*> \brief \b DPPT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, * RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDWORK, N * DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. * DOUBLE PRECISION A( * ), AINV( * ), RWORK( * ), * $ WORK( LDWORK, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> 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. *> \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 DOUBLE PRECISION array, dimension (N*(N+1)/2) *> The original symmetric matrix A, stored as a packed *> triangular matrix. *> \endverbatim *> *> \param[in] AINV *> \verbatim *> AINV is DOUBLE PRECISION array, dimension (N*(N+1)/2) *> The (symmetric) inverse of the matrix A, stored as a packed *> triangular matrix. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LDWORK,N) *> \endverbatim *> *> \param[in] LDWORK *> \verbatim *> LDWORK is INTEGER *> The leading dimension of the array WORK. LDWORK >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is DOUBLE PRECISION *> The reciprocal of the condition number of A, computed as *> ( 1/norm(A) ) / norm(AINV). *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, $ 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 LDWORK, N DOUBLE PRECISION RCOND, RESID * .. * .. Array Arguments .. DOUBLE PRECISION A( * ), AINV( * ), RWORK( * ), $ WORK( LDWORK, * ) * .. * * ===================================================================== * * .. 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