# 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.

## Detailed Description

## 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

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 **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

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

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## Info

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