*> \brief \b SPOT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDAFAC, N * REAL RESID * .. * .. Array Arguments .. * REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SPOT01 reconstructs a symmetric positive definite 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 (LDA,N) *> The original symmetric matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N) *> \endverbatim *> *> \param[in,out] AFAC *> \verbatim *> AFAC is REAL array, dimension (LDAFAC,N) *> On entry, the factor L or U from the L * L**T or U**T * U *> factorization of A. *> Overwritten with the reconstructed matrix, and then with *> the difference L * L**T - A (or U**T * U - A). *> \endverbatim *> *> \param[in] LDAFAC *> \verbatim *> LDAFAC is INTEGER *> The leading dimension of the array AFAC. LDAFAC >= 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 * L**T - A) / ( N * norm(A) * EPS ) *> If UPLO = 'U', norm(U**T * 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 SPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, 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 LDA, LDAFAC, N REAL RESID * .. * .. Array Arguments .. REAL A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J, K REAL ANORM, EPS, T * .. * .. External Functions .. LOGICAL LSAME REAL SDOT, SLAMCH, SLANSY EXTERNAL LSAME, SDOT, SLAMCH, SLANSY * .. * .. External Subroutines .. EXTERNAL SSCAL, SSYR, STRMV * .. * .. 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 = SLANSY( '1', UPLO, N, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute the product U**T * U, overwriting U. * IF( LSAME( UPLO, 'U' ) ) THEN DO 10 K = N, 1, -1 * * Compute the (K,K) element of the result. * T = SDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 ) AFAC( K, K ) = T * * Compute the rest of column K. * CALL STRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC, $ LDAFAC, AFAC( 1, K ), 1 ) * 10 CONTINUE * * Compute the product L * L**T, overwriting L. * ELSE 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+1.LE.N ) $ CALL SSYR( 'Lower', N-K, ONE, AFAC( K+1, K ), 1, $ AFAC( K+1, K+1 ), LDAFAC ) * * Scale column K by the diagonal element. * T = AFAC( K, K ) CALL SSCAL( N-K+1, T, AFAC( K, K ), 1 ) * 20 CONTINUE END IF * * Compute the difference L * L**T - A (or U**T * U - A). * IF( LSAME( UPLO, 'U' ) ) THEN DO 40 J = 1, N DO 30 I = 1, J AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 30 CONTINUE 40 CONTINUE ELSE DO 60 J = 1, N DO 50 I = J, N AFAC( I, J ) = AFAC( I, J ) - A( I, J ) 50 CONTINUE 60 CONTINUE END IF * * Compute norm(L*U - A) / ( N * norm(A) * EPS ) * RESID = SLANSY( '1', UPLO, N, AFAC, LDAFAC, RWORK ) * RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS * RETURN * * End of SPOT01 * END