PLearn 0.1
distr_maths.h
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00001 // -*- C++ -*-4 1999/10/29 20:41:34 dugas
00002 
00003 // distr_math.h
00004 // Copyright (C) 2002 Pascal Vincent
00005 //
00006 // Redistribution and use in source and binary forms, with or without
00007 // modification, are permitted provided that the following conditions are met:
00008 // 
00009 //  1. Redistributions of source code must retain the above copyright
00010 //     notice, this list of conditions and the following disclaimer.
00011 // 
00012 //  2. Redistributions in binary form must reproduce the above copyright
00013 //     notice, this list of conditions and the following disclaimer in the
00014 //     documentation and/or other materials provided with the distribution.
00015 // 
00016 //  3. The name of the authors may not be used to endorse or promote
00017 //     products derived from this software without specific prior written
00018 //     permission.
00019 // 
00020 // THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND ANY EXPRESS OR
00021 // IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
00022 // OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN
00023 // NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
00024 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
00025 // TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
00026 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
00027 // LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
00028 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
00029 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
00030 // 
00031 // This file is part of the PLearn library. For more information on the PLearn
00032 // library, go to the PLearn Web site at www.plearn.org
00033 
00034 
00035 /* *******************************************************      
00036  * $Id: distr_maths.h 9436 2008-09-04 18:48:55Z nouiz $
00037  * This file is part of the PLearn library.
00038  ******************************************************* */
00039 
00040 
00043 #ifndef distr_maths_INC
00044 #define distr_maths_INC
00045 
00046 #include "TMat.h"
00047 
00048 namespace PLearn {
00049 using namespace std;
00050 
00051 // return log of Normal(x;mu, sigma2*I), i.e. density of a spherical Gaussian
00052 real log_of_normal_density(Vec x, Vec mu, real sigma2);
00053 inline real normal_density(Vec x, Vec mu, real sigma2) { return safeexp(log_of_normal_density(x,mu,sigma2)); }
00054 real log_rbf(Vec x, Vec mu, real sigma2);
00055 inline real rbf(Vec x, Vec mu, real sigma2) { return safeexp(log_rbf(x,mu,sigma2)); }
00056 
00057 // return log of Normal(x;mu, diag(sigma2)), i.e. density of a diagonal Gaussian
00058 real log_of_normal_density(Vec x, Vec mu, Vec sigma2);
00059 inline real normal_density(Vec x, Vec mu, Vec sigma2) { return safeexp(log_of_normal_density(x,mu,sigma2)); }
00060 
00061 // return log of Normal(x;mu, Sigma), i.e. density of a full Gaussian,
00062 // where the covariance Sigma is
00063 //    Sigma = remainder_evalue*I + sum_i max(0,evalues[i]-remainder_evalue)*evectors(i)*evectors(i)'
00064 // The eigenvectors are in the ROWS of matrix evectors (because of easier row-wise access in Mat's).
00065 real log_of_normal_density(Vec x, Vec mu, Mat evectors, Vec evalues, real remainder_evalue=0);
00066 inline real normal_density(Vec x, Vec mu, Mat evectors, Vec evalues, real remainder_evalue=0) 
00067 { return safeexp(log_of_normal_density(x,mu,evectors,evalues,remainder_evalue)); }
00068 real log_fullGaussianRBF(Vec x, Vec mu, Mat evectors, Vec evalues, real remainder_evalue=0);
00069 inline real fullGaussianRBF(Vec x, Vec mu, Mat evectors, Vec evalues, real remainder_evalue=0) 
00070 { return safeexp(log_fullGaussianRBF(x,mu,evectors,evalues,remainder_evalue)); }
00071 
00072 real logOfNormal(const Vec& x, const Vec& mu, const Mat& C);
00073 
00077 real logPFittedGaussian(const Vec& x, const Mat& X, real lambda);
00078 
00085 real logOfCompactGaussian(const Vec& x, const Vec& mu, 
00086                           const Vec& eigenvalues, const Mat& eigenvectors, 
00087                           real gamma=1e-6, bool add_gamma_to_eigenval=false);
00088 
00089 
00095 real beta_density(real x, real alpha, real beta);
00097 real log_beta_density(real x, real alpha, real beta);
00098 
00099 // if (inverses) compute the eigendecomposition of C = inv(inv(A) + inv(B)) from eigendecompositions of A and B 
00100 // else compute the eigendecomposition of C = A + B from eigendecompositions of A and B
00101 void addEigenMatrices(Mat A_evec, Vec A_eval, Mat B_evec, Vec B_eval, Mat C_evec, Vec C_eval, bool inverses=false);
00102 
00112 void sums2Gaussian(real sum_w, Vec sum_wx, Mat sum_wx2, Vec mu, Mat cov_evectors, Vec cov_evalues, real min_variance);
00113 
00114 } // end of namespace PLearn
00115 
00116 #endif
00117 
00118 
00119 /*
00120   Local Variables:
00121   mode:c++
00122   c-basic-offset:4
00123   c-file-style:"stroustrup"
00124   c-file-offsets:((innamespace . 0)(inline-open . 0))
00125   indent-tabs-mode:nil
00126   fill-column:79
00127   End:
00128 */
00129 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=79 :
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