public void RunTest1()
{
// Example from https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm
double[,] data =
{
{ 0.03, 0.1947, 0.425, 0.626, 1.253, 2.500, 3.740 },
{ 0.05, 0.127, 0.094, 0.2122, 0.2729, 0.2665, 0.3317 }
};
double[][] inputs = data.GetRow(0).ToArray();
double[] outputs = data.GetRow(1);
RegressionFunction rate = (double[] weights, double[] xi) =>
{
double x = xi[0];
return((weights[0] * x) / (weights[1] + x));
};
RegressionGradientFunction grad = (double[] weights, double[] xi, double[] result) =>
{
double x = xi[0];
FiniteDifferences diff = new FiniteDifferences(2);
diff.Function = (bla) => rate(bla, xi);
double[] compare = diff.Compute(weights);
result[0] = -((-x) / (weights[1] + x));
result[1] = -((weights[0] * x) / Math.Pow(weights[1] + x, 2));
};
NonlinearRegression regression = new NonlinearRegression(2, rate, grad);
NonlinearLeastSquares nls = new NonlinearLeastSquares(regression, new GaussNewton(2));
Assert.IsTrue(nls.Algorithm is GaussNewton);
regression.Coefficients[0] = 0.9; // β1
regression.Coefficients[1] = 0.2; // β2
int iterations = 10;
double[] errors = new double[iterations];
for (int i = 0; i < errors.Length; i++)
{
errors[i] = nls.Run(inputs, outputs);
}
double b1 = regression.Coefficients[0];
double b2 = regression.Coefficients[1];
Assert.AreEqual(0.362, b1, 1e-3);
Assert.AreEqual(0.556, b2, 3e-3);
Assert.IsFalse(Double.IsNaN(b1));
Assert.IsFalse(Double.IsNaN(b2));
for (int i = 1; i < errors.Length; i++)
{
Assert.IsFalse(Double.IsNaN(errors[i - 1]));
Assert.IsTrue(errors[i - 1] >= errors[i]);
}
Assert.AreEqual(1.23859, regression.StandardErrors[0], 1e-3);
Assert.AreEqual(6.06352, regression.StandardErrors[1], 3e-3);
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearRegression"/> class.
/// </summary>
///
/// <param name="parameters">The number of variables (free parameters) in the model.</param>
/// <param name="function">The regression function implementing the regression model.</param>
///
public NonlinearRegression(int parameters, RegressionFunction function)
{
this.coefficients = new double[parameters];
this.standardErrors = new double[parameters];
this.function = function;
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearRegression"/> class.
/// </summary>
///
/// <param name="parameters">The number of variables (free parameters) in the model.</param>
/// <param name="function">The regression function implementing the regression model.</param>
/// <param name="gradient">The function that computes the gradient for <paramref name="function"/>.</param>
///
public NonlinearRegression(int parameters, RegressionFunction function, RegressionGradientFunction gradient)
: this(parameters, function)
{
this.gradient = gradient;
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearRegression"/> class.
/// </summary>
///
/// <param name="parameters">The number of variables (free parameters) in the model.</param>
/// <param name="function">The regression function implementing the regression model.</param>
/// <param name="gradient">The function that computes the gradient for <paramref name="function"/>.</param>
///
public NonlinearRegression(int parameters, RegressionFunction function, RegressionGradientFunction gradient)
: this(parameters, function)
{
this.gradient = gradient;
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearRegression"/> class.
/// </summary>
///
/// <param name="parameters">The number of variables (free parameters) in the model.</param>
/// <param name="function">The regression function implementing the regression model.</param>
///
public NonlinearRegression(int parameters, RegressionFunction function)
{
this.coefficients = new double[parameters];
this.standardErrors = new double[parameters];
this.function = function;
}
