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*> \brief \b DTRTRI |
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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 DTRTRI + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrtri.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/dtrtri.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/dtrtri.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 DTRTRI( 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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* DOUBLE PRECISION 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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*> DTRTRI computes the inverse of a real 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 DOUBLE PRECISION 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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*> \date November 2011 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
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SUBROUTINE DTRTRILAPACK( UPLO, DIAG, N, A, LDA, INFO ) |
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* |
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* -- LAPACK computational routine (version 3.4.0) -- |
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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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* November 2011 |
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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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DOUBLE PRECISION 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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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, 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 DTRMM, DTRSM, DTRTI2, 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( 'DTRTRI', -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, 'DTRTRI', 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 DTRTI2( 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 DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1, |
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$ JB, ONE, A, LDA, A( 1, J ), LDA ) |
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CALL DTRSM( '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 DTRTI2( '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 DTRMM( '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 DTRSM( '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 DTRTI2( '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 DTRTRI |
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* |
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END |
Zhang Xianyi
12 years ago