OpenBLAS/lapack-netlib/SRC/dtptri.f

*> \brief \b DTPTRI
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DTPTRI( UPLO, DIAG, N, AP, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, UPLO
*       INTEGER            INFO, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   AP( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTPTRI computes the inverse of a real upper or lower triangular
*> matrix A stored in packed format.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  A is upper triangular;
*>          = 'L':  A is lower triangular.
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          = 'N':  A is non-unit triangular;
*>          = 'U':  A is unit triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*>          On entry, the upper or lower triangular matrix A, stored
*>          columnwise in a linear array.  The j-th column of A is stored
*>          in the array AP as follows:
*>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
*>          See below for further details.
*>          On exit, the (triangular) inverse of the original matrix, in
*>          the same packed storage format.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  A triangular matrix A can be transferred to packed storage using one
*>  of the following program segments:
*>
*>  UPLO = 'U':                      UPLO = 'L':
*>
*>        JC = 1                           JC = 1
*>        DO 2 J = 1, N                    DO 2 J = 1, N
*>           DO 1 I = 1, J                    DO 1 I = J, N
*>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
*>      1    CONTINUE                    1    CONTINUE
*>           JC = JC + J                      JC = JC + N - J + 1
*>      2 CONTINUE                       2 CONTINUE
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE DTPTRI( UPLO, DIAG, N, AP, INFO )
*
*  -- 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, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOUNIT, UPPER
      INTEGER            J, JC, JCLAST, JJ
      DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSCAL, DTPMV, XERBLA
*     ..
*     .. 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
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DTPTRI', -INFO )
         RETURN
      END IF
*
*     Check for singularity if non-unit.
*
      IF( NOUNIT ) THEN
         IF( UPPER ) THEN
            JJ = 0
            DO 10 INFO = 1, N
               JJ = JJ + INFO
               IF( AP( JJ ).EQ.ZERO )
     $            RETURN
   10       CONTINUE
         ELSE
            JJ = 1
            DO 20 INFO = 1, N
               IF( AP( JJ ).EQ.ZERO )
     $            RETURN
               JJ = JJ + N - INFO + 1
   20       CONTINUE
         END IF
         INFO = 0
      END IF
*
      IF( UPPER ) THEN
*
*        Compute inverse of upper triangular matrix.
*
         JC = 1
         DO 30 J = 1, N
            IF( NOUNIT ) THEN
               AP( JC+J-1 ) = ONE / AP( JC+J-1 )
               AJJ = -AP( JC+J-1 )
            ELSE
               AJJ = -ONE
            END IF
*
*           Compute elements 1:j-1 of j-th column.
*
            CALL DTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
     $                  AP( JC ), 1 )
            CALL DSCAL( J-1, AJJ, AP( JC ), 1 )
            JC = JC + J
   30    CONTINUE
*
      ELSE
*
*        Compute inverse of lower triangular matrix.
*
         JC = N*( N+1 ) / 2
         DO 40 J = N, 1, -1
            IF( NOUNIT ) THEN
               AP( JC ) = ONE / AP( JC )
               AJJ = -AP( JC )
            ELSE
               AJJ = -ONE
            END IF
            IF( J.LT.N ) THEN
*
*              Compute elements j+1:n of j-th column.
*
               CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J,
     $                     AP( JCLAST ), AP( JC+1 ), 1 )
               CALL DSCAL( N-J, AJJ, AP( JC+1 ), 1 )
            END IF
            JCLAST = JC
            JC = JC - N + J - 2
   40    CONTINUE
      END IF
*
      RETURN
*
*     End of DTPTRI
*
      END