dtbcon.c

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/* dtbcon.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 dtbcon_(char *norm, char *uplo, char *diag, integer *n, 
        integer *kd, doublereal *ab, integer *ldab, 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, kase1;
    doublereal scale;
    extern logical lsame_(char *, char *);
    integer isave[3];
    extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, 
            integer *);
    doublereal anorm;
    logical upper;
    doublereal xnorm;
    extern /* Subroutine */ int dlacn2_(integer *, doublereal *, doublereal *, 
             integer *, doublereal *, integer *, integer *);
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern doublereal dlantb_(char *, char *, char *, integer *, integer *, 
            doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *, 
            integer *, integer *, doublereal *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
    doublereal ainvnm;
    logical onenrm;
    char normin[1];
    doublereal smlnum;
    logical nounit;


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

/*  DTBCON estimates the reciprocal of the condition number of a */
/*  triangular band matrix A, in either the 1-norm or the infinity-norm. */

/*  The norm of A is computed and an estimate is obtained for */
/*  norm(inv(A)), then 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. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  A is upper triangular; */
/*          = 'L':  A is lower triangular. */

/*  DIAG    (input) CHARACTER*1 */
/*          = 'N':  A is non-unit triangular; */
/*          = 'U':  A is unit triangular. */

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

/*  KD      (input) INTEGER */
/*          The number of superdiagonals or subdiagonals of the */
/*          triangular band matrix A.  KD >= 0. */

/*  AB      (input) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          The upper or lower triangular band matrix A, stored in the */
/*          first kd+1 rows of the array. The j-th column of A is stored */
/*          in the j-th column of the array AB as follows: */
/*          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd). */
/*          If DIAG = 'U', the diagonal elements of A are not referenced */
/*          and are assumed to be 1. */

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

/*  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) 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");
    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
    nounit = lsame_(diag, "N");

    if (! onenrm && ! lsame_(norm, "I")) {
        *info = -1;
    } else if (! upper && ! lsame_(uplo, "L")) {
        *info = -2;
    } else if (! nounit && ! lsame_(diag, "U")) {
        *info = -3;
    } else if (*n < 0) {
        *info = -4;
    } else if (*kd < 0) {
        *info = -5;
    } else if (*ldab < *kd + 1) {
        *info = -7;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DTBCON", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    *rcond = 0.;
    smlnum = dlamch_("Safe minimum") * (doublereal) max(1,*n);

/*     Compute the norm of the triangular matrix A. */

    anorm = dlantb_(norm, uplo, diag, n, kd, &ab[ab_offset], ldab, &work[1]);

/*     Continue only if ANORM > 0. */

    if (anorm > 0.) {

/*        Estimate the norm of the inverse of A. */

        ainvnm = 0.;
        *(unsigned char *)normin = 'N';
        if (onenrm) {
            kase1 = 1;
        } else {
            kase1 = 2;
        }
        kase = 0;
L10:
        dlacn2_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase, isave);
        if (kase != 0) {
            if (kase == kase1) {

/*              Multiply by inv(A). */

                dlatbs_(uplo, "No transpose", diag, normin, n, kd, &ab[
                        ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 
                        1], info)
                        ;
            } else {

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

                dlatbs_(uplo, "Transpose", diag, normin, n, kd, &ab[ab_offset]
, ldab, &work[1], &scale, &work[(*n << 1) + 1], info);
            }
            *(unsigned char *)normin = 'Y';

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

            if (scale != 1.) {
                ix = idamax_(n, &work[1], &c__1);
                xnorm = (d__1 = work[ix], abs(d__1));
                if (scale < xnorm * 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. / anorm / ainvnm;
        }
    }

L20:
    return 0;

/*     End of DTBCON */

} /* dtbcon_ */