SUBROUTINE DTRTRIF( UPLO, DIAG, N, A, LDA, INFO )

*

*  -- LAPACK routine (version 3.0) --

*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,

*     Courant Institute, Argonne National Lab, and Rice University

*     March 31, 1993

*

*     .. Scalar Arguments ..

      CHARACTER          DIAG, UPLO

      INTEGER            INFO, LDA, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * )

*     ..

*

*  Purpose

*  =======

*

*  DTRTRI computes the inverse of a real upper or lower triangular

*  matrix A.

*

*  This is the Level 3 BLAS version of the algorithm.

*

*  Arguments

*  =========

*

*  UPLO    (input) CHARACTER*1

*          = 'U':  A is upper triangular;

*          = 'L':  A is lower triangular.

*

*  DIAG    (input) CHARACTER*1

*          = 'N':  A is non-unit triangular;

*          = 'U':  A is unit triangular.

*

*  N       (input) INTEGER

*          The order of the matrix A.  N >= 0.

*

*  A       (input/output) 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.

*

*  LDA     (input) INTEGER

*          The leading dimension of the array A.  LDA >= max(1,N).

*

*  INFO    (output) 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.

*

*  =====================================================================

*

*     .. 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

      EXTERNAL           LSAME

*     ..

*     .. 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 = 128

      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