update ast

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_ */
-