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I'm trying to plot a 2-dimensional function (specifically, a 2-d Laplace solution). I defined my function and it returns the right value when I put in specific numbers, but when I try running through an array of values (x,y below), it still returns only one number. I tried with a random function of x and y (e.g., f(x,y) = x^2 + y^2) and it gives me an array of values.

def V_func(x,y):
 a = 5
 b = 4
 Vo = 4
 n = np.arange(1,100,2)
 sum_list = 

 for indx in range(len(n)):
 sum_term = (1/n[indx])*(np.cosh(n[indx]*np.pi*x/a))/(np.cosh(n[indx]*np.pi*b/a))*np.sin(n[indx]*np.pi*y/a)
 sum_list = np.append(sum_list,sum_term)

 summation = np.sum(sum_list)
 V = 4*Vo/np.pi * summation

 return V

x = np.linspace(-4,4,50)
y = np.linspace(0,5,50)
V_func(x,y)

Out: 53.633709914177224

Try this:

def V_func(x,y):
 a = 5
 b = 4
 Vo = 4
 n = np.arange(1,100,2)
 # sum_list = 
 sum_list = np.zeros(50)

 for indx in range(len(n)):
 sum_term = (1/n[indx])*(np.cosh(n[indx]*np.pi*x/a))/(np.cosh(n[indx]*np.pi*b/a))*np.sin(n[indx]*np.pi*y/a)
 # sum_list = np.append(sum_list,sum_term)
 sum_list += sum_term

 # summation = np.sum(sum_list)
 # V = 4*Vo/np.pi * summation
 V = 4*Vo/np.pi * sum_list

 return V

Define a pair of arrays:

In [6]: x = np.arange(3); y = np.arange(10,13)
In [7]: x,y
Out[7]: (array([0, 1, 2]), array([10, 11, 12]))

Try a simple function of the 2

In [8]: x + y
Out[8]: array([10, 12, 14])

Since they have the same size, they can be summed (or otherwise combined) elementwise. The result has the same shape as the 2 inputs.

Now try 'broadcasting'. x[:,None] has shape (3,1)

In [9]: x[:,None] + y
Out[9]: 
array([[10, 11, 12],
 [11, 12, 13],
 [12, 13, 14]])

The result is (3,3), the first 3 from the reshaped x, the second from y.

I can generate the pair of arrays with meshgrid:

In [10]: I,J = np.meshgrid(x,y,sparse=True, indexing='ij')
In [11]: I
Out[11]: 
array([[0],
 [1],
 [2]])
In [12]: J
Out[12]: array([[10, 11, 12]])
In [13]: I + J
Out[13]: 
array([[10, 11, 12],
 [11, 12, 13],
 [12, 13, 14]])

Note the added parameters in meshgrid. So that's how we go about generating 2d values from a pair of 1d arrays.

Now look at what sum does. As you use it in the function:

In [14]: np.sum(I + J)
Out[14]: 108

the result is a scalar. See the docs. If I specify an axis I get an array.

In [15]: np.sum(I + J, axis=0)
Out[15]: array([33, 36, 39])

If you gave V_func the right x and y, sum_list could be a 3d array. That axis-less sum reduces it to a scalar.

In code like this you need to keep track of array shapes. Include test prints if needed; don't just assume anything; test it. Pay attention to how dimensions grow and shrink as they pass through various operations.