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Diffstat (limited to 'ast/cminpack/lmder.c')
| -rw-r--r-- | ast/cminpack/lmder.c | 526 |
1 files changed, 0 insertions, 526 deletions
diff --git a/ast/cminpack/lmder.c b/ast/cminpack/lmder.c deleted file mode 100644 index 7f57428..0000000 --- a/ast/cminpack/lmder.c +++ /dev/null @@ -1,526 +0,0 @@ -#include "cminpack.h" -#include <math.h> -#include "cminpackP.h" - -__cminpack_attr__ -int __cminpack_func__(lmder)(__cminpack_decl_fcnder_mn__ void *p, int m, int n, real *x, - real *fvec, real *fjac, int ldfjac, real ftol, - real xtol, real gtol, int maxfev, real * - diag, int mode, real factor, int nprint, - int *nfev, int *njev, int *ipvt, real *qtf, - real *wa1, real *wa2, real *wa3, real *wa4) -{ - /* Initialized data */ - -#define p1 .1 -#define p5 .5 -#define p25 .25 -#define p75 .75 -#define p0001 1e-4 - - /* System generated locals */ - real d1, d2; - - /* Local variables */ - int i, j, l; - real par, sum; - int iter; - real temp, temp1, temp2; - int iflag; - real delta = 0.; - real ratio; - real fnorm, gnorm, pnorm, xnorm = 0., fnorm1, actred, dirder, - epsmch, prered; - int info; - -/* ********** */ - -/* 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 */ - -/* ********** */ - -/* epsmch is the machine precision. */ - - epsmch = __cminpack_func__(dpmpar)(1); - - info = 0; - iflag = 0; - *nfev = 0; - *njev = 0; - -/* check the input parameters for errors. */ - - if (n <= 0 || m < n || ldfjac < m || ftol < 0. || xtol < 0. || - gtol < 0. || maxfev <= 0 || factor <= 0.) { - goto TERMINATE; - } - if (mode == 2) { - for (j = 0; j < n; ++j) { - if (diag[j] <= 0.) { - goto TERMINATE; - } - } - } - -/* evaluate the function at the starting point */ -/* and calculate its norm. */ - - iflag = fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 1); - *nfev = 1; - if (iflag < 0) { - goto TERMINATE; - } - fnorm = __cminpack_enorm__(m, fvec); - -/* initialize levenberg-marquardt parameter and iteration counter. */ - - par = 0.; - iter = 1; - -/* beginning of the outer loop. */ - - for (;;) { - -/* calculate the jacobian matrix. */ - - iflag = fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 2); - ++(*njev); - if (iflag < 0) { - goto TERMINATE; - } - -/* if requested, call fcn to enable printing of iterates. */ - - if (nprint > 0) { - iflag = 0; - if ((iter - 1) % nprint == 0) { - iflag = fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 0); - } - if (iflag < 0) { - goto TERMINATE; - } - } - -/* compute the qr factorization of the jacobian. */ - - __cminpack_func__(qrfac)(m, n, fjac, ldfjac, TRUE_, ipvt, n, - 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 (mode != 2) { - for (j = 0; j < n; ++j) { - diag[j] = wa2[j]; - if (wa2[j] == 0.) { - diag[j] = 1.; - } - } - } - -/* on the first iteration, calculate the norm of the scaled x */ -/* and initialize the step bound delta. */ - - for (j = 0; j < n; ++j) { - wa3[j] = diag[j] * x[j]; - } - xnorm = __cminpack_enorm__(n, wa3); - delta = factor * xnorm; - if (delta == 0.) { - delta = factor; - } - } - -/* form (q transpose)*fvec and store the first n components in */ -/* qtf. */ - - for (i = 0; i < m; ++i) { - wa4[i] = fvec[i]; - } - for (j = 0; j < n; ++j) { - if (fjac[j + j * ldfjac] != 0.) { - sum = 0.; - for (i = j; i < m; ++i) { - sum += fjac[i + j * ldfjac] * wa4[i]; - } - temp = -sum / fjac[j + j * ldfjac]; - for (i = j; i < m; ++i) { - wa4[i] += fjac[i + j * ldfjac] * temp; - } - } - fjac[j + j * ldfjac] = wa1[j]; - qtf[j] = wa4[j]; - } - -/* compute the norm of the scaled gradient. */ - - gnorm = 0.; - if (fnorm != 0.) { - for (j = 0; j < n; ++j) { - l = ipvt[j]-1; - if (wa2[l] != 0.) { - sum = 0.; - for (i = 0; i <= j; ++i) { - sum += fjac[i + j * ldfjac] * (qtf[i] / fnorm); - } - /* Computing MAX */ - d1 = fabs(sum / wa2[l]); - gnorm = max(gnorm,d1); - } - } - } - -/* test for convergence of the gradient norm. */ - - if (gnorm <= gtol) { - info = 4; - } - if (info != 0) { - goto TERMINATE; - } - -/* rescale if necessary. */ - - if (mode != 2) { - for (j = 0; j < n; ++j) { - /* Computing MAX */ - d1 = diag[j], d2 = wa2[j]; - diag[j] = max(d1,d2); - } - } - -/* beginning of the inner loop. */ - - do { - -/* determine the levenberg-marquardt parameter. */ - - __cminpack_func__(lmpar)(n, fjac, ldfjac, ipvt, diag, qtf, delta, - &par, wa1, wa2, wa3, wa4); - -/* store the direction p and x + p. calculate the norm of p. */ - - for (j = 0; j < n; ++j) { - wa1[j] = -wa1[j]; - wa2[j] = x[j] + wa1[j]; - wa3[j] = diag[j] * wa1[j]; - } - pnorm = __cminpack_enorm__(n, wa3); - -/* 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 = fcnder_mn(p, m, n, wa2, wa4, fjac, ldfjac, 1); - ++(*nfev); - if (iflag < 0) { - goto TERMINATE; - } - fnorm1 = __cminpack_enorm__(m, wa4); - -/* compute the scaled actual reduction. */ - - actred = -1.; - if (p1 * fnorm1 < fnorm) { - /* Computing 2nd power */ - d1 = fnorm1 / fnorm; - actred = 1. - d1 * d1; - } - -/* compute the scaled predicted reduction and */ -/* the scaled directional derivative. */ - - for (j = 0; j < n; ++j) { - wa3[j] = 0.; - l = ipvt[j]-1; - temp = wa1[l]; - for (i = 0; i <= j; ++i) { - wa3[i] += fjac[i + j * ldfjac] * temp; - } - } - temp1 = __cminpack_enorm__(n, wa3) / fnorm; - temp2 = (sqrt(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 = 0.; - if (prered != 0.) { - ratio = actred / prered; - } - -/* update the step bound. */ - - if (ratio <= p25) { - if (actred >= 0.) { - temp = p5; - } else { - temp = p5 * dirder / (dirder + p5 * actred); - } - if (p1 * fnorm1 >= fnorm || temp < p1) { - temp = p1; - } - /* Computing MIN */ - d1 = pnorm / p1; - delta = temp * min(delta,d1); - par /= temp; - } else { - if (par == 0. || 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 < n; ++j) { - x[j] = wa2[j]; - wa2[j] = diag[j] * x[j]; - } - for (i = 0; i < m; ++i) { - fvec[i] = wa4[i]; - } - xnorm = __cminpack_enorm__(n, wa2); - fnorm = fnorm1; - ++iter; - } - -/* tests for convergence. */ - - if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) { - info = 1; - } - if (delta <= xtol * xnorm) { - info = 2; - } - if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info == 2) { - info = 3; - } - if (info != 0) { - goto TERMINATE; - } - -/* tests for termination and stringent tolerances. */ - - if (*nfev >= maxfev) { - info = 5; - } - if (fabs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= 1.) { - info = 6; - } - if (delta <= epsmch * xnorm) { - info = 7; - } - if (gnorm <= epsmch) { - info = 8; - } - if (info != 0) { - goto TERMINATE; - } - -/* end of the inner loop. repeat if iteration unsuccessful. */ - - } while (ratio < p0001); - -/* end of the outer loop. */ - - } -TERMINATE: - -/* termination, either normal or user imposed. */ - - if (iflag < 0) { - info = iflag; - } - if (nprint > 0) { - fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 0); - } - return info; - -/* last card of subroutine lmder. */ - -} /* lmder_ */ - |