.TH "mlpack::kernel::LaplacianKernel" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::kernel::LaplacianKernel \- 
.PP
The standard Laplacian kernel\&.  

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

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.RI "\fBLaplacianKernel\fP ()"
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.RI "\fIDefault constructor; sets bandwidth to 1\&.0\&. \fP"
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.RI "\fBLaplacianKernel\fP (double \fBbandwidth\fP)"
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.RI "\fIConstruct the Laplacian kernel with a custom bandwidth\&. \fP"
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.RI "double \fBBandwidth\fP () const "
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.RI "\fIGet the bandwidth\&. \fP"
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.RI "double & \fBBandwidth\fP ()"
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.RI "\fIModify the bandwidth\&. \fP"
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.RI "template<typename VecType > double \fBEvaluate\fP (const VecType &a, const VecType &b) const "
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.RI "\fIEvaluation of the Laplacian kernel\&. \fP"
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.RI "double \fBEvaluate\fP (const double t) const "
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.RI "\fIEvaluation of the Laplacian kernel given the distance between two points\&. \fP"
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.RI "std::string \fBToString\fP () const "
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.RI "\fIReturn a string representation of the kernel\&. \fP"
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.SS "Private Attributes"

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.RI "double \fBbandwidth\fP"
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.RI "\fIKernel bandwidth\&. \fP"
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.SH "Detailed Description"
.PP 
The standard Laplacian kernel\&. 

Given two vectors $ x $, $ y $, and a bandwidth $ \mu $ (set in the constructor),
.PP
\[ K(x, y) = \exp(-\frac{|| x - y ||}{\mu}). \].PP
The implementation is all in the header file because it is so simple\&. 
.PP
Definition at line 40 of file laplacian_kernel\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "mlpack::kernel::LaplacianKernel::LaplacianKernel ()\fC [inline]\fP"

.PP
Default constructor; sets bandwidth to 1\&.0\&. 
.PP
Definition at line 46 of file laplacian_kernel\&.hpp\&.
.SS "mlpack::kernel::LaplacianKernel::LaplacianKernel (doublebandwidth)\fC [inline]\fP"

.PP
Construct the Laplacian kernel with a custom bandwidth\&. 
.PP
\fBParameters:\fP
.RS 4
\fIbandwidth\fP The bandwidth of the kernel ( $\mu$)\&. 
.RE
.PP

.PP
Definition at line 54 of file laplacian_kernel\&.hpp\&.
.SH "Member Function Documentation"
.PP 
.SS "double mlpack::kernel::LaplacianKernel::Bandwidth () const\fC [inline]\fP"

.PP
Get the bandwidth\&. 
.PP
Definition at line 91 of file laplacian_kernel\&.hpp\&.
.PP
References bandwidth\&.
.SS "double& mlpack::kernel::LaplacianKernel::Bandwidth ()\fC [inline]\fP"

.PP
Modify the bandwidth\&. 
.PP
Definition at line 93 of file laplacian_kernel\&.hpp\&.
.PP
References bandwidth\&.
.SS "template<typename VecType > double mlpack::kernel::LaplacianKernel::Evaluate (const VecType &a, const VecType &b) const\fC [inline]\fP"

.PP
Evaluation of the Laplacian kernel\&. This could be generalized to use any distance metric, not the Euclidean distance, but for now, the Euclidean distance is used\&.
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\fBTemplate Parameters:\fP
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\fIVecType\fP Type of vector (likely arma::vec or arma::spvec)\&. 
.RE
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\fBParameters:\fP
.RS 4
\fIa\fP First vector\&. 
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\fIb\fP Second vector\&. 
.RE
.PP
\fBReturns:\fP
.RS 4
K(a, b) using the bandwidth ( $\mu$) specified in the constructor\&. 
.RE
.PP

.PP
Definition at line 70 of file laplacian_kernel\&.hpp\&.
.PP
References bandwidth, and mlpack::metric::LMetric< Power, TakeRoot >::Evaluate()\&.
.SS "double mlpack::kernel::LaplacianKernel::Evaluate (const doublet) const\fC [inline]\fP"

.PP
Evaluation of the Laplacian kernel given the distance between two points\&. 
.PP
\fBParameters:\fP
.RS 4
\fIt\fP The distance between the two points the kernel should be evaluated on\&. 
.RE
.PP
\fBReturns:\fP
.RS 4
K(t) using the bandwidth ( $\mu$) specified in the constructor\&. 
.RE
.PP

.PP
Definition at line 84 of file laplacian_kernel\&.hpp\&.
.PP
References bandwidth\&.
.SS "std::string mlpack::kernel::LaplacianKernel::ToString () const\fC [inline]\fP"

.PP
Return a string representation of the kernel\&. 
.PP
Definition at line 96 of file laplacian_kernel\&.hpp\&.
.PP
References bandwidth\&.
.SH "Member Data Documentation"
.PP 
.SS "double mlpack::kernel::LaplacianKernel::bandwidth\fC [private]\fP"

.PP
Kernel bandwidth\&. 
.PP
Definition at line 106 of file laplacian_kernel\&.hpp\&.
.PP
Referenced by Bandwidth(), Evaluate(), and ToString()\&.

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