public ExponentialViewModel(double[] xdata, double[] ydata, Tuple <double, double> xlimit, Tuple <double, double> ylimit)
{
displayed = true;
DirectRegressionMethod method = DirectRegressionMethod.QR;
Tuple <double, double> p = Fit.Exponential(xdata, ydata, method);
double a = p.Item1;
double r = p.Item2;
if (!Double.IsNaN(a) && !Double.IsNaN(r))
{
this.FunctionModel = new PlotModel {
Title = "Exponential regresion [ f(x) = " + a + " * exp( " + r + " * x ) ]"
};
Func <double, double> exponentialFunction = (x) => a *Math.Exp(r *x);
FunctionModel.Series.Add(new FunctionSeries(exponentialFunction, xlimit.Item1, xlimit.Item2, 0.0001));
// view limits
FunctionModel.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Minimum = xlimit.Item1, Maximum = xlimit.Item2
});
FunctionModel.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Minimum = ylimit.Item1, Maximum = ylimit.Item2
});
}
else
{
displayed = false;
}
}
/// <summary>
/// Performs an exponential regression.
/// </summary>
/// <param name="x">x data</param>
/// <param name="y">y data</param>
/// <param name="method">Regression method to use.</param>
public static double[] ExponentialFit(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
double[] yHat = Generate.Map(y, Math.Log);
double[] pHat = Fit.LinearCombination(x, yHat, method, t => 1.0, t => t);
double[] coeffs = { Math.Exp(pHat[0]), pHat[1] };
return(Generate.Map(x, xi => coeffs[0] * Math.Exp(coeffs[1] * xi)));
}
public PowerViewModel(double[] xdata, double[] ydata, Tuple <double, double> xlimit, Tuple <double, double> ylimit)
{
DirectRegressionMethod method = DirectRegressionMethod.QR;
Tuple <double, double> p = Fit.Power(xdata, ydata, method);
double a = p.Item1;
double b = p.Item2;
if (!Double.IsNaN(a) && !Double.IsNaN(b))
{
this.FunctionModel = new PlotModel {
Title = "Power regresion [ f(x) = " + a + " x ^ " + b + " ]"
};
Func <double, double> powerFunction = (x) => a *Math.Pow(x, b);
FunctionModel.Series.Add(new FunctionSeries(powerFunction, xlimit.Item1, xlimit.Item2, 0.0001));
// view limits
FunctionModel.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Minimum = xlimit.Item1, Maximum = xlimit.Item2
});
FunctionModel.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Minimum = ylimit.Item1, Maximum = ylimit.Item2
});
}
else
{
displayed = false;
}
}
/// <summary>
/// Least-Squares fitting the points (x,y) to an exponential y : x -> a*exp(r*x),
/// returning its best fitting parameters as (a, r) tuple.
/// </summary>
public static Tuple <double, double> Exponential(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
// Transformation: y_h := ln(y) ~> y_h : x -> ln(a) + r*x;
double[] lny = Generate.Map(y, Math.Log);
double[] p = LinearCombination(x, lny, method, t => 1.0, t => t);
return(Tuple.Create(Math.Exp(p[0]), p[1]));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a power y : x -> a*x^b,
/// returning its best fitting parameters as (a, b) tuple.
/// </summary>
public static (double A, double B) Power(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
// Transformation: y_h := ln(y) ~> y_h : x -> ln(a) + b*ln(x);
double[] lny = Generate.Map(y, Math.Log);
double[] p = LinearCombination(x, lny, method, t => 1.0, Math.Log);
return(Math.Exp(p[0]), p[1]);
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a logarithm y : x -> a + b*ln(x),
/// returning a function y' for the best fitting line.
/// </summary>
public static Func <double, double> LogarithmFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Logarithm(x, y, method);
var a = parameters.Item1;
var b = parameters.Item2;
return(z => a + b * Math.Log(z));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a power y : x -> a*x^b,
/// returning a function y' for the best fitting line.
/// </summary>
public static Func <double, double> PowerFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Power(x, y, method);
var a = parameters.Item1;
var b = parameters.Item2;
return(z => a *Math.Pow(z, b));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to an exponential y : x -> a*exp(r*x),
/// returning a function y' for the best fitting line.
/// </summary>
public static Func <double, double> ExponentialFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Exponential(x, y, method);
var a = parameters.Item1;
var r = parameters.Item2;
return(z => a *Math.Exp(r *z));
}
/// <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.
/// </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 predictor value. Default = false.</param>
/// <param name="method">The direct method to be used to compute the regression.</param>
/// <returns>Best fitting list of model parameters β for each element in the predictor-arrays.</returns>
public static T[] DirectMethod <T>(T[][] x, T[] y, bool intercept = false, DirectRegressionMethod method = DirectRegressionMethod.NormalEquations) where T : struct, IEquatable <T>, IFormattable
{
switch (method)
{
case DirectRegressionMethod.NormalEquations:
return(NormalEquations(x, y, intercept));
case DirectRegressionMethod.QR:
return(QR(x, y, intercept));
case DirectRegressionMethod.Svd:
return(Svd(x, y, intercept));
default:
throw new NotSupportedException(method.ToString());
}
}
/// <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.
