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dlaev2.f(3) LAPACK dlaev2.f(3)

NAME

dlaev2.f -

SYNOPSIS

Functions/Subroutines


subroutine dlaev2 (A, B, C, RT1, RT2, CS1, SN1)
 
DLAEV2

Function/Subroutine Documentation

subroutine dlaev2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2, double precisionCS1, double precisionSN1)

DLAEV2
Purpose:
 
 DLAEV2 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 DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.
 
B
          B is DOUBLE PRECISION
          The (1,2) element and the conjugate of the (2,1) element 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.
 
CS1
          CS1 is DOUBLE PRECISION
 
SN1
          SN1 is DOUBLE PRECISION
          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:
November 2011
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 dlaev2.f.

Author

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