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/* This is better for stocastic optimisation, where the function */
/* being evaluated may have a random component, or is not smooth. */
/*
* Copyright 1999 Graeme W. Gill
* All rights reserved.
*
* This material is licenced under the GNU AFFERO GENERAL PUBLIC LICENSE Version 3 :-
* see the License.txt file for licencing details.
*/
/* A general purpose downhill simplex multivariate optimser, */
/* based on the Nelder and Mead algorithm. */
/* Code is an original expression of the algorithms decsribed in */
/* "Numerical Recipes in C", by W.H.Press, B.P.Flannery, */
/* S.A.Teukolsky & W.T.Vetterling. */
#include "numsup.h"
#undef DEBUG
int dhsx_debug = 1;
static void simplexinit(int di, double *cp, double **p, double *r, double sv, int ii);
static double trypoint(int di,double *cp, double **p, double *y, int hix, double hpfac,
double (*funk)(void *fdata, double *tp), void *fdata, double *tryp);
#ifdef NEVER /* Experimental */
#define ALPHA 0.7 /* Extrapolate hight point through oposite face factor */
#define GAMMA 1.4 /* Aditional extrapolation if ALPHA is good */
#define BETA 0.4 /* One dimensional contraction factor (smaller is more) */
#define DELTA 0.5 /* Multi dimensional contraction factor (smaller is more) */
#define NONEXP 2 /* non expanding passes */
#else /* Standard tuning values */
#define ALPHA 1.0 /* [1.0] Extrapolate hight point through oposite face factor */
#define GAMMA 2.0 /* [2.0] Aditional extrapolation if ALPHA is good */
#define BETA 0.4 /* [0.5] One dimensional contraction factor (smaller is more) */
#define DELTA 0.4 /* [0.5] Multi dimensional contraction factor (smaller is more) */
#define NONEXP 3 /* [3] non expanding passes */
#endif
/* Down hill simplex function */
/* return 0 on sucess, 1 on failure due to excessive itterations */
/* Result will be in cp */
int dhsx(
double *rv, /* If not NULL, return the residual error */
int di, /* Dimentionality */
double *cp, /* Initial starting point, return minimum */
double *s, /* Size of initial search area */
double ftol, /* Finishing tollerance of error change */
double athr, /* Absolute return value threshold. (Set high to not use) */
int maxit, /* Maximum iterations allowed */
double (*funk)(void *fdata, double *tp), /* Error function to evaluate */
void *fdata /* Data needed by function */
) {
int ii = 0; /* Initial simplex orientation */
int i, j;
int nit; /* Number of iterations */
int nsp = di+1; /* Number of simplex verticy points */
double tryy, ysave;
double tol;
double **p; /* Current simplex array */
double *y; /* Values of func at verticies */
double **p2; /* Trial simplex array */
double *y2; /* Trial values of func at verticies */
int lox, hix, nhix; /* Lowest point index, highest point, next highest point */
double *tryp; /* Temporary used by trypoint() */
/* Allocate array arrays */
tryp = dvector(0, di-1); /* Trial value */
p = dmatrix(0, nsp-1, 0, di-1); /* Vertex array of dimentions */
y = dvector(0, nsp-1); /* Value of function at verticies */
p2 = dmatrix(0, nsp-1, 0, di-1); /* Trial vertex array of dimentions */
y2 = dvector(0, nsp-1); /* Trial value of function at verticies */
