dpbcon.c

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/* dpbcon.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 dpbcon_(char *uplo, integer *n, integer *kd, doublereal *
        ab, integer *ldab, doublereal *anorm, doublereal *rcond, doublereal *
        work, integer *iwork, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1;
    doublereal d__1;

    /* Local variables */
    integer ix, kase;
    doublereal scale;
    extern logical lsame_(char *, char *);
    integer isave[3];
    extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, 
            integer *);
    logical upper;
    extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *, 
             integer *, doublereal *, integer *, integer *);
    extern doublereal dlamch_(char *);
    doublereal scalel;
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *, 
            integer *, integer *, doublereal *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *);
    doublereal scaleu;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal ainvnm;
    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 DLACN2 in place of DLACON, 5 Feb 03, SJH. */

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

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

/*  DPBCON estimates the reciprocal of the condition number (in the */
/*  1-norm) of a real symmetric positive definite band matrix using the */
/*  Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF. */

/*  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 */
/*          = 'U':  Upper triangular factor stored in AB; */
/*          = 'L':  Lower triangular factor stored in AB. */

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

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

/*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          The triangular factor U or L from the Cholesky factorization */
/*          A = U**T*U or A = L*L**T of the band matrix A, stored in the */
/*          first KD+1 rows of the array.  The j-th column of U or L is */
/*          stored in the j-th column of the array AB as follows: */
/*          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd). */

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

/*  ANORM   (input) DOUBLE PRECISION */
/*          The 1-norm (or infinity-norm) of the symmetric band 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) DOUBLE PRECISION array, dimension (3*N) */

/*  IWORK   (workspace) INTEGER 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 .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

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

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*kd < 0) {
        *info = -3;
    } else if (*ldab < *kd + 1) {
        *info = -5;
    } else if (*anorm < 0.) {
        *info = -6;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DPBCON", &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 1-norm of the inverse. */

    kase = 0;
    *(unsigned char *)normin = 'N';
L10:
    dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
    if (kase != 0) {
        if (upper) {

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

            dlatbs_("Upper", "Transpose", "Non-unit", normin, n, kd, &ab[
                    ab_offset], ldab, &work[1], &scalel, &work[(*n << 1) + 1], 
                     info);
            *(unsigned char *)normin = 'Y';

/*           Multiply by inv(U). */

            dlatbs_("Upper", "No transpose", "Non-unit", normin, n, kd, &ab[
                    ab_offset], ldab, &work[1], &scaleu, &work[(*n << 1) + 1], 
                     info);
        } else {

/*           Multiply by inv(L). */

            dlatbs_("Lower", "No transpose", "Non-unit", normin, n, kd, &ab[
                    ab_offset], ldab, &work[1], &scalel, &work[(*n << 1) + 1], 
                     info);
            *(unsigned char *)normin = 'Y';

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

            dlatbs_("Lower", "Transpose", "Non-unit", normin, n, kd, &ab[
                    ab_offset], ldab, &work[1], &scaleu, &work[(*n << 1) + 1], 
                     info);
        }

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

        scale = scalel * scaleu;
        if (scale != 1.) {
            ix = idamax_(n, &work[1], &c__1);
            if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) 
                    {
                goto L20;
            }
            drscl_(n, &scale, &work[1], &c__1);
        }
        goto L10;
    }

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

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

L20:

    return 0;

/*     End of DPBCON */

} /* dpbcon_ */