public void RunTest()
{
// Suppose we would like to map the continuous values in the
// second column to the integer values in the first column.
double[,] data =
{
{ -40, -21142.1111111111 },
{ -30, -21330.1111111111 },
{ -20, -12036.1111111111 },
{ -10, 7255.3888888889 },
{ 0, 32474.8888888889 },
{ 10, 32474.8888888889 },
{ 20, 9060.8888888889 },
{ 30, -11628.1111111111 },
{ 40, -15129.6111111111 },
};
// Extract inputs and outputs
double[][] inputs = data.GetColumn(0).ToJagged();
double[] outputs = data.GetColumn(1);
// Create a Nonlinear regression using
NonlinearRegression regression = new NonlinearRegression(4, function, gradient);
NonlinearLeastSquares nls = new NonlinearLeastSquares(regression);
Assert.IsTrue(nls.Algorithm is LevenbergMarquardt);
regression.Coefficients[0] = 0; // m
regression.Coefficients[1] = 80; // s
regression.Coefficients[2] = 53805; // a
regression.Coefficients[3] = -21330.11; //b
double error = Double.PositiveInfinity;
for (int i = 0; i < 100; i++)
{
error = nls.Run(inputs, outputs);
}
double m = regression.Coefficients[0];
double s = regression.Coefficients[1];
double a = regression.Coefficients[2];
double b = regression.Coefficients[3];
Assert.AreEqual(010345587.465428974, error);
Assert.AreEqual(5.316196154830604, m, 1e-3);
Assert.AreEqual(12.792301798208918, s, 1e-3);
Assert.AreEqual(56794.832645792514, a, 1e-3);
Assert.AreEqual(-20219.675997523173, b, 1e-2);
Assert.IsFalse(Double.IsNaN(m));
Assert.IsFalse(Double.IsNaN(s));
Assert.IsFalse(Double.IsNaN(a));
Assert.IsFalse(Double.IsNaN(b));
}
public void RunTest()
{
double[,] data =
{
{ -40, -21142.1111111111 },
{ -30, -21330.1111111111 },
{ -20, -12036.1111111111 },
{ -10, 7255.3888888889 },
{ 0, 32474.8888888889 },
{ 10, 32474.8888888889 },
{ 20, 9060.8888888889 },
{ 30, -11628.1111111111 },
{ 40, -15129.6111111111 },
};
double[][] inputs = data.GetColumn(0).ToArray();
double[] outputs = data.GetColumn(1);
NonlinearRegression regression = new NonlinearRegression(4, function, gradient);
NonlinearLeastSquares nls = new NonlinearLeastSquares(regression);
Assert.IsTrue(nls.Algorithm is LevenbergMarquardt);
regression.Coefficients[0] = 0; // m
regression.Coefficients[1] = 80; // s
regression.Coefficients[2] = 53805; // a
regression.Coefficients[3] = -21330.11; //b
double error = 0;
for (int i = 0; i < 100; i++)
{
error = nls.Run(inputs, outputs);
}
double m = regression.Coefficients[0];
double s = regression.Coefficients[1];
double a = regression.Coefficients[2];
double b = regression.Coefficients[3];
Assert.AreEqual(5.316196154830604, m, 1e-3);
Assert.AreEqual(12.792301798208918, s, 1e-3);
Assert.AreEqual(56794.832645792514, a, 1e-3);
Assert.AreEqual(-20219.675997523173, b, 1e-2);
Assert.IsFalse(Double.IsNaN(m));
Assert.IsFalse(Double.IsNaN(s));
Assert.IsFalse(Double.IsNaN(a));
Assert.IsFalse(Double.IsNaN(b));
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearLeastSquares"/> class.
/// </summary>
///
/// <param name="regression">The regression model.</param>
/// <param name="algorithm">The <see cref="ILeastSquaresMethod">least squares</see>
/// algorithm to be used to estimate the regression parameters. Default is to
/// use a <see cref="LevenbergMarquardt">Levenberg-Marquardt</see> algorithm.</param>
///
public NonlinearLeastSquares(NonlinearRegression regression, ILeastSquaresMethod algorithm)
{
if (regression == null)
throw new ArgumentNullException("regression");
if (algorithm == null)
throw new ArgumentNullException("algorithm");
if (regression.Gradient == null)
throw new ArgumentException("The regression must have a gradient function defined.", "regression");
this.solver = algorithm;
this.solver.Solution = regression.Coefficients;
this.solver.Function = new LeastSquaresFunction(regression.Function);
this.solver.Gradient = new LeastSquaresGradientFunction(regression.Gradient);
this.regression = regression;
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearLeastSquares"/> class.
/// </summary>
///
/// <param name="regression">The regression model.</param>
/// <param name="algorithm">The <see cref="ILeastSquaresMethod">least squares</see>
/// algorithm to be used to estimate the regression parameters. Default is to
/// use a <see cref="LevenbergMarquardt">Levenberg-Marquardt</see> algorithm.</param>
///
public NonlinearLeastSquares(NonlinearRegression regression, ILeastSquaresMethod algorithm)
{
if (regression == null)
{
throw new ArgumentNullException("regression");
}
if (algorithm == null)
{
throw new ArgumentNullException("algorithm");
}
if (regression.Gradient == null)
{
throw new ArgumentException("The regression must have a gradient function defined.", "regression");
}
this.solver = algorithm;
this.solver.Solution = regression.Coefficients;
this.solver.Function = new LeastSquaresFunction(regression.Function);
this.solver.Gradient = new LeastSquaresGradientFunction(regression.Gradient);
this.regression = regression;
}
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="NonlinearLeastSquares"/> class.
