FastNonnegativeLeastSquaresExecution(IROMatrixDouble, IROMatrixDouble, FuncInt32, Boolean, NullableDouble, IMatrixDouble, IMatrixDouble) Method

public static void Execution(
	IROMatrix<double> XtX,
	IROMatrix<double> Xty,
	Func<int, bool> isRestrictedToPositiveValues,
	double? tolerance,
	out IMatrix<double> x,
	out IMatrix<double> w
)

Parameters

XtX  IROMatrixDouble

X transposed multiplied by X, thus a square matrix.

Xty  IROMatrixDouble

X transposed multiplied by Y, thus a matrix with one column and same number of rows as X.

isRestrictedToPositiveValues  FuncInt32, Boolean

Function that takes the parameter index as argument and returns true if the parameter at this index is restricted to positive values; otherwise the return value must be false.

tolerance  NullableDouble

Used to decide if a solution element is less than or equal to zero. If this is null, a default tolerance of tolerance = MAX(SIZE(XtX)) * NORM(XtX,1) * EPS is used.

x  IMatrixDouble

Output: solution vector (matrix with one column and number of rows according to dimension of X.

w  IMatrixDouble

Output: Lagrange vector. Elements which take place in the fit are set to 0. Elements fixed to zero contain a negative number.

Literature: Rasmus Bro and Sijmen De Jong, 'A fast non-negativity-constrained least squares algorithm', Journal of Chemometrics, Vol. 11, 393-401 (1997)

Algorithm modified by Dirk Lellinger 2015 to allow a mixture of restricted and unrestricted parameters.

Reference