zhecon.c

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/* zhecon.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;

/* Subroutine */ int zhecon_(char *uplo, integer *n, doublecomplex *a, 
        integer *lda, integer *ipiv, doublereal *anorm, doublereal *rcond, 
        doublecomplex *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */
    integer i__, kase;
    extern logical lsame_(char *, char *);
    integer isave[3];
    logical upper;
    extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, 
            doublecomplex *, doublereal *, integer *, integer *), xerbla_(
            char *, integer *);
    doublereal ainvnm;
    extern /* Subroutine */ int zhetrs_(char *, integer *, integer *, 
            doublecomplex *, integer *, integer *, doublecomplex *, integer *, 
             integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. */

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

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

/*  ZHECON estimates the reciprocal of the condition number of a complex */
/*  Hermitian matrix A using the factorization A = U*D*U**H or */
/*  A = L*D*L**H computed by ZHETRF. */

/*  An estimate is obtained for norm(inv(A)), and the reciprocal of the */
/*  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). */

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

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the details of the factorization are stored */
/*          as an upper or lower triangular matrix. */
/*          = 'U':  Upper triangular, form is A = U*D*U**H; */
/*          = 'L':  Lower triangular, form is A = L*D*L**H. */

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

/*  A       (input) COMPLEX*16 array, dimension (LDA,N) */
/*          The block diagonal matrix D and the multipliers used to */
/*          obtain the factor U or L as computed by ZHETRF. */

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

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          Details of the interchanges and the block structure of D */
/*          as determined by ZHETRF. */

/*  ANORM   (input) DOUBLE PRECISION */
/*          The 1-norm of the original matrix A. */

/*  RCOND   (output) DOUBLE PRECISION */
/*          The reciprocal of the condition number of the matrix A, */
/*          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an */
/*          estimate of the 1-norm of inv(A) computed in this routine. */

/*  WORK    (workspace) COMPLEX*16 array, dimension (2*N) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;
    --work;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*n)) {
        *info = -4;
    } else if (*anorm < 0.) {
        *info = -6;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZHECON", &i__1);
        return 0;
    }

/*     Quick return if possible */

    *rcond = 0.;
    if (*n == 0) {
        *rcond = 1.;
        return 0;
    } else if (*anorm <= 0.) {
        return 0;
    }

/*     Check that the diagonal matrix D is nonsingular. */

    if (upper) {

/*        Upper triangular storage: examine D from bottom to top */

        for (i__ = *n; i__ >= 1; --i__) {
            i__1 = i__ + i__ * a_dim1;
            if (ipiv[i__] > 0 && (a[i__1].r == 0. && a[i__1].i == 0.)) {
                return 0;
            }
/* L10: */
        }
    } else {

/*        Lower triangular storage: examine D from top to bottom. */

        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            i__2 = i__ + i__ * a_dim1;
            if (ipiv[i__] > 0 && (a[i__2].r == 0. && a[i__2].i == 0.)) {
                return 0;
            }
/* L20: */
        }
    }

/*     Estimate the 1-norm of the inverse. */

    kase = 0;
L30:
    zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
    if (kase != 0) {

/*        Multiply by inv(L*D*L') or inv(U*D*U'). */

        zhetrs_(uplo, n, &c__1, &a[a_offset], lda, &ipiv[1], &work[1], n, 
                info);
        goto L30;
    }

/*     Compute the estimate of the reciprocal condition number. */

    if (ainvnm != 0.) {
        *rcond = 1. / ainvnm / *anorm;
    }

    return 0;

/*     End of ZHECON */

} /* zhecon_ */