DLAED8Run Method

Purpose ======= DLAED8 merges the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. There are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny element in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one.

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,
	ref int K,
	int N,
	int QSIZ,
	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[] Z,
	int offset_z,
	ref double[] DLAMDA,
	int offset_dlamda,
	ref double[] Q2,
	int offset_q2,
	int LDQ2,
	ref double[] W,
	int offset_w,
	ref int[] PERM,
	int offset_perm,
	ref int GIVPTR,
	ref int[] GIVCOL,
	int offset_givcol,
	ref double[] GIVNUM,
	int offset_givnum,
	ref int[] INDXP,
	int offset_indxp,
	ref int[] INDX,
	int offset_indx,
	ref int INFO
)

Public Sub Run ( 
	ICOMPQ As Integer,
	ByRef K As Integer,
	N As Integer,
	QSIZ As Integer,
	ByRef D As Double(),
	offset_d As Integer,
	ByRef Q As Double(),
	offset_q As Integer,
	LDQ As Integer,
	ByRef INDXQ As Integer(),
	offset_indxq As Integer,
	ByRef RHO As Double,
	CUTPNT As Integer,
	ByRef Z As Double(),
	offset_z As Integer,
	ByRef DLAMDA As Double(),
	offset_dlamda As Integer,
	ByRef Q2 As Double(),
	offset_q2 As Integer,
	LDQ2 As Integer,
	ByRef W As Double(),
	offset_w As Integer,
	ByRef PERM As Integer(),
	offset_perm As Integer,
	ByRef GIVPTR As Integer,
	ByRef GIVCOL As Integer(),
	offset_givcol As Integer,
	ByRef GIVNUM As Double(),
	offset_givnum As Integer,
	ByRef INDXP As Integer(),
	offset_indxp As Integer,
	ByRef INDX As Integer(),
	offset_indx As Integer,
	ByRef INFO As Integer
)

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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.
K Int32: (output) INTEGER The number of non-deflated eigenvalues, and the order of the related secular equation.
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.
D Double: (input/output) DOUBLE PRECISION array, dimension (N) On entry, the eigenvalues of the two submatrices to be combined. On exit, the trailing (N-K) updated eigenvalues (those which were deflated) sorted into increasing order.
offset_d Int32
Q Double: (input/output) DOUBLE PRECISION array, dimension (LDQ,N) If ICOMPQ = 0, Q is not referenced. Otherwise, on entry, Q contains the eigenvectors of the partially solved system which has been previously updated in matrix multiplies with other partially solved eigensystems. On exit, Q contains the trailing (N-K) updated eigenvectors (those which were deflated) in its last N-K columns.
offset_q Int32
LDQ Int32: (input) INTEGER The leading dimension of the array Q. LDQ .GE. max(1,N).
INDXQ Int32: (input) INTEGER array, dimension (N) The permutation which separately sorts the two sub-problems in D into ascending order. Note that elements in the second half of this permutation must first have CUTPNT added to their values in order to be accurate.
offset_indxq Int32
RHO Double: (input/output) DOUBLE PRECISION On entry, the off-diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined. On exit, RHO has been modified to the value required by DLAED3.
CUTPNT Int32: (input) INTEGER The location of the last eigenvalue in the leading sub-matrix. min(1,N) .LE. CUTPNT .LE. N.
Z Double: (input) DOUBLE PRECISION array, dimension (N) On entry, Z contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix). On exit, the contents of Z are destroyed by the updating process.
offset_z Int32
DLAMDA Double: (output) DOUBLE PRECISION array, dimension (N) A copy of the first K eigenvalues which will be used by DLAED3 to form the secular equation.
offset_dlamda Int32
Q2 Double: (output) DOUBLE PRECISION array, dimension (LDQ2,N) If ICOMPQ = 0, Q2 is not referenced. Otherwise, a copy of the first K eigenvectors which will be used by DLAED7 in a matrix multiply (DGEMM) to update the new eigenvectors.
offset_q2 Int32
LDQ2 Int32: (input) INTEGER The leading dimension of the array Q2. LDQ2 .GE. max(1,N).
W Double: (output) DOUBLE PRECISION array, dimension (N) The first k values of the final deflation-altered z-vector and will be passed to DLAED3.
offset_w Int32
PERM Int32: (output) INTEGER array, dimension (N) The permutations (from deflation and sorting) to be applied to each eigenblock.
offset_perm Int32
GIVPTR Int32: (output) INTEGER The number of Givens rotations which took place in this subproblem.
GIVCOL Int32: (output) INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
offset_givcol Int32
GIVNUM Double: (output) DOUBLE PRECISION array, dimension (2, N) Each number indicates the S value to be used in the corresponding Givens rotation.
offset_givnum Int32
INDXP Int32: (workspace) INTEGER array, dimension (N) The permutation used to place deflated values of D at the end of the array. INDXP(1:K) points to the nondeflated D-values and INDXP(K+1:N) points to the deflated eigenvalues.
offset_indxp Int32
INDX Int32: (workspace) INTEGER array, dimension (N) The permutation used to sort the contents of D into ascending order.
offset_indx Int32
INFO Int32: (output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value.

Reference

DLAED8 Class

DotNumerics.LinearAlgebra.CSLapack Namespace