/// <summary>
///
/// </summary>
/// <param name="x"></param>
/// <param name="bw"></param>
/// <param name="bwSel"></param>
/// <param name="adjust"></param>
/// <param name="kernel"></param>
/// <param name="weights"></param>
/// <param name="width"></param>
/// <param name="widthSel"></param>
/// <param name="n"></param>
/// <param name="from"></param>
/// <param name="to"></param>
/// <param name="cut"></param>
/// <remarks>Adapted from the R-project (www.r-project.org), Version 2.72, file density.R</remarks>
public static ProbabilityDensityResult ProbabilityDensity(
this IROVector x,
double bw,
string bwSel,
double adjust,
ConvolutionKernel kernel,
IROVector weights,
double width,
string widthSel,
int n,
double from,
double to,
double cut // default: 3
)
{
double wsum;
if (null == weights)
{
weights = VectorMath.GetConstantVector(1.0 / x.Length, x.Length);
wsum = 1;
}
else
{
wsum = weights.Sum();
}
double totMass = 1;
int n_user = n;
n = Math.Max(n, 512);
if (n > 512)
n = BinaryMath.NextPowerOfTwoGreaterOrEqualThan(n);
if (bw.IsNaN() && !(width.IsNaN() && null == widthSel))
{
if (!width.IsNaN())
{
// S has width equal to the length of the support of the kernel
// except for the gaussian where it is 4 * sd.
// R has bw a multiple of the sd.
double fac = 1;
switch (kernel)
{
case ConvolutionKernel.Gaussian:
fac = 4;
break;
case ConvolutionKernel.Rectangular:
fac = 2 * Math.Sqrt(3);
break;
case ConvolutionKernel.Triangular:
fac = 2 * Math.Sqrt(6);
break;
case ConvolutionKernel.Epanechnikov:
fac = 2 * Math.Sqrt(5);
break;
case ConvolutionKernel.Biweight:
fac = 2 * Math.Sqrt(7);
break;
case ConvolutionKernel.Cosine:
fac = 2 / Math.Sqrt(1 / 3 - 2 / (Math.PI * Math.PI));
break;
case ConvolutionKernel.Optcosine:
fac = 2 / Math.Sqrt(1 - 8 / (Math.PI * Math.PI));
break;
default:
throw new ArgumentException("Unknown convolution kernel");
}
bw = width / fac;
}
else
{
bwSel = widthSel;
}
}
if (null != bwSel)
{
if (x.Length < 2)
throw new ArgumentException("need at least 2 points to select a bandwidth automatically");
switch (bwSel.ToLowerInvariant())
{
case "nrd0":
//nrd0 = bw.nrd0(x),
break;
case "nrd":
//nrd = bw.nrd(x),
break;
case "ucv":
//ucv = bw.ucv(x),
break;
case "bcv":
//bcv = bw.bcv(x),
break;
case "sj":
//sj = , "sj-ste" = bw.SJ(x, method="ste"),
break;
case "sj-dpi":
//"sj-dpi" = bw.SJ(x, method="dpi"),
break;
default:
throw new ArgumentException("Unknown bandwith selection rule: " + bwSel.ToString());
}
}
if (!RMath.IsFinite(bw))
throw new ArithmeticException("Bandwidth is not finite");
bw = adjust * bw;
if (!(bw > 0))
throw new ArithmeticException("Bandwith is not positive");
if (from.IsNaN())
from = x.GetMinimum() - cut * bw;
if (to.IsNaN())
to = x.GetMaximum() + cut * bw;
if (!RMath.IsFinite(from))
throw new ArithmeticException("non-finite 'from'");
if (!to.IsFinite())
throw new ArithmeticException("non-finite 'to'");
double lo = from - 4 * bw;
double up = to + 4 * bw;
var y = new DoubleVector(2 * n);
MassDistribution(x, weights, lo, up, y, n);
y.Multiply(totMass);
var kords = new DoubleVector(2 * n);
kords.FillWithLinearSequenceGivenByStartEnd(0, 2 * (up - lo));
for (int i = n + 1, j = n - 1; j >= 0; i++, j--)
kords[i] = -kords[j];
switch (kernel)
{
case ConvolutionKernel.Gaussian:
kords.Apply(new Probability.NormalDistribution(0, bw).PDF);
break;
case ConvolutionKernel.Rectangular:
double a = bw * Math.Sqrt(3);
kords.Apply(delegate(double xx) { return Math.Abs(xx) < a ? 0.5 / a : 0; });
break;
case ConvolutionKernel.Triangular:
a = bw * Math.Sqrt(6);
kords.Apply(delegate(double xx) { return Math.Abs(xx) < a ? (1 - Math.Abs(xx) / a) / a : 0; });
break;
case ConvolutionKernel.Epanechnikov:
a = bw * Math.Sqrt(5);
kords.Apply(delegate(double xx) { return Math.Abs(xx) < a ? 0.75 * (1 - RMath.Pow2(Math.Abs(xx) / a)) / a : 0; });
break;
case ConvolutionKernel.Biweight:
a = bw * Math.Sqrt(7);
kords.Apply(delegate(double xx) { return Math.Abs(xx) < a ? 15.0 / 16.0 * RMath.Pow2(1 - RMath.Pow2(Math.Abs(xx) / a)) / a : 0; });
break;
case ConvolutionKernel.Cosine:
a = bw / Math.Sqrt(1.0 / 3 - 2 / RMath.Pow2(Math.PI));
kords.Apply(delegate(double xx) { return Math.Abs(xx) < a ? (1 + Math.Cos(Math.PI * xx / a)) / (2 * a) : 0; });
break;
case ConvolutionKernel.Optcosine:
a = bw / Math.Sqrt(1 - 8 / RMath.Pow2(Math.PI));
kords.Apply(delegate(double xx) { return Math.Abs(xx) < a ? Math.PI / 4 * Math.Cos(Math.PI * xx / (2 * a)) / a : 0; });
break;
default:
throw new ArgumentException("Unknown convolution kernel");
}
var result = new DoubleVector(2 * n);
Fourier.FastHartleyTransform.CyclicRealConvolution(y.GetInternalData(), kords.GetInternalData(), result.GetInternalData(), 2 * n, null);
y.Multiply(1.0 / (2 * n));
VectorMath.Max(y, 0, y);
var xords = VectorMath.CreateEquidistantSequenceByStartEndLength(lo, up, n);
var xu = VectorMath.CreateEquidistantSequenceByStartEndLength(from, to, n_user);
double[] res2 = new double[xu.Length];
Interpolation.LinearInterpolation.Interpolate(xords, result, n, xu, xu.Length, 0, out res2);
return new ProbabilityDensityResult() { X = xu, Y = VectorMath.ToROVector(res2), Bandwidth = bw };
}