sptt01.f

Go to the documentation of this file.

*> \brief \b SPTT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SPTT01( N, D, E, DF, EF, WORK, RESID )
* 
*       .. Scalar Arguments ..
*       INTEGER            N
*       REAL               RESID
*       ..
*       .. Array Arguments ..
*       REAL               D( * ), DF( * ), E( * ), EF( * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
*> factorization and computes the residual
*>    norm(L*D*L' - A) / ( n * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGTER
*>          The order of the matrix A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is REAL array, dimension (N)
*>          The n diagonal elements of the tridiagonal matrix A.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is REAL array, dimension (N-1)
*>          The (n-1) subdiagonal elements of the tridiagonal matrix A.
*> \endverbatim
*>
*> \param[in] DF
*> \verbatim
*>          DF is REAL array, dimension (N)
*>          The n diagonal elements of the factor L from the L*D*L'
*>          factorization of A.
*> \endverbatim
*>
*> \param[in] EF
*> \verbatim
*>          EF is REAL array, dimension (N-1)
*>          The (n-1) subdiagonal elements of the factor L from the
*>          L*D*L' factorization of A.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is REAL
*>          norm(L*D*L' - A) / (n * norm(A) * EPS)
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup single_lin
*
*  =====================================================================
      SUBROUTINE sptt01( N, D, E, DF, EF, WORK, RESID )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            N
      REAL               RESID
*     ..
*     .. Array Arguments ..
      REAL               D( * ), DF( * ), E( * ), EF( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter                ( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      REAL               ANORM, DE, EPS
*     ..
*     .. External Functions ..
      REAL               SLAMCH
      EXTERNAL           slamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, real
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
      eps = slamch( 'Epsilon' )
*
*     Construct the difference L*D*L' - A.
*
      work( 1 ) = df( 1 ) - d( 1 )
      DO 10 i = 1, n - 1
         de = df( i )*ef( i )
         work( n+i ) = de - e( i )
         work( 1+i ) = de*ef( i ) + df( i+1 ) - d( i+1 )
   10 CONTINUE
*
*     Compute the 1-norms of the tridiagonal matrices A and WORK.
*
      IF( n.EQ.1 ) THEN
         anorm = d( 1 )
         resid = abs( work( 1 ) )
      ELSE
         anorm = max( d( 1 )+abs( e( 1 ) ), d( n )+abs( e( n-1 ) ) )
         resid = max( abs( work( 1 ) )+abs( work( n+1 ) ),
     $           abs( work( n ) )+abs( work( 2*n-1 ) ) )
         DO 20 i = 2, n - 1
            anorm = max( anorm, d( i )+abs( e( i ) )+abs( e( i-1 ) ) )
            resid = max( resid, abs( work( i ) )+abs( work( n+i-1 ) )+
     $              abs( work( n+i ) ) )
   20    CONTINUE
      END IF
*
*     Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
*
      IF( anorm.LE.zero ) THEN
         IF( resid.NE.zero )
     $      resid = one / eps
      ELSE
         resid = ( ( resid / REAL( N ) ) / anorm ) / eps
      END IF
*
      RETURN
*
*     End of SPTT01
*
      END