ValueError when using scipy least_squares

Question

I am trying to fit my data to a function. I've been using this sample code as a guide http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html#example-of-solving-a-fitting-problem. My code is the following:

from scipy.optimize import least_squares
import numpy as np
import matplotlib.pyplot as plt

def model(x, u):
    return -x[0] * np.sqrt((x[1]/u) - 1)

def fun(x, u, y):
    return y - model(x, u)

def jac(x, u, y):
    J = np.empty((u.size, x.size))
    J[:, 0] = np.sqrt((x[1]/u) - 1)
    J[:, 1] = x[0] / (2 * u * np.sqrt((x[1]/u) - 1))
    return J

u = np.array(T_h2)
y = np.array(lnR2)
x0 = np.array([0.1,0.2])
res = least_squares(fun, x0, jac=jac, bounds=(0, 100), args=(u, y), verbose=1)
print(res.x)

u_test = T_h2
y_test = model(res.x, u_test)
plt.plot(u, y, 'o', markersize=4, label='data')
plt.plot(u_test, y_test, label='fitted model')
plt.xlabel("u")
plt.ylabel("y")
plt.legend(loc='lower right')
plt.show()

However, when I run my code I get the error "ValueError: Residuals are not finite in the initial point." How would I fix this?

edit:

    T_h2 = [234.382,  234.353,  234.435,  234.709,  235.169,  235.803,
  236.661,  237.688,  238.697,  239.658,  240.743,  241.813,  242.784,  243.739,
  244.791,  245.675,  246.666,  247.615,  248.579,  249.481,  250.336,  251.311,
  252.211,  253.058,  253.976,  254.831,  255.738,  256.599,  257.594,  258.482,
  259.279,  260.233,  261.112,  262.103,  263.003,  263.9,    264.764,  265.688,
  266.629,  267.491,  268.415,  269.285,  270.188,  271.129,  272.,     272.935,
  273.773,  274.714,  275.581,  276.549,  277.411,  278.334,  279.276,  280.146,
  281.006,  281.905,  282.819,  283.803,  284.681,  285.513,  286.49,   287.324,
  288.173,  289.105,  290.039,  290.991,  291.795,  292.694,  293.648,  294.522,
  295.398,  296.296,  297.25,  298.134,  299.024,  299.912,  300.808,  301.732,
  302.635,  303.603,  304.476,  305.35,   306.223,  307.18,   308.091,  308.938,
  309.902,  310.792,  311.663,  312.566,  313.412,  314.284,  315.252,  316.126,
  317.002,  317.913,  318.81,  319.669,  320.626,  321.523,  322.417,  323.281,
  324.245]

lnR2 = [-16.333025681623091, -14.872111670594926, -14.892057965675207, -15.03694367579511, -14.388711659567424, -16.519631908799834, -14.047440985059174, -13.245512823492424, -12.012664970474015, -11.592570515633696, -11.415244487948224, -11.250423587326582, -11.043358068566182, -10.782270761445371, -10.57008012745084, -10.348870666290271, -10.191384942587591, -10.048855650333838, -9.9256240231933077, -9.7926739093465187, -9.6730532317943059, -9.5334101176483124, -9.3859588951369251, -9.2475985534653571, -9.1166053550752206, -9.0088611502583475, -8.8739120056364289, -8.7650034909964933, -8.6823151628382362, -8.6015380878989749, -8.5167589793011746, -8.4314862875533017, -8.364006279047107, -8.3069822249135825, -8.2571447519527315, -8.2111410588354676, -8.1684964170797887, -8.1396219459464945, -8.1149140801354562, -8.0937213212661057, -8.0742199830459658, -8.057615869538207, -8.0494949879212623, -8.0435977497085211, -8.0409171951906373, -8.0461036780308994, -8.0490116406609502, -8.0525194174270123, -8.0653078013251491, -8.0816100755759432, -8.0974305556597912, -8.1152346160995883, -8.1394956678268393, -8.1664274771185354, -8.1980306181968547, -8.2299693351364844, -8.2652082284364567, -8.3050428664294742, -8.3484319768441626, -8.3927260630797864, -8.4461326801347543, -8.5003378964708105, -8.5595337634985853, -8.6098956222034229, -8.6806395376767043, -8.7463523398937717, -8.819120148846844, -8.8938512284941815, -8.975439857789393, -9.0604311437041982, -9.160016977929974, -9.2544272624693313, -9.360134170694149, -9.48357662093877, -9.5792580093353656, -9.7144993201777972, -9.8715380997132574, -10.027248712603699, -10.177417977875871, -10.352374953002723, -10.517136866838991, -10.715774762340427, -10.913431451028842, -11.123817784132052, -11.345932175131191, -11.567233115011238, -11.775872934970939, -11.992878335292444, -12.21474839185972, -12.382545106102548, -12.45951145012326, -12.697558713087753, -12.870960915450144, -13.122795212623657, -13.096364398875277, -13.3741438677707, -13.323032960465998, -13.436772613480292, -13.561709556757362, -14.198404910172693, -13.896250284916482, -13.535947150817048, -14.727538560421378]

Answer 1

The problem is:

• case A: your initial-point
• case B: your function model

Giving the start-point x0 = np.array([0.1,0.2]) (and also u,y), calling fun(x0, u, y), the following happens:

np.sqrt((x[1]/u) - 1)  # part of model(x, u)
= np.sqrt((0.2 / u) - 1)
= np.sqrt(some_near_zero_vector - 1)  # because u much bigger than 0.2
= np.sqrt(some_near_minus_one_vector)
= NaN-vector, which is not finite!  # because of negative components in sqrt