XploRe Help : nmbrackin

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:	nmbrackout

Quantlet:		nmbrackin
Description:		searches for zero crossings of a given scalar function in n equally spaced subintervals of a given interval

Reference(s):

Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P. (1992). Numerical Recipes in C. 2nd Edition.

Usage:	`{a,b,fa,fb} = nmbrackin(fname {,a0,b0,n})`
Input:
	`fname`	string, name of a function whose root should be bracketed. The function should have just one scalar parameter x. As a result, the function should return a scalar.
	`a0,b0`	optional scalars, distinct initial points for bracketing, default: a0 = -10, b0 = 10
	`n`	optional scalar, a number of equally spaced subintervals of [a0,b0] that will be searched for zero crossings; default n = 100
Output:
	`a,b`	m x 1 vectors, bracketing pairs; a[i] contains the left bracket and b[i] contains the right bracket of the i-th bracketing pair (subinterval containing zero crossing)
	`fa,fb`	m x 1 vectors, function values at a and b

Example:

library("nummath") proc(fval) = ftion(x) fval = x^2 - 16 endp bracket = nmbrackin("ftion") bracket

Result:

In the default interval of [-10,10] divided into 100 (default)
subintervals, two zero crossings in [-4.2,-4] and [3.8,4]
were found:

Contents of bracket.a
[1,]     -4.2
[2,]      3.8
Contents of bracket.b
[1,]       -4
[2,]        4
Contents of bracket.fa
[1,]     1.64
[2,]    -1.56
Contents of bracket.fb
[1,] -3.5527e-15
[2,]  7.1054e-15

Author: L. Cizkova, 20020516 license MD*Tech