Annotation of rpl/lapack/lapack/zlar2v.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLAR2V
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZLAR2V + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlar2v.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlar2v.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlar2v.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INCC, INCX, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION C( * )
! 28: * COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZLAR2V applies a vector of complex plane rotations with real cosines
! 38: *> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
! 39: *> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
! 40: *>
! 41: *> ( x(i) z(i) ) :=
! 42: *> ( conjg(z(i)) y(i) )
! 43: *>
! 44: *> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
! 45: *> ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
! 46: *> \endverbatim
! 47: *
! 48: * Arguments:
! 49: * ==========
! 50: *
! 51: *> \param[in] N
! 52: *> \verbatim
! 53: *> N is INTEGER
! 54: *> The number of plane rotations to be applied.
! 55: *> \endverbatim
! 56: *>
! 57: *> \param[in,out] X
! 58: *> \verbatim
! 59: *> X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
! 60: *> The vector x; the elements of x are assumed to be real.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in,out] Y
! 64: *> \verbatim
! 65: *> Y is COMPLEX*16 array, dimension (1+(N-1)*INCX)
! 66: *> The vector y; the elements of y are assumed to be real.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in,out] Z
! 70: *> \verbatim
! 71: *> Z is COMPLEX*16 array, dimension (1+(N-1)*INCX)
! 72: *> The vector z.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] INCX
! 76: *> \verbatim
! 77: *> INCX is INTEGER
! 78: *> The increment between elements of X, Y and Z. INCX > 0.
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] C
! 82: *> \verbatim
! 83: *> C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
! 84: *> The cosines of the plane rotations.
! 85: *> \endverbatim
! 86: *>
! 87: *> \param[in] S
! 88: *> \verbatim
! 89: *> S is COMPLEX*16 array, dimension (1+(N-1)*INCC)
! 90: *> The sines of the plane rotations.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[in] INCC
! 94: *> \verbatim
! 95: *> INCC is INTEGER
! 96: *> The increment between elements of C and S. INCC > 0.
! 97: *> \endverbatim
! 98: *
! 99: * Authors:
! 100: * ========
! 101: *
! 102: *> \author Univ. of Tennessee
! 103: *> \author Univ. of California Berkeley
! 104: *> \author Univ. of Colorado Denver
! 105: *> \author NAG Ltd.
! 106: *
! 107: *> \date November 2011
! 108: *
! 109: *> \ingroup complex16OTHERauxiliary
! 110: *
! 111: * =====================================================================
1.1 bertrand 112: SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
113: *
1.8 ! bertrand 114: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 115: * -- LAPACK is a software package provided by Univ. of Tennessee, --
116: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 117: * November 2011
1.1 bertrand 118: *
119: * .. Scalar Arguments ..
120: INTEGER INCC, INCX, N
121: * ..
122: * .. Array Arguments ..
123: DOUBLE PRECISION C( * )
124: COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
125: * ..
126: *
127: * =====================================================================
128: *
129: * .. Local Scalars ..
130: INTEGER I, IC, IX
131: DOUBLE PRECISION CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
132: $ ZIR
133: COMPLEX*16 SI, T2, T3, T4, ZI
134: * ..
135: * .. Intrinsic Functions ..
136: INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG
137: * ..
138: * .. Executable Statements ..
139: *
140: IX = 1
141: IC = 1
142: DO 10 I = 1, N
143: XI = DBLE( X( IX ) )
144: YI = DBLE( Y( IX ) )
145: ZI = Z( IX )
146: ZIR = DBLE( ZI )
147: ZII = DIMAG( ZI )
148: CI = C( IC )
149: SI = S( IC )
150: SIR = DBLE( SI )
151: SII = DIMAG( SI )
152: T1R = SIR*ZIR - SII*ZII
153: T1I = SIR*ZII + SII*ZIR
154: T2 = CI*ZI
155: T3 = T2 - DCONJG( SI )*XI
156: T4 = DCONJG( T2 ) + SI*YI
157: T5 = CI*XI + T1R
158: T6 = CI*YI - T1R
159: X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) )
160: Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) )
161: Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I )
162: IX = IX + INCX
163: IC = IC + INCC
164: 10 CONTINUE
165: RETURN
166: *
167: * End of ZLAR2V
168: *
169: END
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