AELS/dfovec.py at main · modestyachts/AELS · GitHub

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# This is a python implementation of dfovec.m, provided at http://www.mcs.anl.gov/~more/dfo/
import numpy as np

def dfovec(m, n, x, nprob):
    # Set lots of constants:
    c13 = 1.3e1
    c14 = 1.4e1
    c29 = 2.9e1
    c45 = 4.5e1
    v  = [4.0e0,2.0e0,1.0e0,5.0e-1,2.5e-1,1.67e-1,1.25e-1,1.0e-1,8.33e-2,7.14e-2,6.25e-2]
    y1 = [1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0]
    y2 = [1.957e-1,1.947e-1,1.735e-1,1.6e-1,8.44e-2,6.27e-2,4.56e-2,3.42e-2,3.23e-2,2.35e-2,2.46e-2]
    y3 = [3.478e4,2.861e4,2.365e4,1.963e4,1.637e4,1.372e4,1.154e4,9.744e3,8.261e3,7.03e3,6.005e3,5.147e3,4.427e3,3.82e3,3.307e3,2.872e3]
    y4 = [8.44e-1,9.08e-1,9.32e-1,9.36e-1,9.25e-1,9.08e-1,8.81e-1,8.5e-1,8.18e-1,7.84e-1,7.51e-1,7.18e-1,6.85e-1,6.58e-1,6.28e-1,6.03e-1,5.8e-1,5.58e-1,5.38e-1,5.22e-1,5.06e-1,4.9e-1,4.78e-1,4.67e-1,4.57e-1,4.48e-1,4.38e-1,4.31e-1,4.24e-1,4.2e-1,4.14e-1,4.11e-1,4.06e-1]
    y5 = [1.366e0,1.191e0,1.112e0,1.013e0,9.91e-1,8.85e-1,8.31e-1,8.47e-1,7.86e-1,7.25e-1,7.46e-1,6.79e-1,6.08e-1,6.55e-1,6.16e-1,6.06e-1,6.02e-1,6.26e-1,6.51e-1,7.24e-1,6.49e-1,6.49e-1,6.94e-1,6.44e-1,6.24e-1,6.61e-1,6.12e-1,5.58e-1,5.33e-1,4.95e-1,5.0e-1,4.23e-1,3.95e-1,3.75e-1,3.72e-1,3.91e-1,3.96e-1,4.05e-1,4.28e-1,4.29e-1,5.23e-1,5.62e-1,6.07e-1,6.53e-1,6.72e-1,7.08e-1,6.33e-1,6.68e-1,6.45e-1,6.32e-1,5.91e-1,5.59e-1,5.97e-1,6.25e-1,7.39e-1,7.1e-1,7.29e-1,7.2e-1,6.36e-1,5.81e-1,4.28e-1,2.92e-1,1.62e-1,9.8e-2,5.4e-2]

    # Initialize things
    fvec = np.zeros(m)
    total = 0

    if nprob == 1:  # Linear function - full rank.
        for j in range(n):
            total = total + x[j]
        temp = 2*total/m + 1
        for i in range(m):
            fvec[i] = -temp
            if i < n:
                fvec[i] = fvec[i] + x[i]
    elif nprob == 2:  # Linear function - rank 1.
        for j in range(n):
            total = total + (j+1) * x[j]
        for i in range(m):
            fvec[i] = (i+1) * total - 1
    elif nprob == 3:  # Linear function - rank 1 with zero columns and rows.
        for j in range(1, n-1):
            total = total + (j+1) * x[j]
        for i in range(m-1):
            fvec[i] = i * total - 1
        fvec[m-1] = -1
    elif nprob == 4:  # Rosenbrock function.
        fvec[0] = 10 * (x[1] - x[0] * x[0])
        fvec[1] = 1 - x[0]
    elif nprob == 5:  # Helical valley function.
