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DGELSRun Method

Purpose ======= DGELS solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A. It is assumed that A has full rank. The following options are provided: 1. If TRANS = 'N' and m .GE. n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||. 2. If TRANS = 'N' and m .LT. n: find the minimum norm solution of an underdetermined system A * X = B. 3. If TRANS = 'T' and m .GE. n: find the minimum norm solution of an undetermined system A**T * X = B. 4. If TRANS = 'T' and m .LT. n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**T * X ||. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X.

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(
	string TRANS,
	int M,
	int N,
	int NRHS,
	ref double[] A,
	int offset_a,
	int LDA,
	ref double[] B,
	int offset_b,
	int LDB,
	ref double[] WORK,
	int offset_work,
	int LWORK,
	ref int INFO
)
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Parameters

TRANS  String
(input) CHARACTER*1 = 'N': the linear system involves A; = 'T': the linear system involves A**T.
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 matrix A. N .GE. 0.
NRHS  Int32
(input) INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS .GE.0.
A  Double
(input/output) DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if M .GE. N, A is overwritten by details of its QR factorization as returned by DGEQRF; if M .LT. N, A is overwritten by details of its LQ factorization as returned by DGELQF.
offset_a  Int32
 
LDA  Int32
(input) INTEGER The leading dimension of the array A. LDA .GE. max(1,M).
B  Double
(input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the matrix B of right hand side vectors, stored columnwise; B is M-by-NRHS if TRANS = 'N', or N-by-NRHS if TRANS = 'T'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise: if TRANS = 'N' and m .GE. n, rows 1 to n of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements N+1 to M in that column; if TRANS = 'N' and m .LT. n, rows 1 to N of B contain the minimum norm solution vectors; if TRANS = 'T' and m .GE. n, rows 1 to M of B contain the minimum norm solution vectors; if TRANS = 'T' and m .LT. n, rows 1 to M of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements M+1 to N in that column.
offset_b  Int32
 
LDB  Int32
(input) INTEGER The leading dimension of the array B. LDB .GE. MAX(1,M,N).
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, MN + max( MN, NRHS ) ). For optimal performance, LWORK .GE. max( 1, MN + max( MN, NRHS )*NB ). where MN = min(M,N) and NB is the optimum block size. 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 .GT. 0: if INFO = i, the i-th diagonal element of the triangular factor of A is zero, so that A does not have full rank; the least squares solution could not be computed.
See Also