Error with Python definite integral using cumtrapz on a matrix

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In order to compute definite integral $\int_{0}^{t}\exp(||e||^2)$

I have written this code

How can I adapt the number of steps with the step mathematically it seems to be true but when I want to write the code I faced to a problem

I have tried to express the upper bound (i.e. t) by using linespace I think my problem is that I could not state the interval in which "t" is located.

Python

import numpy as np
import math
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import math
from scipy import integrate
from scipy.integrate import quad
from scipy.integrate import quad
import scipy.integrate as it
import numpy as np
from scipy.integrate import quad
import matplotlib.pyplot as plt
from numpy import linalg as LA
from numpy.linalg import inv
from numpy.linalg import matrix_power
from scipy import linalg
from sympy import *
from numpy.linalg import eig
import numpy
import cvxopt
import cvxpy as cp
from cvxopt import matrix, solvers
from scipy.linalg import sqrtm
from scipy import integrate
##############################
# Constants

tmax = 10
t = np.arange(0.0, tmax, 0.1)
m=len(t)
#print(t)
e=np.matrix([[0,1,2 ,3],
             [0,1,1, 1]])

e1=e[0]

e2=e[1]
a=np.power(e1,2)
b=np.power(e2,2)
nrm2e=(a+b)
#print(e1)
#print(e2)
#print(a)
#print(b)
print(nrm2e)
num=10*t
x = np.linspace(0.0, t, num)
nrm2e_int=it.cumtrapz(nrm2e,x, initial=0)
print(nrm2e_int)

I got this error

Traceback (most recent call last):
  File "C:/Users/user/OneDrive/Desktop/yyyyyyyyyyyyyyyyyyyyyyyyyyyyy.py", line 45, in <module>
    x = np.linspace(0.0, t, num)
  File "<__array_function__ internals>", line 6, in linspace
  File "C:\Users\user\AppData\Local\Programs\Python\Python37\lib\site-packages\numpy\core\function_base.py", line 120, in linspace
    num = operator.index(num)
TypeError: only integer scalar arrays can be converted to a scalar index

What I have tried:

I guess that it is because of num which is the number of steps (0.1).

Also when I print values of 10*t

I got float numbers while it must be integer.

Could you please guide me? How can I fix it?

Thank u

Posted 9-Aug-21 22:16pm

Sara Collins

Updated 10-Aug-21 2:58am

Richard MacCutchan

v4

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Richard MacCutchan · Accepted Answer · 2021-08-09T22:29:00

Solution 1

Python

x = np.linspace(0.0, t, num)

You cannot use floating point numbers for indexes, you must use integers, thus:

Python

x = np.linspace(0, t, num)

The actual problem is that num is not an integral value.

You also have repeated many of your import statements, you should remove the duplicates.

Posted 9-Aug-21 22:29pm

Richard MacCutchan

Updated 9-Aug-21 23:49pm

v2

Comments

Sara Collins 10-Aug-21 4:44am

Thank you so much. as u advised I changed code

but again I got that error

Sara Collins 10-Aug-21 4:48am

x = np.linspace(0, t, num)
nrm2e_int=it.cumtrapz(nrm2e,x, initial=0)

error is

Traceback (most recent call last):
  File "C:/Users/user/OneDrive/Desktop/nnnnnn.py", line 47, in <module>
    x = np.linspace(0, t, num)
  File "<__array_function__ internals>", line 6, in linspace
  File "C:\Users\user\AppData\Local\Programs\Python\Python37\lib\site-packages\numpy\core\function_base.py", line 120, in linspace
    num = operator.index(num)
TypeError: only integer scalar arrays can be converted to a scalar index

Sara Collins 10-Aug-21 5:04am

When we multiply t by 10 there must not be any float in the num but there are and this is really strange for me.

Richard MacCutchan 10-Aug-21 5:16am

The variable t is an array, so when you multiply it by 10 it is not an integer. As I said previously, spend some time studying the documentation so you understand what types you are dealing with. You cannot assume that they are all integers.

Sara Collins 10-Aug-21 5:25am

I see. u r right. How can I convert it in num to integers?
I used floor and int but they did not work.

Richard MacCutchan 10-Aug-21 5:32am

You cannot convert an array to a single number. What exactly are you trying to do?

