*> \brief \b SSPT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDC, N * REAL RESID * .. * .. Array Arguments .. * INTEGER IPIV( * ) * REAL A( * ), AFAC( * ), C( LDC, * ), RWORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSPT01 reconstructs a symmetric indefinite packed matrix A from its *> block L*D*L' or U*D*U' factorization and computes the residual *> norm( C - A ) / ( N * norm(A) * EPS ), *> where C is the reconstructed matrix and 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] AFAC *> \verbatim *> AFAC is REAL array, dimension (N*(N+1)/2) *> The factored form of the matrix A, stored as a packed *> triangular matrix. AFAC contains the block diagonal matrix D *> and the multipliers used to obtain the factor L or U from the *> block L*D*L' or U*D*U' factorization as computed by SSPTRF. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from SSPTRF. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is REAL array, dimension (LDC,N) *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) *> If UPLO = 'U', norm(U*D*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 single_lin * * ===================================================================== SUBROUTINE SSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, 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 LDC, N REAL RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) REAL A( * ), AFAC( * ), C( LDC, * ), RWORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J, JC REAL ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL SLAMCH, SLANSP, SLANSY EXTERNAL LSAME, SLAMCH, SLANSP, SLANSY * .. * .. External Subroutines .. EXTERNAL SLAVSP, SLASET * .. * .. Intrinsic Functions .. INTRINSIC REAL * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Determine EPS and the norm of A. * EPS = SLAMCH( 'Epsilon' ) ANORM = SLANSP( '1', UPLO, N, A, RWORK ) * * Initialize C to the identity matrix. * CALL SLASET( 'Full', N, N, ZERO, ONE, C, LDC ) * * Call SLAVSP to form the product D * U' (or D * L' ). * CALL SLAVSP( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, IPIV, C, $ LDC, INFO ) * * Call SLAVSP again to multiply by U ( or L ). * CALL SLAVSP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C, $ LDC, INFO ) * * Compute the difference C - A . * IF( LSAME( UPLO, 'U' ) ) THEN JC = 0 DO 20 J = 1, N DO 10 I = 1, J C( I, J ) = C( I, J ) - A( JC+I ) 10 CONTINUE JC = JC + J 20 CONTINUE ELSE JC = 1 DO 40 J = 1, N DO 30 I = J, N C( I, J ) = C( I, J ) - A( JC+I-J ) 30 CONTINUE JC = JC + N - J + 1 40 CONTINUE END IF * * Compute norm( C - A ) / ( N * norm(A) * EPS ) * RESID = SLANSY( '1', UPLO, N, C, LDC, RWORK ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS END IF * RETURN * * End of SSPT01 * END