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*> \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DTRTI2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrti2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrti2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrti2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRTI2 computes the inverse of a real upper or lower triangular
*> matrix.
*>
*> This is the Level 2 BLAS version of the algorithm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the matrix A is upper or lower triangular.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> Specifies whether or not the matrix A is unit triangular.
*> = 'N': Non-unit triangular
*> = 'U': Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, 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.
*>
*> On exit, the (triangular) inverse of the original matrix, in
*> the same storage format.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -k, the k-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 DTRTI2( UPLO, DIAG, N, A, LDA, 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, UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER J
DOUBLE PRECISION AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DTRMV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
NOUNIT = LSAME( DIAG, 'N' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTRTI2', -INFO )
RETURN
END IF
*
IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix.
*
DO 10 J = 1, N
IF( NOUNIT ) THEN
A( J, J ) = ONE / A( J, J )
AJJ = -A( J, J )
ELSE
AJJ = -ONE
END IF
*
* Compute elements 1:j-1 of j-th column.
*
CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
$ A( 1, J ), 1 )
CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
10 CONTINUE
ELSE
*
* Compute inverse of lower triangular matrix.
*
DO 20 J = N, 1, -1
IF( NOUNIT ) THEN
A( J, J ) = ONE / A( J, J )
AJJ = -A( J, J )
ELSE
AJJ = -ONE
END IF
IF( J.LT.N ) THEN
*
* Compute elements j+1:n of j-th column.
*
CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
$ A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
END IF
20 CONTINUE
END IF
*
RETURN
*
* End of DTRTI2
*
END
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