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mpfit.c
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/*
* MINPACK-1 Least Squares Fitting Library
*
* Original public domain version by B. Garbow, K. Hillstrom, J. More'
* (Argonne National Laboratory, MINPACK project, March 1980)
* See the file DISCLAIMER for copyright information.
*
* Tranlation to C Language by S. Moshier (moshier.net)
*
* Enhancements and packaging by C. Markwardt
* (comparable to IDL fitting routine MPFIT
* see http://cow.physics.wisc.edu/~craigm/idl/idl.html)
*/
/* Main mpfit library routines (double precision)
$Id: mpfit.c,v 1.20 2010/11/13 08:15:35 craigm Exp $
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include "mpfit.h"
/* Forward declarations of functions in this module */
static int mp_fdjac2(mp_func funct,
int m, int n, int *ifree, int npar, double *x, double *fvec,
double *fjac, int ldfjac, double epsfcn,
double *wa, void *priv, int *nfev,
double *step, double *dstep, int *dside,
int *qulimited, double *ulimit,
int *ddebug, double *ddrtol, double *ddatol);
static void mp_qrfac(int m, int n, double *a, int lda,
int pivot, int *ipvt, int lipvt,
double *rdiag, double *acnorm, double *wa);
static void mp_qrsolv(int n, double *r, int ldr, int *ipvt, double *diag,
double *qtb, double *x, double *sdiag, double *wa);
static void mp_lmpar(int n, double *r, int ldr, int *ipvt, int *ifree, double *diag,
double *qtb, double delta, double *par, double *x,
double *sdiag, double *wa1, double *wa2);
static double mp_enorm(int n, double *x);
static double mp_dmax1(double a, double b);
static double mp_dmin1(double a, double b);
static int mp_min0(int a, int b);
static int mp_covar(int n, double *r, int ldr, int *ipvt, double tol, double *wa);
/* Macro to call user function */
#define mp_call(funct, m, n, x, fvec, dvec, priv) (*(funct))(m,n,x,fvec,dvec,priv)
/* Macro to safely allocate memory */
#define mp_malloc(dest,type,size) \
dest = (type *) malloc( sizeof(type)*size ); \
if (dest == 0) { \
info = MP_ERR_MEMORY; \
goto CLEANUP; \
} else { \
int _k; \
for (_k=0; _k<(size); _k++) dest[_k] = 0; \
}
/*
* **********
*
* subroutine mpfit
*
* the purpose of mpfit 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. the jacobian is
* then calculated by a finite-difference approximation.
*
* mp_funct funct - function to be minimized
* int m - number of data points
* int npar - number of fit parameters
* double *xall - array of n initial parameter values
* upon return, contains adjusted parameter values
* mp_par *pars - array of npar structures specifying constraints;
* or 0 (null pointer) for unconstrained fitting
* [ see README and mpfit.h for definition & use of mp_par]
* mp_config *config - pointer to structure which specifies the
* configuration of mpfit(); or 0 (null pointer)
* if the default configuration is to be used.
* See README and mpfit.h for definition and use
* of config.
* void *private - any private user data which is to be passed directly
* to funct without modification by mpfit().
* mp_result *result - pointer to structure, which upon return, contains
* the results of the fit. The user should zero this
* structure. If any of the array values are to be
* returned, the user should allocate storage for them
* and assign the corresponding pointer in *result.
* Upon return, *result will be updated, and
* any of the non-null arrays will be filled.
*
*
* FORTRAN DOCUMENTATION BELOW
*
*
* the subroutine statement is
*
* subroutine lmdif(fcn,m,n,x,fvec,ftol,xtol,gtol,maxfev,epsfcn,
* diag,mode,factor,nprint,info,nfev,fjac,
* ldfjac,ipvt,qtf,wa1,wa2,wa3,wa4)
*
* 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(m,n,x,fvec,iflag)
* integer m,n,iflag
* double precision x(n),fvec(m)
* ----------
* 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 lmdif.
* 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.
*
* 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 is at least
* maxfev by the end of an iteration.
*
* 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 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 has reached or
* exceeded 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.
*
* 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.
