418 lines
12 KiB
C++
418 lines
12 KiB
C++
/**
|
|
* @file vcs_root1d.cpp
|
|
* Code for a one dimensional root finder program.
|
|
*/
|
|
/*
|
|
* Copyright (2006) Sandia Corporation. Under the terms of
|
|
* Contract DE-AC04-94AL85000 with Sandia Corporation, the
|
|
* U.S. Government retains certain rights in this software.
|
|
*/
|
|
|
|
#include "cantera/equil/vcs_internal.h"
|
|
|
|
#include <cstdio>
|
|
|
|
namespace VCSnonideal
|
|
{
|
|
|
|
#define TOL_CONV 1.0E-5
|
|
|
|
#ifdef DEBUG_MODE
|
|
static void print_funcEval(FILE* fp, double xval, double fval, int its)
|
|
{
|
|
fprintf(fp,"\n");
|
|
fprintf(fp,"...............................................................\n");
|
|
fprintf(fp,".................. vcs_root1d Function Evaluation .............\n");
|
|
fprintf(fp,".................. iteration = %5d ........................\n", its);
|
|
fprintf(fp,".................. value = %12.5g ......................\n", xval);
|
|
fprintf(fp,".................. funct = %12.5g ......................\n", fval);
|
|
fprintf(fp,"...............................................................\n");
|
|
fprintf(fp,"\n");
|
|
}
|
|
#endif
|
|
|
|
int vcsUtil_root1d(double xmin, double xmax, size_t itmax,
|
|
VCS_FUNC_PTR func, void* fptrPassthrough,
|
|
double FuncTargVal, int varID,
|
|
double* xbest, int printLvl)
|
|
{
|
|
static int callNum = 0;
|
|
const char* stre = "vcs_root1d ERROR: ";
|
|
const char* strw = "vcs_root1d WARNING: ";
|
|
bool converged = false;
|
|
int err = 0;
|
|
#ifdef DEBUG_MODE
|
|
char fileName[80];
|
|
FILE* fp = 0;
|
|
#endif
|
|
double x1, x2, xnew, f1, f2, fnew, slope;
|
|
size_t its = 0;
|
|
int posStraddle = 0;
|
|
int retn = VCS_SUCCESS;
|
|
bool foundPosF = false;
|
|
bool foundNegF = false;
|
|
bool foundStraddle = false;
|
|
double xPosF = 0.0;
|
|
double xNegF = 0.0;
|
|
double fnorm; /* A valid norm for the making the function value
|
|
* dimensionless */
|
|
double c[9], f[3], xn1, xn2, x0 = 0.0, f0 = 0.0, root, theta, xquad;
|
|
|
|
callNum++;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
sprintf(fileName, "rootfd_%d.log", callNum);
|
|
fp = fopen(fileName, "w");
|
|
fprintf(fp, " Iter TP_its xval Func_val | Reasoning\n");
|
|
fprintf(fp, "-----------------------------------------------------"
|
|
"-------------------------------\n");
|
|
}
|
|
#else
|
|
if (printLvl >= 3) {
|
|
plogf("WARNING: vcsUtil_root1d: printlvl >= 3, but debug mode not turned on\n");
|
|
}
|
|
#endif
|
|
if (xmax <= xmin) {
|
|
plogf("%sxmin and xmax are bad: %g %g\n", stre, xmin, xmax);
|
|
return VCS_PUB_BAD;
|
|
}
|
|
x1 = *xbest;
|
|
if (x1 < xmin || x1 > xmax) {
|
|
x1 = (xmin + xmax) / 2.0;
|
|
}
|
|
f1 = func(x1, FuncTargVal, varID, fptrPassthrough, &err);
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
print_funcEval(fp, x1, f1, its);
|
|
fprintf(fp, "%-5d %-5d %-15.5E %-15.5E\n", -2, 0, x1, f1);
|
|
}
|
|
#endif
|
|
if (f1 == 0.0) {
|
|
*xbest = x1;
|
|
return VCS_SUCCESS;
|
|
} else if (f1 > 0.0) {
|
|
foundPosF = true;
|
|
xPosF = x1;
|
|
} else {
|
|
foundNegF = true;
|
|
xNegF = x1;
|
|
}
|
|
x2 = x1 * 1.1;
|
|
if (x2 > xmax) {
|
|
x2 = x1 - (xmax - xmin) / 100.;
|
|
}
|
|
f2 = func(x2, FuncTargVal, varID, fptrPassthrough, &err);
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
print_funcEval(fp, x2, f2, its);
|
|
fprintf(fp, "%-5d %-5d %-15.5E %-15.5E", -1, 0, x2, f2);
|
|
}
|
|
#endif
|
|
|
|
if (FuncTargVal != 0.0) {
|
|
fnorm = fabs(FuncTargVal) + 1.0E-13;
|
|
} else {
|
|
fnorm = 0.5*(fabs(f1) + fabs(f2)) + fabs(FuncTargVal);
|
|
}
|
|
|
|
if (f2 == 0.0) {
|
|
return retn;
|
|
} else if (f2 > 0.0) {
|
|
if (!foundPosF) {
|
|
foundPosF = true;
|
|
xPosF = x2;
|
|
}
|
|
} else {
|
|
if (!foundNegF) {
|
|
foundNegF = true;
|
|
xNegF = x2;
|
|
}
|
|
}
|
|
foundStraddle = foundPosF && foundNegF;
|
|
if (foundStraddle) {
|
|
if (xPosF > xNegF) {
|
|
posStraddle = true;
|
|
} else {
|
|
posStraddle = false;
|
|
}
|
|
}
|
|
|
|
do {
|
|
/*
|
|
* Find an estimate of the next point to try based on
|
|
* a linear approximation.
|
|
*/
|
|
slope = (f2 - f1) / (x2 - x1);
|
|
if (slope == 0.0) {
|
|
plogf("%s functions evals produced the same result, %g, at %g and %g\n",
|
|
strw, f2, x1, x2);
|
|
xnew = 2*x2 - x1 + 1.0E-3;
|
|
} else {
|
|
xnew = x2 - f2 / slope;
|
|
}
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | xlin = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
|
|
/*
|
|
* Do a quadratic fit -> Note this algorithm seems
|
|
* to work OK. The quadratic approximation doesn't kick in until
|
|
* the end of the run, when it becomes reliable.
|
|
*/
|
|
if (its > 0) {
|
|
c[0] = 1.;
|
|
c[1] = 1.;
|
|
c[2] = 1.;
|
|
c[3] = x0;
|
|
c[4] = x1;
|
|
c[5] = x2;
|
|
c[6] = SQUARE(x0);
|
|
c[7] = SQUARE(x1);
|
|
c[8] = SQUARE(x2);
|
|
f[0] = - f0;
|
|
f[1] = - f1;
|
|
f[2] = - f2;
|
|
retn = vcsUtil_mlequ(c, 3, 3, f, 1);
|
|
if (retn == 1) {
|
|
goto QUAD_BAIL;
|
|
}
|
|
root = f[1]* f[1] - 4.0 * f[0] * f[2];
|
|
if (root >= 0.0) {
|
|
xn1 = (- f[1] + sqrt(root)) / (2.0 * f[2]);
|
|
xn2 = (- f[1] - sqrt(root)) / (2.0 * f[2]);
|
|
if (fabs(xn2 - x2) < fabs(xn1 - x2) && xn2 > 0.0) {
|
|
xquad = xn2;
|
|
} else {
|
|
xquad = xn1;
|
|
}
|
|
theta = fabs(xquad - xnew) / fabs(xnew - x2);
|
|
theta = std::min(1.0, theta);
|
|
xnew = theta * xnew + (1.0 - theta) * xquad;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
if (theta != 1.0) {
|
|
fprintf(fp, " | xquad = %-9.4g", xnew);
|
|
}
|
|
}
|
|
#endif
|
|
} else {
|
|
/*
|
|
* Pick out situations where the convergence may be
|
|
* accelerated.
|
|
*/
|
|
if ((DSIGN(xnew - x2) == DSIGN(x2 - x1)) &&
|
|
(DSIGN(x2 - x1) == DSIGN(x1 - x0))) {
|
|
xnew += xnew - x2;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | xquada = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
}
|
|
QUAD_BAIL:
|
|
;
|
|
|
|
|
|
/*
|
|
*
|
|
* Put heuristic bounds on the step jump
|
|
*/
|
|
if ((xnew > x1 && xnew < x2) || (xnew < x1 && xnew > x2)) {
|
|
/*
|
|
*
|
|
* If we are doing a jump in between two points, make sure
|
|
* the new trial is between 10% and 90% of the distance
|
|
* between the old points.
