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227 lines
6.1 KiB
227 lines
6.1 KiB
2 years ago
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*> \brief \b SORT01
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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 SORT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER ROWCOL
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* INTEGER LDU, LWORK, M, N
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL U( LDU, * ), WORK( * )
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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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*> SORT01 checks that the matrix U is orthogonal by computing the ratio
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*>
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*> RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
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*> or
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*> RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
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*>
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*> Alternatively, if there isn't sufficient workspace to form
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*> I - U*U' or I - U'*U, the ratio is computed as
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*>
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*> RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
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*> or
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*> RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
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*>
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*> where EPS is the machine precision. ROWCOL is used only if m = n;
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*> if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
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*> assumed to be 'R'.
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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] ROWCOL
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*> \verbatim
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*> ROWCOL is CHARACTER
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*> Specifies whether the rows or columns of U should be checked
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*> for orthogonality. Used only if M = N.
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*> = 'R': Check for orthogonal rows of U
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*> = 'C': Check for orthogonal columns of U
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*> \endverbatim
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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 U.
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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 U.
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*> \endverbatim
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*>
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*> \param[in] U
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*> \verbatim
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*> U is REAL array, dimension (LDU,N)
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*> The orthogonal matrix U. U is checked for orthogonal columns
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*> if m > n or if m = n and ROWCOL = 'C'. U is checked for
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*> orthogonal rows if m < n or if m = n and ROWCOL = 'R'.
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*> \endverbatim
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*>
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*> \param[in] LDU
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*> \verbatim
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*> LDU is INTEGER
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*> The leading dimension of the array U. LDU >= max(1,M).
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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 length of the array WORK. For best performance, LWORK
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*> should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if
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*> ROWCOL = 'R', but the test will be done even if LWORK is 0.
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is REAL
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*> RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
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*> RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
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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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*> \ingroup single_eig
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*
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* =====================================================================
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SUBROUTINE SORT01( ROWCOL, M, N, U, LDU, WORK, LWORK, RESID )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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CHARACTER ROWCOL
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INTEGER LDU, LWORK, M, N
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL U( LDU, * ), WORK( * )
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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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* ..
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* .. Local Scalars ..
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CHARACTER TRANSU
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INTEGER I, J, K, LDWORK, MNMIN
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REAL EPS, TMP
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SDOT, SLAMCH, SLANSY
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EXTERNAL LSAME, SDOT, SLAMCH, SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL SLASET, SSYRK
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, REAL
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* ..
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* .. Executable Statements ..
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*
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RESID = ZERO
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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*
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EPS = SLAMCH( 'Precision' )
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IF( M.LT.N .OR. ( M.EQ.N .AND. LSAME( ROWCOL, 'R' ) ) ) THEN
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TRANSU = 'N'
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K = N
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ELSE
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TRANSU = 'T'
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K = M
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END IF
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MNMIN = MIN( M, N )
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*
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IF( ( MNMIN+1 )*MNMIN.LE.LWORK ) THEN
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LDWORK = MNMIN
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ELSE
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LDWORK = 0
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END IF
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IF( LDWORK.GT.0 ) THEN
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*
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* Compute I - U*U' or I - U'*U.
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*
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CALL SLASET( 'Upper', MNMIN, MNMIN, ZERO, ONE, WORK, LDWORK )
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CALL SSYRK( 'Upper', TRANSU, MNMIN, K, -ONE, U, LDU, ONE, WORK,
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$ LDWORK )
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*
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* Compute norm( I - U*U' ) / ( K * EPS ) .
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*
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RESID = SLANSY( '1', 'Upper', MNMIN, WORK, LDWORK,
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$ WORK( LDWORK*MNMIN+1 ) )
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RESID = ( RESID / REAL( K ) ) / EPS
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ELSE IF( TRANSU.EQ.'T' ) THEN
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*
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* Find the maximum element in abs( I - U'*U ) / ( m * EPS )
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*
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DO 20 J = 1, N
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DO 10 I = 1, J
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IF( I.NE.J ) THEN
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TMP = ZERO
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ELSE
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TMP = ONE
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END IF
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TMP = TMP - SDOT( M, U( 1, I ), 1, U( 1, J ), 1 )
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RESID = MAX( RESID, ABS( TMP ) )
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10 CONTINUE
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20 CONTINUE
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RESID = ( RESID / REAL( M ) ) / EPS
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ELSE
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*
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* Find the maximum element in abs( I - U*U' ) / ( n * EPS )
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*
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DO 40 J = 1, M
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DO 30 I = 1, J
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IF( I.NE.J ) THEN
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TMP = ZERO
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ELSE
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TMP = ONE
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END IF
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TMP = TMP - SDOT( N, U( J, 1 ), LDU, U( I, 1 ), LDU )
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RESID = MAX( RESID, ABS( TMP ) )
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30 CONTINUE
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40 CONTINUE
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RESID = ( RESID / REAL( N ) ) / EPS
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END IF
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RETURN
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*
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* End of SORT01
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*
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END
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