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nnlsq.cxx |

Solve a non-negative least-squares problem with the LARS algorithm (see nonnegativeLeastSquares()) or the Goldfarb-Idnani algorithm (see quadraticProgramming())
Usage: `example_nnlsq` (no parameters - example data are defined in nnlsq.cxx)

#include <iostream>
#include <vigra/matrix.hxx>
#include <vigra/regression.hxx>
#include <vigra/quadprog.hxx>
double A_data[] = {
1, -3, 2,
-3, 10, -5,
2, -5, 6
};
double b_data[] = {
27,
-78,
64
};
int main()
{
using namespace vigra;
using namespace vigra::linalg;
Matrix<double> A(Shape2(3,3), A_data);
Matrix<double> b(Shape2(3,1), b_data);
Matrix<double> x(Shape2(3,1));
// minimize (A*x-b)^2 s.t. x>=0 using least angle regression (LARS algorithm)
nonnegativeLeastSquares(A, b, x);
std::cout << "solution LARS: ";
for(int k=0; k<3; ++k)
std::cout << x(k,0) << ", ";
std::cout << "\n";
// expected output:
// solution LARS: 18.4493, 0, 4.50725,
Matrix<double> eye(identityMatrix<double>(3)),
zeros(Shape2(3,1)),
empty,
U = transpose(A)*A,
v = -transpose(A)*b;
x = 0;
// minimize (A*x-b)^2 s.t. x>=0 using the Goldfarb-Idnani algorithm
quadraticProgramming(U, v, empty, empty, eye, zeros, x);
std::cout << "solution Goldfarb-Idnani: ";
for(int k=0; k<3; ++k)
std::cout << x(k,0) << ", ";
std::cout << "\n";
// expected output:
// solution Goldfarb-Idnani: 18.4493, 0, 4.50725,
}

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.11.1 (Fri May 19 2017)