zpbt01.c

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/* zpbt01.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 integer c__1 = 1;
static doublereal c_b17 = 1.;

/* Subroutine */ int zpbt01_(char *uplo, integer *n, integer *kd, 
        doublecomplex *a, integer *lda, doublecomplex *afac, integer *ldafac, 
        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;

    /* Builtin functions */
    double d_imag(doublecomplex *);

    /* Local variables */
    integer i__, j, k, kc, ml, mu;
    doublereal akk, eps;
    integer klen;
    extern /* Subroutine */ int zher_(char *, integer *, doublereal *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern logical lsame_(char *, char *);
    doublereal anorm;
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *), zlanhb_(char *, char *, 
            integer *, integer *, doublecomplex *, integer *, doublereal *);
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *);


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

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

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

/*  ZPBT01 reconstructs a Hermitian positive definite band matrix A from */
/*  its L*L' or U'*U factorization and computes the residual */
/*     norm( L*L' - A ) / ( N * norm(A) * EPS ) or */
/*     norm( U'*U - A ) / ( N * norm(A) * EPS ), */
/*  where EPS is the machine epsilon, L' is the conjugate transpose of */
/*  L, and U' is the conjugate transpose of U. */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          Hermitian matrix A is stored: */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

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

/*  KD      (input) INTEGER */
/*          The number of super-diagonals of the matrix A if UPLO = 'U', */
/*          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0. */

/*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*          The original Hermitian band matrix A.  If UPLO = 'U', the */
/*          upper triangular part of A is stored as a band matrix; if */
/*          UPLO = 'L', the lower triangular part of A is stored.  The */
/*          columns of the appropriate triangle are stored in the columns */
/*          of A and the diagonals of the triangle are stored in the rows */
/*          of A.  See ZPBTRF for further details. */

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

/*  AFAC    (input) COMPLEX*16 array, dimension (LDAFAC,N) */
/*          The factored form of the matrix A.  AFAC contains the factor */
/*          L or U from the L*L' or U'*U factorization in band storage */
/*          format, as computed by ZPBTRF. */

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

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

/*  RESID   (output) DOUBLE PRECISION */
/*          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) */
/*          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) */

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


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

/*     Quick exit if 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;
    --rwork;

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

/*     Exit with RESID = 1/EPS if ANORM = 0. */

    eps = dlamch_("Epsilon");
    anorm = zlanhb_("1", uplo, n, kd, &a[a_offset], lda, &rwork[1]);
    if (anorm <= 0.) {
        *resid = 1. / eps;
        return 0;
    }

/*     Check the imaginary parts of the diagonal elements and return with */
/*     an error code if any are nonzero. */

    if (lsame_(uplo, "U")) {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (d_imag(&afac[*kd + 1 + j * afac_dim1]) != 0.) {
                *resid = 1. / eps;
                return 0;
            }
/* L10: */
        }
    } else {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            if (d_imag(&afac[j * afac_dim1 + 1]) != 0.) {
                *resid = 1. / eps;
                return 0;
            }
/* L20: */
        }
    }

/*     Compute the product U'*U, overwriting U. */

    if (lsame_(uplo, "U")) {
        for (k = *n; k >= 1; --k) {
/* Computing MAX */
            i__1 = 1, i__2 = *kd + 2 - k;
            kc = max(i__1,i__2);
            klen = *kd + 1 - kc;

/*           Compute the (K,K) element of the result. */

            i__1 = klen + 1;
            zdotc_(&z__1, &i__1, &afac[kc + k * afac_dim1], &c__1, &afac[kc + 
                    k * afac_dim1], &c__1);
            akk = z__1.r;
            i__1 = *kd + 1 + k * afac_dim1;
            afac[i__1].r = akk, afac[i__1].i = 0.;

/*           Compute the rest of column K. */

            if (klen > 0) {
                i__1 = *ldafac - 1;
                ztrmv_("Upper", "Conjugate", "Non-unit", &klen, &afac[*kd + 1 
                        + (k - klen) * afac_dim1], &i__1, &afac[kc + k * 
                        afac_dim1], &c__1);
            }

/* L30: */
        }

/*     UPLO = 'L':  Compute the product L*L', overwriting L. */

    } else {
        for (k = *n; k >= 1; --k) {
/* Computing MIN */
            i__1 = *kd, i__2 = *n - k;
            klen = min(i__1,i__2);

/*           Add a multiple of column K of the factor L to each of */
/*           columns K+1 through N. */

            if (klen > 0) {
                i__1 = *ldafac - 1;
                zher_("Lower", &klen, &c_b17, &afac[k * afac_dim1 + 2], &c__1, 
                         &afac[(k + 1) * afac_dim1 + 1], &i__1);
            }

/*           Scale column K by the diagonal element. */

            i__1 = k * afac_dim1 + 1;
            akk = afac[i__1].r;
            i__1 = klen + 1;
            zdscal_(&i__1, &akk, &afac[k * afac_dim1 + 1], &c__1);

/* L40: */
        }
    }

/*     Compute the difference  L*L' - A  or  U'*U - A. */

    if (lsame_(uplo, "U")) {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
            i__2 = 1, i__3 = *kd + 2 - j;
            mu = max(i__2,i__3);
            i__2 = *kd + 1;
            for (i__ = mu; 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;
/* L50: */
            }
/* L60: */
        }
    } else {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
            i__2 = *kd + 1, i__3 = *n - j + 1;
            ml = min(i__2,i__3);
            i__2 = ml;
            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;
/* L70: */
            }
/* L80: */
        }
    }

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

    *resid = zlanhb_("1", uplo, n, kd, &afac[afac_offset], ldafac, &rwork[1]);

    *resid = *resid / (doublereal) (*n) / anorm / eps;

    return 0;

/*     End of ZPBT01 */

} /* zpbt01_ */