dlaev2 (l) - Linux Manuals
dlaev2: computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
Command to display dlaev2
manual in Linux: $ man l dlaev2
NAME
DLAEV2 - computes the eigendecomposition of a 2-by-2 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 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 ].
ARGUMENTS
- A (input) DOUBLE PRECISION
-
The (1,1) element of the 2-by-2 matrix.
- B (input) DOUBLE PRECISION
-
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.
- C (input) DOUBLE PRECISION
-
The (2,2) element of the 2-by-2 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*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.
Pages related to dlaev2
- dlaev2 (3)
- dlae2 (l) - computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
- dlaebz (l) - contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
- dlaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
- dlaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
- dlaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
- dlaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
- dlaed4 (l) - subroutine compute the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
- dlaed5 (l) - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
- dlaed6 (l) - computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true