zgbcon.c

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/* zgbcon.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 zgbcon_(char *norm, integer *n, integer *kl, integer *ku, 
         doublecomplex *ab, integer *ldab, integer *ipiv, doublereal *anorm, 
        doublereal *rcond, doublecomplex *work, doublereal *rwork, integer *
        info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;

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

    /* Local variables */
    integer j;
    doublecomplex t;
    integer kd, lm, jp, ix, kase, kase1;
    doublereal scale;
    extern logical lsame_(char *, char *);
    integer isave[3];
    extern /* Double Complex */ VOID zdotc_(doublecomplex *, integer *, 
            doublecomplex *, integer *, doublecomplex *, integer *);
    logical lnoti;
    extern /* Subroutine */ int zaxpy_(integer *, doublecomplex *, 
            doublecomplex *, integer *, doublecomplex *, integer *), zlacn2_(
            integer *, doublecomplex *, doublecomplex *, doublereal *, 
            integer *, integer *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal ainvnm;
    extern integer izamax_(integer *, doublecomplex *, integer *);
    logical onenrm;
    extern /* Subroutine */ int zlatbs_(char *, char *, char *, char *, 
            integer *, integer *, doublecomplex *, integer *, doublecomplex *, 
             doublereal *, doublereal *, integer *), zdrscl_(integer *, doublereal *, doublecomplex *, 
            integer *);
    char normin[1];
    doublereal smlnum;


/*  -- 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 */
/*  ======= */

/*  ZGBCON estimates the reciprocal of the condition number of a complex */
/*  general band matrix A, in either the 1-norm or the infinity-norm, */
/*  using the LU factorization computed by ZGBTRF. */

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

/*  KL      (input) INTEGER */
/*          The number of subdiagonals within the band of A.  KL >= 0. */

/*  KU      (input) INTEGER */
/*          The number of superdiagonals within the band of A.  KU >= 0. */

/*  AB      (input) COMPLEX*16 array, dimension (LDAB,N) */
/*          Details of the LU factorization of the band matrix A, as */
/*          computed by ZGBTRF.  U is stored as an upper triangular band */
/*          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and */
/*          the multipliers used during the factorization are stored in */
/*          rows KL+KU+2 to 2*KL+KU+1. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1. */

/*  IPIV    (input) INTEGER array, dimension (N) */
/*          The pivot indices; for 1 <= i <= N, row i of the matrix was */
/*          interchanged with row IPIV(i). */

/*  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/(norm(A) * norm(inv(A))). */

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

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (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 .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    --ipiv;
    --work;
    --rwork;

    /* 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 (*kl < 0) {
        *info = -3;
    } else if (*ku < 0) {
        *info = -4;
    } else if (*ldab < (*kl << 1) + *ku + 1) {
        *info = -6;
    } else if (*anorm < 0.) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZGBCON", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    smlnum = dlamch_("Safe minimum");

/*     Estimate the norm of inv(A). */

    ainvnm = 0.;
    *(unsigned char *)normin = 'N';
    if (onenrm) {
        kase1 = 1;
    } else {
        kase1 = 2;
    }
    kd = *kl + *ku + 1;
    lnoti = *kl > 0;
    kase = 0;
L10:
    zlacn2_(n, &work[*n + 1], &work[1], &ainvnm, &kase, isave);
    if (kase != 0) {
        if (kase == kase1) {

/*           Multiply by inv(L). */

            if (lnoti) {
                i__1 = *n - 1;
                for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
                    i__2 = *kl, i__3 = *n - j;
                    lm = min(i__2,i__3);
                    jp = ipiv[j];
                    i__2 = jp;
                    t.r = work[i__2].r, t.i = work[i__2].i;
                    if (jp != j) {
                        i__2 = jp;
                        i__3 = j;
                        work[i__2].r = work[i__3].r, work[i__2].i = work[i__3]
                                .i;
                        i__2 = j;
                        work[i__2].r = t.r, work[i__2].i = t.i;
                    }
                    z__1.r = -t.r, z__1.i = -t.i;
                    zaxpy_(&lm, &z__1, &ab[kd + 1 + j * ab_dim1], &c__1, &
                            work[j + 1], &c__1);
/* L20: */
                }
            }

/*           Multiply by inv(U). */

            i__1 = *kl + *ku;
            zlatbs_("Upper", "No transpose", "Non-unit", normin, n, &i__1, &
                    ab[ab_offset], ldab, &work[1], &scale, &rwork[1], info);
        } else {

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

            i__1 = *kl + *ku;
            zlatbs_("Upper", "Conjugate transpose", "Non-unit", normin, n, &
                    i__1, &ab[ab_offset], ldab, &work[1], &scale, &rwork[1], 
                    info);

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

            if (lnoti) {
                for (j = *n - 1; j >= 1; --j) {
/* Computing MIN */
                    i__1 = *kl, i__2 = *n - j;
                    lm = min(i__1,i__2);
                    i__1 = j;
                    i__2 = j;
                    zdotc_(&z__2, &lm, &ab[kd + 1 + j * ab_dim1], &c__1, &
                            work[j + 1], &c__1);
                    z__1.r = work[i__2].r - z__2.r, z__1.i = work[i__2].i - 
                            z__2.i;
                    work[i__1].r = z__1.r, work[i__1].i = z__1.i;
                    jp = ipiv[j];
                    if (jp != j) {
                        i__1 = jp;
                        t.r = work[i__1].r, t.i = work[i__1].i;
                        i__1 = jp;
                        i__2 = j;
                        work[i__1].r = work[i__2].r, work[i__1].i = work[i__2]
                                .i;
                        i__1 = j;
                        work[i__1].r = t.r, work[i__1].i = t.i;
                    }
/* L30: */
                }
            }
        }

/*        Divide X by 1/SCALE if doing so will not cause overflow. */

        *(unsigned char *)normin = 'Y';
        if (scale != 1.) {
            ix = izamax_(n, &work[1], &c__1);
            i__1 = ix;
            if (scale < ((d__1 = work[i__1].r, abs(d__1)) + (d__2 = d_imag(&
                    work[ix]), abs(d__2))) * smlnum || scale == 0.) {
                goto L40;
            }
            zdrscl_(n, &scale, &work[1], &c__1);
        }
        goto L10;
    }

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

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

L40:
    return 0;

/*     End of ZGBCON */

} /* zgbcon_ */