how to pack my numpy variables and arrays when calling curve_fit?

Question

This is my standalone code to reproduce the problem:

import numpy as np
from scipy.optimize import curve_fit


def find_vector_of_minor_axis_from_chunk(data):
    n = 20  # number of points
    time = np.linspace(0, 2 * np.pi, n)

    guess_center_point = data.mean(1)
    guess_center_point = guess_center_point[np.newaxis, :].transpose()
    guess_a_phase = 0
    guess_b_phase = 0
    guess_a = 1
    guess_b = 1
    guess_a_axis_vector = np.array([[1], [0], [0]])
    guess_b_axis_vector = np.array([[0], [1], [0]])

    p0 = np.array([guess_center_point,
                   guess_a, guess_a_axis_vector, guess_a_phase,
                   guess_b, guess_b_axis_vector, guess_b_phase])

    def ellipse_func(t, center_point, a, a_axis_vector, a_phase, b, b_axis_vector, b_phase):
        return center_point + a * a_axis_vector * np.sin(t * a_phase) + b * b_axis_vector * np.sin(t + b_phase)

    popt, pcov = curve_fit(ellipse_func, time, data, p0=p0)
    center_point, a, a_axis_vector, a_phase, b, b_axis_vector, b_phase = popt

    print(str(a_axis_vector, b_axis_vector))
    shorter_vector = a_axis_vector
    if np.abs(a_axis_vector) > np.aps(b_axis_vector):
        shorter_vector = b_axis_vector
    return shorter_vector


def main():
    data = np.array([[-4.62767933, -4.6275775, -4.62735346, -4.62719652, -4.62711625, -4.62717975,
                      -4.62723845, -4.62722407, -4.62713901, -4.62708749, -4.62703238, -4.62689101,
                      -4.62687185, -4.62694013, -4.62701082, -4.62700483, -4.62697488, -4.62686825,
                      -4.62675683, -4.62675204],
                     [-1.58625998, -1.58625039, -1.58619648, -1.58617611, -1.58620606, -1.5861833,
                      -1.5861821, -1.58619169, -1.58615814, -1.58616893, -1.58613179, -1.58615934,
                      -1.58611262, -1.58610782, -1.58613179, -1.58614017, -1.58613059, -1.58612699,
                      -1.58607428, -1.58610183],
                     [-0.96714786, -0.96713827, -0.96715984, -0.96715145, -0.96716703, -0.96712869,
                      -0.96716104, -0.96713228, -0.96719698, -0.9671838, -0.96717062, -0.96717062,
                      -0.96715744, -0.96707717, -0.96709275, -0.96706519, -0.96715026, -0.96711791,
                      -0.96713588, -0.96714786]])

    print(str(find_vector_of_minor_axis_from_chunk(data)))

if __name__ == '__main__':
    main()

That gives me this traceback:

Traceback (most recent call last):
  File "C:/Users/X/PycharmProjects/lissajous-achse/ellipse_fit.py", line 52, in <module>
    main()
  File "C:/Users/X/PycharmProjects/lissajous-achse/ellipse_fit.py", line 49, in main
    print(str(find_vector_of_minor_axis_from_chunk(data)))
  File "C:/Users/X/PycharmProjects/lissajous-achse/ellipse_fit.py", line 25, in find_vector_of_minor_axis_from_chunk
    popt, pcov = curve_fit(ellipse_func, time, data, p0=p0)
  File "C:\Users\X\PycharmProjects\lissajous-achse\venv\lib\site-packages\scipy\optimize\minpack.py", line 763, in curve_fit
    res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
  File "C:\Users\X\PycharmProjects\lissajous-achse\venv\lib\site-packages\scipy\optimize\minpack.py", line 392, in leastsq
    raise TypeError('Improper input: N=%s must not exceed M=%s' % (n, m))
TypeError: Improper input: N=7 must not exceed M=3

Process finished with exit code 1

My code is an adaption of the second answer here. The problem causing the error message is solved by simple packing of variables here.

Why does the problem not surface in the mentioned second answer? And how can I pack my variables, which consist of several 3d vectors and individual scalars, to solve this problem? How do i pass in my t, which is a constant and should not be optimized?

