Equations in Python

Question

I'm trying to implement an equation from a paper in Python (black square equations) -

enter image description here

So far I have a simplified model but I'm unable to generate the intended output (below image); I suspect the issue is with np.exp() though I'm unsure - any suggestions of how I can do this?

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

f     = 1e6
T     = 1/f
Omega = 2*np.pi*f

i = np.arange(0,50e-6,100e-9)
y = np.sin(Omega*i) * (i**2) * np.exp(-i)   

plt.figure(1)
plt.plot(i,y,'b-')
plt.grid()
plt.show()

enter image description here

Have you played with the input values? Try decreasing the frequency and extending the range of i. — Jakob
– Jakob, Commented Oct 27, 2013 at 22:15

Lev Levitsky · Accepted Answer · 2013-10-27 22:25:57Z

2

To illustrate Jacob's comment, here's what you can get by tweaking the constants:

Graph

Code:

import numpy as np
import matplotlib.pyplot as plt

f     = 5
Omega = 2*np.pi*f

i = np.arange(0, 10, 0.001)
y = np.sin(Omega*i) * (i**2) * np.exp(-i)

plt.figure(1)
plt.plot(i,y,'b-')
plt.grid()
plt.show()

Or, you could keep the time scale and introduce an h of about 5e-6, as Bas Swinckels suggests in his answer:

f     = 1e6
Omega = 2*np.pi*f

i = np.arange(0,50e-6,100e-9)
y = np.sin(Omega*i) * (i**2) * np.exp(-i/5e-6)

This produces a very similar output.

edited Oct 27, 2013 at 22:25

answered Oct 27, 2013 at 22:20

Lev Levitsky

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Comments

Bas Swinckels · Accepted Answer · 2013-10-27 22:38:52Z

2

I suggest to use the exact same variable names as in the paper, that makes things so much clearer. For time, always use t or time, no excuses. The variable i is normally used for indices or complex numbers. You are also missing the variables m (which you hard-coded as 2), v_0 and h. I guess you need to set h to the correct value to solve your problem. In this sort of problems, h is usually a decay time, which you, by forgetting it in the formula, implicitly took as 1 second. Given the high frequencies of your problem, this should be much shorter. Looking at your example plot, you should probably set it to a few times T.

edited Oct 27, 2013 at 22:38

answered Oct 27, 2013 at 22:13

Bas Swinckels

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1 Comment

Lev Levitsky Over a year ago

+1, h seems to be the problem, as illustrated in my answer below.

redrivercrayon · Accepted Answer · 2013-10-27 22:17:48Z

0

Also, I think one primary mistake that you are making is that you are plotting yagainst i- which IMHO should be actually a yvs. 1/iplot. this, combined with the comment from @BasSwinckels, when you start fiddling around with the parameters, you should get closer to the aim plot.

Cheers! And all the best!

answered Oct 27, 2013 at 22:17

redrivercrayon

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2 Comments

Harry Lime Over a year ago

OK, thanks all for taking a look - yes t for time makes sense, I was using i as in index. Also, h=1 in my first look, and I know see h as the decay factor.

redrivercrayon Over a year ago

@BasSwinckels I stand corrected. I had tried a few plots with 1/i and it looked like something similar but I was definitely on the wrong track. Sorry for the obfuscation @Jake French

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