SUBROUTINE SORT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RESID ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER ROWCOL INTEGER LDU, LWORK, M, N REAL RESID * .. * .. Array Arguments .. REAL U( LDU, * ), WORK( * ) * .. * * Purpose * ======= * * SORT01 checks that the matrix U is orthogonal by computing the ratio * * RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R', * or * RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'. * * Alternatively, if there isn't sufficient workspace to form * I - U*U' or I - U'*U, the ratio is computed as * * RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R', * or * RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'. * * where EPS is the machine precision. ROWCOL is used only if m = n; * if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is * assumed to be 'R'. * * Arguments * ========= * * ROWCOL (input) CHARACTER * Specifies whether the rows or columns of U should be checked * for orthogonality. Used only if M = N. * = 'R': Check for orthogonal rows of U * = 'C': Check for orthogonal columns of U * * M (input) INTEGER * The number of rows of the matrix U. * * N (input) INTEGER * The number of columns of the matrix U. * * U (input) REAL array, dimension (LDU,N) * The orthogonal matrix U. U is checked for orthogonal columns * if m > n or if m = n and ROWCOL = 'C'. U is checked for * orthogonal rows if m < n or if m = n and ROWCOL = 'R'. * * LDU (input) INTEGER * The leading dimension of the array U. LDU >= max(1,M). * * WORK (workspace) REAL array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. For best performance, LWORK * should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if * ROWCOL = 'R', but the test will be done even if LWORK is 0. * * RESID (output) REAL * RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or * RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. CHARACTER TRANSU INTEGER I, J, K, LDWORK, MNMIN REAL EPS, TMP * .. * .. External Functions .. LOGICAL LSAME REAL SDOT, SLAMCH, SLANSY EXTERNAL LSAME, SDOT, SLAMCH, SLANSY * .. * .. External Subroutines .. EXTERNAL SLASET, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Executable Statements .. * RESID = ZERO * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN * EPS = SLAMCH( 'Precision' ) IF( M.LT.N .OR. ( M.EQ.N .AND. LSAME( ROWCOL, 'R' ) ) ) THEN TRANSU = 'N' K = N ELSE TRANSU = 'T' K = M END IF MNMIN = MIN( M, N ) * IF( ( MNMIN+1 )*MNMIN.LE.LWORK ) THEN LDWORK = MNMIN ELSE LDWORK = 0 END IF IF( LDWORK.GT.0 ) THEN * * Compute I - U*U' or I - U'*U. * CALL SLASET( 'Upper', MNMIN, MNMIN, ZERO, ONE, WORK, LDWORK ) CALL SSYRK( 'Upper', TRANSU, MNMIN, K, -ONE, U, LDU, ONE, WORK, \$ LDWORK ) * * Compute norm( I - U*U' ) / ( K * EPS ) . * RESID = SLANSY( '1', 'Upper', MNMIN, WORK, LDWORK, \$ WORK( LDWORK*MNMIN+1 ) ) RESID = ( RESID / REAL( K ) ) / EPS ELSE IF( TRANSU.EQ.'T' ) THEN * * Find the maximum element in abs( I - U'*U ) / ( m * EPS ) * DO 20 J = 1, N DO 10 I = 1, J IF( I.NE.J ) THEN TMP = ZERO ELSE TMP = ONE END IF TMP = TMP - SDOT( M, U( 1, I ), 1, U( 1, J ), 1 ) RESID = MAX( RESID, ABS( TMP ) ) 10 CONTINUE 20 CONTINUE RESID = ( RESID / REAL( M ) ) / EPS ELSE * * Find the maximum element in abs( I - U*U' ) / ( n * EPS ) * DO 40 J = 1, M DO 30 I = 1, J IF( I.NE.J ) THEN TMP = ZERO ELSE TMP = ONE END IF TMP = TMP - SDOT( N, U( J, 1 ), LDU, U( I, 1 ), LDU ) RESID = MAX( RESID, ABS( TMP ) ) 30 CONTINUE 40 CONTINUE RESID = ( RESID / REAL( N ) ) / EPS END IF RETURN * * End of SORT01 * END