/*! \fn calculatingErrors
*
* function calculates the errors
*/
void calculatingErrors(DATA_NEWTON* solverData, double* delta_x, double* delta_x_scaled, double* delta_f, double* error_f,
double* scaledError_f, int* n, double* x, double* fvec)
{
int i=0;
double scaling_factor;
/* delta_x = || x_new-x_old || */
for (i=0; i<*n; i++)
solverData->delta_x_vec[i] = x[i]-solverData->x_new[i];
*delta_x = enorm_(n,solverData->delta_x_vec);
scaling_factor = enorm_(n,x);
if (scaling_factor > 1)
*delta_x_scaled = *delta_x * 1./ scaling_factor;
else
*delta_x_scaled = *delta_x;
/* delta_f = || f_old - f_new || */
for (i=0; i<*n; i++)
solverData->delta_f[i] = solverData->f_old[i]-fvec[i];
*delta_f=enorm_(n, solverData->delta_f);
*error_f = enorm_(n,fvec);
/* scaling residual vector */
scaling_residual_vector(solverData);
for (i=0; i<*n; i++)
solverData->fvecScaled[i]=fvec[i]/solverData->resScaling[i];
*scaledError_f = enorm_(n,solverData->fvecScaled);
}
/*! \fn damping_heuristic
*
* first damping heuristic:
* x_increment will be halved until the Euclidean norm of the residual function
* is smaller than the Euclidean norm of the current point
*
* treshold for damping = 0.01
* compiler flag: -newton = damped
*/
void damping_heuristic(double* x, int(*f)(int*, double*, double*, void*, int),
double current_fvec_enorm, int* n, double* fvec, double* lambda, int* k, DATA_NEWTON* solverData, void* userdata)
{
int i,j=0;
double enorm_new, treshold = 1e-2;
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_new=enorm_(n,fvec);
if (enorm_new >= current_fvec_enorm)
infoStreamPrint(LOG_NLS_V, 1, "Start Damping: enorm_new : %e; current_fvec_enorm: %e ", enorm_new, current_fvec_enorm);
while (enorm_new >= current_fvec_enorm)
{
j++;
*lambda*=0.5;
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-*lambda*solverData->x_increment[i];
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_new=enorm_(n,fvec);
if (*lambda <= treshold)
{
warningStreamPrint(LOG_NLS_V, 0, "Warning: lambda reached a threshold.");
/* if damping is without success, trying full newton step; after 5 full newton steps try a very little step */
if (*k >= 5)
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-*lambda*solverData->x_increment[i];
else
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-solverData->x_increment[i];
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
(*k)++;
break;
}
}
*lambda = 1;
messageClose(LOG_NLS_V);
}
int main()
{
int m, n, ldfjac, info, lwa, ipvt[3], one=1;
double tol, fnorm;
double x[3], fvec[15], fjac[9], wa[30];
m = 15;
n = 3;
/* the following starting values provide a rough fit. */
x[0] = 1.;
x[1] = 1.;
x[2] = 1.;
ldfjac = 3;
lwa = 30;
/* set tol to the square root of the machine precision.
unless high precision solutions are required,
this is the recommended setting. */
tol = sqrt(dpmpar_(&one));
lmstr1_(&fcn, &m, &n,
x, fvec, fjac, &ldfjac,
&tol, &info, ipvt, wa, &lwa);
fnorm = enorm_(&m, fvec);
printf(" FINAL L2 NORM OF THE RESIDUALS%15.7g\n\n", fnorm);
printf(" EXIT PARAMETER %10i\n\n", info);
printf(" FINAL APPROXIMATE SOLUTION\n\n%15.7g%15.7g%15.7g\n",
x[0], x[1], x[2]);
return 0;
}
/* ********** */
/* Main program */ int MAIN__(void)
{
/* Initialized data */
static integer nread = 5;
static integer nwrite = 6;
static doublereal one = 1.;
static doublereal ten = 10.;
/* Format strings */
static char fmt_50[] = "(3i5)";
static char fmt_60[] = "(////5x,\002 PROBLEM\002,i5,5x,\002 DIMENSION"
"\002,i5,5x//)";
static char fmt_70[] = "(5x,\002 INITIAL L2 NORM OF THE RESIDUALS\002,d1"
"5.7//5x,\002 FINAL L2 NORM OF THE RESIDUALS \002,d15.7//5x,\002"
" NUMBER OF FUNCTION EVALUATIONS \002,i10//5x,\002 EXIT PARAMETER"
"\002,18x,i10//5x,\002 FINAL APPROXIMATE SOLUTION\002//(5x,5d15.7"
"))";
static char fmt_80[] = "(\0021SUMMARY OF \002,i3,\002 CALLS TO HYBRD1"
"\002/)";
static char fmt_90[] = "(\002 NPROB N NFEV INFO FINAL L2 NORM\002"
"/)";
static char fmt_100[] = "(i4,i6,i7,i6,1x,d15.7)";
/* System generated locals */
integer i__1, i__2;
/* Builtin functions */
double sqrt(doublereal);
integer s_rsfe(cilist *), do_fio(integer *, char *, ftnlen), e_rsfe(void),
s_wsfe(cilist *), e_wsfe(void);
/* Subroutine */ int s_stop(char *, ftnlen);
/* Local variables */
static integer i__, k, n;
static doublereal x[40];
static integer ic, na[60], nf[60];
static doublereal wa[2660];
static integer np[60], nx[60];
extern /* Subroutine */ int fcn_();
static doublereal fnm[60];
static integer lwa;
static doublereal tol, fvec[40];
static integer info;
extern doublereal enorm_(integer *, doublereal *);
extern /* Subroutine */ int hybrd1_(U_fp, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *);
static doublereal fnorm1, fnorm2;
extern /* Subroutine */ int vecfcn_(integer *, doublereal *, doublereal *,
integer *);
static doublereal factor;
extern doublereal dpmpar_(integer *);
static integer ntries;
extern /* Subroutine */ int initpt_(integer *, doublereal *, integer *,
doublereal *);
/* Fortran I/O blocks */
static cilist io___8 = { 0, 0, 0, fmt_50, 0 };
static cilist io___16 = { 0, 0, 0, fmt_60, 0 };
static cilist io___25 = { 0, 0, 0, fmt_70, 0 };
static cilist io___27 = { 0, 0, 0, fmt_80, 0 };
static cilist io___28 = { 0, 0, 0, fmt_90, 0 };
static cilist io___29 = { 0, 0, 0, fmt_100, 0 };
/* LOGICAL INPUT UNIT IS ASSUMED TO BE NUMBER 5. */
/* LOGICAL OUTPUT UNIT IS ASSUMED TO BE NUMBER 6. */
tol = sqrt(dpmpar_(&c__1));
lwa = 2660;
ic = 0;
L10:
io___8.ciunit = nread;
s_rsfe(&io___8);
do_fio(&c__1, (char *)&refnum_1.nprob, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&ntries, (ftnlen)sizeof(integer));
e_rsfe();
if (refnum_1.nprob <= 0) {
goto L30;
}
factor = one;
i__1 = ntries;
for (k = 1; k <= i__1; ++k) {
++ic;
initpt_(&n, x, &refnum_1.nprob, &factor);
vecfcn_(&n, x, fvec, &refnum_1.nprob);
fnorm1 = enorm_(&n, fvec);
io___16.ciunit = nwrite;
s_wsfe(&io___16);
do_fio(&c__1, (char *)&refnum_1.nprob, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
e_wsfe();
refnum_1.nfev = 0;
hybrd1_((U_fp)fcn_, &n, x, fvec, &tol, &info, wa, &lwa);
fnorm2 = enorm_(&n, fvec);
np[ic - 1] = refnum_1.nprob;
na[ic - 1] = n;
nf[ic - 1] = refnum_1.nfev;
nx[ic - 1] = info;
fnm[ic - 1] = fnorm2;
io___25.ciunit = nwrite;
s_wsfe(&io___25);
do_fio(&c__1, (char *)&fnorm1, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&fnorm2, (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&refnum_1.nfev, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&info, (ftnlen)sizeof(integer));
i__2 = n;
for (i__ = 1; i__ <= i__2; ++i__) {
do_fio(&c__1, (char *)&x[i__ - 1], (ftnlen)sizeof(doublereal));
}
e_wsfe();
factor = ten * factor;
/* L20: */
}
goto L10;
L30:
io___27.ciunit = nwrite;
s_wsfe(&io___27);
do_fio(&c__1, (char *)&ic, (ftnlen)sizeof(integer));
e_wsfe();
io___28.ciunit = nwrite;
s_wsfe(&io___28);
e_wsfe();
i__1 = ic;
for (i__ = 1; i__ <= i__1; ++i__) {
io___29.ciunit = nwrite;
s_wsfe(&io___29);
do_fio(&c__1, (char *)&np[i__ - 1], (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&na[i__ - 1], (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nf[i__ - 1], (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nx[i__ - 1], (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&fnm[i__ - 1], (ftnlen)sizeof(doublereal));
e_wsfe();
/* L40: */
}
s_stop("", (ftnlen)0);
/* LAST CARD OF DRIVER. */
return 0;
} /* MAIN__ */
/*! \fn solve non-linear system with hybrd method
*
* \param [in] [data]
* [sysNumber] index of the corresponing non-linear system
*
* \author wbraun
*/
int solveHybrd(DATA *data, int sysNumber)
{
NONLINEAR_SYSTEM_DATA* systemData = &(data->simulationInfo.nonlinearSystemData[sysNumber]);
DATA_HYBRD* solverData = (DATA_HYBRD*)systemData->solverData;
/*
* We are given the number of the non-linear system.
* We want to look it up among all equations.
*/
int eqSystemNumber = systemData->equationIndex;
int i, j;
integer iflag = 1;
double xerror, xerror_scaled;
int success = 0;
double local_tol = 1e-12;
double initial_factor = solverData->factor;
int nfunc_evals = 0;
int continuous = 1;
int nonContinuousCase = 0;
int giveUp = 0;
int retries = 0;
int retries2 = 0;
int retries3 = 0;
int assertCalled = 0;
int assertRetries = 0;
int assertMessage = 0;
static state mem_state;
modelica_boolean* relationsPreBackup;
relationsPreBackup = (modelica_boolean*) malloc(data->modelData.nRelations*sizeof(modelica_boolean));
/* debug output */
if(ACTIVE_STREAM(LOG_NLS))
{
INFO2(LOG_NLS, "start solving non-linear system >>%s<< at time %g",
modelInfoXmlGetEquation(&data->modelData.modelDataXml, eqSystemNumber).name,
data->localData[0]->timeValue);
INDENT(LOG_NLS);
for(i=0; i<solverData->n; i++)
{
INFO2(LOG_NLS, "x[%d] = %f", i, systemData->nlsx[i]);
INDENT(LOG_NLS);
INFO3(LOG_NLS, "scaling = %f\nold = %f\nextrapolated = %f",
systemData->nominal[i], systemData->nlsxOld[i], systemData->nlsxExtrapolation[i]);
RELEASE(LOG_NLS);
}
RELEASE(LOG_NLS);
}
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i=0; i<solverData->n; i++)
solverData->xScalefactors[i] = fmax(fabs(solverData->x[i]), systemData->nominal[i]);
/* evaluate with discontinuities */
{
int scaling = solverData->useXScaling;
if(scaling)
solverData->useXScaling = 0;
mem_state = get_memory_state();
/* try */
if(!setjmp(nonlinearJmpbuf))
{
wrapper_fvec_hybrj(&solverData->n, solverData->x, solverData->fvec, solverData->fjac, &solverData->ldfjac, &iflag, data, sysNumber);
restore_memory_state(mem_state);
} else { /* catch */
restore_memory_state(mem_state);
WARNING(LOG_STDOUT, "Non-Linear Solver try to handle a problem with a called assert.");
}
if(scaling) {
solverData->useXScaling = 1;
}
}
/* start solving loop */
while(!giveUp && !success)
{
for(i=0; i<solverData->n; i++)
solverData->xScalefactors[i] = fmax(fabs(solverData->x[i]), systemData->nominal[i]);
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V)) {
printVector(solverData->xScalefactors, &(solverData->n), LOG_NLS_V, "scaling factors x vector");
printVector(solverData->x, &(solverData->n), LOG_NLS_V, "Iteration variable values");
}
/* Scaling x vector */
if(solverData->useXScaling) {
for(i=0; i<solverData->n; i++) {
solverData->x[i] = (1.0/solverData->xScalefactors[i]) * solverData->x[i];
}
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V))
{
printVector(solverData->x, &solverData->n, LOG_NLS_V, "Iteration variable values (scaled)");
}
/* set residual function continuous
*/
if(continuous) {
((DATA*)data)->simulationInfo.solveContinuous = 1;
} else {
((DATA*)data)->simulationInfo.solveContinuous = 0;
}
giveUp = 1;
mem_state = get_memory_state();
/* try */
if(!setjmp(nonlinearJmpbuf))
{
_omc_hybrj_(wrapper_fvec_hybrj, &solverData->n, solverData->x,
solverData->fvec, solverData->fjac, &solverData->ldfjac, &solverData->xtol,
&solverData->maxfev, solverData->diag, &solverData->mode,
&solverData->factor, &solverData->nprint, &solverData->info,
&solverData->nfev, &solverData->njev, solverData->r__,
&solverData->lr, solverData->qtf, solverData->wa1,
solverData->wa2, solverData->wa3, solverData->wa4, data, sysNumber);
restore_memory_state(mem_state);
if(assertCalled)
{
INFO(LOG_NLS, "After asserts was called, values reached which avoided assert call.");
memcpy(systemData->nlsxOld, solverData->x, solverData->n*(sizeof(double)));
}
assertRetries = 0;
assertCalled = 0;
}
else
{ /* catch */
restore_memory_state(mem_state);
if(!assertMessage)
{
INDENT(LOG_STDOUT);
WARNING(LOG_STDOUT, "While solving non-linear system an assert was called.");
WARNING(LOG_STDOUT, "The non-linear solver tries to solve the problem that could take some time.");
WARNING(LOG_STDOUT, "It could help to provide better start-values for the iteration variables.");
WARNING(LOG_STDOUT, "For more information simulate with -lv LOG_NLS");
RELEASE(LOG_STDOUT);
assertMessage = 1;
}
solverData->info = -1;
xerror_scaled = 1;
xerror = 1;
assertCalled = 1;
}
/* set residual function continuous */
if(continuous)
{
((DATA*)data)->simulationInfo.solveContinuous = 0;
}
else
{
((DATA*)data)->simulationInfo.solveContinuous = 1;
}
/* re-scaling x vector */
if(solverData->useXScaling)
for(i=0; i<solverData->n; i++)
solverData->x[i] = solverData->x[i]*solverData->xScalefactors[i];
/* check for proper inputs */
if(solverData->info == 0) {
printErrorEqSyst(IMPROPER_INPUT, modelInfoXmlGetEquation(&data->modelData.modelDataXml, eqSystemNumber),
data->localData[0]->timeValue);
}
if(solverData->info != -1)
{
/* evaluate with discontinuities */
if(data->simulationInfo.discreteCall){
int scaling = solverData->useXScaling;
if(scaling)
solverData->useXScaling = 0;
((DATA*)data)->simulationInfo.solveContinuous = 0;
mem_state = get_memory_state();
/* try */
if(!setjmp(nonlinearJmpbuf))
{
wrapper_fvec_hybrj(&solverData->n, solverData->x, solverData->fvec, solverData->fjac, &solverData->ldfjac, &iflag, data, sysNumber);
restore_memory_state(mem_state);
} else { /* catch */
restore_memory_state(mem_state);
WARNING(LOG_STDOUT, "Non-Linear Solver try to handle a problem with a called assert.");
solverData->info = -1;
xerror_scaled = 1;
xerror = 1;
assertCalled = 1;
}
if(scaling)
solverData->useXScaling = 1;
storeRelations(data);
}
}
if(solverData->info != -1)
{
/* scaling residual vector */
{
int l=0;
for(i=0; i<solverData->n; i++){
solverData->resScaling[i] = 1e-16;
for(j=0; j<solverData->n; j++){
solverData->resScaling[i] = (fabs(solverData->fjacobian[l]) > solverData->resScaling[i])
? fabs(solverData->fjacobian[l]) : solverData->resScaling[i];
l++;
}
solverData->fvecScaled[i] = solverData->fvec[i] * (1 / solverData->resScaling[i]);
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V))
{
INFO(LOG_NLS_V, "scaling factors for residual vector");
INDENT(LOG_NLS_V);
for(i=0; i<solverData->n; i++)
{
INFO2(LOG_NLS_V, "scaled residual [%d] : %.20e", i, solverData->fvecScaled[i]);
INDENT(LOG_NLS_V);
INFO2(LOG_NLS_V, "scaling factor [%d] : %.20e", i, solverData->resScaling[i]);
RELEASE(LOG_NLS_V);
}
RELEASE(LOG_NLS_V);
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_JAC))
{
char buffer[4096];
INFO2(LOG_NLS_JAC, "jacobian matrix [%dx%d]", (int)solverData->n, (int)solverData->n);
INDENT(LOG_NLS_JAC);
for(i=0; i<solverData->n; i++)
{
buffer[0] = 0;
for(j=0; j<solverData->n; j++)
sprintf(buffer, "%s%10g ", buffer, solverData->fjacobian[i*solverData->n+j]);
INFO1(LOG_NLS_JAC, "%s", buffer);
}
RELEASE(LOG_NLS_JAC);
}
/* check for error */
xerror_scaled = enorm_(&solverData->n, solverData->fvecScaled);
xerror = enorm_(&solverData->n, solverData->fvec);
}
}
/* reset non-contunuousCase */
if(nonContinuousCase && xerror > local_tol && xerror_scaled > local_tol)
{
memcpy(data->simulationInfo.relationsPre, relationsPreBackup, sizeof(modelica_boolean)*data->modelData.nRelations);
nonContinuousCase = 0;
}
if(solverData->info < 4 && xerror > local_tol && xerror_scaled > local_tol)
solverData->info = 4;
/* solution found */
if(solverData->info == 1 || xerror <= local_tol || xerror_scaled <= local_tol)
{
int scaling;
success = 1;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS))
{
INFO(LOG_NLS, "system solved");
INDENT(LOG_NLS);
INFO2(LOG_NLS, "%d retries\n%d restarts", retries, retries2+retries3);
RELEASE(LOG_NLS);
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS);
}
scaling = solverData->useXScaling;
if(scaling)
solverData->useXScaling = 0;
/* take the solution */
memcpy(systemData->nlsx, solverData->x, solverData->n*(sizeof(double)));
mem_state = get_memory_state();
/* try */
if(!setjmp(nonlinearJmpbuf))
{
wrapper_fvec_hybrj(&solverData->n, solverData->x, solverData->fvec, solverData->fjac, &solverData->ldfjac, &iflag, data, sysNumber);
restore_memory_state(mem_state);
}
else
{ /* catch */
restore_memory_state(mem_state);
WARNING(LOG_STDOUT, "Non-Linear Solver try to handle a problem with a called assert.");
solverData->info = 4;
xerror_scaled = 1;
xerror = 1;
assertCalled = 1;
success = 0;
giveUp = 0;
}
if(scaling)
solverData->useXScaling = 1;
}
else if((solverData->info == 4 || solverData->info == 5) && assertRetries < 1+solverData->n && assertCalled)
{
/* case only used, when the Modelica code called an assert
* then, we try to modify start values to avoid the assert call.*/
int i;
memcpy(solverData->x, systemData->nlsxOld, solverData->n*(sizeof(double)));
/* set all zero values to nominal values */
if(assertRetries < 1)
{
for(i=0; i<solverData->n; i++)
{
if(systemData->nlsx[i] == 0)
{
systemData->nlsx[i] = systemData->nominal[i];
solverData->x[i] = systemData->nominal[i];
}
}
}
/* change initial guess values one by one */
else if(assertRetries < solverData->n+1)
{
i = assertRetries-1;
solverData->x[i] += 0.01*systemData->nominal[i];
}
giveUp = 0;
nfunc_evals += solverData->nfev;
assertRetries++;
if(ACTIVE_STREAM(LOG_NLS))
{
INFO1(LOG_NLS, " - try to handle a problem with a called assert vary initial value a bit. (Retry: %d)",assertRetries);
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
}
else if((solverData->info == 4 || solverData->info == 5) && retries < 3)
{
/* first try to decrease factor */
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
solverData->factor = solverData->factor / 10.0;
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS))
{
INFO1(LOG_NLS, " - iteration making no progress:\t decreasing initial step bound to %f.", solverData->factor);
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
}
else if((solverData->info == 4 || solverData->info == 5) && retries < 4)
{
/* try to vary the initial values */
for(i = 0; i < solverData->n; i++)
