Matrix.LQRSolve Method ([In] TMtx, [In] TMtx, [In] TMtx, TMtxOperation)

Solve overdetermined or underdetermined system of real linear equations.

Syntax

Visual Basic

public TMtx LQRSolve([In] TMtx B, [In] TMtx X, [In] TMtx R, TMtxOperation op);

Solve overdetermined or underdetermined real linear systems involving a Rows-by-Cols matrix or its transpose, using a QR or LQ factorization of the calling matrix. It is assumed that the calling matrix has full rank. The following options are provided:

1.If Op = opNone and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

minimize || B - A*X ||.

2.If Op = opNone and m < n: find the minimum norm solution of an underdetermined system

A * X = B.

3.If Op = opTrans and m >= n: find the minimum norm solution of an undetermined system

A**T * X = B.

4.If Op = opTran and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

minimize || B - A**T * X ||

5.If Op = opHerm and m >= n: find the minimum norm solution of an undetermined system

A**H * X = B.

6.If Op = opHerm and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem

minimize || B - A**H * X ||.

Note If the parameters are of TVec type (const Vectors), the routine requires less pre and post processing.