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DLAED7Run Method

Purpose ======= DLAED7 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. DLAED1 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 DLAED8. 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 DLAED9). 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.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
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public void Run(
	int ICOMPQ,
	int N,
	int QSIZ,
	int TLVLS,
	int CURLVL,
	int CURPBM,
	ref double[] D,
	int offset_d,
	ref double[] Q,
	int offset_q,
	int LDQ,
	ref int[] INDXQ,
	int offset_indxq,
	ref double RHO,
	int CUTPNT,
	ref double[] QSTORE,
	int offset_qstore,
	ref int[] QPTR,
	int offset_qptr,
	ref int[] PRMPTR,
	int offset_prmptr,
	ref int[] PERM,
	int offset_perm,
	ref int[] GIVPTR,
	int offset_givptr,
	ref int[] GIVCOL,
	int offset_givcol,
	ref double[] GIVNUM,
	int offset_givnum,
	ref double[] WORK,
	int offset_work,
	ref int[] IWORK,
	int offset_iwork,
	ref int INFO
)
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Parameters

ICOMPQ  Int32
(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  Int32
(input) INTEGER The dimension of the symmetric tridiagonal matrix. N .GE. 0.
QSIZ  Int32
(input) INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ .GE. N if ICOMPQ = 1.
TLVLS  Int32
(input) INTEGER The total number of merging levels in the overall divide and conquer tree.
CURLVL  Int32
(input) INTEGER The current level in the overall merge routine, 0 .LE. CURLVL .LE. TLVLS.
CURPBM  Int32
(input) INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right).
D  Double
(input/output) DOUBLE PRECISION array, dimension (N) On entry, the eigenvalues of the rank-1-perturbed matrix. On exit, the eigenvalues of the repaired matrix.
offset_d  Int32
 
Q  Double
(input/output) DOUBLE PRECISION array, dimension (LDQ, N) On entry, the eigenvectors of the rank-1-perturbed matrix. On exit, the eigenvectors of the repaired tridiagonal matrix.
offset_q  Int32
 
LDQ  Int32
(input) INTEGER The leading dimension of the array Q. LDQ .GE. max(1,N).
INDXQ  Int32
(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.
offset_indxq  Int32
 
RHO  Double
(input) DOUBLE PRECISION The subdiagonal element used to create the rank-1 modification.
CUTPNT  Int32
(input) INTEGER Contains the location of the last eigenvalue in the leading sub-matrix. min(1,N) .LE. CUTPNT .LE. N.
QSTORE  Double
(input/output) DOUBLE PRECISION array, dimension (N**2+1) Stores eigenvectors of submatrices encountered during divide and conquer, packed together. QPTR points to beginning of the submatrices.
offset_qstore  Int32
 
QPTR  Int32
(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.
offset_qptr  Int32
 
PRMPTR  Int32
(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.
offset_prmptr  Int32
 
PERM  Int32
(input) INTEGER array, dimension (N lg N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock.
offset_perm  Int32
 
GIVPTR  Int32
(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.
offset_givptr  Int32
 
GIVCOL  Int32
(input) INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
offset_givcol  Int32
 
GIVNUM  Double
(input) DOUBLE PRECISION array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation.
offset_givnum  Int32
 
WORK  Double
(workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)
offset_work  Int32
 
IWORK  Int32
(workspace) INTEGER array, dimension (4*N)
offset_iwork  Int32
 
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value. .GT. 0: if INFO = 1, an eigenvalue did not converge
See Also