SG03BY

Compute a complex Givens rotation in real arithmetic

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.

      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

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.

  The subroutine avoids unnecessary overflow.

  In the interest of speed, this routine does not check the input
  for errors.

Program Text

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