SUBROUTINE ZRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, \$ RWORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION RESULT( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), \$ R( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * Purpose * ======= * * ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n * matrix A, and partially tests ZUNGRQ which forms the n-by-n * orthogonal matrix Q. * * ZRQT01 compares R with A*Q', and checks that Q is orthogonal. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * N (input) INTEGER * The number of columns of the matrix A. N >= 0. * * A (input) COMPLEX*16 array, dimension (LDA,N) * The m-by-n matrix A. * * AF (output) COMPLEX*16 array, dimension (LDA,N) * Details of the RQ factorization of A, as returned by ZGERQF. * See ZGERQF for further details. * * Q (output) COMPLEX*16 array, dimension (LDA,N) * The n-by-n orthogonal matrix Q. * * R (workspace) COMPLEX*16 array, dimension (LDA,max(M,N)) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and L. * LDA >= max(M,N). * * TAU (output) COMPLEX*16 array, dimension (min(M,N)) * The scalar factors of the elementary reflectors, as returned * by ZGERQF. * * WORK (workspace) COMPLEX*16 array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK. * * RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) * * RESULT (output) DOUBLE PRECISION array, dimension (2) * The test ratios: * RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS ) * RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 ROGUE PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) ) * .. * .. Local Scalars .. INTEGER INFO, MINMN DOUBLE PRECISION ANORM, EPS, RESID * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY EXTERNAL DLAMCH, ZLANGE, ZLANSY * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZGERQF, ZHERK, ZLACPY, ZLASET, ZUNGRQ * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX, MIN * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * MINMN = MIN( M, N ) EPS = DLAMCH( 'Epsilon' ) * * Copy the matrix A to the array AF. * CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA ) * * Factorize the matrix A in the array AF. * SRNAMT = 'ZGERQF' CALL ZGERQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) * * Copy details of Q * CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) IF( M.LE.N ) THEN IF( M.GT.0 .AND. M.LT.N ) \$ CALL ZLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA ) IF( M.GT.1 ) \$ CALL ZLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA, \$ Q( N-M+2, N-M+1 ), LDA ) ELSE IF( N.GT.1 ) \$ CALL ZLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA, \$ Q( 2, 1 ), LDA ) END IF * * Generate the n-by-n matrix Q * SRNAMT = 'ZUNGRQ' CALL ZUNGRQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy R * CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), R, \$ LDA ) IF( M.LE.N ) THEN IF( M.GT.0 ) \$ CALL ZLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA, \$ R( 1, N-M+1 ), LDA ) ELSE IF( M.GT.N .AND. N.GT.0 ) \$ CALL ZLACPY( 'Full', M-N, N, AF, LDA, R, LDA ) IF( N.GT.0 ) \$ CALL ZLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA, \$ R( M-N+1, 1 ), LDA ) END IF * * Compute R - A*Q' * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, N, N, \$ DCMPLX( -ONE ), A, LDA, Q, LDA, DCMPLX( ONE ), R, \$ LDA ) * * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . * ANORM = ZLANGE( '1', M, N, A, LDA, RWORK ) RESID = ZLANGE( '1', M, N, R, LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, N ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q*Q' * CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), R, LDA ) CALL ZHERK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, R, \$ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = ZLANSY( '1', 'Upper', N, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / EPS * RETURN * * End of ZRQT01 * END