XploRe Help : nmjacobian

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	nummath
See also:	nmgraddiff nmgraditer

Quantlet:		nmjacobian
Description:		Computes the jacobian of function(s) func (or more generally, the matrix of gradients) at a point x0

Usage:	`jacobi = nmjacobian(func, x0{, h, iter})`
Input:
	`func`	name of function(s) (string or vector of strings) whose gradient matrix (jacobian) is to be computed. The function(s) should take just one parameter x, which is n x k matrix (k >= 1) x = (x1,x2,...,xk); xi (n x 1 vector; i=1..k) represent points in which the function should be evaluated. As a result, the function should return k real numbers in a form of 1 x k vector.
	`x0`	n x 1 vector, the point at which gradient(s) will be computed
	`h`	optional n x 1 vector or scalar (in the latter case, h <- h * matrix(n) will be used); vector of initial stepsizes for partial derivatives; if not given, default value of gradient quantlet will be used
	`iter`	optional number, controls usage of iterative/difference method for computing gradient; if iter is not given or iter = 0, difference method nmgraddiff will be used (quicker), otherwise iterative method nmgraditer will be used (more precise)
Output:
	`jacobi`	dim(func) x n matrix, i-th row containes the gradient of i-th function (it is jacobian for dim(func) = n)

Note:

For jacobian, dimension of func has to be the same as dimension of x0; this function returns the matrix of gradients also when dim(func) <> dim(x0)

Example:

library("nummath") ; ; definition of function f(x1,x2) = sin(x1) + x2^2 ; g(x1,x2) = x1 - x2 ; proc(ff)=f(x) ff=sin(x[1,])+x[2,]^2 endp proc(gg)=g(x) gg=x[1,]-x[2,] endp ; nmjacobian(#("f","g"),#(pi,2))

Result:

Contents of jacobi
[1,]       -1        4
[2,]        1       -1

Author: L. Cizkova, 20010505 license MD*Tech