*> \brief \b DTRTRI
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DTRTRI computes the inverse of a real upper or lower triangular
*> matrix A.
*>
*> This is the Level 3 BLAS version of the algorithm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \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,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 = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
*> matrix is singular and its inverse can not be computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleOTHERcomputational
*
* =====================================================================
SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER J, JB, NB, NN
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DTRMM, DTRSM, DTRTI2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. 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( 'DTRTRI', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Check for singularity if non-unit.
*
IF( NOUNIT ) THEN
DO 10 INFO = 1, N
IF( A( INFO, INFO ).EQ.ZERO )
$ RETURN
10 CONTINUE
INFO = 0
END IF
*
* Determine the block size for this environment.
*
NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 )
IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code
*
CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
ELSE
*
* Use blocked code
*
IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix
*
DO 20 J = 1, N, NB
JB = MIN( NB, N-J+1 )
*
* Compute rows 1:j-1 of current block column
*
CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
$ JB, ONE, A, LDA, A( 1, J ), LDA )
CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
$ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
*
* Compute inverse of current diagonal block
*
CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
20 CONTINUE
ELSE
*
* Compute inverse of lower triangular matrix
*
NN = ( ( N-1 ) / NB )*NB + 1
DO 30 J = NN, 1, -NB
JB = MIN( NB, N-J+1 )
IF( J+JB.LE.N ) THEN
*
* Compute rows j+jb:n of current block column
*
CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG,
$ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
$ A( J+JB, J ), LDA )
CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG,
$ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
$ A( J+JB, J ), LDA )
END IF
*
* Compute inverse of current diagonal block
*
CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
30 CONTINUE
END IF
END IF
*
RETURN
*
* End of DTRTRI
*
END