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This is the function I need to plot: function

This is my code:

pi = np.pi
sin = np.sin
e = np.e

x1 = np.linspace(-10*pi, -pi)
y1 = (4*pi*(e**0.1*x1)) * sin(2*pi*x1)
plt.plot(x1, y1)

x2 = np.linspace(-pi, -pi/2)
y2 = 0
plt.plot(x2, y2)

x3 = np.linspace(-pi/2, pi/2)
y3 = 4/pi * x3**2 - pi
plt.plot(x3, y3)

x4 = np.linspace(pi/2, pi)
y4 = 0
plt.plot(x4, y4)

plt.show()

But every time I try to run it gives me a ValueError:

ValueError: x and y must have same first dimension, but have shapes (50,) and (1,)

I have tried using np.piecewise but haven't gotten anywhere.

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  • You are setting y2 and y4 to a single value of 0. Remember, you are not plotting functions. Even if y2 is always zero, you still need to create a list/array/whatever with all the necessary number of zeros [0, 0, and so on. Commented Nov 18, 2022 at 10:43

3 Answers 3

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enter image description here

To define a piecewise function, I usually use a chained sequence of numpy.where.

First, the domain for the independent variable, then the conditions and the analytical expression, with a difference for the last where, as explained in the docs.
NB: are you sure that the circular frequency of the sines is 2π? when I see a domain expressed in multiples of π I think immediately to frequencies expressed as integer numbers or simple fractions…

from numpy import exp,linspace, pi, sin, where
from matplotlib.pyplot import grid, plot, show

x = linspace(-10*pi, +10*pi, 4001)
y = where(x <  -pi, 4*pi*exp(+x/10)*sin(1*x),
    where(x <-pi/2, 0,
    where(x <+pi/2, 4*x*x/pi-pi,
    where(x <  +pi, 0,
                    4*pi*exp(-x/10)*sin(1*x)))))
    
plot(x, y) ; grid() ; show()

PS

In a comment Davide_sd correctly remarks that the technique I have shown is OK only if the piecewise function is continuous.
If there are discontinuities across sub-domains, you can always use numpy.where but you should assign np.nan values to the y array in the points of discontinuity, so that Matplotlib knows that she has to break the line across the NaN.

— EDIT — I've changed the circular frequency of the sines because I cannot make sense of the OP specification.

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4 Comments

Note that this will connects the point between two pieces, which might get the wrong idea to someone looking at the plot!
@Davide_sd Good general remark, but THIS function is continuous.
@Davide_sd I have edited my answer to incorporate/discuss your useful remark.
I like the structure of this approach. I will be doing piecewise polynomial fits.
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x2 is an array, and y2 is a number, matplotlib expects both to be arrays, so you should switch y2 and y4 definition to be y2 = np.zeros_like(x2), and y4 = np.zeros_like(x4).

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Thank you so much, I'm quite new to matplotlib
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As x and y need to be the same first dimension, you might want to define y2 and y4 to be a function of x, so that an array of the same dimension is produced as a result to plot.

#...
y2 = x2*0
plt.plot(x2, y2)

#...

y4 = x4*0
plt.plot(x4, y4)

Alternatively, you could have y2 and y4 defined as an array of zeros of the same size of x2 and x4 respectively.

y2 = np.zeros(x2.shape)
y4 = np.zeros(x4.shape)
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