Ejemplo n.º 1
0
def main():

    print(__doc__)

    x = symbols('x')

    # a numpy array we can apply the ufuncs to
    grid = np.linspace(-1, 1, 1000)

    # set mpmath precision to 20 significant numbers for verification
    mpmath.mp.dps = 20

    print("Compiling legendre ufuncs and checking results:")

    # Let's also plot the ufunc's we generate
    plot1 = Plot(visible=False)
    for n in range(6):

        # Setup the SymPy expression to ufuncify
        expr = legendre(n, x)
        print("The polynomial of degree %i is" % n)
        pprint(expr)

        # This is where the magic happens:
        binary_poly = ufuncify(x, expr)

        # It's now ready for use with numpy arrays
        polyvector = binary_poly(grid)

        # let's check the values against mpmath's legendre function
        maxdiff = 0
        for j in range(len(grid)):
            precise_val = mpmath.legendre(n, grid[j])
            diff = abs(polyvector[j] - precise_val)
            if diff > maxdiff:
                maxdiff = diff
        print("The largest error in applied ufunc was %e" % maxdiff)
        assert maxdiff < 1e-14

        # We can also attach the autowrapped legendre polynomial to a sympy
        # function and plot values as they are calculated by the binary function
        g = implemented_function('g', binary_poly)
        plot1[n] = g(x), [200]

    print(
        "Here's a plot with values calculated by the wrapped binary functions")
    plot1.show()
Ejemplo n.º 2
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def main():

    print(__doc__)

    x = symbols('x')

    # a numpy array we can apply the ufuncs to
    grid = np.linspace(-1, 1, 1000)

    # set mpmath precision to 20 significant numbers for verification
    mpmath.mp.dps = 20

    print("Compiling legendre ufuncs and checking results:")

    # Let's also plot the ufunc's we generate
    plot1 = Plot(visible=False)
    for n in range(6):

        # Setup the SymPy expression to ufuncify
        expr = legendre(n, x)
        print("The polynomial of degree %i is" % n)
        pprint(expr)

        # This is where the magic happens:
        binary_poly = ufuncify(x, expr)

        # It's now ready for use with numpy arrays
        polyvector = binary_poly(grid)

        # let's check the values against mpmath's legendre function
        maxdiff = 0
        for j in range(len(grid)):
            precise_val = mpmath.legendre(n, grid[j])
            diff = abs(polyvector[j] - precise_val)
            if diff > maxdiff:
                maxdiff = diff
        print("The largest error in applied ufunc was %e" % maxdiff)
        assert maxdiff < 1e-14

        # We can also attach the autowrapped legendre polynomial to a sympy
        # function and plot values as they are calculated by the binary function
        g = implemented_function('g', binary_poly)
        plot1[n] = g(x), [200]

    print("Here's a plot with values calculated by the wrapped binary functions")
    plot1.show()
Ejemplo n.º 3
0
def plot_beam(beam, **kwargs):
    """Plot the beam radius as it propagates in space.
    Uses pyglet and ctype libraries

    Parameters
    ==========
    
    beam : BeamParameter for gaussian beam
    z_range : plot range for the beam propagation coordinate

    See Also
    ========    
    
    BeamParameter
    plot_beam2
    
    Examples
    ========
    
    >>> from sympy.physics.gaussopt import BeamParameter, plot_beam
    >>> b = BeamParameter(530e-9, 1, w=1e-5)
    >>> plot_beam(b,z_range=2*b.z_r)    
    """
    
    if len(kwargs) != 1:
        raise ValueError("The function expects only one named argument")    
    elif 'z_range' in kwargs :
        z_range = sympify(kwargs['z_range'])
    else :
        raise ValueError(filldedent('''
            The functions expects the z_range as a named argument'''))

    x = symbols('x')
    # TODO beam.w_0 * 
    # pyglet needs to have better zoom adjustment for geting a normal view
    weist_d = sqrt(1+(x/beam.z_r)**2)
    
    p = Plot(visible=False)
    
    p[1] = weist_d, 'color=black', [x, -z_range, z_range, int(beam.w_0**-1)]
    p[2] = -weist_d, 'color=black', [x, -z_range, z_range, int(beam.w_0**-1)]
    
