You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
180 lines
4.3 KiB
180 lines
4.3 KiB
*> \brief \b SRZT01
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* REAL FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK,
|
|
* LWORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
|
|
* $ WORK( LWORK )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SRZT01 returns
|
|
*> || A - R*Q || / ( M * eps * ||A|| )
|
|
*> for an upper trapezoidal A that was factored with STZRZF.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrices A and AF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrices A and AF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is REAL array, dimension (LDA,N)
|
|
*> The original upper trapezoidal M by N matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] AF
|
|
*> \verbatim
|
|
*> AF is REAL array, dimension (LDA,N)
|
|
*> The output of STZRZF for input matrix A.
|
|
*> The lower triangle is not referenced.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the arrays A and AF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TAU
|
|
*> \verbatim
|
|
*> TAU is REAL array, dimension (M)
|
|
*> Details of the Householder transformations as returned by
|
|
*> STZRZF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL array, dimension (LWORK)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is INTEGER
|
|
*> The length of the array WORK. LWORK >= m*n + m*nb.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup single_lin
|
|
*
|
|
* =====================================================================
|
|
REAL FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK,
|
|
$ LWORK )
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL A( LDA, * ), AF( LDA, * ), TAU( * ),
|
|
$ WORK( LWORK )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, INFO, J
|
|
REAL NORMA
|
|
* ..
|
|
* .. Local Arrays ..
|
|
REAL RWORK( 1 )
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH, SLANGE
|
|
EXTERNAL SLAMCH, SLANGE
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SAXPY, SLASET, SORMRZ, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, REAL
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
SRZT01 = ZERO
|
|
*
|
|
IF( LWORK.LT.M*N+M ) THEN
|
|
CALL XERBLA( 'SRZT01', 8 )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( M.LE.0 .OR. N.LE.0 )
|
|
$ RETURN
|
|
*
|
|
NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK )
|
|
*
|
|
* Copy upper triangle R
|
|
*
|
|
CALL SLASET( '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)
|
|
*
|
|
CALL SORMRZ( 'Right', 'No transpose', M, N, M, N-M, AF, LDA, TAU,
|
|
$ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO )
|
|
*
|
|
* R = R - A
|
|
*
|
|
DO 30 I = 1, N
|
|
CALL SAXPY( M, -ONE, A( 1, I ), 1, WORK( ( I-1 )*M+1 ), 1 )
|
|
30 CONTINUE
|
|
*
|
|
SRZT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK )
|
|
*
|
|
SRZT01 = SRZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
|
|
IF( NORMA.NE.ZERO )
|
|
$ SRZT01 = SRZT01 / NORMA
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SRZT01
|
|
*
|
|
END
|
|
|