Powell’s method of minimizing user-supplied function in Python，,''' xMin,nCy

Powell’s method of minimizing user-supplied function in Python，,''' xMin,nCy

''' xMin,nCyc = powell(F,x,h=0.1,tol=1.0e-6)    Powell's method of minimizing user-supplied function F(x).    x    = starting point    h   = initial search increment used in 'bracket'    xMin = mimimum point    nCyc = number of cycles'''from numpy import identity,array,dot,zeros,argmaxfrom goldSearch import *from math import sqrtdef powell(F,x,h=0.1,tol=1.0e-6):    def f(s): return F(x + s*v)    # F in direction of v    n = len(x)                     # Number of design variables    df = zeros(n)                  # Decreases of F stored here    u = identity(n)                # Vectors v stored here by rows    for j in range(30):            # Allow for 30 cycles:        xOld = x.copy()            # Save starting point        fOld = F(xOld)      # First n line searches record decreases of F        for i in range(n):            v = u[i]            a,b = bracket(f,0.0,h)            s,fMin = search(f,a,b)            df[i] = fOld - fMin            fOld = fMin            x = x + s*v      # Last line search in the cycle            v = x - xOld        a,b = bracket(f,0.0,h)        s,fLast = search(f,a,b)        x = x + s*v      # Check for convergence        if sqrt(dot(x-xOld,x-xOld)/n) < tol: return x,j+1      # Identify biggest decrease & update search directions        iMax = argmax(df)        for i in range(iMax,n-1):            u[i] = u[i+1]        u[n-1] = v    print "Powell did not converge"