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DLALSARun Method

Purpose ======= DLALSA is an itermediate step in solving the least squares problem by computing the SVD of the coefficient matrix in compact form (The singular vectors are computed as products of simple orthorgonal matrices.). If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector matrix of an upper bidiagonal matrix to the right hand side; and if ICOMPQ = 1, DLALSA applies the right singular vector matrix to the right hand side. The singular vector matrices were generated in compact form by DLALSA.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
Copy
public void Run(
	int ICOMPQ,
	int SMLSIZ,
	int N,
	int NRHS,
	ref double[] B,
	int offset_b,
	int LDB,
	ref double[] BX,
	int offset_bx,
	int LDBX,
	double[] U,
	int offset_u,
	int LDU,
	double[] VT,
	int offset_vt,
	int[] K,
	int offset_k,
	double[] DIFL,
	int offset_difl,
	double[] DIFR,
	int offset_difr,
	double[] Z,
	int offset_z,
	double[] POLES,
	int offset_poles,
	int[] GIVPTR,
	int offset_givptr,
	int[] GIVCOL,
	int offset_givcol,
	int LDGCOL,
	int[] PERM,
	int offset_perm,
	double[] GIVNUM,
	int offset_givnum,
	double[] C,
	int offset_c,
	double[] S,
	int offset_s,
	ref double[] WORK,
	int offset_work,
	ref int[] IWORK,
	int offset_iwork,
	ref int INFO
)
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Parameters

ICOMPQ  Int32
(input) INTEGER Specifies whether the left or the right singular vector matrix is involved. = 0: Left singular vector matrix = 1: Right singular vector matrix
SMLSIZ  Int32
(input) INTEGER The maximum size of the subproblems at the bottom of the computation tree.
N  Int32
(input) INTEGER The row and column dimensions of the upper bidiagonal matrix.
NRHS  Int32
(input) INTEGER The number of columns of B and BX. NRHS must be at least 1.
B  Double
(input/output) DOUBLE PRECISION array, dimension ( LDB, NRHS ) On input, B contains the right hand sides of the least squares problem in rows 1 through M. On output, B contains the solution X in rows 1 through N.
offset_b  Int32
 
LDB  Int32
(input) INTEGER The leading dimension of B in the calling subprogram. LDB must be at least max(1,MAX( M, N ) ).
BX  Double
(output) DOUBLE PRECISION array, dimension ( LDBX, NRHS ) On exit, the result of applying the left or right singular vector matrix to B.
offset_bx  Int32
 
LDBX  Int32
(input) INTEGER The leading dimension of BX.
U  Double
(input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). On entry, U contains the left singular vector matrices of all subproblems at the bottom level.
offset_u  Int32
 
LDU  Int32
(input) INTEGER, LDU = .GT. N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
VT  Double
(input) DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). On entry, VT' contains the right singular vector matrices of all subproblems at the bottom level.
offset_vt  Int32
 
K  Int32
(input) INTEGER array, dimension ( N ).
offset_k  Int32
 
DIFL  Double
(input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
offset_difl  Int32
 
DIFR  Double
(input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record distances between singular values on the I-th level and singular values on the (I -1)-th level, and DIFR(*, 2 * I) record the normalizing factors of the right singular vectors matrices of subproblems on I-th level.
offset_difr  Int32
 
Z  Double
(input) DOUBLE PRECISION array, dimension ( LDU, NLVL ). On entry, Z(1, I) contains the components of the deflation- adjusted updating row vector for subproblems on the I-th level.
offset_z  Int32
 
POLES  Double
(input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old singular values involved in the secular equations on the I-th level.
offset_poles  Int32
 
GIVPTR  Int32
(input) INTEGER array, dimension ( N ). On entry, GIVPTR( I ) records the number of Givens rotations performed on the I-th problem on the computation tree.
offset_givptr  Int32
 
GIVCOL  Int32
(input) INTEGER array, dimension ( LDGCOL, 2 * NLVL ). On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the locations of Givens rotations performed on the I-th level on the computation tree.
offset_givcol  Int32
 
LDGCOL  Int32
(input) INTEGER, LDGCOL = .GT. N. The leading dimension of arrays GIVCOL and PERM.
PERM  Int32
(input) INTEGER array, dimension ( LDGCOL, NLVL ). On entry, PERM(*, I) records permutations done on the I-th level of the computation tree.
offset_perm  Int32
 
GIVNUM  Double
(input) DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- values of Givens rotations performed on the I-th level on the computation tree.
offset_givnum  Int32
 
C  Double
(input) DOUBLE PRECISION array, dimension ( N ). On entry, if the I-th subproblem is not square, C( I ) contains the C-value of a Givens rotation related to the right null space of the I-th subproblem.
offset_c  Int32
 
S  Double
(input) DOUBLE PRECISION array, dimension ( N ). On entry, if the I-th subproblem is not square, S( I ) contains the S-value of a Givens rotation related to the right null space of the I-th subproblem.
offset_s  Int32
 
WORK  Double
(workspace) DOUBLE PRECISION array. The dimension must be at least N.
offset_work  Int32
 
IWORK  Int32
(workspace) INTEGER array. The dimension must be at least 3 * N
offset_iwork  Int32
 
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value.
See Also