dtrtri()

subroutine dtrtri	(	character	uplo,
		character	diag,
		integer	n,
		double precision, dimension( lda, * )	a,
		integer	lda,
		integer	info )

DTRTRI

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Purpose:

!>
!> DTRTRI computes the inverse of a real upper or lower triangular
!> matrix A.
!>
!> This is the Level 3 BLAS version of the algorithm.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': A is upper triangular; !> = 'L': A is lower triangular. !>
[in]	DIAG	!> DIAG is CHARACTER*1 !> = 'N': A is non-unit triangular; !> = 'U': A is unit triangular. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in,out]	A	!> 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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[out]	INFO	!> 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. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 106 of file dtrtri.f.

*
*  -- 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, 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
*

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