Man page - laesy(3)

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Manual

laesy

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine claesy (complex a, complex b, complex c, complex rt1, complexrt2, complex evscal, complex cs1, complex sn1)
subroutine zlaesy (complex*16 a, complex*16 b, complex*16 c, complex*16rt1, complex*16 rt2, complex*16 evscal, complex*16 cs1, complex*16 sn1)
Author

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, complexrt2, 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.

subroutine zlaesy (complex*16 a, complex*16 b, complex*16 c, complex*16rt1, 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.

Author

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