| 1 | /*! |
|---|
| 2 | \file |
|---|
| 3 | \brief Probability distributions for Exponential Family models. |
|---|
| 4 | \author Vaclav Smidl. |
|---|
| 5 | |
|---|
| 6 | ----------------------------------- |
|---|
| 7 | BDM++ - C++ library for Bayesian Decision Making under Uncertainty |
|---|
| 8 | |
|---|
| 9 | Using IT++ for numerical operations |
|---|
| 10 | ----------------------------------- |
|---|
| 11 | */ |
|---|
| 12 | |
|---|
| 13 | #ifndef EF_H |
|---|
| 14 | #define EF_H |
|---|
| 15 | |
|---|
| 16 | |
|---|
| 17 | #include "libBM.h" |
|---|
| 18 | #include "../math/chmat.h" |
|---|
| 19 | #include "../user_info.h" |
|---|
| 20 | |
|---|
| 21 | namespace bdm |
|---|
| 22 | { |
|---|
| 23 | |
|---|
| 24 | |
|---|
| 25 | //! Global Uniform_RNG |
|---|
| 26 | extern Uniform_RNG UniRNG; |
|---|
| 27 | //! Global Normal_RNG |
|---|
| 28 | extern Normal_RNG NorRNG; |
|---|
| 29 | //! Global Gamma_RNG |
|---|
| 30 | extern Gamma_RNG GamRNG; |
|---|
| 31 | |
|---|
| 32 | /*! |
|---|
| 33 | * \brief General conjugate exponential family posterior density. |
|---|
| 34 | |
|---|
| 35 | * More?... |
|---|
| 36 | */ |
|---|
| 37 | |
|---|
| 38 | class eEF : public epdf |
|---|
| 39 | { |
|---|
| 40 | public: |
|---|
| 41 | // eEF() :epdf() {}; |
|---|
| 42 | //! default constructor |
|---|
| 43 | eEF ( ) :epdf ( ) {}; |
|---|
| 44 | //! logarithm of the normalizing constant, \f$\mathcal{I}\f$ |
|---|
| 45 | virtual double lognc() const =0; |
|---|
| 46 | //!TODO decide if it is really needed |
|---|
| 47 | virtual void dupdate ( mat &v ) {it_error ( "Not implemented" );}; |
|---|
| 48 | //!Evaluate normalized log-probability |
|---|
| 49 | virtual double evallog_nn ( const vec &val ) const{it_error ( "Not implemented" );return 0.0;}; |
|---|
| 50 | //!Evaluate normalized log-probability |
|---|
| 51 | virtual double evallog ( const vec &val ) const {double tmp;tmp= evallog_nn ( val )-lognc();it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); return tmp;} |
|---|
| 52 | //!Evaluate normalized log-probability for many samples |
|---|
| 53 | virtual vec evallog ( const mat &Val ) const |
|---|
| 54 | { |
|---|
| 55 | vec x ( Val.cols() ); |
|---|
| 56 | for ( int i=0;i<Val.cols();i++ ) {x ( i ) =evallog_nn ( Val.get_col ( i ) ) ;} |
|---|
| 57 | return x-lognc(); |
|---|
| 58 | } |
|---|
| 59 | //!Power of the density, used e.g. to flatten the density |
|---|
| 60 | virtual void pow ( double p ) {it_error ( "Not implemented" );}; |
|---|
| 61 | }; |
|---|
| 62 | |
|---|
| 63 | /*! |
|---|
| 64 | * \brief Exponential family model. |
|---|
| 65 | |
|---|
| 66 | * More?... |
|---|
| 67 | */ |
|---|
| 68 | |
|---|
| 69 | class mEF : public mpdf |
|---|
| 70 | { |
|---|
| 71 | |
|---|
| 72 | public: |
|---|
| 73 | //! Default constructor |
|---|
| 74 | mEF ( ) :mpdf ( ) {}; |
|---|
| 75 | }; |
|---|
| 76 | |
|---|
| 77 | //! Estimator for Exponential family |
|---|
| 78 | class BMEF : public BM |
|---|
| 79 | { |
|---|
| 80 | protected: |
|---|
| 81 | //! forgetting factor |
|---|
| 82 | double frg; |
|---|
| 83 | //! cached value of lognc() in the previous step (used in evaluation of \c ll ) |
|---|
| 84 | double last_lognc; |
|---|
| 85 | public: |
|---|
| 86 | //! Default constructor (=empty constructor) |
|---|
| 87 | BMEF ( double frg0=1.0 ) :BM ( ), frg ( frg0 ) {} |
|---|
| 88 | //! Copy constructor |
|---|
| 89 | BMEF ( const BMEF &B ) :BM ( B ), frg ( B.frg ), last_lognc ( B.last_lognc ) {} |
|---|
| 90 | //!get statistics from another model |
|---|
| 91 | virtual void set_statistics ( const BMEF* BM0 ) {it_error ( "Not implemented" );}; |
|---|
| 92 | //! Weighted update of sufficient statistics (Bayes rule) |
|---|
| 93 | virtual void bayes ( const vec &data, const double w ) {}; |
|---|
| 94 | //original Bayes |
|---|
| 95 | void bayes ( const vec &dt ); |
|---|
| 96 | //!Flatten the posterior according to the given BMEF (of the same type!) |
|---|
| 97 | virtual void flatten ( const BMEF * B ) {it_error ( "Not implemented" );} |
|---|
| 98 | //!Flatten the posterior as if to keep nu0 data |
|---|
| 99 | // virtual void flatten ( double nu0 ) {it_error ( "Not implemented" );} |
|---|
| 100 | |
|---|
| 101 | BMEF* _copy_ () const {it_error ( "function _copy_ not implemented for this BM" ); return NULL;}; |
|---|
| 102 | }; |
|---|
| 103 | |
|---|
| 104 | template<class sq_T> |
|---|
| 105 | class mlnorm; |
|---|
| 106 | |
|---|
| 107 | /*! |
|---|
| 108 | * \brief Gaussian density with positive definite (decomposed) covariance matrix. |
|---|
| 109 | |
|---|
| 110 | * More?... |
|---|
| 111 | */ |
|---|
| 112 | template<class sq_T> |
|---|
| 113 | class enorm : public eEF |
|---|
| 114 | { |
|---|
| 115 | protected: |
|---|
| 116 | //! mean value |
|---|
| 117 | vec mu; |
|---|
| 118 | //! Covariance matrix in decomposed form |
|---|
| 119 | sq_T R; |
|---|
| 120 | public: |
|---|
| 121 | //!\name Constructors |
|---|
| 122 | //!@{ |
|---|
| 123 | |
|---|
| 124 | enorm ( ) :eEF ( ), mu ( ),R ( ) {}; |
|---|
| 125 | enorm ( const vec &mu,const sq_T &R ) {set_parameters ( mu,R );} |
|---|
| 126 | void set_parameters ( const vec &mu,const sq_T &R ); |
|---|
| 127 | //!@} |
|---|
| 128 | |
|---|
| 129 | //! \name Mathematical operations |
|---|
| 130 | //!@{ |
|---|
| 131 | |
|---|
| 132 | //! dupdate in exponential form (not really handy) |
|---|
| 133 | void dupdate ( mat &v,double nu=1.0 ); |
|---|
| 134 | |
|---|
| 135 | vec sample() const; |
|---|
| 136 | mat sample ( int N ) const; |
|---|
| 137 | double evallog_nn ( const vec &val ) const; |
|---|
| 138 | double lognc () const; |
|---|
| 139 | vec mean() const {return mu;} |
|---|
| 140 | vec variance() const {return diag ( R.to_mat() );} |
|---|
| 141 | // mlnorm<sq_T>* condition ( const RV &rvn ) const ; <=========== fails to cmpile. Why? |
|---|
| 142 | mpdf* condition ( const RV &rvn ) const ; |
|---|
| 143 | enorm<sq_T>* marginal ( const RV &rv ) const; |
|---|
| 144 | // epdf* marginal ( const RV &rv ) const; |
|---|
| 145 | //!@} |
|---|
| 146 | |
|---|
| 147 | //! \name Access to attributes |
|---|
| 148 | //!@{ |
|---|
| 149 | |
|---|
| 150 | vec& _mu() {return mu;} |
|---|
| 151 | void set_mu ( const vec mu0 ) { mu=mu0;} |
|---|
