SUBROUTINE DBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDB, LDC, LDU, M, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION B( LDB, * ), C( LDC, * ), U( LDU, * ), \$ WORK( * ) * .. * * Purpose * ======= * * DBDT02 tests the change of basis C = U' * B by computing the residual * * RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ), * * where B and C are M by N matrices, U is an M by M orthogonal matrix, * and EPS is the machine precision. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrices B and C and the order of * the matrix Q. * * N (input) INTEGER * The number of columns of the matrices B and C. * * B (input) DOUBLE PRECISION array, dimension (LDB,N) * The m by n matrix B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,M). * * C (input) DOUBLE PRECISION array, dimension (LDC,N) * The m by n matrix C, assumed to contain U' * B. * * LDC (input) INTEGER * The leading dimension of the array C. LDC >= max(1,M). * * U (input) DOUBLE PRECISION array, dimension (LDU,M) * The m by m orthogonal matrix U. * * LDU (input) INTEGER * The leading dimension of the array U. LDU >= max(1,M). * * WORK (workspace) DOUBLE PRECISION array, dimension (M) * * RESID (output) DOUBLE PRECISION * RESID = norm( B - U * C ) / ( max(m,n) * norm(B) * EPS ), * * ====================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION BNORM, EPS, REALMN * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DLANGE EXTERNAL DASUM, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Executable Statements .. * * Quick return if possible * RESID = ZERO IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN REALMN = DBLE( MAX( M, N ) ) EPS = DLAMCH( 'Precision' ) * * Compute norm( B - U * C ) * DO 10 J = 1, N CALL DCOPY( M, B( 1, J ), 1, WORK, 1 ) CALL DGEMV( 'No transpose', M, M, -ONE, U, LDU, C( 1, J ), 1, \$ ONE, WORK, 1 ) RESID = MAX( RESID, DASUM( M, WORK, 1 ) ) 10 CONTINUE * * Compute norm of B. * BNORM = DLANGE( '1', M, N, B, LDB, WORK ) * IF( BNORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) \$ RESID = ONE / EPS ELSE IF( BNORM.GE.RESID ) THEN RESID = ( RESID / BNORM ) / ( REALMN*EPS ) ELSE IF( BNORM.LT.ONE ) THEN RESID = ( MIN( RESID, REALMN*BNORM ) / BNORM ) / \$ ( REALMN*EPS ) ELSE RESID = MIN( RESID / BNORM, REALMN ) / ( REALMN*EPS ) END IF END IF END IF RETURN * * End of DBDT02 * END