ZLAESY(3F) ZLAESY(3F)
ZLAESY - compute 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
SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
COMPLEX*16 A, B, C, CS1, EVSCAL, RT1, RT2, SN1
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 ]
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 symmetric.
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 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 (output) COMPLEX*16
SN1 (output) COMPLEX*16 If EVSCAL .NE. 0, ( CS1, SN1 ) is
the unit right eigenvector for RT1.
ZLAESY(3F) ZLAESY(3F)
ZLAESY - compute 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
SUBROUTINE ZLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )
COMPLEX*16 A, B, C, CS1, EVSCAL, RT1, RT2, SN1
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 ]
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 symmetric.
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 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 (output) COMPLEX*16
SN1 (output) COMPLEX*16 If EVSCAL .NE. 0, ( CS1, SN1 ) is
the unit right eigenvector for RT1.
PPPPaaaaggggeeee 1111 [ Back ]
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