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SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
* ..
*
* Purpose
* =======
*
* DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
* matrix in standard form:
*
* [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ]
* [ C D ] [ SN CS ] [ CC DD ] [-SN CS ]
*
* where either
* 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
* 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
* conjugate eigenvalues.
*
* Arguments
* =========
*
* A (input/output) DOUBLE PRECISION
* B (input/output) DOUBLE PRECISION
* C (input/output) DOUBLE PRECISION
* D (input/output) DOUBLE PRECISION
* On entry, the elements of the input matrix.
* On exit, they are overwritten by the elements of the
* standardised Schur form.
*
* RT1R (output) DOUBLE PRECISION
* RT1I (output) DOUBLE PRECISION
* RT2R (output) DOUBLE PRECISION
* RT2I (output) DOUBLE PRECISION
* The real and imaginary parts of the eigenvalues. If the
* eigenvalues are both real, abs(RT1R) >= abs(RT2R); if the
* eigenvalues are a complex conjugate pair, RT1I > 0.
*
* CS (output) DOUBLE PRECISION
* SN (output) DOUBLE PRECISION
* Parameters of the rotation matrix.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, HALF, ONE
PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION AA, BB, CC, CS1, DD, P, SAB, SAC, SIGMA, SN1,
$ TAU, TEMP
* ..
* .. External Functions ..
DOUBLE PRECISION DLAPY2
EXTERNAL DLAPY2
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, SIGN, SQRT
* ..
* .. Executable Statements ..
*
* Initialize CS and SN
*
CS = ONE
SN = ZERO
*
IF( C.EQ.ZERO ) THEN
GO TO 10
*
ELSE IF( B.EQ.ZERO ) THEN
*
* Swap rows and columns
*
CS = ZERO
SN = ONE
TEMP = D
D = A
A = TEMP
B = -C
C = ZERO
GO TO 10
ELSE IF( (A-D).EQ.ZERO .AND. SIGN( ONE, B ).NE.
$ SIGN( ONE, C ) ) THEN
GO TO 10
ELSE
*
* Make diagonal elements equal
*
TEMP = A - D
P = HALF*TEMP
SIGMA = B + C
TAU = DLAPY2( SIGMA, TEMP )
CS1 = SQRT( HALF*( ONE+ABS( SIGMA ) / TAU ) )
SN1 = -( P / ( TAU*CS1 ) )*SIGN( ONE, SIGMA )
*
* Compute [ AA BB ] = [ A B ] [ CS1 -SN1 ]
* [ CC DD ] [ C D ] [ SN1 CS1 ]
*
AA = A*CS1 + B*SN1
BB = -A*SN1 + B*CS1
CC = C*CS1 + D*SN1
DD = -C*SN1 + D*CS1
*
* Compute [ A B ] = [ CS1 SN1 ] [ AA BB ]
* [ C D ] [-SN1 CS1 ] [ CC DD ]
*
A = AA*CS1 + CC*SN1
B = BB*CS1 + DD*SN1
C = -AA*SN1 + CC*CS1
D = -BB*SN1 + DD*CS1
*
* Accumulate transformation
*
TEMP = CS*CS1 - SN*SN1
SN = CS*SN1 + SN*CS1
CS = TEMP
*
TEMP = HALF*( A+D )
A = TEMP
D = TEMP
*
IF( C.NE.ZERO ) THEN
IF( B.NE.ZERO ) THEN
IF( SIGN( ONE, B ).EQ.SIGN( ONE, C ) ) THEN
*
* Real eigenvalues: reduce to upper triangular form
*
SAB = SQRT( ABS( B ) )
SAC = SQRT( ABS( C ) )
P = SIGN( SAB*SAC, C )
TAU = ONE / SQRT( ABS( B+C ) )
A = TEMP + P
D = TEMP - P
B = B - C
C = ZERO
CS1 = SAB*TAU
SN1 = SAC*TAU
TEMP = CS*CS1 - SN*SN1
SN = CS*SN1 + SN*CS1
CS = TEMP
END IF
ELSE
B = -C
C = ZERO
TEMP = CS
CS = -SN
SN = TEMP
END IF
END IF
END IF
*
10 CONTINUE
*
* Store eigenvalues in (RT1R,RT1I) and (RT2R,RT2I).
*
RT1R = A
RT2R = D
IF( C.EQ.ZERO ) THEN
RT1I = ZERO
RT2I = ZERO
ELSE
RT1I = SQRT( ABS( B ) )*SQRT( ABS( C ) )
RT2I = -RT1I
END IF
RETURN
*
* End of DLANV2
*
END
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