claev2.f(3)

NAME
claev2.f

SYNOPSIS

  Functions/Subroutines
subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Function/Subroutine Documentation

  subroutine claev2 (complex A, complex B, complex C, real RT1, real RT2, real CS1, complex SN1)

CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

     CLAEV2 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
             The (1,1) element of the 2-by-2 matrix.

    B

              B is COMPLEX
             The (1,2) element and the conjugate of the (2,1) element of
             the 2-by-2 matrix.

    C

              C is COMPLEX
             The (2,2) element of the 2-by-2 matrix.

    RT1

              RT1 is REAL
             The eigenvalue of larger absolute value.

    RT2

              RT2 is REAL
             The eigenvalue of smaller absolute value.

    CS1

              CS1 is REAL

    SN1

              SN1 is COMPLEX
             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 claev2.f.

Author

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