dtrti2.f

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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/
*
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*> \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.
*
*> \ingroup trti2
*
*  =====================================================================
      SUBROUTINE dtrti2( UPLO, DIAG, N, A, LDA, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. 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