solverData->x[i] += systemData->nominal[i] * 0.1;
solverData->factor = initial_factor;
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS))
{
INFO(LOG_NLS, "iteration making no progress:\t vary solution point by 1%%.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
}
else if((solverData->info == 4 || solverData->info == 5) && retries < 5)
{
/* try old values as x-Scaling factors */
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i=0; i<solverData->n; i++)
solverData->xScalefactors[i] = fmax(fabs(systemData->nlsxOld[i]), systemData->nominal[i]);
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS))
{
INFO(LOG_NLS, "iteration making no progress:\t try old values as scaling factors.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
}
else if((solverData->info == 4 || solverData->info == 5) && retries < 6)
{
int scaling = 0;
/* try to disable x-Scaling */
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
scaling = solverData->useXScaling;
if(scaling)
solverData->useXScaling = 0;
/* reset x-scalling factors */
for(i=0; i<solverData->n; i++)
solverData->xScalefactors[i] = fmax(fabs(solverData->x[i]), systemData->nominal[i]);
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS))
{
INFO(LOG_NLS, "iteration making no progress:\t try without scaling at all.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
}
else if((solverData->info == 4 || solverData->info == 5) && retries < 7 && data->simulationInfo.discreteCall)
{
/* try to solve non-continuous
* work-a-round: since other wise some model does
* stuck in event iteration. e.g.: Modelica.Mechanics.Rotational.Examples.HeatLosses
*/
memcpy(solverData->x, systemData->nlsxOld, solverData->n*(sizeof(double)));
retries++;
/* try to solve a discontinuous system */
continuous = 0;
nonContinuousCase = 1;
memcpy(relationsPreBackup, data->simulationInfo.relationsPre, sizeof(modelica_boolean)*data->modelData.nRelations);
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS, " - iteration making no progress:\t try to solve a discontinuous system.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* Then try with old values (instead of extrapolating )*/
} else if((solverData->info == 4 || solverData->info == 5) && retries2 < 1) {
int scaling = 0;
/* set x vector */
memcpy(solverData->x, systemData->nlsxOld, solverData->n*(sizeof(double)));
scaling = solverData->useXScaling;
if(!scaling)
solverData->useXScaling = 1;
continuous = 1;
solverData->factor = initial_factor;
retries = 0;
retries2++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS, " - iteration making no progress:\t use old values instead extrapolated.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* try to vary the initial values */
} else if((solverData->info == 4 || solverData->info == 5) && retries2 < 2) {
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i = 0; i < solverData->n; i++) {
solverData->x[i] *= 1.01;
};
retries = 0;
retries2++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS,
" - iteration making no progress:\t vary initial point by adding 1%%.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* try to vary the initial values */
} else if((solverData->info == 4 || solverData->info == 5) && retries2 < 3) {
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i = 0; i < solverData->n; i++) {
solverData->x[i] *= 0.99;
};
retries = 0;
retries2++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS, " - iteration making no progress:\t vary initial point by -1%%.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* try to vary the initial values */
} else if((solverData->info == 4 || solverData->info == 5) && retries2 < 4) {
/* set x vector */
memcpy(solverData->x, systemData->nominal, solverData->n*(sizeof(double)));
retries = 0;
retries2++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS, " - iteration making no progress:\t try scaling factor as initial point.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* try own scaling factors */
} else if((solverData->info == 4 || solverData->info == 5) && retries2 < 5 && !assertCalled) {
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i = 0; i < solverData->n; i++) {
solverData->diag[i] = fabs(solverData->resScaling[i]);
if(solverData->diag[i] <= 1e-16)
solverData->diag[i] = 1e-16;
}
retries = 0;
retries2++;
giveUp = 0;
solverData->mode = 2;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS, " - iteration making no progress:\t try with own scaling factors.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* try without internal scaling */
} else if((solverData->info == 4 || solverData->info == 5) && retries3 < 1) {
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i = 0; i < solverData->n; i++)
solverData->diag[i] = 1.0;
solverData->useXScaling = 1;
retries = 0;
retries2 = 0;
retries3++;
solverData->mode = 2;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO(LOG_NLS, " - iteration making no progress:\t disable solver internal scaling.");
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
/* try to reduce the tolerance a bit */
} else if((solverData->info == 4 || solverData->info == 5) && retries3 < 6) {
/* set x vector */
if(data->simulationInfo.discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
/* reduce tolarance */
local_tol = local_tol*10;
solverData->factor = initial_factor;
solverData->mode = 1;
retries = 0;
retries2 = 0;
retries3++;
giveUp = 0;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS)) {
INFO1(LOG_NLS, " - iteration making no progress:\t reduce the tolerance slightly to %e.", local_tol);
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
} else if(solverData->info >= 2 && solverData->info <= 5) {
/* while the initialization it's ok to every time a solution */
if(!data->simulationInfo.initial){
printErrorEqSyst(ERROR_AT_TIME, modelInfoXmlGetEquation(&data->modelData.modelDataXml, eqSystemNumber), data->localData[0]->timeValue);
}
if(ACTIVE_STREAM(LOG_NLS)) {
RELEASE(LOG_NLS);
INFO1(LOG_NLS, "### No Solution! ###\n after %d restarts", retries*retries2*retries3);
printStatus(solverData, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS);
}
/* take the best approximation */
memcpy(systemData->nlsx, solverData->x, solverData->n*(sizeof(double)));
}
}
/* reset some solving data */
solverData->factor = initial_factor;
solverData->mode = 1;
free(relationsPreBackup);
return success;
}
/* Subroutine */ int qrfac_(integer *m, integer *n, doublereal *a, integer *
lda, logical *pivot, integer *ipvt, integer *lipvt, doublereal *rdiag,
doublereal *acnorm, doublereal *wa)
{
/* Initialized data */
static doublereal one = 1.;
static doublereal p05 = .05;
static doublereal zero = 0.;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, j, k, jp1;
static doublereal sum;
static integer kmax;
static doublereal temp;
static integer minmn;
extern doublereal enorm_(integer *, doublereal *);
static doublereal epsmch;
extern doublereal dpmpar_(integer *);
static doublereal ajnorm;
/* ********** */
/* subroutine qrfac */
/* this subroutine uses householder transformations with column */
/* pivoting (optional) to compute a qr factorization of the */
/* m by n matrix a. that is, qrfac determines an orthogonal */
/* matrix q, a permutation matrix p, and an upper trapezoidal */
/* matrix r with diagonal elements of nonincreasing magnitude, */
/* such that a*p = q*r. the householder transformation for */
/* column k, k = 1,2,...,min(m,n), is of the form */
/* t */
/* i - (1/u(k))*u*u */
/* where u has zeros in the first k-1 positions. the form of */
/* this transformation and the method of pivoting first */
/* appeared in the corresponding linpack subroutine. */
/* the subroutine statement is */
/* subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) */
/* where */
/* m is a positive integer input variable set to the number */
/* of rows of a. */
/* n is a positive integer input variable set to the number */
/* of columns of a. */
/* a is an m by n array. on input a contains the matrix for */
/* which the qr factorization is to be computed. on output */
/* the strict upper trapezoidal part of a contains the strict */
/* upper trapezoidal part of r, and the lower trapezoidal */
/* part of a contains a factored form of q (the non-trivial */
/* elements of the u vectors described above). */
/* lda is a positive integer input variable not less than m */
/* which specifies the leading dimension of the array a. */
/* pivot is a logical input variable. if pivot is set true, */
/* then column pivoting is enforced. if pivot is set false, */
/* then no column pivoting is done. */
/* ipvt is an integer output array of length lipvt. ipvt */
/* defines the permutation matrix p such that a*p = q*r. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* if pivot is false, ipvt is not referenced. */
/* lipvt is a positive integer input variable. if pivot is false, */
/* then lipvt may be as small as 1. if pivot is true, then */
/* lipvt must be at least n. */
/* rdiag is an output array of length n which contains the */
/* diagonal elements of r. */
/* acnorm is an output array of length n which contains the */
/* norms of the corresponding columns of the input matrix a. */
/* if this information is not needed, then acnorm can coincide */
/* with rdiag. */
/* wa is a work array of length n. if pivot is false, then wa */
/* can coincide with rdiag. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dmax1,dsqrt,min0 */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa;
--acnorm;
--rdiag;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--ipvt;
/* Function Body */
/* epsmch is the machine precision. */
epsmch = dpmpar_(&c__1);
/* compute the initial column norms and initialize several arrays. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
acnorm[j] = enorm_(m, &a[j * a_dim1 + 1]);
rdiag[j] = acnorm[j];
wa[j] = rdiag[j];
if (*pivot) {
ipvt[j] = j;
}
/* L10: */
}
/* reduce a to r with householder transformations. */
minmn = min(*m,*n);
i__1 = minmn;
for (j = 1; j <= i__1; ++j) {
if (! (*pivot)) {
goto L40;
}
/* bring the column of largest norm into the pivot position. */
kmax = j;
i__2 = *n;
for (k = j; k <= i__2; ++k) {
if (rdiag[k] > rdiag[kmax]) {
kmax = k;
}
/* L20: */
}
if (kmax == j) {
goto L40;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = a[i__ + j * a_dim1];
a[i__ + j * a_dim1] = a[i__ + kmax * a_dim1];
a[i__ + kmax * a_dim1] = temp;
/* L30: */
}
rdiag[kmax] = rdiag[j];
wa[kmax] = wa[j];
k = ipvt[j];
ipvt[j] = ipvt[kmax];
ipvt[kmax] = k;
L40:
/* compute the householder transformation to reduce the */
/* j-th column of a to a multiple of the j-th unit vector. */
i__2 = *m - j + 1;
ajnorm = enorm_(&i__2, &a[j + j * a_dim1]);
if (ajnorm == zero) {
goto L100;
}
if (a[j + j * a_dim1] < zero) {
ajnorm = -ajnorm;
}
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
a[i__ + j * a_dim1] /= ajnorm;
/* L50: */
}
a[j + j * a_dim1] += one;
/* apply the transformation to the remaining columns */
/* and update the norms. */
jp1 = j + 1;
if (*n < jp1) {
goto L100;
}
i__2 = *n;
for (k = jp1; k <= i__2; ++k) {
sum = zero;
i__3 = *m;
for (i__ = j; i__ <= i__3; ++i__) {
sum += a[i__ + j * a_dim1] * a[i__ + k * a_dim1];
/* L60: */
}
temp = sum / a[j + j * a_dim1];
i__3 = *m;
for (i__ = j; i__ <= i__3; ++i__) {
a[i__ + k * a_dim1] -= temp * a[i__ + j * a_dim1];
/* L70: */
}
if (! (*pivot) || rdiag[k] == zero) {
goto L80;
}
temp = a[j + k * a_dim1] / rdiag[k];
/* Computing MAX */
/* Computing 2nd power */
d__3 = temp;
d__1 = zero, d__2 = one - d__3 * d__3;
rdiag[k] *= sqrt((max(d__1,d__2)));
/* Computing 2nd power */
d__1 = rdiag[k] / wa[k];
if (p05 * (d__1 * d__1) > epsmch) {
goto L80;
}
i__3 = *m - j;
rdiag[k] = enorm_(&i__3, &a[jp1 + k * a_dim1]);
wa[k] = rdiag[k];
L80:
/* L90: */
;
}
L100:
rdiag[j] = -ajnorm;
/* L110: */
}
return 0;
/* last card of subroutine qrfac. */
} /* qrfac_ */
/* Subroutine */ void lmstr_(void (*fcn)(const int *m, const int *n, const double *x, double *fvec,
double *fjrow, int *iflag ), const int *m, const int *n, double *x,
double *fvec, double *fjac, const int *ldfjac, const double *ftol,
const double *xtol, const double *gtol, const int *maxfev, double *
diag, const int *mode, const double *factor, const int *nprint, int *
info, int *nfev, int *njev, int *ipvt, double *qtf,
double *wa1, double *wa2, double *wa3, double *wa4)
{
/* Table of constant values */
const int c__1 = 1;
const int c_true = TRUE_;
/* Initialized data */
#define p1 .1
#define p5 .5
#define p25 .25
#define p75 .75
#define p0001 1e-4
/* System generated locals */
int fjac_dim1, fjac_offset, i__1, i__2;
double d__1, d__2, d__3;
/* Local variables */
int i__, j, l;
double par, sum;
int sing;
int iter;
double temp, temp1, temp2;
int iflag;
double delta;
double ratio;
double fnorm, gnorm, pnorm, xnorm, fnorm1, actred, dirder,
epsmch, prered;
/* ********** */
/* subroutine lmstr */
/* the purpose of lmstr is to minimize the sum of the squares of */
/* m nonlinear functions in n variables by a modification of */
/* the levenberg-marquardt algorithm which uses minimal storage. */
/* the user must provide a subroutine which calculates the */
/* functions and the rows of the jacobian. */
/* the subroutine statement is */
/* subroutine lmstr(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol, */
/* maxfev,diag,mode,factor,nprint,info,nfev, */
/* njev,ipvt,qtf,wa1,wa2,wa3,wa4) */
/* where */
/* fcn is the name of the user-supplied subroutine which */
/* calculates the functions and the rows of the jacobian. */
/* fcn must be declared in an external statement in the */
/* user calling program, and should be written as follows. */
/* subroutine fcn(m,n,x,fvec,fjrow,iflag) */
/* integer m,n,iflag */
/* double precision x(n),fvec(m),fjrow(n) */
/* ---------- */
/* if iflag = 1 calculate the functions at x and */
/* return this vector in fvec. */
/* if iflag = i calculate the (i-1)-st row of the */
/* jacobian at x and return this vector in fjrow. */
/* ---------- */
/* return */
/* end */
/* the value of iflag should not be changed by fcn unless */
/* the user wants to terminate execution of lmstr. */
/* in this case set iflag to a negative integer. */
/* m is a positive integer input variable set to the number */
/* of functions. */
/* n is a positive integer input variable set to the number */
/* of variables. n must not exceed m. */
/* x is an array of length n. on input x must contain */
/* an initial estimate of the solution vector. on output x */
/* contains the final estimate of the solution vector. */
/* fvec is an output array of length m which contains */
/* the functions evaluated at the output x. */
/* fjac is an output n by n array. the upper triangle of fjac */
/* contains an upper triangular matrix r such that */
/* t t t */
/* p *(jac *jac)*p = r *r, */
/* where p is a permutation matrix and jac is the final */
/* calculated jacobian. column j of p is column ipvt(j) */
/* (see below) of the identity matrix. the lower triangular */
/* part of fjac contains information generated during */
/* the computation of r. */
/* ldfjac is a positive integer input variable not less than n */
/* which specifies the leading dimension of the array fjac. */
/* ftol is a nonnegative input variable. termination */
/* occurs when both the actual and predicted relative */
/* reductions in the sum of squares are at most ftol. */
/* therefore, ftol measures the relative error desired */
/* in the sum of squares. */
/* xtol is a nonnegative input variable. termination */
/* occurs when the relative error between two consecutive */
/* iterates is at most xtol. therefore, xtol measures the */
/* relative error desired in the approximate solution. */
/* gtol is a nonnegative input variable. termination */
/* occurs when the cosine of the angle between fvec and */
/* any column of the jacobian is at most gtol in absolute */
/* value. therefore, gtol measures the orthogonality */
/* desired between the function vector and the columns */
/* of the jacobian. */
/* maxfev is a positive integer input variable. termination */
/* occurs when the number of calls to fcn with iflag = 1 */
/* has reached maxfev. */
/* diag is an array of length n. if mode = 1 (see */
/* below), diag is internally set. if mode = 2, diag */
/* must contain positive entries that serve as */
/* multiplicative scale factors for the variables. */
/* mode is an integer input variable. if mode = 1, the */
/* variables will be scaled internally. if mode = 2, */
/* the scaling is specified by the input diag. other */
/* values of mode are equivalent to mode = 1. */
/* factor is a positive input variable used in determining the */
/* initial step bound. this bound is set to the product of */
/* factor and the euclidean norm of diag*x if nonzero, or else */
/* to factor itself. in most cases factor should lie in the */
/* interval (.1,100.). 100. is a generally recommended value. */
/* nprint is an integer input variable that enables controlled */
/* printing of iterates if it is positive. in this case, */
/* fcn is called with iflag = 0 at the beginning of the first */
/* iteration and every nprint iterations thereafter and */
/* immediately prior to return, with x and fvec available */
/* for printing. if nprint is not positive, no special calls */
/* of fcn with iflag = 0 are made. */
/* info is an integer output variable. if the user has */
/* terminated execution, info is set to the (negative) */
/* value of iflag. see description of fcn. otherwise, */
