.TH "mlpack::kernel::EpanechnikovKernel" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::kernel::EpanechnikovKernel \- 
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The Epanechnikov kernel, defined as\&.  

.SH SYNOPSIS
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.PP
.SS "Public Member Functions"

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.RI "\fBEpanechnikovKernel\fP (const double \fBbandwidth\fP=1\&.0)"
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.RI "\fIInstantiate the Epanechnikov kernel with the given bandwidth (default 1\&.0)\&. \fP"
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.RI "template<typename VecType > double \fBConvolutionIntegral\fP (const VecType &a, const VecType &b)"
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.RI "\fIObtains the convolution integral [integral of K(||x-a||) K(||b-x||) dx] for the two vectors\&. \fP"
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.RI "template<typename Vec1Type , typename Vec2Type > double \fBEvaluate\fP (const Vec1Type &a, const Vec2Type &b) const "
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.RI "\fIEvaluate the Epanechnikov kernel on the given two inputs\&. \fP"
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.RI "double \fBEvaluate\fP (const double distance) const "
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.RI "\fIEvaluate the Epanechnikov kernel given that the distance between the two input points is known\&. \fP"
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.RI "double \fBNormalizer\fP (const size_t dimension)"
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.RI "\fICompute the normalizer of this Epanechnikov kernel for the given dimension\&. \fP"
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.RI "std::string \fBToString\fP () const "
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.SS "Private Attributes"

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.RI "double \fBbandwidth\fP"
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.RI "\fIBandwidth of the kernel\&. \fP"
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.RI "double \fBinverseBandwidthSquared\fP"
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.RI "\fICached value of the inverse bandwidth squared (to speed up computation)\&. \fP"
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.SH "Detailed Description"
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The Epanechnikov kernel, defined as\&. 

\[ K(x, y) = \max \{0, 1 - || x - y ||^2_2 / b^2 \} \]
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where $ b $ is the bandwidth the of the kernel (defaults to 1\&.0)\&. 
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Definition at line 39 of file epanechnikov_kernel\&.hpp\&.
.SH "Constructor & Destructor Documentation"
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.SS "mlpack::kernel::EpanechnikovKernel::EpanechnikovKernel (const doublebandwidth = \fC1\&.0\fP)\fC [inline]\fP"

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Instantiate the Epanechnikov kernel with the given bandwidth (default 1\&.0)\&. 
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\fBParameters:\fP
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\fIbandwidth\fP Bandwidth of the kernel\&. 
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Definition at line 47 of file epanechnikov_kernel\&.hpp\&.
.SH "Member Function Documentation"
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.SS "template<typename VecType > double mlpack::kernel::EpanechnikovKernel::ConvolutionIntegral (const VecType &a, const VecType &b)"

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Obtains the convolution integral [integral of K(||x-a||) K(||b-x||) dx] for the two vectors\&. 
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\fBTemplate Parameters:\fP
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\fIVecType\fP Type of vector (arma::vec, arma::spvec should be expected)\&. 
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\fBParameters:\fP
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\fIa\fP First vector\&. 
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\fIb\fP Second vector\&. 
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\fBReturns:\fP
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the convolution integral value\&. 
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.SS "template<typename Vec1Type , typename Vec2Type > double mlpack::kernel::EpanechnikovKernel::Evaluate (const Vec1Type &a, const Vec2Type &b) const"

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Evaluate the Epanechnikov kernel on the given two inputs\&. 
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\fBParameters:\fP
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\fIa\fP One input vector\&. 
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\fIb\fP The other input vector\&. 
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.SS "double mlpack::kernel::EpanechnikovKernel::Evaluate (const doubledistance) const"

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Evaluate the Epanechnikov kernel given that the distance between the two input points is known\&. 
.SS "double mlpack::kernel::EpanechnikovKernel::Normalizer (const size_tdimension)"

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Compute the normalizer of this Epanechnikov kernel for the given dimension\&. 
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\fBParameters:\fP
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\fIdimension\fP Dimension to calculate the normalizer for\&. 
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.SS "std::string mlpack::kernel::EpanechnikovKernel::ToString () const"

.SH "Member Data Documentation"
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.SS "double mlpack::kernel::EpanechnikovKernel::bandwidth\fC [private]\fP"

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Bandwidth of the kernel\&. 
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Definition at line 92 of file epanechnikov_kernel\&.hpp\&.
.SS "double mlpack::kernel::EpanechnikovKernel::inverseBandwidthSquared\fC [private]\fP"

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Cached value of the inverse bandwidth squared (to speed up computation)\&. 
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Definition at line 94 of file epanechnikov_kernel\&.hpp\&.

.SH "Author"
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Generated automatically by Doxygen for MLPACK from the source code\&.