public void ScalarMultiplyAndDivide() { DoubleVector a = new DoubleVector(new double[4]{0,1,2,3}); DoubleVector c = new DoubleVector(a); DoubleVector d = new DoubleVector(a); double scal = -4; c.Multiply(scal); d.Divide(scal); Assert.AreEqual(c[0],a[0]*scal); Assert.AreEqual(c[1],a[1]*scal); Assert.AreEqual(c[2],a[2]*scal); Assert.AreEqual(c[3],a[3]*scal); Assert.AreEqual(d[0],a[0]/scal); Assert.AreEqual(d[1],a[1]/scal); Assert.AreEqual(d[2],a[2]/scal); Assert.AreEqual(d[3],a[3]/scal); c = a*scal; Assert.AreEqual(c[0],a[0]*scal); Assert.AreEqual(c[1],a[1]*scal); Assert.AreEqual(c[2],a[2]*scal); Assert.AreEqual(c[3],a[3]*scal); c = scal*a; Assert.AreEqual(c[0],a[0]*scal); Assert.AreEqual(c[1],a[1]*scal); Assert.AreEqual(c[2],a[2]*scal); Assert.AreEqual(c[3],a[3]*scal); }
/// <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 }; }