Answer 1

Apparently python is quite smart regarding the length of the fields of the arguments, depending on the the initial guesses. So i could just pass in ONE variable, and split it up inside the function like so:

import numpy as np
from scipy.optimize import minimize


def find_vector_of_minor_axis_from_chunk(data):
    n = 20  # number of points
    guess_center_point = data.mean(1)
    guess_center_point = guess_center_point[np.newaxis, :].transpose()
    guess_a_phase = 0.0
    guess_b_phase = 0.0
    guess_a = 1.0
    guess_b = 1.0
    guess_a_axis_vector = np.array([[1.0], [0.0], [0.0]])
    guess_b_axis_vector = np.array([[0.0], [1.0], [0.0]])

    p0 = np.array([guess_center_point,
                   guess_a, guess_a_axis_vector, guess_a_phase,
                   guess_b, guess_b_axis_vector, guess_b_phase])

    def ellipse_func(x, data):
        center_point = x[0]
        a = x[1]
        a_axis_vector = x[2]
        a_phase = x[3]
        b = x[4]
        b_axis_vector = x[5]
        b_phase = x[6]
        t = np.linspace(0, 2 * np.pi, n)
        error = center_point + a * a_axis_vector * np.sin(t * a_phase) + b * b_axis_vector * np.sin(t + b_phase) - data
        error_sum = np.sum(error**2)
        print(str(error_sum))
        return error_sum

    popt, pcov = minimize(ellipse_func, p0, args=(data))
    center_point, a, a_axis_vector, a_phase, b, b_axis_vector, b_phase = popt

    print(str(a_axis_vector, b_axis_vector))
    shorter_vector = a_axis_vector
    if np.abs(a_axis_vector) > np.aps(b_axis_vector):
        shorter_vector = b_axis_vector
    return shorter_vector


def main():
    data = np.array([[-4.62767933, -4.6275775, -4.62735346, -4.62719652, -4.62711625, -4.62717975,
                      -4.62723845, -4.62722407, -4.62713901, -4.62708749, -4.62703238, -4.62689101,
                      -4.62687185, -4.62694013, -4.62701082, -4.62700483, -4.62697488, -4.62686825,
                      -4.62675683, -4.62675204],
                     [-1.58625998, -1.58625039, -1.58619648, -1.58617611, -1.58620606, -1.5861833,
                      -1.5861821, -1.58619169, -1.58615814, -1.58616893, -1.58613179, -1.58615934,
                      -1.58611262, -1.58610782, -1.58613179, -1.58614017, -1.58613059, -1.58612699,
                      -1.58607428, -1.58610183],
                     [-0.96714786, -0.96713827, -0.96715984, -0.96715145, -0.96716703, -0.96712869,
                      -0.96716104, -0.96713228, -0.96719698, -0.9671838, -0.96717062, -0.96717062,
                      -0.96715744, -0.96707717, -0.96709275, -0.96706519, -0.96715026, -0.96711791,
                      -0.96713588, -0.96714786]])

    print(str(find_vector_of_minor_axis_from_chunk(data)))

if __name__ == '__main__':
    main()

Also i fixed some floating point vs integer errors in the vector for the initial values.

However now I get a different error:

Traceback (most recent call last):
  File "C:/Users/X/PycharmProjects/lissajous-achse/ellipse_fit.py", line 61, in <module>
    main()
  File "C:/Users/X/PycharmProjects/lissajous-achse/ellipse_fit.py", line 58, in main
    print(str(find_vector_of_minor_axis_from_chunk(data)))
  File "C:/Users/X/PycharmProjects/lissajous-achse/ellipse_fit.py", line 34, in find_vector_of_minor_axis_from_chunk
    popt, pcov = minimize(ellipse_func, p0, args=(data))
  File "C:\Users\X\PycharmProjects\lissajous-achse\venv\lib\site-packages\scipy\optimize\_minimize.py", line 604, in minimize
    return _minimize_bfgs(fun, x0, args, jac, callback, **options)
  File "C:\Users\X\PycharmProjects\lissajous-achse\venv\lib\site-packages\scipy\optimize\optimize.py", line 1063, in _minimize_bfgs
    if isinf(rhok):  # this is patch for numpy
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

I guess that

The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

is some internal error, stemming from the internal decision matrix how to proceed. I don't know how I caused it and how to fix it. When i figure out how it is done properly, I will come back and edit this answer.