REAL FUNCTION CTZT01( 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 .. COMPLEX A( LDA, * ), AF( LDA, * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * CTZT01 returns * || A - R*Q || / ( M * eps * ||A|| ) * for an upper trapezoidal A that was factored with CTZRQF. * * 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) COMPLEX array, dimension (LDA,N) * The original upper trapezoidal M by N matrix A. * * AF (input) COMPLEX array, dimension (LDA,N) * The output of CTZRQF for input matrix A. * The lower triangle is not referenced. * * LDA (input) INTEGER * The leading dimension of the arrays A and AF. * * TAU (input) COMPLEX array, dimension (M) * Details of the Householder transformations as returned by * CTZRQF. * * WORK (workspace) COMPLEX array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= m*n + m. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, J REAL NORMA * .. * .. Local Arrays .. REAL RWORK( 1 ) * .. * .. External Functions .. REAL CLANGE, SLAMCH EXTERNAL CLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CAXPY, CLATZM, CLASET, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, MAX, REAL * .. * .. Executable Statements .. * CTZT01 = ZERO * IF( LWORK.LT.M*N+M ) THEN CALL XERBLA( 'CTZT01', 8 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN * NORMA = CLANGE( 'One-norm', M, N, A, LDA, RWORK ) * * Copy upper triangle R * CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( 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 CLATZM( '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 CAXPY( M, CMPLX( -ONE ), A( 1, I ), 1, \$ WORK( ( I-1 )*M+1 ), 1 ) 40 CONTINUE * CTZT01 = CLANGE( 'One-norm', M, N, WORK, M, RWORK ) * CTZT01 = CTZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) IF( NORMA.NE.ZERO ) \$ CTZT01 = CTZT01 / NORMA * RETURN * * End of CTZT01 * END