255 lines
6.9 KiB
Fortran
255 lines
6.9 KiB
Fortran
*> \brief \b SSTT22
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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 SSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
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* LDWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER KBAND, LDU, LDWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
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* $ SE( * ), U( LDU, * ), WORK( LDWORK, * )
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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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*> SSTT22 checks a set of M eigenvalues and eigenvectors,
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*>
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*> A U = U S
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*>
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*> where A is symmetric tridiagonal, the columns of U are orthogonal,
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*> and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
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*> Two tests are performed:
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*>
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*> RESULT(1) = | U' A U - S | / ( |A| m ulp )
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*>
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*> RESULT(2) = | I - U'U | / ( m 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, SSTT22 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] M
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*> \verbatim
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*> M is INTEGER
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*> The number of eigenpairs to check. If it is zero, SSTT22
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*> does nothing. It must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] KBAND
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*> \verbatim
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*> KBAND is INTEGER
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*> The bandwidth of the matrix S. It may only be zero or one.
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*> If zero, then S is diagonal, and SE is not referenced. If
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*> one, then S is symmetric tri-diagonal.
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*> \endverbatim
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*>
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*> \param[in] AD
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*> \verbatim
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*> AD is REAL array, dimension (N)
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*> The diagonal of the original (unfactored) matrix A. A is
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*> assumed to be symmetric tridiagonal.
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*> \endverbatim
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*>
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*> \param[in] AE
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*> \verbatim
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*> AE is REAL array, dimension (N)
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*> The off-diagonal of the original (unfactored) matrix A. A
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*> is assumed to be symmetric tridiagonal. AE(1) is ignored,
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*> AE(2) is the (1,2) and (2,1) element, etc.
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*> \endverbatim
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*>
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*> \param[in] SD
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*> \verbatim
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*> SD is REAL array, dimension (N)
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*> The diagonal of the (symmetric tri-) diagonal matrix S.
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*> \endverbatim
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*>
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*> \param[in] SE
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*> \verbatim
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*> SE is REAL array, dimension (N)
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*> The off-diagonal of the (symmetric tri-) diagonal matrix S.
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*> Not referenced if KBSND=0. If KBAND=1, then AE(1) is
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*> ignored, SE(2) is the (1,2) and (2,1) element, etc.
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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 in the 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.
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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 (LDWORK, M+1)
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*> \endverbatim
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*>
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*> \param[in] LDWORK
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*> \verbatim
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*> LDWORK is INTEGER
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*> The leading dimension of WORK. LDWORK must be at least
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*> max(1,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 values computed by the two tests described above. The
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*> values are currently limited to 1/ulp, to avoid overflow.
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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 SSTT22( N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK,
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$ LDWORK, 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 KBAND, LDU, LDWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL AD( * ), AE( * ), RESULT( 2 ), SD( * ),
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$ SE( * ), U( LDU, * ), WORK( LDWORK, * )
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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 = 0.0E0, ONE = 1.0E0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, K
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REAL ANORM, AUKJ, ULP, UNFL, WNORM
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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
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, REAL
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* ..
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* .. Executable Statements ..
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*
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RESULT( 1 ) = ZERO
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RESULT( 2 ) = ZERO
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IF( N.LE.0 .OR. M.LE.0 )
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$ RETURN
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*
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UNFL = SLAMCH( 'Safe minimum' )
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ULP = SLAMCH( 'Epsilon' )
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*
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* Do Test 1
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*
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* Compute the 1-norm of A.
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*
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IF( N.GT.1 ) THEN
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ANORM = ABS( AD( 1 ) ) + ABS( AE( 1 ) )
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DO 10 J = 2, N - 1
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ANORM = MAX( ANORM, ABS( AD( J ) )+ABS( AE( J ) )+
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$ ABS( AE( J-1 ) ) )
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10 CONTINUE
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ANORM = MAX( ANORM, ABS( AD( N ) )+ABS( AE( N-1 ) ) )
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ELSE
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ANORM = ABS( AD( 1 ) )
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END IF
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ANORM = MAX( ANORM, UNFL )
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*
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* Norm of U'AU - S
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*
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DO 40 I = 1, M
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DO 30 J = 1, M
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WORK( I, J ) = ZERO
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DO 20 K = 1, N
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AUKJ = AD( K )*U( K, J )
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IF( K.NE.N )
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$ AUKJ = AUKJ + AE( K )*U( K+1, J )
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IF( K.NE.1 )
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$ AUKJ = AUKJ + AE( K-1 )*U( K-1, J )
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WORK( I, J ) = WORK( I, J ) + U( K, I )*AUKJ
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20 CONTINUE
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30 CONTINUE
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WORK( I, I ) = WORK( I, I ) - SD( I )
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IF( KBAND.EQ.1 ) THEN
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IF( I.NE.1 )
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$ WORK( I, I-1 ) = WORK( I, I-1 ) - SE( I-1 )
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IF( I.NE.N )
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$ WORK( I, I+1 ) = WORK( I, I+1 ) - SE( I )
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END IF
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40 CONTINUE
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*
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WNORM = SLANSY( '1', 'L', M, WORK, M, WORK( 1, M+1 ) )
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*
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IF( ANORM.GT.WNORM ) THEN
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RESULT( 1 ) = ( WNORM / ANORM ) / ( M*ULP )
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ELSE
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IF( ANORM.LT.ONE ) THEN
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RESULT( 1 ) = ( MIN( WNORM, M*ANORM ) / ANORM ) / ( M*ULP )
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ELSE
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RESULT( 1 ) = MIN( WNORM / ANORM, REAL( M ) ) / ( M*ULP )
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END IF
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END IF
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*
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* Do Test 2
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*
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* Compute U'U - I
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*
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CALL SGEMM( 'T', 'N', M, M, N, ONE, U, LDU, U, LDU, ZERO, WORK,
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$ M )
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*
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DO 50 J = 1, M
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WORK( J, J ) = WORK( J, J ) - ONE
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50 CONTINUE
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*
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RESULT( 2 ) = MIN( REAL( M ), SLANGE( '1', M, M, WORK, M, WORK( 1,
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$ M+1 ) ) ) / ( M*ULP )
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*
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RETURN
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*
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* End of SSTT22
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*
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END
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