/* Init the search simplex */
simplexinit(di, cp, p, s, 1.0, ii);
/* Compute initial y (function) values at simplex verticies */
for (i = 0; i < nsp; i++) /* For all verticies */
y[i] = (*funk)(fdata, p[i]); /* Compute error function */
/* Locate verticy with best value */
lox = 0;
for (i = 0; i < nsp; i++) {
if (y[i] < y[lox])
lox = i;
}
tryy = (*funk)(fdata, cp); /* Value at initial point */
/* If our initial point is better than any of the simplex verticies */
if (y[lox] > tryy) {
/* Move all the verticies to match moving lox to cp */
for (i = 0; i < nsp; i++) {
if (i == lox)
continue;
for (j = 0; j < di; j++)
p[i][j] += cp[j] - p[lox][j];
y[i] = (*funk)(fdata, p[i]); /* Compute error function */
}
/* Make lox be the input point */
for (j = 0; j < di; j++)
p[lox][j] = cp[j];
y[lox] = tryy;
}
/* Compute current center point location as sum of verticies. */
/* (We use this to compute moves) */
for (j = 0; j < di; j++) { /* For all dimensions */
double sum;
for (i = 0, sum = 0.0; i < nsp; i++) /* For all verticies */
sum += p[i][j];
cp[j] = sum;
}
/* Untill we find a solution or give up */
for (nit = 0; ; nit++) {
/* Find highest, next highest and lowest vertex */
lox = nhix = hix = 0;
for (i = 0; i < nsp; i++) {
if (y[i] < y[lox])
lox = i;
if (y[i] > y[hix]) {
nhix = hix;
hix = i;
} else if (y[i] > y[nhix]) {
nhix = i;
}
}
tol = y[hix] - y[lox];
#ifdef DEBUG
if (dhsx_debug) {
printf("Current vs =\n");
for (i = 0; i < nsp; i++)
printf(" %d: %s\n",i,debPdv(di, p[i]));
printf("Current errs = %s\n",debPdv(nsp,y));
printf("Current y[lox] = %e, y[hix] = %e\n",y[lox], y[hix]);
}
#endif /* DEBUG */
/* If we look like we are about to finish, */
/* see if we should re-start with a new simplex. */
if (tol < ftol && y[lox] < athr /* Found an adequate solution */
&& nit < maxit) {
double scale = 0.0;
int lox2;
#ifdef DEBUG
if (dhsx_debug) printf(" nit %d, tol %e\n",nit, tol);
#endif /* DEBUG */
/* compute center location */
tryy = 1.0/nsp;
for (j = 0; j < di; j++) /* For all dimensions */
cp[j] *= tryy; /* Set cp to center point of simplex */
/* Compute scaled distance of vertexes from center */
for (i = 0; i < nsp; i++) {
double dist = 0.0;
for (j = 0; j < di; j++) {
double tt = (cp[j] - p[i][j])/s[j];
dist += tt * tt;
}
scale += sqrt(dist);
}
scale /= (double)nsp; /* Average scale compared to starting simplex */
#ifdef DEBUG
if (dhsx_debug) printf(" ave scale = %f\n",scale);
#endif /* DEBUG */
/* Enlarge search space, but not more than initial */
scale *= 10.0;
if (scale > 1.0)
scale = 1.0;
/* Compute trial simplex with different orientation */
if (++ii >= (di+1))
ii = 0;
/* Init the search simplex */
simplexinit(di, cp, p2, s, scale, ii);
/* Compute y (function) values at simplex verticies */
for (i = 0; i < nsp; i++) /* For all verticies */
y2[i] = (*funk)(fdata, p2[i]); /* Compute error function */
/* Locate verticy with best value */
lox2 = 0;
for (i = 0; i < nsp; i++) {
if (y2[i] < y2[lox2])
lox2 = i;
}
#ifdef DEBUG
if (dhsx_debug) printf(" y2lox %f ylox %f\n",y2[lox2], y[lox]);
#endif /* DEBUG */
/* If any of its vertexes are better than current best, switch */
/* to it and continue (i.e. re-start) */
if (y2[lox2] < y[lox]) {
#ifdef DEBUG
if (dhsx_debug) printf(" restarting\n");
#endif /* DEBUG */
for (i = 0; i < nsp; i++) {
for (j = 0; j < di; j++)
p[i][j] = p2[i][j];
y[i] = y2[i];
}
/* Compute current center point location as sum of verticies. */
/* (We use this to compute moves) */
for (j = 0; j < di; j++) { /* For all dimensions */
double sum;
for (i = 0, sum = 0.0; i < nsp; i++) /* For all verticies */
sum += p[i][j];
cp[j] = sum;
}
/* Find highest, next highest and lowest vertex */
lox = nhix = hix = 0;
for (i = 0; i < nsp; i++) {
if (y[i] < y[lox])
lox = i;
if (y[i] > y[hix]) {
nhix = hix;
hix = i;
} else if (y[i] > y[nhix]) {
nhix = i;
}
}
tol = y[hix] - y[lox];
}
}
if ((tol < ftol && y[lox] < athr) /* Found an adequate solution */
|| ((nit+1) >= maxit)) { /* Or we are about to fail */
/* convert cp[] to center point location, */
/* and use best out of it and any simplex verticy. */
tryy = 1.0/nsp;
for (j = 0; j < di; j++) /* For all dimensions */
cp[j] *= tryy; /* Set cp to center point of simplex */
#ifdef DEBUG
if (dhsx_debug) printf("C point = %s\n",debPdv(di,cp));
#endif
tryy = (*funk)(fdata, cp); /* Compute error function */
if (tryy > y[lox]) { /* Center point is not the best */
#ifdef DEBUG
if (dhsx_debug) printf("C point val %f is not best, using sx %d val %f instead\n",tryy,lox,y[lox]);
#endif
tryy = y[lox];
for (j = 0; j < di; j++)
cp[j] = p[lox][j];
}
free_dvector(y2, 0, nsp-1);
free_dmatrix(p2, 0, nsp-1, 0, di-1);
free_dvector(y, 0, nsp-1);
free_dmatrix(p, 0, nsp-1, 0, di-1);
free_dvector(tryp, 0, di-1);
#ifdef DEBUG
if (dhsx_debug) printf("Total itterations = %d\n",nit);
#endif
if (rv != NULL)
*rv = tryy;
if ((nit+1) >= maxit)
return 1; /* Failed */
return 0;
}
/* Only try expanding after a couple of iterations */
if (nit > NONEXP) {
/* Try moving the high point through the oposite face by ALPHA */
#ifdef DEBUG
if (dhsx_debug) printf("dhsx: try moving high point %d through oposite face",hix);
#endif
tryy = trypoint(di, cp, p, y, hix, -ALPHA, funk, fdata, tryp);
}
/* If gave good result, continue on in that direction */
if (nit > NONEXP && tryy <= y[lox]) {
#ifdef DEBUG
if (dhsx_debug) printf("dhsx: moving high through oposite face worked");
#endif
tryy = trypoint(di, cp, p, y, hix, GAMMA, funk, fdata, tryp);
/* else if ALPHA move made things worse, do a one dimensional */
/* contraction by a factor BETA */
} else if (nit <= NONEXP || tryy >= y[nhix]) {
#ifdef DEBUG
if (dhsx_debug) printf("dhsx: else try moving contracting point %d, y[ini] = %f",hix,y[hix]);
#endif
ysave = y[hix];
tryy = trypoint(di, cp, p, y, hix, BETA, funk, fdata, tryp);
if (tryy >= ysave) {
#ifdef DEBUG
if (dhsx_debug) printf("dhsx: contracting didn't work, try contracting other points to low");
#endif
/* That still didn't help us, so move all the */
/* other points towards the low point */
for (i = 0; i < nsp; i++) { /* For all verts except low */
if (i != lox) {
for (j = 0; j < di; j++) /* For all dimensions */
p[i][j] = DELTA * p[i][j] + (1.0 - DELTA) * p[lox][j];
y[i] = (*funk)(fdata, p[i]); /* Compute function value for new point */
}
}
/* Re-compute current center point location */
for (j = 0; j < di; j++) {
double sum;
for (i = 0,sum = 0.0;i<nsp;i++)
