SUBROUTINE MA01AD( XR, XI, YR, YI )
C
C PURPOSE
C
C To compute the complex square root YR + i*YI of a complex number
C XR + i*XI in real arithmetic. The returned result is so that
C YR >= 0.0 and SIGN(YI) = SIGN(XI).
C
C ARGUMENTS
C
C Input/Output Parameters
C
C XR (input) DOUBLE PRECISION
C XI (input) DOUBLE PRECISION
C These scalars define the real and imaginary part of the
C complex number of which the square root is sought.
C
C YR (output) DOUBLE PRECISION
C YI (output) DOUBLE PRECISION
C These scalars define the real and imaginary part of the
C complex square root.
C
C METHOD
C
C The complex square root YR + i*YI of the complex number XR + i*XI
C is computed in real arithmetic, taking care to avoid overflow.
C
C REFERENCES
C
C Adapted from EISPACK subroutine CSROOT.
C
C CONTRIBUTOR
C
C P. Benner, Universitaet Bremen, Germany, and
C R. Byers, University of Kansas, Lawrence, USA,
C Aug. 1998, routine DCROOT.
C V. Sima, Research Institute for Informatics, Bucharest, Romania,
C Oct. 1998, SLICOT Library version.
C
C REVISIONS
C
C -
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, HALF
PARAMETER ( ZERO = 0.0D0, HALF = 1.0D0/2.0D0 )
C ..
C .. Scalar Arguments ..
DOUBLE PRECISION XR, XI, YR, YI
C ..
C .. Local Scalars ..
DOUBLE PRECISION S
C ..
C .. External Functions ..
DOUBLE PRECISION DLAPY2
EXTERNAL DLAPY2
C
C .. Intrinsic functions ..
INTRINSIC ABS, SQRT
C ..
C .. Executable Statements ..
C
S = SQRT( HALF*( DLAPY2( XR, XI ) + ABS( XR ) ) )
IF ( XR.GE.ZERO ) YR = S
IF ( XI.LT.ZERO ) S = -S
IF ( XR.LE.ZERO ) THEN
YI = S
IF ( XR.LT.ZERO ) YR = HALF*( XI/S )
ELSE
YI = HALF*( XI/YR )
END IF
C
RETURN
C *** Last line of MA01AD ***
END