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188 lines
4.6 KiB
188 lines
4.6 KiB
*> \brief \b SBDT02
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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 SBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER LDB, LDC, LDU, M, N
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL B( LDB, * ), C( LDC, * ), U( LDU, * ),
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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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*> SBDT02 tests the change of basis C = U**H * B by computing the
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*> residual
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*>
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*> RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
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*>
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*> where B and C are M by N matrices, U is an M by M orthogonal matrix,
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*> and EPS is the machine precision.
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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] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrices B and C and the order of
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*> the matrix Q.
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*> \endverbatim
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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 number of columns of the matrices B and C.
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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 m by n 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 the array B. LDB >= max(1,M).
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C is REAL array, dimension (LDC,N)
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*> The m by n matrix C, assumed to contain U**H * B.
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= max(1,M).
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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,M)
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*> The m by m orthogonal matrix U.
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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 the array U. LDU >= max(1,M).
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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 (M)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is REAL
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*> RESID = norm(B - U * C) / ( max(m,n) * norm(B) * EPS ),
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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 SBDT02( M, N, B, LDB, C, LDC, U, LDU, WORK, RESID )
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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 LDB, LDC, LDU, M, N
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL B( LDB, * ), C( LDC, * ), U( LDU, * ),
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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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INTEGER J
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REAL BNORM, EPS, REALMN
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* ..
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* .. External Functions ..
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REAL SASUM, SLAMCH, SLANGE
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EXTERNAL SASUM, SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SCOPY, SGEMV
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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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* Quick return if possible
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*
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RESID = ZERO
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IF( M.LE.0 .OR. N.LE.0 )
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$ RETURN
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REALMN = REAL( MAX( M, N ) )
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EPS = SLAMCH( 'Precision' )
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*
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* Compute norm(B - U * C)
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*
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DO 10 J = 1, N
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CALL SCOPY( M, B( 1, J ), 1, WORK, 1 )
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CALL SGEMV( 'No transpose', M, M, -ONE, U, LDU, C( 1, J ), 1,
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$ ONE, WORK, 1 )
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RESID = MAX( RESID, SASUM( M, WORK, 1 ) )
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10 CONTINUE
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*
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* Compute norm of B.
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*
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BNORM = SLANGE( '1', M, N, B, LDB, WORK )
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*
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IF( BNORM.LE.ZERO ) THEN
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IF( RESID.NE.ZERO )
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$ RESID = ONE / EPS
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ELSE
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IF( BNORM.GE.RESID ) THEN
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RESID = ( RESID / BNORM ) / ( REALMN*EPS )
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ELSE
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IF( BNORM.LT.ONE ) THEN
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RESID = ( MIN( RESID, REALMN*BNORM ) / BNORM ) /
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$ ( REALMN*EPS )
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ELSE
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RESID = MIN( RESID / BNORM, REALMN ) / ( REALMN*EPS )
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END IF
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END IF
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END IF
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RETURN
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*
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* End of SBDT02
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*
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END
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