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|
// Copyright 2005-2006 Nanorex, Inc. See LICENSE file for details.
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <stdarg.h>
#include <string.h>
#include "simulator.h"
static char const rcsid[] = "$Id$";
// Some of the routines in this file are based on routines found in
// "Numerical Recipes in C, Second Edition", by William H. Press, Saul
// A. Teukolsky, William T. Vetterling, and Brian P. Flannery,
// Cambridge University Press, ISBN 0 521 43108 5. The routines
// mnbrak(), brent(), linmin(), and frprmn() from Chapter 10 were
// heavily adapted for use here. Adaptations included: the
// combination of coordinate, parametric, and gradient information
// into a single structure, addition of a reference count garbage
// collector for those structures, folding of linear parameterization
// from gradients into linear minimization and bracketing, and program
// commentary. Many of the algorithms and variable names are similar
// or identical, so the text can be used as a reference for
// understanding these routines.
// Notes on the reference count garbage collector:
//
// Structures returned from routines are generally considered to have
// a reference to them already, so the return value from a function
// should be assigned directly instead of using SetConfiguration().
// The variable being assigned to in this situation should be NULL
// before the function call. Set it to NULL using SetConfiguration()
// if necessary.
//
// Variables should be created with NULL values in them. Be sure to
// set them back to NULL before returning. Other than as above,
// assignments should be done with SetConfiguration() to track the
// reference counts properly.
//
// Enter() and Leave() allow you to declare the number of items that
// should be allocated by the routine. A message will be printed to
// stderr if the actual count doesn't match. These checks are minimal
// enough compared to a full function or gradient evaluation that they
// can be left in.
//
// Total allocation counts can also be used to insure that all memory
// is being freed properly. See the test routine at the bottom.
//
// To track a single item and watch it's reference count changing, set
// PROBE to the object when it is first allocated.
#define GOLDEN_RATIO 1.61803399
#define DONT_DIVIDE_BY_ZERO 1e-10
#define PARABOLIC_BRACKET_LIMIT 10.0
#define TOLERANCE_AT_ZERO 1e-10
#define LINEAR_ITERATION_LIMIT 100
#define EPSILON 1e-10
static struct configuration *PROBE = NULL;
void
initializeFunctionDefinition(struct functionDefinition *fd,
void (*func)(struct configuration *p),
int dimension,
int messageBufferLength)
{
NULLPTR(func);
fd->func = func;
fd->dfunc = NULL;
fd->freeExtra = NULL;
fd->termination = NULL;
fd->constraints = NULL;
fd->tolerance = 1e-8;
fd->algorithm = PolakRibiereConjugateGradient;
fd->linear_algorithm = LinearMinimize;
fd->gradient_delta = 1e-8;
fd->dimension = dimension;
fd->initial_parameter_guess = 1.0;
fd->parameter_limit = MAXDOUBLE;
fd->functionEvaluationCount = 0;
fd->gradientEvaluationCount = 0;
if (messageBufferLength > 0) {
fd->message = (char *)allocate(messageBufferLength);
fd->message[0] = '\0';
fd->messageBufferLength = messageBufferLength;
} else {
fd->message = "";
fd->messageBufferLength = 0;
}
fd->allocationCount = 0;
fd->freeCount = 0;
fd->maxAllocation = 0;
}
// Append a message to then end of the message buffer. The buffer is
// fixed length, and we just stop appending when it's full.
static void
message(struct functionDefinition *fd, const char *format, ...)
