231 lines
6.2 KiB
Fortran
231 lines
6.2 KiB
Fortran
*> \brief \b SQRT02
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
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* RWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
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* $ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
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* $ WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SQRT02 tests SORGQR, which generates an m-by-n matrix Q with
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*> orthonornmal columns that is defined as the product of k elementary
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*> reflectors.
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*>
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*> Given the QR factorization of an m-by-n matrix A, SQRT02 generates
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*> the orthogonal matrix Q defined by the factorization of the first k
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*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
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*> and checks that the columns of Q are orthonormal.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix Q to be generated. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix Q to be generated.
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*> M >= N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of elementary reflectors whose product defines the
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*> matrix Q. N >= K >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The m-by-n matrix A which was factorized by SQRT01.
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*> \endverbatim
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*>
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*> \param[in] AF
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*> \verbatim
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*> AF is REAL array, dimension (LDA,N)
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*> Details of the QR factorization of A, as returned by SGEQRF.
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*> See SGEQRF for further details.
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is REAL array, dimension (LDA,N)
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*> \endverbatim
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*>
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*> \param[out] R
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*> \verbatim
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*> R is REAL array, dimension (LDA,N)
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the arrays A, AF, Q and R. LDA >= M.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (N)
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*> The scalar factors of the elementary reflectors corresponding
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*> to the QR factorization in AF.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (M)
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (2)
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*> The test ratios:
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*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
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*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
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$ RWORK, RESULT )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
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$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
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$ WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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REAL ROGUE
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PARAMETER ( ROGUE = -1.0E+10 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO
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REAL ANORM, EPS, RESID
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE, SLANSY
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EXTERNAL SLAMCH, SLANGE, SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM, SLACPY, SLASET, SORGQR, SSYRK
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, REAL
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* ..
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* .. Scalars in Common ..
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CHARACTER*32 SRNAMT
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* ..
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* .. Common blocks ..
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Executable Statements ..
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*
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EPS = SLAMCH( 'Epsilon' )
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*
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* Copy the first k columns of the factorization to the array Q
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*
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CALL SLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA )
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CALL SLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
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*
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* Generate the first n columns of the matrix Q
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*
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SRNAMT = 'SORGQR'
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CALL SORGQR( M, N, K, Q, LDA, TAU, WORK, LWORK, INFO )
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*
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* Copy R(1:n,1:k)
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*
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CALL SLASET( 'Full', N, K, ZERO, ZERO, R, LDA )
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CALL SLACPY( 'Upper', N, K, AF, LDA, R, LDA )
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*
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* Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
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*
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CALL SGEMM( 'Transpose', 'No transpose', N, K, M, -ONE, Q, LDA, A,
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$ LDA, ONE, R, LDA )
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*
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* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
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*
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ANORM = SLANGE( '1', M, K, A, LDA, RWORK )
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RESID = SLANGE( '1', N, K, R, LDA, RWORK )
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IF( ANORM.GT.ZERO ) THEN
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RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, M ) ) ) / ANORM ) / EPS
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ELSE
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RESULT( 1 ) = ZERO
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END IF
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*
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* Compute I - Q'*Q
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*
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CALL SLASET( 'Full', N, N, ZERO, ONE, R, LDA )
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CALL SSYRK( 'Upper', 'Transpose', N, M, -ONE, Q, LDA, ONE, R,
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$ LDA )
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*
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* Compute norm( I - Q'*Q ) / ( M * EPS ) .
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*
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RESID = SLANSY( '1', 'Upper', N, R, LDA, RWORK )
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*
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RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS
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*
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RETURN
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*
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* End of SQRT02
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*
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END
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