| 152 | sq_T& _R() {return R;} |
|---|
| 153 | const sq_T& _R() const {return R;} |
|---|
| 154 | //!@} |
|---|
| 155 | |
|---|
| 156 | }; |
|---|
| 157 | |
|---|
| 158 | /*! |
|---|
| 159 | * \brief Gauss-inverse-Wishart density stored in LD form |
|---|
| 160 | |
|---|
| 161 | * For \f$p\f$-variate densities, given rv.count() should be \f$p\times\f$ V.rows(). |
|---|
| 162 | * |
|---|
| 163 | */ |
|---|
| 164 | class egiw : public eEF |
|---|
| 165 | { |
|---|
| 166 | protected: |
|---|
| 167 | //! Extended information matrix of sufficient statistics |
|---|
| 168 | ldmat V; |
|---|
| 169 | //! Number of data records (degrees of freedom) of sufficient statistics |
|---|
| 170 | double nu; |
|---|
| 171 | //! Dimension of the output |
|---|
| 172 | int dimx; |
|---|
| 173 | //! Dimension of the regressor |
|---|
| 174 | int nPsi; |
|---|
| 175 | public: |
|---|
| 176 | //!\name Constructors |
|---|
| 177 | //!@{ |
|---|
| 178 | egiw() :eEF() {}; |
|---|
| 179 | egiw ( int dimx0, ldmat V0, double nu0=-1.0 ) :eEF() {set_parameters ( dimx0,V0, nu0 );}; |
|---|
| 180 | |
|---|
| 181 | void set_parameters ( int dimx0, ldmat V0, double nu0=-1.0 ) |
|---|
| 182 | { |
|---|
| 183 | dimx=dimx0; |
|---|
| 184 | nPsi = V0.rows()-dimx; |
|---|
| 185 | dim = dimx* ( dimx+nPsi ); // size(R) + size(Theta) |
|---|
| 186 | |
|---|
| 187 | V=V0; |
|---|
| 188 | if ( nu0<0 ) |
|---|
| 189 | { |
|---|
| 190 | nu = 0.1 +nPsi +2*dimx +2; // +2 assures finite expected value of R |
|---|
| 191 | // terms before that are sufficient for finite normalization |
|---|
| 192 | } |
|---|
| 193 | else |
|---|
| 194 | { |
|---|
| 195 | nu=nu0; |
|---|
| 196 | } |
|---|
| 197 | } |
|---|
| 198 | //!@} |
|---|
| 199 | |
|---|
| 200 | vec sample() const; |
|---|
| 201 | vec mean() const; |
|---|
| 202 | vec variance() const; |
|---|
| 203 | |
|---|
| 204 | //! LS estimate of \f$\theta\f$ |
|---|
| 205 | vec est_theta() const; |
|---|
| 206 | |
|---|
| 207 | //! Covariance of the LS estimate |
|---|
| 208 | ldmat est_theta_cov() const; |
|---|
| 209 | |
|---|
| 210 | void mean_mat ( mat &M, mat&R ) const; |
|---|
| 211 | //! In this instance, val= [theta, r]. For multivariate instances, it is stored columnwise val = [theta_1 theta_2 ... r_1 r_2 ] |
|---|
| 212 | double evallog_nn ( const vec &val ) const; |
|---|
| 213 | double lognc () const; |
|---|
| 214 | void pow ( double p ) {V*=p;nu*=p;}; |
|---|
| 215 | |
|---|
| 216 | //! \name Access attributes |
|---|
| 217 | //!@{ |
|---|
| 218 | |
|---|
| 219 | ldmat& _V() {return V;} |
|---|
| 220 | const ldmat& _V() const {return V;} |
|---|
| 221 | double& _nu() {return nu;} |
|---|
| 222 | const double& _nu() const {return nu;} |
|---|
| 223 | //!@} |
|---|
| 224 | }; |
|---|
| 225 | |
|---|
| 226 | /*! \brief Dirichlet posterior density |
|---|
| 227 | |
|---|
| 228 | Continuous Dirichlet density of \f$n\f$-dimensional variable \f$x\f$ |
|---|
| 229 | \f[ |
|---|
| 230 | f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^{\beta_i-1} |
|---|
| 231 | \f] |
|---|
| 232 | where \f$\gamma=\sum_i \beta_i\f$. |
|---|
| 233 | */ |
|---|
| 234 | class eDirich: public eEF |
|---|
| 235 | { |
|---|
| 236 | protected: |
|---|
| 237 | //!sufficient statistics |
|---|
| 238 | vec beta; |
|---|
| 239 | public: |
|---|
| 240 | //!\name Constructors |
|---|
| 241 | //!@{ |
|---|
| 242 | |
|---|
| 243 | eDirich () : eEF ( ) {}; |
|---|
| 244 | eDirich ( const eDirich &D0 ) : eEF () {set_parameters ( D0.beta );}; |
|---|
| 245 | eDirich ( const vec &beta0 ) {set_parameters ( beta0 );}; |
|---|
| 246 | void set_parameters ( const vec &beta0 ) |
|---|
| 247 | { |
|---|
| 248 | beta= beta0; |
|---|
| 249 | dim = beta.length(); |
|---|
| 250 | } |
|---|
| 251 | //!@} |
|---|
| 252 | |
|---|
| 253 | vec sample() const {it_error ( "Not implemented" );return vec_1 ( 0.0 );}; |
|---|
| 254 | vec mean() const {return beta/sum(beta);}; |
|---|
| 255 | vec variance() const {double gamma =sum(beta); return elem_mult ( beta, ( beta+1 ) ) / ( gamma* ( gamma+1 ) );} |
|---|
| 256 | //! In this instance, val is ... |
|---|
| 257 | double evallog_nn ( const vec &val ) const |
|---|
| 258 | { |
|---|
| 259 | double tmp; tmp= ( beta-1 ) *log ( val ); it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
|---|
| 260 | return tmp; |
|---|
| 261 | }; |
|---|
| 262 | double lognc () const |
|---|
| 263 | { |
|---|
| 264 | double tmp; |
|---|
| 265 | double gam=sum ( beta ); |
|---|
| 266 | double lgb=0.0; |
|---|
| 267 | for ( int i=0;i<beta.length();i++ ) {lgb+=lgamma ( beta ( i ) );} |
|---|
| 268 | tmp= lgb-lgamma ( gam ); |
|---|
| 269 | it_assert_debug ( std::isfinite ( tmp ),"Infinite value" ); |
|---|
| 270 | return tmp; |
|---|
| 271 | }; |
|---|
| 272 | //!access function |
|---|
| 273 | vec& _beta() {return beta;} |
|---|
| 274 | //!Set internal parameters |
|---|
| 275 | }; |
|---|
| 276 | |
|---|
| 277 | //! \brief Estimator for Multinomial density |
|---|
| 278 | class multiBM : public BMEF |
|---|
| 279 | { |
|---|
| 280 | protected: |
|---|
| 281 | //! Conjugate prior and posterior |
|---|
| 282 | eDirich est; |
|---|
| 283 | //! Pointer inside est to sufficient statistics |
|---|
| 284 | vec β |
|---|
| 285 | public: |
|---|
| 286 | //!Default constructor |
|---|
| 287 | multiBM ( ) : BMEF ( ),est ( ),beta ( est._beta() ) |
|---|
| 288 | { |
|---|
| 289 | if ( beta.length() >0 ) {last_lognc=est.lognc();} |
|---|
| 290 | else{last_lognc=0.0;} |
|---|
| 291 | } |
|---|
| 292 | //!Copy constructor |
|---|
| 293 | multiBM ( const multiBM &B ) : BMEF ( B ),est ( B.est ),beta ( est._beta() ) {} |
|---|
| 294 | //! Sets sufficient statistics to match that of givefrom mB0 |
|---|
| 295 | void set_statistics ( const BM* mB0 ) {const multiBM* mB=dynamic_cast<const multiBM*> ( mB0 ); beta=mB->beta;} |
|---|
| 296 | void bayes ( const vec &dt ) |
|---|
| 297 | { |
|---|
| 298 | if ( frg<1.0 ) {beta*=frg;last_lognc=est.lognc();} |
|---|
| 299 | beta+=dt; |
|---|
| 300 | if ( evalll ) {ll=est.lognc()-last_lognc;} |
|---|
| 301 | } |
|---|
| 302 | double logpred ( const vec &dt ) const |
|---|
| 303 | { |
|---|
| 304 | eDirich pred ( est ); |
|---|
| 305 | vec &beta = pred._beta(); |
|---|
| 306 | |
|---|
| 307 | double lll; |
