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zlaev2.f(3) LAPACK zlaev2.f(3)

zlaev2.f -


subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
 
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

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:
September 2012
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 122 of file zlaev2.f.

Generated automatically by Doxygen for LAPACK from the source code.
Sat Nov 16 2013 Version 3.4.2

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