slaev2.f(3)

NAME
slaev2.f -

SYNOPSIS

  Functions/Subroutines

subroutine slaev2 (A, B, C, RT1, RT2, CS1, SN1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Function/Subroutine Documentation

  subroutine slaev2 (realA, realB, realC, realRT1, realRT2, realCS1, realSN1)

SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

     SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
        [  A   B  ]
        [  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  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
        [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].

Parameters:
    A

              A is REAL
              The (1,1) element of the 2-by-2 matrix.

    B

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

    C

              C is REAL
              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 REAL
              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 121 of file slaev2.f.

Author

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