SUBROUTINE DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, \$ RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDWORK, N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( * ), AINV( * ), RWORK( * ), \$ WORK( LDWORK, * ) * .. * * Purpose * ======= * * DPPT03 computes the residual for a symmetric packed matrix times its * inverse: * norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * 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 (N*(N+1)/2) * The original symmetric matrix A, stored as a packed * triangular matrix. * * AINV (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) * The (symmetric) inverse of the matrix A, stored as a packed * triangular matrix. * * WORK (workspace) DOUBLE PRECISION array, dimension (LDWORK,N) * * LDWORK (input) INTEGER * The leading dimension of the array WORK. LDWORK >= max(1,N). * * RWORK (workspace) DOUBLE PRECISION array, dimension (N) * * RCOND (output) DOUBLE PRECISION * The reciprocal of the condition number of A, computed as * ( 1/norm(A) ) / norm(AINV). * * RESID (output) DOUBLE PRECISION * norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, JJ DOUBLE PRECISION AINVNM, ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANGE, DLANSP EXTERNAL LSAME, DLAMCH, DLANGE, DLANSP * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. External Subroutines .. EXTERNAL DCOPY, DSPMV * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RCOND = ONE RESID = ZERO RETURN END IF * * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. * EPS = DLAMCH( 'Epsilon' ) ANORM = DLANSP( '1', UPLO, N, A, RWORK ) AINVNM = DLANSP( '1', UPLO, N, AINV, RWORK ) IF( ANORM.LE.ZERO .OR. AINVNM.EQ.ZERO ) THEN RCOND = ZERO RESID = ONE / EPS RETURN END IF RCOND = ( ONE / ANORM ) / AINVNM * * UPLO = 'U': * Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and * expand it to a full matrix, then multiply by A one column at a * time, moving the result one column to the left. * IF( LSAME( UPLO, 'U' ) ) THEN * * Copy AINV * JJ = 1 DO 10 J = 1, N - 1 CALL DCOPY( J, AINV( JJ ), 1, WORK( 1, J+1 ), 1 ) CALL DCOPY( J-1, AINV( JJ ), 1, WORK( J, 2 ), LDWORK ) JJ = JJ + J 10 CONTINUE JJ = ( ( N-1 )*N ) / 2 + 1 CALL DCOPY( N-1, AINV( JJ ), 1, WORK( N, 2 ), LDWORK ) * * Multiply by A * DO 20 J = 1, N - 1 CALL DSPMV( 'Upper', N, -ONE, A, WORK( 1, J+1 ), 1, ZERO, \$ WORK( 1, J ), 1 ) 20 CONTINUE CALL DSPMV( 'Upper', N, -ONE, A, AINV( JJ ), 1, ZERO, \$ WORK( 1, N ), 1 ) * * UPLO = 'L': * Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1) * and multiply by A, moving each column to the right. * ELSE * * Copy AINV * CALL DCOPY( N-1, AINV( 2 ), 1, WORK( 1, 1 ), LDWORK ) JJ = N + 1 DO 30 J = 2, N CALL DCOPY( N-J+1, AINV( JJ ), 1, WORK( J, J-1 ), 1 ) CALL DCOPY( N-J, AINV( JJ+1 ), 1, WORK( J, J ), LDWORK ) JJ = JJ + N - J + 1 30 CONTINUE * * Multiply by A * DO 40 J = N, 2, -1 CALL DSPMV( 'Lower', N, -ONE, A, WORK( 1, J-1 ), 1, ZERO, \$ WORK( 1, J ), 1 ) 40 CONTINUE CALL DSPMV( 'Lower', N, -ONE, A, AINV( 1 ), 1, ZERO, \$ WORK( 1, 1 ), 1 ) * END IF * * Add the identity matrix to WORK . * DO 50 I = 1, N WORK( I, I ) = WORK( I, I ) + ONE 50 CONTINUE * * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) * RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK ) * RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N ) * RETURN * * End of DPPT03 * END