Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?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
  • mkl.fi
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.