dlaev2.f man page

dlaev2.f

Synopsis

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.

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.  

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:

A

          A is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.

B

          B is DOUBLE PRECISION
          The (1,2) element and the conjugate of the (2,1) element of
          the 2-by-2 matrix.

C

          C is DOUBLE PRECISION
          The (2,2) element of the 2-by-2 matrix.

RT1

          RT1 is DOUBLE PRECISION
          The eigenvalue of larger absolute value.

RT2

          RT2 is DOUBLE PRECISION
          The eigenvalue of smaller absolute value.

CS1

          CS1 is DOUBLE PRECISION

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:

December 2016

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 dlaev2.f.

Author

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Referenced By

The man page dlaev2(3) is an alias of dlaev2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK