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236 lines
6.3 KiB
236 lines
6.3 KiB
2 years ago
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*> \brief \b DSTT21
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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 DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
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* RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER KBAND, LDU, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
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* $ SE( * ), 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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*> DSTT21 checks a decomposition of the form
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*>
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*> A = U S U'
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*>
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*> where ' means transpose, A is symmetric tridiagonal, U is 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) = | A - U S U' | / ( |A| n ulp )
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*>
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*> RESULT(2) = | I - UU' | / ( 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, DSTT21 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] 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N-1)
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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 the (1,2)
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*> and (2,1) element, AE(2) is the (2,3) and (3,2) 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N-1)
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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 the
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*> (1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
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*> 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N*(N+1))
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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 DOUBLE PRECISION 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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*> RESULT(1) is always modified.
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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 double_eig
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*
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* =====================================================================
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SUBROUTINE DSTT21( N, KBAND, AD, AE, SD, SE, U, LDU, WORK,
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$ RESULT )
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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 KBAND, LDU, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AD( * ), AE( * ), RESULT( 2 ), SD( * ),
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$ SE( * ), 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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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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* ..
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* .. Local Scalars ..
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INTEGER J
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DOUBLE PRECISION ANORM, TEMP1, TEMP2, ULP, UNFL, WNORM
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
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EXTERNAL DLAMCH, DLANGE, DLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMM, DLASET, DSYR, DSYR2
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* 1) Constants
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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 )
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$ RETURN
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*
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UNFL = DLAMCH( 'Safe minimum' )
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ULP = DLAMCH( 'Precision' )
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*
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* Do Test 1
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*
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* Copy A & Compute its 1-Norm:
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*
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CALL DLASET( 'Full', N, N, ZERO, ZERO, WORK, N )
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*
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ANORM = ZERO
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TEMP1 = ZERO
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*
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DO 10 J = 1, N - 1
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WORK( ( N+1 )*( J-1 )+1 ) = AD( J )
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WORK( ( N+1 )*( J-1 )+2 ) = AE( J )
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TEMP2 = ABS( AE( J ) )
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ANORM = MAX( ANORM, ABS( AD( J ) )+TEMP1+TEMP2 )
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TEMP1 = TEMP2
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10 CONTINUE
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*
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WORK( N**2 ) = AD( N )
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ANORM = MAX( ANORM, ABS( AD( N ) )+TEMP1, UNFL )
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*
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* Norm of A - USU'
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*
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DO 20 J = 1, N
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CALL DSYR( 'L', N, -SD( J ), U( 1, J ), 1, WORK, N )
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20 CONTINUE
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*
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IF( N.GT.1 .AND. KBAND.EQ.1 ) THEN
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DO 30 J = 1, N - 1
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CALL DSYR2( 'L', N, -SE( J ), U( 1, J ), 1, U( 1, J+1 ), 1,
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$ WORK, N )
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30 CONTINUE
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END IF
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*
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WNORM = DLANSY( '1', 'L', N, WORK, N, WORK( N**2+1 ) )
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*
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IF( ANORM.GT.WNORM ) THEN
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RESULT( 1 ) = ( WNORM / ANORM ) / ( N*ULP )
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ELSE
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IF( ANORM.LT.ONE ) THEN
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RESULT( 1 ) = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
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ELSE
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RESULT( 1 ) = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*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 UU' - I
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*
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CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
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$ N )
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*
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DO 40 J = 1, N
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WORK( ( N+1 )*( J-1 )+1 ) = WORK( ( N+1 )*( J-1 )+1 ) - ONE
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40 CONTINUE
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*
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RESULT( 2 ) = MIN( DBLE( N ), DLANGE( '1', N, N, WORK, N,
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$ WORK( N**2+1 ) ) ) / ( N*ULP )
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*
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RETURN
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*
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* End of DSTT21
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*
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END
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