SLAEV2 (3) Linux Manual Page

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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