dg()

dg.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 definitions apply:
# g(x) = limit-state function in the original x-space of random variables
# dgdx(x) = gradient vector of the limit-state function in the original space
# ------------------------------------------------------------------------

def dg(x, gValue, gFunction):

    numRV = len(x)
    dgdx = np.zeros(numRV)

    for j in range(numRV):

        # Take a backup of this random variable
        backup = x[j]

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

        # Perturb this random variable
        x[j] = backup + dx

        # Re-evaluate the limit-state function
        gPerturbed = gFunction(x)

        # Re-set the random variable
        x[j] = backup

        # Calculate the sought derivative
        dgdx[j] = (gPerturbed - gValue) / dx

    return dgdx