Python illustrating Downhill simplex method for minimizing the user-supplied scalar function，,''' x = down

Python illustrating Downhill simplex method for minimizing the user-supplied scalar function，,''' x = down

''' x = downhill(F,xStart,side,tol=1.0e-6)    Downhill simplex method for minimizing the user-supplied    scalar function F(x) with respect to the vector x.    xStart = starting vector x.    side   = side length of the starting simplex (default is 0.1)'''from numpy import zeros,dot,argmax,argmin,sumfrom math import sqrtdef downhill(F,xStart,side=0.1,tol=1.0e-6):    n = len(xStart)                 # Number of variables    x = zeros((n+1,n))     f = zeros(n+1)  # Generate starting simplex    x[0] = xStart    for i in range(1,n+1):        x[i] = xStart        x[i,i-1] = xStart[i-1] + side          # Compute values of F at the vertices of the simplex         for i in range(n+1): f[i] = F(x[i])  # Main loop    for k in range(500):      # Find highest and lowest vertices        iLo = argmin(f)        iHi = argmax(f)             # Compute the move vector d        d = (-(n+1)*x[iHi] + sum(x,axis=0))/n      # Check for convergence        if sqrt(dot(d,d)/n) < tol: return x[iLo]      # Try reflection        xNew = x[iHi] + 2.0*d                      fNew = F(xNew)                if fNew <= f[iLo]:        # Accept reflection             x[iHi] = xNew            f[iHi] = fNew          # Try expanding the reflection            xNew = x[iHi] + d                           fNew = F(xNew)            if fNew <= f[iLo]:    # Accept expansion                x[iHi] = xNew                f[iHi] = fNew        else:          # Try reflection again            if fNew <= f[iHi]:    # Accept reflection                x[iHi] = xNew                f[iHi] = fNew            else:              # Try contraction                xNew = x[iHi] + 0.5*d                fNew = F(xNew)                if fNew <= f[iHi]: # Accept contraction                    x[iHi] = xNew                    f[iHi] = fNew                else:                  # Use shrinkage                    for i in range(len(x)):                        if i != iLo:                            x[i] = (x[i] - x[iLo])*0.5                            f[i] = F(x[i])    print "Too many iterations in downhill"    print "Last values of x were"    return x[iLo]