passing numpy ndarray as inputs of a fsolve function

Question

I want to numerically solve a system of nonlinear equations and pass numpy ndarrays as inputs. Consider the arbitrary code below:

import numpy as np
from scipy.optimize import fsolve

def eqs(A, B, C, D):
    eq1 = (A - B * np.sin(C)).tolist()
    eq2 = [5 * B + D * np.sum(A * np.cos(C))]
    return eq1 + eq2

n = 3

A = np.zeros((n))
A0 = np.random.rand(n)
B = 0.0
B0 = np.random.rand(1)[0]

C = np.random.rand(n)
D =  np.random.rand(1)[0]

sol = fsolve(func = eqs, x0 = [A0, B0], args = [C, D])

which leads to

missing required positional arguments

error and changing the function to:

def eqs(A, B, C, D):
    eq1 = A - B * np.sin(C)
    eq2 = C[0] * B + D * np.sum(A * np.cos(C))
    return [eq1, eq2]

also doesn't help. However, I highly doubt that the error has anything to do with passing ndarrays. One approach could be to change all the ndarrays to python lists back and forth. But then I would not be able to use numpy's vectorized functions like np.sin()...

I would appreciate if you could help me know how this should be done.

P.S. Equations above are just arbitrary and they may not have solutions at all.

can you post this non linear equations that you try to solve? — Zaraki Kenpachi, Jun 27 '19 at 10:01
@ZarakiKenpachi mind if I share them in private? got Twitter? — Foad S. Farimani, Jun 27 '19 at 10:20
email? any other way I can share the code privately? the code I'm working on is for non-published research and I can't share it publicly! — Foad S. Farimani, Jun 27 '19 at 11:03

score 2 · Accepted Answer · edited Jun 27 '19 at 11:17

2

Check if this solve your equation:

import numpy as np
from scipy.optimize import fsolve

def eqs(X, Y):
    A, B = X[:3], X[3]
    C, D = Y[:3], Y[3]
    eq1 = A - B * np.sin(C)
    eq2 = C[0] * B + D * np.sum(A * np.cos(C))
    return np.append(eq1, eq2)

n = 3

A = np.zeros((n))
A0 = np.random.rand(n)
B = 0.0
B0 = np.random.rand(1)[0]

C = np.random.rand(n)
D =  np.random.rand(1)[0]

sol = fsolve(func = eqs, x0 = np.append(A0, B0), args = np.append(C, D))
sol

Output:

array([ 0.e+000, -1.e-323,  5.e-324, -1.e-323])

edited Jun 27 '19 at 11:17

Foad S. Farimani

12,396
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answered Jun 27 '19 at 10:31

Zaraki Kenpachi

5,510
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but then how do you pass D and C? I want them to be passed because they are not necessarily constants as shown in the arbitrary code. – Foad S. Farimani Jun 27 '19 at 11:05

score 1 · Answer 2 · answered Jun 27 '19 at 16:48

These scipy.optimize functions require a function with a signature like

f(x, *args)

x is a array (often 1d) that the solver will vary; args is a tuple of arguments that are just passed through from the outside.

Change your eqs to fit this pattern

In [11]: def eqs(X, C, D): 
    ...:     A, B  = X[:-1], X[-1] 
    ...:     eq1 = (A - B * np.sin(C)).tolist() 
    ...:     eq2 = [5 * B + D * np.sum(A * np.cos(C))] 
    ...:     return eq1 + eq2 

    ...: n = 3 
    ...: A0 = np.random.rand(n) 
    ...: B0 = np.random.rand(1) 
    ...:  
    ...: C = np.random.rand(n) 
    ...: D =  np.random.rand(1)

Make a test call to eqs:

In [12]: eqs(np.concatenate((A0,B0)),C,D)                                                            
Out[12]: 
[-0.28460532658572657,
 -0.03649115738682615,
 0.7625781482352719,
 array([5.46430853])]

Now try it in the fsolve:

In [13]: fsolve(eqs, np.concatenate((A0,B0)), args=(C,D))                                            
Out[13]: array([0., 0., 0., 0.])

thanks a lot. How is this is compared to the other solution? is this one better? — Foad S. Farimani, Jun 27 '19 at 20:48

passing numpy ndarray as inputs of a fsolve function

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