SUBROUTINE DSPT01( UPLO, N, A, AFAC, IPIV, C, LDC, 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 LDC, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( * ), AFAC( * ), C( LDC, * ), RWORK( * ) * .. * * Purpose * ======= * * DSPT01 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. * * 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 (N*(N+1)/2) * The original symmetric matrix A, stored as a packed * triangular matrix. * * AFAC (input) DOUBLE PRECISION 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 DSPTRF. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from DSPTRF. * * C (workspace) DOUBLE PRECISION array, dimension (LDC,N) * * LDC (integer) INTEGER * The leading dimension of the array C. LDC >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RESID (output) DOUBLE PRECISION * If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) * If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J, JC DOUBLE PRECISION ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANSP, DLANSY EXTERNAL LSAME, DLAMCH, DLANSP, DLANSY * .. * .. External Subroutines .. EXTERNAL DLASET, DLAVSP * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. 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 = DLAMCH( 'Epsilon' ) ANORM = DLANSP( '1', UPLO, N, A, RWORK ) * * Initialize C to the identity matrix. * CALL DLASET( 'Full', N, N, ZERO, ONE, C, LDC ) * * Call DLAVSP to form the product D * U' (or D * L' ). * CALL DLAVSP( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, IPIV, C, \$ LDC, INFO ) * * Call DLAVSP again to multiply by U ( or L ). * CALL DLAVSP( 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 = DLANSY( '1', UPLO, N, C, LDC, RWORK ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) \$ RESID = ONE / EPS ELSE RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS END IF * RETURN * * End of DSPT01 * END