using System.Collections.Generic; using System.Linq; using Unity.UIWidgets.foundation; using UnityEngine; namespace Unity.UIWidgets.gestures { class _Vector { internal _Vector(int size) { this._offset = 0; this._length = size; this._elements = CollectionUtils.CreateRepeatedList(0.0f, size); } _Vector(List values, int offset, int length) { this._offset = offset; this._length = length; this._elements = values; } internal static _Vector fromVOL(List values, int offset, int length) { return new _Vector(values, offset, length); } readonly int _offset; readonly int _length; readonly List _elements; public float this[int i] { get { return this._elements[i + this._offset]; } set { this._elements[i + this._offset] = value; } } public static float operator *(_Vector a, _Vector b) { float result = 0.0f; for (int i = 0; i < a._length; i += 1) { result += a[i] * b[i]; } return result; } public float norm() { return Mathf.Sqrt(this * this); } } class _Matrix { internal _Matrix(int rows, int cols) { this._columns = cols; this._elements = CollectionUtils.CreateRepeatedList(0.0f, rows * cols); } readonly int _columns; readonly List _elements; public float this[int row, int col] { get { return this._elements[row * this._columns + col]; } set { this._elements[row * this._columns + col] = value; } } public _Vector getRow(int row) { return _Vector.fromVOL( this._elements, row * this._columns, this._columns ); } } public class PolynomialFit { public PolynomialFit(int degree) { this.coefficients = CollectionUtils.CreateRepeatedList(0.0f, degree + 1); } public readonly List coefficients; public float confidence; } public class LeastSquaresSolver { public LeastSquaresSolver(List x, List y, List w) { D.assert(x != null && y != null && w != null); D.assert(x.Count == y.Count); D.assert(y.Count == w.Count); this.x = x; this.y = y; this.w = w; } public readonly List x; public readonly List y; public readonly List w; /// Fits a polynomial of the given degree to the data points. public PolynomialFit solve(int degree) { if (degree > this.x.Count) { // Not enough data to fit a curve. return null; } PolynomialFit result = new PolynomialFit(degree); // Shorthands for the purpose of notation equivalence to original C++ code. int m = this.x.Count; int n = degree + 1; // Expand the X vector to a matrix A, pre-multiplied by the weights. _Matrix a = new _Matrix(n, m); for (int h = 0; h < m; h += 1) { a[0, h] = this.w[h]; for (int i = 1; i < n; i += 1) { a[i, h] = a[i - 1, h] * this.x[h]; } } // Apply the Gram-Schmidt process to A to obtain its QR decomposition. // Orthonormal basis, column-major ordVectorer. _Matrix q = new _Matrix(n, m); // Upper triangular matrix, row-major order. _Matrix r = new _Matrix(n, n); for (int j = 0; j < n; j += 1) { for (int h = 0; h < m; h += 1) { q[j, h] = a[j, h]; } for (int i = 0; i < j; i += 1) { float dot = q.getRow(j) * q.getRow(i); for (int h = 0; h < m; h += 1) { q[j, h] = q[j, h] - dot * q[i, h]; } } float norm = q.getRow(j).norm(); if (norm < 0.000001f) { // Vectors are linearly dependent or zero so no solution. return null; } float inverseNorm = 1.0f / norm; for (int h = 0; h < m; h += 1) { q[j, h] = q[j, h] * inverseNorm; } for (int i = 0; i < n; i += 1) { r[j, i] = i < j ? 0.0f : q.getRow(j) * a.getRow(i); } } // Solve R B = Qt W Y to find B. This is easy because R is upper triangular. // We just work from bottom-right to top-left calculating B's coefficients. _Vector wy = new _Vector(m); for (int h = 0; h < m; h += 1) { wy[h] = this.y[h] * this.w[h]; } for (int i = n - 1; i >= 0; i -= 1) { result.coefficients[i] = q.getRow(i) * wy; for (int j = n - 1; j > i; j -= 1) { result.coefficients[i] -= r[i, j] * result.coefficients[j]; } result.coefficients[i] /= r[i, i]; } // Calculate the coefficient of determination (confidence) as: // 1 - (sumSquaredError / sumSquaredTotal) // ...where sumSquaredError is the residual sum of squares (variance of the // error), and sumSquaredTotal is the total sum of squares (variance of the // data) where each has been weighted. float yMean = 0.0f; for (int h = 0; h < m; h += 1) { yMean += this.y[h]; } yMean /= m; float sumSquaredError = 0.0f; float sumSquaredTotal = 0.0f; for (int h = 0; h < m; h += 1) { float term = 1.0f; float err = this.y[h] - result.coefficients[0]; for (int i = 1; i < n; i += 1) { term *= this.x[h]; err -= term * result.coefficients[i]; } sumSquaredError += this.w[h] * this.w[h] * err * err; float v = this.y[h] - yMean; sumSquaredTotal += this.w[h] * this.w[h] * v * v; } result.confidence = sumSquaredTotal <= 0.000001f ? 1.0f : 1.0f - (sumSquaredError / sumSquaredTotal); return result; } } }