# zlaev2.f - Man Page

SRC/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*16 a, complex*16 b, complex*16 c, double precision rt1, double precision rt2, double precision cs1, complex*16 sn1)

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.

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 120 of file zlaev2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaev2(3) is an alias of zlaev2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK