# claev2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

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

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

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