How to add two functions f(x,n) and f(x,m) and integrate the product of these two functions?

Question

I want to integrate the product of two functions, but it seems like i keep gettin an error

AttributeError: ‘Mul’ object has no attribute ‘cos’

import numpy as np
import sympy as sp

x = sp.symbols('x')

dp_xi = []
dp_eta = []

        
for n in range (1,5,1):
    for m in range (1,5,1):
        dp_xi.append(np.cos((n-2)*(np.pi/180)*x)*(n-2)*np.pi/180)
        dp_eta.append(np.cos((m-2)*(np.pi/180)*x)*(m-2)*np.pi/180)
                   
        df_xi = sum(dp_xi)
        df_eta = sum(dp_eta)

I = sp.integrate(df_xi*df_eta, (x, 0, 1))

print("I=",I)

Any ideas?? Thank you

I tried to replace np with sp but the integral wouldn’t work

Asked By: Ayoub

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Source

Answer 1

As mentioned, you should use only symbols if you want to use analytical integration.

n = sp.symbols('n')
f = sp.cos((n-2)*(sp.pi/180*x)*(n-2)*sp.pi/180)
sp.integrate(f, (x, 0, 1))

Answered By: rdllopes

Answer 2

Where’s the FULL ERROR message?

Look at what I get when running your code

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
AttributeError: 'Mul' object has no attribute 'cos'

The above exception was the direct cause of the following exception:

TypeError                                 Traceback (most recent call last)
Cell In[25], line 9
      7 for n in range (1,5,1):
      8     for m in range (1,5,1):
----> 9         dp_xi.append(np.cos((n-2)*(np.pi/180)*x)*(n-2)*np.pi/180)
     10         dp_eta.append(np.cos((m-2)*(np.pi/180)*x)*(m-2)*np.pi/180)
     12         df_xi = sum(dp_xi)

TypeError: loop of ufunc does not support argument 0 of type Mul which has no callable cos method

It points to the line with the np.cos. Running that expression by itself:

In [26]: np.cos((n-2)*(np.pi/180)*x)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
AttributeError: 'Mul' object has no attribute 'cos'

The above exception was the direct cause of the following exception:

TypeError                                 Traceback (most recent call last)
Cell In[26], line 1
----> 1 np.cos((n-2)*(np.pi/180)*x)

TypeError: loop of ufunc does not support argument 0 of type Mul which has no callable cos method

Strip off the cos, and we see the argument is:

In [28]: print((n-2)*(np.pi/180)*x)
-0.0174532925199433*x

The short answer, as others explain, np.cos cannot be used a sympy.symbol or expression.

sympy‘s own cos runs, though, since x is still a symbol, it won’t try to return a numeric value:

In [30]: print(sp.cos((n-2)*(np.pi/180)*x))
cos(0.0174532925199433*x)

With sp instead:

In [33]: print(df_xi)
2*pi*cos(pi*x/90)/45

In [34]: print(df_eta)
2*pi*cos(pi*x/90)/45

And the integral:

In [35]: I = sp.integrate(df_xi*df_eta, (x, 0, 1))
In [37]: print(I)
8*pi*(sin(pi/90)*cos(pi/90)/2 + pi/180)/45

Answered By: hpaulj

Answer 3

Your code works fine with sp instead of np if you dedent the code in which sum is used. (In addition, there is no need for a double loop since each expression only depends on one loop variable.)

import sympy as sp

x = sp.symbols('x')

a = [sp.cos((n-2)*(sp.pi/180)*x)*(n-2)*sp.pi/180 for n in range(1, 5)]
                   
df_xi = 4*sum(a)
df_eta = df_xi.subs(n, m)

I = sp.integrate(df_xi*df_eta, (x, 0, 1)) # or sp.Integral(df_xi*df_eta, (x, 0, 1))

print("I=",I)

outputs

I= 8*pi*(sin(pi/90)*cos(pi/90)/2 + pi/180)/45

which evaluates to

>>> I.n()
0.0194875985645024

Answered By: smichr

How to add two functions f(x,n) and f(x,m) and integrate the product of these two functions?

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