public static string OutputFitResults(LinearFitBySvd fit, string[] paramNames)
{
// Output of results
Current.Console.WriteLine("");
Current.Console.WriteLine("---- " + DateTime.Now.ToString() + " -----------------------");
Current.Console.WriteLine("Multivariate regression of order {0}", fit.NumberOfParameter);
Current.Console.WriteLine("{0,-15} {1,20} {2,20} {3,20} {4,20}",
"Name", "Value", "Error", "F-Value", "Prob>F");
for (int i = 0; i < fit.Parameter.Length; i++)
{
Current.Console.WriteLine("{0,-15} {1,20} {2,20} {3,20} {4,20}",
paramNames == null ? string.Format("A{0}", i) : paramNames[i],
fit.Parameter[i],
fit.StandardErrorOfParameter(i),
fit.TofParameter(i),
1 - FDistribution.CDF(fit.TofParameter(i), fit.NumberOfParameter, fit.NumberOfData - 1)
);
}
Current.Console.WriteLine("R²: {0}, Adjusted R²: {1}",
fit.RSquared,
fit.AdjustedRSquared);
Current.Console.WriteLine("------------------------------------------------------------");
Current.Console.WriteLine("Source of Degrees of");
Current.Console.WriteLine("variation freedom Sum of Squares Mean Square F0 P value");
double regressionmeansquare = fit.RegressionCorrectedSumOfSquares / fit.NumberOfParameter;
double residualmeansquare = fit.ResidualSumOfSquares / (fit.NumberOfData - fit.NumberOfParameter - 1);
Current.Console.WriteLine("Regression {0,10} {1,20} {2,20} {3,20} {4,20}",
fit.NumberOfParameter,
fit.RegressionCorrectedSumOfSquares,
fit.RegressionCorrectedSumOfSquares / fit.NumberOfParameter,
regressionmeansquare / residualmeansquare,
1 - FDistribution.CDF(regressionmeansquare / residualmeansquare, fit.NumberOfParameter, fit.NumberOfData - 1)
);
Current.Console.WriteLine("Residual {0,10} {1,20} {2,20}",
fit.NumberOfData - 1 - fit.NumberOfParameter,
fit.ResidualSumOfSquares,
residualmeansquare
);
Current.Console.WriteLine("Total {0,10} {1,20}",
fit.NumberOfData - 1,
fit.TotalCorrectedSumOfSquares
);
Current.Console.WriteLine("------------------------------------------------------------");
return(null);
}
public static string Fit(Altaxo.Gui.Graph.Gdi.Viewing.IGraphController ctrl, int order, double fitCurveXmin, double fitCurveXmax, bool showFormulaOnGraph)
{
string error;
error = GetActivePlotPoints(ctrl, out var xarr, out var yarr);
int numberOfDataPoints = xarr.Length;
if (null != error)
{
return(error);
}
string[] plotNames = GetActivePlotName(ctrl);
int numberOfParameter = order + 1;
double[] parameter = new double[numberOfParameter];
var fit = LinearFitBySvd.FitPolymomialDestructive(order, xarr, yarr, null, numberOfDataPoints);
// Output of results
Current.Console.WriteLine("");
Current.Console.WriteLine("---- " + DateTime.Now.ToString() + " -----------------------");
Current.Console.WriteLine("Polynomial regression of order {0} of {1} over {2}", order, plotNames[1], plotNames[0]);
Current.Console.WriteLine(
"Name Value Error F-Value Prob>F");
for (int i = 0; i < fit.Parameter.Length; i++)
{
Current.Console.WriteLine("A{0,-3} {1,20} {2,20} {3,20} {4,20}",
i,
fit.Parameter[i],
fit.StandardErrorOfParameter(i),
fit.TofParameter(i),
1 - FDistribution.CDF(fit.TofParameter(i), numberOfParameter, numberOfDataPoints - 1)
);
}
Current.Console.WriteLine("R²: {0}, Adjusted R²: {1}",
fit.RSquared,
fit.AdjustedRSquared);
Current.Console.WriteLine("Condition number: {0}, Loss of precision (digits): {1}", fit.ConditionNumber, Math.Log10(fit.ConditionNumber));
Current.Console.WriteLine("------------------------------------------------------------");
Current.Console.WriteLine("Source of Degrees of");
Current.Console.WriteLine("variation freedom Sum of Squares Mean Square F0 P value");
double regressionmeansquare = fit.RegressionCorrectedSumOfSquares / numberOfParameter;
double residualmeansquare = fit.ResidualSumOfSquares / (numberOfDataPoints - numberOfParameter - 1);
Current.Console.WriteLine("Regression {0,10} {1,20} {2,20} {3,20} {4,20}",
numberOfParameter,
fit.RegressionCorrectedSumOfSquares,
fit.RegressionCorrectedSumOfSquares / numberOfParameter,
