Homepage > Man Pages > Category > Subroutines
Homepage > Man Pages > Name > L

# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of

```NAME
LAPACK-3 - 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

SYNOPSIS
SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )

COMPLEX*16     A, B, C, CS1, EVSCAL, RT1, RT2, SN1

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 ]

ARGUMENTS
A       (input) COMPLEX*16
The ( 1, 1 ) element of input matrix.

B       (input) 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       (input) COMPLEX*16
The ( 2, 2 ) element of input matrix.

RT1     (output) COMPLEX*16
The eigenvalue of larger modulus.

RT2     (output) COMPLEX*16
The eigenvalue of smaller modulus.

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

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```