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plot with varying color line

asked 2023-08-18 06:46:17 +0200

takashi gravatar image

updated 2023-08-18 17:18:47 +0200

slelievre gravatar image

Is there a way to plot a complex function of a single real variable so that the color of the line represents the argument of the complex function and the vertical position of the line represents the norm of the complex function.

For example can this be modified so that the color of the line represents the argument of the function?

f(x) = exp(5*i*x) * exp(-x^2/20)  # complex gaussian wave packet
plot(abs(f(x)), x, -10,10)  # plot magnitude of the function

Is there anything available along the lines of this:

plot(abs(f(x), x, -10, 10, linecolor = hue(complex_to_hue(f(x))))
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answered 2023-08-18 13:04:30 +0200

Emmanuel Charpentier gravatar image

This is implemented in Sagefor 3D plotting, but not for 2D plotting... One possible workaround is to use ggplot2, whch you can reach though the Python package plotnine or via R's ggplot2 package.

HTH,

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answered 2023-08-19 01:11:26 +0200

slelievre gravatar image

updated 2023-08-19 01:24:17 +0200

One could compute f(x) for a list of x along the interval.

Then add intermediate points until the angle difference between any two successive f(x) is small enough.

Finally, draw a line segment of the appropriate color to join each pair of points. The collection of these colored line segments gives the desired plot.

Here is a function to do that.

def plot_cx(f, x_range, plot_points=200, epsilon_turn=1/32, **opt):
    r"""
    Return a plot of this complex-valued function of one real variable.

    The plot is a plot $y = abs(f(x))$ with varying line color
    indicating the argument of $f(x)$.

    Assumes $f$ is nonzero along the interval, and its argument
    varies not too steeply.

    INPUT:

    - ``f`` -- a complex-valued function of one real variable
    - ``x_range`` -- the range for the variable `x`, a pair ``(xmin, xmax)``
    - ``plot_points`` -- number of points in the initial subdivision
    - ``epsilon_turn`` -- threshold for how far to refine the subdivision:
      we refine until the angle between the images of two successive points
      is less than ``epsilon_turn`` turns

    EXAMPLES::

        sage: f(x) = exp(5*i*x) * exp(-x^2/20)  # complex gaussian wave packet
        sage: plot_cx(f, (-10, 10))
        Launched png viewer for Graphics object consisting of 796 graphics primitives
    """
    from more_itertools import pairwise
    xmin, xmax = x_range
    xmin = RDF(xmin)
    xmax = RDF(xmax)
    h = (xmax - xmin) / (plot_points - 1)
    data = [(x, f(x)) for x in srange(xmin, xmax - h/2, h)]
    data.append((xmax, f(xmax)))
    pi = math.pi
    tau = math.tau
    n = 0
    nn = 1
    while nn < len(data):
        x, z = data[n]
        xx, zz = data[nn]
        while abs(arg(zz / z))/tau > epsilon_turn:
            xx = (x + xx) / 2
            zz = f(xx)
            data.insert(nn, (xx, zz))
        n += 1
        nn += 1
    return sum(line2d([(x, abs(z)), (xx, abs(zz))], hue=(pi + arg(z))/tau, **opt)
               for (x, z), (xx, zz) in pairwise(data))

Usage:

sage: f(x) = exp(5*i*x) * exp(-x^2/20)
sage: p = plot_cx(f, (-10, 10))
sage: p.show()
Launched png viewer for Graphics object consisting of 796 graphics primitives

Complex-valued function of one real variable

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Asked: 2023-08-18 06:46:17 +0200

Seen: 132 times

Last updated: Aug 19 '23