*> \brief \b CRZT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * REAL FUNCTION CRZT02( M, N, AF, LDA, TAU, WORK, * LWORK ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX AF( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CRZT02 returns *> || I - Q'*Q || / ( M * eps) *> where the matrix Q is defined by the Householder transformations *> generated by CTZRZF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix AF. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix AF. *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is COMPLEX array, dimension (LDA,N) *> The output of CTZRZF. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array AF. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX array, dimension (M) *> Details of the Householder transformations as returned by *> CTZRZF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> Length of WORK array. LWORK >= N*N+N. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex_lin * * ===================================================================== REAL FUNCTION CRZT02( M, N, AF, LDA, TAU, WORK, $ LWORK ) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX AF( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, INFO * .. * .. Local Arrays .. REAL RWORK( 1 ) * .. * .. External Functions .. REAL CLANGE, SLAMCH EXTERNAL CLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CLASET, CUNMRZ, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, MAX, REAL * .. * .. Executable Statements .. * CRZT02 = ZERO * IF( LWORK.LT.N*N+N ) THEN CALL XERBLA( 'CRZT02', 7 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * * Q := I * CALL CLASET( 'Full', N, N, CMPLX( ZERO ), CMPLX( ONE ), WORK, N ) * * Q := P(1) * ... * P(m) * Q * CALL CUNMRZ( 'Left', 'No transpose', N, N, M, N-M, AF, LDA, TAU, $ WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO ) * * Q := P(m)' * ... * P(1)' * Q * CALL CUNMRZ( 'Left', 'Conjugate transpose', N, N, M, N-M, AF, LDA, $ TAU, WORK, N, WORK( N*N+1 ), LWORK-N*N, INFO ) * * Q := Q - I * DO 10 I = 1, N WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE 10 CONTINUE * CRZT02 = CLANGE( 'One-norm', N, N, WORK, N, RWORK ) / $ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) RETURN * * End of CRZT02 * END