regressionmeansquare / residualmeansquare,
1 - FDistribution.CDF(regressionmeansquare / residualmeansquare, numberOfParameter, numberOfDataPoints - 1)
);
Current.Console.WriteLine("Residual {0,10} {1,20} {2,20}",
numberOfDataPoints - 1 - numberOfParameter,
fit.ResidualSumOfSquares,
residualmeansquare
);
Current.Console.WriteLine("Total {0,10} {1,20}",
numberOfDataPoints - 1,
fit.TotalCorrectedSumOfSquares
);
Current.Console.WriteLine("------------------------------------------------------------");
// add the fit curve to the graph
IScalarFunctionDD plotfunction = new PolynomialFunction(fit.Parameter);
var fittedCurve = new XYFunctionPlotItem(new XYFunctionPlotData(plotfunction), new G2DPlotStyleCollection(LineScatterPlotStyleKind.Line, ctrl.Doc.GetPropertyContext()));
var xylayer = ctrl.ActiveLayer as XYPlotLayer;
if (null != xylayer)
{
xylayer.PlotItems.Add(fittedCurve);
}
return(null);
}
public static string Fit(Altaxo.Graph.GUI.GraphController ctrl, int order, double fitCurveXmin, double fitCurveXmax, bool showFormulaOnGraph)
{
string error;
int numberOfDataPoints;
double[] xarr = null, yarr = null, earr = null;
error = GetActivePlotPoints(ctrl, ref xarr, ref yarr, out numberOfDataPoints);
if (null != error)
{
return(error);
}
string[] plotNames = GetActivePlotName(ctrl);
// Error-Array
earr = new double[numberOfDataPoints];
for (int i = 0; i < earr.Length; i++)
{
earr[i] = 1;
}
int numberOfParameter = order + 1;
double[] parameter = new double[numberOfParameter];
LinearFitBySvd fit =
new LinearFitBySvd(
xarr, yarr, earr, numberOfDataPoints, order + 1, new FunctionBaseEvaluator(EvaluatePolynomialBase), 1E-5);
// Output of results
Current.Console.WriteLine("");
Current.Console.WriteLine("---- " + DateTime.Now.ToString() + " -----------------------");
Current.Console.WriteLine("Polynomial regression of order {0} of {1} over {2}", order, plotNames[1], plotNames[0]);
Current.Console.WriteLine(
"Name Value Error F-Value Prob>F");
for (int i = 0; i < fit.Parameter.Length; i++)
{
Current.Console.WriteLine("A{0,-3} {1,20} {2,20} {3,20} {4,20}",
i,
fit.Parameter[i],
fit.StandardErrorOfParameter(i),
fit.TofParameter(i),
1 - FDistribution.CDF(fit.TofParameter(i), numberOfParameter, numberOfDataPoints - 1)
);
}
Current.Console.WriteLine("R²: {0}, Adjusted R²: {1}",
fit.RSquared,
fit.AdjustedRSquared);
Current.Console.WriteLine("------------------------------------------------------------");
Current.Console.WriteLine("Source of Degrees of");
Current.Console.WriteLine("variation freedom Sum of Squares Mean Square F0 P value");
double regressionmeansquare = fit.RegressionCorrectedSumOfSquares / numberOfParameter;
double residualmeansquare = fit.ResidualSumOfSquares / (numberOfDataPoints - numberOfParameter - 1);
Current.Console.WriteLine("Regression {0,10} {1,20} {2,20} {3,20} {4,20}",
numberOfParameter,
fit.RegressionCorrectedSumOfSquares,
fit.RegressionCorrectedSumOfSquares / numberOfParameter,
regressionmeansquare / residualmeansquare,
1 - FDistribution.CDF(regressionmeansquare / residualmeansquare, numberOfParameter, numberOfDataPoints - 1)
);
Current.Console.WriteLine("Residual {0,10} {1,20} {2,20}",
numberOfDataPoints - 1 - numberOfParameter,
fit.ResidualSumOfSquares,
residualmeansquare
);
Current.Console.WriteLine("Total {0,10} {1,20}",
numberOfDataPoints - 1,
fit.TotalCorrectedSumOfSquares
);
Current.Console.WriteLine("------------------------------------------------------------");
// add the fit curve to the graph
IScalarFunctionDD plotfunction = new PolynomialFunction(fit.Parameter);
XYFunctionPlotItem fittedCurve = new XYFunctionPlotItem(new XYFunctionPlotData(plotfunction), new G2DPlotStyleCollection(LineScatterPlotStyleKind.Line));
ctrl.ActiveLayer.PlotItems.Add(fittedCurve);
return(null);
}
public void TestFDistributionCDF()
{
// N[CDF[FRatioDistribution[3, 4], 1 - 1/20] , 25]
Assert.AreEqual(0.5034356763953920149093067, FDistribution.CDF(0.95, 3, 4), 1E-14);
}