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252 lines
6.8 KiB
252 lines
6.8 KiB
2 years ago
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*> \brief \b SGET53
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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 SGET53( A, LDA, B, LDB, SCALE, WR, WI, RESULT, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDB
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* REAL RESULT, SCALE, WI, WR
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), B( LDB, * )
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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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*> SGET53 checks the generalized eigenvalues computed by SLAG2.
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*>
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*> The basic test for an eigenvalue is:
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*>
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*> | det( s A - w B ) |
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*> RESULT = ---------------------------------------------------
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*> ulp max( s norm(A), |w| norm(B) )*norm( s A - w B )
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*>
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*> Two "safety checks" are performed:
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*>
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*> (1) ulp*max( s*norm(A), |w|*norm(B) ) must be at least
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*> safe_minimum. This insures that the test performed is
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*> not essentially det(0*A + 0*B)=0.
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*>
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*> (2) s*norm(A) + |w|*norm(B) must be less than 1/safe_minimum.
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*> This insures that s*A - w*B will not overflow.
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*>
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*> If these tests are not passed, then s and w are scaled and
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*> tested anyway, if this is possible.
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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] A
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*> \verbatim
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*> A is REAL array, dimension (LDA, 2)
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*> The 2x2 matrix A.
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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. It must be at least 2.
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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 2x2 upper-triangular matrix B.
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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. It must be at least 2.
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*> \endverbatim
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*>
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*> \param[in] SCALE
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*> \verbatim
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*> SCALE is REAL
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*> The "scale factor" s in the formula s A - w B . It is
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*> assumed to be non-negative.
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*> \endverbatim
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*>
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*> \param[in] WR
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*> \verbatim
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*> WR is REAL
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*> The real part of the eigenvalue w in the formula
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*> s A - w B .
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*> \endverbatim
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*>
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*> \param[in] WI
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*> \verbatim
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*> WI is REAL
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*> The imaginary part of the eigenvalue w in the formula
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*> s A - w B .
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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
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*> If INFO is 2 or less, the value computed by the test
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*> described above.
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*> If INFO=3, this will just be 1/ulp.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> =0: The input data pass the "safety checks".
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*> =1: s*norm(A) + |w|*norm(B) > 1/safe_minimum.
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*> =2: ulp*max( s*norm(A), |w|*norm(B) ) < safe_minimum
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*> =3: same as INFO=2, but s and w could not be scaled so
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*> as to compute the test.
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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 SGET53( A, LDA, B, LDB, SCALE, WR, WI, RESULT, INFO )
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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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INTEGER INFO, LDA, LDB
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REAL RESULT, SCALE, WI, WR
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), B( LDB, * )
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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 = 0.0, ONE = 1.0 )
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* ..
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* .. Local Scalars ..
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REAL ABSW, ANORM, BNORM, CI11, CI12, CI22, CNORM,
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$ CR11, CR12, CR21, CR22, CSCALE, DETI, DETR, S1,
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$ SAFMIN, SCALES, SIGMIN, TEMP, ULP, WIS, WRS
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Initialize
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*
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INFO = 0
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RESULT = ZERO
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SCALES = SCALE
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WRS = WR
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WIS = WI
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*
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* Machine constants and norms
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*
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SAFMIN = SLAMCH( 'Safe minimum' )
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ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
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ABSW = ABS( WRS ) + ABS( WIS )
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ANORM = MAX( ABS( A( 1, 1 ) )+ABS( A( 2, 1 ) ),
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$ ABS( A( 1, 2 ) )+ABS( A( 2, 2 ) ), SAFMIN )
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BNORM = MAX( ABS( B( 1, 1 ) ), ABS( B( 1, 2 ) )+ABS( B( 2, 2 ) ),
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$ SAFMIN )
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*
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* Check for possible overflow.
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*
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TEMP = ( SAFMIN*BNORM )*ABSW + ( SAFMIN*ANORM )*SCALES
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IF( TEMP.GE.ONE ) THEN
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*
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* Scale down to avoid overflow
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*
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INFO = 1
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TEMP = ONE / TEMP
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SCALES = SCALES*TEMP
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WRS = WRS*TEMP
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WIS = WIS*TEMP
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ABSW = ABS( WRS ) + ABS( WIS )
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END IF
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S1 = MAX( ULP*MAX( SCALES*ANORM, ABSW*BNORM ),
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$ SAFMIN*MAX( SCALES, ABSW ) )
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*
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* Check for W and SCALE essentially zero.
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*
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IF( S1.LT.SAFMIN ) THEN
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INFO = 2
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IF( SCALES.LT.SAFMIN .AND. ABSW.LT.SAFMIN ) THEN
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INFO = 3
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RESULT = ONE / ULP
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RETURN
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END IF
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*
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* Scale up to avoid underflow
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*
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TEMP = ONE / MAX( SCALES*ANORM+ABSW*BNORM, SAFMIN )
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SCALES = SCALES*TEMP
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WRS = WRS*TEMP
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WIS = WIS*TEMP
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ABSW = ABS( WRS ) + ABS( WIS )
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S1 = MAX( ULP*MAX( SCALES*ANORM, ABSW*BNORM ),
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$ SAFMIN*MAX( SCALES, ABSW ) )
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IF( S1.LT.SAFMIN ) THEN
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INFO = 3
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RESULT = ONE / ULP
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RETURN
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END IF
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END IF
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*
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* Compute C = s A - w B
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*
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CR11 = SCALES*A( 1, 1 ) - WRS*B( 1, 1 )
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CI11 = -WIS*B( 1, 1 )
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CR21 = SCALES*A( 2, 1 )
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CR12 = SCALES*A( 1, 2 ) - WRS*B( 1, 2 )
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CI12 = -WIS*B( 1, 2 )
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CR22 = SCALES*A( 2, 2 ) - WRS*B( 2, 2 )
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CI22 = -WIS*B( 2, 2 )
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*
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* Compute the smallest singular value of s A - w B:
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*
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* |det( s A - w B )|
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* sigma_min = ------------------
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* norm( s A - w B )
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*
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CNORM = MAX( ABS( CR11 )+ABS( CI11 )+ABS( CR21 ),
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$ ABS( CR12 )+ABS( CI12 )+ABS( CR22 )+ABS( CI22 ), SAFMIN )
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CSCALE = ONE / SQRT( CNORM )
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DETR = ( CSCALE*CR11 )*( CSCALE*CR22 ) -
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$ ( CSCALE*CI11 )*( CSCALE*CI22 ) -
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$ ( CSCALE*CR12 )*( CSCALE*CR21 )
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DETI = ( CSCALE*CR11 )*( CSCALE*CI22 ) +
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$ ( CSCALE*CI11 )*( CSCALE*CR22 ) -
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$ ( CSCALE*CI12 )*( CSCALE*CR21 )
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SIGMIN = ABS( DETR ) + ABS( DETI )
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RESULT = SIGMIN / S1
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RETURN
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*
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* End of SGET53
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*
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END
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