277 lines
7.6 KiB
Fortran
277 lines
7.6 KiB
Fortran
*> \brief \b STRCON
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download STRCON + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/strcon.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/strcon.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/strcon.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE STRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
|
|
* IWORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER DIAG, NORM, UPLO
|
|
* INTEGER INFO, LDA, N
|
|
* REAL RCOND
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IWORK( * )
|
|
* REAL A( LDA, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> STRCON estimates the reciprocal of the condition number of a
|
|
*> triangular 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)) ).
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] NORM
|
|
*> \verbatim
|
|
*> NORM is 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.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> = 'U': A is upper triangular;
|
|
*> = 'L': A is lower triangular.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] DIAG
|
|
*> \verbatim
|
|
*> DIAG is CHARACTER*1
|
|
*> = 'N': A is non-unit triangular;
|
|
*> = 'U': A is unit triangular.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The order of the matrix A. N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is REAL array, dimension (LDA,N)
|
|
*> The triangular matrix A. If UPLO = 'U', the leading N-by-N
|
|
*> upper triangular part of the array A contains the upper
|
|
*> triangular matrix, and the strictly lower triangular part of
|
|
*> A is not referenced. If UPLO = 'L', the leading N-by-N lower
|
|
*> triangular part of the array A contains the lower triangular
|
|
*> matrix, and the strictly upper triangular part of A is not
|
|
*> referenced. If DIAG = 'U', the diagonal elements of A are
|
|
*> also not referenced and are assumed to be 1.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,N).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RCOND
|
|
*> \verbatim
|
|
*> RCOND is REAL
|
|
*> The reciprocal of the condition number of the matrix A,
|
|
*> computed as RCOND = 1/(norm(A) * norm(inv(A))).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL array, dimension (3*N)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] IWORK
|
|
*> \verbatim
|
|
*> IWORK is INTEGER array, dimension (N)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] INFO
|
|
*> \verbatim
|
|
*> INFO is INTEGER
|
|
*> = 0: successful exit
|
|
*> < 0: if INFO = -i, the i-th argument had an illegal value
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup realOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE STRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
|
|
$ IWORK, INFO )
|
|
*
|
|
* -- 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 ..
|
|
CHARACTER DIAG, NORM, UPLO
|
|
INTEGER INFO, LDA, N
|
|
REAL RCOND
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IWORK( * )
|
|
REAL A( LDA, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ONE, ZERO
|
|
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL NOUNIT, ONENRM, UPPER
|
|
CHARACTER NORMIN
|
|
INTEGER IX, KASE, KASE1
|
|
REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
|
|
* ..
|
|
* .. Local Arrays ..
|
|
INTEGER ISAVE( 3 )
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ISAMAX
|
|
REAL SLAMCH, SLANTR
|
|
EXTERNAL LSAME, ISAMAX, SLAMCH, SLANTR
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SLACN2, SLATRS, SRSCL, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, MAX, REAL
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Test the input parameters.
|
|
*
|
|
INFO = 0
|
|
UPPER = LSAME( UPLO, 'U' )
|
|
ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
|
|
NOUNIT = LSAME( DIAG, 'N' )
|
|
*
|
|
IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
|
|
INFO = -1
|
|
ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
|
|
INFO = -2
|
|
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
|
|
INFO = -3
|
|
ELSE IF( N.LT.0 ) THEN
|
|
INFO = -4
|
|
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
|
|
INFO = -6
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'STRCON', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.EQ.0 ) THEN
|
|
RCOND = ONE
|
|
RETURN
|
|
END IF
|
|
*
|
|
RCOND = ZERO
|
|
SMLNUM = SLAMCH( 'Safe minimum' )*REAL( MAX( 1, N ) )
|
|
*
|
|
* Compute the norm of the triangular matrix A.
|
|
*
|
|
ANORM = SLANTR( NORM, UPLO, DIAG, N, N, A, LDA, WORK )
|
|
*
|
|
* Continue only if ANORM > 0.
|
|
*
|
|
IF( ANORM.GT.ZERO ) THEN
|
|
*
|
|
* Estimate the norm of the inverse of A.
|
|
*
|
|
AINVNM = ZERO
|
|
NORMIN = 'N'
|
|
IF( ONENRM ) THEN
|
|
KASE1 = 1
|
|
ELSE
|
|
KASE1 = 2
|
|
END IF
|
|
KASE = 0
|
|
10 CONTINUE
|
|
CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
|
|
IF( KASE.NE.0 ) THEN
|
|
IF( KASE.EQ.KASE1 ) THEN
|
|
*
|
|
* Multiply by inv(A).
|
|
*
|
|
CALL SLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
|
|
$ LDA, WORK, SCALE, WORK( 2*N+1 ), INFO )
|
|
ELSE
|
|
*
|
|
* Multiply by inv(A**T).
|
|
*
|
|
CALL SLATRS( UPLO, 'Transpose', DIAG, NORMIN, N, A, LDA,
|
|
$ WORK, SCALE, WORK( 2*N+1 ), INFO )
|
|
END IF
|
|
NORMIN = 'Y'
|
|
*
|
|
* Multiply by 1/SCALE if doing so will not cause overflow.
|
|
*
|
|
IF( SCALE.NE.ONE ) THEN
|
|
IX = ISAMAX( N, WORK, 1 )
|
|
XNORM = ABS( WORK( IX ) )
|
|
IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
|
|
$ GO TO 20
|
|
CALL SRSCL( N, SCALE, WORK, 1 )
|
|
END IF
|
|
GO TO 10
|
|
END IF
|
|
*
|
|
* Compute the estimate of the reciprocal condition number.
|
|
*
|
|
IF( AINVNM.NE.ZERO )
|
|
$ RCOND = ( ONE / ANORM ) / AINVNM
|
|
END IF
|
|
*
|
|
20 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of STRCON
|
|
*
|
|
END
|