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Python scipy fsolve "mismatch between input and output of func argument"

Before getting to my problem, I searched the relevant threads on stackoverflow with the same problem:

From what I understand after reading about this error,

raise TypeError (msg)
TypeError: fsolve: there is a mismatch between the input and output form of the 'func' argument 'fsolve_function'

The problem is that the form of input and output is not the same.

In the example code below, I have the following:

  • initialGuess

    (an initial estimate to be used in a function fsolve

    in scipy.optimize). Input, initialGuess

    has 3 initial estimates for coordinates x, y and z. Therefore, I expect my initial baseline estimate to always have three inputs.
  • out

    (nonlinear synchronous equations). In this example, I have 4 non-linear equations.
  • scipy.optimize.fsolve

    raises the error noted above because the input and output do not have the same shape. In my particular case, I want my input to always have three values ​​(in order to guess the starting starting points x, y and z). The output in this case has 4 non-linear equations to be solved using the initial input estimate.
  • Side note: using the same form of input and output, eg. input form 3 [x, y, z] and output 3 non-linear equations, fsolve

    will do the calculation accordingly. I'm just wondering how you could extend fsolve

    to use let say equal or more than 4 non-linear synchronous equations with 3 input initial estimates?

  • Code below:

    from scipy.optimize import fsolve

def fsolve_function(arguments):
    x = arguments[0]
    y = arguments[1]
    z = arguments[2]

    out = [(35.85 - x)**2 + (93.23 - y)**2 + (-39.50 - z)**2 - 15**2]
    out.append((42.1 - x)**2 + (81.68 - y)**2 + (-14.64 - z)**2 - 27**2)
    out.append((-70.90 - x)**2 + (-55.94 - y)**2 + (-68.62 - z)**2 - 170**2)
    out.append((-118.69 - x)**2 + (-159.80 - y)**2 + (-39.29 - z)**2 - 277**2)

    return out

initialGuess = [35, 93, -39]
result = fsolve(fsolve_function, initialGuess)
print result
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1 answer


fsolve

is a MINPACK wrapper hybrd

that requires the function argument and output to have the same cardinality. You can try other algorithms from more general ones scipy.optimize.root

that do not have this limitation (for example lm

):

from scipy.optimize import fsolve, root

def fsolve_function(arguments):
    x = arguments[0]
    y = arguments[1]
    z = arguments[2]

    out = [(35.85 - x)**2 + (93.23 - y)**2 + (-39.50 - z)**2 - 15**2]
    out.append((42.1 - x)**2 + (81.68 - y)**2 + (-14.64 - z)**2 - 27**2)
    out.append((-70.90 - x)**2 + (-55.94 - y)**2 + (-68.62 - z)**2 - 170**2)
    out.append((-118.69 - x)**2 + (-159.80 - y)**2 + (-39.29 - z)**2 - 277**2)

    return out

initialGuess = [35, 93, -39]
result = root(fsolve_function, initialGuess, method='lm')
print(result.x)

By the way, it can't find a null zero - should there be one?



You can also force fsolve

your function to be used if you give it an initial guess with a "dummy" fourth variable:

initialGuess = [35, 93, -39, 0]

but I'm not sure how reliable the results are in this case.

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