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DGGLSERun Method

Purpose ======= DGGLSE solves the linear equality-constrained least squares (LSE) problem: minimize || c - A*x ||_2 subject to B*x = d where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vector, and d is a given P-vector. It is assumed that P .LE. N .LE. M+P, and rank(B) = P and rank( (A) ) = N. ( (B) ) These conditions ensure that the LSE problem has a unique solution, which is obtained using a generalized RQ factorization of the matrices (B, A) given by B = (0 R)*Q, A = Z*T*Q.

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

M  Int32
(input) INTEGER The number of rows of the matrix A. M .GE. 0.
N  Int32
(input) INTEGER The number of columns of the matrices A and B. N .GE. 0.
P  Int32
(input) INTEGER The number of rows of the matrix B. 0 .LE. P .LE. N .LE. M+P.
A  Double
(input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix T.
offset_a  Int32
 
LDA  Int32
(input) INTEGER The leading dimension of the array A. LDA .GE. max(1,M).
B  Double
= (0 R)*Q, A = Z*T*Q.
offset_b  Int32
 
LDB  Int32
(input) INTEGER The leading dimension of the array B. LDB .GE. max(1,P).
C  Double
(input/output) DOUBLE PRECISION array, dimension (M) On entry, C contains the right hand side vector for the least squares part of the LSE problem. On exit, the residual sum of squares for the solution is given by the sum of squares of elements N-P+1 to M of vector C.
offset_c  Int32
 
D  Double
(input/output) DOUBLE PRECISION array, dimension (P) On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed.
offset_d  Int32
 
X  Double
(output) DOUBLE PRECISION array, dimension (N) On exit, X is the solution of the LSE problem.
offset_x  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,M+N+P). For optimum performance LWORK .GE. P+min(M,N)+max(M,N)*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 B in the generalized RQ factorization of the pair (B, A) is singular, so that rank(B) .LT. P; the least squares solution could not be computed. = 2: the (N-P) by (N-P) part of the upper trapezoidal factor T associated with A in the generalized RQ factorization of the pair (B, A) is singular, so that rank( (A) ) .LT. N; the least squares solution could not ( (B) ) be computed.
See Also