Calculate (accurate) numerical approximations to derivatives.
The main functions are
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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.
Paul Gilbert, based on work by Xingqiao Liu, and Ravi Varadhan (who wrote complex-step derivative codes)
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.