/// </summary>
///
/// <param name="regression">The regression model.</param>
///
public NonlinearLeastSquares(NonlinearRegression regression)
: this(regression, new LevenbergMarquardt(regression.Coefficients.Length))
{
}
public void ExampleTest()
{
// Suppose we would like to map the continuous values in the
// second column to the integer values in the first column.
double[,] data =
{
{ -40, -21142.1111111111 },
{ -30, -21330.1111111111 },
{ -20, -12036.1111111111 },
{ -10, 7255.3888888889 },
{ 0, 32474.8888888889 },
{ 10, 32474.8888888889 },
{ 20, 9060.8888888889 },
{ 30, -11628.1111111111 },
{ 40, -15129.6111111111 },
};
// Extract inputs and outputs
double[][] inputs = data.GetColumn(0).ToJagged();
double[] outputs = data.GetColumn(1);
// Create a Nonlinear regression using
var regression = new NonlinearRegression(3,
// Let's assume a quadratic model function: ax² + bx + c
function: (w, x) => w[0] * x[0] * x[0] + w[1] * x[0] + w[2],
// Derivative in respect to the weights:
gradient: (w, x, r) =>
{
r[0] = 2 * w[0]; // w.r.t a: 2a
r[1] = w[1]; // w.r.t b: b
r[2] = w[2]; // w.r.t c: 0
}
);
// Create a non-linear least squares teacher
var nls = new NonlinearLeastSquares(regression);
// Initialize to some random values
regression.Coefficients[0] = 4.2;
regression.Coefficients[1] = 0.3;
regression.Coefficients[2] = 1;
// Run the function estimation algorithm
double error = Double.PositiveInfinity;
for (int i = 0; i < 100; i++)
{
error = nls.Run(inputs, outputs);
}
// Use the function to compute the input values
double[] predict = inputs.Apply(regression.Compute);
Assert.IsTrue(nls.Algorithm is LevenbergMarquardt);
Assert.AreEqual(1318374605.8436923d, error);
Assert.AreEqual(-12.025250289329851, regression.Coefficients[0], 1e-3);
Assert.AreEqual(-0.082208180694676766, regression.Coefficients[1], 1e-3);
Assert.AreEqual(-0.27402726898225627, regression.Coefficients[2], 1e-3);
Assert.AreEqual(-19237.386162968953, predict[0]);
Assert.AreEqual(-10820.533042245008, predict[1]);
Assert.AreEqual(-4808.7299793870288, predict[2]);
Assert.AreEqual(-1203.6211380089139, predict[5]);
}
/// <summary>
/// Initializes a new instance of the <see cref="NonlinearLeastSquares"/> class.
/// </summary>
///
/// <param name="regression">The regression model.</param>
///
public NonlinearLeastSquares(NonlinearRegression regression)
: this(regression, new LevenbergMarquardt(regression.Coefficients.Length))
{
}
public void ExampleTest()
{
// Suppose we would like to map the continuous values in the
// second column to the integer values in the first column.
double[,] data =
{
{ -40, -21142.1111111111 },
{ -30, -21330.1111111111 },
{ -20, -12036.1111111111 },
{ -10, 7255.3888888889 },
{ 0, 32474.8888888889 },
{ 10, 32474.8888888889 },
{ 20, 9060.8888888889 },
{ 30, -11628.1111111111 },
{ 40, -15129.6111111111 },
};
// Extract inputs and outputs
double[][] inputs = data.GetColumn(0).ToJagged();
double[] outputs = data.GetColumn(1);
// Create a Nonlinear regression using
var regression = new NonlinearRegression(3,
// Let's assume a quadratic model function: ax² + bx + c
function: (w, x) => w[0] * x[0] * x[0] + w[1] * x[0] + w[2],
// Derivative in respect to the weights:
gradient: (w, x, r) =>
{
r[0] = 2 * w[0]; // w.r.t a: 2a
r[1] = w[1]; // w.r.t b: b
r[2] = w[2]; // w.r.t c: 0
}
);
// Create a non-linear least squares teacher
var nls = new NonlinearLeastSquares(regression);
// Initialize to some random values
regression.Coefficients[0] = 4.2;
regression.Coefficients[1] = 0.3;
regression.Coefficients[2] = 1;
// Run the function estimation algorithm
double error = Double.PositiveInfinity;
for (int i = 0; i < 100; i++)
{
error = nls.Run(inputs, outputs);
}
// Use the function to compute the input values
double[] predict = inputs.Apply(regression.Compute);
Assert.IsTrue(nls.Algorithm is LevenbergMarquardt);
Assert.AreEqual(2145404235.739383, error, 1e-7);
Assert.AreEqual(-11.916652026711853, regression.Coefficients[0], 1e-3);
Assert.AreEqual(-358.9758898959638, regression.Coefficients[1], 1e-3);
Assert.AreEqual(-107.31273008811895, regression.Coefficients[2], 1e-3);
Assert.AreEqual(-4814.9203769986034, predict[0], 1e-10);
Assert.AreEqual(-63.02285725721211, predict[1], 1e-10);
Assert.AreEqual(2305.5442571416661, predict[2], 1e-10);
Assert.AreEqual(-4888.736831716782, predict[5], 1e-10);
}
public void ComputeRAResult()
{
Regression = LeastSquares.Learn(Inputs, Outputs);
RAResult = new RAResultNonLinear(this);
RAResult.ComputeValuations();
}
