---
name: "slaev2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slaev2/3lapack"
---

# slaev2(3lapack)

computes the eigendecomposition of a 2-by-2 symmetric matrix \[ A B \] \[ B C \]

## NAME

SLAEV2 - computes the eigendecomposition of a 2-by-2 symmetric matrix  \[ A B \]  \[ B C \]

## SYNOPSIS

- SUBROUTINE SLAEV2(

  A, B, C, RT1, RT2, CS1, SN1 )

- REAL

  A, B, C, CS1, RT1, RT2, SN1

## PURPOSE

SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix\
    \[  A   B  \]\
    \[  B   C  \]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition\
\
    \[ CS1  SN1 \] \[  A   B  \] \[ CS1 -SN1 \]  =  \[ RT1  0  \]\
\
    \[-SN1  CS1 \] \[  B   C  \] \[ SN1  CS1 \]     \[  0  RT2 \].

## ARGUMENTS

- A (input) REAL

  The (1,1) element of the 2-by-2 matrix.

- B (input) REAL

  The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.

- C (input) REAL

  The (2,2) element of the 2-by-2 matrix.

- RT1 (output) REAL

  The eigenvalue of larger absolute value.

- RT2 (output) REAL

  The eigenvalue of smaller absolute value.

- CS1 (output) REAL

  SN1     (output) REAL The vector (CS1, SN1) is a unit right eigenvector for RT1.

## 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.\
 CS1 and SN1 are accurate to a few ulps barring over/underflow. 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.\