|---|
| 308 | if ( frg<1.0 ) |
|---|
| 309 | {beta*=frg;lll=pred.lognc();} |
|---|
| 310 | else |
|---|
| 311 | if ( evalll ) {lll=last_lognc;} |
|---|
| 312 | else{lll=pred.lognc();} |
|---|
| 313 | |
|---|
| 314 | beta+=dt; |
|---|
| 315 | return pred.lognc()-lll; |
|---|
| 316 | } |
|---|
| 317 | void flatten ( const BMEF* B ) |
|---|
| 318 | { |
|---|
| 319 | const multiBM* E=dynamic_cast<const multiBM*> ( B ); |
|---|
| 320 | // sum(beta) should be equal to sum(B.beta) |
|---|
| 321 | const vec &Eb=E->beta;//const_cast<multiBM*> ( E )->_beta(); |
|---|
| 322 | beta*= ( sum ( Eb ) /sum ( beta ) ); |
|---|
| 323 | if ( evalll ) {last_lognc=est.lognc();} |
|---|
| 324 | } |
|---|
| 325 | const epdf& posterior() const {return est;}; |
|---|
| 326 | const eDirich* _e() const {return &est;}; |
|---|
| 327 | void set_parameters ( const vec &beta0 ) |
|---|
| 328 | { |
|---|
| 329 | est.set_parameters ( beta0 ); |
|---|
| 330 | if ( evalll ) {last_lognc=est.lognc();} |
|---|
| 331 | } |
|---|
| 332 | }; |
|---|
| 333 | |
|---|
| 334 | /*! |
|---|
| 335 | \brief Gamma posterior density |
|---|
| 336 | |
|---|
| 337 | Multivariate Gamma density as product of independent univariate densities. |
|---|
| 338 | \f[ |
|---|
| 339 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
|---|
| 340 | \f] |
|---|
| 341 | */ |
|---|
| 342 | |
|---|
| 343 | class egamma : public eEF |
|---|
| 344 | { |
|---|
| 345 | protected: |
|---|
| 346 | //! Vector \f$\alpha\f$ |
|---|
| 347 | vec alpha; |
|---|
| 348 | //! Vector \f$\beta\f$ |
|---|
| 349 | vec beta; |
|---|
| 350 | public : |
|---|
| 351 | //! \name Constructors |
|---|
| 352 | //!@{ |
|---|
| 353 | egamma ( ) :eEF ( ), alpha ( 0 ), beta ( 0 ) {}; |
|---|
| 354 | egamma ( const vec &a, const vec &b ) {set_parameters ( a, b );}; |
|---|
| 355 | void set_parameters ( const vec &a, const vec &b ) {alpha=a,beta=b;dim = alpha.length();}; |
|---|
| 356 | //!@} |
|---|
| 357 | |
|---|
| 358 | vec sample() const; |
|---|
| 359 | //! TODO: is it used anywhere? |
|---|
| 360 | // mat sample ( int N ) const; |
|---|
| 361 | double evallog ( const vec &val ) const; |
|---|
| 362 | double lognc () const; |
|---|
| 363 | //! Returns poiter to alpha and beta. Potentially dengerous: use with care! |
|---|
| 364 | vec& _alpha() {return alpha;} |
|---|
| 365 | vec& _beta() {return beta;} |
|---|
| 366 | vec mean() const {return elem_div ( alpha,beta );} |
|---|
| 367 | vec variance() const {return elem_div ( alpha,elem_mult ( beta,beta ) ); } |
|---|
| 368 | }; |
|---|
| 369 | |
|---|
| 370 | /*! |
|---|
| 371 | \brief Inverse-Gamma posterior density |
|---|
| 372 | |
|---|
| 373 | Multivariate inverse-Gamma density as product of independent univariate densities. |
|---|
| 374 | \f[ |
|---|
| 375 | f(x|\alpha,\beta) = \prod f(x_i|\alpha_i,\beta_i) |
|---|
| 376 | \f] |
|---|
| 377 | |
|---|
| 378 | Vector \f$\beta\f$ has different meaning (in fact it is 1/beta as used in definition of iG) |
|---|
| 379 | |
|---|
| 380 | Inverse Gamma can be converted to Gamma using \f[ |
|---|
| 381 | x\sim iG(a,b) => 1/x\sim G(a,1/b) |
|---|
| 382 | \f] |
|---|
| 383 | This relation is used in sampling. |
|---|
| 384 | */ |
|---|
| 385 | |
|---|
| 386 | class eigamma : public egamma |
|---|
| 387 | { |
|---|
| 388 | protected: |
|---|
| 389 | public : |
|---|
| 390 | //! \name Constructors |
|---|
| 391 | //! All constructors are inherited |
|---|
| 392 | //!@{ |
|---|
| 393 | //!@} |
|---|
| 394 | |
|---|
| 395 | vec sample() const {return 1.0/egamma::sample();}; |
|---|
| 396 | //! Returns poiter to alpha and beta. Potentially dangerous: use with care! |
|---|
| 397 | vec mean() const {return elem_div ( beta,alpha-1 );} |
|---|
| 398 | vec variance() const {vec mea=mean(); return elem_div ( elem_mult ( mea,mea ),alpha-2 );} |
|---|
| 399 | }; |
|---|
| 400 | /* |
|---|
| 401 | //! Weighted mixture of epdfs with external owned components. |
|---|
| 402 | class emix : public epdf { |
|---|
| 403 | protected: |
|---|
| 404 | int n; |
|---|
| 405 | vec &w; |
|---|
| 406 | Array<epdf*> Coms; |
|---|
| 407 | public: |
|---|
| 408 | //! Default constructor |
|---|
| 409 | emix ( const RV &rv, vec &w0): epdf(rv), n(w0.length()), w(w0), Coms(n) {}; |
|---|
| 410 | void set_parameters( int &i, double wi, epdf* ep){w(i)=wi;Coms(i)=ep;} |
|---|
| 411 | vec mean(){vec pom; for(int i=0;i<n;i++){pom+=Coms(i)->mean()*w(i);} return pom;}; |
|---|
| 412 | vec sample() {it_error ( "Not implemented" );return 0;} |
|---|
| 413 | }; |
|---|
| 414 | */ |
|---|
| 415 | |
|---|
| 416 | //! Uniform distributed density on a rectangular support |
|---|
| 417 | |
|---|
| 418 | class euni: public epdf |
|---|
| 419 | { |
|---|
| 420 | protected: |
|---|
| 421 | //! lower bound on support |
|---|
| 422 | vec low; |
|---|
| 423 | //! upper bound on support |
|---|
| 424 | vec high; |
|---|
| 425 | //! internal |
|---|
| 426 | vec distance; |
|---|
| 427 | //! normalizing coefficients |
|---|
| 428 | double nk; |
|---|
| 429 | //! cache of log( \c nk ) |
|---|
| 430 | double lnk; |
|---|
| 431 | public: |
|---|
| 432 | //! \name Constructors |
|---|
| 433 | //!@{ |
|---|
| 434 | euni ( ) :epdf ( ) {} |
|---|
| 435 | euni ( const vec &low0, const vec &high0 ) {set_parameters ( low0,high0 );} |
|---|
| 436 | void set_parameters ( const vec &low0, const vec &high0 ) |
|---|
| 437 | { |
|---|
| 438 | distance = high0-low0; |
|---|
| 439 | it_assert_debug ( min ( distance ) >0.0,"bad support" ); |
|---|
| 440 | low = low0; |
|---|
| 441 | high = high0; |
|---|
| 442 | nk = prod ( 1.0/distance ); |
|---|
| 443 | lnk = log ( nk ); |
|---|
| 444 | dim = low.length(); |
|---|
| 445 | } |
|---|
| 446 | //!@} |
|---|
| 447 | |
|---|
| 448 | double eval ( const vec &val ) const {return nk;} |
|---|
| 449 | double evallog ( const vec &val ) const {return lnk;} |
|---|
| 450 | vec sample() const |
|---|
| 451 | { |
|---|
| 452 | vec smp ( dim ); |
|---|
| 453 | #pragma omp critical |
|---|
| 454 | UniRNG.sample_vector ( dim ,smp ); |
|---|
| 455 | return low+elem_mult ( distance,smp ); |
|---|
| 456 | } |
|---|
| 457 | //! set values of \c low and \c high |
|---|
| 458 | vec mean() const {return ( high-low ) /2.0;} |
|---|
