SUBROUTINE DQLT02( M, N, K, A, AF, Q, L, 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 K, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ), \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * DQLT02 tests DORGQL, which generates an m-by-n matrix Q with * orthonornmal columns that is defined as the product of k elementary * reflectors. * * Given the QL factorization of an m-by-n matrix A, DQLT02 generates * the orthogonal matrix Q defined by the factorization of the last k * columns of A; it compares L(m-n+1:m,n-k+1:n) with * Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are * orthonormal. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix Q to be generated. M >= 0. * * N (input) INTEGER * The number of columns of the matrix Q to be generated. * M >= N >= 0. * * K (input) INTEGER * The number of elementary reflectors whose product defines the * matrix Q. N >= K >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The m-by-n matrix A which was factorized by DQLT01. * * AF (input) DOUBLE PRECISION array, dimension (LDA,N) * Details of the QL factorization of A, as returned by DGEQLF. * See DGEQLF for further details. * * Q (workspace) DOUBLE PRECISION array, dimension (LDA,N) * * L (workspace) DOUBLE PRECISION array, dimension (LDA,N) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and L. LDA >= M. * * TAU (input) DOUBLE PRECISION array, dimension (N) * The scalar factors of the elementary reflectors corresponding * to the QL factorization in AF. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK. * * RWORK (workspace) DOUBLE PRECISION array, dimension (M) * * RESULT (output) DOUBLE PRECISION array, dimension (2) * The test ratios: * RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS ) * RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D+10 ) * .. * .. Local Scalars .. INTEGER INFO DOUBLE PRECISION ANORM, EPS, RESID * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE, DLANSY EXTERNAL DLAMCH, DLANGE, DLANSY * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY, DLASET, DORGQL, DSYRK * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO RETURN END IF * EPS = DLAMCH( 'Epsilon' ) * * Copy the last k columns of the factorization to the array Q * CALL DLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA ) IF( K.LT.M ) \$ CALL DLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA, \$ Q( 1, N-K+1 ), LDA ) IF( K.GT.1 ) \$ CALL DLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA, \$ Q( M-K+1, N-K+2 ), LDA ) * * Generate the last n columns of the matrix Q * SRNAMT = 'DORGQL' CALL DORGQL( M, N, K, Q, LDA, TAU( N-K+1 ), WORK, LWORK, INFO ) * * Copy L(m-n+1:m,n-k+1:n) * CALL DLASET( 'Full', N, K, ZERO, ZERO, L( M-N+1, N-K+1 ), LDA ) CALL DLACPY( 'Lower', K, K, AF( M-K+1, N-K+1 ), LDA, \$ L( M-K+1, N-K+1 ), LDA ) * * Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n) * CALL DGEMM( 'Transpose', 'No transpose', N, K, M, -ONE, Q, LDA, \$ A( 1, N-K+1 ), LDA, ONE, L( M-N+1, N-K+1 ), LDA ) * * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) . * ANORM = DLANGE( '1', M, K, A( 1, N-K+1 ), LDA, RWORK ) RESID = DLANGE( '1', N, K, L( M-N+1, N-K+1 ), LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q'*Q * CALL DLASET( 'Full', N, N, ZERO, ONE, L, LDA ) CALL DSYRK( 'Upper', 'Transpose', N, M, -ONE, Q, LDA, ONE, L, \$ LDA ) * * Compute norm( I - Q'*Q ) / ( M * EPS ) . * RESID = DLANSY( '1', 'Upper', N, L, LDA, RWORK ) * RESULT( 2 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / EPS * RETURN * * End of DQLT02 * END