SUBROUTINE DPOT01( UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDAFAC, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * ) * .. * * Purpose * ======= * * DPOT01 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. * * Arguments * ========== * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * symmetric matrix A is stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The original symmetric matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N) * * AFAC (input/output) DOUBLE PRECISION array, dimension (LDAFAC,N) * On entry, the factor L or U from the L*L' or U'*U * factorization of A. * Overwritten with the reconstructed matrix, and then with the * difference L*L' - A (or U'*U - A). * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. LDAFAC >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) * If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, K DOUBLE PRECISION ANORM, EPS, T * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DDOT, DLAMCH, DLANSY EXTERNAL LSAME, DDOT, DLAMCH, DLANSY * .. * .. External Subroutines .. EXTERNAL DSCAL, DSYR, DTRMV * .. * .. 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 = DLANSY( '1', UPLO, N, A, LDA, RWORK ) IF( ANORM.LE.ZERO ) THEN RESID = ONE / EPS RETURN END IF * * Compute the product U'*U, overwriting U. * IF( LSAME( UPLO, 'U' ) ) THEN DO 10 K = N, 1, -1 * * Compute the (K,K) element of the result. * T = DDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 ) AFAC( K, K ) = T * * Compute the rest of column K. * CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC, \$ LDAFAC, AFAC( 1, K ), 1 ) * 10 CONTINUE * * Compute the product L*L', 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 DSYR( '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 DSCAL( N-K+1, T, AFAC( K, K ), 1 ) * 20 CONTINUE END IF * * Compute the difference L*L' - A (or U'*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 = DLANSY( '1', UPLO, N, AFAC, LDAFAC, RWORK ) * RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS * RETURN * * End of DPOT01 * END