org.netlib.lapack
Class DLAED1
java.lang.Object
org.netlib.lapack.DLAED1
public class DLAED1
 extends java.lang.Object
DLAED1 is a simplified interface to the JLAPACK routine dlaed1.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* DLAED1 computes the updated eigensystem of a diagonal
* matrix after modification by a rankone symmetric matrix. This
* routine is used only for the eigenproblem which requires all
* eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
* the case in which eigenvalues only or eigenvalues and eigenvectors
* of a full symmetric matrix (which was reduced to tridiagonal form)
* are desired.
*
* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
*
* where Z = Q'u, u is a vector of length N with ones in the
* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
*
* The eigenvectors of the original matrix are stored in Q, and the
* eigenvalues are in D. The algorithm consists of three stages:
*
* The first stage consists of deflating the size of the problem
* when there are multiple eigenvalues or if there is a zero in
* the Z vector. For each such occurence the dimension of the
* secular equation problem is reduced by one. This stage is
* performed by the routine DLAED2.
*
* The second stage consists of calculating the updated
* eigenvalues. This is done by finding the roots of the secular
* equation via the routine DLAED4 (as called by DLAED3).
* This routine also calculates the eigenvectors of the current
* problem.
*
* The final stage consists of computing the updated eigenvectors
* directly using the updated eigenvalues. The eigenvectors for
* the current problem are multiplied with the eigenvectors from
* the overall problem.
*
* Arguments
* =========
*
* N (input) INTEGER
* The dimension of the symmetric tridiagonal matrix. N >= 0.
*
* D (input/output) DOUBLE PRECISION array, dimension (N)
* On entry, the eigenvalues of the rank1perturbed matrix.
* On exit, the eigenvalues of the repaired matrix.
*
* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
* On entry, the eigenvectors of the rank1perturbed matrix.
* On exit, the eigenvectors of the repaired tridiagonal matrix.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= max(1,N).
*
* INDXQ (input/output) INTEGER array, dimension (N)
* On entry, the permutation which separately sorts the two
* subproblems in D into ascending order.
* On exit, the permutation which will reintegrate the
* subproblems back into sorted order,
* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
*
* RHO (input) DOUBLE PRECISION
* The subdiagonal entry used to create the rank1 modification.
*
* CUTPNT (input) INTEGER
* The location of the last eigenvalue in the leading submatrix.
* min(1,N) <= CUTPNT <= N/2.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)
*
* IWORK (workspace) INTEGER array, dimension (4*N)
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = i, the ith argument had an illegal value.
* > 0: if INFO = 1, an eigenvalue did not converge
*
* Further Details
* ===============
*
* Based on contributions by
* Jeff Rutter, Computer Science Division, University of California
* at Berkeley, USA
* Modified by Francoise Tisseur, University of Tennessee.
*
* =====================================================================
*
* .. Local Scalars ..
Method Summary 
static void 
DLAED1(int n,
double[] d,
double[][] q,
int[] indxq,
doubleW rho,
int cutpnt,
double[] work,
int[] iwork,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
DLAED1
public DLAED1()
DLAED1
public static void DLAED1(int n,
double[] d,
double[][] q,
int[] indxq,
doubleW rho,
int cutpnt,
double[] work,
int[] iwork,
intW info)