|
|
*/
|
|
slope = fabs(x2 - x1) / 10.;
|
|
if (fabs(xnew - x1) < slope) {
|
|
xnew = x1 + DSIGN(xnew-x1) * slope;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | x10%% = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
}
|
|
if (fabs(xnew - x2) < slope) {
|
|
xnew = x2 + DSIGN(xnew-x2) * slope;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | x10%% = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
}
|
|
} else {
|
|
/*
|
|
* If we are venturing into new ground, only allow the step jump
|
|
* to increase by 100% at each iteration
|
|
*/
|
|
slope = 2.0 * fabs(x2 - x1);
|
|
if (fabs(slope) < fabs(xnew - x2)) {
|
|
xnew = x2 + DSIGN(xnew-x2) * slope;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | xlimitsize = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
|
|
|
|
if (xnew > xmax) {
|
|
xnew = x2 + (xmax - x2) / 2.0;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | xlimitmax = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
}
|
|
if (xnew < xmin) {
|
|
xnew = x2 + (x2 - xmin) / 2.0;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | xlimitmin = %-9.4g", xnew);
|
|
}
|
|
#endif
|
|
}
|
|
if (foundStraddle) {
|
|
#ifdef DEBUG_MODE
|
|
slope = xnew;
|
|
#endif
|
|
if (posStraddle) {
|
|
if (f2 > 0.0) {
|
|
if (xnew > x2) {
|
|
xnew = (xNegF + x2)/2;
|
|
}
|
|
if (xnew < xNegF) {
|
|
xnew = (xNegF + x2)/2;
|
|
}
|
|
} else {
|
|
if (xnew < x2) {
|
|
xnew = (xPosF + x2)/2;
|
|
}
|
|
if (xnew > xPosF) {
|
|
xnew = (xPosF + x2)/2;
|
|
}
|
|
}
|
|
} else {
|
|
if (f2 > 0.0) {
|
|
if (xnew < x2) {
|
|
xnew = (xNegF + x2)/2;
|
|
}
|
|
if (xnew > xNegF) {
|
|
xnew = (xNegF + x2)/2;
|
|
}
|
|
} else {
|
|
if (xnew > x2) {
|
|
xnew = (xPosF + x2)/2;
|
|
}
|
|
if (xnew < xPosF) {
|
|
xnew = (xPosF + x2)/2;
|
|
}
|
|
}
|
|
}
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
if (slope != xnew) {
|
|
fprintf(fp, " | xstraddle = %-9.4g", xnew);
|
|
}
|
|
}
|
|
#endif
|
|
}
|
|
|
|
fnew = func(xnew, FuncTargVal, varID, fptrPassthrough, &err);
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp,"\n");
|
|
print_funcEval(fp, xnew, fnew, its);
|
|
fprintf(fp, "%-5d %-5d %-15.5E %-15.5E", its, 0, xnew, fnew);
|
|
}
|
|
#endif
|
|
|
|
if (foundStraddle) {
|
|
if (posStraddle) {
|
|
if (fnew > 0.0) {
|
|
if (xnew < xPosF) {
|
|
xPosF = xnew;
|
|
}
|
|
} else {
|
|
if (xnew > xNegF) {
|
|
xNegF = xnew;
|
|
}
|
|
}
|
|
} else {
|
|
if (fnew > 0.0) {
|
|
if (xnew > xPosF) {
|
|
xPosF = xnew;
|
|
}
|
|
} else {
|
|
if (xnew < xNegF) {
|
|
xNegF = xnew;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (! foundStraddle) {
|
|
if (fnew > 0.0) {
|
|
if (!foundPosF) {
|
|
foundPosF = true;
|
|
xPosF = xnew;
|
|
foundStraddle = true;
|
|
posStraddle = (xPosF > xNegF);
|
|
}
|
|
} else {
|
|
if (!foundNegF) {
|
|
foundNegF = true;
|
|
xNegF = xnew;
|
|
foundStraddle = true;
|
|
posStraddle = (xPosF > xNegF);
|
|
}
|
|
}
|
|
}
|
|
|
|
x0 = x1;
|
|
f0 = f1;
|
|
x1 = x2;
|
|
f1 = f2;
|
|
x2 = xnew;
|
|
f2 = fnew;
|
|
if (fabs(fnew / fnorm) < 1.0E-5) {
|
|
converged = true;
|
|
}
|
|
its++;
|
|
} while (! converged && its < itmax);
|
|
if (converged) {
|
|
if (printLvl >= 1) {
|
|
plogf("vcs_root1d success: convergence achieved\n");
|
|
}
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, " | vcs_root1d success in %d its, fnorm = %g\n", its, fnorm);
|
|
}
|
|
#endif
|
|
} else {
|
|
retn = VCS_FAILED_CONVERGENCE;
|
|
if (printLvl >= 1) {
|
|
plogf("vcs_root1d ERROR: maximum iterations exceeded without convergence\n");
|
|
}
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fprintf(fp, "\nvcs_root1d failure in %lu its\n", its);
|
|
}
|
|
#endif
|
|
}
|
|
*xbest = x2;
|
|
#ifdef DEBUG_MODE
|
|
if (printLvl >= 3) {
|
|
fclose(fp);
|
|
}
|
|
#endif
|
|
return retn;
|
|
}
|
|
|
|
}
|