SUBROUTINE SQLT01( M, N, 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 LDA, LWORK, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ), \$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * SQLT01 tests SGEQLF, which computes the QL factorization of an m-by-n * matrix A, and partially tests SORGQL which forms the m-by-m * orthogonal matrix Q. * * SQLT01 compares L with Q'*A, 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) REAL array, dimension (LDA,N) * The m-by-n matrix A. * * AF (output) REAL array, dimension (LDA,N) * Details of the QL factorization of A, as returned by SGEQLF. * See SGEQLF for further details. * * Q (output) REAL array, dimension (LDA,M) * The m-by-m orthogonal matrix Q. * * L (workspace) REAL array, dimension (LDA,max(M,N)) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and R. * LDA >= max(M,N). * * TAU (output) REAL array, dimension (min(M,N)) * The scalar factors of the elementary reflectors, as returned * by SGEQLF. * * WORK (workspace) REAL array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK. * * RWORK (workspace) REAL array, dimension (M) * * RESULT (output) REAL 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 .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) REAL ROGUE PARAMETER ( ROGUE = -1.0E+10 ) * .. * .. Local Scalars .. INTEGER INFO, MINMN REAL ANORM, EPS, RESID * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SGEMM, SGEQLF, SLACPY, SLASET, SORGQL, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * MINMN = MIN( M, N ) EPS = SLAMCH( 'Epsilon' ) * * Copy the matrix A to the array AF. * CALL SLACPY( 'Full', M, N, A, LDA, AF, LDA ) * * Factorize the matrix A in the array AF. * SRNAMT = 'SGEQLF' CALL SGEQLF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) * * Copy details of Q * CALL SLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) IF( M.GE.N ) THEN IF( N.LT.M .AND. N.GT.0 ) \$ CALL SLACPY( 'Full', M-N, N, AF, LDA, Q( 1, M-N+1 ), LDA ) IF( N.GT.1 ) \$ CALL SLACPY( 'Upper', N-1, N-1, AF( M-N+1, 2 ), LDA, \$ Q( M-N+1, M-N+2 ), LDA ) ELSE IF( M.GT.1 ) \$ CALL SLACPY( 'Upper', M-1, M-1, AF( 1, N-M+2 ), LDA, \$ Q( 1, 2 ), LDA ) END IF * * Generate the m-by-m matrix Q * SRNAMT = 'SORGQL' CALL SORGQL( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy L * CALL SLASET( 'Full', M, N, ZERO, ZERO, L, LDA ) IF( M.GE.N ) THEN IF( N.GT.0 ) \$ CALL SLACPY( 'Lower', N, N, AF( M-N+1, 1 ), LDA, \$ L( M-N+1, 1 ), LDA ) ELSE IF( N.GT.M .AND. M.GT.0 ) \$ CALL SLACPY( 'Full', M, N-M, AF, LDA, L, LDA ) IF( M.GT.0 ) \$ CALL SLACPY( 'Lower', M, M, AF( 1, N-M+1 ), LDA, \$ L( 1, N-M+1 ), LDA ) END IF * * Compute L - Q'*A * CALL SGEMM( 'Transpose', 'No transpose', M, N, M, -ONE, Q, LDA, A, \$ LDA, ONE, L, LDA ) * * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) . * ANORM = SLANGE( '1', M, N, A, LDA, RWORK ) RESID = SLANGE( '1', M, N, L, LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, M ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q'*Q * CALL SLASET( 'Full', M, M, ZERO, ONE, L, LDA ) CALL SSYRK( 'Upper', 'Transpose', M, M, -ONE, Q, LDA, ONE, L, \$ LDA ) * * Compute norm( I - Q'*Q ) / ( M * EPS ) . * RESID = SLANSY( '1', 'Upper', M, L, LDA, RWORK ) * RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS * RETURN * * End of SQLT01 * END