sum += p[i][j];
cp[j] = sum;
}
} else {
#ifdef DEBUG
if (dhsx_debug) printf("dhsx: contracting point %d worked, tryy = %e, ysave = %e",hix,tryy,ysave);
#endif
}
}
}
}
/* Try moving the high point through the opposite face */
/* by a factor of fac, and replaces the high point if */
/* that proves to be better. Return the failed or new */
/* function value. */
static double trypoint(
int di, /* Dimentionality */
double *cp, /* nsp * center coord/Returned coordinate */
double **p, /* Starting/Current simplex (modified by dhsx) */
double *y, /* values of func at verticies */
int hix, /* Index of high point we are moving */
double hpfac, /* factor to move high point */
double (*funk)(void *fdata, double tp[]), /* Error function to evaluate */
void *fdata, /* Data needed by function */
double *tryp /* temporary array of size di-1 */
) {
int j;
double tt, tryy;
/* Compute trial high point */
tt = (1.0 - hpfac)/di;
for (j = 0; j < di; j++)
tryp[j] = cp[j] * tt - p[hix][j] * (tt - hpfac);
/* Evaluate trial point */
tryy = (*funk)(fdata, tryp); /* Compute error function */
/* If new high point pos. is better */
if (tryy < y[hix]) {
#ifdef DEBUG
if (dhsx_debug) printf("Try gave improved %e from sx %d",tryy,hix);
#endif
y[hix] = tryy; /* Replace func val of hi with trial */
for (j = 0; j < di; j++) {
cp[j] += tryp[j] - p[hix][j]; /* Recompute cp */
p[hix][j] = tryp[j]; /* Replace co-ords of hi with trial */
}
} else {
#ifdef DEBUG
if (dhsx_debug) printf("Try gave worse %e from sx %d",tryy,hix);
#endif
}
return tryy; /* Function value of trial point */
}
/* Make up an initial simplex for dhsx routine */
static void
simplexinit(
int di, /* Dimentionality */
double *cp, /* Initial solution location */
double **p, /* Simplex to initialize */
double *s, /* initial radius for each dimention */
double sv, /* Radius scaling value */
int ii /* Coordinate to start with */
) {
double bb;
double hh = 0.5; /* Constant */
double rr = sqrt(3.0)/2.0; /* Constant */
int i, j;
for (i = 0; i < (di+1); i++) { /* For each vertex */
/* The bounding points form a equalateral simplex */
/* whose vertexes are on a sphere about the data */
/* point center. The coordinate sequence is: */
/* B = sphere radius */
/* H = 0.5 */
/* R = sqrt(3)/2 */
/* 0 0 0 +B */
/* 0 0 0 -B */
/* 0 0 0 +B */
/* 0 0 +RB -HB */
/* 0 0 -RB -HB */
/* 0 0 0 +B */
/* 0 0 +RB -HB */
/* 0 +RRb -HRB -HB */
/* 0 -RRb -HRB -HB */
/* 0 0 0 +B */
/* 0 0 +RB -HB */
/* 0 +RRb -HRB -HB */
/* +RRRb -HRRb -HRB -HB */
/* -RRRb -HRRb -HRB -HB */
/* etc. */
bb = 1.0; /* Initial unscaled radius */
for (j = 0; j < di; j++) { /* For each coordinate in vertex */
if (j > ii)
p[i][j] = cp[j] + sv * s[j] * 0.0; /* If beyond last */
else if (j == ii) /* If last non-zero */
p[i][j] = cp[j] + sv * s[j] * bb;
else if (ii == di && j == (di-1)) /* If last of last */
p[i][j] = cp[j] + sv * s[j] * -1.0 * bb;
else /* If before last */
p[i][j] = cp[j] + sv * s[j] * -hh * bb;
bb *= rr;
}
/* Increment coordinate number with wrap around */
if (++ii >= (di+1))
ii = 0;
}
#ifdef DEBUG
if (dhsx_debug) {
for (i = 0; i < (di+1); i++)
printf(" p[%d] = %s\n",i,debPdv(di,p[i]));
}
#endif
}
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