/// </summary>
/// <param name="x">Predictor matrix X</param>
/// <param name="y">Response matrix Y</param>
/// <param name="method">The direct method to be used to compute the regression.</param>
/// <returns>Best fitting vector for model parameters β</returns>
public static Matrix <T> DirectMethod <T>(Matrix <T> x, Matrix <T> y, DirectRegressionMethod method = DirectRegressionMethod.NormalEquations) where T : struct, IEquatable <T>, IFormattable
{
switch (method)
{
case DirectRegressionMethod.NormalEquations:
return(NormalEquations(x, y));
case DirectRegressionMethod.QR:
return(QR(x, y));
case DirectRegressionMethod.Svd:
return(Svd(x, y));
default:
throw new NotSupportedException(method.ToString());
}
}
public void Analyze(List <ReceivedMeasurement> measurements, AnalysisVM viewmodel)
{
var measurementDates = measurements.Select(x => x.RecordCreateTime.ToOADate()).ToArray();
DirectRegressionMethod regressionMethod = (DirectRegressionMethod)Enum.Parse(typeof(DirectRegressionMethod), viewmodel.regressionMethod);
var polynomialCoefficients = Fit.Polynomial(measurementDates,
measurements.Select(y => y.Value).ToArray(), viewmodel.polynomialDegree, regressionMethod).ToList();
var functionFormula = GetPolynomialFormula(polynomialCoefficients);
var newDates = GenerateNewDates(measurementDates);
var approximationResults = GetApproximationResults(newDates.ToArray(), polynomialCoefficients);
_result = new ComputationResultVM()
{
X_values = measurementDates.Select(x => DateTime.FromOADate(x).ToString("yyyy-MM-dd HH:mm:ss")).ToList(),
X2_values = newDates.Select(x => DateTime.FromOADate(x).ToString("yyyy-MM-dd HH:mm:ss")).ToList(),
Y_values = measurements.Select(x => x.Value).ToList(),
Y2_values = approximationResults,
Formula = functionFormula
};
}
public void Analyze(List <ReceivedMeasurement> measurements, AnalysisVM viewmodel)
{
var dates = measurements.Select(x => x.RecordCreateTime.ToOADate()).ToArray();
DirectRegressionMethod regressionMethod = (DirectRegressionMethod)Enum.Parse(typeof(DirectRegressionMethod), viewmodel.regressionMethod);
var polynomialCoefficients = Fit.Polynomial(dates,
measurements.Select(y => y.Value).ToArray(), viewmodel.polynomialDegree, regressionMethod).ToList();
var predictionDate = DateTime.Parse(viewmodel.predictionDate);
var predictionResults = GetPredictionResults(predictionDate.ToOADate(), polynomialCoefficients);
List <string> predictionDates = new List <string>()
{
viewmodel.predictionDate
};
_result = new ComputationResultVM()
{
X_values = predictionDates,
Y_values = predictionResults,
Formula = ""
};
}
/// <summary>
/// Least-Squares fitting the points (T,y) = (T,y) to an arbitrary linear combination y : X -> p0*f0(T) + p1*f1(T) + ... + pk*fk(T),
/// returning a function y' for the best fitting combination.
/// </summary>
public static Func <T, double> LinearGenericFunc <T>(T[] x, double[] y, DirectRegressionMethod method, params Func <T, double>[] functions)
{
var parameters = LinearGeneric(x, y, method, functions);
return(z => functions.Zip(parameters, (f, p) => p * f(z)).Sum());
}
/// <summary>
/// Least-Squares fitting the points (T,y) = (T,y) to an arbitrary linear combination y : X -> p0*f0(T) + p1*f1(T) + ... + pk*fk(T),
/// returning its best fitting parameters as [p0, p1, p2, ..., pk] array.
/// </summary>
public static double[] LinearGeneric <T>(T[] x, double[] y, DirectRegressionMethod method, params Func <T, double>[] functions)
{
var design = Matrix <double> .Build.Dense(x.Length, functions.Length, (i, j) => functions[j](x[i]));
return(MultipleRegression.DirectMethod(design, Vector <double> .Build.Dense(y), method).ToArray());
}
/// <summary>
/// Least-Squares fitting the points (X,y) = ((x0,x1,..,xk),y) to an arbitrary linear combination y : X -> p0*f0(x) + p1*f1(x) + ... + pk*fk(x),
/// returning a function y' for the best fitting combination.
/// </summary>
public static Func <double[], double> LinearMultiDimFunc(double[][] x, double[] y, DirectRegressionMethod method, params Func <double[], double>[] functions)
{
var parameters = LinearMultiDim(x, y, method, functions);
return(z => functions.Zip(parameters, (f, p) => p * f(z)).Sum());
}
/// <summary>
/// Least-Squares fitting the points (X,y) = ((x0,x1,..,xk),y) to a linear surface y : X -> p0*x0 + p1*x1 + ... + pk*xk,
/// returning a function y' for the best fitting combination.
