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195 lines
4.8 KiB
195 lines
4.8 KiB
2 years ago
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*> \brief \b SLAQZ1
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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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*> \htmlonly
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*> Download SLAQZ1 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slaqz1.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slaqz1.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slaqz1.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLAQZ1( A, LDA, B, LDB, SR1, SR2, SI, BETA1, BETA2,
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* $ V )
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* IMPLICIT NONE
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*
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* Arguments
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* INTEGER, INTENT( IN ) :: LDA, LDB
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* REAL, INTENT( IN ) :: A( LDA, * ), B( LDB, * ), SR1, SR2, SI,
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* $ BETA1, BETA2
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* REAL, INTENT( OUT ) :: V( * )
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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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*> Given a 3-by-3 matrix pencil (A,B), SLAQZ1 sets v to a
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*> scalar multiple of the first column of the product
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*>
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*> (*) K = (A - (beta2*sr2 - i*si)*B)*B^(-1)*(beta1*A - (sr2 + i*si2)*B)*B^(-1).
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*>
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*> It is assumed that either
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*>
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*> 1) sr1 = sr2
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*> or
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*> 2) si = 0.
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*>
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*> This is useful for starting double implicit shift bulges
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*> in the QZ algorithm.
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*> \endverbatim
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*
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*
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* Arguments:
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* ==========
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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 3-by-3 matrix A in (*).
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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 A as declared in
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*> the calling procedure.
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*> \endverbatim
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*
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*> \param[in] B
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*> \verbatim
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*> B is REAL array, dimension (LDB,N)
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*> The 3-by-3 matrix B in (*).
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of B as declared in
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*> the calling procedure.
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*> \endverbatim
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*>
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*> \param[in] SR1
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*> \verbatim
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*> SR1 is REAL
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*> \endverbatim
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*>
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*> \param[in] SR2
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*> \verbatim
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*> SR2 is REAL
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*> \endverbatim
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*>
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*> \param[in] SI
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*> \verbatim
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*> SI is REAL
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*> \endverbatim
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*>
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*> \param[in] BETA1
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*> \verbatim
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*> BETA1 is REAL
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*> \endverbatim
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*>
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*> \param[in] BETA2
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*> \verbatim
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*> BETA2 is REAL
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*> \endverbatim
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*>
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*> \param[out] V
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*> \verbatim
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*> V is REAL array, dimension (N)
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*> A scalar multiple of the first column of the
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*> matrix K in (*).
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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 Thijs Steel, KU Leuven
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*
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*> \date May 2020
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*
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*> \ingroup doubleGEcomputational
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*>
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* =====================================================================
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SUBROUTINE SLAQZ1( A, LDA, B, LDB, SR1, SR2, SI, BETA1, BETA2,
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$ V )
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IMPLICIT NONE
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*
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* Arguments
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INTEGER, INTENT( IN ) :: LDA, LDB
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REAL, INTENT( IN ) :: A( LDA, * ), B( LDB, * ), SR1, SR2, SI,
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$ BETA1, BETA2
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REAL, INTENT( OUT ) :: V( * )
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*
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* Parameters
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REAL :: ZERO, ONE, HALF
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PARAMETER( ZERO = 0.0, ONE = 1.0, HALF = 0.5 )
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*
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* Local scalars
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REAL :: W( 2 ), SAFMIN, SAFMAX, SCALE1, SCALE2
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*
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* External Functions
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REAL, EXTERNAL :: SLAMCH
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LOGICAL, EXTERNAL :: SISNAN
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*
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SAFMIN = SLAMCH( 'SAFE MINIMUM' )
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SAFMAX = ONE/SAFMIN
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*
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* Calculate first shifted vector
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*
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W( 1 ) = BETA1*A( 1, 1 )-SR1*B( 1, 1 )
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W( 2 ) = BETA1*A( 2, 1 )-SR1*B( 2, 1 )
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SCALE1 = SQRT( ABS( W( 1 ) ) ) * SQRT( ABS( W( 2 ) ) )
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IF( SCALE1 .GE. SAFMIN .AND. SCALE1 .LE. SAFMAX ) THEN
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W( 1 ) = W( 1 )/SCALE1
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W( 2 ) = W( 2 )/SCALE1
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END IF
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*
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* Solve linear system
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*
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W( 2 ) = W( 2 )/B( 2, 2 )
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W( 1 ) = ( W( 1 )-B( 1, 2 )*W( 2 ) )/B( 1, 1 )
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SCALE2 = SQRT( ABS( W( 1 ) ) ) * SQRT( ABS( W( 2 ) ) )
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IF( SCALE2 .GE. SAFMIN .AND. SCALE2 .LE. SAFMAX ) THEN
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W( 1 ) = W( 1 )/SCALE2
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W( 2 ) = W( 2 )/SCALE2
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END IF
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*
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* Apply second shift
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*
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V( 1 ) = BETA2*( A( 1, 1 )*W( 1 )+A( 1, 2 )*W( 2 ) )-SR2*( B( 1,
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$ 1 )*W( 1 )+B( 1, 2 )*W( 2 ) )
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V( 2 ) = BETA2*( A( 2, 1 )*W( 1 )+A( 2, 2 )*W( 2 ) )-SR2*( B( 2,
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$ 1 )*W( 1 )+B( 2, 2 )*W( 2 ) )
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V( 3 ) = BETA2*( A( 3, 1 )*W( 1 )+A( 3, 2 )*W( 2 ) )-SR2*( B( 3,
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$ 1 )*W( 1 )+B( 3, 2 )*W( 2 ) )
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*
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* Account for imaginary part
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*
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V( 1 ) = V( 1 )+SI*SI*B( 1, 1 )/SCALE1/SCALE2
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*
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* Check for overflow
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*
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IF( ABS( V( 1 ) ).GT.SAFMAX .OR. ABS( V( 2 ) ) .GT. SAFMAX .OR.
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$ ABS( V( 3 ) ).GT.SAFMAX .OR. SISNAN( V( 1 ) ) .OR.
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$ SISNAN( V( 2 ) ) .OR. SISNAN( V( 3 ) ) ) THEN
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V( 1 ) = ZERO
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V( 2 ) = ZERO
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V( 3 ) = ZERO
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END IF
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*
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* End of SLAQZ1
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*
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END SUBROUTINE
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