Non-negative least squares

A non-negative least squares problem seeks a solution to the problem

\[\min_x \| A z - y \|_2 \text{ such that } z \ge 0.\]

The following routines attempt to solve such problems by recognizing the equivalence to the quadratic program

\[\min_z \frac{1}{2} z^T P z + q^T z \text{ such that } z \ge 0\]

with \(P = A^T A\) and \(q = -A^T y\).

C++ API

Int NonNegativeLeastSquares(const Matrix<Real> &A, const Matrix<Real> &Y, Matrix<Real> &Z, Real rho = 1, Real alpha = 1.2, Int maxIter = 500, Real absTol = 1e-6, Real relTol = 1e-4, bool inv = true, bool progress = true)

Int NonNegativeLeastSquares(const AbstractDistMatrix<Real> &A, const AbstractDistMatrix<Real> &Y, AbstractDistMatrix<Real> &Z, Real rho = 1, Real alpha = 1.2, Int maxIter = 500, Real absTol = 1e-6, Real relTol = 1e-4, bool inv = true, bool progress = true)

C API

ElError ElNonNegativeLeastSquares_s(ElConstMatrix_s A, ElConstMatrix_s Y, ElMatrix_s Z, ElInt* numIts)

ElError ElNonNegativeLeastSquares_d(ElConstMatrix_d A, ElConstMatrix_d Y, ElMatrix_d Z, ElInt* numIts)

ElError ElNonNegativeLeastSquaresDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_s Y, ElDistMatrix_s Z, ElInt* numIts)

ElError ElNonNegativeLeastSquaresDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_d Y, ElDistMatrix_d Z, ElInt* numIts)