[FIXED] Plotting periods of a trig function in matplotlib

Issue

I am writing some simple scripts to plot a graph given a trigonometric function (in this example, a sine).

My issue is that I'd like to plot JUST two periods of the given trig function. To clarify, in trigonometry a Period is the length (on a graph) that ONE wave takes up. For sin and cos, one period is 2pi.

I'd like to take my existing code, and (preferably) using matplotlib, plot two periods of my given trig function, and line up a couple of points on the graph with a couple of points on my function.

If it's possible, I would like to be able to plot my function so that the start of the first period lines up with my first label, the highest point of the first period lines up with the second label, the point where my function crosses the x-axis with the third label, the lowest point with the fourth label, and the end of my first period/beginning of my second period with the fifth label. This pattern would then repeat for the second period. From here on, I'm going to refer to the x labels as the "Period Markings".

I've come up with three possible solutions for this:

1. I could set the borders of my graph (in this case x = -4 and x = 4) to be labeled as the first and ninth Period Markings respectively, then constrain my function to just be within the graph somehow.
2. I could somehow set a parameter in matplotlib to only plot 4pi (the length of two periods) units worth of line, although in that case, however, I don't think that the Period Markings would match up with their desired points.
3. If matplotlib supports it, I could find the low points, x-intercepts, and high points of the graph, then assign my Period Markers to each one from left to right. This would have the advantage of removing the necessity to plot ONLY two periods, as the Period Markers would dictate the beginning and end of the two periods.

Below I've inserted a couple of things:

1. A copy of the plotting part of my code, containing a sample equation and some sample Period Markings
2. A screenshot of the graph of the given sample equation
3. A visual representation of where each Period Marking would line up with, ideally, as well as a line demarcating an estimation of two full periods.

The standard form of a sin function is y = aSIN(bx-c)+d. The equation here is just sin(x), but you can see how variables c and d play a role in determining the graph. Usually, the xlabels array would be filled in with variables that are determined earlier in the script, as would all the variables at the top (func, a, b, c, d).

import math
import matplotlib.pyplot as plt
import numpy as np

func = sin
a = 1
b = 1
c = 0
d = 0
xlabels = np.array(['-2pi', '-3pi/2', '-pi', '-pi/2',
                    '0','pi/2', 'pi', '3pi/2','2pi'])

xlabelcount = -4, -3, -2, -1, 0, 1, 2, 3, 4
x = np.arange(-4, 4, 0.01)
if func == 'sin':
    ypoints = a*np.sin(2*x-c)+d
if func == 'cos':
    ypoints = a*np.cos(2*x+c)+d
if b < 0:
    plt.gca().invert_yaxis()

plt.title('Wave Function')
plt.xlabel('Period (Not to Scale)')
plt.ylabel('Amplitude')
plt.grid(True, which='both')
plt.axhline(y=0, color='k')
plt.plot(x, ypoints)
plt.xticks(ticks=xlabelcount,labels=xlabels)
plt.show()

Plot of sin(x) Preferred Period Marking placements

I hope this can provide a comprehensive understanding of the issue I face, and any help would be greatly appreciated. I feel that I've done a fair amount of Googling around, but nothing has yielded a good answer. I apologize in advance if I'm missing something really obvious.

Thanks, dreadlearner

Solution

If I understand this correctly, you would like to add points on the curve at certain predefined locations on x-axis (period markings). If this is correct, the best way is to evaluate the value of the function at those particular "period markings" and plot this as a single point. Something like:

fn = "sin"

if fn == "sin":
    fn = np.sin

elif fn == "cos":
    fn = np.cos

# if required, the next three statements can be 
# customized for each function by shifting them
# inside the if ... else blocks
 
x = np.linspace(-2*np.pi, 2*np.pi, 1000)
points = [i * np.pi/2 for i in range(-4, 5)]
labels = ["-2π", "-3π/2", "-π", "-π/2", "0", "π/2", "π", "3π/2", "2π"]

fig, ax  = plt.subplots()
ax.plot(x, fn(x))
ax.set_xticks(points)
ax.set_xticklabels(labels)

# the next line is what you probably want
for pt in points:
    ax.plot(pt, fn(pt), "ok")

ax.hlines(0, x[0], x[-1], "r")

plt.show()

Looks like this:

Answered By - krm