org.netlib.lapack
Class SLAED7
java.lang.Object
org.netlib.lapack.SLAED7
public class SLAED7
- extends java.lang.Object
SLAED7 is a simplified interface to the JLAPACK routine slaed7.
This interface converts Java-style 2D row-major arrays into
the 1D column-major 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
* =======
*
* SLAED7 computes the updated eigensystem of a diagonal
* matrix after modification by a rank-one symmetric matrix. This
* routine is used only for the eigenproblem which requires all
* eigenvalues and optionally eigenvectors of a dense symmetric matrix
* that has been reduced to tridiagonal form. SLAED1 handles
* the case in which all eigenvalues and eigenvectors of a symmetric
* tridiagonal matrix 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 SLAED8.
*
* The second stage consists of calculating the updated
* eigenvalues. This is done by finding the roots of the secular
* equation via the routine SLAED4 (as called by SLAED9).
* 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
* =========
*
* ICOMPQ (input) INTEGER
* = 0: Compute eigenvalues only.
* = 1: Compute eigenvectors of original dense symmetric matrix
* also. On entry, Q contains the orthogonal matrix used
* to reduce the original matrix to tridiagonal form.
*
* N (input) INTEGER
* The dimension of the symmetric tridiagonal matrix. N >= 0.
*
* QSIZ (input) INTEGER
* The dimension of the orthogonal matrix used to reduce
* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
*
* TLVLS (input) INTEGER
* The total number of merging levels in the overall divide and
* conquer tree.
*
* CURLVL (input) INTEGER
* The current level in the overall merge routine,
* 0 <= CURLVL <= TLVLS.
*
* CURPBM (input) INTEGER
* The current problem in the current level in the overall
* merge routine (counting from upper left to lower right).
*
* D (input/output) REAL array, dimension (N)
* On entry, the eigenvalues of the rank-1-perturbed matrix.
* On exit, the eigenvalues of the repaired matrix.
*
* Q (input/output) REAL array, dimension (LDQ, N)
* On entry, the eigenvectors of the rank-1-perturbed 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 (output) INTEGER array, dimension (N)
* The permutation which will reintegrate the subproblem just
* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) )
* will be in ascending order.
*
* RHO (input) REAL
* The subdiagonal element used to create the rank-1
* modification.
*
* CUTPNT (input) INTEGER
* Contains the location of the last eigenvalue in the leading
* sub-matrix. min(1,N) <= CUTPNT <= N.
*
* QSTORE (input/output) REAL array, dimension (N**2+1)
* Stores eigenvectors of submatrices encountered during
* divide and conquer, packed together. QPTR points to
* beginning of the submatrices.
*
* QPTR (input/output) INTEGER array, dimension (N+2)
* List of indices pointing to beginning of submatrices stored
* in QSTORE. The submatrices are numbered starting at the
* bottom left of the divide and conquer tree, from left to
* right and bottom to top.
*
* PRMPTR (input) INTEGER array, dimension (N lg N)
* Contains a list of pointers which indicate where in PERM a
* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
* indicates the size of the permutation and also the size of
* the full, non-deflated problem.
*
* PERM (input) INTEGER array, dimension (N lg N)
* Contains the permutations (from deflation and sorting) to be
* applied to each eigenblock.
*
* GIVPTR (input) INTEGER array, dimension (N lg N)
* Contains a list of pointers which indicate where in GIVCOL a
* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
* indicates the number of Givens rotations.
*
* GIVCOL (input) INTEGER array, dimension (2, N lg N)
* Each pair of numbers indicates a pair of columns to take place
* in a Givens rotation.
*
* GIVNUM (input) REAL array, dimension (2, N lg N)
* Each number indicates the S value to be used in the
* corresponding Givens rotation.
*
* WORK (workspace) REAL array, dimension (3*N+QSIZ*N)
*
* IWORK (workspace) INTEGER array, dimension (4*N)
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th 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
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
SLAED7(int icompq,
int n,
int qsiz,
int tlvls,
int curlvl,
int curpbm,
float[] d,
float[][] q,
int[] indxq,
floatW rho,
int cutpnt,
float[] qstore,
int[] qptr,
int[] prmptr,
int[] perm,
int[] givptr,
int[][] givcol,
float[][] givnum,
float[] work,
int[] iwork,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SLAED7
public SLAED7()
SLAED7
public static void SLAED7(int icompq,
int n,
int qsiz,
int tlvls,
int curlvl,
int curpbm,
float[] d,
float[][] q,
int[] indxq,
floatW rho,
int cutpnt,
float[] qstore,
int[] qptr,
int[] prmptr,
int[] perm,
int[] givptr,
int[][] givcol,
float[][] givnum,
float[] work,
int[] iwork,
intW info)