zgtcon.c

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/* zgtcon.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 zgtcon_(char *norm, integer *n, doublecomplex *dl, 
        doublecomplex *d__, doublecomplex *du, doublecomplex *du2, integer *
        ipiv, doublereal *anorm, doublereal *rcond, doublecomplex *work, 
        integer *info)
{
    /* System generated locals */
    integer i__1, i__2;

    /* Local variables */
    integer i__, kase, kase1;
    extern logical lsame_(char *, char *);
    integer isave[3];
    extern /* Subroutine */ int zlacn2_(integer *, doublecomplex *, 
            doublecomplex *, doublereal *, integer *, integer *), xerbla_(
            char *, integer *);
    doublereal ainvnm;
    logical onenrm;
    extern /* Subroutine */ int zgttrs_(char *, integer *, integer *, 
            doublecomplex *, doublecomplex *, doublecomplex *, doublecomplex *
, 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 */
/*  ======= */

/*  ZGTCON estimates the reciprocal of the condition number of a complex */
/*  tridiagonal matrix A using the LU factorization as computed by */
/*  ZGTTRF. */

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

/*  NORM    (input) CHARACTER*1 */
/*          Specifies whether the 1-norm condition number or the */
/*          infinity-norm condition number is required: */
/*          = '1' or 'O':  1-norm; */
/*          = 'I':         Infinity-norm. */

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

/*  DL      (input) COMPLEX*16 array, dimension (N-1) */
/*          The (n-1) multipliers that define the matrix L from the */
/*          LU factorization of A as computed by ZGTTRF. */

/*  D       (input) COMPLEX*16 array, dimension (N) */
/*          The n diagonal elements of the upper triangular matrix U from */
/*          the LU factorization of A. */

/*  DU      (input) COMPLEX*16 array, dimension (N-1) */
/*          The (n-1) elements of the first superdiagonal of U. */

/*  DU2     (input) COMPLEX*16 array, dimension (N-2) */
/*          The (n-2) elements of the second superdiagonal of U. */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          The pivot indices; for 1 <= i <= n, row i of the matrix was */
/*          interchanged with row IPIV(i).  IPIV(i) will always be either */
/*          i or i+1; IPIV(i) = i indicates a row interchange was not */
/*          required. */

/*  ANORM   (input) DOUBLE PRECISION */
/*          If NORM = '1' or 'O', the 1-norm of the original matrix A. */
/*          If NORM = 'I', the infinity-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 arguments. */

    /* Parameter adjustments */
    --work;
    --ipiv;
    --du2;
    --du;
    --d__;
    --dl;

    /* Function Body */
    *info = 0;
    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
    if (! onenrm && ! lsame_(norm, "I")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*anorm < 0.) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGTCON", &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 D(1:N) is non-zero. */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        i__2 = i__;
        if (d__[i__2].r == 0. && d__[i__2].i == 0.) {
            return 0;
        }
/* L10: */
    }

    ainvnm = 0.;
    if (onenrm) {
        kase1 = 1;
    } else {
        kase1 = 2;
    }
    kase = 0;
L20:
    zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
    if (kase != 0) {
        if (kase == kase1) {

/*           Multiply by inv(U)*inv(L). */

            zgttrs_("No transpose", n, &c__1, &dl[1], &d__[1], &du[1], &du2[1]
, &ipiv[1], &work[1], n, info);
        } else {

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

            zgttrs_("Conjugate transpose", n, &c__1, &dl[1], &d__[1], &du[1], 
                    &du2[1], &ipiv[1], &work[1], n, info);
        }
        goto L20;
    }

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

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

    return 0;

/*     End of ZGTCON */

} /* zgtcon_ */