# zlaev2 (3) - Linux Man Pages

zlaev2.f -

## SYNOPSIS

### Functions/Subroutines

subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

## Function/Subroutine Documentation

### subroutine zlaev2 (complex*16A, complex*16B, complex*16C, double precisionRT1, double precisionRT2, double precisionCS1, complex*16SN1)

ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

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:

A

```          A is COMPLEX*16
The (1,1) element of the 2-by-2 matrix.
```

B

```          B is COMPLEX*16
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.
```

C

```          C is COMPLEX*16
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 COMPLEX*16
The vector (CS1, SN1) is a unit right eigenvector for RT1.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

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 122 of file zlaev2.f.

## Author

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