| 459 | vec variance() const {return ( pow ( high,2 ) +pow ( low,2 ) +elem_mult ( high,low ) ) /3.0;} |
|---|
| 460 | }; |
|---|
| 461 | |
|---|
| 462 | |
|---|
| 463 | /*! |
|---|
| 464 | \brief Normal distributed linear function with linear function of mean value; |
|---|
| 465 | |
|---|
| 466 | Mean value \f$mu=A*rvc+mu_0\f$. |
|---|
| 467 | */ |
|---|
| 468 | template<class sq_T> |
|---|
| 469 | class mlnorm : public mEF |
|---|
| 470 | { |
|---|
| 471 | protected: |
|---|
| 472 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 473 | enorm<sq_T> epdf; |
|---|
| 474 | mat A; |
|---|
| 475 | vec mu_const; |
|---|
| 476 | vec& _mu; //cached epdf.mu; |
|---|
| 477 | public: |
|---|
| 478 | //! \name Constructors |
|---|
| 479 | //!@{ |
|---|
| 480 | mlnorm ( ) :mEF (),epdf ( ),A ( ),_mu ( epdf._mu() ) {ep =&epdf; }; |
|---|
| 481 | mlnorm ( const mat &A, const vec &mu0, const sq_T &R ) :epdf ( ),_mu ( epdf._mu() ) |
|---|
| 482 | { |
|---|
| 483 | ep =&epdf; set_parameters ( A,mu0,R ); |
|---|
| 484 | }; |
|---|
| 485 | //! Set \c A and \c R |
|---|
| 486 | void set_parameters ( const mat &A, const vec &mu0, const sq_T &R ); |
|---|
| 487 | //!@} |
|---|
| 488 | //! Set value of \c rvc . Result of this operation is stored in \c epdf use function \c _ep to access it. |
|---|
| 489 | void condition ( const vec &cond ); |
|---|
| 490 | |
|---|
| 491 | //!access function |
|---|
| 492 | vec& _mu_const() {return mu_const;} |
|---|
| 493 | //!access function |
|---|
| 494 | mat& _A() {return A;} |
|---|
| 495 | //!access function |
|---|
| 496 | mat _R() {return epdf._R().to_mat();} |
|---|
| 497 | |
|---|
| 498 | template<class sq_M> |
|---|
| 499 | friend std::ostream &operator<< ( std::ostream &os, mlnorm<sq_M> &ml ); |
|---|
| 500 | }; |
|---|
| 501 | |
|---|
| 502 | //! Mpdf with general function for mean value |
|---|
| 503 | template<class sq_T> |
|---|
| 504 | class mgnorm : public mEF |
|---|
| 505 | { |
|---|
| 506 | protected: |
|---|
| 507 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 508 | enorm<sq_T> epdf; |
|---|
| 509 | vec μ |
|---|
| 510 | fnc* g; |
|---|
| 511 | public: |
|---|
| 512 | //!default constructor |
|---|
| 513 | mgnorm() :mu ( epdf._mu() ) {ep=&epdf;} |
|---|
| 514 | //!set mean function |
|---|
| 515 | void set_parameters ( fnc* g0, const sq_T &R0 ) {g=g0; epdf.set_parameters ( zeros ( g->dimension() ), R0 );} |
|---|
| 516 | void condition ( const vec &cond ) {mu=g->eval ( cond );}; |
|---|
| 517 | |
|---|
| 518 | |
|---|
| 519 | /*! UI for mgnorm |
|---|
| 520 | |
|---|
| 521 | The mgnorm is constructed from a structure with fields: |
|---|
| 522 | \code |
|---|
| 523 | system = { |
|---|
| 524 | type = "mgnorm"; |
|---|
| 525 | // function for mean value evolution |
|---|
| 526 | g = {type="fnc"; ... } |
|---|
| 527 | |
|---|
| 528 | // variance |
|---|
| 529 | R = [1, 0, |
|---|
| 530 | 0, 1]; |
|---|
| 531 | // --OR -- |
|---|
| 532 | dR = [1, 1]; |
|---|
| 533 | |
|---|
| 534 | // == OPTIONAL == |
|---|
| 535 | |
|---|
| 536 | // description of y variables |
|---|
| 537 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 538 | // description of u variable |
|---|
| 539 | u = {type="rv"; names=[];} |
|---|
| 540 | }; |
|---|
| 541 | \endcode |
|---|
| 542 | |
|---|
| 543 | Result if |
|---|
| 544 | */ |
|---|
| 545 | |
|---|
| 546 | void from_setting( const Setting &root ) |
|---|
| 547 | { |
|---|
| 548 | fnc* g = UI::build<fnc>( root, "g" ); |
|---|
| 549 | |
|---|
| 550 | mat R; |
|---|
| 551 | if ( root.exists( "dR" ) ) |
|---|
| 552 | { |
|---|
| 553 | vec dR; |
|---|
| 554 | UI::get( dR, root, "dR" ); |
|---|
| 555 | R=diag(dR); |
|---|
| 556 | } |
|---|
| 557 | else |
|---|
| 558 | UI::get( R, root, "R"); |
|---|
| 559 | |
|---|
| 560 | set_parameters(g,R); |
|---|
| 561 | } |
|---|
| 562 | |
|---|
| 563 | /*void mgnorm::to_setting( Setting &root ) const |
|---|
| 564 | { |
|---|
| 565 | Transport::to_setting( root ); |
|---|
| 566 | |
|---|
| 567 | Setting &kilometers_setting = root.add("kilometers", Setting::TypeInt ); |
|---|
| 568 | kilometers_setting = kilometers; |
|---|
| 569 | |
|---|
| 570 | UI::save( passengers, root, "passengers" ); |
|---|
| 571 | }*/ |
|---|
| 572 | |
|---|
| 573 | }; |
|---|
| 574 | |
|---|
| 575 | UIREGISTER(mgnorm<chmat>); |
|---|
| 576 | |
|---|
| 577 | |
|---|
| 578 | /*! (Approximate) Student t density with linear function of mean value |
|---|
| 579 | |
|---|
| 580 | The internal epdf of this class is of the type of a Gaussian (enorm). |
|---|
| 581 | However, each conditioning is trying to assure the best possible approximation by taking into account the zeta function. See [] for reference. |
|---|
| 582 | |
|---|
| 583 | Perhaps a moment-matching technique? |
|---|
| 584 | */ |
|---|
| 585 | class mlstudent : public mlnorm<ldmat> |
|---|
| 586 | { |
|---|
| 587 | protected: |
|---|
| 588 | ldmat Lambda; |
|---|
| 589 | ldmat &_R; |
|---|
| 590 | ldmat Re; |
|---|
| 591 | public: |
|---|
| 592 | mlstudent ( ) :mlnorm<ldmat> (), |
|---|
| 593 | Lambda (), _R ( epdf._R() ) {} |
|---|
| 594 | void set_parameters ( const mat &A0, const vec &mu0, const ldmat &R0, const ldmat& Lambda0 ) |
|---|
| 595 | { |
|---|
| 596 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
|---|
| 597 | it_assert_debug ( R0.rows() ==A0.rows(),"" ); |
|---|
| 598 | |
|---|
| 599 | epdf.set_parameters ( mu0,Lambda ); // |
|---|
| 600 | A = A0; |
|---|
| 601 | mu_const = mu0; |
|---|
| 602 | Re=R0; |
|---|
| 603 | Lambda = Lambda0; |
|---|
| 604 | } |
|---|
| 605 | void condition ( const vec &cond ) |
|---|
| 606 | { |
|---|
| 607 | _mu = A*cond + mu_const; |
|---|
| 608 | double zeta; |
|---|
| 609 | //ugly hack! |
|---|
| 610 | if ( ( cond.length() +1 ) ==Lambda.rows() ) |
|---|
| 611 | { |
|---|
| 612 | zeta = Lambda.invqform ( concat ( cond, vec_1 ( 1.0 ) ) ); |
|---|
| 613 | } |
|---|
| 614 | else |
|---|
| 615 | { |
|---|
| 616 | zeta = Lambda.invqform ( cond ); |
|---|
| 617 | } |
|---|
| 618 | _R = Re; |
|---|
| 619 | _R*= ( 1+zeta );// / ( nu ); << nu is in Re!!!!!! |
|---|
| 620 | }; |
|---|
| 621 | |
|---|
| 622 | }; |
|---|
| 623 | /*! |
|---|
| 624 | \brief Gamma random walk |
|---|
| 625 | |
|---|
| 626 | Mean value, \f$\mu\f$, of this density is given by \c rvc . |
