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SUBROUTINE SQRT02( 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 * ======= * * SQRT02 tests SORGQR, which generates an m-by-n matrix Q with * orthonornmal columns that is defined as the product of k elementary * reflectors. * * Given the QR factorization of an m-by-n matrix A, SQRT02 generates * the orthogonal matrix Q defined by the factorization of the first k * columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), * 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) REAL array, dimension (LDA,N) * The m-by-n matrix A which was factorized by SQRT01. * * AF (input) REAL array, dimension (LDA,N) * Details of the QR factorization of A, as returned by SGEQRF. * See SGEQRF for further details. * * Q (workspace) REAL array, dimension (LDA,N) * * R (workspace) REAL array, dimension (LDA,N) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and R. LDA >= M. * * TAU (input) REAL array, dimension (N) * The scalar factors of the elementary reflectors corresponding * to the QR 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 - 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 REAL ANORM, EPS, RESID * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SGEMM, SLACPY, SLASET, SORGQR, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC MAX, REAL * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * EPS = SLAMCH( 'Epsilon' ) * * Copy the first k columns of the factorization to the array Q * CALL SLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA ) CALL SLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) * * Generate the first n columns of the matrix Q * SRNAMT = 'SORGQR' CALL SORGQR( M, N, K, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy R(1:n,1:k) * CALL SLASET( 'Full', N, K, ZERO, ZERO, R, LDA ) CALL SLACPY( 'Upper', N, K, AF, LDA, R, LDA ) * * Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k) * CALL SGEMM( 'Transpose', 'No transpose', N, K, M, -ONE, Q, LDA, A, $ LDA, ONE, R, LDA ) * * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . * ANORM = SLANGE( '1', M, K, A, LDA, RWORK ) RESID = SLANGE( '1', N, K, R, 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', N, N, ZERO, ONE, R, LDA ) CALL SSYRK( 'Upper', 'Transpose', N, M, -ONE, Q, LDA, ONE, R, $ LDA ) * * Compute norm( I - Q'*Q ) / ( M * EPS ) . * RESID = SLANSY( '1', 'Upper', N, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS * RETURN * * End of SQRT02 * END |