SUBROUTINE SRQT02( M, N, K, 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 K, LDA, LWORK, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ), \$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * SRQT02 tests SORGRQ, which generates an m-by-n matrix Q with * orthonornmal rows that is defined as the product of k elementary * reflectors. * * Given the RQ factorization of an m-by-n matrix A, SRQT02 generates * the orthogonal matrix Q defined by the factorization of the last k * rows of A; it compares R(m-k+1:m,n-m+1:n) with * A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows 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. * N >= M >= 0. * * K (input) INTEGER * The number of elementary reflectors whose product defines the * matrix Q. M >= K >= 0. * * A (input) REAL array, dimension (LDA,N) * The m-by-n matrix A which was factorized by SRQT01. * * AF (input) REAL array, dimension (LDA,N) * Details of the RQ factorization of A, as returned by SGERQF. * See SGERQF for further details. * * Q (workspace) REAL array, dimension (LDA,N) * * R (workspace) REAL array, dimension (LDA,M) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and L. LDA >= N. * * TAU (input) REAL array, dimension (M) * The scalar factors of the elementary reflectors corresponding * to the RQ factorization in AF. * * 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( R - A*Q' ) / ( N * norm(A) * EPS ) * RESULT(2) = norm( I - Q*Q' ) / ( N * 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 REAL ANORM, EPS, RESID * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SGEMM, SLACPY, SLASET, SORGRQ, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC MAX, REAL * .. * .. 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 = SLAMCH( 'Epsilon' ) * * Copy the last k rows of the factorization to the array Q * CALL SLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA ) IF( K.LT.N ) \$ CALL SLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA, \$ Q( M-K+1, 1 ), LDA ) IF( K.GT.1 ) \$ CALL SLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA, \$ Q( M-K+2, N-K+1 ), LDA ) * * Generate the last n rows of the matrix Q * SRNAMT = 'SORGRQ' CALL SORGRQ( M, N, K, Q, LDA, TAU( M-K+1 ), WORK, LWORK, INFO ) * * Copy R(m-k+1:m,n-m+1:n) * CALL SLASET( 'Full', K, M, ZERO, ZERO, R( M-K+1, N-M+1 ), LDA ) CALL SLACPY( 'Upper', K, K, AF( M-K+1, N-K+1 ), LDA, \$ R( M-K+1, N-K+1 ), LDA ) * * Compute R(m-k+1:m,n-m+1:n) - A(m-k+1:m,1:n) * Q(n-m+1:n,1:n)' * CALL SGEMM( 'No transpose', 'Transpose', K, M, N, -ONE, \$ A( M-K+1, 1 ), LDA, Q, LDA, ONE, R( M-K+1, N-M+1 ), \$ LDA ) * * Compute norm( R - A*Q' ) / ( N * norm(A) * EPS ) . * ANORM = SLANGE( '1', K, N, A( M-K+1, 1 ), LDA, RWORK ) RESID = SLANGE( '1', K, M, R( M-K+1, N-M+1 ), LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, N ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q*Q' * CALL SLASET( 'Full', M, M, ZERO, ONE, R, LDA ) CALL SSYRK( 'Upper', 'No transpose', M, N, -ONE, Q, LDA, ONE, R, \$ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = SLANSY( '1', 'Upper', M, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS * RETURN * * End of SRQT02 * END