zlaesy(3)
NAME
- ZLAESY - compute the eigendecomposition of a 2-by-2 sym
- metric matrix ( ( A, B );( B, C ) ) provided the norm of the ma
- trix 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 symmet
- ric 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 symmet
- ric.
- 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 eigen
- vectors were not computed. This means one of two things: the
- 2-by-2 matrix could not be diagonalized, or the norm of the ma
- trix 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 version 3.0 15 June 2000