|---|
| 627 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 628 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 629 | |
|---|
| 630 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 631 | */ |
|---|
| 632 | class mgamma : public mEF |
|---|
| 633 | { |
|---|
| 634 | protected: |
|---|
| 635 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 636 | egamma epdf; |
|---|
| 637 | //! Constant \f$k\f$ |
|---|
| 638 | double k; |
|---|
| 639 | //! cache of epdf.beta |
|---|
| 640 | vec &_beta; |
|---|
| 641 | |
|---|
| 642 | public: |
|---|
| 643 | //! Constructor |
|---|
| 644 | mgamma ( ) : mEF ( ), epdf (), _beta ( epdf._beta() ) {ep=&epdf;}; |
|---|
| 645 | //! Set value of \c k |
|---|
| 646 | void set_parameters ( double k, const vec &beta0 ); |
|---|
| 647 | void condition ( const vec &val ) {_beta=k/val;}; |
|---|
| 648 | }; |
|---|
| 649 | |
|---|
| 650 | /*! |
|---|
| 651 | \brief Inverse-Gamma random walk |
|---|
| 652 | |
|---|
| 653 | Mean value, \f$ \mu \f$, of this density is given by \c rvc . |
|---|
| 654 | Standard deviation of the random walk is proportional to one \f$ k \f$-th the mean. |
|---|
| 655 | This is achieved by setting \f$ \alpha=\mu/k^2+2 \f$ and \f$ \beta=\mu(\alpha-1)\f$. |
|---|
| 656 | |
|---|
| 657 | The standard deviation of the walk is then: \f$ \mu/\sqrt(k)\f$. |
|---|
| 658 | */ |
|---|
| 659 | class migamma : public mEF |
|---|
| 660 | { |
|---|
| 661 | protected: |
|---|
| 662 | //! Internal epdf that arise by conditioning on \c rvc |
|---|
| 663 | eigamma epdf; |
|---|
| 664 | //! Constant \f$k\f$ |
|---|
| 665 | double k; |
|---|
| 666 | //! cache of epdf.alpha |
|---|
| 667 | vec &_alpha; |
|---|
| 668 | //! cache of epdf.beta |
|---|
| 669 | vec &_beta; |
|---|
| 670 | |
|---|
| 671 | public: |
|---|
| 672 | //! \name Constructors |
|---|
| 673 | //!@{ |
|---|
| 674 | migamma ( ) : mEF (), epdf ( ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;}; |
|---|
| 675 | migamma ( const migamma &m ) : mEF (), epdf ( m.epdf ), _alpha ( epdf._alpha() ), _beta ( epdf._beta() ) {ep=&epdf;}; |
|---|
| 676 | //!@} |
|---|
| 677 | |
|---|
| 678 | //! Set value of \c k |
|---|
| 679 | void set_parameters ( int len, double k0 ) |
|---|
| 680 | { |
|---|
| 681 | k=k0; |
|---|
| 682 | epdf.set_parameters ( ( 1.0/ ( k*k ) +2.0 ) *ones ( len ) /*alpha*/, ones ( len ) /*beta*/ ); |
|---|
| 683 | dimc = dimension(); |
|---|
| 684 | }; |
|---|
| 685 | void condition ( const vec &val ) |
|---|
| 686 | { |
|---|
| 687 | _beta=elem_mult ( val, ( _alpha-1.0 ) ); |
|---|
| 688 | }; |
|---|
| 689 | }; |
|---|
| 690 | |
|---|
| 691 | |
|---|
| 692 | /*! |
|---|
| 693 | \brief Gamma random walk around a fixed point |
|---|
| 694 | |
|---|
| 695 | Mean value, \f$\mu\f$, of this density is given by a geometric combination of \c rvc and given fixed point, \f$p\f$. \f$l\f$ is the coefficient of the geometric combimation |
|---|
| 696 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
|---|
| 697 | |
|---|
| 698 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 699 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 700 | |
|---|
| 701 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 702 | */ |
|---|
| 703 | class mgamma_fix : public mgamma |
|---|
| 704 | { |
|---|
| 705 | protected: |
|---|
| 706 | //! parameter l |
|---|
| 707 | double l; |
|---|
| 708 | //! reference vector |
|---|
| 709 | vec refl; |
|---|
| 710 | public: |
|---|
| 711 | //! Constructor |
|---|
| 712 | mgamma_fix ( ) : mgamma ( ),refl () {}; |
|---|
| 713 | //! Set value of \c k |
|---|
| 714 | void set_parameters ( double k0 , vec ref0, double l0 ) |
|---|
| 715 | { |
|---|
| 716 | mgamma::set_parameters ( k0, ref0 ); |
|---|
| 717 | refl=pow ( ref0,1.0-l0 );l=l0; |
|---|
| 718 | dimc=dimension(); |
|---|
| 719 | }; |
|---|
| 720 | |
|---|
| 721 | void condition ( const vec &val ) {vec mean=elem_mult ( refl,pow ( val,l ) ); _beta=k/mean;}; |
|---|
| 722 | }; |
|---|
| 723 | |
|---|
| 724 | |
|---|
| 725 | /*! |
|---|
| 726 | \brief Inverse-Gamma random walk around a fixed point |
|---|
| 727 | |
|---|
| 728 | Mean value, \f$\mu\f$, of this density is given by a geometric combination of \c rvc and given fixed point, \f$p\f$. \f$l\f$ is the coefficient of the geometric combimation |
|---|
| 729 | \f[ \mu = \mu_{t-1} ^{l} p^{1-l}\f] |
|---|
| 730 | |
|---|
| 731 | ==== Check == vv = |
|---|
| 732 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 733 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 734 | |
|---|
| 735 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 736 | */ |
|---|
| 737 | class migamma_ref : public migamma |
|---|
| 738 | { |
|---|
| 739 | protected: |
|---|
| 740 | //! parameter l |
|---|
| 741 | double l; |
|---|
| 742 | //! reference vector |
|---|
| 743 | vec refl; |
|---|
| 744 | public: |
|---|
| 745 | //! Constructor |
|---|
| 746 | migamma_ref ( ) : migamma (),refl ( ) {}; |
|---|
| 747 | //! Set value of \c k |
|---|
| 748 | void set_parameters ( double k0 , vec ref0, double l0 ) |
|---|
| 749 | { |
|---|
| 750 | migamma::set_parameters ( ref0.length(), k0 ); |
|---|
| 751 | refl=pow ( ref0,1.0-l0 ); |
|---|
| 752 | l=l0; |
|---|
| 753 | dimc = dimension(); |
|---|
| 754 | }; |
|---|
| 755 | |
|---|
| 756 | void condition ( const vec &val ) |
|---|
| 757 | { |
|---|
| 758 | vec mean=elem_mult ( refl,pow ( val,l ) ); |
|---|
| 759 | migamma::condition ( mean ); |
|---|
| 760 | }; |
|---|
| 761 | |
|---|
| 762 | /*! UI for migamma_ref |
|---|
| 763 | |
|---|
| 764 | The migamma_ref is constructed from a structure with fields: |
|---|
| 765 | \code |
|---|
| 766 | system = { |
|---|
| 767 | type = "migamma_ref"; |
|---|
| 768 | ref = [1e-5; 1e-5; 1e-2 1e-3]; // reference vector |
|---|
| 769 | l = 0.999; // constant l |
|---|
| 770 | k = 0.1; // constant k |
|---|
| 771 | |
|---|
| 772 | // == OPTIONAL == |
|---|
| 773 | // description of y variables |
|---|
| 774 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 775 | // description of u variable |
|---|
| 776 | u = {type="rv"; names=[];} |
|---|
| 777 | }; |
|---|
| 778 | \endcode |
|---|
| 779 | |
|---|
| 780 | Result if |
|---|
| 781 | */ |
|---|
| 782 | void from_setting( const Setting &root ); |