Richard MacCutchan · Accepted Answer · 2021-08-09T23:34:00

Solution 3

I have tidied up your code, and added some useful print statements, and this is the output:

t: [0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.  1.1 1.2 1.3 1.4 1.5 1.6 1.7
 1.8 1.9 2.  2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.  3.1 3.2 3.3 3.4 3.5
 3.6 3.7 3.8 3.9 4.  4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.  5.1 5.2 5.3
 5.4 5.5 5.6 5.7 5.8 5.9 6.  6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.  7.1
 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.  8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9
 9.  9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9]
e1: [[0 1 2 3]]
e2: [[0 1 1 1]]
a: [[0 1 4 9]]
b: [[0 1 1 1]]
nrm2e: [[ 0  2  5 10]]
num: [ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12. 13. 14. 15. 16. 17.
 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.
 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.
 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71.
 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89.
 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.]
Traceback (most recent call last):
  File "C:\Users\rjmac\Documents\VSCode\Python\cp.py", line 31, in <module>
    x = np.linspace(0, t, num)
  File "<__array_function__ internals>", line 5, in linspace
  File "C:\Users\rjmac\AppData\Local\Python\Python39\lib\site-packages\numpy\core\function_base.py", line 120, in linspace
    num = operator.index(num)
TypeError: only integer scalar arrays can be converted to a scalar index

As you can see, t and num are arrays of floats, so they are not valid in the call to linspace.

Posted 9-Aug-21 23:34pm

Richard MacCutchan

Comments

Sara Collins 10-Aug-21 6:05am

Thank you so much. I see but how can I convert the mode of it so that I can use it in line space

I have tried the int() and floor() but I did not get the required result

Richard MacCutchan 10-Aug-21 6:37am

I have run a few tests, and the issue is that num needs to be an integer. So you need to set it to the number of values that you want linspace to generate. So something like

num = len(t)
x = np.linspace(0.0, t, num)

Sara Collins 10-Aug-21 7:51am

Thank you so much here the length of t differs in the x = np.linspace(0,t,num)
and np.arange(0.0, tmax, 0.1). in the case of linespace "t" is the upper bound of the integral and for determining the segment that t is located in I have multiplied it by 10. because t is variable in linspace I cannot use the length command but if I multiply it at 10 (steps) then the segment which t is located will be obtained the problem is that python considers it as float number and I cannot convert it to integer by current commands such as int() and floor(), so is there another way to convert data to integer or is there a way that gives the length for t (t is not fixed)? .

Richard MacCutchan 10-Aug-21 8:23am

That was just a suggestion to get a value. I have no idea what this code is supposed to do so I had to make a guess.

Richard MacCutchan 10-Aug-21 8:26am

As I told you earlier, t is an array so you cannot use its value(s) as the basis for the num value in linspace. You need to work out how many elements you want linspace to generate.

Sara Collins 10-Aug-21 8:26am

I want to compute definite integral $\int_{0}^{t}\exp(||e||^2)$.

You helped me a lot. I really appreciate it.

Richard MacCutchan 10-Aug-21 8:27am

Sorry, that means nothing. I am a programmer, not a mathematician.

Sara Collins 10-Aug-21 8:28am

I see. If we can convert the members to integer then it will be without any error.
Again many thanks for replying me your suggestion was great.

Richard MacCutchan 10-Aug-21 8:33am

We are not making a lot of headway here. The linspace method requires that parameter 3 is an integer, which tells it how many elements to generate from the first two parameters (which may be arrays). So the issue that you need to decide on is: how many elements do you want? You can use the number of items in t (using len(t)) or any multiple of that. Or indeed any other value, but I have no idea what that value needs to be.

Sara Collins 10-Aug-21 8:49am

In fact, for about the linspace I am going to divide the closed interval [0,t] so that each segment length be equal to the 0.1 (because before of this I have considered a partition in np.arange(0.0, tmax, 0.1) and each step length is 0.1) so the inteval which "t" in the linespace will belong to would be (t-0)/0.1 or 10t if we look at the values of t we have for example : t=0,0.1,0.2,...
This means that according to linespace partitioning the t will belong to the
segments or num=0*10,0.1*10,0.2*10,0,3*10,...
or num=0,1,2,3, (0th segment,1th segment,2th segment,...)

unfortunately when python computes this part it gives
num=0.,1.0,2.0,...

I do not know if I could illustrate what I have considered or I did not succeed plz let me know. Thank you so much for your consideration.

Richard MacCutchan 10-Aug-21 8:55am

And as I keep repeating: num must be an integral value. So whatever all these numbers mean (and I have no idea) you must create a num value that is a simple count "of something".

Sara Collins · Accepted Answer · 2021-08-10T02:58:00

Solution 4

Dear Richard thank you so much it has worked. I really appreciate it.

Posted 10-Aug-21 2:58am

Sara Collins

Comments

Richard Deeming 10-Aug-21 9:46am

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Do not post your comment as another "solution" to your question. And do not mark your comment as the accepted solution to your question.

Sara Collins 11-Aug-21 2:51am

ok thank you so much.