*
* 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,fdjac2,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
*
* ********** */
int mpfit(mp_func funct, int m, int npar,
double *xall, mp_par *pars, mp_config *config, void *private_data,
mp_result *result)
{
mp_config conf;
int i, j, info, iflag, nfree, npegged, iter;
int qanylim = 0, qanypegged = 0;
int ij,jj,l;
double actred,delta,dirder,fnorm,fnorm1,gnorm, orignorm;
double par,pnorm,prered,ratio;
double sum,temp,temp1,temp2,temp3,xnorm, alpha;
static double one = 1.0;
static double p1 = 0.1;
static double p5 = 0.5;
static double p25 = 0.25;
static double p75 = 0.75;
static double p0001 = 1.0e-4;
static double zero = 0.0;
int nfev = 0;
double *step = 0, *dstep = 0, *llim = 0, *ulim = 0;
int *pfixed = 0, *mpside = 0, *ifree = 0, *qllim = 0, *qulim = 0;
int *ddebug = 0;
double *ddrtol = 0, *ddatol = 0;
double *fvec = 0, *qtf = 0;
double *x = 0, *xnew = 0, *fjac = 0, *diag = 0;
double *wa1 = 0, *wa2 = 0, *wa3 = 0, *wa4 = 0;
int *ipvt = 0;
int ldfjac;
/* Default configuration */
conf.ftol = 1e-10;
conf.xtol = 1e-10;
conf.gtol = 1e-10;
conf.stepfactor = 100.0;
conf.nprint = 1;
conf.epsfcn = MP_MACHEP0;
conf.maxiter = 200;
conf.douserscale = 0;
conf.maxfev = 0;
conf.covtol = 1e-14;
conf.nofinitecheck = 0;
if (config) {
/* Transfer any user-specified configurations */
if (config->ftol > 0) conf.ftol = config->ftol;
if (config->xtol > 0) conf.xtol = config->xtol;
if (config->gtol > 0) conf.gtol = config->gtol;
if (config->stepfactor > 0) conf.stepfactor = config->stepfactor;
if (config->nprint >= 0) conf.nprint = config->nprint;
if (config->epsfcn > 0) conf.epsfcn = config->epsfcn;
if (config->maxiter > 0) conf.maxiter = config->maxiter;
if (config->douserscale != 0) conf.douserscale = config->douserscale;
if (config->covtol > 0) conf.covtol = config->covtol;
if (config->nofinitecheck > 0) conf.nofinitecheck = config->nofinitecheck;
conf.maxfev = config->maxfev;
}
info = 0;
iflag = 0;
nfree = 0;
npegged = 0;
if (funct == 0) {
return MP_ERR_FUNC;
}
if ((m <= 0) || (xall == 0)) {
return MP_ERR_NPOINTS;
}
if (npar <= 0) {
return MP_ERR_NFREE;
}
fnorm = -1.0;
fnorm1 = -1.0;
xnorm = -1.0;
delta = 0.0;
/* FIXED parameters? */
mp_malloc(pfixed, int, npar);
if (pars) for (i=0; i<npar; i++) {
pfixed[i] = (pars[i].fixed)?1:0;
}
/* Finite differencing step, absolute and relative, and sidedness of deriv */
mp_malloc(step, double, npar);
mp_malloc(dstep, double, npar);
mp_malloc(mpside, int, npar);
mp_malloc(ddebug, int, npar);
mp_malloc(ddrtol, double, npar);
mp_malloc(ddatol, double, npar);
if (pars) for (i=0; i<npar; i++) {
step[i] = pars[i].step;
dstep[i] = pars[i].relstep;
mpside[i] = pars[i].side;
ddebug[i] = pars[i].deriv_debug;
ddrtol[i] = pars[i].deriv_reltol;
ddatol[i] = pars[i].deriv_abstol;
}
/* Finish up the free parameters */
nfree = 0;
mp_malloc(ifree, int, npar);
for (i=0, j=0; i<npar; i++) {
if (pfixed[i] == 0) {
nfree++;
ifree[j++] = i;
}
}
if (nfree == 0) {
info = MP_ERR_NFREE;
goto CLEANUP;
}
if (pars) {
for (i=0; i<npar; i++) {
if ( (pars[i].limited[0] && (xall[i] < pars[i].limits[0])) ||
