5.2 Solving a Least Squares Problem

Here is a simple program which reads in a matrix and a right side, builds a least squares factorization object, and then calculates the solution to the least squares problem. The program is nearly identical to the first factorization example problem in the previous chapter.

#include <iostream.h>                                // 1
#include <rw/flsqr.h>

main()
{
    RWGenMat<float> A;                               // 2
    RWMathVec<float> b;
    cin >> A >> b;
    FloatLeastSqQR ls(A);                            // 3
    RWMathVec<float> x = solve(ls, b);               // 4
    cout << x << endl;
}

//1	The header file `fchls.h` includes the declaration of the least squares class *FloatLeastSqQR*. This is the QR decomposition implementation of the least squares class. Other implementations are described subsequently.
//2	Here the matrix `A` and the vector `b` are defined and read from standard input.
//3	The least squares decomposition is created from the matrix `A`.
//4	The solution vector is calculated. If the system is overdetermined, this will be the solution that best fits in a least squares sense. If the system is underdetermined, this will be the solution with the smallest norm.