zlaev2.f - Online Linux Manual PageSection : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzlaev2.f
SYNOPSIS
Functions/Subroutinessubroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Function/Subroutine Documentation
subroutine zlaev2 (complex*16 A, complex*16 B, complex*16 C, double precision RT1, double precision RT2, double precision CS1, complex*16 SN1)ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose: ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
[ A B ]
[ CONJG(B) C ].
On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
eigenvector for RT1, giving the decomposition
[ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
[-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].Parameters: A A is COMPLEX*16
The (1,1) element of the 2-by-2 matrix.
B B is COMPLEX*16
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.
C C is COMPLEX*16
The (2,2) element of the 2-by-2 matrix.
RT1 RT1 is DOUBLE PRECISION
The eigenvalue of larger absolute value.
RT2 RT2 is DOUBLE PRECISION
The eigenvalue of smaller absolute value.
CS1 CS1 is DOUBLE PRECISION
SN1 SN1 is COMPLEX*16
The vector (CS1, SN1) is a unit right eigenvector for RT1.Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: December 2016 Further Details: RT1 is accurate to a few ulps barring over/underflow.
RT2 may be inaccurate if there is massive cancellation in the
determinant A*C-B*B; higher precision or correctly rounded or
correctly truncated arithmetic would be needed to compute RT2
accurately in all cases.
CS1 and SN1 are accurate to a few ulps barring over/underflow.
Overflow is possible only if RT1 is within a factor of 5 of overflow.
Underflow is harmless if the input data is 0 or exceeds
underflow_threshold / macheps.Definition at line 123 of file zlaev2.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code. 0
Johanes Gumabo
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