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 108 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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