.TH "mlpack::gmm" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
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.SH NAME
mlpack::gmm \- 
.PP
Gaussian Mixture Models\&.  

.SH SYNOPSIS
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.SS "Classes"

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.RI "class \fBDiagonalConstraint\fP"
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.RI "\fIForce a covariance matrix to be diagonal\&. \fP"
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.RI "class \fBEigenvalueRatioConstraint\fP"
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.RI "\fIGiven a vector of eigenvalue ratios, ensure that the covariance matrix always has those eigenvalue ratios\&. \fP"
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.RI "class \fBEMFit\fP"
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.RI "\fIThis class contains methods which can fit a \fBGMM\fP to observations using the EM algorithm\&. \fP"
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.RI "class \fBGMM\fP"
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.RI "\fIA Gaussian Mixture Model (\fBGMM\fP)\&. \fP"
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.RI "class \fBNoConstraint\fP"
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.RI "\fIThis class enforces no constraint on the covariance matrix\&. \fP"
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.RI "class \fBPositiveDefiniteConstraint\fP"
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.RI "\fIGiven a covariance matrix, force the matrix to be positive definite\&. \fP"
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.SS "Functions"

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.RI "double \fBphi\fP (const double x, const double mean, const double var)"
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.RI "\fICalculates the univariate Gaussian probability density function\&. \fP"
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.RI "double \fBphi\fP (const arma::vec &x, const arma::vec &mean, const arma::mat &cov)"
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.RI "\fICalculates the multivariate Gaussian probability density function\&. \fP"
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.RI "double \fBphi\fP (const arma::vec &x, const arma::vec &mean, const arma::mat &cov, const std::vector< arma::mat > &d_cov, arma::vec &g_mean, arma::vec &g_cov)"
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.RI "\fICalculates the multivariate Gaussian probability density function and also the gradients with respect to the mean and the variance\&. \fP"
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.RI "void \fBphi\fP (const arma::mat &x, const arma::vec &mean, const arma::mat &cov, arma::vec &probabilities)"
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.RI "\fICalculates the multivariate Gaussian probability density function for each data point (column) in the given matrix, with respect to the given mean and variance\&. \fP"
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.SH "Detailed Description"
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Gaussian Mixture Models\&. 


.SH "Function Documentation"
.PP 
.SS "double mlpack::gmm::phi (const doublex, const doublemean, const doublevar)\fC [inline]\fP"

.PP
Calculates the univariate Gaussian probability density function\&. Example use: 
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double x, mean, var;
\&.\&.\&.\&.
double f = phi(x, mean, var);

.fi
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\fBParameters:\fP
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\fIx\fP Observation\&. 
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\fImean\fP Mean of univariate Gaussian\&. 
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\fIvar\fP Variance of univariate Gaussian\&. 
.RE
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\fBReturns:\fP
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Probability of x being observed from the given univariate Gaussian\&. 
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Definition at line 46 of file phi\&.hpp\&.
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References M_PI\&.
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Referenced by mlpack::distribution::GaussianDistribution::Probability()\&.
.SS "double mlpack::gmm::phi (const arma::vec &x, const arma::vec &mean, const arma::mat &cov)\fC [inline]\fP"

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Calculates the multivariate Gaussian probability density function\&. Example use: 
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extern arma::vec x, mean;
extern arma::mat cov;
\&.\&.\&.\&.
double f = phi(x, mean, cov);

.fi
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\fBParameters:\fP
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\fIx\fP Observation\&. 
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\fImean\fP Mean of multivariate Gaussian\&. 
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\fIcov\fP Covariance of multivariate Gaussian\&. 
.RE
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\fBReturns:\fP
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Probability of x being observed from the given multivariate Gaussian\&. 
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Definition at line 68 of file phi\&.hpp\&.
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References M_PI\&.
.SS "double mlpack::gmm::phi (const arma::vec &x, const arma::vec &mean, const arma::mat &cov, const std::vector< arma::mat > &d_cov, arma::vec &g_mean, arma::vec &g_cov)\fC [inline]\fP"

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Calculates the multivariate Gaussian probability density function and also the gradients with respect to the mean and the variance\&. Example use: 
.PP
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extern arma::vec x, mean, g_mean, g_cov;
std::vector<arma::mat> d_cov; // the dSigma
\&.\&.\&.\&.
double f = phi(x, mean, cov, d_cov, &g_mean, &g_cov);

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Definition at line 94 of file phi\&.hpp\&.
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References M_PI\&.
.SS "void mlpack::gmm::phi (const arma::mat &x, const arma::vec &mean, const arma::mat &cov, arma::vec &probabilities)\fC [inline]\fP"

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Calculates the multivariate Gaussian probability density function for each data point (column) in the given matrix, with respect to the given mean and variance\&. 
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\fBParameters:\fP
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\fIx\fP List of observations\&. 
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\fImean\fP Mean of multivariate Gaussian\&. 
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\fIcov\fP Covariance of multivariate Gaussian\&. 
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\fIprobabilities\fP Output probabilities for each input observation\&. 
.RE
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Definition at line 138 of file phi\&.hpp\&.
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References M_PI\&.
.SH "Author"
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Generated automatically by Doxygen for MLPACK from the source code\&.