# dlae2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlae2.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlae2 (A, B, C, RT1, RT2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

## Function/Subroutine Documentation

### subroutine dlae2 (double precision A, double precision B, double precision C, double precision RT1, double precision RT2)

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Purpose:

``` DLAE2  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 DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
```

B

```          B is DOUBLE PRECISION
The (1,2) and (2,1) elements of the 2-by-2 matrix.
```

C

```          C is DOUBLE PRECISION
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.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

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 104 of file dlae2.f.

## Author

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