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Annotation of rpl/lapack/lapack/zlar2v.f, revision 1.7

1.1       bertrand    1:       SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
                      2: *
                      3: *  -- LAPACK auxiliary routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       INTEGER            INCC, INCX, N
                     10: *     ..
                     11: *     .. Array Arguments ..
                     12:       DOUBLE PRECISION   C( * )
                     13:       COMPLEX*16         S( * ), X( * ), Y( * ), Z( * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  ZLAR2V applies a vector of complex plane rotations with real cosines
                     20: *  from both sides to a sequence of 2-by-2 complex Hermitian matrices,
                     21: *  defined by the elements of the vectors x, y and z. For i = 1,2,...,n
                     22: *
                     23: *     (       x(i)  z(i) ) :=
                     24: *     ( conjg(z(i)) y(i) )
                     25: *
                     26: *       (  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
                     27: *       ( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )
                     28: *
                     29: *  Arguments
                     30: *  =========
                     31: *
                     32: *  N       (input) INTEGER
                     33: *          The number of plane rotations to be applied.
                     34: *
                     35: *  X       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
                     36: *          The vector x; the elements of x are assumed to be real.
                     37: *
                     38: *  Y       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
                     39: *          The vector y; the elements of y are assumed to be real.
                     40: *
                     41: *  Z       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
                     42: *          The vector z.
                     43: *
                     44: *  INCX    (input) INTEGER
                     45: *          The increment between elements of X, Y and Z. INCX > 0.
                     46: *
                     47: *  C       (input) DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
                     48: *          The cosines of the plane rotations.
                     49: *
                     50: *  S       (input) COMPLEX*16 array, dimension (1+(N-1)*INCC)
                     51: *          The sines of the plane rotations.
                     52: *
                     53: *  INCC    (input) INTEGER
                     54: *          The increment between elements of C and S. INCC > 0.
                     55: *
                     56: *  =====================================================================
                     57: *
                     58: *     .. Local Scalars ..
                     59:       INTEGER            I, IC, IX
                     60:       DOUBLE PRECISION   CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
                     61:      $                   ZIR
                     62:       COMPLEX*16         SI, T2, T3, T4, ZI
                     63: *     ..
                     64: *     .. Intrinsic Functions ..
                     65:       INTRINSIC          DBLE, DCMPLX, DCONJG, DIMAG
                     66: *     ..
                     67: *     .. Executable Statements ..
                     68: *
                     69:       IX = 1
                     70:       IC = 1
                     71:       DO 10 I = 1, N
                     72:          XI = DBLE( X( IX ) )
                     73:          YI = DBLE( Y( IX ) )
                     74:          ZI = Z( IX )
                     75:          ZIR = DBLE( ZI )
                     76:          ZII = DIMAG( ZI )
                     77:          CI = C( IC )
                     78:          SI = S( IC )
                     79:          SIR = DBLE( SI )
                     80:          SII = DIMAG( SI )
                     81:          T1R = SIR*ZIR - SII*ZII
                     82:          T1I = SIR*ZII + SII*ZIR
                     83:          T2 = CI*ZI
                     84:          T3 = T2 - DCONJG( SI )*XI
                     85:          T4 = DCONJG( T2 ) + SI*YI
                     86:          T5 = CI*XI + T1R
                     87:          T6 = CI*YI - T1R
                     88:          X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) )
                     89:          Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) )
                     90:          Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I )
                     91:          IX = IX + INCX
                     92:          IC = IC + INCC
                     93:    10 CONTINUE
                     94:       RETURN
                     95: *
                     96: *     End of ZLAR2V
                     97: *
                     98:       END