00001 #ifndef pdf1d_epanech_kernel_pdf_sampler_h_ 00002 #define pdf1d_epanech_kernel_pdf_sampler_h_ 00003 //: 00004 // \file 00005 // \brief Implements sampling for an Epanechnikov kernel PDF 00006 // \author Tim Cootes 00007 00008 #include <vnl/vnl_random.h> 00009 #include <pdf1d/pdf1d_sampler.h> 00010 #include <pdf1d/pdf1d_epanech_kernel_pdf.h> 00011 00012 class pdf1d_epanech_kernel_pdf; 00013 00014 //: Generates random samples from an Epanechnikov kernel estimate 00015 class pdf1d_epanech_kernel_pdf_sampler : public pdf1d_sampler 00016 { 00017 protected: 00018 //: The random number generator 00019 vnl_random rng_; 00020 public: 00021 00022 //: Dflt ctor 00023 pdf1d_epanech_kernel_pdf_sampler(); 00024 00025 //: Destructor 00026 virtual ~pdf1d_epanech_kernel_pdf_sampler(); 00027 00028 const pdf1d_epanech_kernel_pdf& epanech_kernel_pdf() const; 00029 00030 //: Draw random sample from distribution 00031 virtual double sample(); 00032 00033 //: Fill x with samples possibly chosen so as to represent the distribution 00034 // Samples equal numbers from each kernel. 00035 virtual void regular_samples(vnl_vector<double>& x); 00036 00037 //: Reseeds the static random number generator (one per derived class) 00038 virtual void reseed(unsigned long); 00039 00040 //: Version number for I/O 00041 short version_no() const; 00042 00043 //: Name of the class 00044 virtual vcl_string is_a() const; 00045 00046 //: Does the name of the class match the argument? 00047 virtual bool is_class(vcl_string const& s) const; 00048 00049 //: Create a copy on the heap and return base class pointer 00050 virtual pdf1d_sampler* clone() const; 00051 00052 //: Transform a unit uniform distribution x into an Epanech distribution y 00053 // $0 <= x <= 1 => -sqrt(5) <= y <= sqrt(5)$ 00054 // Matlab found 6 solutions to 00055 // ${\frac {3}{20}}\,\left |{\it Dy}\right |\sqrt {5}\left (1-1/5\,{y}^{2}\right )=1$ 00056 // The 6th, which has the correct properties is 00057 // $-1/2\,\sqrt [3]{-10\,\sqrt {5}x+5\,\sqrt {-5+20\,{x}^{2}}}-5/2\, 00058 // {\frac {1}{\sqrt [3]{-10\,\sqrt {5}x+5\,\sqrt {-5+20\,{x}^{2}}}}}-1/2\, 00059 // \sqrt {-1}\sqrt {3}\left (\sqrt [3]{-10\,\sqrt {5}x+5\,\sqrt {-5+20\, 00060 // {x}^{2}}}-5\,{\frac {1}{\sqrt [3]{-10\,\sqrt {5}x+5\,\sqrt {-5+20\, 00061 // {x}^{2}}}}}\right )$ 00062 static double epan_transform(double x); 00063 }; 00064 00065 #endif // pdf1d_epanech_kernel_pdf_sampler_h_
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