/* info is set as follows. */
/* info = 0 improper input parameters. */
/* info = 1 both actual and predicted relative reductions */
/* in the sum of squares are at most ftol. */
/* info = 2 relative error between two consecutive iterates */
/* is at most xtol. */
/* info = 3 conditions for info = 1 and info = 2 both hold. */
/* info = 4 the cosine of the angle between fvec and any */
/* column of the jacobian is at most gtol in */
/* absolute value. */
/* info = 5 number of calls to fcn with iflag = 1 has */
/* reached maxfev. */
/* info = 6 ftol is too small. no further reduction in */
/* the sum of squares is possible. */
/* info = 7 xtol is too small. no further improvement in */
/* the approximate solution x is possible. */
/* info = 8 gtol is too small. fvec is orthogonal to the */
/* columns of the jacobian to machine precision. */
/* nfev is an integer output variable set to the number of */
/* calls to fcn with iflag = 1. */
/* njev is an integer output variable set to the number of */
/* calls to fcn with iflag = 2. */
/* ipvt is an integer output array of length n. ipvt */
/* defines a permutation matrix p such that jac*p = q*r, */
/* where jac is the final calculated jacobian, q is */
/* orthogonal (not stored), and r is upper triangular. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* qtf is an output array of length n which contains */
/* the first n elements of the vector (q transpose)*fvec. */
/* wa1, wa2, and wa3 are work arrays of length n. */
/* wa4 is a work array of length m. */
/* subprograms called */
/* user-supplied ...... fcn */
/* minpack-supplied ... dpmpar,enorm,lmpar,qrfac,rwupdt */
/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, dudley v. goetschel, kenneth e. hillstrom, */
/* jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa4;
--fvec;
--wa3;
--wa2;
--wa1;
--qtf;
--ipvt;
--diag;
--x;
fjac_dim1 = *ldfjac;
fjac_offset = 1 + fjac_dim1 * 1;
fjac -= fjac_offset;
/* Function Body */
/* epsmch is the machine precision. */
epsmch = dpmpar_(&c__1);
*info = 0;
iflag = 0;
*nfev = 0;
*njev = 0;
/* check the input parameters for errors. */
if (*n <= 0 || *m < *n || *ldfjac < *n || *ftol < 0. || *xtol < 0. ||
*gtol < 0. || *maxfev <= 0 || *factor <= 0.) {
goto L340;
}
if (*mode != 2) {
goto L20;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (diag[j] <= 0.) {
goto L340;
}
/* L10: */
}
L20:
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = 1;
(*fcn)(m, n, &x[1], &fvec[1], &wa3[1], &iflag);
*nfev = 1;
if (iflag < 0) {
goto L340;
}
fnorm = enorm_(m, &fvec[1]);
/* initialize levenberg-marquardt parameter and iteration counter. */
par = 0.;
iter = 1;
/* beginning of the outer loop. */
L30:
/* if requested, call fcn to enable printing of iterates. */
if (*nprint <= 0) {
goto L40;
}
iflag = 0;
if ((iter - 1) % *nprint == 0) {
(*fcn)(m, n, &x[1], &fvec[1], &wa3[1], &iflag);
}
if (iflag < 0) {
goto L340;
}
L40:
/* compute the qr factorization of the jacobian matrix */
/* calculated one row at a time, while simultaneously */
/* forming (q transpose)*fvec and storing the first */
/* n components in qtf. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
qtf[j] = 0.;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
fjac[i__ + j * fjac_dim1] = 0.;
/* L50: */
}
/* L60: */
}
iflag = 2;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
(*fcn)(m, n, &x[1], &fvec[1], &wa3[1], &iflag);
if (iflag < 0) {
goto L340;
}
temp = fvec[i__];
rwupdt_(n, &fjac[fjac_offset], ldfjac, &wa3[1], &qtf[1], &temp, &wa1[
1], &wa2[1]);
++iflag;
/* L70: */
}
++(*njev);
/* if the jacobian is rank deficient, call qrfac to */
/* reorder its columns and update the components of qtf. */
sing = FALSE_;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) {
sing = TRUE_;
}
ipvt[j] = j;
wa2[j] = enorm_(&j, &fjac[j * fjac_dim1 + 1]);
/* L80: */
}
if (! sing) {
goto L130;
}
qrfac_(n, n, &fjac[fjac_offset], ldfjac, &c_true, &ipvt[1], n, &wa1[1], &
wa2[1], &wa3[1]);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (fjac[j + j * fjac_dim1] == 0.) {
goto L110;
}
sum = 0.;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * qtf[i__];
/* L90: */
}
temp = -sum / fjac[j + j * fjac_dim1];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
qtf[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L100: */
}
L110:
fjac[j + j * fjac_dim1] = wa1[j];
/* L120: */
}
L130:
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if (iter != 1) {
goto L170;
}
if (*mode == 2) {
goto L150;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
diag[j] = wa2[j];
if (wa2[j] == 0.) {
diag[j] = 1.;
}
/* L140: */
}
L150:
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa3[j] = diag[j] * x[j];
/* L160: */
}
xnorm = enorm_(n, &wa3[1]);
delta = *factor * xnorm;
if (delta == 0.) {
delta = *factor;
}
L170:
/* compute the norm of the scaled gradient. */
gnorm = 0.;
if (fnorm == 0.) {
goto L210;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = ipvt[j];
if (wa2[l] == 0.) {
goto L190;
}
sum = 0.;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm);
/* L180: */
}
/* Computing MAX */
d__2 = gnorm, d__3 = (d__1 = sum / wa2[l], abs(d__1));
gnorm = max(d__2,d__3);
L190:
/* L200: */
;
}
L210:
/* test for convergence of the gradient norm. */
if (gnorm <= *gtol) {
*info = 4;
}
if (*info != 0) {
goto L340;
}
/* rescale if necessary. */
if (*mode == 2) {
goto L230;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2);
/* L220: */
}
L230:
/* beginning of the inner loop. */
L240:
/* determine the levenberg-marquardt parameter. */
lmpar_(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], &delta,
&par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]);
/* store the direction p and x + p. calculate the norm of p. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j];
/* L250: */
}
pnorm = enorm_(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */
if (iter == 1) {
delta = min(delta,pnorm);
}
/* evaluate the function at x + p and calculate its norm. */
iflag = 1;
(*fcn)(m, n, &wa2[1], &wa4[1], &wa3[1], &iflag);
++(*nfev);
if (iflag < 0) {
goto L340;
}
fnorm1 = enorm_(m, &wa4[1]);
/* compute the scaled actual reduction. */
actred = -1.;
if (p1 * fnorm1 < fnorm) {
/* Computing 2nd power */
d__1 = fnorm1 / fnorm;
actred = 1. - d__1 * d__1;
}
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa3[j] = 0.;
l = ipvt[j];
temp = wa1[l];
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
wa3[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L260: */
}
/* L270: */
}
temp1 = enorm_(n, &wa3[1]) / fnorm;
temp2 = sqrt(par) * pnorm / fnorm;
/* Computing 2nd power */
d__1 = temp1;
/* Computing 2nd power */
d__2 = temp2;
prered = d__1 * d__1 + d__2 * d__2 / p5;
/* Computing 2nd power */
d__1 = temp1;
/* Computing 2nd power */
d__2 = temp2;
dirder = -(d__1 * d__1 + d__2 * d__2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = 0.;
if (prered != 0.) {
ratio = actred / prered;
}
/* update the step bound. */
if (ratio > p25) {
goto L280;
}
if (actred >= 0.) {
temp = p5;
}
if (actred < 0.) {
temp = p5 * dirder / (dirder + p5 * actred);
}
if (p1 * fnorm1 >= fnorm || temp < p1) {
temp = p1;
}
/* Computing MIN */
d__1 = delta, d__2 = pnorm / p1;
delta = temp * min(d__1,d__2);
par /= temp;
goto L300;
L280:
if (par != 0. && ratio < p75) {
goto L290;
}
delta = pnorm / p5;
par = p5 * par;
L290:
L300:
/* test for successful iteration. */
if (ratio < p0001) {
goto L330;
}
/* successful iteration. update x, fvec, and their norms. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
x[j] = wa2[j];
wa2[j] = diag[j] * x[j];
/* L310: */
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
fvec[i__] = wa4[i__];
/* L320: */
}
xnorm = enorm_(n, &wa2[1]);
fnorm = fnorm1;
++iter;
L330:
/* tests for convergence. */
if (abs(actred) <= *ftol && prered <= *ftol && p5 * ratio <= 1.) {
*info = 1;
}
if (delta <= *xtol * xnorm) {
*info = 2;
}
if (abs(actred) <= *ftol && prered <= *ftol && p5 * ratio <= 1. && *info
== 2) {
*info = 3;
}
if (*info != 0) {
goto L340;
}
/* tests for termination and stringent tolerances. */
if (*nfev >= *maxfev) {
*info = 5;
}
if (abs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= 1.) {
*info = 6;
}
if (delta <= epsmch * xnorm) {
*info = 7;
}
if (gnorm <= epsmch) {
*info = 8;
}
if (*info != 0) {
goto L340;
}
/* end of the inner loop. repeat if iteration unsuccessful. */
if (ratio < p0001) {
goto L240;
}
/* end of the outer loop. */
goto L30;
L340:
/* termination, either normal or user imposed. */
if (iflag < 0) {
*info = iflag;
}
iflag = 0;
if (*nprint > 0) {
(*fcn)(m, n, &x[1], &fvec[1], &wa3[1], &iflag);
}
return;
/* last card of subroutine lmstr. */
} /* lmstr_ */
/* Subroutine */ int lmpar_(integer *n, doublereal *r__, integer *ldr,
integer *ipvt, doublereal *diag, doublereal *qtb, doublereal *delta,
doublereal *par, doublereal *x, doublereal *sdiag, doublereal *wa1,
doublereal *wa2)
{
/* Initialized data */
static doublereal p1 = .1;
static doublereal p001 = .001;
static doublereal zero = 0.;
/* System generated locals */
integer r_dim1, r_offset, i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, j, k, l;
static doublereal fp;
static integer jm1, jp1;
static doublereal sum, parc, parl;
static integer iter;
static doublereal temp, paru, dwarf;
static integer nsing;
extern doublereal enorm_(integer *, doublereal *);
static doublereal gnorm;
extern doublereal dpmpar_(integer *);
static doublereal dxnorm;
extern /* Subroutine */ int qrsolv_(integer *, doublereal *, integer *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
/* ********** */
/* subroutine lmpar */
/* given an m by n matrix a, an n by n nonsingular diagonal */
/* matrix d, an m-vector b, and a positive number delta, */
/* the problem is to determine a value for the parameter */
/* par such that if x solves the system */
/* a*x = b , sqrt(par)*d*x = 0 , */
/* in the least squares sense, and dxnorm is the euclidean */
/* norm of d*x, then either par is zero and */
/* (dxnorm-delta) .le. 0.1*delta , */
/* or par is positive and */
/* abs(dxnorm-delta) .le. 0.1*delta . */
/* this subroutine completes the solution of the problem */
/* if it is provided with the necessary information from the */
/* qr factorization, with column pivoting, of a. that is, if */
/* a*p = q*r, where p is a permutation matrix, q has orthogonal */
/* columns, and r is an upper triangular matrix with diagonal */
/* elements of nonincreasing magnitude, then lmpar expects */
/* the full upper triangle of r, the permutation matrix p, */
/* and the first n components of (q transpose)*b. on output */
/* lmpar also provides an upper triangular matrix s such that */
/* t t t */
/* p *(a *a + par*d*d)*p = s *s . */
/* s is employed within lmpar and may be of separate interest. */
/* only a few iterations are generally needed for convergence */
/* of the algorithm. if, however, the limit of 10 iterations */
/* is reached, then the output par will contain the best */
/* value obtained so far. */
/* the subroutine statement is */
/* subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag, */
/* wa1,wa2) */
/* where */
/* n is a positive integer input variable set to the order of r. */
/* r is an n by n array. on input the full upper triangle */
/* must contain the full upper triangle of the matrix r. */
/* on output the full upper triangle is unaltered, and the */
/* strict lower triangle contains the strict upper triangle */
/* (transposed) of the upper triangular matrix s. */
/* ldr is a positive integer input variable not less than n */
/* which specifies the leading dimension of the array r. */
/* ipvt is an integer input array of length n which defines the */
/* permutation matrix p such that a*p = q*r. column j of p */
/* is column ipvt(j) of the identity matrix. */
/* diag is an input array of length n which must contain the */
/* diagonal elements of the matrix d. */
/* qtb is an input array of length n which must contain the first */
/* n elements of the vector (q transpose)*b. */
/* delta is a positive input variable which specifies an upper */
/* bound on the euclidean norm of d*x. */
/* par is a nonnegative variable. on input par contains an */
/* initial estimate of the levenberg-marquardt parameter. */
/* on output par contains the final estimate. */
/* x is an output array of length n which contains the least */
/* squares solution of the system a*x = b, sqrt(par)*d*x = 0, */
/* for the output par. */
/* sdiag is an output array of length n which contains the */
/* diagonal elements of the upper triangular matrix s. */
/* wa1 and wa2 are work arrays of length n. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm,qrsolv */
/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa2;
--wa1;
--sdiag;
--x;
--qtb;
--diag;
--ipvt;
r_dim1 = *ldr;
r_offset = r_dim1 + 1;
r__ -= r_offset;
/* Function Body */
/* dwarf is the smallest positive magnitude. */
dwarf = dpmpar_(&c__2);
/* compute and store in x the gauss-newton direction. if the */
/* jacobian is rank-deficient, obtain a least squares solution. */
nsing = *n;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa1[j] = qtb[j];
if (r__[j + j * r_dim1] == zero && nsing == *n) {
nsing = j - 1;
}
if (nsing < *n) {
wa1[j] = zero;
}
/* L10: */
}
if (nsing < 1) {
goto L50;
}
i__1 = nsing;
for (k = 1; k <= i__1; ++k) {
j = nsing - k + 1;
wa1[j] /= r__[j + j * r_dim1];
temp = wa1[j];
jm1 = j - 1;
if (jm1 < 1) {
goto L30;
}
i__2 = jm1;
for (i__ = 1; i__ <= i__2; ++i__) {
wa1[i__] -= r__[i__ + j * r_dim1] * temp;
/* L20: */
}
L30:
/* L40: */
;
}
L50:
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = ipvt[j];
x[l] = wa1[j];
/* L60: */
}
/* initialize the iteration counter. */
/* evaluate the function at the origin, and test */
/* for acceptance of the gauss-newton direction. */
iter = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa2[j] = diag[j] * x[j];
/* L70: */
}
dxnorm = enorm_(n, &wa2[1]);
fp = dxnorm - *delta;
if (fp <= p1 * *delta) {
goto L220;
}
/* if the jacobian is not rank deficient, the newton */
/* step provides a lower bound, parl, for the zero of */
/* the function. otherwise set this bound to zero. */
parl = zero;
if (nsing < *n) {
goto L120;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = ipvt[j];
wa1[j] = diag[l] * (wa2[l] / dxnorm);
/* L80: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = zero;
jm1 = j - 1;
if (jm1 < 1) {
goto L100;
}
i__2 = jm1;
for (i__ = 1; i__ <= i__2; ++i__) {
sum += r__[i__ + j * r_dim1] * wa1[i__];
/* L90: */
}
L100:
wa1[j] = (wa1[j] - sum) / r__[j + j * r_dim1];
/* L110: */
}
temp = enorm_(n, &wa1[1]);
parl = fp / *delta / temp / temp;
L120:
/* calculate an upper bound, paru, for the zero of the function. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = zero;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
sum += r__[i__ + j * r_dim1] * qtb[i__];
/* L130: */
}
l = ipvt[j];
wa1[j] = sum / diag[l];
/* L140: */
}
gnorm = enorm_(n, &wa1[1]);
paru = gnorm / *delta;
if (paru == zero) {
paru = dwarf / min(*delta,p1);
}
/* if the input par lies outside of the interval (parl,paru), */
/* set par to the closer endpoint. */
*par = max(*par,parl);
*par = min(*par,paru);
if (*par == zero) {
*par = gnorm / dxnorm;
}
/* beginning of an iteration. */
L150:
++iter;
/* evaluate the function at the current value of par. */
if (*par == zero) {
/* Computing MAX */
d__1 = dwarf, d__2 = p001 * paru;
*par = max(d__1,d__2);
}
temp = sqrt(*par);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa1[j] = temp * diag[j];
/* L160: */
}
qrsolv_(n, &r__[r_offset], ldr, &ipvt[1], &wa1[1], &qtb[1], &x[1], &sdiag[
1], &wa2[1]);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa2[j] = diag[j] * x[j];
/* L170: */
}
dxnorm = enorm_(n, &wa2[1]);
temp = fp;
fp = dxnorm - *delta;
/* if the function is small enough, accept the current value */
/* of par. also test for the exceptional cases where parl */
/* is zero or the number of iterations has reached 10. */
if (abs(fp) <= p1 * *delta || (parl == zero && fp <= temp && temp < zero) ||
iter == 10) {
goto L220;
}
/* compute the newton correction. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = ipvt[j];
wa1[j] = diag[l] * (wa2[l] / dxnorm);
/* L180: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa1[j] /= sdiag[j];
temp = wa1[j];
jp1 = j + 1;
if (*n < jp1) {
goto L200;
}
i__2 = *n;
for (i__ = jp1; i__ <= i__2; ++i__) {
wa1[i__] -= r__[i__ + j * r_dim1] * temp;
/* L190: */
}
L200:
/* L210: */
;
}
temp = enorm_(n, &wa1[1]);
parc = fp / *delta / temp / temp;
/* depending on the sign of the function, update parl or paru. */
if (fp > zero) {
parl = max(parl,*par);
}
if (fp < zero) {
paru = min(paru,*par);
}
/* compute an improved estimate for par. */
/* Computing MAX */
d__1 = parl, d__2 = *par + parc;
*par = max(d__1,d__2);
/* end of an iteration. */
goto L150;
L220:
/* termination. */
if (iter == 0) {
*par = zero;
}
return 0;
/* last card of subroutine lmpar. */
} /* lmpar_ */
/* DECK SCOV */
/* Subroutine */ int scov_(S_fp fcn, integer *iopt, integer *m, integer *n,
real *x, real *fvec, real *r__, integer *ldr, integer *info, real *
wa1, real *wa2, real *wa3, real *wa4)
{
/* Initialized data */
static real zero = 0.f;
static real one = 1.f;
/* System generated locals */
integer r_dim1, r_offset, i__1, i__2, i__3;
/* Local variables */
static integer i__, j, k, kp1, nm1, idum;
static logical sing;
static real temp;
static integer nrow, iflag;
extern /* Subroutine */ int qrfac_(integer *, integer *, real *, integer *
