claev2.f man page

claev2.f

Synopsis

Functions/Subroutines

subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Function/Subroutine Documentation

subroutine claev2 (complex A, complex B, complex C, real RT1, real RT2, real CS1, complex SN1)

CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

CLAEV2 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:

A

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

B

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

C

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

RT1

RT1 is REAL
The eigenvalue of larger absolute value.

RT2

RT2 is REAL
The eigenvalue of smaller absolute value.

CS1

CS1 is REAL

SN1

SN1 is COMPLEX
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 123 of file claev2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page claev2(3) is an alias of claev2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK