Hello Stackoverflow community,
I am trying to fit data to a Faddeeva function (optimize.special.wofz) using pyhton's optimize.leastsq() or optimize.curve_fit(). The fit parameters are the following two: z1 and z2. They are complex, whereas the independent variable (time) and the output of the function (meas_data) are purely real numbers. This is my first attempt to fit the data:
import numpy as np
from scipy import optimize
from scipy import special
meas_data = np.loadtxt('directory')
time = np.loadtxt('directory')
def test(params, time):
z1 = params[0]
z2 = params[1]
a = z1*np.sqrt(time)
b = z2*np.sqrt(time)
a = np.complex(0, a)
b = np.complex(0, b)
c = special.wofz(a)
d = special.wofz(b)
return np.real(c*d)
def test_error(params, time, t_error):
return test(params, time) - t_error
initial_guess = (300+200j, 300-200j)
params_fit, cov_x, infodict, mesg, ier = optimize.leastsq(test_error, initial_guess, args = (time, meas_data), full_output = True)
My second attempt looks like :
import numpy as np
from scipy import optimize
from scipy import special
meas_data = np.loadtxt('directory')
time = np.loadtxt('directory')
def test(time, z1, z2):
a = z1*np.sqrt(time)
b = z2*np.sqrt(time)
a = np.complex(0, a)
b = np.complex(0, b)
c = special.wofz(a)
d = special.wofz(b)
return np.real(c*d)
popt, pcov = optimize.curve_fit(test, time, meas_data)
For both cases, I get a similar error message:
for the first attempt:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-13-9286b2981692> in <module>()
22
23 initial_guess = (300+200j, 300-200j)
---> 24 params_fit, cov_x, infodict, mesg, ier = optimize.leastsq(test_error, initial_guess, args = (time, msd), full_output = True)
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
375 if not isinstance(args, tuple):
376 args = (args,)
--> 377 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
378 m = shape[0]
379 if n > m:
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
24 def _check_func(checker, argname, thefunc, x0, args, numinputs,
25 output_shape=None):
---> 26 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
27 if (output_shape is not None) and (shape(res) != output_shape):
28 if (output_shape[0] != 1):
<ipython-input-13-9286b2981692> in test_error(params, time, t_error)
19
20 def test_error(params, time, t_error):
---> 21 return test(params, time) - t_error
22
23 initial_guess = (z1, z2)
<ipython-input-13-9286b2981692> in test(params, time)
10 b = z2*np.sqrt(time)
11
---> 12 a = np.complex(0, a)
13 b = np.complex(0, b)
14
TypeError: only length-1 arrays can be converted to Python scalars
and for the second attempt:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-8-8f631a7ede54> in <module>()
16 return np.real(c*d)
17
---> 18 popt, pcov = optimize.curve_fit(test, time, msd)
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
674 # Remove full_output from kwargs, otherwise we're passing it in twice.
675 return_full = kwargs.pop('full_output', False)
--> 676 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
677 popt, pcov, infodict, errmsg, ier = res
678 cost = np.sum(infodict['fvec'] ** 2)
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
375 if not isinstance(args, tuple):
376 args = (args,)
--> 377 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
378 m = shape[0]
379 if n > m:
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
24 def _check_func(checker, argname, thefunc, x0, args, numinputs,
25 output_shape=None):
---> 26 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
27 if (output_shape is not None) and (shape(res) != output_shape):
28 if (output_shape[0] != 1):
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in func_wrapped(params)
453 if weights is None:
454 def func_wrapped(params):
--> 455 return func(xdata, *params) - ydata
456 else:
457 def func_wrapped(params):
<ipython-input-8-8f631a7ede54> in test(time, z1, z2)
7 b = z2*np.sqrt(time)
8
----> 9 a = np.complex(0, a)
10 b = np.complex(0, b)
11
TypeError: only length-1 arrays can be converted to Python scalars
The data I am using for fitting are times in the range of 10e-6 to 10e-2 and measurement data in the range of 10e-19 to 10e-16. Both test functions used for calculating individual numbers given that the z1 and z2 are known work. I think that it has something to do with python's fitting routines which maybe not can handle complex values during their calculation?
I would be very happy, if someone could help me fixing this problem.