, logical *, integer *, integer *, real *, real *, real *);
static real sigma;
extern doublereal enorm_(integer *, real *);
extern /* Subroutine */ int fdjac3_(S_fp, integer *, integer *, real *,
real *, real *, integer *, integer *, real *, real *), xermsg_(
char *, char *, char *, integer *, integer *, ftnlen, ftnlen,
ftnlen), rwupdt_(integer *, real *, integer *, real *, real *,
real *, real *, real *);
/* ***BEGIN PROLOGUE SCOV */
/* ***PURPOSE Calculate the covariance matrix for a nonlinear data */
/* fitting problem. It is intended to be used after a */
/* successful return from either SNLS1 or SNLS1E. */
/* ***LIBRARY SLATEC */
/* ***CATEGORY K1B1 */
/* ***TYPE SINGLE PRECISION (SCOV-S, DCOV-D) */
/* ***KEYWORDS COVARIANCE MATRIX, NONLINEAR DATA FITTING, */
/* NONLINEAR LEAST SQUARES */
/* ***AUTHOR Hiebert, K. L., (SNLA) */
/* ***DESCRIPTION */
/* 1. Purpose. */
/* SCOV calculates the covariance matrix for a nonlinear data */
/* fitting problem. It is intended to be used after a */
/* successful return from either SNLS1 or SNLS1E. SCOV */
/* and SNLS1 (and SNLS1E) have compatible parameters. The */
/* required external subroutine, FCN, is the same */
/* for all three codes, SCOV, SNLS1, and SNLS1E. */
/* 2. Subroutine and Type Statements. */
/* SUBROUTINE SCOV(FCN,IOPT,M,N,X,FVEC,R,LDR,INFO, */
/* WA1,WA2,WA3,WA4) */
/* INTEGER IOPT,M,N,LDR,INFO */
/* REAL X(N),FVEC(M),R(LDR,N),WA1(N),WA2(N),WA3(N),WA4(M) */
/* EXTERNAL FCN */
/* 3. Parameters. */
/* FCN is the name of the user-supplied subroutine which calculates */
/* the functions. If the user wants to supply the Jacobian */
/* (IOPT=2 or 3), then FCN must be written to calculate the */
/* Jacobian, as well as the functions. See the explanation */
/* of the IOPT argument below. FCN must be declared in an */
/* EXTERNAL statement in the calling program and should be */
/* written as follows. */
/* SUBROUTINE FCN(IFLAG,M,N,X,FVEC,FJAC,LDFJAC) */
/* INTEGER IFLAG,LDFJAC,M,N */
/* REAL X(N),FVEC(M) */
/* ---------- */
/* FJAC and LDFJAC may be ignored , if IOPT=1. */
/* REAL FJAC(LDFJAC,N) , if IOPT=2. */
/* REAL FJAC(N) , if IOPT=3. */
/* ---------- */
/* IFLAG will never be zero when FCN is called by SCOV. */
/* RETURN */
/* ---------- */
/* If IFLAG=1, calculate the functions at X and return */
/* this vector in FVEC. */
/* RETURN */
/* ---------- */
/* If IFLAG=2, calculate the full Jacobian at X and return */
/* this matrix in FJAC. Note that IFLAG will never be 2 unless */
/* IOPT=2. FVEC contains the function values at X and must */
/* not be altered. FJAC(I,J) must be set to the derivative */
/* of FVEC(I) with respect to X(J). */
/* RETURN */
/* ---------- */
/* If IFLAG=3, calculate the LDFJAC-th row of the Jacobian */
/* and return this vector in FJAC. Note that IFLAG will */
/* never be 3 unless IOPT=3. FJAC(J) must be set to */
/* the derivative of FVEC(LDFJAC) with respect to X(J). */
/* RETURN */
/* ---------- */
/* END */
/* The value of IFLAG should not be changed by FCN unless the */
/* user wants to terminate execution of SCOV. In this case, set */
/* IFLAG to a negative integer. */
/* IOPT is an input variable which specifies how the Jacobian will */
/* be calculated. If IOPT=2 or 3, then the user must supply the */
/* Jacobian, as well as the function values, through the */
/* subroutine FCN. If IOPT=2, the user supplies the full */
/* Jacobian with one call to FCN. If IOPT=3, the user supplies */
/* one row of the Jacobian with each call. (In this manner, */
/* storage can be saved because the full Jacobian is not stored.) */
/* If IOPT=1, the code will approximate the Jacobian by forward */
/* differencing. */
/* M is a positive integer input variable set to the number of */
/* functions. */
/* N is a positive integer input variable set to the number of */
/* variables. N must not exceed M. */
/* X is an array of length N. On input X must contain the value */
/* at which the covariance matrix is to be evaluated. This is */
/* usually the value for X returned from a successful run of */
/* SNLS1 (or SNLS1E). The value of X will not be changed. */
/* FVEC is an output array of length M which contains the functions */
/* evaluated at X. */
/* R is an output array. For IOPT=1 and 2, R is an M by N array. */
/* For IOPT=3, R is an N by N array. On output, if INFO=1, */
/* the upper N by N submatrix of R contains the covariance */
/* matrix evaluated at X. */
/* LDR is a positive integer input variable which specifies */
/* the leading dimension of the array R. For IOPT=1 and 2, */
/* LDR must not be less than M. For IOPT=3, LDR must not */
/* be less than N. */
/* INFO is an integer output variable. If the user has terminated */
/* execution, INFO is set to the (negative) value of IFLAG. See */
/* description of FCN. Otherwise, INFO is set as follows. */
/* INFO = 0 Improper input parameters (M.LE.0 or N.LE.0). */
/* INFO = 1 Successful return. The covariance matrix has been */
/* calculated and stored in the upper N by N */
/* submatrix of R. */
/* INFO = 2 The Jacobian matrix is singular for the input value */
/* of X. The covariance matrix cannot be calculated. */
/* The upper N by N submatrix of R contains the QR */
/* factorization of the Jacobian (probably not of */
/* interest to the user). */
/* WA1 is a work array of length N. */
/* WA2 is a work array of length N. */
/* WA3 is a work array of length N. */
/* WA4 is a work array of length M. */
/* ***REFERENCES (NONE) */
/* ***ROUTINES CALLED ENORM, FDJAC3, QRFAC, RWUPDT, XERMSG */
/* ***REVISION HISTORY (YYMMDD) */
/* 810522 DATE WRITTEN */
/* 890505 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) */
/* 900510 Fixed an error message. (RWC) */
/* ***END PROLOGUE SCOV */
/* REVISED 820707-1100 */
/* REVISED YYMMDD HHMM */
/* Parameter adjustments */
--x;
--fvec;
r_dim1 = *ldr;
r_offset = 1 + r_dim1;
r__ -= r_offset;
--wa1;
--wa2;
--wa3;
--wa4;
/* Function Body */
/* ***FIRST EXECUTABLE STATEMENT SCOV */
sing = FALSE_;
iflag = 0;
if (*m <= 0 || *n <= 0) {
goto L300;
}
/* CALCULATE SIGMA = (SUM OF THE SQUARED RESIDUALS) / (M-N) */
iflag = 1;
(*fcn)(&iflag, m, n, &x[1], &fvec[1], &r__[r_offset], ldr);
if (iflag < 0) {
goto L300;
}
temp = enorm_(m, &fvec[1]);
sigma = one;
if (*m != *n) {
sigma = temp * temp / (*m - *n);
}
/* CALCULATE THE JACOBIAN */
if (*iopt == 3) {
goto L200;
}
/* STORE THE FULL JACOBIAN USING M*N STORAGE */
if (*iopt == 1) {
goto L100;
}
/* USER SUPPLIES THE JACOBIAN */
iflag = 2;
(*fcn)(&iflag, m, n, &x[1], &fvec[1], &r__[r_offset], ldr);
goto L110;
/* CODE APPROXIMATES THE JACOBIAN */
L100:
fdjac3_((S_fp)fcn, m, n, &x[1], &fvec[1], &r__[r_offset], ldr, &iflag, &
zero, &wa4[1]);
L110:
if (iflag < 0) {
goto L300;
}
/* COMPUTE THE QR DECOMPOSITION */
qrfac_(m, n, &r__[r_offset], ldr, &c_false, &idum, &c__1, &wa1[1], &wa1[1]
, &wa1[1]);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* L120: */
r__[i__ + i__ * r_dim1] = wa1[i__];
}
goto L225;
/* COMPUTE THE QR FACTORIZATION OF THE JACOBIAN MATRIX CALCULATED ONE */
/* ROW AT A TIME AND STORED IN THE UPPER TRIANGLE OF R. */
/* ( (Q TRANSPOSE)*FVEC IS ALSO CALCULATED BUT NOT USED.) */
L200:
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa2[j] = zero;
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
r__[i__ + j * r_dim1] = zero;
/* L205: */
}
/* L210: */
}
iflag = 3;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
nrow = i__;
(*fcn)(&iflag, m, n, &x[1], &fvec[1], &wa1[1], &nrow);
if (iflag < 0) {
goto L300;
}
temp = fvec[i__];
rwupdt_(n, &r__[r_offset], ldr, &wa1[1], &wa2[1], &temp, &wa3[1], &
wa4[1]);
/* L220: */
}
/* CHECK IF R IS SINGULAR. */
L225:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (r__[i__ + i__ * r_dim1] == zero) {
sing = TRUE_;
}
/* L230: */
}
if (sing) {
goto L300;
}
/* R IS UPPER TRIANGULAR. CALCULATE (R TRANSPOSE) INVERSE AND STORE */
/* IN THE UPPER TRIANGLE OF R. */
if (*n == 1) {
goto L275;
}
nm1 = *n - 1;
i__1 = nm1;
for (k = 1; k <= i__1; ++k) {
/* INITIALIZE THE RIGHT-HAND SIDE (WA1(*)) AS THE K-TH COLUMN OF THE */
/* IDENTITY MATRIX. */
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
wa1[i__] = zero;
/* L240: */
}
wa1[k] = one;
r__[k + k * r_dim1] = wa1[k] / r__[k + k * r_dim1];
kp1 = k + 1;
i__2 = *n;
for (i__ = kp1; i__ <= i__2; ++i__) {
/* SUBTRACT R(K,I-1)*R(I-1,*) FROM THE RIGHT-HAND SIDE, WA1(*). */
i__3 = *n;
for (j = i__; j <= i__3; ++j) {
wa1[j] -= r__[k + (i__ - 1) * r_dim1] * r__[i__ - 1 + j *
r_dim1];
/* L250: */
}
r__[k + i__ * r_dim1] = wa1[i__] / r__[i__ + i__ * r_dim1];
/* L260: */
}
/* L270: */
}
L275:
r__[*n + *n * r_dim1] = one / r__[*n + *n * r_dim1];
/* CALCULATE R-INVERSE * (R TRANSPOSE) INVERSE AND STORE IN THE UPPER */
/* TRIANGLE OF R. */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n;
for (j = i__; j <= i__2; ++j) {
temp = zero;
i__3 = *n;
for (k = j; k <= i__3; ++k) {
temp += r__[i__ + k * r_dim1] * r__[j + k * r_dim1];
/* L280: */
}
r__[i__ + j * r_dim1] = temp * sigma;
/* L290: */
}
}
*info = 1;
L300:
if (*m <= 0 || *n <= 0) {
*info = 0;
}
if (iflag < 0) {
*info = iflag;
}
if (sing) {
*info = 2;
}
if (*info < 0) {
xermsg_("SLATEC", "SCOV", "EXECUTION TERMINATED BECAUSE USER SET IFL"
"AG NEGATIVE.", &c__1, &c__1, (ftnlen)6, (ftnlen)4, (ftnlen)53)
;
}
if (*info == 0) {
xermsg_("SLATEC", "SCOV", "INVALID INPUT PARAMETER.", &c__2, &c__1, (
ftnlen)6, (ftnlen)4, (ftnlen)24);
}
if (*info == 2) {
xermsg_("SLATEC", "SCOV", "SINGULAR JACOBIAN MATRIX, COVARIANCE MATR"
"IX CANNOT BE CALCULATED.", &c__1, &c__1, (ftnlen)6, (ftnlen)4,
(ftnlen)65);
}
return 0;
} /* scov_ */
int qrfac_(int m, int n, double *a, int lda, int *ipvt,
double *rdiag, double *acnorm, double *wa)
{
const double p05 = .05;
const double epsmch = DBL_EPSILON;
double ajnorm, d, sum, temp;
int kmax, minmn, jp1;
int i, j, k;
/* compute the initial column norms and initialize several arrays */
for (j = 0; j < n; ++j) {
acnorm[j] = enorm_(m, a + j * lda);
rdiag[j] = acnorm[j];
wa[j] = rdiag[j];
ipvt[j] = j;
}
/* reduce a to r with Householder transformations */
minmn = min(m, n);
for (j = 0; j < minmn; ++j) {
/* bring the column of largest norm into the pivot position */
kmax = j;
for (k = j; k < n; ++k) {
if (rdiag[k] > rdiag[kmax]) {
kmax = k;
}
}
if (kmax != j) {
for (i = 0; i < m; ++i) {
temp = a[i + j * lda];
a[i + j * lda] = a[i + kmax * lda];
a[i + kmax * lda] = temp;
}
rdiag[kmax] = rdiag[j];
wa[kmax] = wa[j];
k = ipvt[j];
ipvt[j] = ipvt[kmax];
ipvt[kmax] = k;
}
/* compute the Householder transformation to reduce the
j-th column of a to a multiple of the j-th unit vector
*/
ajnorm = enorm_(m - j, &a[j + j * lda]);
if (ajnorm == 0.0) {
rdiag[j] = -ajnorm;
continue;
}
if (a[j + j * lda] < 0.0) {
ajnorm = -ajnorm;
}
for (i = j; i < m; ++i) {
a[i + j * lda] /= ajnorm;
}
a[j + j * lda] += 1.0;
/* apply the transformation to the remaining columns
and update the norms
*/
jp1 = j + 1;
for (k = jp1; k < n; ++k) {
sum = 0.0;
for (i = j; i < m; ++i) {
sum += a[i + j * lda] * a[i + k * lda];
}
temp = sum / a[j + j * lda];
for (i = j; i < m; ++i) {
a[i + k * lda] -= temp * a[i + j * lda];
}
if (rdiag[k] != 0.0) {
temp = a[j + k * lda] / rdiag[k];
d = 1.0 - temp * temp;
if (d > 0) {
rdiag[k] *= sqrt(d);
} else {
rdiag[k] = 0.0;
}
d = rdiag[k] / wa[k];
if (p05 * (d * d) <= epsmch) {
rdiag[k] = enorm_(m - jp1, &a[jp1 + k * lda]);
wa[k] = rdiag[k];
}
}
}
rdiag[j] = -ajnorm;
}
return 0;
}
/*! \fn LineSearch
*
* third damping heuristic:
* Along the tangent 5 five points are selected. For every point the Euclidean norm of
* the residual function will be calculated and the minimum is chosen for the further iteration.
*
* compiler flag: -newton = damped_ls
*/
void LineSearch(double* x, int(*f)(int*, double*, double*, void*, int),
double current_fvec_enorm, int* n, double* fvec, int* k, DATA_NEWTON* solverData, void* userdata)
{
int i,j;
double enorm_new, enorm_minimum=current_fvec_enorm, lambda_minimum=0;
double lambda[5]={1.25,1,0.75,0.5,0.25};
for (j=0; j<5; j++)
{
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-lambda[j]*solverData->x_increment[i];
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_new=enorm_(n,fvec);
/* searching minimal enorm */
if (enorm_new < enorm_minimum)
{
enorm_minimum = enorm_new;
lambda_minimum = lambda[j];
memcpy(solverData->fvec_minimum, fvec,*n*sizeof(double));
}
}
infoStreamPrint(LOG_NLS_V,0,"lambda_minimum = %e", lambda_minimum);
if (lambda_minimum == 0)
{
warningStreamPrint(LOG_NLS_V, 0, "Warning: lambda_minimum = 0 ");
/* if damping is without success, trying full newton step; after 5 full newton steps try a very little step */
if (*k >= 5)
{
lambda_minimum = 0.125;
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
}
else
{
lambda_minimum = 1;
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
}
(*k)++;
}
else
{
/* save new function values */
memcpy(fvec, solverData->fvec_minimum, *n*sizeof(double));
}
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-lambda_minimum*solverData->x_increment[i];
}
/*! \fn solve system with Newton-Raphson
*
* \param [in] [n] size of equation
* [eps] tolerance for x
* [h] tolerance for f'
* [k] maximum number of iterations
* [work] work array size of (n*X)
* [f] user provided function
* [data] userdata
* [info]
* [calculate_jacobian] flag which decides whether Jacobian is calculated
* (0) once for the first calculation
* (i) every i steps (=1 means original newton method)
* (-1) never, factorization has to be given in A
*
*/
int _omc_newton(int(*f)(int*, double*, double*, void*, int), DATA_NEWTON* solverData, void* userdata)
{
int i, j, k = 0, l = 0, nrsh = 1;
int *n = &(solverData->n);
double *x = solverData->x;
double *fvec = solverData->fvec;
double *eps = &(solverData->ftol);
double *fdeps = &(solverData->epsfcn);
int * maxfev = &(solverData->maxfev);
double *fjac = solverData->fjac;
double *work = solverData->rwork;
int *iwork = solverData->iwork;
int *info = &(solverData->info);
int calc_jac = 1;
double error_f = 1.0 + *eps, scaledError_f = 1.0 + *eps, delta_x = 1.0 + *eps, delta_f = 1.0 + *eps, delta_x_scaled = 1.0 + *eps, lambda = 1.0;
double current_fvec_enorm, enorm_new;
if(ACTIVE_STREAM(LOG_NLS_V))
{
infoStreamPrint(LOG_NLS_V, 1, "######### Start Newton maxfev: %d #########", (int)*maxfev);
infoStreamPrint(LOG_NLS_V, 1, "x vector");
for(i=0; i<*n; i++)
infoStreamPrint(LOG_NLS_V, 0, "x[%d]: %e ", i, x[i]);
messageClose(LOG_NLS_V);
messageClose(LOG_NLS_V);
}
*info = 1;
/* calculate the function values */
(*f)(n, x, fvec, userdata, 1);
solverData->nfev++;
/* save current fvec in f_old*/
memcpy(solverData->f_old, fvec, *n*sizeof(double));
error_f = current_fvec_enorm = enorm_(n, fvec);
while(error_f > *eps && scaledError_f > *eps && delta_x > *eps && delta_f > *eps && delta_x_scaled > *eps)
{
if(ACTIVE_STREAM(LOG_NLS_V))
{
infoStreamPrint(LOG_NLS_V, 0, "\n**** start Iteration: %d *****", (int) l);
/* Debug output */
infoStreamPrint(LOG_NLS_V, 1, "function values");
for(i=0; i<*n; i++)
infoStreamPrint(LOG_NLS_V, 0, "fvec[%d]: %e ", i, fvec[i]);
messageClose(LOG_NLS_V);
}
/* calculate jacobian if no matrix is given */
if (calc_jac == 1 && solverData->calculate_jacobian >= 0)
{
(*f)(n, x, fvec, userdata, 0);
solverData->factorization = 0;
calc_jac = solverData->calculate_jacobian;
}
else
{
solverData->factorization = 1;
calc_jac--;
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_JAC))
{
char buffer[4096];
infoStreamPrint(LOG_NLS_JAC, 1, "jacobian matrix [%dx%d]", (int)*n, (int)*n);
for(i=0; i<solverData->n;i++)
{
buffer[0] = 0;
for(j=0; j<solverData->n; j++)
sprintf(buffer, "%s%10g ", buffer, fjac[i*(*n)+j]);
infoStreamPrint(LOG_NLS_JAC, 0, "%s", buffer);
}
messageClose(LOG_NLS_JAC);
}
if (solveLinearSystem(n, iwork, fvec, fjac, solverData) != 0)
{
*info=-1;
break;
}
else
{
for (i =0; i<*n; i++)
solverData->x_new[i]=x[i]-solverData->x_increment[i];
infoStreamPrint(LOG_NLS_V,1,"x_increment");
for(i=0; i<*n; i++)
infoStreamPrint(LOG_NLS_V, 0, "x_increment[%d] = %e ", i, solverData->x_increment[i]);
messageClose(LOG_NLS_V);
if (solverData->newtonStrategy == NEWTON_DAMPED)
{
damping_heuristic(x, f, current_fvec_enorm, n, fvec, &lambda, &k, solverData, userdata);
}
else if (solverData->newtonStrategy == NEWTON_DAMPED2)
{
damping_heuristic2(0.75, x, f, current_fvec_enorm, n, fvec, &k, solverData, userdata);
}
else if (solverData->newtonStrategy == NEWTON_DAMPED_LS)
{
LineSearch(x, f, current_fvec_enorm, n, fvec, &k, solverData, userdata);
}
else if (solverData->newtonStrategy == NEWTON_DAMPED_BT)
{
Backtracking(x, f, current_fvec_enorm, n, fvec, solverData, userdata);
}
else
{
/* calculate the function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
}
calculatingErrors(solverData, &delta_x, &delta_x_scaled, &delta_f, &error_f, &scaledError_f, n, x, fvec);
/* updating x */
memcpy(x, solverData->x_new, *n*sizeof(double));
/* updating f_old */
memcpy(solverData->f_old, fvec, *n*sizeof(double));
current_fvec_enorm = error_f;
/* check if maximum iteration is reached */
if (++l > *maxfev)
{
*info = -1;
warningStreamPrint(LOG_NLS_V, 0, "Warning: maximal number of iteration reached but no root found");
break;
}
}
if(ACTIVE_STREAM(LOG_NLS_V))
{
infoStreamPrint(LOG_NLS_V,1,"x vector");
for(i=0; i<*n; i++)
infoStreamPrint(LOG_NLS_V, 0, "x[%d] = %e ", i, x[i]);
messageClose(LOG_NLS_V);
printErrors(delta_x, delta_x_scaled, delta_f, error_f, scaledError_f, eps);
}
}
solverData->numberOfIterations += l;
solverData->numberOfFunctionEvaluations += solverData->nfev;
return 0;
}
/*< >*/
/* Subroutine */ int lmder_(
void (*fcn)(v3p_netlib_integer*,
v3p_netlib_integer*,
v3p_netlib_doublereal*,
v3p_netlib_doublereal*,
v3p_netlib_doublereal*,
v3p_netlib_integer*,
v3p_netlib_integer*,
void*),
integer *m, integer *n, doublereal *x,
doublereal *fvec, doublereal *fjac, integer *ldfjac, doublereal *ftol,
doublereal *xtol, doublereal *gtol, integer *maxfev, doublereal *
diag, integer *mode, doublereal *factor, integer *nprint, integer *
info, integer *nfev, integer *njev, integer *ipvt, doublereal *qtf,
doublereal *wa1, doublereal *wa2, doublereal *wa3, doublereal *wa4,
void* userdata)
{
/* Initialized data */
static doublereal one = 1.; /* constant */
static doublereal p1 = .1; /* constant */
static doublereal p5 = .5; /* constant */
static doublereal p25 = .25; /* constant */
static doublereal p75 = .75; /* constant */
static doublereal p0001 = 1e-4; /* constant */
static doublereal zero = 0.; /* constant */
/* System generated locals */
integer fjac_dim1, fjac_offset, i__1, i__2;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, l;
doublereal par, sum;
integer iter;
doublereal temp=0, temp1, temp2;
integer iflag;
doublereal delta;
extern /* Subroutine */ int qrfac_(integer *, integer *, doublereal *,
integer *, logical *, integer *, integer *, doublereal *,
doublereal *, doublereal *), lmpar_(integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *);
doublereal ratio;
extern doublereal enorm_(integer *, doublereal *);
doublereal fnorm, gnorm, pnorm, xnorm=0, fnorm1, actred, dirder, epsmch,
prered;
extern doublereal dpmpar_(integer *);
/*< integer m,n,ldfjac,maxfev,mode,nprint,info,nfev,njev >*/
/*< integer ipvt(n) >*/
/*< double precision ftol,xtol,gtol,factor >*/
/*< >*/
/* ********** */
/* subroutine lmder */
/* the purpose of lmder is to minimize the sum of the squares of */
/* m nonlinear functions in n variables by a modification of */
/* the levenberg-marquardt algorithm. the user must provide a */
/* subroutine which calculates the functions and the jacobian. */
/* the subroutine statement is */
/* subroutine lmder(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol, */
/* maxfev,diag,mode,factor,nprint,info,nfev, */
/* njev,ipvt,qtf,wa1,wa2,wa3,wa4) */
/* where */
/* fcn is the name of the user-supplied subroutine which */
/* calculates the functions and the jacobian. fcn must */
/* be declared in an external statement in the user */
/* calling program, and should be written as follows. */
/* subroutine fcn(m,n,x,fvec,fjac,ldfjac,iflag) */
/* integer m,n,ldfjac,iflag */
/* double precision x(n),fvec(m),fjac(ldfjac,n) */
/* ---------- */
/* if iflag = 1 calculate the functions at x and */
/* return this vector in fvec. do not alter fjac. */
/* if iflag = 2 calculate the jacobian at x and */
/* return this matrix in fjac. do not alter fvec. */
/* ---------- */
/* return */
/* end */
/* the value of iflag should not be changed by fcn unless */
/* the user wants to terminate execution of lmder. */
/* in this case set iflag to a negative integer. */
/* m is a positive integer input variable set to the number */
/* of functions. */
/* n is a positive integer input variable set to the number */
/* of variables. n must not exceed m. */
/* x is an array of length n. on input x must contain */
/* an initial estimate of the solution vector. on output x */
/* contains the final estimate of the solution vector. */
/* fvec is an output array of length m which contains */
/* the functions evaluated at the output x. */
/* fjac is an output m by n array. the upper n by n submatrix */
/* of fjac contains an upper triangular matrix r with */
/* diagonal elements of nonincreasing magnitude such that */
/* t t t */
/* p *(jac *jac)*p = r *r, */
/* where p is a permutation matrix and jac is the final */
/* calculated jacobian. column j of p is column ipvt(j) */
/* (see below) of the identity matrix. the lower trapezoidal */
/* part of fjac contains information generated during */
/* the computation of r. */
/* ldfjac is a positive integer input variable not less than m */
/* which specifies the leading dimension of the array fjac. */
/* ftol is a nonnegative input variable. termination */
/* occurs when both the actual and predicted relative */
/* reductions in the sum of squares are at most ftol. */
/* therefore, ftol measures the relative error desired */
/* in the sum of squares. */
/* xtol is a nonnegative input variable. termination */
/* occurs when the relative error between two consecutive */
/* iterates is at most xtol. therefore, xtol measures the */
/* relative error desired in the approximate solution. */
/* gtol is a nonnegative input variable. termination */
/* occurs when the cosine of the angle between fvec and */
/* any column of the jacobian is at most gtol in absolute */
/* value. therefore, gtol measures the orthogonality */
/* desired between the function vector and the columns */
/* of the jacobian. */
/* maxfev is a positive integer input variable. termination */
/* occurs when the number of calls to fcn with iflag = 1 */
/* has reached maxfev. */
/* diag is an array of length n. if mode = 1 (see */
/* below), diag is internally set. if mode = 2, diag */
/* must contain positive entries that serve as */
/* multiplicative scale factors for the variables. */
/* mode is an integer input variable. if mode = 1, the */
/* variables will be scaled internally. if mode = 2, */
/* the scaling is specified by the input diag. other */
/* values of mode are equivalent to mode = 1. */
/* factor is a positive input variable used in determining the */
/* initial step bound. this bound is set to the product of */
/* factor and the euclidean norm of diag*x if nonzero, or else */
/* to factor itself. in most cases factor should lie in the */
/* interval (.1,100.).100. is a generally recommended value. */
/* nprint is an integer input variable that enables controlled */
/* printing of iterates if it is positive. in this case, */
/* fcn is called with iflag = 0 at the beginning of the first */
/* iteration and every nprint iterations thereafter and */
/* immediately prior to return, with x, fvec, and fjac */
/* available for printing. fvec and fjac should not be */
/* altered. if nprint is not positive, no special calls */
/* of fcn with iflag = 0 are made. */
/* info is an integer output variable. if the user has */
/* terminated execution, info is set to the (negative) */
/* value of iflag. see description of fcn. otherwise, */
/* info is set as follows. */
/* info = 0 improper input parameters. */
/* info = 1 both actual and predicted relative reductions */
/* in the sum of squares are at most ftol. */
/* info = 2 relative error between two consecutive iterates */
/* is at most xtol. */
/* info = 3 conditions for info = 1 and info = 2 both hold. */
/* info = 4 the cosine of the angle between fvec and any */
/* column of the jacobian is at most gtol in */
/* absolute value. */
/* info = 5 number of calls to fcn with iflag = 1 has */
/* reached maxfev. */
/* info = 6 ftol is too small. no further reduction in */
/* the sum of squares is possible. */
/* info = 7 xtol is too small. no further improvement in */
/* the approximate solution x is possible. */
/* info = 8 gtol is too small. fvec is orthogonal to the */
/* columns of the jacobian to machine precision. */
/* nfev is an integer output variable set to the number of */
/* calls to fcn with iflag = 1. */
/* njev is an integer output variable set to the number of */
/* calls to fcn with iflag = 2. */
/* ipvt is an integer output array of length n. ipvt */
/* defines a permutation matrix p such that jac*p = q*r, */
/* where jac is the final calculated jacobian, q is */
/* orthogonal (not stored), and r is upper triangular */
/* with diagonal elements of nonincreasing magnitude. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* qtf is an output array of length n which contains */
/* the first n elements of the vector (q transpose)*fvec. */
/* wa1, wa2, and wa3 are work arrays of length n. */
/* wa4 is a work array of length m. */
/* subprograms called */
/* user-supplied ...... fcn */
/* minpack-supplied ... dpmpar,enorm,lmpar,qrfac */
/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/*< integer i,iflag,iter,j,l >*/
/*< >*/
/*< double precision dpmpar,enorm >*/
/*< >*/
/* Parameter adjustments */
--wa4;
--fvec;
--wa3;
--wa2;
--wa1;
--qtf;
--ipvt;
--diag;
--x;
fjac_dim1 = *ldfjac;
fjac_offset = 1 + fjac_dim1;
fjac -= fjac_offset;
/* Function Body */
/* epsmch is the machine precision. */
/*< epsmch = dpmpar(1) >*/
epsmch = dpmpar_(&c__1);
/*< info = 0 >*/
*info = 0;
/*< iflag = 0 >*/
iflag = 0;
/*< nfev = 0 >*/
*nfev = 0;
/*< njev = 0 >*/
*njev = 0;
/* check the input parameters for errors. */
/*< >*/
if (*n <= 0 || *m < *n || *ldfjac < *m || *ftol < zero || *xtol < zero ||
*gtol < zero || *maxfev <= 0 || *factor <= zero) {
goto L300;
}
/*< if (mode .ne. 2) go to 20 >*/
if (*mode != 2) {
goto L20;
}
/*< do 10 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< if (diag(j) .le. zero) go to 300 >*/
if (diag[j] <= zero) {
goto L300;
}
/*< 10 continue >*/
/* L10: */
}
/*< 20 continue >*/
L20:
/* evaluate the function at the starting point */
/* and calculate its norm. */
/*< iflag = 1 >*/
iflag = 1;
/*< call fcn(m,n,x,fvec,fjac,ldfjac,iflag) >*/
(*fcn)(m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, &iflag,
userdata);
/*< nfev = 1 >*/
*nfev = 1;
/*< if (iflag .lt. 0) go to 300 >*/
if (iflag < 0) {
goto L300;
}
/*< fnorm = enorm(m,fvec) >*/
fnorm = enorm_(m, &fvec[1]);
/* initialize levenberg-marquardt parameter and iteration counter. */
/*< par = zero >*/
par = zero;
/*< iter = 1 >*/
iter = 1;
/* beginning of the outer loop. */
/*< 30 continue >*/
L30:
/* calculate the jacobian matrix. */
/*< iflag = 2 >*/
iflag = 2;
/*< call fcn(m,n,x,fvec,fjac,ldfjac,iflag) >*/
(*fcn)(m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, &iflag,
userdata);
/*< njev = njev + 1 >*/
++(*njev);
/*< if (iflag .lt. 0) go to 300 >*/
if (iflag < 0) {
goto L300;
}
/* if requested, call fcn to enable printing of iterates. */
/*< if (nprint .le. 0) go to 40 >*/
if (*nprint <= 0) {
goto L40;
}
/*< iflag = 0 >*/
iflag = 0;
/*< >*/
if ((iter - 1) % *nprint == 0) {
(*fcn)(m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, &iflag,
userdata);
}
/*< if (iflag .lt. 0) go to 300 >*/
if (iflag < 0) {
goto L300;
}
/*< 40 continue >*/
L40:
/* compute the qr factorization of the jacobian. */
/*< call qrfac(m,n,fjac,ldfjac,.true.,ipvt,n,wa1,wa2,wa3) >*/
qrfac_(m, n, &fjac[fjac_offset], ldfjac, &c_true, &ipvt[1], n, &wa1[1], &
wa2[1], &wa3[1]);
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
/*< if (iter .ne. 1) go to 80 >*/
if (iter != 1) {
goto L80;
}
/*< if (mode .eq. 2) go to 60 >*/
if (*mode == 2) {
goto L60;
}
/*< do 50 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< diag(j) = wa2(j) >*/
diag[j] = wa2[j];
/*< if (wa2(j) .eq. zero) diag(j) = one >*/
if (wa2[j] == zero) {
diag[j] = one;
}
/*< 50 continue >*/
/* L50: */
}
/*< 60 continue >*/
L60:
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
/*< do 70 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< wa3(j) = diag(j)*x(j) >*/
wa3[j] = diag[j] * x[j];
/*< 70 continue >*/
/* L70: */
}
/*< xnorm = enorm(n,wa3) >*/
xnorm = enorm_(n, &wa3[1]);
/*< delta = factor*xnorm >*/
delta = *factor * xnorm;
/*< if (delta .eq. zero) delta = factor >*/
if (delta == zero) {
delta = *factor;
}
/*< 80 continue >*/
L80:
/* form (q transpose)*fvec and store the first n components in */
/* qtf. */
/*< do 90 i = 1, m >*/
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< wa4(i) = fvec(i) >*/
wa4[i__] = fvec[i__];
/*< 90 continue >*/
/* L90: */
}
/*< do 130 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< if (fjac(j,j) .eq. zero) go to 120 >*/
if (fjac[j + j * fjac_dim1] == zero) {
goto L120;
}
/*< sum = zero >*/
sum = zero;
/*< do 100 i = j, m >*/
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
/*< sum = sum + fjac(i,j)*wa4(i) >*/
sum += fjac[i__ + j * fjac_dim1] * wa4[i__];
/*< 100 continue >*/
/* L100: */
}
/*< temp = -sum/fjac(j,j) >*/
temp = -sum / fjac[j + j * fjac_dim1];
/*< do 110 i = j, m >*/
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
/*< wa4(i) = wa4(i) + fjac(i,j)*temp >*/
wa4[i__] += fjac[i__ + j * fjac_dim1] * temp;
/*< 110 continue >*/
/* L110: */
}
/*< 120 continue >*/
L120:
/*< fjac(j,j) = wa1(j) >*/
fjac[j + j * fjac_dim1] = wa1[j];
/*< qtf(j) = wa4(j) >*/
qtf[j] = wa4[j];
/*< 130 continue >*/
/* L130: */
}
/* compute the norm of the scaled gradient. */
/*< gnorm = zero >*/
gnorm = zero;
/*< if (fnorm .eq. zero) go to 170 >*/
if (fnorm == zero) {
goto L170;
}
/*< do 160 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< l = ipvt(j) >*/
l = ipvt[j];
/*< if (wa2(l) .eq. zero) go to 150 >*/
if (wa2[l] == zero) {
goto L150;
}
/*< sum = zero >*/
sum = zero;
/*< do 140 i = 1, j >*/
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< sum = sum + fjac(i,j)*(qtf(i)/fnorm) >*/
sum += fjac[i__ + j * fjac_dim1] * (qtf[i__] / fnorm);
/*< 140 continue >*/
/* L140: */
}
/*< gnorm = dmax1(gnorm,dabs(sum/wa2(l))) >*/
/* Computing MAX */
d__2 = gnorm, d__3 = (d__1 = sum / wa2[l], abs(d__1));
gnorm = max(d__2,d__3);
/*< 150 continue >*/
L150:
/*< 160 continue >*/
/* L160: */
;
}
/*< 170 continue >*/
L170:
/* test for convergence of the gradient norm. */
/*< if (gnorm .le. gtol) info = 4 >*/
if (gnorm <= *gtol) {
*info = 4;
}
/*< if (info .ne. 0) go to 300 >*/
if (*info != 0) {
goto L300;
}
/* rescale if necessary. */
/*< if (mode .eq. 2) go to 190 >*/
if (*mode == 2) {
goto L190;
}
/*< do 180 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< diag(j) = dmax1(diag(j),wa2(j)) >*/
/* Computing MAX */
d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2);
/*< 180 continue >*/
/* L180: */
}
/*< 190 continue >*/
L190:
/* beginning of the inner loop. */
/*< 200 continue >*/
L200:
/* determine the levenberg-marquardt parameter. */
/*< >*/
lmpar_(n, &fjac[fjac_offset], ldfjac, &ipvt[1], &diag[1], &qtf[1], &delta,
&par, &wa1[1], &wa2[1], &wa3[1], &wa4[1]);
/* store the direction p and x + p. calculate the norm of p. */
/*< do 210 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< wa1(j) = -wa1(j) >*/
wa1[j] = -wa1[j];
/*< wa2(j) = x(j) + wa1(j) >*/
wa2[j] = x[j] + wa1[j];
/*< wa3(j) = diag(j)*wa1(j) >*/
wa3[j] = diag[j] * wa1[j];
/*< 210 continue >*/
/* L210: */
}
/*< pnorm = enorm(n,wa3) >*/
pnorm = enorm_(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */
/*< if (iter .eq. 1) delta = dmin1(delta,pnorm) >*/
if (iter == 1) {
delta = min(delta,pnorm);
}
/* evaluate the function at x + p and calculate its norm. */
/*< iflag = 1 >*/
iflag = 1;
/*< call fcn(m,n,wa2,wa4,fjac,ldfjac,iflag) >*/
(*fcn)(m, n, &wa2[1], &wa4[1], &fjac[fjac_offset], ldfjac, &iflag,
userdata);
/*< nfev = nfev + 1 >*/
++(*nfev);
/*< if (iflag .lt. 0) go to 300 >*/
if (iflag < 0) {
goto L300;
}
/*< fnorm1 = enorm(m,wa4) >*/
fnorm1 = enorm_(m, &wa4[1]);
/* compute the scaled actual reduction. */
/*< actred = -one >*/
actred = -one;
/*< if (p1*fnorm1 .lt. fnorm) actred = one - (fnorm1/fnorm)**2 >*/
if (p1 * fnorm1 < fnorm) {
/* Computing 2nd power */
d__1 = fnorm1 / fnorm;
actred = one - d__1 * d__1;
}
/* compute the scaled predicted reduction and */
/* the scaled directional derivative. */
/*< do 230 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< wa3(j) = zero >*/
wa3[j] = zero;
/*< l = ipvt(j) >*/
l = ipvt[j];
/*< temp = wa1(l) >*/
temp = wa1[l];
/*< do 220 i = 1, j >*/
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< wa3(i) = wa3(i) + fjac(i,j)*temp >*/
wa3[i__] += fjac[i__ + j * fjac_dim1] * temp;
/*< 220 continue >*/
/* L220: */
}
/*< 230 continue >*/
/* L230: */
}
/*< temp1 = enorm(n,wa3)/fnorm >*/
temp1 = enorm_(n, &wa3[1]) / fnorm;
/*< temp2 = (dsqrt(par)*pnorm)/fnorm >*/
temp2 = sqrt(par) * pnorm / fnorm;
/*< prered = temp1**2 + temp2**2/p5 >*/
/* Computing 2nd power */
d__1 = temp1;
/* Computing 2nd power */
d__2 = temp2;
prered = d__1 * d__1 + d__2 * d__2 / p5;
/*< dirder = -(temp1**2 + temp2**2) >*/
/* Computing 2nd power */
d__1 = temp1;
/* Computing 2nd power */
d__2 = temp2;
dirder = -(d__1 * d__1 + d__2 * d__2);
/* compute the ratio of the actual to the predicted */
/* reduction. */
/*< ratio = zero >*/
ratio = zero;
/*< if (prered .ne. zero) ratio = actred/prered >*/
if (prered != zero) {
ratio = actred / prered;
}
/* update the step bound. */
/*< if (ratio .gt. p25) go to 240 >*/
if (ratio > p25) {
goto L240;
}
/*< if (actred .ge. zero) temp = p5 >*/
if (actred >= zero) {
temp = p5;
}
/*< >*/
if (actred < zero) {
temp = p5 * dirder / (dirder + p5 * actred);
}
/*< if (p1*fnorm1 .ge. fnorm .or. temp .lt. p1) temp = p1 >*/
if (p1 * fnorm1 >= fnorm || temp < p1) {
temp = p1;
}
/*< delta = temp*dmin1(delta,pnorm/p1) >*/
/* Computing MIN */
d__1 = delta, d__2 = pnorm / p1;
delta = temp * min(d__1,d__2);
/*< par = par/temp >*/
par /= temp;
/*< go to 260 >*/
goto L260;
/*< 240 continue >*/
L240:
/*< if (par .ne. zero .and. ratio .lt. p75) go to 250 >*/
if (par != zero && ratio < p75) {
goto L250;
}
/*< delta = pnorm/p5 >*/
delta = pnorm / p5;
/*< par = p5*par >*/
par = p5 * par;
/*< 250 continue >*/
L250:
/*< 260 continue >*/
L260:
/* test for successful iteration. */
/*< if (ratio .lt. p0001) go to 290 >*/
if (ratio < p0001) {
goto L290;
}
/* successful iteration. update x, fvec, and their norms. */
