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LAPACK: Linear Algebra PACKage
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dlaev2.f File Reference

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Functions/Subroutines

subroutine dlaev2 (A, B, C, RT1, RT2, CS1, SN1)
 DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. More...
 

Function/Subroutine Documentation

subroutine dlaev2 ( double precision  A,
double precision  B,
double precision  C,
double precision  RT1,
double precision  RT2,
double precision  CS1,
double precision  SN1 
)

DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Download DLAEV2 + dependencies [TGZ] [ZIP] [TXT]

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 ].
Parameters
[in]A
          A is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.
[in]B
          B is DOUBLE PRECISION
          The (1,2) element and the conjugate of the (2,1) element of
          the 2-by-2 matrix.
[in]C
          C is DOUBLE PRECISION
          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 DOUBLE PRECISION
          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
September 2012
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 121 of file dlaev2.f.

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