|---|
| 783 | |
|---|
| 784 | // TODO dodelat void to_setting( Setting &root ) const; |
|---|
| 785 | }; |
|---|
| 786 | |
|---|
| 787 | |
|---|
| 788 | UIREGISTER(migamma_ref); |
|---|
| 789 | |
|---|
| 790 | /*! Log-Normal probability density |
|---|
| 791 | only allow diagonal covariances! |
|---|
| 792 | |
|---|
| 793 | Density of the form \f$ \log(x)\sim \mathcal{N}(\mu,\sigma^2), i.e. |
|---|
| 794 | \f[ |
|---|
| 795 | x \sim \frac{1}{x\sigma\sqrt{2\pi}}\exp{-\frac{1}{2\sigma^2}(\log(x)-\mu)} |
|---|
| 796 | \f] |
|---|
| 797 | |
|---|
| 798 | */ |
|---|
| 799 | class elognorm: public enorm<ldmat> |
|---|
| 800 | { |
|---|
| 801 | public: |
|---|
| 802 | vec sample() const {return exp ( enorm<ldmat>::sample() );}; |
|---|
| 803 | vec mean() const {vec var=enorm<ldmat>::variance();return exp ( mu - 0.5*var );}; |
|---|
| 804 | |
|---|
| 805 | }; |
|---|
| 806 | |
|---|
| 807 | /*! |
|---|
| 808 | \brief Log-Normal random walk |
|---|
| 809 | |
|---|
| 810 | Mean value, \f$\mu\f$, is... |
|---|
| 811 | |
|---|
| 812 | ==== Check == vv = |
|---|
| 813 | Standard deviation of the random walk is proportional to one \f$k\f$-th the mean. |
|---|
| 814 | This is achieved by setting \f$\alpha=k\f$ and \f$\beta=k/\mu\f$. |
|---|
| 815 | |
|---|
| 816 | The standard deviation of the walk is then: \f$\mu/\sqrt(k)\f$. |
|---|
| 817 | */ |
|---|
| 818 | class mlognorm : public mpdf |
|---|
| 819 | { |
|---|
| 820 | protected: |
|---|
| 821 | elognorm eno; |
|---|
| 822 | //! parameter 1/2*sigma^2 |
|---|
| 823 | double sig2; |
|---|
| 824 | //! access |
|---|
| 825 | vec μ |
|---|
| 826 | public: |
|---|
| 827 | //! Constructor |
|---|
| 828 | mlognorm ( ) : eno (), mu ( eno._mu() ) {ep=&eno;}; |
|---|
| 829 | //! Set value of \c k |
|---|
| 830 | void set_parameters ( int size, double k ) |
|---|
| 831 | { |
|---|
| 832 | sig2 = 0.5*log ( k*k+1 ); |
|---|
| 833 | eno.set_parameters ( zeros ( size ),2*sig2*eye ( size ) ); |
|---|
| 834 | |
|---|
| 835 | dimc = size; |
|---|
| 836 | }; |
|---|
| 837 | |
|---|
| 838 | void condition ( const vec &val ) |
|---|
| 839 | { |
|---|
| 840 | mu=log ( val )-sig2;//elem_mult ( refl,pow ( val,l ) ); |
|---|
| 841 | }; |
|---|
| 842 | |
|---|
| 843 | /*! UI for mlognorm |
|---|
| 844 | |
|---|
| 845 | The mlognorm is constructed from a structure with fields: |
|---|
| 846 | \code |
|---|
| 847 | system = { |
|---|
| 848 | type = "mlognorm"; |
|---|
| 849 | k = 0.1; // constant k |
|---|
| 850 | mu0 = [1., 1.]; |
|---|
| 851 | |
|---|
| 852 | // == OPTIONAL == |
|---|
| 853 | // description of y variables |
|---|
| 854 | y = {type="rv"; names=["y", "u"];}; |
|---|
| 855 | // description of u variable |
|---|
| 856 | u = {type="rv"; names=[];} |
|---|
| 857 | }; |
|---|
| 858 | \endcode |
|---|
| 859 | |
|---|
| 860 | */ |
|---|
| 861 | void from_setting( const Setting &root ); |
|---|
| 862 | |
|---|
| 863 | // TODO dodelat void to_setting( Setting &root ) const; |
|---|
| 864 | |
|---|
| 865 | }; |
|---|
| 866 | |
|---|
| 867 | UIREGISTER(mlognorm); |
|---|
| 868 | |
|---|
| 869 | /*! inverse Wishart density defined on Choleski decomposition |
|---|
| 870 | |
|---|
| 871 | */ |
|---|
| 872 | class eWishartCh : public epdf |
|---|
| 873 | { |
|---|
| 874 | protected: |
|---|
| 875 | //! Upper-Triagle of Choleski decomposition of \f$ \Psi \f$ |
|---|
| 876 | chmat Y; |
|---|
| 877 | //! dimension of matrix \f$ \Psi \f$ |
|---|
| 878 | int p; |
|---|
| 879 | //! degrees of freedom \f$ \nu \f$ |
|---|
| 880 | double delta; |
|---|
| 881 | public: |
|---|
| 882 | void set_parameters ( const mat &Y0, const double delta0 ) {Y=chmat ( Y0 );delta=delta0; p=Y.rows(); dim = p*p; } |
|---|
| 883 | mat sample_mat() const |
|---|
| 884 | { |
|---|
| 885 | mat X=zeros ( p,p ); |
|---|
| 886 | |
|---|
| 887 | //sample diagonal |
|---|
| 888 | for ( int i=0;i<p;i++ ) |
|---|
| 889 | { |
|---|
| 890 | GamRNG.setup ( 0.5* ( delta-i ) , 0.5 ); // no +1 !! index if from 0 |
|---|
| 891 | #pragma omp critical |
|---|
| 892 | X ( i,i ) =sqrt ( GamRNG() ); |
|---|
| 893 | } |
|---|
| 894 | //do the rest |
|---|
| 895 | for ( int i=0;i<p;i++ ) |
|---|
| 896 | { |
|---|
| 897 | for ( int j=i+1;j<p;j++ ) |
|---|
| 898 | { |
|---|
| 899 | #pragma omp critical |
|---|
| 900 | X ( i,j ) =NorRNG.sample(); |
|---|
| 901 | } |
|---|
| 902 | } |
|---|
| 903 | return X*Y._Ch();// return upper triangular part of the decomposition |
|---|
| 904 | } |
|---|
| 905 | vec sample () const |
|---|
| 906 | { |
|---|
| 907 | return vec ( sample_mat()._data(),p*p ); |
|---|
| 908 | } |
|---|
| 909 | //! fast access function y0 will be copied into Y.Ch. |
|---|
| 910 | void setY ( const mat &Ch0 ) {copy_vector ( dim,Ch0._data(), Y._Ch()._data() );} |
|---|
| 911 | //! fast access function y0 will be copied into Y.Ch. |
|---|
| 912 | void _setY ( const vec &ch0 ) {copy_vector ( dim, ch0._data(), Y._Ch()._data() ); } |
|---|
| 913 | //! access function |
|---|
| 914 | const chmat& getY()const {return Y;} |
|---|
| 915 | }; |
|---|
| 916 | |
|---|
| 917 | class eiWishartCh: public epdf |
|---|
| 918 | { |
|---|
| 919 | protected: |
|---|
| 920 | eWishartCh W; |
|---|
| 921 | int p; |
|---|
| 922 | double delta; |
|---|
| 923 | public: |
|---|
| 924 | void set_parameters ( const mat &Y0, const double delta0) { |
|---|
| 925 | delta = delta0; |
|---|
| 926 | W.set_parameters ( inv ( Y0 ),delta0 ); |
|---|
| 927 | dim = W.dimension(); p=Y0.rows(); |
|---|
| 928 | } |
|---|
| 929 | vec sample() const {mat iCh; iCh=inv ( W.sample_mat() ); return vec ( iCh._data(),dim );} |
|---|
| 930 | void _setY ( const vec &y0 ) |
|---|
| 931 | { |
|---|
| 932 | mat Ch ( p,p ); |
|---|
| 933 | mat iCh ( p,p ); |
|---|
| 934 | copy_vector ( dim, y0._data(), Ch._data() ); |
|---|
| 935 | |
|---|
| 936 | iCh=inv ( Ch ); |
|---|
| 937 | W.setY ( iCh ); |
|---|
| 938 | } |
|---|
| 939 | virtual double evallog ( const vec &val ) const { |
|---|
| 940 | chmat X(p); |
|---|
| 941 | const chmat& Y=W.getY(); |
|---|
| 942 | |
|---|
| 943 | copy_vector(p*p,val._data(),X._Ch()._data()); |
|---|
| 944 | chmat iX(p);X.inv(iX); |
|---|
| 945 | // compute |
|---|
| 946 | // \frac{ |\Psi|^{m/2}|X|^{-(m+p+1)/2}e^{-tr(\Psi X^{-1})/2} }{ 2^{mp/2}\Gamma_p(m/2)}, |
