lapack/TESTING/LIN/dppt01.f

*> \brief \b DPPT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            N
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( * ), AFAC( * ), RWORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DPPT01 reconstructs a symmetric positive definite packed matrix A
*> from its L*L' or U'*U factorization and computes the residual
*>    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*>    norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          symmetric matrix A is stored:
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of rows and columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*>          The original symmetric matrix A, stored as a packed
*>          triangular matrix.
*> \endverbatim
*>
*> \param[in,out] AFAC
*> \verbatim
*>          AFAC is DOUBLE PRECISION array, dimension (N*(N+1)/2)
*>          On entry, the factor L or U from the L*L' or U'*U
*>          factorization of A, stored as a packed triangular matrix.
*>          Overwritten with the reconstructed matrix, and then with the
*>          difference L*L' - A (or U'*U - A).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*>          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE DPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
*  -- LAPACK test 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          UPLO
      INTEGER            N
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( * ), AFAC( * ), RWORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, K, KC, NPP
      DOUBLE PRECISION   ANORM, EPS, T
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DDOT, DLAMCH, DLANSP
      EXTERNAL           LSAME, DDOT, DLAMCH, DLANSP
*     ..
*     .. External Subroutines ..
      EXTERNAL           DSCAL, DSPR, DTPMV
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DBLE
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0
*
      IF( N.LE.0 ) THEN
         RESID = ZERO
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      EPS = DLAMCH( 'Epsilon' )
      ANORM = DLANSP( '1', UPLO, N, A, RWORK )
      IF( ANORM.LE.ZERO ) THEN
         RESID = ONE / EPS
         RETURN
      END IF
*
*     Compute the product U'*U, overwriting U.
*
      IF( LSAME( UPLO, 'U' ) ) THEN
         KC = ( N*( N-1 ) ) / 2 + 1
         DO 10 K = N, 1, -1
*
*           Compute the (K,K) element of the result.
*
            T = DDOT( K, AFAC( KC ), 1, AFAC( KC ), 1 )
            AFAC( KC+K-1 ) = T
*
*           Compute the rest of column K.
*
            IF( K.GT.1 ) THEN
               CALL DTPMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
     $                     AFAC( KC ), 1 )
               KC = KC - ( K-1 )
            END IF
   10    CONTINUE
*
*     Compute the product L*L', overwriting L.
*
      ELSE
         KC = ( N*( N+1 ) ) / 2
         DO 20 K = N, 1, -1
*
*           Add a multiple of column K of the factor L to each of
*           columns K+1 through N.
*
            IF( K.LT.N )
     $         CALL DSPR( 'Lower', N-K, ONE, AFAC( KC+1 ), 1,
     $                    AFAC( KC+N-K+1 ) )
*
*           Scale column K by the diagonal element.
*
            T = AFAC( KC )
            CALL DSCAL( N-K+1, T, AFAC( KC ), 1 )
*
            KC = KC - ( N-K+2 )
   20    CONTINUE
      END IF
*
*     Compute the difference  L*L' - A (or U'*U - A).
*
      NPP = N*( N+1 ) / 2
      DO 30 I = 1, NPP
         AFAC( I ) = AFAC( I ) - A( I )
   30 CONTINUE
*
*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
      RESID = DLANSP( '1', UPLO, N, AFAC, RWORK )
*
      RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
*
      RETURN
*
*     End of DPPT01
*
      END