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LOGICAL FUNCTION SB02MV( REIG, IEIG )
C
C RELEASE 4.0, WGS COPYRIGHT 1999.
C
C PURPOSE
C
C To select the stable eigenvalues
C
C ARGUMENTS
C
C Input/Output Parameters
C
C REIG (input) DOUBLE PRECISION
C The real part of the current eigenvalue considered.
C
C IEIG (input) DOUBLE PRECISION
C The imaginary part of the current eigenvalue considered.
C
C METHOD
C
C The function value SB02MV is set to .TRUE. for a stable eigenvalue
C and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C V. Sima, Katholieke Univ. Leuven, Belgium, Aug. 1997.
C
C REVISIONS
C
C -
C
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C .. Scalar Arguments ..
DOUBLE PRECISION IEIG, REIG
C .. Executable Statements ..
C
SB02MV = REIG.LT.ZERO
C
RETURN
C *** Last line of SB02MV ***
END
LOGICAL FUNCTION SB02MW( REIG, IEIG )
C
C RELEASE 4.0, WGS COPYRIGHT 1999.
C
C PURPOSE
C
C To select the stable eigenvalues for discrete-time
C
C ARGUMENTS
C
C Input/Output Parameters
C
C REIG (input) DOUBLE PRECISION
C The real part of the current eigenvalue considered.
C
C IEIG (input) DOUBLE PRECISION
C The imaginary part of the current eigenvalue considered.
C
C METHOD
C
C The function value SB02MW is set to .TRUE. for a stable
C eigenvalue (i.e., with modulus less than one) and to .FALSE.,
C otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C V. Sima, Katholieke Univ. Leuven, Belgium, Aug. 1997.
C
C REVISIONS
C
C -
C
C .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
C .. Scalar Arguments ..
DOUBLE PRECISION IEIG, REIG
C .. External Functions ..
DOUBLE PRECISION DLAPY2
EXTERNAL DLAPY2
C .. Executable Statements ..
C
SB02MW = DLAPY2( REIG, IEIG ).LT.ONE
C
RETURN
C *** Last line of SB02MW ***
END
LOGICAL FUNCTION SB02OW( ALPHAR, ALPHAI, BETA )
C
C RELEASE 4.0, WGS COPYRIGHT 1999.
C
C PURPOSE
C
C To select the stable generalized eigenvalues for continuous-time
C
C ARGUMENTS
C
C Input/Output Parameters
C
C ALPHAR (input) DOUBLE PRECISION
C The real part of the numerator of the current eigenvalue
C considered.
C
C ALPHAI (input) DOUBLE PRECISION
C The imaginary part of the numerator of the current
C eigenvalue considered.
C
C BETA (input) DOUBLE PRECISION
C The (real) denominator of the current eigenvalue
C considered. It is assumed that BETA <> 0 (regular case).
C
C METHOD
C
C The function value SB02OW is set to .TRUE. for a stable eigenvalue
C and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Sep. 1997.
C Supersedes Release 2.0 routine SB02CW by P. Van Dooren, Philips
C Research Laboratory, Brussels, Belgium.
C
C REVISIONS
C
C -
C
C ******************************************************************
C
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C .. Scalar Arguments ..
DOUBLE PRECISION ALPHAR, ALPHAI, BETA
C .. Executable Statements ..
C
SB02OW = (( ALPHAR.LT.ZERO .AND. BETA.GT.ZERO ) .OR.
$ ( ALPHAR.GT.ZERO .AND. BETA.LT.ZERO )) .AND.
$ abs(BETA).GT. abs(ALPHAR)*dlamch('p')
C
RETURN
C *** Last line of SB02OW ***
END
LOGICAL FUNCTION SB02OX( ALPHAR, ALPHAI, BETA )
C
C RELEASE 4.0, WGS COPYRIGHT 1999.
C
C PURPOSE
C
C To select the stable generalized eigenvalues for
C discrete-time
C
C ARGUMENTS
C
C Input/Output Parameters
C
C ALPHAR (input) DOUBLE PRECISION
C The real part of the numerator of the current eigenvalue
C considered.
C
C ALPHAI (input) DOUBLE PRECISION
C The imaginary part of the numerator of the current
C eigenvalue considered.
C
C BETA (input) DOUBLE PRECISION
C The (real) denominator of the current eigenvalue
C considered.
C
C METHOD
C
C The function value SB02OX is set to .TRUE. for a stable eigenvalue
C (i.e., with modulus less than one) and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C Release 3.0: V. Sima, Katholieke Univ. Leuven, Belgium, Sep. 1997.
C Supersedes Release 2.0 routine SB02CX by P. Van Dooren, Philips
C Research Laboratory, Brussels, Belgium.
C
C REVISIONS
C
C -
C
C ******************************************************************
C
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
C .. Scalar Arguments ..
