laesy(3)

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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