{
va_list args;
char subbuf[200];
char *message = fd->message;
int messageBufferLength = fd->messageBufferLength;
int len;
if (message == NULL || messageBufferLength == 0) {
return;
}
len = strlen(message);
message += len;
messageBufferLength -= len;
if (messageBufferLength <= 1) {
return;
}
*message++ = ' ';
*message = '\0';
va_start(args, format);
len = vsprintf(subbuf, format, args);
va_end(args);
if (messageBufferLength < len)
len = messageBufferLength;
strncpy(message, subbuf, len);
message[len] = '\0';
}
struct configuration *
makeConfiguration(struct functionDefinition *fd)
{
struct configuration *ret;
ret = (struct configuration *)allocate(sizeof(struct configuration));
ret->functionValue = 0.0;
ret->coordinate = (double *)allocate(sizeof(double) * fd->dimension);
ret->gradient = NULL;
ret->parameter = 0.0;
ret->functionDefinition = fd;
ret->extra = NULL;
ret->functionValueValid = 0;
ret->referenceCount = 1;
fd->allocationCount++;
if (fd->allocationCount - fd->freeCount > fd->maxAllocation) {
fd->maxAllocation = fd->allocationCount - fd->freeCount;
}
return ret;
}
void
freeConfiguration(struct configuration *conf)
{
conf->functionDefinition->freeCount++;
if (conf == PROBE) {
fprintf(stderr, "freeing PROBE\n");
return;
}
if (conf->extra != NULL && conf->functionDefinition->freeExtra != NULL) {
(*conf->functionDefinition->freeExtra)(conf);
}
if (conf->coordinate != NULL) {
free(conf->coordinate);
}
if (conf->gradient != NULL) {
free(conf->gradient);
}
free(conf);
}
void
SetConfiguration(struct configuration **dst, struct configuration *src)
{
if (*dst == src) {
return;
}
if (*dst != NULL) {
if (*dst == PROBE) {
fprintf(stderr, "decrementing PROBE from %d\n", (*dst)->referenceCount);
}
if (--((*dst)->referenceCount) < 1) {
freeConfiguration(*dst);
}
}
*dst = src;
if (*dst != NULL) {
if (*dst == PROBE) {
fprintf(stderr, "incrementing PROBE from %d\n", (*dst)->referenceCount);
}
(*dst)->referenceCount++;
}
}
#if 0
#define CheckRef(p, rc) CheckReferenceCount(p, rc, __LINE__, # p)
static void
CheckReferenceCount(struct configuration *p, int rc, int line, char *name)
{
if (p->referenceCount != rc) {
fprintf(stderr, "refcount of %s (%d) != %d at line %d\n", name, p->referenceCount, rc, line);
}
}
#endif
#define Enter(config) int _used = config->functionDefinition->allocationCount - config->functionDefinition->freeCount
#define Leave(name, config, count) LeaveRoutine(# name, config, count, _used)
static void
LeaveRoutine(char *name, struct configuration *config, int count, int used)
{
struct functionDefinition *fd = config->functionDefinition;
int usedNow = fd->allocationCount - fd->freeCount;
if (usedNow - used != count) {
fprintf(stderr, "%s allocated %d instead of %d\n", name, usedNow - used, count);
}
}
double
evaluate(struct configuration *p)
{
struct functionDefinition *fd;
NULLPTRR(p, 0.0);
fd = p->functionDefinition;
if (p->functionValueValid == 0) {
NULLPTRR(fd->func, 0.0);
(*fd->func)(p);
CHECKNANR(p->functionValue, 0.0);
p->functionValueValid = 1;
fd->functionEvaluationCount++;
}
return p->functionValue;
}
void
evaluateGradientFromPotential(struct configuration *p)
{
struct functionDefinition *fd;
struct configuration *pPlusDelta = NULL;
