# zlaev2.f man page

zlaev2.f —

## Synopsis

### Functions/Subroutines

subroutinezlaev2(A, B, C, RT1, RT2, CS1, SN1)ZLAEV2computes 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

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 122 of file zlaev2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlaev2(3) is an alias of zlaev2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK