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155 lines
4.1 KiB
155 lines
4.1 KiB
2 years ago
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*> \brief \b DLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
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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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*> \htmlonly
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*> Download DLAR2V + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlar2v.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlar2v.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlar2v.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLAR2V( N, X, Y, Z, INCX, C, S, INCC )
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*
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* .. Scalar Arguments ..
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* INTEGER INCC, INCX, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION C( * ), S( * ), X( * ), Y( * ), Z( * )
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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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*> DLAR2V applies a vector of real plane rotations from both sides to
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*> a sequence of 2-by-2 real symmetric matrices, defined by the elements
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*> of the vectors x, y and z. For i = 1,2,...,n
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*>
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*> ( x(i) z(i) ) := ( c(i) s(i) ) ( x(i) z(i) ) ( c(i) -s(i) )
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*> ( z(i) y(i) ) ( -s(i) c(i) ) ( z(i) y(i) ) ( s(i) c(i) )
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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 number of plane rotations to be applied.
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*> \endverbatim
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*>
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*> \param[in,out] X
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*> \verbatim
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*> X is DOUBLE PRECISION array,
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*> dimension (1+(N-1)*INCX)
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*> The vector x.
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*> \endverbatim
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*>
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*> \param[in,out] Y
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*> \verbatim
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*> Y is DOUBLE PRECISION array,
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*> dimension (1+(N-1)*INCX)
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*> The vector y.
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*> \endverbatim
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*>
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*> \param[in,out] Z
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*> \verbatim
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*> Z is DOUBLE PRECISION array,
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*> dimension (1+(N-1)*INCX)
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*> The vector z.
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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is INTEGER
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*> The increment between elements of X, Y and Z. INCX > 0.
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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 DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
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*> The cosines of the plane rotations.
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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 DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
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*> The sines of the plane rotations.
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*> \endverbatim
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*>
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*> \param[in] INCC
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*> \verbatim
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*> INCC is INTEGER
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*> The increment between elements of C and S. INCC > 0.
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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 doubleOTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE DLAR2V( N, X, Y, Z, INCX, C, S, INCC )
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*
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* -- LAPACK auxiliary 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 INCC, INCX, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION C( * ), S( * ), X( * ), Y( * ), Z( * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER I, IC, IX
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DOUBLE PRECISION CI, SI, T1, T2, T3, T4, T5, T6, XI, YI, ZI
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* ..
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* .. Executable Statements ..
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*
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IX = 1
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IC = 1
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DO 10 I = 1, N
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XI = X( IX )
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YI = Y( IX )
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ZI = Z( IX )
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CI = C( IC )
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SI = S( IC )
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T1 = SI*ZI
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T2 = CI*ZI
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T3 = T2 - SI*XI
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T4 = T2 + SI*YI
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T5 = CI*XI + T1
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T6 = CI*YI - T1
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X( IX ) = CI*T5 + SI*T4
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Y( IX ) = CI*T6 - SI*T3
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Z( IX ) = CI*T4 - SI*T5
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IX = IX + INCX
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IC = IC + INCC
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10 CONTINUE
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*
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* End of DLAR2V
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*
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RETURN
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END
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