lmder1.c

来自「InsightToolkit-1.4.0(有大量的优化算法程序)」· C语言 代码 · 共 171 行

#include "f2c.h"
#include "netlib.h"

/* Subroutine */ void lmder1_(fcn, m, n, x, fvec, fjac, ldfjac, tol, info, ipvt, wa, lwa)
void (*fcn)(integer*,integer*,doublereal*,doublereal*,doublereal*,integer*,integer*);
integer *m, *n;
doublereal *x, *fvec, *fjac;
integer *ldfjac;
doublereal *tol;
integer *info, *ipvt;
doublereal *wa;
integer *lwa;
{
    /* Initialized data */

    static doublereal factor = 100.;

    /* Local variables */
    static integer mode, nfev, njev;
    static doublereal ftol, gtol, xtol;
    static integer maxfev, nprint;

/*     ********** */

/*     subroutine lmder1 */

/*     the purpose of lmder1 is to minimize the sum of the squares of */
/*     m nonlinear functions in n variables by a modification of the */
/*     levenberg-marquardt algorithm. this is done by using the more */
/*     general least-squares solver lmder. the user must provide a */
/*     subroutine which calculates the functions and the jacobian. */

/*     the subroutine statement is */

/*       subroutine lmder1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info, */
/*                         ipvt,wa,lwa) */

/*     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 lmder1. */
/*         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. */

/*       tol is a nonnegative input variable. termination occurs */
/*         when the algorithm estimates either that the relative */
/*         error in the sum of squares is at most tol or that */
/*         the relative error between x and the solution is at */
/*         most tol. */

/*       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  algorithm estimates that the relative error */
/*                   in the sum of squares is at most tol. */

/*         info = 2  algorithm estimates that the relative error */
/*                   between x and the solution is at most tol. */

/*         info = 3  conditions for info = 1 and info = 2 both hold. */

/*         info = 4  fvec is orthogonal to the columns of the */
/*                   jacobian to machine precision. */

/*         info = 5  number of calls to fcn with iflag = 1 has */
/*                   reached 100*(n+1). */

/*         info = 6  tol is too small. no further reduction in */
/*                   the sum of squares is possible. */

/*         info = 7  tol is too small. no further improvement in */
/*                   the approximate solution x is possible. */

/*       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. */

/*       wa is a work array of length lwa. */

/*       lwa is a positive integer input variable not less than 5*n+m. */

/*     subprograms called */

/*       user-supplied ...... fcn */

/*       minpack-supplied ... lmder */

/*     argonne national laboratory. minpack project. march 1980. */
/*     burton s. garbow, kenneth e. hillstrom, jorge j. more */

/*     ********** */

    *info = 0;

/*     check the input parameters for errors. */

    if (*n <= 0 || *m < *n || *ldfjac < *m || *tol < 0. || *lwa < *n * 5 + *m)
        return;

/*     call lmder. */

    maxfev = (*n + 1) * 100;
    ftol = *tol;
    xtol = *tol;
    gtol = 0.;
    mode = 1;
    nprint = 0;
    lmder_(fcn, m, n, x, fvec, fjac, ldfjac, &ftol, &xtol, &gtol, &maxfev, wa, &mode, &factor, &nprint,
           info, &nfev, &njev, ipvt, &wa[*n], &wa[*n << 1], &wa[*n * 3], &wa[(*n << 2)], &wa[*n * 5]);

#ifdef NUMERICS_DEBUG
    printf("INFO = %d\n", *info);
#endif
    if (*info == 8) {
        *info = 4;
    }

} /* lmder1_ */