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/*
* probplot.c - routines used for probability plots
*
* Author: Sean Casey
* Modified 6/93 by Kenny Toh
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define ERRORRETURN -9.0e30
#define MAXITER 3000
#ifndef EXIT_FAILURE
# define EXIT_FAILURE 1
# define EXIT_SUCCESS 0
#endif
#ifndef FLT_EPSILON
# define FLT_EPSILON 1e-7
#endif
/* Local procedure declarations */
double CNnorm_vert_distance();
#ifdef TEST
static void calc_prob_axes();
#endif
/*
*
* double CNnorm_vert_distance(p, rc)
* Function to return the vertical distance on a probability plot given
* a fraction between 0 and 1.
* No allocated memory.
*
* This returns a value between -5 and +5. If x=0.5 (50%), f(x)=0
*/
double CNnorm_vert_distance(p, rc)
double p; /* Fraction between 0 and 1 */
int *rc; /* Return code, gets EXIT_SUCCESS for successful termination */
{
/* Simple Newton's method plus bisection. */
/* Taylored specifically to this application. */
double fb = 0, fu, fv;
double b, u, v;
double sqrt2, derivative, step;
int count = 2, nbis = 25, debug = 0;
*rc = EXIT_FAILURE;
sqrt2 = sqrt(2.0);
#ifdef DEBUG
debug = 1;
#endif
u = -5.0; /* Upper and lower limits on solution. */
v = 5.0; /* These will reach alomost to 1 */
fu = .5 * ( erf( u / sqrt2 ) + 1) - p;
fv = .5 * ( erf( v / sqrt2 ) + 1) - p;
if (fu * fv > 0 ) {
*rc = EXIT_FAILURE;
return(ERRORRETURN);
}
step = v - u;
for ( count = 0; count <= MAXITER; count++) {
if ( count % nbis == 0 ) {
b = u + (v - u) / 2; /* Bisect the interval. */
if (debug)
(void) printf("Bisect\n");
} else {
derivative = ( 1 / ( sqrt2 * sqrt(M_PI) * exp(b * b / 2) ) );
if (debug)
(void) printf(
"Derivative f'(b) = f'(%-8f) = %-10f step=%-10f ",
b, derivative, fb / derivative);
step = fb / derivative;
b -= fb / derivative ;
if (debug)
(void) printf("new b=%-10f\n", b);
if (b < u || b > v) {
if (debug)
(void) printf("b = %-10f Out of bounds. Bisect.\n", b);
b = u + (v - u) / 2; /* Bisect the interval. */
}
}
fb = .5 * ( erf( b / sqrt2 ) + 1 ) - p;
if (fb * fu > 0) {
fu = fb;
u = b;
} else {
fv = fb;
v = b;
}
if (debug)
(void) printf(
"count=%d b=%f fb=%-10f u=%-10f v=%-10f (u-v)=%-10f\n",
count, b, fb, u, v, u - v);
if ( fabs(v - u) <= FLT_EPSILON || fabs(step) <= FLT_EPSILON ) {
*rc = EXIT_SUCCESS;
return b;
}
}
*rc = EXIT_FAILURE;
return(ERRORRETURN);
}
#ifdef TEST
/*
* Figure out the position of the axes and tickmarks
*/
static void calc_prob_axes()
{
/*
* Figure out the axis position (0-1) for x=0.0001, 0.001, 0.01, 0.1,
* 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99, 0.999, 0.9999
*
* x=0.0001 => 0
* x=0.9999 => 1
*/
double upper_lim, lower_lim;
double x, y, Y, delta;
int i,j;
int error;
/*
* lower_lim => 0 upper_lim => 1
* (y-0)/(1-0) = (Y-lower_lim)/(upper_lim-lower_lim)
*/
lower_lim = CNnorm_vert_distance(0.0001, &error);
upper_lim = CNnorm_vert_distance(0.9999, &error);
/* Calculate axes from 0.0001 (0.01%) to 0.10 (10%) */
delta = 0.0001;
for (j=0; j<3; j++) {
x = delta;
for (i=0; i<10; i++) {
Y = CNnorm_vert_distance(x, &error);
y = 100*(Y - lower_lim)/(upper_lim - lower_lim);
(void) printf("%s x=%10.5f y=%10.5f\n",(i==0 ? "M" : " "),x,y);
x += delta;
}
delta = delta*10.0;
(void) printf("\n");
}
/* Calculate axes from 0.1 (10%) to 0.9 (90%) */
delta = 0.01;
for (j=1; j<9; j++) {
x = 0.1*j;
for (i=0; i<10; i++) {
Y = CNnorm_vert_distance(x, &error);
y = 100*(Y - lower_lim)/(upper_lim - lower_lim);
(void) printf("%s x=%10.5f y=%10.5f\n",(i==0 ? "M" : " "),x,y);
x += delta;
}
(void) printf("\n");
}
/* Calculate axes from 0.9 (90%) to 0.9999 */
delta = 0.01;
for (j=0; j<3; j++) {
x = 1.0 - 10.0*delta;
for (i=0; i<10; i++) {
Y = CNnorm_vert_distance(x, &error);
y = 100*(Y - lower_lim)/(upper_lim - lower_lim);
(void) printf("%s x=%10.5f y=%10.5f\n",(i==0 ? "M" : " "),x,y);
x += delta;
}
delta = delta*0.10;
(void) printf("\n");
}
}
main(argc, argv)
int argc;
char *argv[];
{
int rc, n, i;
if (argc < 2) {
(void) printf("To test, type a.out <fraction value>, e.g., a.out .6\n");
(void) printf("To test, type a.out <fraction value> <integer value>, e.g., a.out .6 10 \n");
exit(1);
}
(void) printf("Input=%f verticalDistance=%g\n", atof(argv[1]), CNnorm_vert_distance( atof(argv[1]) , &rc ) );
if (rc == 0)
(void) printf("SUCCESS\n");
else
(void) printf("FAILURE\n");
if (argc > 2) {
n = atoi(argv[2]);
for (i = 1; i <= n; i++) {
(void) printf("%-10f verticalDistance=%-10f\n",
(2.0 * i - 1.0) / (2.0 * n),
CNnorm_vert_distance( (2.0 * i -1.0) / (2.0 * n), &rc));
if (rc != 0)
(void) printf("FAILURE\n");
}
}
/* Test the axes routine */
calc_prob_axes();
exit(0);
}
#endif
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