?lae2

Computes the eigenvalues of a 2-by-2 symmetric matrix.

Syntax

call slae2( a, b, c, rt1, rt2 )

call dlae2( a, b, c, rt1, rt2 )

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The routines sla2/dlae2 compute the eigenvalues of a 2-by-2 symmetric matrix


Equation

On return, rt1 is the eigenvalue of larger absolute value, and rt1 is the eigenvalue of smaller absolute value.

Input Parameters

a, b, c

REAL for slae2

DOUBLE PRECISION for dlae2

The elements a, b, and c of the 2-by-2 matrix above.

Output Parameters

rt1, rt2

REAL for slae2

DOUBLE PRECISION for dlae2

The computed eigenvalues of larger and smaller absolute value, respectively.

Application Notes

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.

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.

For more complete information about compiler optimizations, see our Optimization Notice.