dlaev2 (l)  Linux Man Pages
dlaev2: computes the eigendecomposition of a 2by2 symmetric matrix [ A B ] [ B C ]
Command to display dlaev2
manual in Linux: $ man l dlaev2
NAME
DLAEV2  computes the eigendecomposition of a 2by2 symmetric matrix [ A B ] [ B C ]
SYNOPSIS
 SUBROUTINE DLAEV2(

A, B, C, RT1, RT2, CS1, SN1 )

DOUBLE
PRECISION A, B, C, CS1, RT1, RT2, SN1
PURPOSE
DLAEV2 computes the eigendecomposition of a 2by2 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 ].
ARGUMENTS
 A (input) DOUBLE PRECISION

The (1,1) element of the 2by2 matrix.
 B (input) DOUBLE PRECISION

The (1,2) element and the conjugate of the (2,1) element of
the 2by2 matrix.
 C (input) DOUBLE PRECISION

The (2,2) element of the 2by2 matrix.
 RT1 (output) DOUBLE PRECISION

The eigenvalue of larger absolute value.
 RT2 (output) DOUBLE PRECISION

The eigenvalue of smaller absolute value.
 CS1 (output) DOUBLE PRECISION

SN1 (output) DOUBLE PRECISION
The vector (CS1, SN1) is a unit right eigenvector for RT1.
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*CB*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.
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