/*< do 270 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< x(j) = wa2(j) >*/
x[j] = wa2[j];
/*< wa2(j) = diag(j)*x(j) >*/
wa2[j] = diag[j] * x[j];
/*< 270 continue >*/
/* L270: */
}
/*< do 280 i = 1, m >*/
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< fvec(i) = wa4(i) >*/
fvec[i__] = wa4[i__];
/*< 280 continue >*/
/* L280: */
}
/*< xnorm = enorm(n,wa2) >*/
xnorm = enorm_(n, &wa2[1]);
/*< fnorm = fnorm1 >*/
fnorm = fnorm1;
/*< iter = iter + 1 >*/
++iter;
/*< 290 continue >*/
L290:
/* tests for convergence. */
/*< >*/
if (abs(actred) <= *ftol && prered <= *ftol && p5 * ratio <= one) {
*info = 1;
}
/*< if (delta .le. xtol*xnorm) info = 2 >*/
if (delta <= *xtol * xnorm) {
*info = 2;
}
/*< >*/
if (abs(actred) <= *ftol && prered <= *ftol && p5 * ratio <= one && *info
== 2) {
*info = 3;
}
/*< if (info .ne. 0) go to 300 >*/
if (*info != 0) {
goto L300;
}
/* tests for termination and stringent tolerances. */
/*< if (nfev .ge. maxfev) info = 5 >*/
if (*nfev >= *maxfev) {
*info = 5;
}
/*< >*/
if (abs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= one) {
*info = 6;
}
/*< if (delta .le. epsmch*xnorm) info = 7 >*/
if (delta <= epsmch * xnorm) {
*info = 7;
}
/*< if (gnorm .le. epsmch) info = 8 >*/
if (gnorm <= epsmch) {
*info = 8;
}
/*< if (info .ne. 0) go to 300 >*/
if (*info != 0) {
goto L300;
}
/* end of the inner loop. repeat if iteration unsuccessful. */
/*< if (ratio .lt. p0001) go to 200 >*/
if (ratio < p0001) {
goto L200;
}
/* end of the outer loop. */
/*< go to 30 >*/
goto L30;
/*< 300 continue >*/
L300:
/* termination, either normal or user imposed. */
/*< if (iflag .lt. 0) info = iflag >*/
if (iflag < 0) {
*info = iflag;
}
/*< iflag = 0 >*/
iflag = 0;
/*< if (nprint .gt. 0) call fcn(m,n,x,fvec,fjac,ldfjac,iflag) >*/
if (*nprint > 0) {
(*fcn)(m, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, &iflag,
userdata);
}
/*< return >*/
return 0;
/* last card of subroutine lmder. */
/*< end >*/
} /* lmder_ */
/* Subroutine */ int _omc_hybrd_(S_fp fcn, integer *n, doublereal *x, doublereal *
fvec, doublereal *xtol, integer *maxfev, integer *ml, integer *mu,
doublereal *epsfcn, doublereal *diag, integer *mode, doublereal *
factor, integer *nprint, integer *info, integer *nfev, doublereal *
fjac, doublereal * fjacobian, integer *ldfjac, doublereal *r__, integer *lr, doublereal *qtf,
doublereal *wa1, doublereal *wa2, doublereal *wa3, doublereal *wa4, void* userdata)
{
/* Initialized data */
static doublereal one = 1.;
static doublereal p1 = .1;
static doublereal p5 = .5;
static doublereal p001 = .001;
static doublereal p0001 = 1e-4;
static doublereal zero = 0.;
/* System generated locals */
integer fjac_dim1, fjac_offset, i__1, i__2;
doublereal d__1, d__2;
/* Local variables */
integer i__, j, l, jm1, iwa[1];
doublereal sum;
logical sing;
integer iter;
doublereal temp;
integer msum, iflag;
doublereal delta;
extern /* Subroutine */ int qrfac_(integer *, integer *, doublereal *,
integer *, logical *, integer *, integer *, doublereal *,
doublereal *, doublereal *);
logical jeval;
integer ncsuc;
doublereal ratio;
extern doublereal enorm_(integer *, doublereal *);
doublereal fnorm;
extern /* Subroutine */ int qform_(integer *, integer *, doublereal *,
integer *, doublereal *), fdjac1_(S_fp, integer *, doublereal *,
doublereal *, doublereal *, integer *, integer *, integer *,
integer *, doublereal *, doublereal *, doublereal *, void *);
doublereal pnorm, xnorm, fnorm1;
extern /* Subroutine */ int r1updt_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, logical *);
integer nslow1, nslow2;
extern /* Subroutine */ int r1mpyq_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *);
integer ncfail;
extern /* Subroutine */ int dogleg_(integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *);
doublereal actred, epsmch, prered;
extern doublereal dpmpar_(integer *);
/* ********** */
/* subroutine hybrd */
/* the purpose of hybrd is to find a zero of a system of */
/* n nonlinear functions in n variables by a modification */
/* of the powell hybrid method. the user must provide a */
/* subroutine which calculates the functions. the jacobian is */
/* then calculated by a forward-difference approximation. */
/* the subroutine statement is */
/* subroutine hybrd(fcn,n,x,fvec,xtol,maxfev,ml,mu,epsfcn, */
/* diag,mode,factor,nprint,info,nfev,fjac,fjac, */
/* ldfjac,r,lr,qtf,wa1,wa2,wa3,wa4, userdata) */
/* where */
/* fcn is the name of the user-supplied subroutine which */
/* calculates the functions. fcn must be declared */
/* in an external statement in the user calling */
/* program, and should be written as follows. */
/* subroutine fcn(n,x,fvec,iflag) */
/* integer n,iflag */
/* double precision x(n),fvec(n) */
/* ---------- */
/* calculate the functions at x and */
/* return this vector in fvec. */
/* --------- */
/* return */
/* end */
/* the value of iflag should not be changed by fcn unless */
/* the user wants to terminate execution of hybrd. */
/* in this case set iflag to a negative integer. */
/* n is a positive integer input variable set to the number */
/* of functions and variables. */
/* x is an array of length n. on input x must contain */
/* an initial estimate of the solution vector. on output x */
/* contains the final estimate of the solution vector. */
/* fvec is an output array of length n which contains */
/* the functions evaluated at the output x. */
/* xtol is a nonnegative input variable. termination */
/* occurs when the relative error between two consecutive */
/* iterates is at most xtol. */
/* maxfev is a positive integer input variable. termination */
/* occurs when the number of calls to fcn is at least maxfev */
/* by the end of an iteration. */
/* ml is a nonnegative integer input variable which specifies */
/* the number of subdiagonals within the band of the */
/* jacobian matrix. if the jacobian is not banded, set */
/* ml to at least n - 1. */
/* mu is a nonnegative integer input variable which specifies */
/* the number of superdiagonals within the band of the */
/* jacobian matrix. if the jacobian is not banded, set */
/* mu to at least n - 1. */
/* epsfcn is an input variable used in determining a suitable */
/* step length for the forward-difference approximation. this */
/* approximation assumes that the relative errors in the */
/* functions are of the order of epsfcn. if epsfcn is less */
/* than the machine precision, it is assumed that the relative */
/* errors in the functions are of the order of the machine */
/* precision. */
/* diag is an array of length n. if mode = 1 (see */
/* below), diag is internally set. if mode = 2, diag */
/* must contain positive entries that serve as */
/* multiplicative scale factors for the variables. */
/* mode is an integer input variable. if mode = 1, the */
/* variables will be scaled internally. if mode = 2, */
/* the scaling is specified by the input diag. other */
/* values of mode are equivalent to mode = 1. */
/* factor is a positive input variable used in determining the */
/* initial step bound. this bound is set to the product of */
/* factor and the euclidean norm of diag*x if nonzero, or else */
/* to factor itself. in most cases factor should lie in the */
/* interval (.1,100.). 100. is a generally recommended value. */
/* nprint is an integer input variable that enables controlled */
/* printing of iterates if it is positive. in this case, */
/* fcn is called with iflag = 0 at the beginning of the first */
/* iteration and every nprint iterations thereafter and */
/* immediately prior to return, with x and fvec available */
/* for printing. if nprint is not positive, no special calls */
/* of fcn with iflag = 0 are made. */
/* info is an integer output variable. if the user has */
/* terminated execution, info is set to the (negative) */
/* value of iflag. see description of fcn. otherwise, */
/* info is set as follows. */
/* info = 0 improper input parameters. */
/* info = 1 relative error between two consecutive iterates */
/* is at most xtol. */
/* info = 2 number of calls to fcn has reached or exceeded */
/* maxfev. */
/* info = 3 xtol is too small. no further improvement in */
/* the approximate solution x is possible. */
/* info = 4 iteration is not making good progress, as */
/* measured by the improvement from the last */
/* five jacobian evaluations. */
/* info = 5 iteration is not making good progress, as */
/* measured by the improvement from the last */
/* ten iterations. */
/* nfev is an integer output variable set to the number of */
/* calls to fcn. */
/* fjac is an output n by n array which contains the */
/* orthogonal matrix q produced by the qr factorization */
/* of the final approximate jacobian. */
/* fjacobian is an output n by n array which contains the */
/* of the final approximate jacobian. */
/* ldfjac is a positive integer input variable not less than n */
/* which specifies the leading dimension of the array fjac. */
/* r is an output array of length lr which contains the */
/* upper triangular matrix produced by the qr factorization */
/* of the final approximate jacobian, stored rowwise. */
/* lr is a positive integer input variable not less than */
/* (n*(n+1))/2. */
/* qtf is an output array of length n which contains */
/* the vector (q transpose)*fvec. */
/* wa1, wa2, wa3, and wa4 are work arrays of length n. */
/* subprograms called */
/* user-supplied ...... fcn */
/* minpack-supplied ... dogleg,dpmpar,enorm,fdjac1, */
/* qform,qrfac,r1mpyq,r1updt */
/* fortran-supplied ... dabs,dmax1,dmin1,min0,mod */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa4;
--wa3;
--wa2;
--wa1;
--qtf;
--diag;
--fvec;
--x;
fjac_dim1 = *ldfjac;
fjac_offset = 1 + fjac_dim1;
fjac -= fjac_offset;
--fjacobian;
--r__;
/* Function Body */
/* epsmch is the machine precision. */
epsmch = dpmpar_(&c__1);
*info = 0;
iflag = 0;
*nfev = 0;
/* check the input parameters for errors. */
if(*n <= 0 || *xtol < zero || *maxfev <= 0 || *ml < 0 || *mu < 0 || *
factor <= zero || *ldfjac < *n || *lr < *n * (*n + 1) / 2) {
goto L300;
}
if(*mode != 2) {
goto L20;
}
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
if(diag[j] <= zero) {
goto L300;
}
/* L10: */
}
L20:
/* evaluate the function at the starting point */
/* and calculate its norm. */
iflag = 1;
(*fcn)(n, &x[1], &fvec[1], &iflag, userdata);
*nfev = 1;
if(iflag < 0) {
goto L300;
}
fnorm = enorm_(n, &fvec[1]);
/* determine the number of calls to fcn needed to compute */
/* the jacobian matrix. */
/* Computing MIN */
i__1 = *ml + *mu + 1;
msum = min(i__1,*n);
/* initialize iteration counter and monitors. */
iter = 1;
ncsuc = 0;
ncfail = 0;
nslow1 = 0;
nslow2 = 0;
/* beginning of the outer loop. */
L30:
jeval = TRUE_;
/* calculate the jacobian matrix. */
iflag = 2;
fdjac1_((S_fp)fcn, n, &x[1], &fvec[1], &fjac[fjac_offset], ldfjac, &iflag,
ml, mu, epsfcn, &wa1[1], &wa2[1], userdata);
*nfev += msum;
/* store the calculate jacobain matrix */
/* added by wbraun for scaling residuals */
{
int l = fjac_offset;
int k = 1;
for(j = 1; j <= *n; ++j){
for(i__ = 1; i__<= *n; ++i__, l++, k++){
fjacobian[k] = fjac[l];
}
}
}
if(iflag < 0) {
goto L300;
}
/* compute the qr factorization of the jacobian. */
qrfac_(n, n, &fjac[fjac_offset], ldfjac, &c_false, iwa, &c__1, &wa1[1], &
wa2[1], &wa3[1]);
/* on the first iteration and if mode is 1, scale according */
/* to the norms of the columns of the initial jacobian. */
if(iter != 1) {
goto L70;
}
if(*mode == 2) {
goto L50;
}
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
diag[j] = wa2[j];
if(wa2[j] == zero) {
diag[j] = one;
}
/* L40: */
}
L50:
/* on the first iteration, calculate the norm of the scaled x */
/* and initialize the step bound delta. */
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
wa3[j] = diag[j] * x[j];
/* L60: */
}
xnorm = enorm_(n, &wa3[1]);
delta = *factor * xnorm;
if(delta == zero) {
delta = *factor;
}
L70:
/* form (q transpose)*fvec and store in qtf. */
i__1 = *n;
for(i__ = 1; i__ <= i__1; ++i__) {
qtf[i__] = fvec[i__];
/* L80: */
}
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
if(fjac[j + j * fjac_dim1] == zero) {
goto L110;
}
sum = zero;
i__2 = *n;
for(i__ = j; i__ <= i__2; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * qtf[i__];
/* L90: */
}
temp = -sum / fjac[j + j * fjac_dim1];
i__2 = *n;
for(i__ = j; i__ <= i__2; ++i__) {
qtf[i__] += fjac[i__ + j * fjac_dim1] * temp;
/* L100: */
}
L110:
/* L120: */
;
}
/* copy the triangular factor of the qr factorization into r. */
sing = FALSE_;
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
l = j;
jm1 = j - 1;
if(jm1 < 1) {
goto L140;
}
i__2 = jm1;
for(i__ = 1; i__ <= i__2; ++i__) {
r__[l] = fjac[i__ + j * fjac_dim1];
l = l + *n - i__;
/* L130: */
}
L140:
r__[l] = wa1[j];
if(wa1[j] == zero) {
sing = TRUE_;
}
/* L150: */
}
/* accumulate the orthogonal factor in fjac. */
qform_(n, n, &fjac[fjac_offset], ldfjac, &wa1[1]);
/* rescale if necessary. */
if(*mode == 2) {
goto L170;
}
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
/* Computing MAX */
d__1 = diag[j], d__2 = wa2[j];
diag[j] = max(d__1,d__2);
/* L160: */
}
L170:
/* beginning of the inner loop. */
L180:
/* if requested, call fcn to enable printing of iterates. */
if(*nprint <= 0) {
goto L190;
}
iflag = 0;
if((iter - 1) % *nprint == 0) {
(*fcn)(n, &x[1], &fvec[1], &iflag, userdata);
}
if(iflag < 0) {
goto L300;
}
L190:
/* determine the direction p. */
dogleg_(n, &r__[1], lr, &diag[1], &qtf[1], &delta, &wa1[1], &wa2[1], &wa3[
1]);
/* store the direction p and x + p. calculate the norm of p. */
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
wa1[j] = -wa1[j];
wa2[j] = x[j] + wa1[j];
wa3[j] = diag[j] * wa1[j];
/* L200: */
}
pnorm = enorm_(n, &wa3[1]);
/* on the first iteration, adjust the initial step bound. */
if(iter == 1) {
delta = min(delta,pnorm);
}
/* evaluate the function at x + p and calculate its norm. */
iflag = 1;
(*fcn)(n, &wa2[1], &wa4[1], &iflag, userdata);
++(*nfev);
/* Scaling Residual vector */
/* added by wbraun */
/*
{
for(i__=1;i__<*n;i__++)
wa4[i__] = diagres[i__] * wa4[i__];
}
*/
if(iflag < 0) {
goto L300;
}
fnorm1 = enorm_(n, &wa4[1]);
/* compute the scaled actual reduction. */
actred = -one;
if(fnorm1 < fnorm) {
/* Computing 2nd power */
d__1 = fnorm1 / fnorm;
actred = one - d__1 * d__1;
}
/* compute the scaled predicted reduction. */
l = 1;
i__1 = *n;
for(i__ = 1; i__ <= i__1; ++i__) {
sum = zero;
i__2 = *n;
for(j = i__; j <= i__2; ++j) {
sum += r__[l] * wa1[j];
++l;
/* L210: */
}
wa3[i__] = qtf[i__] + sum;
/* L220: */
}
temp = enorm_(n, &wa3[1]);
prered = zero;
if(temp < fnorm) {
/* Computing 2nd power */
d__1 = temp / fnorm;
prered = one - d__1 * d__1;
}
/* compute the ratio of the actual to the predicted */
/* reduction. */
ratio = zero;
if(prered > zero) {
ratio = actred / prered;
}
/* update the step bound. */
if(ratio >= p1) {
goto L230;
}
ncsuc = 0;
++ncfail;
delta = p5 * delta;
goto L240;
L230:
ncfail = 0;
++ncsuc;
if(ratio >= p5 || ncsuc > 1) {
/* Computing MAX */
d__1 = delta, d__2 = pnorm / p5;
delta = max(d__1,d__2);
}
if((d__1 = ratio - one, abs(d__1)) <= p1) {
delta = pnorm / p5;
}
L240:
/* test for successful iteration. */
if(ratio < p0001) {
goto L260;
}
/* successful iteration. update x, fvec, and their norms. */
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
x[j] = wa2[j];
wa2[j] = diag[j] * x[j];
fvec[j] = wa4[j];
/* L250: */
}
xnorm = enorm_(n, &wa2[1]);
fnorm = fnorm1;
++iter;
L260:
/* determine the progress of the iteration. */
++nslow1;
if(actred >= p001) {
nslow1 = 0;
}
if(jeval) {
++nslow2;
}
if(actred >= p1) {
nslow2 = 0;
}
/* test for convergence. */
if(delta <= *xtol * xnorm || fnorm == zero) {
*info = 1;
}
if(*info != 0) {
goto L300;
}
/* tests for termination and stringent tolerances. */
if(*nfev >= *maxfev) {
*info = 2;
}
/* Computing MAX */
d__1 = p1 * delta;
if(p1 * max(d__1,pnorm) <= epsmch * xnorm) {
*info = 3;
}
if(nslow2 == 5) {
*info = 4;
}
if(nslow1 == 10) {
*info = 5;
}
if(*info != 0) {
goto L300;
}
/* criterion for recalculating jacobian approximation */
/* by forward differences. */
if(ncfail == 2) {
goto L290;
}
/* calculate the rank one modification to the jacobian */
/* and update qtf if necessary. */
i__1 = *n;
for(j = 1; j <= i__1; ++j) {
sum = zero;
i__2 = *n;
for(i__ = 1; i__ <= i__2; ++i__) {
sum += fjac[i__ + j * fjac_dim1] * wa4[i__];
/* L270: */
}
wa2[j] = (sum - wa3[j]) / pnorm;
wa1[j] = diag[j] * (diag[j] * wa1[j] / pnorm);
if(ratio >= p0001) {
qtf[j] = sum;
}
/* L280: */
}
/* compute the qr factorization of the updated jacobian. */
r1updt_(n, n, &r__[1], lr, &wa1[1], &wa2[1], &wa3[1], &sing);
r1mpyq_(n, n, &fjac[fjac_offset], ldfjac, &wa2[1], &wa3[1]);
r1mpyq_(&c__1, n, &qtf[1], &c__1, &wa2[1], &wa3[1]);
/* end of the inner loop. */
jeval = FALSE_;
goto L180;
L290:
/* end of the outer loop. */
goto L30;
L300:
/* termination, either normal or user imposed. */
if(iflag < 0) {
*info = iflag;
}
iflag = 0;
if(*nprint > 0) {
(*fcn)(n, &x[1], &fvec[1], &iflag, userdata);
}
return 0;
/* last card of subroutine hybrd. */
} /* _omc_hybrd_ */
/*! \fn solve non-linear system with hybrd method
*
* \param [in] [data]
* [sysNumber] index of the corresponing non-linear system
*
* \author wbraun
*/
int solveHybrd(DATA *data, threadData_t *threadData, int sysNumber)
{
NONLINEAR_SYSTEM_DATA* systemData = &(data->simulationInfo->nonlinearSystemData[sysNumber]);
DATA_HYBRD* solverData = (DATA_HYBRD*)systemData->solverData;
/*
* We are given the number of the non-linear system.
* We want to look it up among all equations.
*/
int eqSystemNumber = systemData->equationIndex;
int i, j;
integer iflag = 1;
double xerror, xerror_scaled;
int success = 0;
double local_tol = 1e-12;
double initial_factor = solverData->factor;
int nfunc_evals = 0;
int continuous = 1;
int nonContinuousCase = 0;
int giveUp = 0;
int retries = 0;
int retries2 = 0;
int retries3 = 0;
int assertCalled = 0;
int assertRetries = 0;
int assertMessage = 0;
modelica_boolean* relationsPreBackup;
struct dataAndSys dataAndSysNumber = {data, threadData, sysNumber};
relationsPreBackup = (modelica_boolean*) malloc(data->modelData->nRelations*sizeof(modelica_boolean));
solverData->numberOfFunctionEvaluations = 0;
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V))
{
int indexes[2] = {1,eqSystemNumber};
infoStreamPrintWithEquationIndexes(LOG_NLS_V, 1, indexes, "start solving non-linear system >>%d<< at time %g", eqSystemNumber, data->localData[0]->timeValue);
for(i=0; i<solverData->n; i++)
{
infoStreamPrint(LOG_NLS_V, 1, "%d. %s = %f", i+1, modelInfoGetEquation(&data->modelData->modelDataXml,eqSystemNumber).vars[i], systemData->nlsx[i]);
infoStreamPrint(LOG_NLS_V, 0, " nominal = %f\nold = %f\nextrapolated = %f",
systemData->nominal[i], systemData->nlsxOld[i], systemData->nlsxExtrapolation[i]);
messageClose(LOG_NLS_V);
}
messageClose(LOG_NLS_V);
}
/* set x vector */
if(data->simulationInfo->discreteCall)
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
else
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
for(i=0; i<solverData->n; i++){
solverData->xScalefactors[i] = fmax(fabs(solverData->x[i]), systemData->nominal[i]);
}
/* start solving loop */
while(!giveUp && !success)
{
for(i=0; i<solverData->n; i++)
solverData->xScalefactors[i] = fmax(fabs(solverData->x[i]), systemData->nominal[i]);
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V)) {
printVector(solverData->xScalefactors, &(solverData->n), LOG_NLS_V, "scaling factors x vector");
printVector(solverData->x, &(solverData->n), LOG_NLS_V, "Iteration variable values");
}
/* Scaling x vector */
if(solverData->useXScaling) {
for(i=0; i<solverData->n; i++) {
solverData->x[i] = (1.0/solverData->xScalefactors[i]) * solverData->x[i];
}
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V))
{
printVector(solverData->x, &solverData->n, LOG_NLS_V, "Iteration variable values (scaled)");
}
/* set residual function continuous
*/
if(continuous) {
((DATA*)data)->simulationInfo->solveContinuous = 1;
} else {
((DATA*)data)->simulationInfo->solveContinuous = 0;
}
giveUp = 1;
/* try */
{
int success = 0;
#ifndef OMC_EMCC
MMC_TRY_INTERNAL(simulationJumpBuffer)
#endif
hybrj_(wrapper_fvec_hybrj, &solverData->n, solverData->x,
solverData->fvec, solverData->fjac, &solverData->ldfjac, &solverData->xtol,
&solverData->maxfev, solverData->diag, &solverData->mode, &solverData->factor,
&solverData->nprint, &solverData->info, &solverData->nfev, &solverData->njev, solverData->r__,
&solverData->lr, solverData->qtf, solverData->wa1, solverData->wa2,
solverData->wa3, solverData->wa4, (void*) &dataAndSysNumber);
success = 1;
if(assertCalled)
{
infoStreamPrint(LOG_NLS, 0, "After assertions failed, found a solution for which assertions did not fail.");
/* re-scaling x vector */
for(i=0; i<solverData->n; i++){
if(solverData->useXScaling)
systemData->nlsxOld[i] = solverData->x[i]*solverData->xScalefactors[i];
else
systemData->nlsxOld[i] = solverData->x[i];
}
}
assertRetries = 0;
assertCalled = 0;
success = 1;
#ifndef OMC_EMCC
MMC_CATCH_INTERNAL(simulationJumpBuffer)
#endif
/* catch */
if (!success)
{
if (!assertMessage)
{
if (ACTIVE_WARNING_STREAM(LOG_STDOUT))
{
if(data->simulationInfo->initial)
warningStreamPrint(LOG_STDOUT, 1, "While solving non-linear system an assertion failed during initialization.");
else
warningStreamPrint(LOG_STDOUT, 1, "While solving non-linear system an assertion failed at time %g.", data->localData[0]->timeValue);
warningStreamPrint(LOG_STDOUT, 0, "The non-linear solver tries to solve the problem that could take some time.");
warningStreamPrint(LOG_STDOUT, 0, "It could help to provide better start-values for the iteration variables.");
if (!ACTIVE_STREAM(LOG_NLS))
warningStreamPrint(LOG_STDOUT, 0, "For more information simulate with -lv LOG_NLS");
messageClose(LOG_STDOUT);
}
assertMessage = 1;
}
solverData->info = -1;
xerror_scaled = 1;
xerror = 1;
assertCalled = 1;
}
}
/* set residual function continuous */
if(continuous)
{
((DATA*)data)->simulationInfo->solveContinuous = 0;
}
else
{
((DATA*)data)->simulationInfo->solveContinuous = 1;
}
/* re-scaling x vector */
if(solverData->useXScaling)
for(i=0; i<solverData->n; i++)
solverData->x[i] = solverData->x[i]*solverData->xScalefactors[i];
/* check for proper inputs */
if(solverData->info == 0) {
printErrorEqSyst(IMPROPER_INPUT, modelInfoGetEquation(&data->modelData->modelDataXml, eqSystemNumber),
data->localData[0]->timeValue);
}
if(solverData->info != -1)
{
/* evaluate with discontinuities */
if(data->simulationInfo->discreteCall){
int scaling = solverData->useXScaling;
int success = 0;
if(scaling)
solverData->useXScaling = 0;
((DATA*)data)->simulationInfo->solveContinuous = 0;
/* try */
#ifndef OMC_EMCC
MMC_TRY_INTERNAL(simulationJumpBuffer)
#endif
wrapper_fvec_hybrj(&solverData->n, solverData->x, solverData->fvec, solverData->fjac, &solverData->ldfjac, &iflag, (void*) &dataAndSysNumber);
success = 1;
#ifndef OMC_EMCC
MMC_CATCH_INTERNAL(simulationJumpBuffer)
#endif
/* catch */
if (!success)
{
warningStreamPrint(LOG_STDOUT, 0, "Non-Linear Solver try to handle a problem with a called assert.");
solverData->info = -1;
xerror_scaled = 1;
xerror = 1;
assertCalled = 1;
}
if(scaling)
solverData->useXScaling = 1;
updateRelationsPre(data);
}
}
if(solverData->info != -1)
{
/* scaling residual vector */
{
int l=0;
for(i=0; i<solverData->n; i++){
solverData->resScaling[i] = 1e-16;
for(j=0; j<solverData->n; j++){
solverData->resScaling[i] = (fabs(solverData->fjacobian[l]) > solverData->resScaling[i])
? fabs(solverData->fjacobian[l]) : solverData->resScaling[i];
l++;
}
solverData->fvecScaled[i] = solverData->fvec[i] * (1 / solverData->resScaling[i]);
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V))
{
infoStreamPrint(LOG_NLS_V, 1, "scaling factors for residual vector");
for(i=0; i<solverData->n; i++)
{
infoStreamPrint(LOG_NLS_V, 1, "scaled residual [%d] : %.20e", i, solverData->fvecScaled[i]);
infoStreamPrint(LOG_NLS_V, 0, "scaling factor [%d] : %.20e", i, solverData->resScaling[i]);
messageClose(LOG_NLS_V);
}
messageClose(LOG_NLS_V);
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_JAC))
{
char buffer[4096];
infoStreamPrint(LOG_NLS_JAC, 1, "jacobian matrix [%dx%d]", (int)solverData->n, (int)solverData->n);
for(i=0; i<solverData->n; i++)
{
buffer[0] = 0;
for(j=0; j<solverData->n; j++)
sprintf(buffer, "%s%10g ", buffer, solverData->fjacobian[i*solverData->n+j]);
infoStreamPrint(LOG_NLS_JAC, 0, "%s", buffer);
}
messageClose(LOG_NLS_JAC);
}
/* check for error */
xerror_scaled = enorm_(&solverData->n, solverData->fvecScaled);
xerror = enorm_(&solverData->n, solverData->fvec);
}
}
/* reset non-contunuousCase */
if(nonContinuousCase && xerror > local_tol && xerror_scaled > local_tol)
{
memcpy(data->simulationInfo->relationsPre, relationsPreBackup, sizeof(modelica_boolean)*data->modelData->nRelations);
nonContinuousCase = 0;
}
if(solverData->info < 4 && xerror > local_tol && xerror_scaled > local_tol)
solverData->info = 4;
/* solution found */
if(solverData->info == 1 || xerror <= local_tol || xerror_scaled <= local_tol)
{
int scaling;
success = 1;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS))
{
int indexes[2] = {1,eqSystemNumber};
/* output solution */
infoStreamPrintWithEquationIndexes(LOG_NLS, 1, indexes, "solution for NLS %d at t=%g", eqSystemNumber, data->localData[0]->timeValue);
for(i=0; i<solverData->n; ++i)
{
infoStreamPrint(LOG_NLS, 0, "[%d] %s = %g", i+1, modelInfoGetEquation(&data->modelData->modelDataXml,eqSystemNumber).vars[i], solverData->x[i]);
}
messageClose(LOG_NLS);
}else if (ACTIVE_STREAM(LOG_NLS_V)){
infoStreamPrint(LOG_NLS_V, 1, "system solved");
infoStreamPrint(LOG_NLS_V, 0, "%d retries\n%d restarts", retries, retries2+retries3);
messageClose(LOG_NLS_V);
printStatus(data, solverData, eqSystemNumber, &nfunc_evals, &xerror, &xerror_scaled, LOG_NLS_V);
}
scaling = solverData->useXScaling;
if(scaling)
solverData->useXScaling = 0;
/* take the solution */
memcpy(systemData->nlsx, solverData->x, solverData->n*(sizeof(double)));
/* try */
{
int success = 0;
#ifndef OMC_EMCC
MMC_TRY_INTERNAL(simulationJumpBuffer)
#endif
wrapper_fvec_hybrj(&solverData->n, solverData->x, solverData->fvec, solverData->fjac, &solverData->ldfjac, &iflag, (void*) &dataAndSysNumber);
success = 1;
#ifndef OMC_EMCC
MMC_CATCH_INTERNAL(simulationJumpBuffer)
#endif
/* catch */
if (!success) {
warningStreamPrint(LOG_STDOUT, 0, "Non-Linear Solver try to handle a problem with a called assert.");
solverData->info = 4;
xerror_scaled = 1;
xerror = 1;
assertCalled = 1;
success = 0;
giveUp = 0;
}
}
if(scaling)
solverData->useXScaling = 1;
}
/*! \fn Backtracking
*
* forth damping heuristic:
* Calculate new function h:R^n->R ; h(x) = 1/2 * ||f(x)|| ^2
* g(lambda) = h(x_old + lambda * x_increment)
* find minimum of g with golden ratio method
* tau = golden ratio
*
* compiler flag: -newton = damped_bt
*/
void Backtracking(double* x, int(*f)(int*, double*, double*, void*, int),
double current_fvec_enorm, int* n, double* fvec, DATA_NEWTON* solverData, void* userdata)
{
int i,j;
double enorm_new, enorm_f, lambda, a1, b1, a, b, tau, g1, g2;
double tolerance = 1e-3;
/* saving current function values in f_old */
memcpy(solverData->f_old, fvec, *n*sizeof(double));
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-solverData->x_increment[i];
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
/* calculate new enorm */
enorm_new = enorm_(n,fvec);
/* Backtracking only if full newton step is useless */
if (enorm_new >= current_fvec_enorm)
{
infoStreamPrint(LOG_NLS_V, 0, "Start Backtracking\n enorm_new= %f \t current_fvec_enorm=%f",enorm_new, current_fvec_enorm);
/* h(x) = 1/2 * ||f(x)|| ^2
* g(lambda) = h(x_old + lambda * x_increment)
* find minimum of g with golden ratio method
* tau = golden ratio
* */
a = 0;
b = 1;
tau = 0.61803398875;
a1 = a + (1-tau)*(b-a);
/* g1 = g(a1) = h(x_old - a1 * x_increment) = 1/2 * ||f(x_old- a1 * x_increment)||^2 */
solverData->x_new[i] = x[i]- a1 * solverData->x_increment[i];
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_f= enorm_(n,fvec);
g1 = 0.5 * enorm_f * enorm_f;
b1 = a + tau * (b-a);
/* g2 = g(b1) = h(x_old - b1 * x_increment) = 1/2 * ||f(x_old- b1 * x_increment)||^2 */
solverData->x_new[i] = x[i]- b1 * solverData->x_increment[i];
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_f= enorm_(n,fvec);
g2 = 0.5 * enorm_f * enorm_f;
while ( (b - a) > tolerance)
{
if (g1<g2)
{
b = b1;
b1 = a1;
a1 = a + (1-tau)*(b-a);
g2 = g1;
/* g1 = g(a1) = h(x_old - a1 * x_increment) = 1/2 * ||f(x_old- a1 * x_increment)||^2 */
solverData->x_new[i] = x[i]- a1 * solverData->x_increment[i];
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_f= enorm_(n,fvec);
g1 = 0.5 * enorm_f * enorm_f;
}
else
{
a = a1;
a1 = b1;
b1 = a + tau * (b-a);
g1 = g2;
/* g2 = g(b1) = h(x_old - b1 * x_increment) = 1/2 * ||f(x_old- b1 * x_increment)||^2 */
solverData->x_new[i] = x[i]- b1 * solverData->x_increment[i];
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
enorm_f= enorm_(n,fvec);
g2 = 0.5 * enorm_f * enorm_f;
}
}
lambda = (a+b)/2;
/* print lambda */
infoStreamPrint(LOG_NLS_V, 0, "Backtracking - lambda = %e", lambda);
for (i=0; i<*n; i++)
solverData->x_new[i]=x[i]-lambda*solverData->x_increment[i];
/* calculate new function values */
(*f)(n, solverData->x_new, fvec, userdata, 1);
solverData->nfev++;
}
}
/*< subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) >*/
/* Subroutine */ int qrfac_(integer *m, integer *n, doublereal *a, integer *
lda, logical *pivot, integer *ipvt, integer *lipvt, doublereal *rdiag,
doublereal *acnorm, doublereal *wa)
{
/* Initialized data */
static doublereal one = 1.; /* constant */
static doublereal p05 = .05; /* constant */
static doublereal zero = 0.; /* constant */
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, k, jp1;
doublereal sum;
integer kmax;
doublereal temp;
integer minmn;
extern doublereal enorm_(integer *, doublereal *);
doublereal epsmch;
extern doublereal dpmpar_(integer *);
doublereal ajnorm;
(void)lipvt;
/*< integer m,n,lda,lipvt >*/
/*< integer ipvt(lipvt) >*/
/*< logical pivot >*/
/*< double precision a(lda,n),rdiag(n),acnorm(n),wa(n) >*/
/* ********** */
/* subroutine qrfac */
/* this subroutine uses householder transformations with column */
/* pivoting (optional) to compute a qr factorization of the */
/* m by n matrix a. that is, qrfac determines an orthogonal */
/* matrix q, a permutation matrix p, and an upper trapezoidal */
/* matrix r with diagonal elements of nonincreasing magnitude, */
/* such that a*p = q*r. the householder transformation for */
/* column k, k = 1,2,...,min(m,n), is of the form */
/* t */
/* i - (1/u(k))*u*u */
/* where u has zeros in the first k-1 positions. the form of */
/* this transformation and the method of pivoting first */
/* appeared in the corresponding linpack subroutine. */
/* the subroutine statement is */
/* subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) */
/* where */
/* m is a positive integer input variable set to the number */
/* of rows of a. */
/* n is a positive integer input variable set to the number */
/* of columns of a. */
/* a is an m by n array. on input a contains the matrix for */
/* which the qr factorization is to be computed. on output */
/* the strict upper trapezoidal part of a contains the strict */
/* upper trapezoidal part of r, and the lower trapezoidal */
/* part of a contains a factored form of q (the non-trivial */
/* elements of the u vectors described above). */
/* lda is a positive integer input variable not less than m */
/* which specifies the leading dimension of the array a. */
/* pivot is a logical input variable. if pivot is set true, */
/* then column pivoting is enforced. if pivot is set false, */
/* then no column pivoting is done. */
/* ipvt is an integer output array of length lipvt. ipvt */
/* defines the permutation matrix p such that a*p = q*r. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* if pivot is false, ipvt is not referenced. */
/* lipvt is a positive integer input variable. if pivot is false, */
/* then lipvt may be as small as 1. if pivot is true, then */
/* lipvt must be at least n. */
/* rdiag is an output array of length n which contains the */
/* diagonal elements of r. */
/* acnorm is an output array of length n which contains the */
/* norms of the corresponding columns of the input matrix a. */
/* if this information is not needed, then acnorm can coincide */
/* with rdiag. */
/* wa is a work array of length n. if pivot is false, then wa */
/* can coincide with rdiag. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dmax1,dsqrt,min0 */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/*< integer i,j,jp1,k,kmax,minmn >*/
/*< double precision ajnorm,epsmch,one,p05,sum,temp,zero >*/
/*< double precision dpmpar,enorm >*/
/*< data one,p05,zero /1.0d0,5.0d-2,0.0d0/ >*/
/* Parameter adjustments */
--wa;
--acnorm;
--rdiag;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipvt;
/* Function Body */
/* epsmch is the machine precision. */
/*< epsmch = dpmpar(1) >*/
epsmch = dpmpar_(&c__1);
/* compute the initial column norms and initialize several arrays. */
/*< do 10 j = 1, n >*/
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/*< acnorm(j) = enorm(m,a(1,j)) >*/
acnorm[j] = enorm_(m, &a[j * a_dim1 + 1]);
/*< rdiag(j) = acnorm(j) >*/
rdiag[j] = acnorm[j];
/*< wa(j) = rdiag(j) >*/
wa[j] = rdiag[j];
/*< if (pivot) ipvt(j) = j >*/
