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167 lines
4.6 KiB
167 lines
4.6 KiB
2 years ago
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*> \brief \b CLAR2V applies a vector of plane rotations with real cosines and complex 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 CLAR2V + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clar2v.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/clar2v.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/clar2v.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 CLAR2V( 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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* REAL C( * )
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* COMPLEX 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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*> CLAR2V applies a vector of complex plane rotations with real cosines
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*> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
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*> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
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*>
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*> ( x(i) z(i) ) :=
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*> ( conjg(z(i)) y(i) )
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*>
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*> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
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*> ( -s(i) c(i) ) ( conjg(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 COMPLEX array, dimension (1+(N-1)*INCX)
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*> The vector x; the elements of x are assumed to be real.
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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 COMPLEX array, dimension (1+(N-1)*INCX)
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*> The vector y; the elements of y are assumed to be real.
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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 COMPLEX array, 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 REAL 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 COMPLEX 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 complexOTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE CLAR2V( 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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REAL C( * )
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COMPLEX 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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REAL CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
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$ ZIR
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COMPLEX SI, T2, T3, T4, ZI
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC AIMAG, CMPLX, CONJG, REAL
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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 = REAL( X( IX ) )
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YI = REAL( Y( IX ) )
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ZI = Z( IX )
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ZIR = REAL( ZI )
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ZII = AIMAG( ZI )
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CI = C( IC )
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SI = S( IC )
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SIR = REAL( SI )
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SII = AIMAG( SI )
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T1R = SIR*ZIR - SII*ZII
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T1I = SIR*ZII + SII*ZIR
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T2 = CI*ZI
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T3 = T2 - CONJG( SI )*XI
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T4 = CONJG( T2 ) + SI*YI
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T5 = CI*XI + T1R
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T6 = CI*YI - T1R
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X( IX ) = CI*T5 + ( SIR*REAL( T4 )+SII*AIMAG( T4 ) )
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Y( IX ) = CI*T6 - ( SIR*REAL( T3 )-SII*AIMAG( T3 ) )
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Z( IX ) = CI*T3 + CONJG( SI )*CMPLX( T6, T1I )
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IX = IX + INCX
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IC = IC + INCC
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10 CONTINUE
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RETURN
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*
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* End of CLAR2V
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*
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END
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