DOUBLE PRECISION ALPHAR, ALPHAI, BETA
C .. External Functions ..
DOUBLE PRECISION DLAPY2
EXTERNAL DLAPY2
C .. Intrinsic Functions ..
INTRINSIC ABS
C .. Executable Statements ..
C
SB02OX = DLAPY2( ALPHAR, ALPHAI ).LT.ABS( BETA )
C
RETURN
C *** Last line of SB02OX ***
END
LOGICAL FUNCTION ZB02MV( EIG )
C
C RELEASE 4.0, WGS COPYRIGHT 2001.
C
C PURPOSE
C
C To select the stable eigenvalues in ordering the Schur form
C of a matrix.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C EIG (input) COMPLEX*16
C The current eigenvalue considered.
C
C METHOD
C
C The function value ZB02MV is set to .TRUE. for a stable eigenvalue
C and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Algebraic Riccati equation, closed loop system, continuous-time
C system, optimal regulator, Schur form.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C .. Scalar Arguments ..
COMPLEX*16 EIG
C .. Intrinsic Functions ..
INTRINSIC DREAL
C .. Executable Statements ..
C
ZB02MV = DREAL(EIG).LT.ZERO
C
RETURN
C *** Last line of ZB02MV ***
END
LOGICAL FUNCTION ZB02MW( EIG )
C
C RELEASE 4.0, WGS COPYRIGHT 2001.
C
C PURPOSE
C
C To select the eigenvalues inside the unit circle in ordering
C the Schur form of a matrix.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C EIG (input) COMPLEX*16
C The current eigenvalue considered.
C
C METHOD
C
C The function value ZB02MW is set to .TRUE. for an eigenvalue which
C is inside the unit circle and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Algebraic Riccati equation, closed loop system, continuous-time
C system, optimal regulator, Schur form.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
C .. Scalar Arguments ..
COMPLEX*16 EIG
C .. Intrinsic Functions ..
INTRINSIC ABS
C .. Executable Statements ..
C
ZB02MW = ABS(EIG).LT.ONE
C
RETURN
C *** Last line of ZB02MW ***
END
LOGICAL FUNCTION ZB02OW( ALPHA, BETA )
C
C RELEASE 4.0, WGS COPYRIGHT 2000.
C
C PURPOSE
C
C To select the stable generalized eigenvalues for the
C continuous-time.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C ALPHAR (input) DOUBLE PRECISION
C The real part of the numerator of the current eigenvalue
C considered.
C
C ALPHAI (input) DOUBLE PRECISION
C The imaginary part of the numerator of the current
C eigenvalue considered.
C
C BETA (input) DOUBLE PRECISION
C The (real) denominator of the current eigenvalue
C considered. It is assumed that BETA <> 0 (regular case).
C
C METHOD
C
C The function value ZB02OW is set to .TRUE. for a stable eigenvalue
C and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Algebraic Riccati equation, closed loop system, continuous-time
C system, optimal regulator, Schur form.
C
C ******************************************************************
C
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C .. Scalar Arguments ..
COMPLEX*16 ALPHA, BETA
INTRINSIC DREAL
C .. Executable Statements ..
C
if (abs(BETA).ne.ZERO) then
ZB02OW = DREAL(ALPHA/BETA).LT.ZERO
else
ZB02OW = .FALSE.
endif
C
RETURN
C *** Last line of zb02ow ***
END
LOGICAL FUNCTION ZB02OX( ALPHA, BETA )
C
C RELEASE 4.0, WGS COPYRIGHT 1999.
C
C PURPOSE
C
C To select the stable generalized eigenvalues for the
C discrete-time algebraic.
C
C ARGUMENTS
C
C Input/Output Parameters
C
C ALPHAR (input) DOUBLE PRECISION
C The real part of the numerator of the current eigenvalue
C considered.
C
C ALPHAI (input) DOUBLE PRECISION
C The imaginary part of the numerator of the current
C eigenvalue considered.
C
C BETA (input) DOUBLE PRECISION
C The (real) denominator of the current eigenvalue
C considered.
C
C METHOD
C
C The function value ZB02OX is set to .TRUE. for a stable eigenvalue
C (i.e., with modulus less than one) and to .FALSE., otherwise.
C
C REFERENCES
C
C None.
C
C NUMERICAL ASPECTS
C
C None.
C
C CONTRIBUTOR
C
C REVISIONS
C
C -
C
C KEYWORDS
C
C Algebraic Riccati equation, closed loop system, continuous-time
C system, optimal regulator, Schur form.
C
C ******************************************************************
C
C .. Scalar Arguments ..
COMPLEX*16 ALPHA, BETA
C .. External Functions ..
C .. Intrinsic Functions ..
INTRINSIC ABS
C .. Executable Statements ..
C
ZB02OX = ABS( ALPHA ).LT.ABS( BETA )
C
RETURN
C *** Last line of ZB02OX ***
END
|
