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DLALS0Run Method

Purpose ======= DLALS0 applies back the multiplying factors of either the left or the right singular vector matrix of a diagonal matrix appended by a row to the right hand side matrix B in solving the least squares problem using the divide-and-conquer SVD approach. For the left singular vector matrix, three types of orthogonal matrices are involved: (1L) Givens rotations: the number of such rotations is GIVPTR; the pairs of columns/rows they were applied to are stored in GIVCOL; and the C- and S-values of these rotations are stored in GIVNUM. (2L) Permutation. The (NL+1)-st row of B is to be moved to the first row, and for J=2:N, PERM(J)-th row of B is to be moved to the J-th row. (3L) The left singular vector matrix of the remaining matrix. For the right singular vector matrix, four types of orthogonal matrices are involved: (1R) The right singular vector matrix of the remaining matrix. (2R) If SQRE = 1, one extra Givens rotation to generate the right null space. (3R) The inverse transformation of (2L). (4R) The inverse transformation of (1L).

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 NL,
	int NR,
	int SQRE,
	int NRHS,
	ref double[] B,
	int offset_b,
	int LDB,
	ref double[] BX,
	int offset_bx,
	int LDBX,
	int[] PERM,
	int offset_perm,
	int GIVPTR,
	int[] GIVCOL,
	int offset_givcol,
	int LDGCOL,
	double[] GIVNUM,
	int offset_givnum,
	int LDGNUM,
	double[] POLES,
	int offset_poles,
	double[] DIFL,
	int offset_difl,
	double[] DIFR,
	int offset_difr,
	double[] Z,
	int offset_z,
	int K,
	double C,
	double S,
	ref double[] WORK,
	int offset_work,
	ref int INFO
)
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Parameters

ICOMPQ  Int32
(input) INTEGER Specifies whether singular vectors are to be computed in factored form: = 0: Left singular vector matrix. = 1: Right singular vector matrix.
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 row dimension N = NL + NR + 1, and column dimension M = N + SQRE.
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. LDB must be at least max(1,MAX( M, N ) ).
BX  Double
(workspace) DOUBLE PRECISION array, dimension ( LDBX, NRHS )
offset_bx  Int32
 
LDBX  Int32
(input) INTEGER The leading dimension of BX.
PERM  Int32
(input) INTEGER array, dimension ( N ) The permutations (from deflation and sorting) applied to the two blocks.
offset_perm  Int32
 
GIVPTR  Int32
(input) INTEGER The number of Givens rotations which took place in this subproblem.
GIVCOL  Int32
(input) INTEGER array, dimension ( LDGCOL, 2 ) Each pair of numbers indicates a pair of rows/columns involved in a Givens rotation.
offset_givcol  Int32
 
LDGCOL  Int32
(input) INTEGER The leading dimension of GIVCOL, must be at least N.
GIVNUM  Double
(input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) Each number indicates the C or S value used in the corresponding Givens rotation.
offset_givnum  Int32
 
LDGNUM  Int32
(input) INTEGER The leading dimension of arrays DIFR, POLES and GIVNUM, must be at least K.
POLES  Double
(input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) On entry, POLES(1:K, 1) contains the new singular values obtained from solving the secular equation, and POLES(1:K, 2) is an array containing the poles in the secular equation.
offset_poles  Int32
 
DIFL  Double
(input) DOUBLE PRECISION array, dimension ( K ). On entry, DIFL(I) is the distance between I-th updated (undeflated) singular value and the I-th (undeflated) old singular value.
offset_difl  Int32
 
DIFR  Double
(input) DOUBLE PRECISION array, dimension ( LDGNUM, 2 ). On entry, DIFR(I, 1) contains the distances between I-th updated (undeflated) singular value and the I+1-th (undeflated) old singular value. And DIFR(I, 2) is the normalizing factor for the I-th right singular vector.
offset_difr  Int32
 
Z  Double
(input) DOUBLE PRECISION array, dimension ( K ) Contain the components of the deflation-adjusted updating row vector.
offset_z  Int32
 
K  Int32
(input) INTEGER Contains the dimension of the non-deflated matrix, This is the order of the related secular equation. 1 .LE. K .LE.N.
C  Double
(input) 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
(input) 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.
WORK  Double
(workspace) DOUBLE PRECISION array, dimension ( K )
offset_work  Int32
 
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value.
See Also