using MathNet.Numerics.LinearAlgebra;
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using MathNet.Numerics.LinearAlgebra.Double;
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namespace IStation.Test
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{
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public class NonlinearRegressionHelper
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{
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//static void Main(string[] args)
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//{
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// // 示例数据：Flow1 和 Pressure1
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// double[] flow1 = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0 };
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// double[] pressure1 = { 2.1, 4.5, 6.8, 9.2, 11.5, 13.8, 16.1, 18.4, 20.7, 23.0 };
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// // 多项式回归的阶数（例如，二次多项式）
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// int degree = 2;
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// // 拟合多项式回归模型
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// double[] coefficients = FitPolynomial(flow1, pressure1, degree);
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// // 输出回归系数
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// Console.WriteLine("多项式回归系数：");
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// for (int i = 0; i <= degree; i++)
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// {
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// Console.WriteLine($"系数 {i}: {coefficients[i]}");
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// }
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// // 使用模型进行预测
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// double xNew = 11.0;
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// double yPredicted = PredictPolynomial(xNew, coefficients);
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// Console.WriteLine($"\n当 Flow1 = {xNew} 时，预测的 Pressure1 = {yPredicted}");
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// // 计算 R² 和 MSE
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// double rSquared = CalculateRSquared(flow1, pressure1, coefficients);
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// double mse = CalculateMSE(flow1, pressure1, coefficients);
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// Console.WriteLine($"\nR² = {rSquared}");
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// Console.WriteLine($"MSE = {mse}");
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//}
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public static void Test(DataCellViewModel xCell, DataCellViewModel yCell)
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{
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var x = xCell.ValueList.ToArray();
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var y = yCell.ValueList.ToArray();
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// 多项式回归的阶数（例如，二次多项式）
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int degree = 4;
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// 拟合多项式回归模型
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double[] coefficients = FitPolynomial(x, y, degree);
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// 输出回归系数
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Console.WriteLine("多项式回归系数：");
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for (int i = 0; i <= degree; i++)
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{
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Console.WriteLine($"系数 {i}: {coefficients[i]}");
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}
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// 使用模型进行预测
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double xNew = x.Average();
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double yPredicted = PredictPolynomial(xNew, coefficients);
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Console.WriteLine($"\n当 {xCell.Name} = {xNew} 时，预测的 {yCell.Name} = {yPredicted}");
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// 计算 R² 和 MSE
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double rSquared = CalculateRSquared(x, y, coefficients);
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double mse = CalculateMSE(x, y, coefficients);
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Console.WriteLine($"\nR² = {rSquared}");
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Console.WriteLine($"MSE = {mse}");
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Console.WriteLine();
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Console.WriteLine();
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}
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// 多项式回归拟合
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public static double[] FitPolynomial(double[] x, double[] y, int degree)
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{
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// 构建设计矩阵
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Matrix<double> X = DenseMatrix.OfArray(new double[x.Length, degree + 1]);
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for (int i = 0; i < x.Length; i++)
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{
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for (int j = 0; j <= degree; j++)
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{
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X[i, j] = Math.Pow(x[i], j);
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}
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}
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// 构建目标向量
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Vector<double> Y = DenseVector.OfArray(y);
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// 使用最小二乘法求解
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var qr = X.QR();
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Vector<double> coefficients = qr.Solve(Y);
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return coefficients.ToArray();
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}
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// 使用多项式模型进行预测
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public static double PredictPolynomial(double x, double[] coefficients)
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{
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double prediction = 0.0;
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for (int i = 0; i < coefficients.Length; i++)
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{
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prediction += coefficients[i] * Math.Pow(x, i);
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}
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return prediction;
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}
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// 计算 R²（决定系数）
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public static double CalculateRSquared(double[] x, double[] y, double[] coefficients)
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{
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double yMean = 0.0;
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double ssTotal = 0.0;
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double ssResidual = 0.0;
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for (int i = 0; i < y.Length; i++)
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{
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yMean += y[i];
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}
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yMean /= y.Length;
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for (int i = 0; i < y.Length; i++)
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{
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double yPredicted = PredictPolynomial(x[i], coefficients);
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ssTotal += Math.Pow(y[i] - yMean, 2);
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ssResidual += Math.Pow(y[i] - yPredicted, 2);
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}
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return 1.0 - (ssResidual / ssTotal);
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}
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// 计算 MSE（均方误差）
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public static double CalculateMSE(double[] x, double[] y, double[] coefficients)
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{
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double mse = 0.0;
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for (int i = 0; i < y.Length; i++)
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{
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double yPredicted = PredictPolynomial(x[i], coefficients);
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mse += Math.Pow(y[i] - yPredicted, 2);
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}
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return mse / y.Length;
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}
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//static void Main(string[] args)
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//{
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// // 示例数据：Flow 和 Pressure
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// double[] flow = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0 };
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// double[] pressure = { 2.1, 4.5, 6.8, 9.2, 11.5, 13.8, 16.1, 18.4, 20.7, 23.0 };
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// // 指数回归
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// double[] exponentialCoefficients = FitExponentialRegression(flow, pressure);
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// Console.WriteLine("指数回归系数：");
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// Console.WriteLine($"a = {Math.Exp(exponentialCoefficients[0])}");
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// Console.WriteLine($"b = {exponentialCoefficients[1]}");
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// double flowNew = 11.0;
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// double pressurePredictedExponential = PredictExponential(flowNew, exponentialCoefficients);
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// Console.WriteLine($"\n当 Flow = {flowNew} 时，指数回归预测的 Pressure = {pressurePredictedExponential}");
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// // 对数回归
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// double[] logarithmicCoefficients = FitLogarithmicRegression(flow, pressure);
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// Console.WriteLine("\n对数回归系数：");
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// Console.WriteLine($"a = {logarithmicCoefficients[0]}");
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// Console.WriteLine($"b = {logarithmicCoefficients[1]}");
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// double pressurePredictedLogarithmic = PredictLogarithmic(flowNew, logarithmicCoefficients);
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// Console.WriteLine($"\n当 Flow = {flowNew} 时，对数回归预测的 Pressure = {pressurePredictedLogarithmic}");
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// // 模型评估
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// double rSquaredExponential = CalculateRSquaredExponential(flow, pressure, exponentialCoefficients);
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// double mseExponential = CalculateMSEExponential(flow, pressure, exponentialCoefficients);
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// Console.WriteLine($"\n指数回归模型评估：");
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// Console.WriteLine($"R² = {rSquaredExponential}");
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// Console.WriteLine($"MSE = {mseExponential}");
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// double rSquaredLogarithmic = CalculateRSquaredLogarithmic(flow, pressure, logarithmicCoefficients);
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// double mseLogarithmic = CalculateMSELogarithmic(flow, pressure, logarithmicCoefficients);
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// Console.WriteLine($"\n对数回归模型评估：");
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// Console.WriteLine($"R² = {rSquaredLogarithmic}");
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// Console.WriteLine($"MSE = {mseLogarithmic}");
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//}
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//public static void Test(DataCellViewModel xCell, DataCellViewModel yCell)
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//{
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// // 示例数据：Flow 和 Pressure
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// double[] x = xCell.ValueList.ToArray();
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// double[] y = yCell.ValueList.ToArray();
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// // 指数回归
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// double[] exponentialCoefficients = FitExponentialRegression(x, y);
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// Console.WriteLine("指数回归系数：");
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// Console.WriteLine($"a = {Math.Exp(exponentialCoefficients[0])}");
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// Console.WriteLine($"b = {exponentialCoefficients[1]}");
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// double flowNew = x.Average();
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// double pressurePredictedExponential = PredictExponential(flowNew, exponentialCoefficients);
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// Console.WriteLine($"\n当 {xCell.Name} = {flowNew} 时，指数回归预测的 {yCell.Name} = {pressurePredictedExponential}");
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// // 对数回归
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// double[] logarithmicCoefficients = FitLogarithmicRegression(x, y);
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// Console.WriteLine("\n对数回归系数：");
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// Console.WriteLine($"a = {logarithmicCoefficients[0]}");
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// Console.WriteLine($"b = {logarithmicCoefficients[1]}");
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// double pressurePredictedLogarithmic = PredictLogarithmic(flowNew, logarithmicCoefficients);
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// Console.WriteLine($"\n当 {xCell.Name} = {flowNew} 时，对数回归预测的 {yCell.Name} = {pressurePredictedLogarithmic}");
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// // 模型评估
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// double rSquaredExponential = CalculateRSquaredExponential(x, y, exponentialCoefficients);
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// double mseExponential = CalculateMSEExponential(x, y, exponentialCoefficients);
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// Console.WriteLine($"\n指数回归模型评估：");
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// Console.WriteLine($"R² = {rSquaredExponential}");
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// Console.WriteLine($"MSE = {mseExponential}");
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// double rSquaredLogarithmic = CalculateRSquaredLogarithmic(x, y, logarithmicCoefficients);
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// double mseLogarithmic = CalculateMSELogarithmic(x, y, logarithmicCoefficients);
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// Console.WriteLine($"\n对数回归模型评估：");
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// Console.WriteLine($"R² = {rSquaredLogarithmic}");
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// Console.WriteLine($"MSE = {mseLogarithmic}");
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//}
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// 指数回归拟合
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public static double[] FitExponentialRegression(double[] x, double[] y)
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{
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// 将 y 转换为自然对数
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double[] logY = new double[y.Length];
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for (int i = 0; i < y.Length; i++)
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{
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logY[i] = Math.Log(y[i]);
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}
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// 构建设计矩阵
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Matrix<double> X = DenseMatrix.OfArray(new double[x.Length, 2]);
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for (int i = 0; i < x.Length; i++)
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{
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X[i, 0] = 1.0; // 常数项
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X[i, 1] = x[i];
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}
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// 构建目标向量
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Vector<double> Y = DenseVector.OfArray(logY);
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// 使用最小二乘法求解
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var qr = X.QR();
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Vector<double> coefficients = qr.Solve(Y);
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return coefficients.ToArray();
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}
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// 指数回归预测
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public static double PredictExponential(double x, double[] coefficients)
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{
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double a = Math.Exp(coefficients[0]);
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double b = coefficients[1];
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return a * Math.Exp(b * x);
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}
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// 对数回归拟合
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public static double[] FitLogarithmicRegression(double[] x, double[] y)
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{
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// 将 x 转换为自然对数
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double[] logX = new double[x.Length];
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for (int i = 0; i < x.Length; i++)
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{
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logX[i] = Math.Log(x[i]);
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}
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// 构建设计矩阵
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Matrix<double> X = DenseMatrix.OfArray(new double[x.Length, 2]);
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for (int i = 0; i < x.Length; i++)
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{
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X[i, 0] = 1.0; // 常数项
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X[i, 1] = logX[i];
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}
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// 构建目标向量
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Vector<double> Y = DenseVector.OfArray(y);
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// 使用最小二乘法求解
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var qr = X.QR();
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Vector<double> coefficients = qr.Solve(Y);
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return coefficients.ToArray();
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}
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// 对数回归预测
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public static double PredictLogarithmic(double x, double[] coefficients)
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{
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double a = coefficients[0];
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double b = coefficients[1];
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return a + b * Math.Log(x);
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}
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// 计算指数回归的 R²
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public static double CalculateRSquaredExponential(double[] x, double[] y, double[] coefficients)
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{
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double yMean = 0.0;
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double ssTotal = 0.0;
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double ssResidual = 0.0;
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for (int i = 0; i < y.Length; i++)
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{
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yMean += y[i];
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}
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yMean /= y.Length;
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for (int i = 0; i < y.Length; i++)
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{
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double yPredicted = PredictExponential(x[i], coefficients);
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ssTotal += Math.Pow(y[i] - yMean, 2);
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ssResidual += Math.Pow(y[i] - yPredicted, 2);
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}
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return 1.0 - (ssResidual / ssTotal);
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}
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// 计算指数回归的 MSE
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public static double CalculateMSEExponential(double[] x, double[] y, double[] coefficients)
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{
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double mse = 0.0;
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for (int i = 0; i < y.Length; i++)
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{
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double yPredicted = PredictExponential(x[i], coefficients);
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mse += Math.Pow(y[i] - yPredicted, 2);
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}
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return mse / y.Length;
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}
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// 计算对数回归的 R²
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public static double CalculateRSquaredLogarithmic(double[] x, double[] y, double[] coefficients)
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{
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double yMean = 0.0;
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double ssTotal = 0.0;
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double ssResidual = 0.0;
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for (int i = 0; i < y.Length; i++)
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{
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yMean += y[i];
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}
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yMean /= y.Length;
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for (int i = 0; i < y.Length; i++)
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{
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double yPredicted = PredictLogarithmic(x[i], coefficients);
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ssTotal += Math.Pow(y[i] - yMean, 2);
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ssResidual += Math.Pow(y[i] - yPredicted, 2);
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}
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return 1.0 - (ssResidual / ssTotal);
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}
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// 计算对数回归的 MSE
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public static double CalculateMSELogarithmic(double[] x, double[] y, double[] coefficients)
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{
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double mse = 0.0;
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for (int i = 0; i < y.Length; i++)
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{
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double yPredicted = PredictLogarithmic(x[i], coefficients);
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mse += Math.Pow(y[i] - yPredicted, 2);
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}
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return mse / y.Length;
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}
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}
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}
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