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DGGGLMRun Method

Purpose ======= DGGGLM solves a general Gauss-Markov linear model (GLM) problem: minimize || y ||_2 subject to d = A*x + B*y x where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M .LE. N .LE. M+P, and rank(A) = M and rank( A B ) = N. Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by A = Q*(R), B = Q*T*Z. (0) In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem minimize || inv(B)*(d-A*x) ||_2 x where inv(B) denotes the inverse of B.

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 N,
	int M,
	int P,
	ref double[] A,
	int offset_a,
	int LDA,
	ref double[] B,
	int offset_b,
	int LDB,
	ref double[] D,
	int offset_d,
	ref double[] X,
	int offset_x,
	ref double[] Y,
	int offset_y,
	ref double[] WORK,
	int offset_work,
	int LWORK,
	ref int INFO
)
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Parameters

N  Int32
(input) INTEGER The number of rows of the matrices A and B. N .GE. 0.
M  Int32
(input) INTEGER The number of columns of the matrix A. 0 .LE. M .LE. N.
P  Int32
(input) INTEGER The number of columns of the matrix B. P .GE. N-M.
A  Double
= Q*(R), B = Q*T*Z. (0)
offset_a  Int32
 
LDA  Int32
(input) INTEGER The leading dimension of the array A. LDA .GE. max(1,N).
B  Double
(input/output) DOUBLE PRECISION array, dimension (LDB,P) On entry, the N-by-P matrix B. On exit, if N .LE. P, the upper triangle of the subarray B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; if N .GT. P, the elements on and above the (N-P)th subdiagonal contain the N-by-P upper trapezoidal matrix T.
offset_b  Int32
 
LDB  Int32
(input) INTEGER The leading dimension of the array B. LDB .GE. max(1,N).
D  Double
(input/output) DOUBLE PRECISION array, dimension (N) On entry, D is the left hand side of the GLM equation. On exit, D is destroyed.
offset_d  Int32
 
X  Double
(output) DOUBLE PRECISION array, dimension (M)
offset_x  Int32
 
Y  Double
(output) DOUBLE PRECISION array, dimension (P) On exit, X and Y are the solutions of the GLM problem.
offset_y  Int32
 
WORK  Double
(workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
offset_work  Int32
 
LWORK  Int32
(input) INTEGER The dimension of the array WORK. LWORK .GE. max(1,N+M+P). For optimum performance, LWORK .GE. M+min(N,P)+max(N,P)*NB, where NB is an upper bound for the optimal blocksizes for DGEQRF, SGERQF, DORMQR and SORMRQ. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value. = 1: the upper triangular factor R associated with A in the generalized QR factorization of the pair (A, B) is singular, so that rank(A) .LT. M; the least squares solution could not be computed. = 2: the bottom (N-M) by (N-M) part of the upper trapezoidal factor T associated with B in the generalized QR factorization of the pair (A, B) is singular, so that rank( A B ) .LT. N; the least squares solution could not be computed.
See Also