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.

   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.

Author

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