Using numPy and matplotlib for plotting maximum values of a function with respect to two variables

Question

Hi I want to plot a graph using the maximum values of I with respect to changes in variable r.

I'm using the Euler Method solution for an DE with my code being:

import numpy as np
from matplotlib import pyplot as plt 

B=0.001
r=0.06
n=101
dt=1
t0=0
tf=10

t = np.linspace(t0,tf,n)
S = np.zeros([n])
I = np.zeros([n])

S[0]=199
I[0]=1

for i in range(1,n):
 S[i] = S[i-1] + (- B * (S[i-1]) )* I[i-1] * dt
 I[i] = I[i-1] + (I[i-1] * (B * S[i-1] - r)) * dt

This would plot against variable t in the x-axis, with r being constant

But when I tried coding for a plot of I against r, by changing r into a variable, the values I get from print() is not equal to when I manually change the value of constant r(like above)

So I tried using np.max and r=np.linspace but I'm not getting the expected plots

import numpy as np
from matplotlib import pyplot as plt 

B=0.001
n=101
dt=1
t0=0
tf=10

t = np.linspace(t0,tf,n)
r = np.linspace(0.01,0.5,n)
S = np.zeros([n])
I = np.zeros([n])

S[0]=199
I[0]=1

for i in range(1,n):
 r[i] = r[i]
 S[i] = S[i-1] + (- B * (S[i-1]) )* I[i-1] * dt
 I[i] = I[i-1] + (I[i-1] * (B * S[i-1] - r[i])) * dt
Imax=np.max(I)
Imax2=np.array(Imax)

plt.plot(r,Imax2)

If I didn't use r=linspace I would get the size-1 array error in my I[i] line. Any ideas how do I get maximum value of I vs r?

Welcome to StackOverflow! I tried to run your code, but it is very buggy. First, tf and t0 aren't defined, and the for loop is on j while the content of the loop uses i indexing (undefined). Finally, the I array is always 1D. Could you make sure to run your code before posting? — Léonard
– Léonard, Commented Sep 28, 2020 at 7:46

cvanelteren · Accepted Answer · 2020-09-28 07:45:05Z

0

Use the numpy function maximum for elementwise max.

The np.max function reduces the array to float (if no axis is specified).

I edited your code to allow it to run:

import numpy as np
from matplotlib import pyplot as plt 

B=0.001
n=101
dt=1
t0 = 0 # inferred not in the actual code
tf = 10 # inferred not in the actual code
t = np.linspace(t0,tf,n)
r = np.linspace(0.01,0.5,n)
S = np.zeros([n])
I = np.zeros([n])

S[0]=199
I[0]=1
# error with index, changed to i
for i in range(1,n):
 r[i] = r[i]
 S[i] = S[i-1] + (- B * (S[i-1]) )* I[i-1] * dt
 I[i] = I[i-1] + (I[i-1] * (B * S[i-1] - r[i])) * dt
# get max of I and S element wise
Imax=np.maximum(S, I)

plt.plot(r,Imax)

answered Sep 28, 2020 at 7:45

cvanelteren

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