LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
zlaev2.f File Reference

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Functions/Subroutines

subroutine ZLAEV2 (A, B, C, RT1, RT2, CS1, SN1)
 ZLAEV2

Function/Subroutine Documentation

subroutine ZLAEV2 ( COMPLEX*16  A,
COMPLEX*16  B,
COMPLEX*16  C,
DOUBLE PRECISION  RT1,
DOUBLE PRECISION  RT2,
DOUBLE PRECISION  CS1,
COMPLEX*16  SN1 
)

ZLAEV2

Download ZLAEV2 + dependencies [TGZ] [ZIP] [TXT]
Purpose: 

 ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
    [  A         B  ]
    [  CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
 [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
Parameters:
[in]A
          A is COMPLEX*16
         The (1,1) element of the 2-by-2 matrix.
[in]B
          B is COMPLEX*16
         The (1,2) element and the conjugate of the (2,1) element of
         the 2-by-2 matrix.
[in]C
          C is COMPLEX*16
         The (2,2) element of the 2-by-2 matrix.
[out]RT1
          RT1 is DOUBLE PRECISION
         The eigenvalue of larger absolute value.
[out]RT2
          RT2 is DOUBLE PRECISION
         The eigenvalue of smaller absolute value.
[out]CS1
          CS1 is DOUBLE PRECISION
[out]SN1
          SN1 is COMPLEX*16
         The vector (CS1, SN1) is a unit right eigenvector for RT1.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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.

Definition at line 122 of file zlaev2.f.

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