# slae2.f man page

slae2.f —

## Synopsis

### Functions/Subroutines

subroutineslae2(A, B, C, RT1, RT2)SLAE2computes the eigenvalues of a 2-by-2 symmetric matrix.

## Function/Subroutine Documentation

### subroutine slae2 (realA, realB, realC, realRT1, realRT2)

**SLAE2** computes the eigenvalues of a 2-by-2 symmetric matrix.

**Purpose:**

```
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
[ A B ]
[ B C ].
On return, RT1 is the eigenvalue of larger absolute value, and RT2
is the eigenvalue of smaller absolute value.
```

**Parameters:**

*A*

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

*B*

```
B is REAL
The (1,2) and (2,1) elements 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.
```

**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.
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 103 of file slae2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slae2(3) is an alias of slae2.f(3).