(pars[i].limited[1] && (xall[i] > pars[i].limits[1])) ) {
info = MP_ERR_INITBOUNDS;
goto CLEANUP;
}
if ( (pars[i].fixed == 0) && pars[i].limited[0] && pars[i].limited[1] &&
(pars[i].limits[0] >= pars[i].limits[1])) {
info = MP_ERR_BOUNDS;
goto CLEANUP;
}
}
mp_malloc(qulim, int, nfree);
mp_malloc(qllim, int, nfree);
mp_malloc(ulim, double, nfree);
mp_malloc(llim, double, nfree);
for (i=0; i<nfree; i++) {
qllim[i] = pars[ifree[i]].limited[0];
qulim[i] = pars[ifree[i]].limited[1];
llim[i] = pars[ifree[i]].limits[0];
ulim[i] = pars[ifree[i]].limits[1];
if (qllim[i] || qulim[i]) qanylim = 1;
}
}
/* Sanity checking on input configuration */
if ((npar <= 0) || (conf.ftol <= 0) || (conf.xtol <= 0) ||
(conf.gtol <= 0) || (conf.maxiter < 0) ||
(conf.stepfactor <= 0)) {
info = MP_ERR_PARAM;
goto CLEANUP;
}
/* Ensure there are some degrees of freedom */
if (m < nfree) {
info = MP_ERR_DOF;
goto CLEANUP;
}
/* Allocate temporary storage */
mp_malloc(fvec, double, m);
mp_malloc(qtf, double, nfree);
mp_malloc(x, double, nfree);
mp_malloc(xnew, double, npar);
mp_malloc(fjac, double, m*nfree);
ldfjac = m;
mp_malloc(diag, double, npar);
mp_malloc(wa1, double, npar);
mp_malloc(wa2, double, npar);
mp_malloc(wa3, double, npar);
mp_malloc(wa4, double, m);
mp_malloc(ipvt, int, npar);
/* Evaluate user function with initial parameter values */
iflag = mp_call(funct, m, npar, xall, fvec, 0, private_data);
nfev += 1;
if (iflag < 0) {
goto CLEANUP;
}
fnorm = mp_enorm(m, fvec);
orignorm = fnorm*fnorm;
/* Make a new copy */
for (i=0; i<npar; i++) {
xnew[i] = xall[i];
}
/* Transfer free parameters to 'x' */
for (i=0; i<nfree; i++) {
x[i] = xall[ifree[i]];
}
/* Initialize Levelberg-Marquardt parameter and iteration counter */
par = 0.0;
iter = 1;
for (i=0; i<nfree; i++) {
qtf[i] = 0;
}
/* Beginning of the outer loop */
OUTER_LOOP:
for (i=0; i<nfree; i++) {
xnew[ifree[i]] = x[i];
}
/* XXX call iterproc */
/* Calculate the jacobian matrix */
iflag = mp_fdjac2(funct, m, nfree, ifree, npar, xnew, fvec, fjac, ldfjac,
conf.epsfcn, wa4, private_data, &nfev,
step, dstep, mpside, qulim, ulim,
ddebug, ddrtol, ddatol);
if (iflag < 0) {
goto CLEANUP;
}
/* Determine if any of the parameters are pegged at the limits */
qanypegged = 0;
if (qanylim) {
for (j=0; j<nfree; j++) {
int lpegged = (qllim[j] && (x[j] == llim[j]));
int upegged = (qulim[j] && (x[j] == ulim[j]));
sum = 0;
if (lpegged || upegged) {
qanypegged = 1;
ij = j*ldfjac;
for (i=0; i<m; i++, ij++) {
sum += fvec[i] * fjac[ij];
}
}
if (lpegged && (sum > 0)) {
ij = j*ldfjac;
for (i=0; i<m; i++, ij++) fjac[ij] = 0;
}
if (upegged && (sum < 0)) {
ij = j*ldfjac;
for (i=0; i<m; i++, ij++) fjac[ij] = 0;
}
}
}
/* Compute the QR factorization of the jacobian */
mp_qrfac(m,nfree,fjac,ldfjac,1,ipvt,nfree,wa1,wa2,wa3);
/*
* on the first iteration and if mode is 1, scale according
* to the norms of the columns of the initial jacobian.
*/
if (iter == 1) {
if (conf.douserscale == 0) {
for (j=0; j<nfree; j++) {
diag[ifree[j]] = wa2[j];
if (wa2[j] == zero ) {
diag[ifree[j]] = one;
}
}
}
/*
* on the first iteration, calculate the norm of the scaled x
* and initialize the step bound delta.
*/
for (j=0; j<nfree; j++ ) {
wa3[j] = diag[ifree[j]] * x[j];
}
xnorm = mp_enorm(nfree, wa3);
delta = conf.stepfactor*xnorm;
if (delta == zero) delta = conf.stepfactor;
}
/*
* form (q transpose)*fvec and store the first n components in
* qtf.
*/
for (i=0; i<m; i++ ) {
wa4[i] = fvec[i];
}
jj = 0;
for (j=0; j<nfree; j++ ) {
temp3 = fjac[jj];
if (temp3 != zero) {
sum = zero;
ij = jj;
for (i=j; i<m; i++ ) {
sum += fjac[ij] * wa4[i];
ij += 1; /* fjac[i+m*j] */
}
temp = -sum / temp3;
ij = jj;
for (i=j; i<m; i++ ) {
wa4[i] += fjac[ij] * temp;
ij += 1; /* fjac[i+m*j] */
}
}
fjac[jj] = wa1[j];
jj += m+1; /* fjac[j+m*j] */
qtf[j] = wa4[j];
}
/* ( From this point on, only the square matrix, consisting of the
triangle of R, is needed.) */
if (conf.nofinitecheck) {
/* Check for overflow. This should be a cheap test here since FJAC
has been reduced to a (small) square matrix, and the test is
O(N^2). */
int off = 0, nonfinite = 0;
for (j=0; j<nfree; j++) {
for (i=0; i<nfree; i++) {
if (mpfinite(fjac[off+i]) == 0) nonfinite = 1;
}
off += ldfjac;
}
if (nonfinite) {
info = MP_ERR_NAN;
goto CLEANUP;
}
}
/*
* compute the norm of the scaled gradient.
*/
gnorm = zero;
if (fnorm != zero) {
jj = 0;
for (j=0; j<nfree; j++ ) {
l = ipvt[j];
if (wa2[l] != zero) {
sum = zero;
ij = jj;
for (i=0; i<=j; i++ ) {
sum += fjac[ij]*(qtf[i]/fnorm);
ij += 1; /* fjac[i+m*j] */
}
gnorm = mp_dmax1(gnorm,fabs(sum/wa2[l]));
}
jj += m;
}
}
/*
* test for convergence of the gradient norm.
*/
if (gnorm <= conf.gtol) info = MP_OK_DIR;
if (info != 0) goto L300;
if (conf.maxiter == 0) goto L300;
/*
* rescale if necessary.
*/
if (conf.douserscale == 0) {
for (j=0; j<nfree; j++ ) {
diag[ifree[j]] = mp_dmax1(diag[ifree[j]],wa2[j]);
}
}
/*
* beginning of the inner loop.
*/
L200:
/*
* determine the levenberg-marquardt parameter.
*/
mp_lmpar(nfree,fjac,ldfjac,ipvt,ifree,diag,qtf,delta,&par,wa1,wa2,wa3,wa4);
/*
* store the direction p and x + p. calculate the norm of p.
*/
for (j=0; j<nfree; j++ ) {
wa1[j] = -wa1[j];
}
alpha = 1.0;
if (qanylim == 0) {
/* No parameter limits, so just move to new position WA2 */
for (j=0; j<nfree; j++ ) {
wa2[j] = x[j] + wa1[j];
}
} else {
/* Respect the limits. If a step were to go out of bounds, then
* we should take a step in the same direction but shorter distance.
* The step should take us right to the limit in that case.
*/
for (j=0; j<nfree; j++) {
int lpegged = (qllim[j] && (x[j] <= llim[j]));
int upegged = (qulim[j] && (x[j] >= ulim[j]));
int dwa1 = fabs(wa1[j]) > MP_MACHEP0;
if (lpegged && (wa1[j] < 0)) wa1[j] = 0;
if (upegged && (wa1[j] > 0)) wa1[j] = 0;
if (dwa1 && qllim[j] && ((x[j] + wa1[j]) < llim[j])) {
alpha = mp_dmin1(alpha, (llim[j]-x[j])/wa1[j]);
}
if (dwa1 && qulim[j] && ((x[j] + wa1[j]) > ulim[j])) {
alpha = mp_dmin1(alpha, (ulim[j]-x[j])/wa1[j]);
}
}
/* Scale the resulting vector, advance to the next position */
for (j=0; j<nfree; j++) {
double sgnu, sgnl;
double ulim1, llim1;
wa1[j] = wa1[j] * alpha;
wa2[j] = x[j] + wa1[j];
/* Adjust the output values. If the step put us exactly
* on a boundary, make sure it is exact.