        if x[0] > 0:
            th = np.arctan(x[1]/x[0])/(2*np.pi)
        elif x[0] < 0:
            th = np.arctan(x[1]/x[0])/(2*np.pi) + 0.5
        elif x[0] == x[1] and x[1] == 0:
            th = 0.0
        else:
            th = 0.25
        r = np.sqrt(x[0]*x[0] + x[1]*x[1])
        fvec[0] = 10 * (x[2] - 10*th)
        fvec[1] = 10 * (r-1)
        fvec[2] = x[2]
    elif nprob == 6:  # Powell singular function.
        fvec[0] = x[0] + 10 * x[1]
        fvec[1] = np.sqrt(5) * (x[2] - x[3])
        fvec[2] = (x[1] - 2*x[2])**2
        fvec[3] = np.sqrt(10) * (x[0] - x[3])**2
    elif nprob == 7:  # Freudenstein and Roth function.
        fvec[0] = -c13 + x[0] + ((5 - x[1])*x[1] - 2)*x[1]
        fvec[1] = -c29 + x[0] + ((1 + x[1])*x[1] - c14)*x[1]
    elif nprob == 8:  # Bard function.
        for i in range(15):
            tmp1 = i + 1
            tmp2 = 15 - i
            tmp3 = tmp1
            if i > 7:
                tmp3 = tmp2
            fvec[i] = y1[i] - (x[0] + tmp1 / (x[1]*tmp2 + x[2]*tmp3))
    elif nprob == 9:  # Kowalik and Osborne function.
        for i in range(11):
            tmp1 = v[i] * (v[i] + x[1])
            tmp2 = v[i] * (v[i] + x[2]) + x[3]
            fvec[i] = y2[i] - x[0]*tmp1/tmp2
    elif nprob == 10:  # Meyer function.
        for i in range(16):
            temp = 5 * (i+1) + c45 + x[2]
            tmp1 = x[1] / temp
            tmp2 = np.exp(tmp1)
            fvec[i] = x[0] * tmp2 - y3[i]
    elif nprob == 11:  # Watson function.
        for i in range(29):
            div = (i+1) / c29
            s1 = 0
            dx = 1
            for j in range(1, n):
                s1 = s1 + j*dx*x[j]
                dx = div*dx
            s2 = 0
            dx = 1
            for j in range(n):
                s2 = s2 + dx*x[j]
                dx = div*dx
            fvec[i] = s1 - s2*s2 - 1
        fvec[29] = x[0]
        fvec[30] = x[1] - x[0]*x[0] - 1
    elif nprob == 12:  # Box 3-dimensional function.
        for i in range(m):
            temp = i+1
            tmp1 = temp / 10
            fvec[i] = np.exp(-tmp1*x[0]) - np.exp(-tmp1*x[1]) + (np.exp(-temp) - np.exp(-tmp1))*x[2]
    elif nprob == 13:  # Jennrich and Sampson function.
        for i in range(m):
            temp = i+1
            fvec[i] = 2 + 2*temp - np.exp(temp*x[0]) - np.exp(temp*x[1])
    elif nprob == 14:  # Brown and Dennis function.
        for i in range(m):
            temp = (i+1)/5
            tmp1 = x[0] + temp*x[1] - np.exp(temp)
            tmp2 = x[2] + np.sin(temp)*x[3] - np.cos(temp)
            fvec[i] = tmp1*tmp1 + tmp2*tmp2
    elif nprob == 15:  # Chebyquad function.
        for j in range(n):
            t1 = 1
            t2 = 2*x[j] - 1
            t = 2*t2
            for i in range(m):
                fvec[i] = fvec[i] + t2
                th = t*t2 - t1
                t1 = t2
                t2 = th
        iev = -1
        for i in range(m):
            fvec[i] = fvec[i]/n
            if iev > 0:
                fvec[i] = fvec[i] + 1/((i+1)**2 - 1)
            iev = -iev
    elif nprob == 16:  # Brown almost-linear function.
