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SUBROUTINE DPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
$ PIV, RWORK, RESID, RANK ) * * -- LAPACK test routine (version 3.1) -- * Craig Lucas, University of Manchester / NAG Ltd. * October, 2008 * * .. Scalar Arguments .. DOUBLE PRECISION RESID INTEGER LDA, LDAFAC, LDPERM, N, RANK CHARACTER UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), $ PERM( LDPERM, * ), RWORK( * ) INTEGER PIV( * ) * .. * * Purpose * ======= * * DPST01 reconstructs a symmetric positive semidefinite matrix A * from its L or U factors and the permutation matrix P and computes * the residual * norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or * norm( P*U'*U*P' - 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) DOUBLE PRECISION array, dimension (LDAFAC,N) * The factor L or U from the L*L' or U'*U * factorization of A. * * LDAFAC (input) INTEGER * The leading dimension of the array AFAC. LDAFAC >= max(1,N). * * PERM (output) DOUBLE PRECISION array, dimension (LDPERM,N) * Overwritten with the reconstructed matrix, and then with the * difference P*L*L'*P' - A (or P*U'*U*P' - A) * * LDPERM (input) INTEGER * The leading dimension of the array PERM. * LDAPERM >= max(1,N). * * PIV (input) INTEGER array, dimension (N) * PIV is such that the nonzero entries are * P( PIV( K ), K ) = 1. * * 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 .. DOUBLE PRECISION ANORM, EPS, T INTEGER I, J, K * .. * .. External Functions .. DOUBLE PRECISION DDOT, DLAMCH, DLANSY LOGICAL LSAME EXTERNAL DDOT, DLAMCH, DLANSY, LSAME * .. * .. 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 * IF( RANK.LT.N ) THEN DO 110 J = RANK + 1, N DO 100 I = RANK + 1, J AFAC( I, J ) = ZERO 100 CONTINUE 110 CONTINUE END IF * DO 120 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 ) * 120 CONTINUE * * Compute the product L*L', overwriting L. * ELSE * IF( RANK.LT.N ) THEN DO 140 J = RANK + 1, N DO 130 I = J, N AFAC( I, J ) = ZERO 130 CONTINUE 140 CONTINUE END IF * DO 150 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 ) 150 CONTINUE * END IF * * Form P*L*L'*P' or P*U'*U*P' * IF( LSAME( UPLO, 'U' ) ) THEN * DO 170 J = 1, N DO 160 I = 1, N IF( PIV( I ).LE.PIV( J ) ) THEN IF( I.LE.J ) THEN PERM( PIV( I ), PIV( J ) ) = AFAC( I, J ) ELSE PERM( PIV( I ), PIV( J ) ) = AFAC( J, I ) END IF END IF 160 CONTINUE 170 CONTINUE * * ELSE * DO 190 J = 1, N DO 180 I = 1, N IF( PIV( I ).GE.PIV( J ) ) THEN IF( I.GE.J ) THEN PERM( PIV( I ), PIV( J ) ) = AFAC( I, J ) ELSE PERM( PIV( I ), PIV( J ) ) = AFAC( J, I ) END IF END IF 180 CONTINUE 190 CONTINUE * END IF * * Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A). * IF( LSAME( UPLO, 'U' ) ) THEN DO 210 J = 1, N DO 200 I = 1, J PERM( I, J ) = PERM( I, J ) - A( I, J ) 200 CONTINUE 210 CONTINUE ELSE DO 230 J = 1, N DO 220 I = J, N PERM( I, J ) = PERM( I, J ) - A( I, J ) 220 CONTINUE 230 CONTINUE END IF * * Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or * ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ). * RESID = DLANSY( '1', UPLO, N, PERM, LDAFAC, RWORK ) * RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS * RETURN * * End of DPST01 * END |