|---|
| 947 | mat M=Y.to_mat()*iX.to_mat(); |
|---|
| 948 | |
|---|
| 949 | double log1 = 0.5*p*(2*Y.logdet())-0.5*(delta+p+1)*(2*X.logdet())-0.5*trace(M); |
|---|
| 950 | //Fixme! Multivariate gamma omitted!! it is ok for sampling, but not otherwise!! |
|---|
| 951 | |
|---|
| 952 | /* if (0) { |
|---|
| 953 | mat XX=X.to_mat(); |
|---|
| 954 | mat YY=Y.to_mat(); |
|---|
| 955 | |
|---|
| 956 | double log2 = 0.5*p*log(det(YY))-0.5*(delta+p+1)*log(det(XX))-0.5*trace(YY*inv(XX)); |
|---|
| 957 | cout << log1 << "," << log2 << endl; |
|---|
| 958 | }*/ |
|---|
| 959 | return log1; |
|---|
| 960 | }; |
|---|
| 961 | |
|---|
| 962 | }; |
|---|
| 963 | |
|---|
| 964 | class rwiWishartCh : public mpdf |
|---|
| 965 | { |
|---|
| 966 | protected: |
|---|
| 967 | eiWishartCh eiW; |
|---|
| 968 | //!square root of \f$ \nu-p-1 \f$ - needed for computation of \f$ \Psi \f$ from conditions |
|---|
| 969 | double sqd; |
|---|
| 970 | //reference point for diagonal |
|---|
| 971 | vec refl; |
|---|
| 972 | double l; |
|---|
| 973 | int p; |
|---|
| 974 | public: |
|---|
| 975 | void set_parameters ( int p0, double k, vec ref0, double l0 ) |
|---|
| 976 | { |
|---|
| 977 | p=p0; |
|---|
| 978 | double delta = 2/(k*k)+p+3; |
|---|
| 979 | sqd=sqrt ( delta-p-1 ); |
|---|
| 980 | l=l0; |
|---|
| 981 | refl=pow(ref0,1-l); |
|---|
| 982 | |
|---|
| 983 | eiW.set_parameters ( eye ( p ),delta ); |
|---|
| 984 | ep=&eiW; |
|---|
| 985 | dimc=eiW.dimension(); |
|---|
| 986 | } |
|---|
| 987 | void condition ( const vec &c ) { |
|---|
| 988 | vec z=c; |
|---|
| 989 | int ri=0; |
|---|
| 990 | for(int i=0;i<p*p;i+=(p+1)){//trace diagonal element |
|---|
| 991 | z(i) = pow(z(i),l)*refl(ri); |
|---|
| 992 | ri++; |
|---|
| 993 | } |
|---|
| 994 | |
|---|
| 995 | eiW._setY ( sqd*z ); |
|---|
| 996 | } |
|---|
| 997 | }; |
|---|
| 998 | |
|---|
| 999 | //! Switch between various resampling methods. |
|---|
| 1000 | enum RESAMPLING_METHOD { MULTINOMIAL = 0, STRATIFIED = 1, SYSTEMATIC = 3 }; |
|---|
| 1001 | /*! |
|---|
| 1002 | \brief Weighted empirical density |
|---|
| 1003 | |
|---|
| 1004 | Used e.g. in particle filters. |
|---|
| 1005 | */ |
|---|
| 1006 | class eEmp: public epdf |
|---|
| 1007 | { |
|---|
| 1008 | protected : |
|---|
| 1009 | //! Number of particles |
|---|
| 1010 | int n; |
|---|
| 1011 | //! Sample weights \f$w\f$ |
|---|
| 1012 | vec w; |
|---|
| 1013 | //! Samples \f$x^{(i)}, i=1..n\f$ |
|---|
| 1014 | Array<vec> samples; |
|---|
| 1015 | public: |
|---|
| 1016 | //! \name Constructors |
|---|
| 1017 | //!@{ |
|---|
| 1018 | eEmp ( ) :epdf ( ),w ( ),samples ( ) {}; |
|---|
| 1019 | eEmp ( const eEmp &e ) : epdf ( e ), w ( e.w ), samples ( e.samples ) {}; |
|---|
| 1020 | //!@} |
|---|
| 1021 | |
|---|
| 1022 | //! Set samples and weights |
|---|
| 1023 | void set_statistics ( const vec &w0, const epdf* pdf0 ); |
|---|
| 1024 | //! Set samples and weights |
|---|
| 1025 | void set_statistics ( const epdf* pdf0 , int n ) {set_statistics ( ones ( n ) /n,pdf0 );}; |
|---|
| 1026 | //! Set sample |
|---|
| 1027 | void set_samples ( const epdf* pdf0 ); |
|---|
| 1028 | //! Set sample |
|---|
| 1029 | void set_parameters ( int n0, bool copy=true ) {n=n0; w.set_size ( n0,copy );samples.set_size ( n0,copy );}; |
|---|
| 1030 | //! Potentially dangerous, use with care. |
|---|
| 1031 | vec& _w() {return w;}; |
|---|
| 1032 | //! Potentially dangerous, use with care. |
|---|
| 1033 | const vec& _w() const {return w;}; |
|---|
| 1034 | //! access function |
|---|
| 1035 | Array<vec>& _samples() {return samples;}; |
|---|
| 1036 | //! access function |
|---|
| 1037 | const Array<vec>& _samples() const {return samples;}; |
|---|
| 1038 | //! Function performs resampling, i.e. removal of low-weight samples and duplication of high-weight samples such that the new samples represent the same density. |
|---|
| 1039 | ivec resample ( RESAMPLING_METHOD method=SYSTEMATIC ); |
|---|
| 1040 | //! inherited operation : NOT implemneted |
|---|
| 1041 | vec sample() const {it_error ( "Not implemented" );return 0;} |
|---|
| 1042 | //! inherited operation : NOT implemneted |
|---|
| 1043 | double evallog ( const vec &val ) const {it_error ( "Not implemented" );return 0.0;} |
|---|
| 1044 | vec mean() const |
|---|
| 1045 | { |
|---|
| 1046 | vec pom=zeros ( dim ); |
|---|
| 1047 | for ( int i=0;i<n;i++ ) {pom+=samples ( i ) *w ( i );} |
|---|
| 1048 | return pom; |
|---|
| 1049 | } |
|---|
| 1050 | vec variance() const |
|---|
| 1051 | { |
|---|
| 1052 | vec pom=zeros ( dim ); |
|---|
| 1053 | for ( int i=0;i<n;i++ ) {pom+=pow ( samples ( i ),2 ) *w ( i );} |
|---|
| 1054 | return pom-pow ( mean(),2 ); |
|---|
| 1055 | } |
|---|
| 1056 | //! For this class, qbounds are minimum and maximum value of the population! |
|---|
| 1057 | void qbounds ( vec &lb, vec &ub, double perc=0.95 ) const |
|---|
| 1058 | { |
|---|
| 1059 | // lb in inf so than it will be pushed below; |
|---|
| 1060 | lb.set_size ( dim ); |
|---|
| 1061 | ub.set_size ( dim ); |
|---|
| 1062 | lb = std::numeric_limits<double>::infinity(); |
|---|
| 1063 | ub = -std::numeric_limits<double>::infinity(); |
|---|
| 1064 | int j; |
|---|
| 1065 | for ( int i=0;i<n;i++ ) |
|---|
| 1066 | { |
|---|
| 1067 | for ( j=0;j<dim; j++ ) |
|---|
| 1068 | { |
|---|
| 1069 | if ( samples ( i ) ( j ) <lb ( j ) ) {lb ( j ) =samples ( i ) ( j );} |
|---|
| 1070 | if ( samples ( i ) ( j ) >ub ( j ) ) {ub ( j ) =samples ( i ) ( j );} |
|---|
| 1071 | } |
|---|
| 1072 | } |
|---|
| 1073 | } |
|---|
| 1074 | }; |
|---|
| 1075 | |
|---|
| 1076 | |
|---|
| 1077 | //////////////////////// |
|---|
| 1078 | |
|---|
| 1079 | template<class sq_T> |
|---|
| 1080 | void enorm<sq_T>::set_parameters ( const vec &mu0, const sq_T &R0 ) |
|---|
| 1081 | { |
|---|
| 1082 | //Fixme test dimensions of mu0 and R0; |
|---|
| 1083 | mu = mu0; |
|---|
| 1084 | R = R0; |
|---|
| 1085 | dim = mu0.length(); |
|---|
| 1086 | }; |
|---|
| 1087 | |
|---|
| 1088 | template<class sq_T> |
|---|
| 1089 | void enorm<sq_T>::dupdate ( mat &v, double nu ) |
|---|
| 1090 | { |
|---|
| 1091 | // |
|---|
| 1092 | }; |
|---|
| 1093 | |
|---|
| 1094 | // template<class sq_T> |
|---|
