250 lines
6.4 KiB
Fortran
250 lines
6.4 KiB
Fortran
*> \brief \b SGET54
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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 SGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
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* LDV, WORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDB, LDS, LDT, LDU, LDV, N
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* REAL RESULT
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), B( LDB, * ), S( LDS, * ),
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* $ T( LDT, * ), U( LDU, * ), V( LDV, * ),
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* $ 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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*> SGET54 checks a generalized decomposition of the form
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*>
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*> A = U*S*V' and B = U*T* V'
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*>
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*> where ' means transpose and U and V are orthogonal.
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*>
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*> Specifically,
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*>
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*> RESULT = ||( A - U*S*V', B - U*T*V' )|| / (||( A, B )||*n*ulp )
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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] N
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*> \verbatim
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*> N is INTEGER
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*> The size of the matrix. If it is zero, SGET54 does nothing.
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*> It must be at least zero.
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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 original (unfactored) 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 1
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*> and at least N.
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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 original (unfactored) 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 1
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*> and at least N.
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*> \endverbatim
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*>
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*> \param[in] S
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*> \verbatim
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*> S is REAL array, dimension (LDS, N)
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*> The factored matrix S.
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*> \endverbatim
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*>
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*> \param[in] LDS
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*> \verbatim
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*> LDS is INTEGER
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*> The leading dimension of S. It must be at least 1
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*> and at least N.
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*> \endverbatim
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*>
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*> \param[in] T
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*> \verbatim
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*> T is REAL array, dimension (LDT, N)
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*> The factored matrix T.
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*> \endverbatim
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*>
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*> \param[in] LDT
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*> \verbatim
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*> LDT is INTEGER
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*> The leading dimension of T. It must be at least 1
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*> and at least N.
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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 on the left-hand side in the
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*> decomposition.
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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 U. LDU must be at least N and
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*> at least 1.
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*> \endverbatim
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*>
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*> \param[in] V
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*> \verbatim
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*> V is REAL array, dimension (LDV, N)
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*> The orthogonal matrix on the left-hand side in the
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*> decomposition.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of V. LDV must be at least N and
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*> at least 1.
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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 (3*N**2)
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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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*> The value RESULT, It is currently limited to 1/ulp, to
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*> avoid overflow. Errors are flagged by RESULT=10/ulp.
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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_eig
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*
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* =====================================================================
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SUBROUTINE SGET54( N, A, LDA, B, LDB, S, LDS, T, LDT, U, LDU, V,
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$ LDV, WORK, 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 LDA, LDB, LDS, LDT, LDU, LDV, N
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REAL RESULT
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), B( LDB, * ), S( LDS, * ),
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$ T( LDT, * ), U( LDU, * ), V( LDV, * ),
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$ 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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REAL ABNORM, ULP, UNFL, WNORM
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* ..
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* .. Local Arrays ..
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REAL DUM( 1 )
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* ..
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* .. External Functions ..
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REAL SLAMCH, SLANGE
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EXTERNAL SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SGEMM, SLACPY
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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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RESULT = ZERO
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IF( N.LE.0 )
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$ RETURN
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*
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* Constants
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*
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UNFL = SLAMCH( 'Safe minimum' )
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ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
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*
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* compute the norm of (A,B)
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*
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CALL SLACPY( 'Full', N, N, A, LDA, WORK, N )
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CALL SLACPY( 'Full', N, N, B, LDB, WORK( N*N+1 ), N )
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ABNORM = MAX( SLANGE( '1', N, 2*N, WORK, N, DUM ), UNFL )
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*
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* Compute W1 = A - U*S*V', and put in the array WORK(1:N*N)
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*
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CALL SLACPY( ' ', N, N, A, LDA, WORK, N )
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CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, S, LDS, ZERO,
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$ WORK( N*N+1 ), N )
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*
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CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( N*N+1 ), N, V, LDV,
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$ ONE, WORK, N )
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*
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* Compute W2 = B - U*T*V', and put in the workarray W(N*N+1:2*N*N)
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*
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CALL SLACPY( ' ', N, N, B, LDB, WORK( N*N+1 ), N )
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CALL SGEMM( 'N', 'N', N, N, N, ONE, U, LDU, T, LDT, ZERO,
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$ WORK( 2*N*N+1 ), N )
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*
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CALL SGEMM( 'N', 'C', N, N, N, -ONE, WORK( 2*N*N+1 ), N, V, LDV,
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$ ONE, WORK( N*N+1 ), N )
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*
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* Compute norm(W)/ ( ulp*norm((A,B)) )
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*
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WNORM = SLANGE( '1', N, 2*N, WORK, N, DUM )
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*
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IF( ABNORM.GT.WNORM ) THEN
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RESULT = ( WNORM / ABNORM ) / ( 2*N*ULP )
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ELSE
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IF( ABNORM.LT.ONE ) THEN
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RESULT = ( MIN( WNORM, 2*N*ABNORM ) / ABNORM ) / ( 2*N*ULP )
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ELSE
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RESULT = MIN( WNORM / ABNORM, REAL( 2*N ) ) / ( 2*N*ULP )
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END IF
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END IF
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*
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RETURN
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*
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* End of SGET54
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*
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END
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