struct configuration *pMinusDelta = NULL;
int i;
int j;
NULLPTR(p);
fd = p->functionDefinition;
NULLPTR(fd);
if (fd->gradient_delta == 0.0) {
fd->gradient_delta = 1e-8;
}
for (i=0; i<fd->dimension; i++) {
pPlusDelta = makeConfiguration(fd);
for (j=0; j<fd->dimension; j++) {
pPlusDelta->coordinate[j] = p->coordinate[j];
}
pPlusDelta->coordinate[i] += fd->gradient_delta / 2.0;
pMinusDelta = makeConfiguration(fd);
for (j=0; j<fd->dimension; j++) {
pMinusDelta->coordinate[j] = p->coordinate[j];
}
pMinusDelta->coordinate[i] -= fd->gradient_delta / 2.0;
p->gradient[i] = (evaluate(pMinusDelta) - evaluate(pPlusDelta)) / fd->gradient_delta;
BAIL();
SetConfiguration(&pPlusDelta, NULL);
SetConfiguration(&pMinusDelta, NULL);
}
}
void
evaluateGradient(struct configuration *p)
{
struct functionDefinition *fd;
int i;
double gradientCoordinate;
NULLPTR(p);
fd = p->functionDefinition;
NULLPTR(fd);
if (p->gradient == NULL) {
p->gradient = (double *)allocate(sizeof(double) * fd->dimension);
if (fd->dfunc == NULL) {
evaluateGradientFromPotential(p); BAIL();
} else {
(*fd->dfunc)(p); BAIL();
}
fd->gradientEvaluationCount++;
p->parameter = 0.0;
p->maximumCoordinateInGradient = 0.0;
for (i=fd->dimension-1; i>=0; i--) {
CHECKNAN(p->gradient[i]);
gradientCoordinate = fabs(p->gradient[i]);
if (p->maximumCoordinateInGradient < gradientCoordinate) {
p->maximumCoordinateInGradient = gradientCoordinate;
}
}
}
}
// Return a new configuration which is p+q*gradient(p)
struct configuration *
gradientOffset(struct configuration *p, double q)
{
struct functionDefinition *fd = p->functionDefinition;
struct configuration *r;
int i;
r = makeConfiguration(fd);
evaluateGradient(p); BAILR(p);
for (i=fd->dimension-1; i>=0; i--) {
r->coordinate[i] = p->coordinate[i] + q * p->gradient[i];
}
r->parameter = q;
if (fd->constraints != NULL) {
(*fd->constraints)(r);
}
return r;
}
// return value, unless it is outside the range [-max..max], in which
// case return +/- max
static double
signClamp(double value, double max)
{
return (value > max) ? max : ((value < -max) ? -max : value);
}
// Given a configuration p, find three configurations (a, b, c) such
// that f(b) < f(a) and f(b) < f(c), where a, b, and c are colinear in
// configuration space, with b between a and c. This assures that a
// local minimum exists between a and c.
//
// If the function is monotonic to parameterLimit, we could exit with
// b and c having the same parameter value (but being distinct
// configuration objects). It looks like this won't confuse brent(),
// but it would be nice to be sure...
static void
bracketMinimum(struct configuration **ap,
struct configuration **bp,
struct configuration **cp,
struct configuration *p)
{
struct configuration *a = NULL;
struct configuration *b = NULL;
struct configuration *c = NULL;
struct configuration *u = NULL;
double nx;
double r;
double q;
double denom;
double ulimit;
double parameterLimit;
Enter(p);
SetConfiguration(&a, p);
a->parameter = 0.0;
evaluateGradient(p); // this lets (*dfunc)() set initial_parameter_guess
BAIL();
parameterLimit = fabs(p->functionDefinition->parameter_limit);
// when we step GOLDEN_RATIO beyond b, we don't want to exceed parameterLimit.