/// If an intercept is added, its coefficient will be prepended to the resulting parameters.
/// </summary>
public static Func <double[], double> MultiDimFunc(double[][] x, double[] y, bool intercept = false, DirectRegressionMethod method = DirectRegressionMethod.NormalEquations)
{
var parameters = MultipleRegression.DirectMethod(x, y, intercept, method);
return(z => LinearAlgebraControl.Provider.DotProduct(parameters, z));
}
/// <summary>
/// Least-Squares fitting the points (X,y) = ((x0,x1,..,xk),y) to a linear surface y : X -> p0*x0 + p1*x1 + ... + pk*xk,
/// returning its best fitting parameters as [p0, p1, p2, ..., pk] array.
/// If an intercept is added, its coefficient will be prepended to the resulting parameters.
/// </summary>
public static double[] MultiDim(double[][] x, double[] y, bool intercept = false, DirectRegressionMethod method = DirectRegressionMethod.NormalEquations)
{
return(MultipleRegression.DirectMethod(x, y, intercept, method));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
/// returning a function y' for the best fitting polynomial.
/// A polynomial with order/degree k has (k+1) coefficients and thus requires at least (k+1) samples.
/// </summary>
public static Func <double, double> PolynomialFunc(double[] x, double[] y, int order, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var parameters = Polynomial(x, y, order, method);
return(z => Evaluate.Polynomial(z, parameters));
}
//Супер функция регрессии
public static void /*double[]*/ MultiDim(Tuple <double, double> x, double[] y, bool intercept = false, DirectRegressionMethod method = DirectRegressionMethod.NormalEquations)
{
//return SimpleRegression.Fit(x);
Matrix <double> m = Matrix <double> .Build.Random(3, 4);
m = m * m;
m.Transpose();
m.Inverse();
}
/// <summary>
/// Least-Squares fitting the points (x,y) to an exponential y : x -> a*exp(r*x),
/// returning a function y' for the best fitting line.
/// </summary>
public static Func <double, double> ExponentialFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
(double a, double r) = Exponential(x, y, method);
return(z => a *Math.Exp(r *z));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a logarithm y : x -> a + b*ln(x),
/// returning a function y' for the best fitting line.
/// </summary>
public static Func <double, double> LogarithmFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
(double a, double b) = Logarithm(x, y, method);
return(z => a + b * Math.Log(z));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k
/// </summary>
public static Polynomial Fit(double[] x, double[] y, int order, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var pArr = MathNet.Numerics.Fit.Polynomial(x, y, order, method);
return(new Polynomial(pArr));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a power y : x -> a*x^b,
/// returning a function y' for the best fitting line.
/// </summary>
public static Func <double, double> PowerFunc(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
(double a, double b) = Power(x, y, method);
return(z => a *Math.Pow(z, b));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k,
/// returning its best fitting parameters as [p0, p1, p2, ..., pk] array, compatible with Evaluate.Polynomial.
/// A polynomial with order/degree k has (k+1) coefficients and thus requires at least (k+1) samples.
/// </summary>
public static double[] Polynomial(double[] x, double[] y, int order, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var design = Matrix <double> .Build.Dense(x.Length, order + 1, (i, j) => Math.Pow(x[i], j));
return(MultipleRegression.DirectMethod(design, Vector <double> .Build.Dense(y), method).ToArray());
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k
/// </summary>
public static Polynomial Fit(double[] x, double[] y, int order, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
var coefficients = Numerics.Fit.Polynomial(x, y, order, method);
return(new Polynomial(coefficients));
}
private double[] Exponential(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
double[] y_hat = Generate.Map(y, Math.Log);
double[] p_hat = Fit.LinearCombination(x, y_hat, method, t => 1.0, t => t);
return(new[] { Math.Exp(p_hat[0]), p_hat[1] });
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a logarithm y : x -> a + b*ln(x),
/// returning its best fitting parameters as (a, b) tuple.
/// </summary>
public static Tuple <double, double> Logarithm(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
double[] lnx = Generate.Map(x, Math.Log);
double[] p = LinearCombination(lnx, y, method, t => 1.0, t => t);
return(Tuple.Create(p[0], p[1]));
}
/// <summary>
/// Least-Squares fitting the points (x,y) to a logarithm y : x -> a + b*ln(x),
/// returning its best fitting parameters as (a, b) tuple.
/// </summary>
public static (double A, double B) Logarithm(double[] x, double[] y, DirectRegressionMethod method = DirectRegressionMethod.QR)
{
double[] lnx = Generate.Map(x, Math.Log);
double[] p = LinearCombination(lnx, y, method, _ => 1.0, t => t);
return(p[0], p[1]);
}