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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
-*
-* -- LAPACK auxiliary routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1
-* ..
-*
-* Purpose
-* =======
-*
-* DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
-* [ A B ]
-* [ B C ].
-* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
-* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
-* eigenvector for RT1, giving the decomposition
-*
-* [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
-* [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
-*
-* Arguments
-* =========
-*
-* A (input) DOUBLE PRECISION
-* The (1,1) element of the 2-by-2 matrix.
-*
-* B (input) DOUBLE PRECISION
-* The (1,2) element and the conjugate of the (2,1) element of
-* the 2-by-2 matrix.
-*
-* C (input) DOUBLE PRECISION
-* The (2,2) element of the 2-by-2 matrix.
-*
-* RT1 (output) DOUBLE PRECISION
-* The eigenvalue of larger absolute value.
-*
-* RT2 (output) DOUBLE PRECISION
-* The eigenvalue of smaller absolute value.
-*
-* CS1 (output) DOUBLE PRECISION
-* SN1 (output) DOUBLE PRECISION
-* The vector (CS1, SN1) is a unit right eigenvector for RT1.
-*
-* 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.
-*
-* CS1 and SN1 are accurate to a few ulps barring over/underflow.
-*
-* 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 ..
- DOUBLE PRECISION ONE
- PARAMETER ( ONE = 1.0D0 )
- DOUBLE PRECISION TWO
- PARAMETER ( TWO = 2.0D0 )
- DOUBLE PRECISION ZERO
- PARAMETER ( ZERO = 0.0D0 )
- DOUBLE PRECISION HALF
- PARAMETER ( HALF = 0.5D0 )
-* ..
-* .. Local Scalars ..
- INTEGER SGN1, SGN2
- DOUBLE PRECISION AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM,
- $ TB, TN
-* ..
-* .. 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 )
- SGN1 = -1
-*
-* 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 )
- SGN1 = 1
-*
-* 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
- SGN1 = 1
- END IF
-*
-* Compute the eigenvector
-*
- IF( DF.GE.ZERO ) THEN
- CS = DF + RT
- SGN2 = 1
- ELSE
- CS = DF - RT
- SGN2 = -1
- END IF
- ACS = ABS( CS )
- IF( ACS.GT.AB ) THEN
- CT = -TB / CS
- SN1 = ONE / SQRT( ONE+CT*CT )
- CS1 = CT*SN1
- ELSE
- IF( AB.EQ.ZERO ) THEN
- CS1 = ONE
- SN1 = ZERO
- ELSE
- TN = -CS / TB
- CS1 = ONE / SQRT( ONE+TN*TN )
- SN1 = TN*CS1
- END IF
- END IF
- IF( SGN1.EQ.SGN2 ) THEN
- TN = CS1
- CS1 = -SN1
- SN1 = TN
- END IF
- RETURN
-*
-* End of DLAEV2
-*
- END