241 lines
6.7 KiB
Fortran
241 lines
6.7 KiB
Fortran
*> \brief \b CTRTRI
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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 CTRTRI + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctrtri.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/ctrtri.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/ctrtri.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 CTRTRI( UPLO, DIAG, N, A, LDA, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, UPLO
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* INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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* COMPLEX A( LDA, * )
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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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*> CTRTRI computes the inverse of a complex upper or lower triangular
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*> matrix A.
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*>
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*> This is the Level 3 BLAS version of the algorithm.
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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] 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,out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,N)
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*> On entry, the triangular matrix A. If UPLO = 'U', the
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*> leading N-by-N upper triangular part of the array A contains
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*> the upper triangular matrix, and the strictly lower
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*> triangular part of A is not referenced. If UPLO = 'L', the
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*> leading N-by-N lower triangular part of the array A contains
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*> the lower triangular matrix, and the strictly upper
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*> triangular part of A is not referenced. If DIAG = 'U', the
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*> diagonal elements of A are also not referenced and are
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*> assumed to be 1.
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*> On exit, the (triangular) inverse of the original matrix, in
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*> the same storage format.
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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] 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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*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
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*> matrix is singular and its inverse can not be computed.
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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 complexOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE CTRTRI( UPLO, DIAG, N, A, LDA, 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, UPLO
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INTEGER INFO, LDA, N
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* ..
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* .. Array Arguments ..
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COMPLEX A( LDA, * )
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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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COMPLEX ONE, ZERO
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PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
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$ ZERO = ( 0.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL NOUNIT, UPPER
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INTEGER J, JB, NB, NN
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL CTRMM, CTRSM, CTRTI2, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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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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NOUNIT = LSAME( DIAG, 'N' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
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INFO = -2
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ELSE IF( N.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CTRTRI', -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 )
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$ RETURN
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*
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* Check for singularity if non-unit.
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*
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IF( NOUNIT ) THEN
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DO 10 INFO = 1, N
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IF( A( INFO, INFO ).EQ.ZERO )
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$ RETURN
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10 CONTINUE
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INFO = 0
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END IF
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*
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* Determine the block size for this environment.
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*
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NB = ILAENV( 1, 'CTRTRI', UPLO // DIAG, N, -1, -1, -1 )
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IF( NB.LE.1 .OR. NB.GE.N ) THEN
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*
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* Use unblocked code
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*
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CALL CTRTI2( UPLO, DIAG, N, A, LDA, INFO )
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ELSE
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*
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* Use blocked code
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*
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IF( UPPER ) THEN
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*
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* Compute inverse of upper triangular matrix
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*
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DO 20 J = 1, N, NB
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JB = MIN( NB, N-J+1 )
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*
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* Compute rows 1:j-1 of current block column
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*
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CALL CTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
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$ JB, ONE, A, LDA, A( 1, J ), LDA )
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CALL CTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
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$ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
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*
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* Compute inverse of current diagonal block
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*
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CALL CTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
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20 CONTINUE
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ELSE
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*
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* Compute inverse of lower triangular matrix
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*
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NN = ( ( N-1 ) / NB )*NB + 1
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DO 30 J = NN, 1, -NB
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JB = MIN( NB, N-J+1 )
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IF( J+JB.LE.N ) THEN
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*
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* Compute rows j+jb:n of current block column
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*
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CALL CTRMM( 'Left', 'Lower', 'No transpose', DIAG,
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$ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
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$ A( J+JB, J ), LDA )
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CALL CTRSM( 'Right', 'Lower', 'No transpose', DIAG,
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$ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
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$ A( J+JB, J ), LDA )
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END IF
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*
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* Compute inverse of current diagonal block
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*
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CALL CTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
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30 CONTINUE
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END IF
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END IF
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*
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RETURN
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*
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* End of CTRTRI
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*
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END
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