Calculate (accurate) numerical approximations to derivatives.
Details
The main functions are
grad to calculate the gradient (first derivative) of a scalar
real valued function (possibly applied to all elements
of a vector argument).
jacobian to calculate the gradient of a real m-vector valued
function with real n-vector argument.
hessian to calculate the Hessian (second derivative) of a scalar
real valued function with real n-vector argument.
genD to calculate the gradient and second derivative of a
real m-vector valued function with real n-vector
argument.
Author(s)
Paul Gilbert, based on work by Xingqiao Liu, and Ravi Varadhan (who wrote complex-step derivative codes)
References
Linfield, G. R. and Penny, J. E. T. (1989) Microcomputers in Numerical
Analysis. New York: Halsted Press.
Fornberg, B. and Sloan, D, M. (1994) “A review of pseudospectral methods
for solving partial differential equations.” Acta Numerica, 3, 203-267.
Lyness, J. N. and Moler, C. B. (1967) “Numerical Differentiation of Analytic
Functions.” SIAM Journal for Numerical Analysis,
4(2), 202-210.