Purpose
  To compute the parameters for the complex Givens rotation
     (  CR-CI*I   SR-SI*I )   ( XR+XI*I )   ( Z )
     (                    ) * (         ) = (   ),
     ( -SR-SI*I   CR+CI*I )   ( YR+YI*I )   ( 0 )
  where CR, CI, SR, SI, XR, XI, YR, YI are real numbers and I is the
  imaginary unit, I = SQRT(-1). Z is a non-negative real number.
Specification
      SUBROUTINE SG03BY( XR, XI, YR, YI, CR, CI, SR, SI, Z )
C     .. Scalar Arguments ..
       DOUBLE PRECISION  CI, CR, SI, SR, XI, XR, YI, YR, Z
Arguments
Input/Output Parameters
  XR, XI, (input) DOUBLE PRECISION
  YR, YI  (input) DOUBLE PRECISION
          The given real scalars XR, XI, YR, YI.
  CR, CI, (output) DOUBLE PRECISION
  SR, SI, (output) DOUBLE PRECISION
  Z       (output) DOUBLE PRECISION
          The computed real scalars CR, CI, SR, SI, Z, defining the
          complex Givens rotation and Z.
Numerical Aspects
The subroutine avoids unnecessary overflow.Further Comments
In the interest of speed, this routine does not check the input for errors.Example
Program Text
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