax - 10) < 1e-2

def test_plot_size():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')

    p1 = plot(sin(x), backend="matplotlib", size=(8, 4))
    s1 = p1._backend.fig.get_size_inches()
    assert (s1[0] == 8) and (s1[1] == 4)
    p2 = plot(sin(x), backend="matplotlib", size=(5, 10))
    s2 = p2._backend.fig.get_size_inches()
    assert (s2[0] == 5) and (s2[1] == 10)
    p3 = PlotGrid(2, 1, p1, p2, size=(6, 2))
    s3 = p3._backend.fig.get_size_inches()
    assert (s3[0] == 6) and (s3[1] == 2)

    with raises(ValueError):
        plot(sin(x), backend="matplotlib", size=(-1, 3))

def test_issue_20113():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')

    # verify the capability to use custom backends
    with raises(TypeError):
        plot(sin(x), backend=Plot, show=False)
    p2 = plot(sin(x), backend=MatplotlibBackend, show=False)
    assert p2.backend == MatplotlibBackend
    assert len(p2[0].get_data()[0]) >= 30
    p3 = plot(sin(x), backend=DummyBackendOk, show=False)
    assert p3.backend == DummyBackendOk
    assert len(p3[0].get_data()[0]) >= 30

    # test for an improper coded backend
    p4 = plot(sin(x), backend=DummyBackendNotOk, show=False)
    assert p4.backend == DummyBackendNotOk
    assert len(p4[0].get_data()[0]) >= 30
    with raises(NotImplementedError):
        p4.show()
    with raises(NotImplementedError):
        p4.save("test/path")
    with raises(NotImplementedError):
        p4._backend.close()

def test_custom_coloring():
    x = Symbol('x')
    y = Symbol('y')
    plot(cos(x), line_color=lambda a: a)
    plot(cos(x), line_color=1)
    plot(cos(x), line_color="r")
    plot_parametric(cos(x), sin(x), line_color=lambda a: a)
    plot_parametric(cos(x), sin(x), line_color=1)
    plot_parametric(cos(x), sin(x), line_color="r")
    plot3d_parametric_line(cos(x), sin(x), x, line_color=lambda a: a)
    plot3d_parametric_line(cos(x), sin(x), x, line_color=1)
    plot3d_parametric_line(cos(x), sin(x), x, line_color="r")
    plot3d_parametric_surface(cos(x + y), sin(x - y), x - y,
            (x, -5, 5), (y, -5, 5),
            surface_color=lambda a, b: a**2 + b**2)
    plot3d_parametric_surface(cos(x + y), sin(x - y), x - y,
            (x, -5, 5), (y, -5, 5),
            surface_color=1)
    plot3d_parametric_surface(cos(x + y), sin(x - y), x - y,
            (x, -5, 5), (y, -5, 5),
            surface_color="r")
    plot3d(x*y, (x, -5, 5), (y, -5, 5),
            surface_color=lambda a, b: a**2 + b**2)
    plot3d(x*y, (x, -5, 5), (y, -5, 5), surface_color=1)
    plot3d(x*y, (x, -5, 5), (y, -5, 5), surface_color="r")

def test_deprecated_get_segments():
    if not matplotlib:
        skip("Matplotlib not the default backend")

    x = Symbol('x')
    f = sin(x)
    p = plot(f, (x, -10, 10), show=False)
    with warns_deprecated_sympy():
        p[0].get_segments()