.TH "mlpack::metric::MahalanobisDistance< TakeRoot >" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::metric::MahalanobisDistance< TakeRoot > \- 
.PP
The Mahalanobis distance, which is essentially a stretched Euclidean distance\&.  

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

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.RI "\fBMahalanobisDistance\fP ()"
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.RI "\fIInitialize the Mahalanobis distance with the empty matrix as covariance\&. \fP"
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.RI "\fBMahalanobisDistance\fP (const size_t dimensionality)"
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.RI "\fIInitialize the Mahalanobis distance with the identity matrix of the given dimensionality\&. \fP"
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.RI "\fBMahalanobisDistance\fP (const arma::mat &\fBcovariance\fP)"
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.RI "\fIInitialize the Mahalanobis distance with the given covariance matrix\&. \fP"
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.RI "const arma::mat & \fBCovariance\fP () const "
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.RI "\fIAccess the covariance matrix\&. \fP"
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.RI "arma::mat & \fBCovariance\fP ()"
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.RI "\fIModify the covariance matrix\&. \fP"
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.RI "template<typename VecType1 , typename VecType2 > double \fBEvaluate\fP (const VecType1 &a, const VecType2 &b)"
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.RI "std::string \fBToString\fP () const "
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.RI "\fIEvaluate the distance between the two given points using this Mahalanobis distance\&. \fP"
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.SS "Private Attributes"

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.RI "arma::mat \fBcovariance\fP"
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.RI "\fIThe covariance matrix associated with this distance\&. \fP"
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.SH "Detailed Description"
.PP 

.SS "template<bool TakeRoot = false>class mlpack::metric::MahalanobisDistance< TakeRoot >"
The Mahalanobis distance, which is essentially a stretched Euclidean distance\&. 

Given a square covariance matrix $ Q $ of size $ d $ x $ d $, where $ d $ is the dimensionality of the points it will be evaluating, and given two vectors $ x $ and $ y $ also of dimensionality $ d $,
.PP
\[ d(x, y) = \sqrt{(x - y)^T Q (x - y)} \].PP
where Q is the covariance matrix\&.
.PP
Because each evaluation multiplies (x_1 - x_2) by the covariance matrix, it may be much quicker to use an \fBLMetric\fP and simply stretch the actual dataset itself before performing any evaluations\&. However, this class is provided for convenience\&.
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Similar to the \fBLMetric\fP class, this offers a template parameter TakeRoot which, when set to false, will instead evaluate the distance
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\[ d(x, y) = (x - y)^T Q (x - y) \].PP
which is faster to evaluate\&.
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\fBTemplate Parameters:\fP
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\fITakeRoot\fP If true, takes the root of the output\&. It is slightly faster to leave this at the default of false\&. 
.RE
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.PP
Definition at line 61 of file mahalanobis_distance\&.hpp\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "template<bool TakeRoot = false> \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::\fBMahalanobisDistance\fP ()\fC [inline]\fP"

.PP
Initialize the Mahalanobis distance with the empty matrix as covariance\&. Don't call \fBEvaluate()\fP until you set the covariance with \fBCovariance()\fP! 
.PP
Definition at line 68 of file mahalanobis_distance\&.hpp\&.
.SS "template<bool TakeRoot = false> \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::\fBMahalanobisDistance\fP (const size_tdimensionality)\fC [inline]\fP"

.PP
Initialize the Mahalanobis distance with the identity matrix of the given dimensionality\&. 
.PP
\fBParameters:\fP
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\fIdimensionality\fP Dimesnsionality of the covariance matrix\&. 
.RE
.PP

.PP
Definition at line 76 of file mahalanobis_distance\&.hpp\&.
.SS "template<bool TakeRoot = false> \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::\fBMahalanobisDistance\fP (const arma::mat &covariance)\fC [inline]\fP"

.PP
Initialize the Mahalanobis distance with the given covariance matrix\&. The given covariance matrix will be copied (this is not optimal)\&.
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\fBParameters:\fP
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\fIcovariance\fP The covariance matrix to use for this distance\&. 
.RE
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.PP
Definition at line 85 of file mahalanobis_distance\&.hpp\&.
.SH "Member Function Documentation"
.PP 
.SS "template<bool TakeRoot = false> const arma::mat& \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::Covariance () const\fC [inline]\fP"

.PP
Access the covariance matrix\&. 
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\fBReturns:\fP
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Constant reference to the covariance matrix\&. 
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.PP
Definition at line 107 of file mahalanobis_distance\&.hpp\&.
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References mlpack::metric::MahalanobisDistance< TakeRoot >::covariance\&.
.SS "template<bool TakeRoot = false> arma::mat& \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::Covariance ()\fC [inline]\fP"

.PP
Modify the covariance matrix\&. 
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\fBReturns:\fP
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Reference to the covariance matrix\&. 
.RE
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.PP
Definition at line 114 of file mahalanobis_distance\&.hpp\&.
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References mlpack::metric::MahalanobisDistance< TakeRoot >::covariance\&.
.SS "template<bool TakeRoot = false> template<typename VecType1 , typename VecType2 > double \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::Evaluate (const VecType1 &a, const VecType2 &b)"

.SS "template<bool TakeRoot = false> std::string \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::ToString () const"

.PP
Evaluate the distance between the two given points using this Mahalanobis distance\&. If the covariance matrix has not been set (i\&.e\&. if you used the empty constructor and did not later modify the covariance matrix), calling this method will probably result in a crash\&.
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\fBParameters:\fP
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\fIa\fP First vector\&. 
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\fIb\fP Second vector\&. 
.RE
.PP

.SH "Member Data Documentation"
.PP 
.SS "template<bool TakeRoot = false> arma::mat \fBmlpack::metric::MahalanobisDistance\fP< TakeRoot >::covariance\fC [private]\fP"

.PP
The covariance matrix associated with this distance\&. 
.PP
Definition at line 117 of file mahalanobis_distance\&.hpp\&.
.PP
Referenced by mlpack::metric::MahalanobisDistance< TakeRoot >::Covariance()\&.

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