        total1 = -(n+1)
        prod1 = 1
        for j in range(n):
            total1 = total1 + x[j]
            prod1 = x[j] * prod1
        for i in range(n-1):
            fvec[i] = x[i] + total1
        fvec[n-1] = prod1 - 1
    elif nprob == 17:  # Osborne 1 function.
        for i in range(33):
            temp = 10 * i
            tmp1 = np.exp(-x[3]*temp)
            tmp2 = np.exp(-x[4]*temp)
            fvec[i] = y4[i] - (x[0] + x[1]*tmp1 + x[2]*tmp2)
    elif nprob == 18:  # Osborne 2 function.
        for i in range(65):
            temp = i / 10
            tmp1 = np.exp(-x[4]*temp)
            tmp2 = np.exp(-x[5]*(temp-x[8])**2)
            tmp3 = np.exp(-x[6]*(temp-x[9])**2)
            tmp4 = np.exp(-x[7]*(temp-x[10])**2)
            fvec[i] = y5[i] - (x[0]*tmp1 + x[1]*tmp2 + x[2]*tmp3 + x[3]*tmp4)
    elif nprob == 19:  # Bdqrtic
        # n >= 5, m = (n-4)*2
        for i in range(n-4):
            fvec[i] = (-4*x[i] + 3.0)
            fvec[n-4+i] = x[i]**2 + 2*x[i+1]**2 + 3*x[i+2]**2 + 4*x[i+3]**2 + 5*x[n-1]**2
    elif nprob == 20:  # Cube
        # n = 2, m = n
        fvec[1] = x[0] - 1.0
        for i in range(1, n):
        	fvec[i] = 10*(x[i] - x[i-1]**3)
    elif nprob == 21:  # Mancino
        # n = 2, m = n
        for i in range(n):
            ss = 0
            for j in range(n):
                v2 = np.sqrt(x[i]**2 + (i+1)/(j+1))
                ss = ss + v2*((np.sin(np.log(v2)))**5 + (np.cos(np.log(v2)))**5)
            fvec[i]=1400 * x[i] + (i-49)**3 + ss
    elif nprob == 22:  # Heart8ls
        # m = n = 8
        fvec[0] = x[0] + x[1] + 0.69
        fvec[1] = x[2] + x[3] + 0.044
        fvec[2] = x[4]*x[0] + x[5]*x[1] - x[6]*x[2] - x[7]*x[3] + 1.57
        fvec[3] = x[6]*x[0] + x[7]*x[1] + x[4]*x[2] + x[5]*x[3] + 1.31
        fvec[4] = x[0]*(x[4]**2 - x[6]**2) - 2.0*x[2]*x[4]*x[6] + x[1]*(x[5]**2 - x[7]**2) - 2.0*x[3]*x[5]*x[7] + 2.65
        fvec[5] = x[2]*(x[4]**2 - x[6]**2) + 2.0*x[0]*x[4]*x[6] + x[3]*(x[5]**2 - x[7]**2) + 2.0*x[1]*x[5]*x[7] - 2.0
        fvec[6] = x[0]*x[4]*(x[4]**2 - 3.0*x[6]**2) + x[2]*x[6]*(x[6]**2 - 3.0*x[4]**2) + x[1]*x[5]*(x[5]**2 - 3.0*x[7]**2) + x[3]*x[7]*(x[7]**2 - 3.0*x[5]**2) + 12.6
        fvec[7] = x[2]*x[4]*(x[4]**2 - 3.0*x[6]**2) - x[0]*x[6]*(x[6]**2 - 3.0*x[4]**2) + x[3]*x[5]*(x[5]**2 - 3.0*x[7]**2) - x[1]*x[7]*(x[7]**2 - 3.0*x[6]**2) - 9.48
    else:
       print(f'unrecognized function number {nprob}')
       return None
    return fvec