dtrtri.f

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*> \brief \b DTRTRI
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
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*> \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 November 2011
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE dtrtri( 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, 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