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DOUBLE PRECISION FUNCTION DQPT01( M, N, K, A, AF, LDA, TAU, JPVT,
$ WORK, LWORK ) * * -- 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 .. INTEGER JPVT( * ) DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), TAU( * ), $ WORK( LWORK ) * .. * * Purpose * ======= * * DQPT01 tests the QR-factorization with pivoting of a matrix A. The * array AF contains the (possibly partial) QR-factorization of A, where * the upper triangle of AF(1:k,1:k) is a partial triangular factor, * the entries below the diagonal in the first k columns are the * Householder vectors, and the rest of AF contains a partially updated * matrix. * * This function returns ||A*P - Q*R||/(||norm(A)||*eps*M) * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrices A and AF. * * N (input) INTEGER * The number of columns of the matrices A and AF. * * K (input) INTEGER * The number of columns of AF that have been reduced * to upper triangular form. * * A (input) DOUBLE PRECISION array, dimension (LDA, N) * The original matrix A. * * AF (input) DOUBLE PRECISION array, dimension (LDA,N) * The (possibly partial) output of DGEQPF. The upper triangle * of AF(1:k,1:k) is a partial triangular factor, the entries * below the diagonal in the first k columns are the Householder * vectors, and the rest of AF contains a partially updated * matrix. * * LDA (input) INTEGER * The leading dimension of the arrays A and AF. * * TAU (input) DOUBLE PRECISION array, dimension (K) * Details of the Householder transformations as returned by * DGEQPF. * * JPVT (input) INTEGER array, dimension (N) * Pivot information as returned by DGEQPF. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= M*N+N. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J DOUBLE PRECISION NORMA * .. * .. Local Arrays .. DOUBLE PRECISION RWORK( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DAXPY, DCOPY, DORMQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Executable Statements .. * DQPT01 = ZERO * * Test if there is enough workspace * IF( LWORK.LT.M*N+N ) THEN CALL XERBLA( 'DQPT01', 10 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * NORMA = DLANGE( 'One-norm', M, N, A, LDA, RWORK ) * DO 30 J = 1, K DO 10 I = 1, MIN( J, M ) WORK( ( J-1 )*M+I ) = AF( I, J ) 10 CONTINUE DO 20 I = J + 1, M WORK( ( J-1 )*M+I ) = ZERO 20 CONTINUE 30 CONTINUE DO 40 J = K + 1, N CALL DCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 ) 40 CONTINUE * CALL DORMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK, $ M, WORK( M*N+1 ), LWORK-M*N, INFO ) * DO 50 J = 1, N * * Compare i-th column of QR and jpvt(i)-th column of A * CALL DAXPY( M, -ONE, A( 1, JPVT( J ) ), 1, WORK( ( J-1 )*M+1 ), $ 1 ) 50 CONTINUE * DQPT01 = DLANGE( 'One-norm', M, N, WORK, M, RWORK ) / $ ( DBLE( MAX( M, N ) )*DLAMCH( 'Epsilon' ) ) IF( NORMA.NE.ZERO ) $ DQPT01 = DQPT01 / NORMA * RETURN * * End of DQPT01 * END |