DOUBLE PRECISION FUNCTION DTZT01( M, N, A, AF, LDA, TAU, WORK, \$ LWORK ) * * -- 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 .. DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * DTZT01 returns * || A - R*Q || / ( M * eps * ||A|| ) * for an upper trapezoidal A that was factored with DTZRQF. * * 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. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The original upper trapezoidal M by N matrix A. * * AF (input) DOUBLE PRECISION array, dimension (LDA,N) * The output of DTZRQF for input matrix A. * The lower triangle is not referenced. * * LDA (input) INTEGER * The leading dimension of the arrays A and AF. * * TAU (input) DOUBLE PRECISION array, dimension (M) * Details of the Householder transformations as returned by * DTZRQF. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= m*n + m. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION NORMA * .. * .. Local Arrays .. DOUBLE PRECISION RWORK( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DAXPY, DLASET, DLATZM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX * .. * .. Executable Statements .. * DTZT01 = ZERO * IF( LWORK.LT.M*N+M ) THEN CALL XERBLA( 'DTZT01', 8 ) 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 ) * * Copy upper triangle R * CALL DLASET( 'Full', M, N, ZERO, ZERO, WORK, M ) DO 20 J = 1, M DO 10 I = 1, J WORK( ( J-1 )*M+I ) = AF( I, J ) 10 CONTINUE 20 CONTINUE * * R = R * P(1) * ... *P(m) * DO 30 I = 1, M CALL DLATZM( 'Right', I, N-M+1, AF( I, M+1 ), LDA, TAU( I ), \$ WORK( ( I-1 )*M+1 ), WORK( M*M+1 ), M, \$ WORK( M*N+1 ) ) 30 CONTINUE * * R = R - A * DO 40 I = 1, N CALL DAXPY( M, -ONE, A( 1, I ), 1, WORK( ( I-1 )*M+1 ), 1 ) 40 CONTINUE * DTZT01 = DLANGE( 'One-norm', M, N, WORK, M, RWORK ) * DTZT01 = DTZT01 / ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) ) IF( NORMA.NE.ZERO ) \$ DTZT01 = DTZT01 / NORMA * RETURN * * End of DTZT01 * END