scipy.optimize.leastsq calls objective function with NaN

Since your problem definition uses a linear solver on a non-linear problem (noise), the solver will freak out, unless the noise level is below the threshold of noticeability.

In order to solve this problem, you could try using a nonlinear solver.For instance using the broyden1 solving algorithm instead of leastsq:

import scipy.optimizeimport numpy as npxF = np.array([1.0, 2.0, 3.0, 4.0]) # Target value for fitNOISE_LEVEL = 1.e-6 # The random noise levelRETURN_LEN = 1000  # The objective function return vector lengthdef func(x):    if np.isnan(np.sum(x)):        raise ValueError('Invalid x: %s' % x)    v = np.random.rand(RETURN_LEN) * NOISE_LEVEL    v[:len(x)] += xF - x    return v[:len(x)]iteration = 0while iteration < 10:    iteration += 1    x = np.random.rand(len(xF))    y = scipy.optimize.broyden1(func, x)    print('%04d %s' % (iteration, y))

returns as output:

0001 [ 1.00000092  2.00000068  3.00000051  4.00000097]0002 [ 1.0000012   2.00000214  3.00000272  4.00000369]0003 [ 0.99999991  1.99999931  2.99999815  3.9999978 ]0004 [ 1.00000097  2.00000198  3.00000345  4.00000425]0005 [ 1.00000047  1.99999983  2.99999938  3.99999922]0006 [ 1.00000024  2.00000021  3.00000071  4.00000136]0007 [ 1.00000116  2.00000102  3.00000225  4.00000357]0008 [ 1.00000006  2.00000002  3.00000017  4.00000039]0009 [ 1.0000002   2.00000034  3.00000062  4.00000051]0010 [ 1.00000137  2.0000015   3.00000193  4.00000344]