cal/cal/root.cal

{ RCSid $Id: root.cal,v 1.3 2011/10/11 15:40:54 greg Exp $ }
{
        root.cal - calculate zeroes of functions using Newton's method.

        2/3/88
}

FTINY : 1e-9;

root(f, x0) = root2(f, x0, x0-f(x0)/lim(f1(f,x0)), nit);

root2(f, x0, x1, i) = if(i,
                        if(err-abs(x1-x0),
                                x1,
                                root2(f,x1,x1-f(x1)/lim(f1(f,x1)),i-1)),
                        0);

abs(x) = if(x, x, -x);
lim(x) = if(x, max(x,err), -max(-x,err));

f1(f,x) = (f(x+FTINY)-f(x-FTINY))/(2*FTINY);    { numerical derivative }

err = 1e-5;
nit = 100;
Revision:	1.4
Committed:	Mon Jun 10 13:56:52 2019 UTC (4 years, 11 months ago) by greg
Branch:	MAIN
CVS Tags:	rad5R4, rad5R3, HEAD
Changes since 1.3:	+1 -2 lines
Log Message:	Added max() and min() as .cal library functions
#	User	Rev	Content
1	greg	1.4	{ RCSid $Id: root.cal,v 1.3 2011/10/11 15:40:54 greg Exp $ }
2	greg	1.1	{
3			root.cal - calculate zeroes of functions using Newton's method.
4
5			2/3/88
6			}
7
8	greg	1.3	FTINY : 1e-9;
9	greg	1.1
10			root(f, x0) = root2(f, x0, x0-f(x0)/lim(f1(f,x0)), nit);
11
12			root2(f, x0, x1, i) = if(i,
13			if(err-abs(x1-x0),
14			x1,
15			root2(f,x1,x1-f(x1)/lim(f1(f,x1)),i-1)),
16			0);
17
18			abs(x) = if(x, x, -x);
19			lim(x) = if(x, max(x,err), -max(-x,err));
20
21	greg	1.2	f1(f,x) = (f(x+FTINY)-f(x-FTINY))/(2*FTINY); { numerical derivative }
22	greg	1.1
23	greg	1.3	err = 1e-5;
24	greg	1.1	nit = 100;