Solving a Least Squares Problem

Linear Algebra Module User's Guide
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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>                                  // 1
#include <rw/math/genmat.h>
#include <rw/math/mathvec.h>
#include <rw/lapack/lsqr.h>
#include <rw/lapack/qrcalcp3.h>

int main()
{
    RWGenMat<float> A;                               // 2
    RWMathVec<float> b;
    std::cin >> A >> b;
    RWLeastSqQR<float, RWQRCalcP3<float> > ls(A);    // 3
    RWMathVec<float> x = ls.solve(b);                // 4
    std::cout << x << std::endl;

    return 0;
}

`//1`	The header file `lsqr.h` includes the declaration of the least squares class *RWLeastSqQR<T,QRCalc>*. 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`. The second template parameter for the class *RWLeastSqQR* indicates that we are using the class *RWQRCalcP3<float>* to compute the QR decomposition of `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.

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