如何在Python中调用scipy.optimize.fmin_cg（func）的函数

Question

I will simply explain the problem in short. This problem is exactly similar as shown in scipy.doc . The problem is on error occurance as float argument required, not numpy.ndarray

What I have:

• Function: y = s*z^t

Variable length/dimensions

• t - 1...m,
• s - 1...m and 1...n. So, m is row number, n - col number.
• z - 1...n.
• y - this can be y 1 , y[2], y[3],..., y[m],
• T - s[m,n] matrix

Like this :

1. y[1] = s[1][1]*z[1]^t[1]+s[1][2]*z[2]^t[1]+...s[1][n]*z[n]^t[1])

2. y[2] = s[2][1]*z[1]^t[2]+s[2][2]*z[2]^t[2]+...s[2][n]*z[n]^t[2])

   ...

3. y[m] = s[m][1]*z[1]^t[m]+s[m][2]*z[2]^t[2]+...s[m][n]*z[n]^t[m])

Problem: Error occured.

Optimization terminated successfully.

Traceback (most recent call last):
    solution = optimize.fmin_cg(func, z, fprime=gradf, args=args)
  File "C:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 952, in fmin_cg
    res = _minimize_cg(f, x0, args, fprime, callback=callback, **opts)
  File "C:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 1072, in _minimize_cg
    print "         Current function value: %f" % fval
TypeError: float argument required, not numpy.ndarray

Here is the code

import numpy as np
import scipy as sp
import scipy.optimize as optimize

def func(z, *args):
    y,T,t = args[0]
    return y - counter(T,z,t)

def counter(T, z, t):
    rows,cols = np.shape(T)
    res = np.zeros(rows)
    for i,row_val in enumerate(T):
        res[i] = np.dot(row_val, z**t[i])
    return res


def gradf(z, *args):
    y,T,t = args[0]
    return np.dot(t,counter(T,z,t-1))

def main():
    # Inputs
    N = 30
    M = 20
    z0 = np.zeros(N) # initial guess
    y = 30*np.random.random(M)
    T = 10*np.random.random((M,N))
    t = 5*np.random.random(M)
    args = [y, T, t]

    solution = optimize.fmin_cg(func, z0, fprime=gradf, args=args)
    print 'solution: ', solution

if __name__ == '__main__':
    main()

I also tried to find similar examples but could not find something very similar. Here is the code for your consideration. Thanks in advance.

Answer 1

The root of your problem is that fmin_cg expects the function to return a single scalar value for the misfit instead of an array.

Basically, you want something vaguely similar to:

def func(z, y, T, t):
    return np.linalg.norm(y - counter(T,z,t))

I'm using np.linalg.norm here because there's no builtin function in numpy for the root-mean-square. The actual RMS would be norm(x) / sqrt(x.size) , but for minimization the constant multiplier doesn't make any difference.

There are also other minor problems in your code (eg args[0] is going to be a single item. You want y, T, t = args or better yet, just func(z, y, T, t) ). Your gradient function doesn't make any sense to me, but it's optional regardless. Also, there's no way the solution can produce reasonable values at the moment, as you're testing it against pure noise. I assume those are just meant to be placeholder values, though.

However, you have a larger problem. You're trying to minimize in 30-dimensional space. Most non-linear solvers aren't going to work well with that high of a dimensionality. It may work fine, but you're very likely to run into problems.

All that having been said, you may find it more intuitive to use the scipy.optimize.curve_fit interface rather than using the others, if you're okay with LM instead of CG (they're fairly similar methods).

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One final thing: You're trying to solve for 30 model parameters with 20 observations. This is an underdetermined problem. This problem doesn't have a unique solution. You're going to need to apply some a-priori knowledge to get a reasonable answer.