*/
sgnu = (ulim[j] >= 0) ? (+1) : (-1);
sgnl = (llim[j] >= 0) ? (+1) : (-1);
ulim1 = ulim[j]*(1-sgnu*MP_MACHEP0) - ((ulim[j] == 0)?(MP_MACHEP0):0);
llim1 = llim[j]*(1+sgnl*MP_MACHEP0) + ((llim[j] == 0)?(MP_MACHEP0):0);
if (qulim[j] && (wa2[j] >= ulim1)) {
wa2[j] = ulim[j];
}
if (qllim[j] && (wa2[j] <= llim1)) {
wa2[j] = llim[j];
}
}
}
for (j=0; j<nfree; j++ ) {
wa3[j] = diag[ifree[j]]*wa1[j];
}
pnorm = mp_enorm(nfree,wa3);
/*
* on the first iteration, adjust the initial step bound.
*/
if (iter == 1) {
delta = mp_dmin1(delta,pnorm);
}
/*
* evaluate the function at x + p and calculate its norm.
*/
for (i=0; i<nfree; i++) {
xnew[ifree[i]] = wa2[i];
}
iflag = mp_call(funct, m, npar, xnew, wa4, 0, private_data);
nfev += 1;
if (iflag < 0) goto L300;
fnorm1 = mp_enorm(m,wa4);
/*
* compute the scaled actual reduction.
*/
actred = -one;
if ((p1*fnorm1) < fnorm) {
temp = fnorm1/fnorm;
actred = one - temp * temp;
}
/*
* compute the scaled predicted reduction and
* the scaled directional derivative.
*/
jj = 0;
for (j=0; j<nfree; j++ ) {
wa3[j] = zero;
l = ipvt[j];
temp = wa1[l];
ij = jj;
for (i=0; i<=j; i++ ) {
wa3[i] += fjac[ij]*temp;
ij += 1; /* fjac[i+m*j] */
}
jj += m;
}
/* Remember, alpha is the fraction of the full LM step actually
* taken
*/
temp1 = mp_enorm(nfree,wa3)*alpha/fnorm;
temp2 = (sqrt(alpha*par)*pnorm)/fnorm;
prered = temp1*temp1 + (temp2*temp2)/p5;
dirder = -(temp1*temp1 + temp2*temp2);
/*
* compute the ratio of the actual to the predicted
* reduction.
*/
ratio = zero;
if (prered != zero) {
ratio = actred/prered;
}
/*
* update the step bound.
*/
if (ratio <= p25) {
if (actred >= zero) {
temp = p5;
} else {
temp = p5*dirder/(dirder + p5*actred);
}
if (((p1*fnorm1) >= fnorm)
|| (temp < p1) ) {
temp = p1;
}
delta = temp*mp_dmin1(delta,pnorm/p1);
par = par/temp;
} else {
if ((par == zero) || (ratio >= p75) ) {
delta = pnorm/p5;
par = p5*par;
}
}
/*
* test for successful iteration.
*/
if (ratio >= p0001) {
/*
* successful iteration. update x, fvec, and their norms.
*/
for (j=0; j<nfree; j++ ) {
x[j] = wa2[j];
wa2[j] = diag[ifree[j]]*x[j];
}
for (i=0; i<m; i++ ) {
fvec[i] = wa4[i];
}
xnorm = mp_enorm(nfree,wa2);
fnorm = fnorm1;
iter += 1;
}
/*
* tests for convergence.
*/
if ((fabs(actred) <= conf.ftol) && (prered <= conf.ftol) &&
(p5*ratio <= one) ) {
info = MP_OK_CHI;
}
if (delta <= conf.xtol*xnorm) {
info = MP_OK_PAR;
}
if ((fabs(actred) <= conf.ftol) && (prered <= conf.ftol) && (p5*ratio <= one)
&& ( info == 2) ) {
info = MP_OK_BOTH;
}
if (info != 0) {
goto L300;
}
/*
* tests for termination and stringent tolerances.
