mathnet-numerics/src/Numerics/LinearRegression/MultipleRegression.cs

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using System;
using System.Collections.Generic;
using MathNet.Numerics.LinearAlgebra;

namespace MathNet.Numerics.LinearRegression
{
    public static class MultipleRegression
    {
        /// <summary>
        /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
        /// Uses the cholesky decomposition of the normal equations.
        /// </summary>
        /// <param name="x">Predictor matrix X</param>
        /// <param name="y">Response vector Y</param>
        /// <returns>Best fitting vector for model parameters β</returns>
        public static Vector<T> NormalEquations<T>(Matrix<T> x, Vector<T> y) where T : struct, IEquatable<T>, IFormattable
        {
            return x.TransposeThisAndMultiply(x).Cholesky().Solve(x.Transpose()*y);
        }

        /// <summary>
        /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
        /// Uses the cholesky decomposition of the normal equations.
        /// </summary>
        /// <param name="x">Predictor matrix X</param>
        /// <param name="y">Response vector Y</param>
        /// <returns>Best fitting vector for model parameters β</returns>
        public static Matrix<T> NormalEquations<T>(Matrix<T> x, Matrix<T> y) where T : struct, IEquatable<T>, IFormattable
        {
            return x.TransposeThisAndMultiply(x).Cholesky().Solve(x.Transpose() * y);
        }

        /// <summary>
        /// Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals.
        /// Uses the cholesky decomposition of the normal equations.
        /// </summary>
        /// <param name="x">List of predictor-arrays.</param>
        /// <param name="y">List of responses</param>
        /// <param name="intercept">True if an intercept should be added as first artificial perdictor value. Default = false.</param>
        /// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
        public static T[] NormalEquations<T>(T[][] x, T[] y, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
        {
            var predictor = Matrix<T>.Build.DenseMatrixOfRowArrays(x);
            if (intercept)
            {
                predictor = predictor.InsertColumn(0, Vector<T>.Build.DenseVector(predictor.RowCount, Vector<T>.One));
            }
            var response = Matrix<T>.Build.DenseVector(y);
            return predictor.TransposeThisAndMultiply(predictor).Cholesky().Solve(predictor.Transpose()*response).ToArray();
        }

        /// <summary>
        /// Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals.
        /// Uses the cholesky decomposition of the normal equations.
        /// </summary>
        /// <param name="samples">Sequence of predictor-arrays and their response.</param>
        /// <param name="intercept">True if an intercept should be added as first artificial perdictor value. Default = false.</param>
        /// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
        public static T[] NormalEquations<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
        {
            var xy = samples.UnpackSinglePass();
            return NormalEquations(xy.Item1, xy.Item2, intercept);
        }

        /// <summary>
        /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
        /// Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
        /// </summary>
        /// <param name="x">Predictor matrix X</param>
        /// <param name="y">Response vector Y</param>
        /// <returns>Best fitting vector for model parameters β</returns>
        public static Vector<T> QR<T>(Matrix<T> x, Vector<T> y) where T : struct, IEquatable<T>, IFormattable
        {
            return x.QR().Solve(y);
        }

        /// <summary>
        /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
        /// Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
        /// </summary>
        /// <param name="x">Predictor matrix X</param>
        /// <param name="y">Response vector Y</param>
        /// <returns>Best fitting vector for model parameters β</returns>
        public static Matrix<T> QR<T>(Matrix<T> x, Matrix<T> y) where T : struct, IEquatable<T>, IFormattable
        {
            return x.QR().Solve(y);
        }

        /// <summary>
        /// Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals.
        /// Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
        /// </summary>
        /// <param name="x">List of predictor-arrays.</param>
        /// <param name="y">List of responses</param>
        /// <param name="intercept">True if an intercept should be added as first artificial perdictor value. Default = false.</param>
        /// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
        public static T[] QR<T>(T[][] x, T[] y, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
        {
            var predictor = Matrix<T>.Build.DenseMatrixOfRowArrays(x);
            if (intercept)
            {
                predictor = predictor.InsertColumn(0, Vector<T>.Build.DenseVector(predictor.RowCount, Vector<T>.One));
            }
            return predictor.QR().Solve(Matrix<T>.Build.DenseVector(y)).ToArray();
        }

        /// <summary>
        /// Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals.
        /// Uses an orthogonal decomposition and is therefore more numerically stable than the normal equations but also slower.
        /// </summary>
        /// <param name="samples">Sequence of predictor-arrays and their response.</param>
        /// <param name="intercept">True if an intercept should be added as first artificial perdictor value. Default = false.</param>
        /// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
        public static T[] QR<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
        {
            var xy = samples.UnpackSinglePass();
            return QR(xy.Item1, xy.Item2, intercept);
        }

        /// <summary>
        /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
        /// Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
        /// </summary>
        /// <param name="x">Predictor matrix X</param>
        /// <param name="y">Response vector Y</param>
        /// <returns>Best fitting vector for model parameters β</returns>
        public static Vector<T> Svd<T>(Matrix<T> x, Vector<T> y) where T : struct, IEquatable<T>, IFormattable
        {
            return x.Svd().Solve(y);
        }

        /// <summary>
        /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
        /// Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
        /// </summary>
        /// <param name="x">Predictor matrix X</param>
        /// <param name="y">Response vector Y</param>
        /// <returns>Best fitting vector for model parameters β</returns>
        public static Matrix<T> Svd<T>(Matrix<T> x, Matrix<T> y) where T : struct, IEquatable<T>, IFormattable
        {
            return x.Svd().Solve(y);
        }

        /// <summary>
        /// Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals.
        /// Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
        /// </summary>
        /// <param name="x">List of predictor-arrays.</param>
        /// <param name="y">List of responses</param>
        /// <param name="intercept">True if an intercept should be added as first artificial perdictor value. Default = false.</param>
        /// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
        public static T[] Svd<T>(T[][] x, T[] y, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
        {
            var predictor = Matrix<T>.Build.DenseMatrixOfRowArrays(x);
            if (intercept)
            {
                predictor = predictor.InsertColumn(0, Vector<T>.Build.DenseVector(predictor.RowCount, Vector<T>.One));
            }
            return predictor.Svd().Solve(Matrix<T>.Build.DenseVector(y)).ToArray();
        }

        /// <summary>
        /// Find the model parameters β such that their linear combination with all predictor-arrays in X become as close to their response in Y as possible, with least squares residuals.
        /// Uses a singular value decomposition and is therefore more numerically stable (especially if ill-conditioned) than the normal equations or QR but also slower.
        /// </summary>
        /// <param name="samples">Sequence of predictor-arrays and their response.</param>
        /// <param name="intercept">True if an intercept should be added as first artificial perdictor value. Default = false.</param>
        /// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
        public static T[] Svd<T>(IEnumerable<Tuple<T[], T>> samples, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
        {
            var xy = samples.UnpackSinglePass();
            return Svd(xy.Item1, xy.Item2, intercept);
        }
    }
}