laesy - Man Page

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.

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.

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.