strtri.f

          SUBROUTINE STRTRI( UPLO, DIAG, N, A, LDA, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          DIAG, UPLO
          INTEGER            INFO, LDA, N
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  STRTRI 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) REAL 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 ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            NOUNIT, UPPER
          INTEGER            J, JB, NB, NN
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          EXTERNAL           LSAME, ILAENV
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           STRMM, STRSM, STRTI2, 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( 'STRTRI', -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, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 )
          IF( NB.LE.1 .OR. NB.GE.N ) THEN
    *
    *        Use unblocked code
    *
             CALL STRTI2( 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 STRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
         $                     JB, ONE, A, LDA, A( 1, J ), LDA )
                   CALL STRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
         $                     JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
    *
    *              Compute inverse of current diagonal block
    *
                   CALL STRTI2( '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 STRMM( 'Left', 'Lower', 'No transpose', DIAG,
         $                        N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
         $                        A( J+JB, J ), LDA )
                      CALL STRSM( '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 STRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
       30       CONTINUE
             END IF
          END IF
    *
          RETURN
    *
    *     End of STRTRI
    *
          END