143 lines
3.0 KiB
C
143 lines
3.0 KiB
C
/**
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* @author Parikshit Ram (pram@cc.gatech.edu)
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* @file phi.h
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*
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* This file computes the Gaussian probability
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* density function
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*/
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#include "fastlib/fastlib.h"
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#include "fastlib/fastlib_int.h"
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#include <cmath>
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/**
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* Calculates the multivariate Gaussian probability density function
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*
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* Example use:
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* @code
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* Vector x, mean;
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* Matrix cov;
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* ....
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* long double f = phi(x, mean, cov);
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* @endcode
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*/
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long double phi(Vector& x , Vector& mean , Matrix& cov) {
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long double det, f;
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double exponent;
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index_t dim;
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Matrix inv;
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Vector diff, tmp;
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dim = x.length();
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la::InverseInit(cov, &inv);
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det = la::Determinant(cov);
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if( det < 0){
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det = -det;
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}
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la::SubInit(mean,x,&diff);
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la::MulInit(inv, diff, &tmp);
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exponent = la::Dot(diff, tmp);
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long double tmp1, tmp2, tmp3;
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tmp1 = 1;
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tmp2 = dim;
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tmp2 = tmp2/2;
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tmp2 = pow((2*(math::PI)),tmp2);
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tmp1 = tmp1/tmp2;
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tmp3 = 1;
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tmp2 = sqrt(det);
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tmp3 = tmp3/tmp2;
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tmp2 = -exponent;
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tmp2 = tmp2 / 2;
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f = (tmp1*tmp3*exp(tmp2));
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return f;
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}
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/**
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* Calculates the univariate Gaussian probability density function
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*
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* Example use:
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* @code
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* double x, mean, var;
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* ....
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* long double f = phi(x, mean, var);
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* @endcode
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*/
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long double phi(double x, double mean, double var) {
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long double f;
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f = exp(-1.0*((x-mean)*(x-mean)/(2*var)))/sqrt(2*math::PI*var);
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return f;
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}
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/**
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* Calculates the multivariate Gaussian probability density function
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* and also the gradients with respect to the mean and the variance
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*
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* Example use:
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* @code
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* Vector x, mean, g_mean, g_cov;
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* ArrayList<Matrix> d_cov; // the dSigma
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* ....
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* long double f = phi(x, mean, cov, d_cov, &g_mean, &g_cov);
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* @endcode
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*/
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long double phi(Vector& x, Vector& mean, Matrix& cov, ArrayList<Matrix>& d_cov, Vector *g_mean, Vector *g_cov){
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long double det, f;
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double exponent;
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index_t dim;
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Matrix inv;
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Vector diff, tmp;
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dim = x.length();
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la::InverseInit(cov, &inv);
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det = la::Determinant(cov);
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if( det < 0){
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det = -det;
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}
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la::SubInit(mean,x,&diff);
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la::MulInit(inv, diff, &tmp);
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exponent = la::Dot(diff, tmp);
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long double tmp1, tmp2, tmp3;
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tmp1 = 1;
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tmp2 = dim;
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tmp2 = tmp2/2;
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tmp2 = pow((2*(math::PI)),tmp2);
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tmp1 = tmp1/tmp2;
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tmp3 = 1;
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tmp2 = sqrt(det);
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tmp3 = tmp3/tmp2;
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tmp2 = -exponent;
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tmp2 = tmp2 / 2;
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f = (tmp1*tmp3*exp(tmp2));
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// Calculating the g_mean values which would be a (1 X dim) vector
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la::ScaleInit(f,tmp,g_mean);
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// Calculating the g_cov values which would be a (1 X (dim*(dim+1)/2)) vector
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double *g_cov_tmp;
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g_cov_tmp = (double*)malloc(d_cov.size()*sizeof(double));
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for(index_t i = 0; i < d_cov.size(); i++){
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Vector tmp_d;
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Matrix inv_d;
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long double tmp_d_cov_d_r;
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la::MulInit(d_cov[i],tmp,&tmp_d);
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tmp_d_cov_d_r = la::Dot(tmp_d,tmp);
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la::MulInit(inv,d_cov[i],&inv_d);
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for(index_t j = 0; j < dim; j++)
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tmp_d_cov_d_r += inv_d.get(j,j);
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g_cov_tmp[i] = f*tmp_d_cov_d_r/2;
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}
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g_cov->Copy(g_cov_tmp,d_cov.size());
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return f;
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}
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