zget01.c

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/* zget01.f -- translated by f2c (version 20061008).
   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
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;

/* Subroutine */ int zget01_(integer *m, integer *n, doublecomplex *a, 
        integer *lda, doublecomplex *afac, integer *ldafac, integer *ipiv, 
        doublereal *rwork, doublereal *resid)
{
    /* System generated locals */
    integer a_dim1, a_offset, afac_dim1, afac_offset, i__1, i__2, i__3, i__4, 
            i__5;
    doublecomplex z__1, z__2;

    /* Local variables */
    integer i__, j, k;
    doublecomplex t;
    doublereal eps, anorm;
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
            doublecomplex *, integer *), zgemv_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
            integer *, doublecomplex *, doublecomplex *, integer *);
    extern /* Double Complex */ VOID zdotu_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *), zlange_(char *, integer *, 
            integer *, doublecomplex *, integer *, doublereal *);
    extern /* Subroutine */ int zlaswp_(integer *, doublecomplex *, integer *, 
             integer *, integer *, integer *, integer *);


/*  -- LAPACK test routine (version 3.1) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZGET01 reconstructs a matrix A from its L*U factorization and */
/*  computes the residual */
/*     norm(L*U - A) / ( N * norm(A) * EPS ), */
/*  where EPS is the machine epsilon. */

/*  Arguments */
/*  ========== */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix A.  M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix A.  N >= 0. */

/*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*          The original M x N matrix A. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,M). */

/*  AFAC    (input/output) COMPLEX*16 array, dimension (LDAFAC,N) */
/*          The factored form of the matrix A.  AFAC contains the factors */
/*          L and U from the L*U factorization as computed by ZGETRF. */
/*          Overwritten with the reconstructed matrix, and then with the */
/*          difference L*U - A. */

/*  LDAFAC  (input) INTEGER */
/*          The leading dimension of the array AFAC.  LDAFAC >= max(1,M). */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          The pivot indices from ZGETRF. */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (M) */

/*  RESID   (output) DOUBLE PRECISION */
/*          norm(L*U - A) / ( N * norm(A) * EPS ) */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Quick exit if M = 0 or N = 0. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    afac_dim1 = *ldafac;
    afac_offset = 1 + afac_dim1;
    afac -= afac_offset;
    --ipiv;
    --rwork;

    /* Function Body */
    if (*m <= 0 || *n <= 0) {
        *resid = 0.;
        return 0;
    }

/*     Determine EPS and the norm of A. */

    eps = dlamch_("Epsilon");
    anorm = zlange_("1", m, n, &a[a_offset], lda, &rwork[1]);

/*     Compute the product L*U and overwrite AFAC with the result. */
/*     A column at a time of the product is obtained, starting with */
/*     column N. */

    for (k = *n; k >= 1; --k) {
        if (k > *m) {
            ztrmv_("Lower", "No transpose", "Unit", m, &afac[afac_offset], 
                    ldafac, &afac[k * afac_dim1 + 1], &c__1);
        } else {

/*           Compute elements (K+1:M,K) */

            i__1 = k + k * afac_dim1;
            t.r = afac[i__1].r, t.i = afac[i__1].i;
            if (k + 1 <= *m) {
                i__1 = *m - k;
                zscal_(&i__1, &t, &afac[k + 1 + k * afac_dim1], &c__1);
                i__1 = *m - k;
                i__2 = k - 1;
                zgemv_("No transpose", &i__1, &i__2, &c_b1, &afac[k + 1 + 
                        afac_dim1], ldafac, &afac[k * afac_dim1 + 1], &c__1, &
                        c_b1, &afac[k + 1 + k * afac_dim1], &c__1)
                        ;
            }

/*           Compute the (K,K) element */

            i__1 = k + k * afac_dim1;
            i__2 = k - 1;
            zdotu_(&z__2, &i__2, &afac[k + afac_dim1], ldafac, &afac[k * 
                    afac_dim1 + 1], &c__1);
            z__1.r = t.r + z__2.r, z__1.i = t.i + z__2.i;
            afac[i__1].r = z__1.r, afac[i__1].i = z__1.i;

/*           Compute elements (1:K-1,K) */

            i__1 = k - 1;
            ztrmv_("Lower", "No transpose", "Unit", &i__1, &afac[afac_offset], 
                     ldafac, &afac[k * afac_dim1 + 1], &c__1);
        }
/* L10: */
    }
    i__1 = min(*m,*n);
    zlaswp_(n, &afac[afac_offset], ldafac, &c__1, &i__1, &ipiv[1], &c_n1);

/*     Compute the difference  L*U - A  and store in AFAC. */

    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        i__2 = *m;
        for (i__ = 1; i__ <= i__2; ++i__) {
            i__3 = i__ + j * afac_dim1;
            i__4 = i__ + j * afac_dim1;
            i__5 = i__ + j * a_dim1;
            z__1.r = afac[i__4].r - a[i__5].r, z__1.i = afac[i__4].i - a[i__5]
                    .i;
            afac[i__3].r = z__1.r, afac[i__3].i = z__1.i;
/* L20: */
        }
/* L30: */
    }

/*     Compute norm( L*U - A ) / ( N * norm(A) * EPS ) */

    *resid = zlange_("1", m, n, &afac[afac_offset], ldafac, &rwork[1]);

    if (anorm <= 0.) {
        if (*resid != 0.) {
            *resid = 1. / eps;
        }
    } else {
        *resid = *resid / (doublereal) (*n) / anorm / eps;
    }

    return 0;

/*     End of ZGET01 */

} /* zget01_ */