dlae2-f(3)

dlae2.f –

Synopsis

Functions/Subroutines

subroutine dlae2 (A, B, C, RT1, RT2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Function/Subroutine Documentation

subroutine dlae2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2)

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Purpose:

 DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
 [ A B ]
 [ B C ].
 On return, RT1 is the eigenvalue of larger absolute value, and RT2
 is the eigenvalue of smaller absolute value.

 

Parameters:

A

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

B

 B is DOUBLE PRECISION
 The (1,2) and (2,1) elements of the 2-by-2 matrix.

C

 C is DOUBLE PRECISION
 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.

 

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.
 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 103 of file dlae2.f.

Author

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