b = gradientOffset(p,
signClamp(p->functionDefinition->initial_parameter_guess,
parameterLimit / (GOLDEN_RATIO + 1.0)));
BAIL();
if (evaluate(b) > evaluate(a)) {
// swap a and b, so b is downhill of a
u = a;
a = b;
b = u;
u = NULL;
}
nx = b->parameter + GOLDEN_RATIO * (b->parameter - a->parameter);
c = gradientOffset(p, nx); BAIL();
while (evaluate(b) > evaluate(c) && !Interrupted && !EXCEPTION) {
// u is the extreme point for a parabola passing through a, b, and c:
r = (b->parameter - a->parameter) * (evaluate(b) - evaluate(c));
q = (b->parameter - c->parameter) * (evaluate(b) - evaluate(a));
denom = q - r;
if (denom < 0.0) {
if (denom > -DONT_DIVIDE_BY_ZERO) {
denom = -DONT_DIVIDE_BY_ZERO;
}
} else {
if (denom < DONT_DIVIDE_BY_ZERO) {
denom = DONT_DIVIDE_BY_ZERO;
}
}
nx = b->parameter -
((b->parameter - c->parameter) * q - (b->parameter - a->parameter) * r) /
(2.0 * denom);
nx = signClamp(nx, parameterLimit);
SetConfiguration(&u, NULL);
u = gradientOffset(p, nx); BAIL();
// a, b, and c are in order, ulimit is far past c
ulimit = b->parameter + PARABOLIC_BRACKET_LIMIT * (c->parameter - b->parameter);
ulimit = signClamp(ulimit, parameterLimit);
if ((b->parameter-u->parameter) * (u->parameter-c->parameter) > 0.0) {
// u is between b and c, also f(c) < f(b) and f(b) < f(a)
if (evaluate(u) < evaluate(c)) { // success: (b, u, c) brackets
*ap = b;
*bp = u;
*cp = c;
SetConfiguration(&a, NULL);
Leave(bracketMinimum, p, (p == *ap || p == *bp || p == *cp) ? 2 : 3);
return;
}
if (evaluate(u) > evaluate(b)) { // success: (a, b, u) brackets
*ap = a;
*bp = b;
*cp = u;
SetConfiguration(&c, NULL);
Leave(bracketMinimum, p, (p == *ap || p == *bp || p == *cp) ? 2 : 3);
return;
}
// b, u, c monotonically decrease, u is useless.
// try default golden ration extension for u:
nx = c->parameter + GOLDEN_RATIO * (c->parameter - b->parameter);
nx = signClamp(nx, parameterLimit);
SetConfiguration(&u, NULL);
u = gradientOffset(p, nx);
} else if ((c->parameter-u->parameter) * (u->parameter-ulimit) > 0.0) {
// u is between c and ulimit
if (evaluate(u) < evaluate(c)) {
// we're still going down, keep going
SetConfiguration(&b, c);
SetConfiguration(&c, u);
SetConfiguration(&u, NULL);
nx = c->parameter + GOLDEN_RATIO * (c->parameter - b->parameter);
nx = signClamp(nx, parameterLimit);
u = gradientOffset(p, nx);
}
} else if ((u->parameter-ulimit) * (ulimit-c->parameter) >= 0.0) {
// u is past ulimit, reign it in
nx = ulimit;
SetConfiguration(&u, NULL);
u = gradientOffset(p, nx);
// XXX we did an extra gradientOffset of the old ux that we're
// discarding. would be nice to avoid that.
} else {
// u must be before b
// since (a b c) are monotonic decreasing, u should be a
// maximum, so we reject it.
nx = c->parameter + GOLDEN_RATIO * (c->parameter - b->parameter);
nx = signClamp(nx, parameterLimit);
SetConfiguration(&u, NULL);
u = gradientOffset(p, nx);
}
SetConfiguration(&a, b);
SetConfiguration(&b, c);
SetConfiguration(&c, u);
SetConfiguration(&u, NULL);
}
if (Interrupted) {
SetConfiguration(&a, NULL);
evaluateGradient(p);
BAIL();
parameterLimit = fabs(p->functionDefinition->parameter_limit);
*bp = gradientOffset(p,
signClamp(p->functionDefinition->initial_parameter_guess,
parameterLimit / (GOLDEN_RATIO + 1.0)));
SetConfiguration(&c, NULL);
SetConfiguration(&u, NULL);
Leave(bracketMinimum, p, 0);
return;
}
if (EXCEPTION) {
// We haven't succeeded in bracketing, so we leave the results
// as all NULL's. Caller needs to check for this.
