public static void InitSievingRequest(BigInteger N, int B, PolynomialFunction f, SieveRequest sievereq)
{
sievereq.AStart = (int)N.Sqrt() + 1;
StartIdx = 0;
sievereq.polyFunction = f;
//the max amount of data we need to find the quadratic residues is the Bth prime (the highest one)
sievereq.L = primeSupply[B];
SievingData sievedat = new SievingData();
EvaluatePoly(sievereq, sievedat);
List <List <int> > tmpPrimeStarts = new List <List <int> >();
List <int> tmpPrimeIntervals = new List <int>();
for (int pI = 0; pI < B; pI++)
{
int p = primeSupply[pI];
List <int> tmp = new List <int>();
for (int a = 0; a < p; a++)
{
if (sievedat.V[a] % p == 0)
{
//we found a quadratic residue (there are two for each prime that isn't 2)
tmp.Add(a);
}
}
if (tmp.Count > 0)
{
//if the ith value is divisible by the prime k, then every k results after that will also be divisible
tmpPrimeIntervals.Add(p);
tmpPrimeStarts.Add(tmp);
}
}
sievereq.PrimeIntervals = tmpPrimeIntervals.ToArray();
sievereq.PrimeStarts = tmpPrimeStarts.ToArray();
//remove primes with no quadratic residues
sievereq.B = sievereq.PrimeIntervals.Length;
}
/// <summary> v cQ1
/// Initializes a SievingRequest based on given parameters, and finds the quadratic residues for primes specified
/// </summary>
/// <param name="N">The number to factor</param>
/// <param name="B">The limit for smooth numbers</param>
/// <param name="f">The polynomial to sieve</param>
/// <param name="sievereq">The SieveRequest that will be initialized</param>
public static void InitSievingRequest(BigInteger N, int B, PolynomialFunction f, SieveRequest sievereq)
{
sievereq.AStart = (int)N.Sqrt() + 1;
sievereq.StartIdx = 0;
sievereq.polyFunction = f;
sievereq.L = primeSupply[B];
SievingData sievedat = new SievingData();
EvaluatePoly(sievereq, sievedat);
List<List<int>> tmpPrimeStarts = new List<List<int>>();
List<int> tmpPrimeIntervals = new List<int>();
for (int pI = 0; pI < B; pI++)
{
int p = primeSupply[pI];
List<int> tmp = new List<int>();
for (int a = 0; a < p; a++)
{
if (sievedat.V[a] % p == 0)
{
tmp.Add(a);
}
}
if (tmp.Count > 0)
{
tmpPrimeIntervals.Add(p);
tmpPrimeStarts.Add(tmp);
}
}
sievereq.PrimeIntervals = tmpPrimeIntervals.ToArray();
sievereq.PrimeStarts = tmpPrimeStarts.ToArray();
sievereq.B = sievereq.PrimeIntervals.Length;
}
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);
}
static NormalDistribution()
{
double[] coeffs = { 0.31938153, -0.356563782, 1.781477937,
-1.821255978, 1.330274429 };
_errorFunctionSeries = new PolynomialFunction(coeffs);
}
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 PolynomialFunction PolyFunction; //The polynomial function f(a) to seive for smooth things
public SieveInitInfo(int B, PolynomialFunction f)
{
this.B = B;
PolyFunction = f;
AStart = f.PositivePoint();
}
