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*> \brief \b SPPT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER N
* REAL RESID
* ..
* .. Array Arguments ..
* REAL A( * ), AFAC( * ), RWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SPPT01 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 REAL 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 REAL 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 REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is REAL
*> 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.
*
*> \date November 2011
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SPPT01( UPLO, N, A, AFAC, RWORK, 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 ..
CHARACTER UPLO
INTEGER N
REAL RESID
* ..
* .. Array Arguments ..
REAL A( * ), AFAC( * ), RWORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, K, KC, NPP
REAL ANORM, EPS, T
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SDOT, SLAMCH, SLANSP
EXTERNAL LSAME, SDOT, SLAMCH, SLANSP
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, SSPR, STPMV
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL
* ..
* .. 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 = SLAMCH( 'Epsilon' )
ANORM = SLANSP( '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 = SDOT( K, AFAC( KC ), 1, AFAC( KC ), 1 )
AFAC( KC+K-1 ) = T
*
* Compute the rest of column K.
*
IF( K.GT.1 ) THEN
CALL STPMV( '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 SSPR( 'Lower', N-K, ONE, AFAC( KC+1 ), 1,
$ AFAC( KC+N-K+1 ) )
*
* Scale column K by the diagonal element.
*
T = AFAC( KC )
CALL SSCAL( 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 = SLANSP( '1', UPLO, N, AFAC, RWORK )
*
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
*
RETURN
*
* End of SPPT01
*
END
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