---
name: "slae2.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/slae2.f"
---

# slae2.f(3)

## NAME

SRC/slae2.f

## SYNOPSIS

### Functions/Subroutines

subroutine **slae2** (a, b, c, rt1, rt2)\
 **SLAE2** computes the eigenvalues of a 2-by-2 symmetric matrix.

## Function/Subroutine Documentation

### subroutine slae2 (real a, real b, real c, real rt1, real rt2)

**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.

**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 **101** of file **slae2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.