---
name: "laesy"
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/laesy"
---

# laesy(3)

laesy: 2x2 eig

## NAME

laesy - laesy: 2x2 eig

## SYNOPSIS

### Functions

subroutine **claesy** (a, b, c, rt1, rt2, evscal, cs1, sn1)\
 **CLAESY** computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.  subroutine **zlaesy** (a, b, c, rt1, rt2, evscal, cs1, sn1)\
 **ZLAESY** computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

## Detailed Description

## Function Documentation

### subroutine claesy (complex a, complex b, complex c, complex rt1, complex rt2, complex evscal, complex cs1, complex sn1)

**CLAESY** computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

**Purpose:**

```
!>
!> CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    ( ( A, B );( B, C ) )
!> provided the norm of the matrix of eigenvectors is larger than
!> some threshold value.
!>
!> RT1 is the eigenvalue of larger absolute value, and RT2 of
!> smaller absolute value.  If the eigenvectors are computed, then
!> on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence
!>
!> [  CS1     SN1   ] . [ A  B ] . [ CS1    -SN1   ] = [ RT1  0  ]
!> [ -SN1     CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]
!>
```

**Parameters**

*A*

```
!>          A is COMPLEX
!>          The ( 1, 1 ) element of input matrix.
!>
```

*B*

```
!>          B is COMPLEX
!>          The ( 1, 2 ) element of input matrix.  The ( 2, 1 ) element
!>          is also given by B, since the 2-by-2 matrix is symmetric.
!>
```

*C*

```
!>          C is COMPLEX
!>          The ( 2, 2 ) element of input matrix.
!>
```

*RT1*

```
!>          RT1 is COMPLEX
!>          The eigenvalue of larger modulus.
!>
```

*RT2*

```
!>          RT2 is COMPLEX
!>          The eigenvalue of smaller modulus.
!>
```

*EVSCAL*

```
!>          EVSCAL is COMPLEX
!>          The complex value by which the eigenvector matrix was scaled
!>          to make it orthonormal.  If EVSCAL is zero, the eigenvectors
!>          were not computed.  This means one of two things:  the 2-by-2
!>          matrix could not be diagonalized, or the norm of the matrix
!>          of eigenvectors before scaling was larger than the threshold
!>          value THRESH (set below).
!>
```

*CS1*

```
!>          CS1 is COMPLEX
!>
```

*SN1*

```
!>          SN1 is COMPLEX
!>          If EVSCAL .NE. 0,  ( CS1, SN1 ) is the unit right eigenvector
!>          for RT1.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **114** of file **claesy.f**.

### subroutine zlaesy (complex\*16 a, complex\*16 b, complex\*16 c, complex\*16 rt1, complex\*16 rt2, complex\*16 evscal, complex\*16 cs1, complex\*16 sn1)

**ZLAESY** computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

**Purpose:**

```
!>
!> ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    ( ( A, B );( B, C ) )
!> provided the norm of the matrix of eigenvectors is larger than
!> some threshold value.
!>
!> RT1 is the eigenvalue of larger absolute value, and RT2 of
!> smaller absolute value.  If the eigenvectors are computed, then
!> on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence
!>
!> [  CS1     SN1   ] . [ A  B ] . [ CS1    -SN1   ] = [ RT1  0  ]
!> [ -SN1     CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]
!>
```

**Parameters**

*A*

```
!>          A is COMPLEX*16
!>          The ( 1, 1 ) element of input matrix.
!>
```

*B*

```
!>          B is COMPLEX*16
!>          The ( 1, 2 ) element of input matrix.  The ( 2, 1 ) element
!>          is also given by B, since the 2-by-2 matrix is symmetric.
!>
```

*C*

```
!>          C is COMPLEX*16
!>          The ( 2, 2 ) element of input matrix.
!>
```

*RT1*

```
!>          RT1 is COMPLEX*16
!>          The eigenvalue of larger modulus.
!>
```

*RT2*

```
!>          RT2 is COMPLEX*16
!>          The eigenvalue of smaller modulus.
!>
```

*EVSCAL*

```
!>          EVSCAL is COMPLEX*16
!>          The complex value by which the eigenvector matrix was scaled
!>          to make it orthonormal.  If EVSCAL is zero, the eigenvectors
!>          were not computed.  This means one of two things:  the 2-by-2
!>          matrix could not be diagonalized, or the norm of the matrix
!>          of eigenvectors before scaling was larger than the threshold
!>          value THRESH (set below).
!>
```

*CS1*

```
!>          CS1 is COMPLEX*16
!>
```

*SN1*

```
!>          SN1 is COMPLEX*16
!>          If EVSCAL .NE. 0,  ( CS1, SN1 ) is the unit right eigenvector
!>          for RT1.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **114** of file **zlaesy.f**.

## Author

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