Derivative of Multivariate Objective Function

nablaF.py

# ------------------------------------------------------------------------
# The following function is implemented in Python by Professor Terje Haukaas
# at the University of British Columbia in Vancouver, Canada. It is made
# freely available online at terje.civil.ubc.ca together with notes,
# examples, and additional Python code. Please be cautious when using
# this code; it may contain bugs and comes without any form of warranty.
#
# The following notation applies:
# F(x) = objective function
# nablaF = dF/dx = gradient vector
# ------------------------------------------------------------------------

def nablaF(x, F, F0):

    # Extract number of design variables
    numDVs = len(x)

    # Initialize the gradient vector
    gradient = np.zeros(numDVs)

    # Loop over design variables and do finite difference
    for i in range(numDVs):

        # Backup of design variable value
        backup  = x[i]

        # Set the perturbation as a fraction of the x-value
        dx = 0.001
        if x[i] != 0.0:
            dx = dx * x[i]

        # Perturbed vector of design variables
        x[i] += dx

        # Perturbed function value
        perturbedF = F(x)

        # Sought derivative
        gradient[i] = (perturbedF - F0) / dx

        # Reset the design variable
        x[i] = backup

    # Return the gradient vector
    return gradient