zqrdc.c

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/* linpack/zqrdc.f -- translated by f2c (version 20050501).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"

/* Table of constant values */

static integer c__1 = 1;
static doublecomplex c_b28 = {1.,0.};

/*<       subroutine zqrdc(x,ldx,n,p,qraux,jpvt,work,job) >*/
/* Subroutine */ int zqrdc_(doublecomplex *x, integer *ldx, integer *n, 
        integer *p, doublecomplex *qraux, integer *jpvt, doublecomplex *work, 
        integer *job)
{
    /* System generated locals */
    integer x_dim1, x_offset, i__1, i__2, i__3, i__4;
    doublereal d__1, d__2, d__3, d__4;
    doublecomplex z__1, z__2, z__3;

    /* Builtin functions */
    double z_abs(doublecomplex *);
    void z_div(doublecomplex *, doublecomplex *, doublecomplex *), z_sqrt(
            doublecomplex *, doublecomplex *);

    /* Local variables */
    integer j, l;
    doublecomplex t;
    integer jj, jp, pl, pu;
    doublereal tt;
    integer lp1, lup;
    logical negj;
    integer maxj;
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
            doublecomplex *, integer *);
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    logical swapj;
    doublecomplex nrmxl;
    extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zaxpy_(integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
    doublereal maxnrm;

/*<       integer ldx,n,p,job >*/
/*<       integer jpvt(1) >*/
/*<       complex*16 x(ldx,1),qraux(1),work(1) >*/

/*     zqrdc uses householder transformations to compute the qr */
/*     factorization of an n by p matrix x.  column pivoting */
/*     based on the 2-norms of the reduced columns may be */
/*     performed at the users option. */

/*     on entry */

/*        x       complex*16(ldx,p), where ldx .ge. n. */
/*                x contains the matrix whose decomposition is to be */
/*                computed. */

/*        ldx     integer. */
/*                ldx is the leading dimension of the array x. */

/*        n       integer. */
/*                n is the number of rows of the matrix x. */

/*        p       integer. */
/*                p is the number of columns of the matrix x. */

/*        jpvt    integer(p). */
/*                jpvt contains integers that control the selection */
/*                of the pivot columns.  the k-th column x(k) of x */
/*                is placed in one of three classes according to the */
/*                value of jpvt(k). */

/*                   if jpvt(k) .gt. 0, then x(k) is an initial */
/*                                      column. */

/*                   if jpvt(k) .eq. 0, then x(k) is a free column. */

/*                   if jpvt(k) .lt. 0, then x(k) is a final column. */

/*                before the decomposition is computed, initial columns */
/*                are moved to the beginning of the array x and final */
/*                columns to the end.  both initial and final columns */
/*                are frozen in place during the computation and only */
/*                free columns are moved.  at the k-th stage of the */
/*                reduction, if x(k) is occupied by a free column */
/*                it is interchanged with the free column of largest */
/*                reduced norm.  jpvt is not referenced if */
/*                job .eq. 0. */

/*        work    complex*16(p). */
/*                work is a work array.  work is not referenced if */
/*                job .eq. 0. */

/*        job     integer. */
/*                job is an integer that initiates column pivoting. */
/*                if job .eq. 0, no pivoting is done. */
/*                if job .ne. 0, pivoting is done. */

/*     on return */

/*        x       x contains in its upper triangle the upper */
/*                triangular matrix r of the qr factorization. */
/*                below its diagonal x contains information from */
/*                which the unitary part of the decomposition */
/*                can be recovered.  note that if pivoting has */
/*                been requested, the decomposition is not that */
/*                of the original matrix x but that of x */
/*                with its columns permuted as described by jpvt. */

/*        qraux   complex*16(p). */
/*                qraux contains further information required to recover */
/*                the unitary part of the decomposition. */

/*        jpvt    jpvt(k) contains the index of the column of the */
/*                original matrix that has been interchanged into */
/*                the k-th column, if pivoting was requested. */

/*     linpack. this version dated 08/14/78 . */
/*     g.w. stewart, university of maryland, argonne national lab. */

