# lae2 - Man Page

lae2: 2x2 eig, step in steqr, stemr

## Synopsis

### Functions

subroutine dlae2 (a, b, c, rt1, rt2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
subroutine slae2 (a, b, c, rt1, rt2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

## Function 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.

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 dlae2.f.

### 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

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.

## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK