python - Scipiy.optimize.minimaze unconstrained error -


i want perform constrained least square methon polynom. before that, decided try unconstrined optimalization. here problem:

my polynom looks

$f(x) = ax^4 + bx^3 + cx^2 + dx + e$

so want find best coefficients a, b, c, d , e. function want minimize looks like

def lsq(args, x, y):     return sum([(y[i] - (args[0]*x[i]**4 + args[1]*x[i]**3 + args[2]*x**2 + args[3]*x + args[4]))**2                 in np.arange(len(x))])

where x , y lists of coordinates of points. thus, code may like:

import numpy np import scipy.optimize ph = np.array([8,8,8,7,7,7,7,7,7,7,7,7,6,3,2,2,2,1]) def rank2(y):     return np.array([(i+1)/len(y) in range(len(y))]) x = rank2(ph) y = ph def lsq(args, x, y):     return sum([(y[i] - (args[0]*x[i]**4 + args[1]*x[i]**3 + args[2]*x**2 + args[3]*x + args[4]))**2                 in np.arange(len(x))])   params = scipy.optimize.minimize(nejmensi_ctverce, [1.0, 1.0, 1.0, 1.0, 1.0], args = (x, y))

but here got error:

file "c:\users\robert\desktop\winpython-64bit-3.6.1.0qt5\python- 3.6.1.amd64\lib\site-packages\scipy\optimize\optimize.py", line 628, in _approx_fprime_helper grad[k] = (f(*((xk + d,) + args)) - f0) / d[k]  valueerror: setting array element sequence

can me? guess not cempletely understand how parse arguments minimize function.

some xs in lsq not indexed i:

args[0]*x[i]**4 + args[1]*x[i]**3 + args[2]*x**2 + args[3]*x + args[4]                                          ---^           ---^

this led lsq returning array of values instead of scalar:

in [9]: lsq([1.0, 1.0, 1.0, 1.0, 1.0], x, y) out[9]:  array([ 468.00714962,  458.38490951,  448.01979096,  436.95911906,         425.25433416,  412.9609918 ,  400.13876277,  386.85143307,         373.16690395,  359.15719185,  344.89842847,  330.47086072,         315.95885075,  301.45087591,  287.0395288 ,  272.82151724,         258.89766428,  245.37290818])

this leads valueerror since scipy.optimize.minimze expects lsq return scalar values minimized. 1 way fix problem replace bare xs x[i]s.

a better way solve problem replace x[i]s xs, remove for in np.arange(len(x)) , use numpy array-based arithmetic:

def lsq(args, x, y):     return ((y - (args[0]*x**4 + args[1]*x**3 + args[2]*x**2                    + args[3]*x + args[4]))**2).sum()

for example,

import numpy np import scipy.optimize optimize  ph = np.array([8,8,8,7,7,7,7,7,7,7,7,7,6,3,2,2,2,1]) def rank2(y):     return np.array([(i+1)/len(y) in range(len(y))]) x = rank2(ph) y = ph  def lsq(args, x, y):     a, b, c, d, e = args     return ((y - (a*x**4 + b*x**3 + c*x**2 + d*x + e))**2).sum()  params = optimize.minimize(lsq, [1.0, 1.0, 1.0, 1.0, 1.0], args = (x, y)) print(params.x)

yields

[  94.48618936 -211.42358992  144.93063545  -37.24078798   10.23934514]

with minimum lsq value of:

print(lsq(params.x, x, y)) # 6.91284752049

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