public void RootsTest3(double step)
{
Test.Begin("cubic roots tests");
var range = new Range1d(-1.0, 1.0);
double half = 0.5 * step;
double epsilon = Fun.Cbrt(Constant <double> .PositiveTinyValue);
Report.Value("epsilon", epsilon);
var stats = Stats <bool> .ComputeMaxMean;
var uniqueStats = Stats <bool> .ComputeMaxMean;
var multipleStats = Stats <bool> .ComputeMaxMean;
var residualStats = Stats <bool> .ComputeMaxMean;
var uniqueHisto = new Histogram(-16, -8, 8);
var multipleHisto = new Histogram(-16, 0, 16);
var uniqueResidualStats = Stats <bool> .ComputeMaxMean;
var multipleResidualStats = Stats <bool> .ComputeMaxMean;
long multipleCount = 0;
for (double x0 = range.Min; x0 < range.Max + half; x0 += step)
{
var p0 = new double[] { -x0, 1.0 };
for (double x1 = range.Min; x1 < range.Max + half; x1 += step)
{
var p1 = new double[] { -x1, 1.0 };
var p01 = Polynomial.Multiply(p0, p1);
for (double x2 = range.Min; x2 < range.Max + half; x2 += step)
{
var p2 = new double[] { -x2, 1.0 };
var p012 = Polynomial.Multiply(p01, p2);
var t = Triple.CreateAscending(x0, x1, x2);
var exact = new double[] { t.E0, t.E1, t.E2 };
var roots = p012.RealRoots();
var multiple = CountDoubles(exact, 0.0001);
if (multiple > 0)
{
++multipleCount;
}
var rootCountsOk = exact.Length == roots.Length;
Test.IsTrue(rootCountsOk, "wrong number of roots found");
if (!rootCountsOk)
{
using (Report.Job("problematic roots:"))
{
Report.Line("exact: [" + exact.Select(x => x.ToString()).Join(",") + "]");
Report.Line("roots: [" + roots.Select(x => x.ToString()).Join(",") + "]");
}
continue;
}
for (int i = 0; i < 3; i++)
{
var err = (exact[i] - roots[i]).Abs();
Test.IsTrue(err < epsilon, "root differs significantly from exact value {0}", err);
double res = p012.Evaluate(roots[i]).Abs();
stats.Add(err);
residualStats.Add(res);
if (multiple == 0)
{
uniqueStats.Add(err);
uniqueHisto.AddLog10(err);
uniqueResidualStats.Add(res);
}
else
{
multipleStats.Add(err);
multipleHisto.AddLog10(err);
multipleResidualStats.Add(res);
}
}
}
}
}
Report.Value("roots error", stats);
Report.Value("unique roots error", uniqueStats);
Report.Value("unique roots log error histogram", uniqueHisto);
Report.Value("multiple roots error", multipleStats);
Report.Value("multiple roots log error histogram", multipleHisto);
Report.Value("residual error", residualStats);
Report.Value("unique roots residual error", uniqueResidualStats);
Report.Value("multiple residual error", multipleResidualStats);
Test.End();
}