XploRe Help : nmgraditer

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 nmjacobian

Quantlet:		nmgraditer
Description:		Computes the gradient of a function func at a point x0 using Ridders' method of polynomial extrapolation

Usage:	`z = nmgraditer(func, x0{, h})`
Input:
	`func`	name of function (string) whose gradient is to be computed. The function 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 is to 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; (h need not to be very small) default value is 0.001
Output:
	`z.grad`	n x 1 vector, computed gradient
	`z.err`	n x 1 vector, estimates of errors of partial derivatives
	`z.hfin`	n x 1 vector, stepsizes for partial derivatives in last iteration

Example:

library("nummath") ; ; definition of function f(x) = 1 - x1 + x2^2 ; proc(r)=f(x) r=1-x[1,]+x[2,]^2 endp ; z = nmgraditer("f",#(1,2)) z.grad

Result:

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

Example:

library("nummath") z = nmgraditer("sin",0,1) z

Result:

Contents of z.grad
[1,]        1

Contents of z.err
[1,]  3.3307e-16

Contents of z.hfin
[1,]  0.06776

Author: L. Cizkova, 20010505 license MD*Tech