.TH "mlpack::metric::LMetric< Power, TakeRoot >" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::metric::LMetric< Power, TakeRoot > \- 
.PP
The L_p metric for arbitrary integer p, with an option to take the root\&.  

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

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.RI "\fBLMetric\fP ()"
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.RI "std::string \fBToString\fP () const "
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.SS "Static Public Member Functions"

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.RI "template<typename VecType1 , typename VecType2 > static double \fBEvaluate\fP (const VecType1 &a, const VecType2 &b)"
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.RI "\fIComputes the distance between two points\&. \fP"
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.SH "Detailed Description"
.PP 

.SS "template<int Power, bool TakeRoot = true>class mlpack::metric::LMetric< Power, TakeRoot >"
The L_p metric for arbitrary integer p, with an option to take the root\&. 

This class implements the standard L_p metric for two arbitrary vectors $ x $ and $ y $ of dimensionality $ n $:
.PP
\[ d(x, y) = \left( \sum_{i = 1}^{n} | x_i - y_i |^p \right)^{\frac{1}{p}}. \].PP
The value of p is given as a template parameter\&.
.PP
In addition, the function $ d(x, y) $ can be simplified, neglecting the p-root calculation\&. This is done by specifying the TakeRoot template parameter to be false\&. Then,
.PP
\[ d(x, y) = \sum_{i = 1}^{n} | x_i - y_i |^p \].PP
It is faster to compute that distance, so TakeRoot is by default off\&. However, when TakeRoot is false, the distance given is not actually a true metric -- it does not satisfy the triangle inequality\&. Some MLPACK methods do not require the triangle inequality to operate correctly (such as the BinarySpaceTree), but setting TakeRoot = false in some cases will cause incorrect results\&.
.PP
A few convenience typedefs are given:
.PP
.IP "\(bu" 2
ManhattanDistance
.IP "\(bu" 2
EuclideanDistance
.IP "\(bu" 2
SquaredEuclideanDistance
.PP
.PP
\fBTemplate Parameters:\fP
.RS 4
\fIPower\fP Power of metric; i\&.e\&. Power = 1 gives the L1-norm (Manhattan distance)\&. 
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\fITakeRoot\fP If true, the Power'th root of the result is taken before it is returned\&. Setting this to false causes the metric to not satisfy the Triangle Inequality (be careful!)\&. 
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Definition at line 73 of file lmetric\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "template<int Power, bool TakeRoot = true> \fBmlpack::metric::LMetric\fP< Power, TakeRoot >::\fBLMetric\fP ()\fC [inline]\fP"

.PP
Definition at line 80 of file lmetric\&.hpp\&.
.SH "Member Function Documentation"
.PP 
.SS "template<int Power, bool TakeRoot = true> template<typename VecType1 , typename VecType2 > static double \fBmlpack::metric::LMetric\fP< Power, TakeRoot >::Evaluate (const VecType1 &a, const VecType2 &b)\fC [static]\fP"

.PP
Computes the distance between two points\&. 
.PP
Referenced by mlpack::kernel::SphericalKernel::ConvolutionIntegral(), mlpack::kernel::GaussianKernel::ConvolutionIntegral(), mlpack::kernel::SphericalKernel::Evaluate(), mlpack::kernel::TriangularKernel::Evaluate(), mlpack::kernel::LaplacianKernel::Evaluate(), and mlpack::kernel::GaussianKernel::Evaluate()\&.
.SS "template<int Power, bool TakeRoot = true> std::string \fBmlpack::metric::LMetric\fP< Power, TakeRoot >::ToString () const"


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