ConstrainedLinearFit Class

Constrained linear least-squares fit via SVD, using an IConstraintsProjector to enforce equality and inequality constraints on the parameter vector. The method iterates: 1. Project current beta onto the feasible set → learn which parameters are fixed/constrained at this point. 2. Solve the reduced unconstrained LS (SVD) for the remaining free parameters only. 3. Project the new beta back; repeat until convergence. For pure equality constraints this converges in one outer iteration. Inequality constraints may need a few iterations (active-set style).

Inheritance Hierarchy

SystemObject
Altaxo.Calc.RegressionConstrainedLinearFit

Namespace: Altaxo.Calc.Regression
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3618.0 (4.8.3618.0)

Syntax

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public static class ConstrainedLinearFit

The ConstrainedLinearFit type exposes the following members.

Methods

	Name	Description
	Fit	Fits beta such that A*beta ≈ y subject to the constraints encoded in projector.

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Remarks

Usage example:


             // Equality: beta[0] + beta[1] = 1.0
             var A_eq = Matrix<double>.Build.DenseOfArray(new double[,] { { 1, 1, 0 } });
             var b_eq = Vector<double>.Build.Dense(new double[] { 1.0 });
             
             // Inequality: beta[2] >= 0  →  -beta[2] <= 0
             var C_ineq = Matrix<double>.Build.DenseOfArray(new double[,] { { 0, 0, -1 } });
             var d_ineq = Vector<double>.Build.Dense(new double[] { 0.0 });
             
             var projector = new LinearConstraintsProjector(A_eq, b_eq, C_ineq, d_ineq);
             
             // Design matrix and observations
             var A = Matrix<double>.Build.DenseOfArray(new double[,] {
               { 1, 0, 1 },
               { 0, 1, 1 },
               { 1, 1, 0 },
               { 1, 0, 0 },
             });
             var y = Vector<double>.Build.Dense(new double[] { 1.5, 0.8, 1.0, 0.3 });
             
             var beta = ConstrainedLinearFit.Fit(A, y, projector);
             // beta[0] + beta[1] == 1.0  ✓
             // beta[2] >= 0              ✓

Reference

Altaxo.Calc.Regression Namespace