/*     zqrdc uses the following functions and subprograms. */

/*     blas zaxpy,zdotc,zscal,zswap,dznrm2 */
/*     fortran dabs,dmax1,cdabs,dcmplx,cdsqrt,min0 */

/*     internal variables */

/*<       integer j,jp,l,lp1,lup,maxj,pl,pu >*/
/*<       double precision maxnrm,dznrm2,tt >*/
/*<       complex*16 zdotc,nrmxl,t >*/
/*<       logical negj,swapj >*/

/*<       complex*16 csign,zdum,zdum1,zdum2 >*/
/*<       double precision cabs1 >*/
/*<       double precision dreal,dimag >*/
/*<       complex*16 zdumr,zdumi >*/
/*<       dreal(zdumr) = zdumr >*/
/*<       dimag(zdumi) = (0.0d0,-1.0d0)*zdumi >*/
/*<       csign(zdum1,zdum2) = cdabs(zdum1)*(zdum2/cdabs(zdum2)) >*/
/*<       cabs1(zdum) = dabs(dreal(zdum)) + dabs(dimag(zdum)) >*/

/*<       pl = 1 >*/
    /* Parameter adjustments */
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    --qraux;
    --jpvt;
    --work;

    /* Function Body */
    pl = 1;
/*<       pu = 0 >*/
    pu = 0;
/*<       if (job .eq. 0) go to 60 >*/
    if (*job == 0) {
        goto L60;
    }

/*        pivoting has been requested.  rearrange the columns */
/*        according to jpvt. */

/*<          do 20 j = 1, p >*/
    i__1 = *p;
    for (j = 1; j <= i__1; ++j) {
/*<             swapj = jpvt(j) .gt. 0 >*/
        swapj = jpvt[j] > 0;
/*<             negj = jpvt(j) .lt. 0 >*/
        negj = jpvt[j] < 0;
/*<             jpvt(j) = j >*/
        jpvt[j] = j;
/*<             if (negj) jpvt(j) = -j >*/
        if (negj) {
            jpvt[j] = -j;
        }
/*<             if (.not.swapj) go to 10 >*/
        if (! swapj) {
            goto L10;
        }
/*<                if (j .ne. pl) call zswap(n,x(1,pl),1,x(1,j),1) >*/
        if (j != pl) {
            zswap_(n, &x[pl * x_dim1 + 1], &c__1, &x[j * x_dim1 + 1], &c__1);
        }
/*<                jpvt(j) = jpvt(pl) >*/
        jpvt[j] = jpvt[pl];
/*<                jpvt(pl) = j >*/
        jpvt[pl] = j;
/*<                pl = pl + 1 >*/
        ++pl;
/*<    10       continue >*/
L10:
/*<    20    continue >*/
/* L20: */
        ;
    }
/*<          pu = p >*/
    pu = *p;
/*<          do 50 jj = 1, p >*/
    i__1 = *p;
    for (jj = 1; jj <= i__1; ++jj) {
/*<             j = p - jj + 1 >*/
        j = *p - jj + 1;
/*<             if (jpvt(j) .ge. 0) go to 40 >*/
        if (jpvt[j] >= 0) {
            goto L40;
        }
/*<                jpvt(j) = -jpvt(j) >*/
        jpvt[j] = -jpvt[j];
/*<                if (j .eq. pu) go to 30 >*/
        if (j == pu) {
            goto L30;
        }
/*<                   call zswap(n,x(1,pu),1,x(1,j),1) >*/
        zswap_(n, &x[pu * x_dim1 + 1], &c__1, &x[j * x_dim1 + 1], &c__1);
/*<                   jp = jpvt(pu) >*/
        jp = jpvt[pu];
/*<                   jpvt(pu) = jpvt(j) >*/
        jpvt[pu] = jpvt[j];
/*<                   jpvt(j) = jp >*/
        jpvt[j] = jp;
/*<    30          continue >*/
L30:
/*<                pu = pu - 1 >*/
        --pu;
/*<    40       continue >*/
L40:
/*<    50    continue >*/
/* L50: */
        ;
    }
/*<    60 continue >*/
L60: