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    1:       SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          DIAG, UPLO
   10:       INTEGER            INFO, LDA, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   A( LDA, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DTRTRI computes the inverse of a real upper or lower triangular
   20: *  matrix A.
   21: *
   22: *  This is the Level 3 BLAS version of the algorithm.
   23: *
   24: *  Arguments
   25: *  =========
   26: *
   27: *  UPLO    (input) CHARACTER*1
   28: *          = 'U':  A is upper triangular;
   29: *          = 'L':  A is lower triangular.
   30: *
   31: *  DIAG    (input) CHARACTER*1
   32: *          = 'N':  A is non-unit triangular;
   33: *          = 'U':  A is unit triangular.
   34: *
   35: *  N       (input) INTEGER
   36: *          The order of the matrix A.  N >= 0.
   37: *
   38: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   39: *          On entry, the triangular matrix A.  If UPLO = 'U', the
   40: *          leading N-by-N upper triangular part of the array A contains
   41: *          the upper triangular matrix, and the strictly lower
   42: *          triangular part of A is not referenced.  If UPLO = 'L', the
   43: *          leading N-by-N lower triangular part of the array A contains
   44: *          the lower triangular matrix, and the strictly upper
   45: *          triangular part of A is not referenced.  If DIAG = 'U', the
   46: *          diagonal elements of A are also not referenced and are
   47: *          assumed to be 1.
   48: *          On exit, the (triangular) inverse of the original matrix, in
   49: *          the same storage format.
   50: *
   51: *  LDA     (input) INTEGER
   52: *          The leading dimension of the array A.  LDA >= max(1,N).
   53: *
   54: *  INFO    (output) INTEGER
   55: *          = 0: successful exit
   56: *          < 0: if INFO = -i, the i-th argument had an illegal value
   57: *          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
   58: *               matrix is singular and its inverse can not be computed.
   59: *
   60: *  =====================================================================
   61: *
   62: *     .. Parameters ..
   63:       DOUBLE PRECISION   ONE, ZERO
   64:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   65: *     ..
   66: *     .. Local Scalars ..
   67:       LOGICAL            NOUNIT, UPPER
   68:       INTEGER            J, JB, NB, NN
   69: *     ..
   70: *     .. External Functions ..
   71:       LOGICAL            LSAME
   72:       INTEGER            ILAENV
   73:       EXTERNAL           LSAME, ILAENV
   74: *     ..
   75: *     .. External Subroutines ..
   76:       EXTERNAL           DTRMM, DTRSM, DTRTI2, XERBLA
   77: *     ..
   78: *     .. Intrinsic Functions ..
   79:       INTRINSIC          MAX, MIN
   80: *     ..
   81: *     .. Executable Statements ..
   82: *
   83: *     Test the input parameters.
   84: *
   85:       INFO = 0
   86:       UPPER = LSAME( UPLO, 'U' )
   87:       NOUNIT = LSAME( DIAG, 'N' )
   88:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
   89:          INFO = -1
   90:       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
   91:          INFO = -2
   92:       ELSE IF( N.LT.0 ) THEN
   93:          INFO = -3
   94:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
   95:          INFO = -5
   96:       END IF
   97:       IF( INFO.NE.0 ) THEN
   98:          CALL XERBLA( 'DTRTRI', -INFO )
   99:          RETURN
  100:       END IF
  101: *
  102: *     Quick return if possible
  103: *
  104:       IF( N.EQ.0 )
  105:      $   RETURN
  106: *
  107: *     Check for singularity if non-unit.
  108: *
  109:       IF( NOUNIT ) THEN
  110:          DO 10 INFO = 1, N
  111:             IF( A( INFO, INFO ).EQ.ZERO )
  112:      $         RETURN
  113:    10    CONTINUE
  114:          INFO = 0
  115:       END IF
  116: *
  117: *     Determine the block size for this environment.
  118: *
  119:       NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 )
  120:       IF( NB.LE.1 .OR. NB.GE.N ) THEN
  121: *
  122: *        Use unblocked code
  123: *
  124:          CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
  125:       ELSE
  126: *
  127: *        Use blocked code
  128: *
  129:          IF( UPPER ) THEN
  130: *
  131: *           Compute inverse of upper triangular matrix
  132: *
  133:             DO 20 J = 1, N, NB
  134:                JB = MIN( NB, N-J+1 )
  135: *
  136: *              Compute rows 1:j-1 of current block column
  137: *
  138:                CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
  139:      $                     JB, ONE, A, LDA, A( 1, J ), LDA )
  140:                CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
  141:      $                     JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
  142: *
  143: *              Compute inverse of current diagonal block
  144: *
  145:                CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
  146:    20       CONTINUE
  147:          ELSE
  148: *
  149: *           Compute inverse of lower triangular matrix
  150: *
  151:             NN = ( ( N-1 ) / NB )*NB + 1
  152:             DO 30 J = NN, 1, -NB
  153:                JB = MIN( NB, N-J+1 )
  154:                IF( J+JB.LE.N ) THEN
  155: *
  156: *                 Compute rows j+jb:n of current block column
  157: *
  158:                   CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG,
  159:      $                        N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
  160:      $                        A( J+JB, J ), LDA )
  161:                   CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG,
  162:      $                        N-J-JB+1, JB, -ONE, A( J, J ), LDA,
  163:      $                        A( J+JB, J ), LDA )
  164:                END IF
  165: *
  166: *              Compute inverse of current diagonal block
  167: *
  168:                CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
  169:    30       CONTINUE
  170:          END IF
  171:       END IF
  172: *
  173:       RETURN
  174: *
  175: *     End of DTRTRI
  176: *
  177:       END