SetConfiguration(&a, NULL);
SetConfiguration(&b, NULL);
SetConfiguration(&c, NULL);
SetConfiguration(&u, NULL);
Leave(bracketMinimum, p, 0);
return;
}
// success: (a, b, c) brackets
*ap = a;
*bp = b;
*cp = c;
SetConfiguration(&u, NULL);
Leave(bracketMinimum, p, (p == *ap || p == *bp || p == *cp) ? 2 : 3);
}
// Brent's method of inverse parabolic interpolation.
// parent is only used to make new configurations along it's gradient line.
// (a, b, c) bracket a minimum. Returns a new configuration within
// tolerance of the actual minimum within the bracketing interval.
static struct configuration *
brent(struct configuration *parent,
struct configuration *initial_a,
struct configuration *initial_b,
struct configuration *initial_c,
double tolerance)
{
struct configuration *a = NULL; // left side of bracketing interval
struct configuration *b = NULL; // right side of bracketing interval
struct configuration *u = NULL; // most recent function evaluation
struct configuration *v = NULL; // previous value of w
struct configuration *w = NULL; // second least function value
struct configuration *x = NULL; // least function value found so far
double d; // how far to move x
double e; // previous value of d
double r;
double q;
double p;
double ux; // parameter value used to construct new point u
double etemp;
double xm; // midpoint between a and b
double tol; // tolerance scaled by x position
double maxp; // maximum coordinate in gradient, multiply parameters by this for tolerance testing
int iteration;
Enter(parent);
SetConfiguration(&x, initial_b);
SetConfiguration(&w, initial_b);
SetConfiguration(&v, initial_b);
// a and b may be swapped, put them in the right order
if (initial_a->parameter > initial_c->parameter) {
SetConfiguration(&a, initial_c);
SetConfiguration(&b, initial_a);
} else {
SetConfiguration(&a, initial_a);
SetConfiguration(&b, initial_c);
}
maxp = parent->maximumCoordinateInGradient;
// At this point, a is the left side of the interval, b is the right
// side. v, w, and x are all our middle point between the ends.
d = 0.0;
e = 0.0;
Leave(brent_beforeLoop, parent, 0);
for (iteration=1; iteration<=LINEAR_ITERATION_LIMIT && !Interrupted && !EXCEPTION; iteration++) {
xm = 0.5 * (a->parameter + b->parameter); // midpoint of bracketing interval
tol = tolerance * fabs(x->parameter) + TOLERANCE_AT_ZERO ;
DPRINT3(D_MINIMIZE, "brent: x: %e xm: %e |x-xm|: %e\n",
x->parameter, xm, fabs(x->parameter - xm));
DPRINT3(D_MINIMIZE, "brent: tol: %e (b-a)/2: %e 2*tol-(b-a)/2: %e\n",
tol, 0.5 * (b->parameter - a->parameter),
2.0 * tol - 0.5 * (b->parameter - a->parameter));
// if (b - a > 4 * tol) then right hand side of following is < 0
if (fabs(x->parameter - xm) <= (tol * 2.0 - 0.5 * (b->parameter - a->parameter))) {
// width of interval (a, b) is less than 4 * tol
// x is close to the center of the interval
// we're done!
SetConfiguration(&a, NULL);
SetConfiguration(&b, NULL);
SetConfiguration(&u, NULL);
SetConfiguration(&v, NULL);
SetConfiguration(&w, NULL);
Leave(brent, parent, (x == initial_b) ? 0 : 1);
DPRINT3(D_MINIMIZE, "leaving brent, parameter %e * %e == %e\n",
x->parameter, maxp, x->parameter * maxp);
return x;
}
if (fabs(e) > tol) {
// v, w, and x are our best points so far, compute the minimum
// of a parabola passing through them.
r = (x->parameter - w->parameter) * (evaluate(x) - evaluate(v)) ;
q = (x->parameter - v->parameter) * (evaluate(x) - evaluate(w)) ;
p = (x->parameter - v->parameter) * q - (x->parameter - w->parameter) * r ;
q = 2.0 * (q - r) ;
if (q > 0.0) {
p = -p ;
} else {
q = -q;
}
// parabolic minimum is at: x->parameter + p / q
// q >= 0
etemp = e;
e = d;
if (fabs(p) >= fabs(0.5 * q * etemp) || // step >= prev_step / 2
p <= q * (a->parameter - x->parameter) || // step goes to the left of a
p >= q * (b->parameter - x->parameter)) // step goes to the right of b
{
// we don't like the parabolic step, try golden mean instead
e = (x->parameter >= xm) ?