| 1095 | // void enorm<sq_T>::tupdate ( double phi, mat &vbar, double nubar ) { |
|---|
| 1096 | // // |
|---|
| 1097 | // }; |
|---|
| 1098 | |
|---|
| 1099 | template<class sq_T> |
|---|
| 1100 | vec enorm<sq_T>::sample() const |
|---|
| 1101 | { |
|---|
| 1102 | vec x ( dim ); |
|---|
| 1103 | #pragma omp critical |
|---|
| 1104 | NorRNG.sample_vector ( dim,x ); |
|---|
| 1105 | vec smp = R.sqrt_mult ( x ); |
|---|
| 1106 | |
|---|
| 1107 | smp += mu; |
|---|
| 1108 | return smp; |
|---|
| 1109 | }; |
|---|
| 1110 | |
|---|
| 1111 | template<class sq_T> |
|---|
| 1112 | mat enorm<sq_T>::sample ( int N ) const |
|---|
| 1113 | { |
|---|
| 1114 | mat X ( dim,N ); |
|---|
| 1115 | vec x ( dim ); |
|---|
| 1116 | vec pom; |
|---|
| 1117 | int i; |
|---|
| 1118 | |
|---|
| 1119 | for ( i=0;i<N;i++ ) |
|---|
| 1120 | { |
|---|
| 1121 | #pragma omp critical |
|---|
| 1122 | NorRNG.sample_vector ( dim,x ); |
|---|
| 1123 | pom = R.sqrt_mult ( x ); |
|---|
| 1124 | pom +=mu; |
|---|
| 1125 | X.set_col ( i, pom ); |
|---|
| 1126 | } |
|---|
| 1127 | |
|---|
| 1128 | return X; |
|---|
| 1129 | }; |
|---|
| 1130 | |
|---|
| 1131 | // template<class sq_T> |
|---|
| 1132 | // double enorm<sq_T>::eval ( const vec &val ) const { |
|---|
| 1133 | // double pdfl,e; |
|---|
| 1134 | // pdfl = evallog ( val ); |
|---|
| 1135 | // e = exp ( pdfl ); |
|---|
| 1136 | // return e; |
|---|
| 1137 | // }; |
|---|
| 1138 | |
|---|
| 1139 | template<class sq_T> |
|---|
| 1140 | double enorm<sq_T>::evallog_nn ( const vec &val ) const |
|---|
| 1141 | { |
|---|
| 1142 | // 1.83787706640935 = log(2pi) |
|---|
| 1143 | double tmp=-0.5* ( R.invqform ( mu-val ) );// - lognc(); |
|---|
| 1144 | return tmp; |
|---|
| 1145 | }; |
|---|
| 1146 | |
|---|
| 1147 | template<class sq_T> |
|---|
| 1148 | inline double enorm<sq_T>::lognc () const |
|---|
| 1149 | { |
|---|
| 1150 | // 1.83787706640935 = log(2pi) |
|---|
| 1151 | double tmp=0.5* ( R.cols() * 1.83787706640935 +R.logdet() ); |
|---|
| 1152 | return tmp; |
|---|
| 1153 | }; |
|---|
| 1154 | |
|---|
| 1155 | template<class sq_T> |
|---|
| 1156 | void mlnorm<sq_T>::set_parameters ( const mat &A0, const vec &mu0, const sq_T &R0 ) |
|---|
| 1157 | { |
|---|
| 1158 | it_assert_debug ( A0.rows() ==mu0.length(),"" ); |
|---|
| 1159 | it_assert_debug ( A0.rows() ==R0.rows(),"" ); |
|---|
| 1160 | |
|---|
| 1161 | epdf.set_parameters ( zeros ( A0.rows() ),R0 ); |
|---|
| 1162 | A = A0; |
|---|
| 1163 | mu_const = mu0; |
|---|
| 1164 | dimc=A0.cols(); |
|---|
| 1165 | } |
|---|
| 1166 | |
|---|
| 1167 | // template<class sq_T> |
|---|
| 1168 | // vec mlnorm<sq_T>::samplecond (const vec &cond, double &lik ) { |
|---|
| 1169 | // this->condition ( cond ); |
|---|
| 1170 | // vec smp = epdf.sample(); |
|---|
| 1171 | // lik = epdf.eval ( smp ); |
|---|
| 1172 | // return smp; |
|---|
| 1173 | // } |
|---|
| 1174 | |
|---|
| 1175 | // template<class sq_T> |
|---|
| 1176 | // mat mlnorm<sq_T>::samplecond (const vec &cond, vec &lik, int n ) { |
|---|
| 1177 | // int i; |
|---|
| 1178 | // int dim = rv.count(); |
|---|
| 1179 | // mat Smp ( dim,n ); |
|---|
| 1180 | // vec smp ( dim ); |
|---|
| 1181 | // this->condition ( cond ); |
|---|
| 1182 | // |
|---|
| 1183 | // for ( i=0; i<n; i++ ) { |
|---|
| 1184 | // smp = epdf.sample(); |
|---|
| 1185 | // lik ( i ) = epdf.eval ( smp ); |
|---|
| 1186 | // Smp.set_col ( i ,smp ); |
|---|
| 1187 | // } |
|---|
| 1188 | // |
|---|
| 1189 | // return Smp; |
|---|
| 1190 | // } |
|---|
| 1191 | |
|---|
| 1192 | template<class sq_T> |
|---|
| 1193 | void mlnorm<sq_T>::condition ( const vec &cond ) |
|---|
| 1194 | { |
|---|
| 1195 | _mu = A*cond + mu_const; |
|---|
| 1196 | //R is already assigned; |
|---|
| 1197 | } |
|---|
| 1198 | |
|---|
| 1199 | template<class sq_T> |
|---|
| 1200 | enorm<sq_T>* enorm<sq_T>::marginal ( const RV &rvn ) const |
|---|
| 1201 | { |
|---|
| 1202 | it_assert_debug ( isnamed(), "rv description is not assigned" ); |
|---|
| 1203 | ivec irvn = rvn.dataind ( rv ); |
|---|
| 1204 | |
|---|
| 1205 | sq_T Rn ( R,irvn ); //select rows and columns of R |
|---|
| 1206 | |
|---|
| 1207 | enorm<sq_T>* tmp = new enorm<sq_T>; |
|---|
| 1208 | tmp->set_rv ( rvn ); |
|---|
| 1209 | tmp->set_parameters ( mu ( irvn ), Rn ); |
|---|
| 1210 | return tmp; |
|---|
| 1211 | } |
|---|
| 1212 | |
|---|
| 1213 | template<class sq_T> |
|---|
| 1214 | mpdf* enorm<sq_T>::condition ( const RV &rvn ) const |
|---|
| 1215 | { |
|---|
| 1216 | |
|---|
| 1217 | it_assert_debug ( isnamed(),"rvs are not assigned" ); |
|---|
| 1218 | |
|---|
| 1219 | RV rvc = rv.subt ( rvn ); |
|---|
| 1220 | it_assert_debug ( ( rvc._dsize() +rvn._dsize() ==rv._dsize() ),"wrong rvn" ); |
|---|
| 1221 | //Permutation vector of the new R |
|---|
| 1222 | ivec irvn = rvn.dataind ( rv ); |
|---|
| 1223 | ivec irvc = rvc.dataind ( rv ); |
|---|
| 1224 | ivec perm=concat ( irvn , irvc ); |
|---|
| 1225 | sq_T Rn ( R,perm ); |
|---|
| 1226 | |
|---|
| 1227 | //fixme - could this be done in general for all sq_T? |
|---|
| 1228 | mat S=Rn.to_mat(); |
|---|
| 1229 | //fixme |
|---|
| 1230 | int n=rvn._dsize()-1; |
|---|
| 1231 | int end=R.rows()-1; |
|---|
| 1232 | mat S11 = S.get ( 0,n, 0, n ); |
|---|
| 1233 | mat S12 = S.get ( 0, n , rvn._dsize(), end ); |
|---|
| 1234 | mat S22 = S.get ( rvn._dsize(), end, rvn._dsize(), end ); |
|---|
| 1235 | |
|---|
| 1236 | vec mu1 = mu ( irvn ); |
|---|
| 1237 | vec mu2 = mu ( irvc ); |
|---|
| 1238 | mat A=S12*inv ( S22 ); |
|---|
| 1239 | sq_T R_n ( S11 - A *S12.T() ); |
|---|
| 1240 | |
|---|
| 1241 | mlnorm<sq_T>* tmp=new mlnorm<sq_T> ( ); |
|---|
| 1242 | tmp->set_rv ( rvn ); tmp->set_rvc ( rvc ); |
|---|
| 1243 | tmp->set_parameters ( A,mu1-A*mu2,R_n ); |
|---|
| 1244 | return tmp; |
|---|
| 1245 | } |
|---|
| 1246 | |
|---|
| 1247 | /////////// |
|---|
| 1248 | |
|---|
| 1249 | template<class sq_T> |
|---|
| 1250 | std::ostream &operator<< ( std::ostream &os, mlnorm<sq_T> &ml ) |
|---|
| 1251 | { |
|---|
| 1252 | os << "A:"<< ml.A<<endl; |
|---|
| 1253 | os << "mu:"<< ml.mu_const<<endl; |
|---|
| 1254 | os << "R:" << ml.epdf._R().to_mat() <<endl; |
|---|
| 1255 | return os; |
|---|
| 1256 | }; |
|---|
| 1257 | |
|---|
| 1258 | } |
|---|
| 1259 | #endif //EF_H |
|---|