*/
if ((conf.maxfev > 0) && (nfev >= conf.maxfev)) {
/* Too many function evaluations */
info = MP_MAXITER;
}
if (iter >= conf.maxiter) {
/* Too many iterations */
info = MP_MAXITER;
}
if ((fabs(actred) <= MP_MACHEP0) && (prered <= MP_MACHEP0) && (p5*ratio <= one) ) {
info = MP_FTOL;
}
if (delta <= MP_MACHEP0*xnorm) {
info = MP_XTOL;
}
if (gnorm <= MP_MACHEP0) {
info = MP_GTOL;
}
if (info != 0) {
goto L300;
}
/*
* end of the inner loop. repeat if iteration unsuccessful.
*/
if (ratio < p0001) goto L200;
/*
* end of the outer loop.
*/
goto OUTER_LOOP;
L300:
/*
* termination, either normal or user imposed.
*/
if (iflag < 0) {
info = iflag;
}
iflag = 0;
for (i=0; i<nfree; i++) {
xall[ifree[i]] = x[i];
}
if ((conf.nprint > 0) && (info > 0)) {
iflag = mp_call(funct, m, npar, xall, fvec, 0, private_data);
nfev += 1;
}
/* Compute number of pegged parameters */
npegged = 0;
if (pars) for (i=0; i<npar; i++) {
if ((pars[i].limited[0] && (pars[i].limits[0] == xall[i])) ||
(pars[i].limited[1] && (pars[i].limits[1] == xall[i]))) {
npegged ++;
}
}
/* Compute and return the covariance matrix and/or parameter errors */
if (result && (result->covar || result->xerror)) {
mp_covar(nfree, fjac, ldfjac, ipvt, conf.covtol, wa2);
if (result->covar) {
/* Zero the destination covariance array */
for (j=0; j<(npar*npar); j++) result->covar[j] = 0;
/* Transfer the covariance array */
for (j=0; j<nfree; j++) {
for (i=0; i<nfree; i++) {
result->covar[ifree[j]*npar+ifree[i]] = fjac[j*ldfjac+i];
}
}
}
if (result->xerror) {
for (j=0; j<npar; j++) result->xerror[j] = 0;
for (j=0; j<nfree; j++) {
double cc = fjac[j*ldfjac+j];
if (cc > 0) result->xerror[ifree[j]] = sqrt(cc);
}
}
}
if (result) {
strcpy(result->version, MPFIT_VERSION);
result->bestnorm = mp_dmax1(fnorm,fnorm1);
result->bestnorm *= result->bestnorm;
result->orignorm = orignorm;
result->status = info;
result->niter = iter;
result->nfev = nfev;
result->npar = npar;
result->nfree = nfree;
result->npegged = npegged;
result->nfunc = m;
/* Copy residuals if requested */
if (result->resid) {
for (j=0; j<m; j++) result->resid[j] = fvec[j];
}
}
CLEANUP:
if (fvec) free(fvec);
if (qtf) free(qtf);
if (x) free(x);
if (xnew) free(xnew);
if (fjac) free(fjac);
if (diag) free(diag);
if (wa1) free(wa1);
if (wa2) free(wa2);
if (wa3) free(wa3);
if (wa4) free(wa4);
if (ipvt) free(ipvt);
if (pfixed) free(pfixed);
if (step) free(step);
if (dstep) free(dstep);
if (mpside) free(mpside);
if (ddebug) free(ddebug);
if (ddrtol) free(ddrtol);
if (ddatol) free(ddatol);
if (ifree) free(ifree);
if (qllim) free(qllim);
if (qulim) free(qulim);
if (llim) free(llim);
if (ulim) free(ulim);
return info;
}
/************************fdjac2.c*************************/
static
int mp_fdjac2(mp_func funct,
int m, int n, int *ifree, int npar, double *x, double *fvec,
double *fjac, int ldfjac, double epsfcn,
double *wa, void *priv, int *nfev,
double *step, double *dstep, int *dside,
int *qulimited, double *ulimit,
int *ddebug, double *ddrtol, double *ddatol)
{
/*
* **********
*
* subroutine fdjac2
*
* this subroutine computes a forward-difference approximation
* to the m by n jacobian matrix associated with a specified
* problem of m functions in n variables.
*
* the subroutine statement is
*
* subroutine fdjac2(fcn,m,n,x,fvec,fjac,ldfjac,iflag,epsfcn,wa)
*
* where
*
* fcn is the name of the user-supplied subroutine which