Error solving a system of non linear equation using scipy

Question

I'm trying to solve this system of non linear equations using scipy.optimize.fsolve , I took this from an example in one other post here

my system of equation is the follow :

for i in range(len(self.time)-1):

            def equations(variable):
                k1,k2 = variable 
                f1 = -k1 + self.f(self.time[i]+ (0.5+np.sqrt(3)/6)* self.dt , self.u[i]+0.25*self.dt* k1+ (0.25+ np.sqrt(3)/6)*self.dt*k2) 
                f2 = -k2 + self.f(self.time[i]+ (0.5-np.sqrt(3)/6)* self.dt , self.u[i]+(0.25-np.sqrt(3)/6)*self.dt *k1 + 0.25*self.dt* k2)
                return (f1,f2)


            k1,k2 = fsolve(equations,(5,5))

when I run the code I got :

TypeError: fsolve: there is a mismatch between the input and output shape of the 'func' argument 'equations'.Shape should be (2,) but it is (2, 1).

EDIT I don't know why this mismatch and how to fix it .. I tried :

for i in range(len(self.time)-1):
            ui = self.u[i]
            ti = self.time[i]

            def equations(variable):
                k1,k2 = variable 
                f1 = -k1 + self.f(ti+ (0.5+np.sqrt(3)/6)* self.dt , ui+0.25*self.dt* k1+ (0.25+ np.sqrt(3)/6)*self.dt*k2) 
                f2 = -k2 + self.f(ti+ (0.5-np.sqrt(3)/6)* self.dt , ui+(0.25-np.sqrt(3)/6)*self.dt *k1 + 0.25*self.dt* k2)
                return (f1,f2)


            k1,k2 = fsolve(equations,(1,1))

EDIT I've tried : return np.array([f1,f2]) and I got the same mismatch error!

Answer 1

Apparently the problem is here:

Shape should be (2,) but it is (2, 1).

Even if you have just two values, in numpy it is different to have an "unidimensional vector" with two values, and a "bidimensional matrix" with two values.

I suggest that you call ravel() or flatten() to convert your (2,1) shape to a (2,) shape:

import numpy as np

a = np.array([[1,2]])

print("before:")
print("array: ", a)
print("shape: ", a.shape)
print()

b = a.ravel()

print("after:")
print("array: ", b)
print("shape: ", b.shape)

> before:
> array:  [[1 2]]
> shape:  (1, 2)

> after:
> array:  [1 2]
> shape:  (2,)