(a->parameter - x->parameter) :
(b->parameter - x->parameter) ;
d = (2.0 - GOLDEN_RATIO) * e ;
} else {
d = p / q ;
ux = x->parameter + d ; // this is the pure parabolic minimum
if (ux - a->parameter < tol * 2.0 || b->parameter - ux < tol * 2.0) {
// too close to left or right bound
// step in just a bit towards the middle instead
d = (xm - x->parameter < 0) ? -tol : tol ;
}
}
} else {
// not enough points for parabolic interpolation
// use golden mean instead
e = (x->parameter >= xm) ?
(a->parameter - x->parameter) :
(b->parameter - x->parameter) ;
d = (2.0 - GOLDEN_RATIO) * e ;
}
// u = x + d, but is at least tol different from x
ux = (fabs(d) >= tol) ?
(x->parameter + d) :
(x->parameter + ((d<0) ? -tol : tol)) ;
SetConfiguration(&u, NULL);
u = gradientOffset(parent, ux);
if (evaluate(u) <= evaluate(x)) {
// u is better than x (the best up until now)
// pull the opposite side bound in to x
if (u->parameter >= x->parameter) {
SetConfiguration(&a, x);
} else {
SetConfiguration(&b, x);
}
// ratchet all vars down one step so x is new best
SetConfiguration(&v, w);
SetConfiguration(&w, x);
SetConfiguration(&x, u);
SetConfiguration(&u, NULL);
} else {
// u doesn't beat the current x
// since u is closer to x than the bound
// pull the appropriate bound in to u
if (u->parameter < x->parameter) {
SetConfiguration(&a, u);
} else {
SetConfiguration(&b, u);
}
if (evaluate(u) <= evaluate(w) || u->parameter == w->parameter) {
// u is better than w (the second best until now)
// ratchet v and w down, but leave x alone (still the best)
SetConfiguration(&v, w);
SetConfiguration(&w, u);
} else if (evaluate(u) <= evaluate(v) ||
v->parameter == x->parameter ||
v->parameter == w->parameter)
{
// u is third best, so set v to record that
SetConfiguration(&v, u);
}
}
}
// For either an interrupt or an exception, x should always be the
// best value found so far, so we can safely return it.
if (!Interrupted && !EXCEPTION) {
message(parent->functionDefinition, "reached iteration limit in linearMinimize\n");
}
// too many iterations without getting close enough
SetConfiguration(&a, NULL);
SetConfiguration(&b, NULL);
SetConfiguration(&u, NULL);
SetConfiguration(&v, NULL);
SetConfiguration(&w, NULL);
if (x == initial_b) {
Leave(brent, parent, 0);
} else {
Leave(brent, parent, 1);
}
return x;
}
// Perform a one dimensional minimization starting at configuration p.
// The gradient of the function at p is calculated, and the
// minimization is along the line of that gradient. The resulting
// minimum configuration point is returned.