    p.adjust_all_bounds()
    p.show()
Ejemplo n.º 4
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def test_plot_2d():
    from sympy import Plot
    p=Plot(x, [x, -5, 5, 4], visible=False)
    p.wait_for_calculations()
Ejemplo n.º 5
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def test_plot_integral():
    # Make sure it doesn't treat x as an independent variable
    from sympy import Plot, Integral
    p = Plot(Integral(z*x, (x, 1, z), (z, 1, y)), visible=False)
    p.wait_for_calculations()
Ejemplo n.º 6
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 def _test_plot_log(self):
     from sympy import Plot
     p=Plot(log(x), [x,0,6.282,4], 'mode=polar', visible=False)
     p.wait_for_calculations()
Ejemplo n.º 7
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 def test_plot_3d_spherical(self):
     from sympy import Plot
     p=Plot(1, [x,0,6.282,4], [y,0,3.141,4], 'mode=spherical;style=wireframe', visible=False)
     p.wait_for_calculations()
Ejemplo n.º 8
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 def test_plot_2d_polar(self):
     from sympy import Plot
     p=Plot(1/x, [x,-1,1,4], 'mode=polar', visible=False)
     p.wait_for_calculations()
Ejemplo n.º 9
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 def test_plot_3d(self):
     from sympy import Plot
     p=Plot(x*y, [x, -5, 5, 5], [y, -5, 5, 5], visible=False)
     p.wait_for_calculations()
Ejemplo n.º 10
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def test_plot_3d_discontinuous():
    from sympy import Plot
    p = Plot(1 / x, [x, -3, 3, 6], [y, -1, 1, 1], visible=False)
    p.wait_for_calculations()
Ejemplo n.º 11
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def test_plot_3d():
    from sympy import Plot
    p = Plot(x * y, [x, -5, 5, 5], [y, -5, 5, 5], visible=False)
    p.wait_for_calculations()
Ejemplo n.º 12
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def test_plot_2d():
    from sympy import Plot
    p = Plot(x, [x, -5, 5, 4], visible=False)
    p.wait_for_calculations()
Ejemplo n.º 13
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def test_plot_integral():
    # Make sure it doesn't treat x as an independent variable
    from sympy import Plot, Integral
    p = Plot(Integral(z * x, (x, 1, z), (z, 1, y)), visible=False)
    p.wait_for_calculations()
Ejemplo n.º 14
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def test_plot_2d_discontinuous():
    from sympy import Plot
    p=Plot(1/x, [x, -1, 1, 2], visible=False)
    p.wait_for_calculations()
Ejemplo n.º 15
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def test_plot_2d_polar():
    from sympy import Plot
    p = Plot(1 / x, [x, -1, 1, 4], 'mode=polar', visible=False)
    p.wait_for_calculations()
Ejemplo n.º 16
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#import fos
#print fos.__file__

from sympy import symbols, Plot
x, y, z = symbols('xyz')
Plot(x * y**3 - y * x**3)
Ejemplo n.º 17
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def test_plot_3d_cylinder():
    from sympy import Plot
    p = Plot(1 / y, [x, 0, 6.282, 4], [y, -1, 1, 4],
             'mode=polar;style=solid',
             visible=False)
    p.wait_for_calculations()
Ejemplo n.º 18
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 def test_plot_3d_discontinuous(self):
     from sympy import Plot
     p=Plot(1/x, [x, -3, 3, 6], [y, -1, 1, 1], visible=False)
     p.wait_for_calculations()
Ejemplo n.º 19
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def test_plot_3d_spherical():
    from sympy import Plot
    p = Plot(1, [x, 0, 6.282, 4], [y, 0, 3.141, 4],
             'mode=spherical;style=wireframe',
             visible=False)
    p.wait_for_calculations()
Ejemplo n.º 20
0
 def test_plot_3d_cylinder(self):
     from sympy import Plot
     p=Plot(1/y, [x,0,6.282,4], [y,-1,1,4], 'mode=polar;style=solid', visible=False)
     p.wait_for_calculations()
Ejemplo n.º 21
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def test_plot_3d_parametric():
    from sympy import Plot
    p = Plot(sin(x), cos(x), x / 5.0, [x, 0, 6.282, 4], visible=False)
    p.wait_for_calculations()
Ejemplo n.º 22
0
 def test_plot_3d_parametric(self):
     from sympy import Plot
     p=Plot(sin(x), cos(x), x/5.0, [x, 0, 6.282, 4], visible=False)
     p.wait_for_calculations()
Ejemplo n.º 23
0
def _test_plot_log():
    from sympy import Plot
    p = Plot(log(x), [x, 0, 6.282, 4], 'mode=polar', visible=False)
    p.wait_for_calculations()
Ejemplo n.º 24
0
def main():
    x, y, z = symbols('xyz')

