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282 lines
7.7 KiB
FortranFixed
282 lines
7.7 KiB
FortranFixed
*> \brief \b STBCON
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download STBCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stbcon.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stbcon.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stbcon.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
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* IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, NORM, UPLO
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* INTEGER INFO, KD, LDAB, N
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* REAL RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* REAL AB( LDAB, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> STBCON estimates the reciprocal of the condition number of a
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*> triangular band matrix A, in either the 1-norm or the infinity-norm.
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*>
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*> The norm of A is computed and an estimate is obtained for
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*> norm(inv(A)), then the reciprocal of the condition number is
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*> computed as
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*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NORM
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*> \verbatim
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*> NORM is CHARACTER*1
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*> Specifies whether the 1-norm condition number or the
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*> infinity-norm condition number is required:
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*> = '1' or 'O': 1-norm;
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*> = 'I': Infinity-norm.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> = 'U': A is upper triangular;
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*> = 'L': A is lower triangular.
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> = 'N': A is non-unit triangular;
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*> = 'U': A is unit triangular.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KD
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*> \verbatim
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*> KD is INTEGER
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*> The number of superdiagonals or subdiagonals of the
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*> triangular band matrix A. KD >= 0.
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*> \endverbatim
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*>
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*> \param[in] AB
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*> \verbatim
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*> AB is REAL array, dimension (LDAB,N)
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*> The upper or lower triangular band matrix A, stored in the
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*> first kd+1 rows of the array. The j-th column of A is stored
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*> in the j-th column of the array AB as follows:
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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*> If DIAG = 'U', the diagonal elements of A are not referenced
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*> and are assumed to be 1.
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KD+1.
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*> \endverbatim
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*>
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*> \param[out] RCOND
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*> \verbatim
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*> RCOND is REAL
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*> The reciprocal of the condition number of the matrix A,
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*> computed as RCOND = 1/(norm(A) * norm(inv(A))).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (3*N)
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup realOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE STBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
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$ IWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, NORM, UPLO
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INTEGER INFO, KD, LDAB, N
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REAL RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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REAL AB( LDAB, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT, ONENRM, UPPER
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CHARACTER NORMIN
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INTEGER IX, KASE, KASE1
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REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ISAMAX
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REAL SLAMCH, SLANTB
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EXTERNAL LSAME, ISAMAX, SLAMCH, SLANTB
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* ..
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* .. External Subroutines ..
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EXTERNAL SLACN2, SLATBS, SRSCL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, REAL
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
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NOUNIT = LSAME( DIAG, 'N' )
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*
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IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -2
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ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( KD.LT.0 ) THEN
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INFO = -5
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ELSE IF( LDAB.LT.KD+1 ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'STBCON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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END IF
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*
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RCOND = ZERO
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SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) )
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*
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* Compute the norm of the triangular matrix A.
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*
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ANORM = SLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, WORK )
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*
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* Continue only if ANORM > 0.
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*
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IF( ANORM.GT.ZERO ) THEN
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*
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* Estimate the norm of the inverse of A.
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*
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AINVNM = ZERO
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NORMIN = 'N'
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IF( ONENRM ) THEN
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KASE1 = 1
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ELSE
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KASE1 = 2
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END IF
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KASE = 0
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10 CONTINUE
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CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( KASE.EQ.KASE1 ) THEN
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*
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* Multiply by inv(A).
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*
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CALL SLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
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$ AB, LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
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ELSE
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*
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* Multiply by inv(A**T).
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*
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CALL SLATBS( UPLO, 'Transpose', DIAG, NORMIN, N, KD, AB,
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$ LDAB, WORK, SCALE, WORK( 2*N+1 ), INFO )
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END IF
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NORMIN = 'Y'
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*
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* Multiply by 1/SCALE if doing so will not cause overflow.
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*
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IF( SCALE.NE.ONE ) THEN
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IX = ISAMAX( N, WORK, 1 )
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XNORM = ABS( WORK( IX ) )
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IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
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$ GO TO 20
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CALL SRSCL( N, SCALE, WORK, 1 )
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / ANORM ) / AINVNM
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END IF
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*
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20 CONTINUE
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RETURN
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*
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* End of STBCON
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*
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END
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