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SUBROUTINE SLAE2( A, B, C, RT1, RT2 )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* October 31, 1992
*
* .. Scalar Arguments ..
REAL A, B, C, RT1, RT2
* ..
*
* Purpose
* =======
*
* SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
* [ A B ]
* [ B C ].
* On return, RT1 is the eigenvalue of larger absolute value, and RT2
* is the eigenvalue of smaller absolute value.
*
* Arguments
* =========
*
* A (input) REAL
* The (1,1) element of the 2-by-2 matrix.
*
* B (input) REAL
* The (1,2) and (2,1) elements of the 2-by-2 matrix.
*
* C (input) REAL
* The (2,2) element of the 2-by-2 matrix.
*
* RT1 (output) REAL
* The eigenvalue of larger absolute value.
*
* RT2 (output) REAL
* The eigenvalue of smaller absolute value.
*
* Further Details
* ===============
*
* RT1 is accurate to a few ulps barring over/underflow.
*
* RT2 may be inaccurate if there is massive cancellation in the
* determinant A*C-B*B; higher precision or correctly rounded or
* correctly truncated arithmetic would be needed to compute RT2
* accurately in all cases.
*
* Overflow is possible only if RT1 is within a factor of 5 of overflow.
* Underflow is harmless if the input data is 0 or exceeds
* underflow_threshold / macheps.
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E0 )
REAL TWO
PARAMETER ( TWO = 2.0E0 )
REAL ZERO
PARAMETER ( ZERO = 0.0E0 )
REAL HALF
PARAMETER ( HALF = 0.5E0 )
* ..
* .. Local Scalars ..
REAL AB, ACMN, ACMX, ADF, DF, RT, SM, TB
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
* Compute the eigenvalues
*
SM = A + C
DF = A - C
ADF = ABS( DF )
TB = B + B
AB = ABS( TB )
IF( ABS( A ).GT.ABS( C ) ) THEN
ACMX = A
ACMN = C
ELSE
ACMX = C
ACMN = A
END IF
IF( ADF.GT.AB ) THEN
RT = ADF*SQRT( ONE+( AB / ADF )**2 )
ELSE IF( ADF.LT.AB ) THEN
RT = AB*SQRT( ONE+( ADF / AB )**2 )
ELSE
*
* Includes case AB=ADF=0
*
RT = AB*SQRT( TWO )
END IF
IF( SM.LT.ZERO ) THEN
RT1 = HALF*( SM-RT )
*
* Order of execution important.
* To get fully accurate smaller eigenvalue,
* next line needs to be executed in higher precision.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE IF( SM.GT.ZERO ) THEN
RT1 = HALF*( SM+RT )
*
* Order of execution important.
* To get fully accurate smaller eigenvalue,
* next line needs to be executed in higher precision.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE
*
* Includes case RT1 = RT2 = 0
*
RT1 = HALF*RT
RT2 = -HALF*RT
END IF
RETURN
*
* End of SLAE2
*
END
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