# slaev2.f man page

slaev2.f —

## Synopsis

### Functions/Subroutines

subroutineslaev2(A, B, C, RT1, RT2, CS1, SN1)SLAEV2computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

## Function/Subroutine Documentation

### subroutine slaev2 (realA, realB, realC, realRT1, realRT2, realCS1, realSN1)

**SLAEV2** computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

**Purpose:**

```
SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
[ A B ]
[ 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 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ]
[-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
```

**Parameters:**

*A*

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

*B*

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

*C*

```
C is REAL
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 REAL
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 121 of file slaev2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slaev2(3) is an alias of slaev2.f(3).