dlaed4 (l) - Linux Manuals

dlaed4: 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

NAME

DLAED4 - 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

SYNOPSIS

SUBROUTINE DLAED4(
N, I, D, Z, DELTA, RHO, DLAM, INFO )

    
INTEGER I, INFO, N

    
DOUBLE PRECISION DLAM, RHO

    
DOUBLE PRECISION D( * ), DELTA( * ), Z( * )

PURPOSE

This subroutine computes 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 no loss in generality. The rank-one modified system is thus
     diag( D )  +  RHO *  Z * Z_transpose.
where we assume the Euclidean norm of Z is 1.
The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.

ARGUMENTS

N (input) INTEGER
The length of all arrays.
I (input) INTEGER
The index of the eigenvalue to be computed. 1 <= I <= N.
D (input) DOUBLE PRECISION array, dimension (N)
The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J.
Z (input) DOUBLE PRECISION array, dimension (N)
The components of the updating vector.
DELTA (output) DOUBLE PRECISION array, dimension (N)
If N .GT. 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by DLAED3 and DLAED9.
RHO (input) DOUBLE PRECISION
The scalar in the symmetric updating formula.
DLAM (output) DOUBLE PRECISION
The computed lambda_I, the I-th updated eigenvalue.
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = 1, the updating process failed.

PARAMETERS

Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin. ORGATI = .true. origin at i ORGATI = .false. origin at i+1 Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles! MAXIT is the maximum number of iterations allowed for each eigenvalue. Further Details =============== Based on contributions by Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Pages related to dlaed4

  • dlaed4 (3)
  • 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
  • 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
  • dlaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • dlaed8 (l) - merges the two sets of eigenvalues together into a single sorted set
  • dlaed9 (l) - finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
  • dlaeda (l) - computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem