Esempio n. 1
0
/* Subroutine */ int dgbcon_(char *norm, integer *n, integer *kl, integer *ku,
	 doublereal *ab, integer *ldab, integer *ipiv, doublereal *anorm, 
	doublereal *rcond, doublereal *work, integer *iwork, integer *info, 
	ftnlen norm_len)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, i__1, i__2, i__3;
    doublereal d__1;

    /* Local variables */
    static integer j;
    static doublereal t;
    static integer kd, lm, jp, ix, kase;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    static integer kase1;
    static doublereal scale;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    extern /* Subroutine */ int drscl_(integer *, doublereal *, doublereal *, 
	    integer *);
    static logical lnoti;
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *);
    extern doublereal dlamch_(char *, ftnlen);
    extern /* Subroutine */ int dlacon_(integer *, doublereal *, doublereal *,
	     integer *, doublereal *, integer *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlatbs_(char *, char *, char *, char *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, ftnlen, ftnlen, ftnlen, 
	    ftnlen), xerbla_(char *, integer *, ftnlen);
    static doublereal ainvnm;
    static logical onenrm;
    static char normin[1];
    static doublereal smlnum;


/*  -- LAPACK routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     September 30, 1994 */

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

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

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

/*  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) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          Details of the LU factorization of the band matrix A, as */
/*          computed by DGBTRF.  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) 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 .. */
/*     .. */
/*     .. 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;
    --ipiv;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O", (ftnlen)1, (
	    ftnlen)1);
    if (! onenrm && ! lsame_(norm, "I", (ftnlen)1, (ftnlen)1)) {
	*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_("DGBCON", &i__1, (ftnlen)6);
	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", (ftnlen)12);

/*     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:
    dlacon_(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase);
    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];
		    t = work[jp];
		    if (jp != j) {
			work[jp] = work[j];
			work[j] = t;
		    }
		    d__1 = -t;
		    daxpy_(&lm, &d__1, &ab[kd + 1 + j * ab_dim1], &c__1, &
			    work[j + 1], &c__1);
/* L20: */
		}
	    }

/*           Multiply by inv(U). */

	    i__1 = *kl + *ku;
	    dlatbs_("Upper", "No transpose", "Non-unit", normin, n, &i__1, &
		    ab[ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 
		    1], info, (ftnlen)5, (ftnlen)12, (ftnlen)8, (ftnlen)1);
	} else {

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

	    i__1 = *kl + *ku;
	    dlatbs_("Upper", "Transpose", "Non-unit", normin, n, &i__1, &ab[
		    ab_offset], ldab, &work[1], &scale, &work[(*n << 1) + 1], 
		    info, (ftnlen)5, (ftnlen)9, (ftnlen)8, (ftnlen)1);

/*           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);
		    work[j] -= ddot_(&lm, &ab[kd + 1 + j * ab_dim1], &c__1, &
			    work[j + 1], &c__1);
		    jp = ipiv[j];
		    if (jp != j) {
			t = work[jp];
			work[jp] = work[j];
			work[j] = t;
		    }
/* L30: */
		}
	    }
	}

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

	*(unsigned char *)normin = 'Y';
	if (scale != 1.) {
	    ix = idamax_(n, &work[1], &c__1);
	    if (scale < (d__1 = work[ix], abs(d__1)) * smlnum || scale == 0.) 
		    {
		goto L40;
	    }
	    drscl_(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 DGBCON */

} /* dgbcon_ */
Esempio n. 2
0
/* 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 computational routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. 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**T). */
            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**T). */
            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], f2c_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 */
}
Esempio n. 3
0
/* 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;
    integer isave[3];
    doublereal anorm;
    logical upper;
    doublereal xnorm;
    doublereal ainvnm;
    logical onenrm;
    char normin[1];
    doublereal smlnum;
    logical nounit;

/*  -- LAPACK routine (version 3.2) -- */
/*     November 2006 */

/*     Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. */

/*  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 */

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

/*     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_ */