    # toggle axes visibility with F5, colors with F6
    axes_options = 'visible=false; colored=true; label_ticks=true; label_axes=true; overlay=true; stride=0.5'
    #axes_options = 'colored=false; overlay=false; stride=(1.0, 0.5, 0.5)'

    p = Plot(width=600,
             height=500,
             ortho=False,
             invert_mouse_zoom=False,
             axes=axes_options,
             antialiasing=True)

    examples = []

    def example_wrapper(f):
        examples.append(f)
        return f

    @example_wrapper
    def mirrored_saddles():
        p[5] = x**2 - y**2, [20], [20]
        p[6] = y**2 - x**2, [20], [20]

    @example_wrapper
    def mirrored_saddles_saveimage():
        p[5] = x**2 - y**2, [20], [20]
        p[6] = y**2 - x**2, [20], [20]
        p.wait_for_calculations()
        # although the calculation is complete,
        # we still need to wait for it to be
        # rendered, so we'll sleep to be sure.
        sleep(1)
        p.saveimage("plot_example.png")

    @example_wrapper
    def mirrored_ellipsoids():
        p[2] = x**2 + y**2, [40], [40], 'color=zfade'
        p[3] = -x**2 - y**2, [40], [40], 'color=zfade'

    @example_wrapper
    def saddle_colored_by_derivative():
        f = x**2 - y**2
        p[1] = f, 'style=solid'
        p[1].color = abs(f.diff(x)), abs(f.diff(x) + f.diff(y)), abs(f.diff(y))

    @example_wrapper
    def ding_dong_surface():
        f = sqrt(1.0 - y) * y
        p[1] = f, [x, 0, 2 * pi,
                   40], [y, -1, 4,
                         100], 'mode=cylindrical; style=solid; color=zfade4'

    @example_wrapper
    def polar_circle():
        p[7] = 1, 'mode=polar'

    @example_wrapper
    def polar_flower():
        p[8] = 1.5 * sin(4 * x), [160], 'mode=polar'
        p[8].color = z, x, y, (0.5, 0.5, 0.5), (0.8, 0.8,
                                                0.8), (x, y, None, z
                                                       )  # z is used for t

    @example_wrapper
    def simple_cylinder():
        p[9] = 1, 'mode=cylindrical'

    @example_wrapper
    def cylindrical_hyperbola():
        ## (note that polar is an alias for cylindrical)
        p[10] = 1 / y, 'mode=polar', [x], [y, -2, 2, 20]

    @example_wrapper
    def extruded_hyperbolas():
        p[11] = 1 / x, [x, -10, 10, 100], [1], 'style=solid'
        p[12] = -1 / x, [x, -10, 10, 100], [1], 'style=solid'

    @example_wrapper
    def torus():
        a, b = 1, 0.5  # radius, thickness
        p[13] = (a + b * cos(x)) * cos(y), (a +
                                            b * cos(x)) * sin(y), b * sin(x), [
                                                x, 0, pi * 2, 40
                                            ], [y, 0, pi * 2, 40]

    @example_wrapper
    def warped_torus():
        a, b = 2, 1  # radius, thickness
        p[13] = (a + b * cos(x)) * cos(y), (
            a + b * cos(x)) * sin(y), b * sin(x) + 0.5 * sin(4 * y), [
                x, 0, pi * 2, 40
            ], [y, 0, pi * 2, 40]

    @example_wrapper
    def parametric_spiral():
        p[14] = cos(y), sin(y), y / 10.0, [y, -4 * pi, 4 * pi, 100]
        p[14].color = x, (0.1, 0.9), y, (0.1, 0.9), z, (0.1, 0.9)