if (*pivot) {
ipvt[j] = j;
}
/*< 10 continue >*/
/* L10: */
}
/* reduce a to r with householder transformations. */
/*< minmn = min0(m,n) >*/
minmn = min(*m,*n);
/*< do 110 j = 1, minmn >*/
i__1 = minmn;
for (j = 1; j <= i__1; ++j) {
/*< if (.not.pivot) go to 40 >*/
if (! (*pivot)) {
goto L40;
}
/* bring the column of largest norm into the pivot position. */
/*< kmax = j >*/
kmax = j;
/*< do 20 k = j, n >*/
i__2 = *n;
for (k = j; k <= i__2; ++k) {
/*< if (rdiag(k) .gt. rdiag(kmax)) kmax = k >*/
if (rdiag[k] > rdiag[kmax]) {
kmax = k;
}
/*< 20 continue >*/
/* L20: */
}
/*< if (kmax .eq. j) go to 40 >*/
if (kmax == j) {
goto L40;
}
/*< do 30 i = 1, m >*/
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
/*< temp = a(i,j) >*/
temp = a[i__ + j * a_dim1];
/*< a(i,j) = a(i,kmax) >*/
a[i__ + j * a_dim1] = a[i__ + kmax * a_dim1];
/*< a(i,kmax) = temp >*/
a[i__ + kmax * a_dim1] = temp;
/*< 30 continue >*/
/* L30: */
}
/*< rdiag(kmax) = rdiag(j) >*/
rdiag[kmax] = rdiag[j];
/*< wa(kmax) = wa(j) >*/
wa[kmax] = wa[j];
/*< k = ipvt(j) >*/
k = ipvt[j];
/*< ipvt(j) = ipvt(kmax) >*/
ipvt[j] = ipvt[kmax];
/*< ipvt(kmax) = k >*/
ipvt[kmax] = k;
/*< 40 continue >*/
L40:
/* compute the householder transformation to reduce the */
/* j-th column of a to a multiple of the j-th unit vector. */
/*< ajnorm = enorm(m-j+1,a(j,j)) >*/
i__2 = *m - j + 1;
ajnorm = enorm_(&i__2, &a[j + j * a_dim1]);
/*< if (ajnorm .eq. zero) go to 100 >*/
if (ajnorm == zero) {
goto L100;
}
/*< if (a(j,j) .lt. zero) ajnorm = -ajnorm >*/
if (a[j + j * a_dim1] < zero) {
ajnorm = -ajnorm;
}
/*< do 50 i = j, m >*/
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
/*< a(i,j) = a(i,j)/ajnorm >*/
a[i__ + j * a_dim1] /= ajnorm;
/*< 50 continue >*/
/* L50: */
}
/*< a(j,j) = a(j,j) + one >*/
a[j + j * a_dim1] += one;
/* apply the transformation to the remaining columns */
/* and update the norms. */
/*< jp1 = j + 1 >*/
jp1 = j + 1;
/*< if (n .lt. jp1) go to 100 >*/
if (*n < jp1) {
goto L100;
}
/*< do 90 k = jp1, n >*/
i__2 = *n;
for (k = jp1; k <= i__2; ++k) {
/*< sum = zero >*/
sum = zero;
/*< do 60 i = j, m >*/
i__3 = *m;
for (i__ = j; i__ <= i__3; ++i__) {
/*< sum = sum + a(i,j)*a(i,k) >*/
sum += a[i__ + j * a_dim1] * a[i__ + k * a_dim1];
/*< 60 continue >*/
/* L60: */
}
/*< temp = sum/a(j,j) >*/
temp = sum / a[j + j * a_dim1];
/*< do 70 i = j, m >*/
i__3 = *m;
for (i__ = j; i__ <= i__3; ++i__) {
/*< a(i,k) = a(i,k) - temp*a(i,j) >*/
a[i__ + k * a_dim1] -= temp * a[i__ + j * a_dim1];
/*< 70 continue >*/
/* L70: */
}
/*< if (.not.pivot .or. rdiag(k) .eq. zero) go to 80 >*/
if (! (*pivot) || rdiag[k] == zero) {
goto L80;
}
/*< temp = a(j,k)/rdiag(k) >*/
temp = a[j + k * a_dim1] / rdiag[k];
/*< rdiag(k) = rdiag(k)*dsqrt(dmax1(zero,one-temp**2)) >*/
/* Computing MAX */
/* Computing 2nd power */
d__3 = temp;
d__1 = zero, d__2 = one - d__3 * d__3;
rdiag[k] *= sqrt((max(d__1,d__2)));
/*< if (p05*(rdiag(k)/wa(k))**2 .gt. epsmch) go to 80 >*/
/* Computing 2nd power */
d__1 = rdiag[k] / wa[k];
if (p05 * (d__1 * d__1) > epsmch) {
goto L80;
}
/*< rdiag(k) = enorm(m-j,a(jp1,k)) >*/
i__3 = *m - j;
rdiag[k] = enorm_(&i__3, &a[jp1 + k * a_dim1]);
/*< wa(k) = rdiag(k) >*/
wa[k] = rdiag[k];
/*< 80 continue >*/
L80:
/*< 90 continue >*/
/* L90: */
;
}
/*< 100 continue >*/
L100:
/*< rdiag(j) = -ajnorm >*/
rdiag[j] = -ajnorm;
/*< 110 continue >*/
/* L110: */
}
/*< return >*/
return 0;
/* last card of subroutine qrfac. */
/*< end >*/
} /* qrfac_ */
/*! \fn solve non-linear system with newton method
*
* \param [in] [data]
* [sysNumber] index of the corresponding non-linear system
*
* \author wbraun
*/
int solveNewton(DATA *data, threadData_t *threadData, int sysNumber)
{
NONLINEAR_SYSTEM_DATA* systemData = &(data->simulationInfo->nonlinearSystemData[sysNumber]);
DATA_NEWTON* solverData = (DATA_NEWTON*)(systemData->solverData);
int eqSystemNumber = 0;
int i;
double xerror = -1, xerror_scaled = -1;
int success = 0;
int nfunc_evals = 0;
int continuous = 1;
double local_tol = solverData->ftol;
int giveUp = 0;
int retries = 0;
int retries2 = 0;
int nonContinuousCase = 0;
modelica_boolean *relationsPreBackup = NULL;
int casualTearingSet = data->simulationInfo->nonlinearSystemData[sysNumber].strictTearingFunctionCall != NULL;
DATA_USER* userdata = (DATA_USER*)malloc(sizeof(DATA_USER));
assert(userdata != NULL);
userdata->data = (void*)data;
userdata->threadData = threadData;
userdata->sysNumber = sysNumber;
/*
* We are given the number of the non-linear system.
* We want to look it up among all equations.
*/
eqSystemNumber = systemData->equationIndex;
local_tol = solverData->ftol;
relationsPreBackup = (modelica_boolean*) malloc(data->modelData->nRelations*sizeof(modelica_boolean));
solverData->nfev = 0;
/* try to calculate jacobian only once at the beginning of the iteration */
solverData->calculate_jacobian = 0;
// Initialize lambda variable
if (data->simulationInfo->nonlinearSystemData[sysNumber].homotopySupport) {
solverData->x[solverData->n] = 1.0;
solverData->x_new[solverData->n] = 1.0;
}
else {
solverData->x[solverData->n] = 0.0;
solverData->x_new[solverData->n] = 0.0;
}
/* debug output */
if(ACTIVE_STREAM(LOG_NLS_V))
{
int indexes[2] = {1,eqSystemNumber};
infoStreamPrintWithEquationIndexes(LOG_NLS_V, 1, indexes, "Start solving Non-Linear System %d at time %g with Newton Solver",
eqSystemNumber, data->localData[0]->timeValue);
for(i = 0; i < solverData->n; i++) {
infoStreamPrint(LOG_NLS_V, 1, "x[%d] = %.15e", i, data->simulationInfo->discreteCall ? systemData->nlsx[i] : systemData->nlsxExtrapolation[i]);
infoStreamPrint(LOG_NLS_V, 0, "nominal = %g +++ nlsx = %g +++ old = %g +++ extrapolated = %g",
systemData->nominal[i], systemData->nlsx[i], systemData->nlsxOld[i], systemData->nlsxExtrapolation[i]);
messageClose(LOG_NLS_V);
}
messageClose(LOG_NLS_V);
}
/* set x vector */
if(data->simulationInfo->discreteCall) {
memcpy(solverData->x, systemData->nlsx, solverData->n*(sizeof(double)));
} else {
memcpy(solverData->x, systemData->nlsxExtrapolation, solverData->n*(sizeof(double)));
}
/* start solving loop */
while(!giveUp && !success)
{
giveUp = 1;
solverData->newtonStrategy = data->simulationInfo->newtonStrategy;
_omc_newton(wrapper_fvec_newton, solverData, (void*)userdata);
/* check for proper inputs */
if(solverData->info == 0)
printErrorEqSyst(IMPROPER_INPUT, modelInfoGetEquation(&data->modelData->modelDataXml,eqSystemNumber), data->localData[0]->timeValue);
/* reset non-contunuousCase */
if(nonContinuousCase && xerror > local_tol && xerror_scaled > local_tol)
{
memcpy(data->simulationInfo->relationsPre, relationsPreBackup, sizeof(modelica_boolean)*data->modelData->nRelations);
nonContinuousCase = 0;
}
/* check for error */
xerror_scaled = enorm_(&solverData->n, solverData->fvecScaled);
xerror = enorm_(&solverData->n, solverData->fvec);
/* solution found */
if((xerror <= local_tol || xerror_scaled <= local_tol) && solverData->info > 0)
{
success = 1;
nfunc_evals += solverData->nfev;
if(ACTIVE_STREAM(LOG_NLS_V))
{
infoStreamPrint(LOG_NLS_V, 0, "*** System solved ***\n%d restarts", retries);
infoStreamPrint(LOG_NLS_V, 0, "nfunc = %d +++ error = %.15e +++ error_scaled = %.15e", nfunc_evals, xerror, xerror_scaled);
for(i = 0; i < solverData->n; i++)
infoStreamPrint(LOG_NLS_V, 0, "x[%d] = %.15e\n\tresidual = %e", i, solverData->x[i], solverData->fvec[i]);
}
/* take the solution */
memcpy(systemData->nlsx, solverData->x, solverData->n*(sizeof(double)));
/* Then try with old values (instead of extrapolating )*/
}
// If this is the casual tearing set (only exists for dynamic tearing), break after first try
else if(retries < 1 && casualTearingSet)
{
giveUp = 1;
infoStreamPrint(LOG_NLS_V, 0, "### No Solution for the casual tearing set at the first try! ###");
}
else if(retries < 1)
{
memcpy(solverData->x, systemData->nlsxOld, solverData->n*(sizeof(double)));
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
infoStreamPrint(LOG_NLS_V, 0, " - iteration making no progress:\t try old values.");
/* try to vary the initial values */
/* evaluate jacobian in every step now */
solverData->calculate_jacobian = 1;
}
else if(retries < 2)
{
for(i = 0; i < solverData->n; i++)
solverData->x[i] += systemData->nominal[i] * 0.01;
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
infoStreamPrint(LOG_NLS_V, 0, " - iteration making no progress:\t vary solution point by 1%%.");
/* try to vary the initial values */
}
else if(retries < 3)
{
for(i = 0; i < solverData->n; i++)
solverData->x[i] = systemData->nominal[i];
retries++;
giveUp = 0;
nfunc_evals += solverData->nfev;
infoStreamPrint(LOG_NLS_V, 0, " - iteration making no progress:\t try nominal values as initial solution.");
}
else if(retries < 4 && data->simulationInfo->discreteCall)
{
/* try to solve non-continuous
* work-a-round: since other wise some model does
* stuck in event iteration. e.g.: Modelica.Mechanics.Rotational.Examples.HeatLosses
*/
memcpy(solverData->x, systemData->nlsxOld, solverData->n*(sizeof(double)));
retries++;
/* try to solve a discontinuous system */
continuous = 0;
nonContinuousCase = 1;
memcpy(relationsPreBackup, data->simulationInfo->relationsPre, sizeof(modelica_boolean)*data->modelData->nRelations);
giveUp = 0;
nfunc_evals += solverData->nfev;
infoStreamPrint(LOG_NLS_V, 0, " - iteration making no progress:\t try to solve a discontinuous system.");
}
else if(retries2 < 4)
{
memcpy(solverData->x, systemData->nlsxOld, solverData->n*(sizeof(double)));
/* reduce tolarance */
local_tol = local_tol*10;
retries = 0;
retries2++;
giveUp = 0;
nfunc_evals += solverData->nfev;
infoStreamPrint(LOG_NLS_V, 0, " - iteration making no progress:\t reduce the tolerance slightly to %e.", local_tol);
}
else
{
printErrorEqSyst(ERROR_AT_TIME, modelInfoGetEquation(&data->modelData->modelDataXml,eqSystemNumber), data->localData[0]->timeValue);
if(ACTIVE_STREAM(LOG_NLS_V))
{
infoStreamPrint(LOG_NLS_V, 0, "### No Solution! ###\n after %d restarts", retries);
infoStreamPrint(LOG_NLS_V, 0, "nfunc = %d +++ error = %.15e +++ error_scaled = %.15e", nfunc_evals, xerror, xerror_scaled);
if(ACTIVE_STREAM(LOG_NLS_V))
for(i = 0; i < solverData->n; i++)
infoStreamPrint(LOG_NLS_V, 0, "x[%d] = %.15e\n\tresidual = %e", i, solverData->x[i], solverData->fvec[i]);
}
}
}
if(ACTIVE_STREAM(LOG_NLS_V))
messageClose(LOG_NLS_V);
free(relationsPreBackup);
/* write statistics */
systemData->numberOfFEval = solverData->numberOfFunctionEvaluations;
systemData->numberOfIterations = solverData->numberOfIterations;
return success;
}
/* Subroutine */ int dogleg_(integer *n, doublereal *r__, integer *lr,
doublereal *diag, doublereal *qtb, doublereal *delta, doublereal *x,
doublereal *wa1, doublereal *wa2)
{
/* Initialized data */
static doublereal one = 1.;
static doublereal zero = 0.;
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2, d__3, d__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, j, k, l, jj, jp1;
static doublereal sum, temp, alpha, bnorm;
extern doublereal enorm_(integer *, doublereal *);
static doublereal gnorm, qnorm, epsmch;
extern doublereal dpmpar_(integer *);
static doublereal sgnorm;
/* ********** */
/* subroutine dogleg */
/* given an m by n matrix a, an n by n nonsingular diagonal */
/* matrix d, an m-vector b, and a positive number delta, the */
/* problem is to determine the convex combination x of the */
/* gauss-newton and scaled gradient directions that minimizes */
/* (a*x - b) in the least squares sense, subject to the */
/* restriction that the euclidean norm of d*x be at most delta. */
/* this subroutine completes the solution of the problem */
/* if it is provided with the necessary information from the */
/* qr factorization of a. that is, if a = q*r, where q has */
/* orthogonal columns and r is an upper triangular matrix, */
/* then dogleg expects the full upper triangle of r and */
/* the first n components of (q transpose)*b. */
/* the subroutine statement is */
/* subroutine dogleg(n,r,lr,diag,qtb,delta,x,wa1,wa2) */
/* where */
/* n is a positive integer input variable set to the order of r. */
/* r is an input array of length lr which must contain the upper */
/* triangular matrix r stored by rows. */
/* lr is a positive integer input variable not less than */
/* (n*(n+1))/2. */
/* diag is an input array of length n which must contain the */
/* diagonal elements of the matrix d. */
/* qtb is an input array of length n which must contain the first */
/* n elements of the vector (q transpose)*b. */
/* delta is a positive input variable which specifies an upper */
/* bound on the euclidean norm of d*x. */
/* x is an output array of length n which contains the desired */
/* convex combination of the gauss-newton direction and the */
/* scaled gradient direction. */
/* wa1 and wa2 are work arrays of length n. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
/* Parameter adjustments */
--wa2;
--wa1;
--x;
--qtb;
--diag;
--r__;
/* Function Body */
/* epsmch is the machine precision. */
epsmch = dpmpar_(&c__1);
/* first, calculate the gauss-newton direction. */
jj = *n * (*n + 1) / 2 + 1;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
j = *n - k + 1;
jp1 = j + 1;
jj -= k;
l = jj + 1;
sum = zero;
if (*n < jp1) {
goto L20;
}
i__2 = *n;
for (i__ = jp1; i__ <= i__2; ++i__) {
sum += r__[l] * x[i__];
++l;
/* L10: */
}
L20:
temp = r__[jj];
if (temp != zero) {
goto L40;
}
l = j;
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = temp, d__3 = (d__1 = r__[l], abs(d__1));
temp = max(d__2,d__3);
l = l + *n - i__;
/* L30: */
}
temp = epsmch * temp;
if (temp == zero) {
temp = epsmch;
}
L40:
x[j] = (qtb[j] - sum) / temp;
/* L50: */
}
/* test whether the gauss-newton direction is acceptable. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa1[j] = zero;
wa2[j] = diag[j] * x[j];
/* L60: */
}
qnorm = enorm_(n, &wa2[1]);
if (qnorm <= *delta) {
goto L140;
}
/* the gauss-newton direction is not acceptable. */
/* next, calculate the scaled gradient direction. */
l = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp = qtb[j];
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
wa1[i__] += r__[l] * temp;
++l;
/* L70: */
}
wa1[j] /= diag[j];
/* L80: */
}
/* calculate the norm of the scaled gradient and test for */
/* the special case in which the scaled gradient is zero. */
gnorm = enorm_(n, &wa1[1]);
sgnorm = zero;
alpha = *delta / qnorm;
if (gnorm == zero) {
goto L120;
}
/* calculate the point along the scaled gradient */
/* at which the quadratic is minimized. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
wa1[j] = wa1[j] / gnorm / diag[j];
/* L90: */
}
l = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = zero;
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
sum += r__[l] * wa1[i__];
++l;
/* L100: */
}
wa2[j] = sum;
/* L110: */
}
temp = enorm_(n, &wa2[1]);
sgnorm = gnorm / temp / temp;
/* test whether the scaled gradient direction is acceptable. */
alpha = zero;
if (sgnorm >= *delta) {
goto L120;
}
/* the scaled gradient direction is not acceptable. */
/* finally, calculate the point along the dogleg */
/* at which the quadratic is minimized. */
bnorm = enorm_(n, &qtb[1]);
temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / *delta);
/* Computing 2nd power */
d__1 = sgnorm / *delta;
/* Computing 2nd power */
d__2 = temp - *delta / qnorm;
/* Computing 2nd power */
d__3 = *delta / qnorm;
/* Computing 2nd power */
d__4 = sgnorm / *delta;
temp = temp - *delta / qnorm * (d__1 * d__1) + sqrt(d__2 * d__2 + (one -
d__3 * d__3) * (one - d__4 * d__4));
/* Computing 2nd power */
d__1 = sgnorm / *delta;
alpha = *delta / qnorm * (one - d__1 * d__1) / temp;
L120:
/* form appropriate convex combination of the gauss-newton */
/* direction and the scaled gradient direction. */
temp = (one - alpha) * min(sgnorm,*delta);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
x[j] = temp * wa1[j] + alpha * x[j];
/* L130: */
}
L140:
return 0;
/* last card of subroutine dogleg. */
} /* dogleg_ */
