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*> \brief \b ZTZT02
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION ZTZT02( M, N, AF, LDA, TAU, WORK,
* LWORK )
*
* .. Scalar Arguments ..
* INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTZT02 returns
*> || I - Q'*Q || / ( M * eps)
*> where the matrix Q is defined by the Householder transformations
*> generated by ZTZRQF.
*> \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*16 array, dimension (LDA,N)
*> The output of ZTZRQF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array AF.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is COMPLEX*16 array, dimension (M)
*> Details of the Householder transformations as returned by
*> ZTZRQF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> length of WORK array. Must be >= N*N+N
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
DOUBLE PRECISION FUNCTION ZTZT02( M, N, AF, LDA, TAU, WORK,
$ LWORK )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
COMPLEX*16 AF( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER I
* ..
* .. Local Arrays ..
DOUBLE PRECISION RWORK( 1 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, ZLANGE
EXTERNAL DLAMCH, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLASET, ZLATZM
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, DCONJG, MAX
* ..
* .. Executable Statements ..
*
ZTZT02 = ZERO
*
IF( LWORK.LT.N*N+N ) THEN
CALL XERBLA( 'ZTZT02', 7 )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* Q := I
*
CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), WORK,
$ N )
*
* Q := P(1) * ... * P(m) * Q
*
DO 10 I = M, 1, -1
CALL ZLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA, TAU( I ),
$ WORK( I ), WORK( M+1 ), N, WORK( N*N+1 ) )
10 CONTINUE
*
* Q := P(m)' * ... * P(1)' * Q
*
DO 20 I = 1, M
CALL ZLATZM( 'Left', N-M+1, N, AF( I, M+1 ), LDA,
$ DCONJG( TAU( I ) ), WORK( I ), WORK( M+1 ), N,
$ WORK( N*N+1 ) )
20 CONTINUE
*
* Q := Q - I
*
DO 30 I = 1, N
WORK( ( I-1 )*N+I ) = WORK( ( I-1 )*N+I ) - ONE
30 CONTINUE
*
ZTZT02 = ZLANGE( 'One-norm', N, N, WORK, N, RWORK ) /
$ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
RETURN
*
* End of ZTZT02
*
END
|
