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281 lines
7.8 KiB
281 lines
7.8 KiB
2 years ago
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*> \brief \b ZTRCON
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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 ZTRCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrcon.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/ztrcon.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/ztrcon.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 ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
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* RWORK, 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, LDA, N
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* DOUBLE PRECISION RCOND
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( LDA, * ), 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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*> ZTRCON estimates the reciprocal of the condition number of a
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*> triangular 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] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> The triangular matrix A. If UPLO = 'U', the leading N-by-N
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*> upper triangular part of the array A contains the upper
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*> triangular matrix, and the strictly lower triangular part of
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*> A is not referenced. If UPLO = 'L', the leading N-by-N lower
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*> triangular part of the array A contains the lower triangular
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*> matrix, and the strictly upper triangular part of A is not
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*> referenced. If DIAG = 'U', the diagonal elements of A are
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*> also not referenced and are assumed to be 1.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N).
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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 DOUBLE PRECISION
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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 COMPLEX*16 array, dimension (2*N)
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION 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 complex16OTHERcomputational
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*
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* =====================================================================
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SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
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$ RWORK, 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, LDA, N
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DOUBLE PRECISION RCOND
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( LDA, * ), 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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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+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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DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
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COMPLEX*16 ZDUM
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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 IZAMAX
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DOUBLE PRECISION DLAMCH, ZLANTR
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EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTR
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, DIMAG, MAX
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* ..
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* .. Statement Functions ..
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DOUBLE PRECISION CABS1
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* ..
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* .. Statement Function definitions ..
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CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
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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( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTRCON', -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 = DLAMCH( 'Safe minimum' )*DBLE( 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 = ZLANTR( NORM, UPLO, DIAG, N, N, A, LDA, RWORK )
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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 ZLACN2( N, WORK( N+1 ), WORK, 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 ZLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
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$ LDA, WORK, SCALE, RWORK, INFO )
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ELSE
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*
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* Multiply by inv(A**H).
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*
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CALL ZLATRS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
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$ N, A, LDA, WORK, SCALE, RWORK, 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 = IZAMAX( N, WORK, 1 )
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XNORM = CABS1( 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 ZDRSCL( 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 ZTRCON
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*
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END
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