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DLASD7Run Method

Purpose ======= DLASD7 merges the two sets of singular values 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 singular values are close together or if there is a tiny entry in the Z vector. For each such occurrence the order of the related secular equation problem is reduced by one. DLASD7 is called from DLASD6.

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 NL,
	int NR,
	int SQRE,
	ref int K,
	ref double[] D,
	int offset_d,
	ref double[] Z,
	int offset_z,
	ref double[] ZW,
	int offset_zw,
	ref double[] VF,
	int offset_vf,
	ref double[] VFW,
	int offset_vfw,
	ref double[] VL,
	int offset_vl,
	ref double[] VLW,
	int offset_vlw,
	double ALPHA,
	double BETA,
	ref double[] DSIGMA,
	int offset_dsigma,
	ref int[] IDX,
	int offset_idx,
	ref int[] IDXP,
	int offset_idxp,
	ref int[] IDXQ,
	int offset_idxq,
	ref int[] PERM,
	int offset_perm,
	ref int GIVPTR,
	ref int[] GIVCOL,
	int offset_givcol,
	int LDGCOL,
	ref double[] GIVNUM,
	int offset_givnum,
	int LDGNUM,
	ref double C,
	ref double S,
	ref int INFO
)
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Parameters

ICOMPQ  Int32
(input) INTEGER Specifies whether singular vectors are to be computed in compact form, as follows: = 0: Compute singular values only. = 1: Compute singular vectors of upper bidiagonal matrix in compact form.
NL  Int32
(input) INTEGER The row dimension of the upper block. NL .GE. 1.
NR  Int32
(input) INTEGER The row dimension of the lower block. NR .GE. 1.
SQRE  Int32
(input) INTEGER = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE .GE. N columns.
K  Int32
(output) INTEGER Contains the dimension of the non-deflated matrix, this is the order of the related secular equation. 1 .LE. K .LE.N.
D  Double
(input/output) DOUBLE PRECISION array, dimension ( N ) On entry D contains the singular values of the two submatrices to be combined. On exit D contains the trailing (N-K) updated singular values (those which were deflated) sorted into increasing order.
offset_d  Int32
 
Z  Double
(output) DOUBLE PRECISION array, dimension ( M ) On exit Z contains the updating row vector in the secular equation.
offset_z  Int32
 
ZW  Double
(workspace) DOUBLE PRECISION array, dimension ( M ) Workspace for Z.
offset_zw  Int32
 
VF  Double
(input/output) DOUBLE PRECISION array, dimension ( M ) On entry, VF(1:NL+1) contains the first components of all right singular vectors of the upper block; and VF(NL+2:M) contains the first components of all right singular vectors of the lower block. On exit, VF contains the first components of all right singular vectors of the bidiagonal matrix.
offset_vf  Int32
 
VFW  Double
(workspace) DOUBLE PRECISION array, dimension ( M ) Workspace for VF.
offset_vfw  Int32
 
VL  Double
(input/output) DOUBLE PRECISION array, dimension ( M ) On entry, VL(1:NL+1) contains the last components of all right singular vectors of the upper block; and VL(NL+2:M) contains the last components of all right singular vectors of the lower block. On exit, VL contains the last components of all right singular vectors of the bidiagonal matrix.
offset_vl  Int32
 
VLW  Double
(workspace) DOUBLE PRECISION array, dimension ( M ) Workspace for VL.
offset_vlw  Int32
 
ALPHA  Double
(input) DOUBLE PRECISION Contains the diagonal element associated with the added row.
BETA  Double
(input) DOUBLE PRECISION Contains the off-diagonal element associated with the added row.
DSIGMA  Double
(output) DOUBLE PRECISION array, dimension ( N ) Contains a copy of the diagonal elements (K-1 singular values and one zero) in the secular equation.
offset_dsigma  Int32
 
IDX  Int32
(workspace) INTEGER array, dimension ( N ) This will contain the permutation used to sort the contents of D into ascending order.
offset_idx  Int32
 
IDXP  Int32
(workspace) INTEGER array, dimension ( N ) This will contain the permutation used to place deflated values of D at the end of the array. On output IDXP(2:K) points to the nondeflated D-values and IDXP(K+1:N) points to the deflated singular values.
offset_idxp  Int32
 
IDXQ  Int32
(input) INTEGER array, dimension ( N ) This contains the permutation which separately sorts the two sub-problems in D into ascending order. Note that entries in the first half of this permutation must first be moved one position backward; and entries in the second half must first have NL+1 added to their values.
offset_idxq  Int32
 
PERM  Int32
(output) INTEGER array, dimension ( N ) The permutations (from deflation and sorting) to be applied to each singular block. Not referenced if ICOMPQ = 0.
offset_perm  Int32
 
GIVPTR  Int32
(output) INTEGER The number of Givens rotations which took place in this subproblem. Not referenced if ICOMPQ = 0.
GIVCOL  Int32
(output) INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. Not referenced if ICOMPQ = 0.
offset_givcol  Int32
 
LDGCOL  Int32
(input) INTEGER The leading dimension of GIVCOL, must be at least N.
GIVNUM  Double
(output) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value to be used in the corresponding Givens rotation. Not referenced if ICOMPQ = 0.
offset_givnum  Int32
 
LDGNUM  Int32
(input) INTEGER The leading dimension of GIVNUM, must be at least N.
C  Double
(output) DOUBLE PRECISION C contains garbage if SQRE =0 and the C-value of a Givens rotation related to the right null space if SQRE = 1.
S  Double
(output) DOUBLE PRECISION S contains garbage if SQRE =0 and the S-value of a Givens rotation related to the right null space if SQRE = 1.
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value.
See Also