static struct configuration *
linearMinimize(struct configuration *p,
double tolerance,
enum linearAlgorithm algorithm)
{
struct configuration *a = NULL;
struct configuration *b = NULL;
struct configuration *c = NULL;
struct configuration *min = NULL;
Enter(p);
bracketMinimum(&a, &b, &c, p);
BAILR(NULL);
if (Interrupted) return b;
NULLPTRR(a, p);
NULLPTRR(b, p);
NULLPTRR(c, p);
if (DEBUG(D_MINIMIZE)) {
message(p->functionDefinition, "bmin: a %e[%e] b %e[%e] c %e[%e]",
evaluate(a), a->parameter,
evaluate(b), b->parameter,
evaluate(c), c->parameter);
}
if (algorithm == LinearBracket && b != p) {
SetConfiguration(&min, b);
} else {
min = brent(p, a, b, c, tolerance);
}
//printf("minimum at parameter value: %e, function value: %e\n", min->parameter, evaluate(min));
SetConfiguration(&a, NULL);
SetConfiguration(&b, NULL);
SetConfiguration(&c, NULL);
if (DEBUG(D_MINIMIZE) && min == p) {
message(p->functionDefinition, "linearMinimize returning argument");
}
Leave(linearMinimize, p, (min == p) ? 0 : 1);
return min;
}
int
defaultTermination(struct functionDefinition *fd,
struct configuration *previous,
struct configuration *current)
{
double fp = evaluate(previous);
double fq = evaluate(current);
double tolerance = fd->tolerance;
DPRINT2(D_MINIMIZE, "delta %e, tol*avgVal %e\n",
fabs(fq-fp), tolerance * (fabs(fq)+fabs(fp)+EPSILON)/2.0);
if (2.0 * fabs(fq-fp) <= tolerance * (fabs(fq)+fabs(fp)+EPSILON)) {
if (DEBUG(D_MINIMIZE)) {
message(fd,
"fp: %e fq: %e || delta %e <= tolerance %e * averageValue %e",
fp, fq,
fabs(fq-fp), tolerance, (fabs(fq)+fabs(fp)+EPSILON)/2.0);
}
return 1;
}
return 0;
}
// Starting with an initial configuration p, find the configuration
// which minimizes the value of the function (as defined by fd). The
// number of iterations used is returned in iteration.
static struct configuration *
minimize_one_tolerance(struct configuration *initial_p,
int *iteration,
int iterationLimit)
{
struct functionDefinition *fd;
double fp;
double dgg;
double gg;
double gamma;
struct configuration *p = NULL;
struct configuration *q = NULL;
int i;
Enter(initial_p);
NULLPTRR(initial_p, NULL);
NULLPTRR(iteration, initial_p);
fd = initial_p->functionDefinition;
NULLPTRR(fd, initial_p);
if (fd->termination == NULL) {
fd->termination = defaultTermination;
}
SetConfiguration(&p, initial_p);
fp = evaluate(p);
BAILR(initial_p);
for ((*iteration)=0; (*iteration) < iterationLimit && !Interrupted; (*iteration)++) {
SetConfiguration(&q, NULL);
q = linearMinimize(p, fd->tolerance, fd->linear_algorithm);
// If linearMinimize made some progress, but threw an
// exception, then we want the best result, which is q. If it
// threw an exception and returned NULL, the best we can do
// at this point is p. Beyond this point, we can bail with q.
BAILR(q == NULL ? p : q);
if ((fd->termination)(fd, p, q)) {
SetConfiguration(&p, NULL);
Leave(minimize_one_tolerance, initial_p, (q == initial_p) ? 0 :1);
return q;
}
evaluateGradient(p); // should have been evaluated by linearMinimize already
BAILR(q);
evaluateGradient(q);
BAILR(q);
if (fd->algorithm != SteepestDescent) {
dgg = gg = 0.0;
if (fd->algorithm == PolakRibiereConjugateGradient) {
for (i=fd->dimension-1; i>=0; i--) {
gg += p->gradient[i] * p->gradient[i];
// following line implements Polak-Ribiere
dgg += (q->gradient[i] + p->gradient[i]) * q->gradient[i] ;
}
} else { // fd->algorithm == FletcherReevesConjugateGradient
// NOTE: Polak-Ribiere may handle non-quadratic minima better
// than Fletcher-Reeves
for (i=fd->dimension-1; i>=0; i--) {
gg += p->gradient[i] * p->gradient[i];
// following line implements Fletcher-Reeves
dgg += q->gradient[i] * q->gradient[i] ;
}
}
if (gg == 0.0) {
// rather than divide by zero below, note that the gradient
// is zero, so we must be done.
DPRINT(D_MINIMIZE, "gg==0 in minimize_one_tolerance\n");
SetConfiguration(&p, NULL);
Leave(minimize_one_tolerance, initial_p, 1);
return q;
}
gamma = dgg / gg;
DPRINT3(D_MINIMIZE, "gamma[%e] = %e / %e\n", gamma, dgg, gg);
for (i=fd->dimension-1; i>=0; i--) {
q->gradient[i] += gamma * p->gradient[i];
}
}
fp = evaluate(q); // previous value of function
BAILR(q);
SetConfiguration(&p, q);
}
if (Interrupted) {
message(fd, "minimization interrupted");
} else {
message(fd, "reached iteration limit");
}
SetConfiguration(&p, NULL);
Leave(minimize_one_tolerance, initial_p, 1);
return q;
}
// Starting with an initial configuration p, find the configuration
// which minimizes the value of the function (as defined by fd). The
// number of iterations used is returned in iteration.
struct configuration *
minimize(struct configuration *initial_p,
int *iteration,
int iterationLimit)
{
struct functionDefinition *fd;
struct configuration *final = NULL;
Enter(initial_p);
NULLPTRR(initial_p, NULL);
fd = initial_p->functionDefinition;
NULLPTRR(fd, initial_p);
NULLPTRR(iteration, initial_p);
final = minimize_one_tolerance(initial_p,
iteration,
iterationLimit);
Leave(minimize, initial_p, (final == initial_p) ? 0 :1);
// final probably shouldn't ever be NULL, but it's conceivable in
// some exception processing cases. If that happens, then we
// haven't made any progress, so return initial_p.
return final == NULL ? initial_p : final;
}
#ifdef TEST
static double
test(double x, double y)
{
double rsquared = x*x + y*y;
//return cos(sqrt(rsquared) + atan2(x, y) + 3.1415926) * exp(-rsquared/700);
double r = sqrt(rsquared);
double theta = atan2(x, y);
double phi = r + theta + 3.1415926;
double expterm = exp(-rsquared/700);
double costerm = cos(phi);
double result = costerm * expterm;
return result;
}
static void
testFunction(struct configuration *p)
{
p->functionValue = test(p->coordinate[0], p->coordinate[1]);
//printf("%f %f\n", p->coordinate[0], p->coordinate[1]);
}
#define DELTA 1e-5
static void
testGradient(struct configuration *p)
{
double x = p->coordinate[0];
double y = p->coordinate[1];
printf("%f %f\n", p->coordinate[0], p->coordinate[1]);
p->gradient[0] = (test(x, y) - test(x+DELTA, y)) / DELTA;
p->gradient[1] = (test(x, y) - test(x, y+DELTA)) / DELTA;
}
static void
testMinimize()
{
struct functionDefinition fd;
struct configuration *initial = NULL;
struct configuration *final = NULL;
int iteration;
initializeFunctionDefinition(&fd, testFunction, 2, 0);
fd.func = testFunction;
fd.coarse_tolerance = 1e-5;
fd.fine_tolerance = 1e-8;
initial = makeConfiguration(&fd);
initial->coordinate[0] = 6.0;
initial->coordinate[1] = -5.0;
final = minimize(initial, &iteration, 400);
fprintf(stderr, "final minimum at (%f %f): %f\n",
final->coordinate[0],
final->coordinate[1],
evaluate(final));
SetConfiguration(&initial, NULL);
SetConfiguration(&final, NULL);
fprintf(stderr, "after %d iterations, %d function evals, %d gradient evals\n",
iteration,
fd.functionEvaluationCount,
fd.gradientEvaluationCount);
fprintf(stderr, "allocation: %d, free: %d, remaining: %d, maximum: %d\n",
fd->allocationCount,
fd->freeCount,
fd->allocationCount - fd->freeCount,
fd->maxAllocation);
}
int
main(int argc, char **argv)
{
testMinimize();
exit(0);
}
#endif
/*
* Local Variables:
* c-basic-offset: 4
* tab-width: 8
* End:
*/
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