    @example_wrapper
    def multistep_gradient():
        p[1] = 1, 'mode=spherical', 'style=both'
        #p[1] = exp(-x**2-y**2+(x*y)/4), [-1.7,1.7,100], [-1.7,1.7,100], 'style=solid'
        #p[1] = 5*x*y*exp(-x**2-y**2), [-2,2,100], [-2,2,100]
        gradient = [
            0.0, (0.3, 0.3, 1.0), 0.30, (0.3, 1.0, 0.3),
            0.55, (0.95, 1.0, 0.2), 0.65, (1.0, 0.95, 0.2), 0.85,
            (1.0, 0.7, 0.2), 1.0, (1.0, 0.3, 0.2)
        ]
        p[1].color = z, [None, None, z], gradient
        #p[1].color = 'zfade'
        #p[1].color = 'zfade3'

    @example_wrapper
    def lambda_vs_sympy_evaluation():
        start = clock()
        p[4] = x**2 + y**2, [100], [100], 'style=solid'
        p.wait_for_calculations()
        print "lambda-based calculation took %s seconds." % (clock() - start)

        start = clock()
        p[4] = x**2 + y**2, [100], [100], 'style=solid; use_sympy_eval'
        p.wait_for_calculations()
        print "sympy substitution-based calculation took %s seconds." % (
            clock() - start)

    @example_wrapper
    def gradient_vectors():
        def gradient_vectors_inner(f, i):
            from sympy import lambdify
            from sympy.plotting.plot_interval import PlotInterval
            from pyglet.gl import glBegin, glColor3f
            from pyglet.gl import glVertex3f, glEnd, GL_LINES

            def draw_gradient_vectors(f, iu, iv):
                """
                Create a function which draws vectors
                representing the gradient of f.
                """
                dx, dy, dz = f.diff(x), f.diff(y), 0
                FF = lambdify([x, y], [x, y, f])
                FG = lambdify([x, y], [dx, dy, dz])
                iu.v_steps /= 5
                iv.v_steps /= 5
                Gvl = list(
                    list([FF(u, v), FG(u, v)] for v in iv.frange())
                    for u in iu.frange())

                def draw_arrow(p1, p2):
                    """
                    Draw a single vector.
                    """
                    glColor3f(0.4, 0.4, 0.9)
                    glVertex3f(*p1)

                    glColor3f(0.9, 0.4, 0.4)
                    glVertex3f(*p2)

                def draw():
                    """
                    Iterate through the calculated
                    vectors and draw them.
                    """
                    glBegin(GL_LINES)
                    for u in Gvl:
                        for v in u:
                            point = [[v[0][0], v[0][1], v[0][2]],
                                     [
                                         v[0][0] + v[1][0], v[0][1] + v[1][1],
                                         v[0][2] + v[1][2]
                                     ]]
                            draw_arrow(point[0], point[1])
                    glEnd()

                return draw

            p[i] = f, [-0.5, 0.5, 25], [-0.5, 0.5, 25], 'style=solid'
            iu = PlotInterval(p[i].intervals[0])
            iv = PlotInterval(p[i].intervals[1])
            p[i].postdraw.append(draw_gradient_vectors(f, iu, iv))

        gradient_vectors_inner(x**2 + y**2, 1)
        gradient_vectors_inner(-x**2 - y**2, 2)

    def help_str():
        s = ("\nPlot p has been created. Useful commands: \n"
             "    help(p), p[1] = x**2, print p, p.clear() \n\n"
             "Available examples (see source in plotting.py):\n\n")
        for i in xrange(len(examples)):
            s += "(%i) %s\n" % (i, examples[i].__name__)
        s += "\n"
        s += "e.g. >>> example(2)\n"
        s += "     >>> ding_dong_surface()\n"
        return s

    def example(i):
        if callable(i):
            p.clear()
            i()
        elif i >= 0 and i < len(examples):
            p.clear()
            examples[i]()
        else:
            print "Not a valid example.\n"
        print p

    #ding_dong_surface()
    mirrored_saddles()
    #parametric_spiral()
    #multistep_gradient()
    #gradient_vectors()
    #example(0)
    print help_str()
Ejemplo n.º 25
0
def main():
    fun1 = cos(x) * sin(y)
    fun2 = sin(x) * sin(y)
    fun3 = cos(y) + log(tan(y / 2)) + 0.2 * x

    Plot(fun1, fun2, fun3, [x, -0.00, 12.4, 40], [y, 0.1, 2, 40])