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*> \brief \b DTRCON
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DTRCON + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrcon.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrcon.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrcon.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
* IWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, NORM, UPLO
* INTEGER INFO, LDA, N
* DOUBLE PRECISION RCOND
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRCON 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 DOUBLE PRECISION 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 DOUBLE PRECISION
*> 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 DOUBLE PRECISION 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 doubleOTHERcomputational
*
* =====================================================================
SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
$ IWORK, INFO )
*
* -- LAPACK computational routine (version 3.2) --
* -- 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
DOUBLE PRECISION RCOND
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, ONENRM, UPPER
CHARACTER NORMIN
INTEGER IX, KASE, KASE1
DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
DOUBLE PRECISION DLAMCH, DLANTR
EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTR
* ..
* .. External Subroutines ..
EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX
* ..
* .. 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( 'DTRCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
END IF
*
RCOND = ZERO
SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
*
* Compute the norm of the triangular matrix A.
*
ANORM = DLANTR( 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 DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.KASE1 ) THEN
*
* Multiply by inv(A).
*
CALL DLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
$ LDA, WORK, SCALE, WORK( 2*N+1 ), INFO )
ELSE
*
* Multiply by inv(A**T).
*
CALL DLATRS( 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 = IDAMAX( N, WORK, 1 )
XNORM = ABS( WORK( IX ) )
IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
$ GO TO 20
CALL DRSCL( 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 DTRCON
*
END
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