{"id":116324,"date":"2026-10-21T07:25:16","date_gmt":"2026-10-20T23:25:16","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/116324.html"},"modified":"2026-10-21T07:25:16","modified_gmt":"2026-10-20T23:25:16","slug":"c%e4%bb%a3%e7%a0%81%e5%ae%9e%e7%8e%b0matlab%e4%b8%ad%e7%9a%84hdphmm%e5%87%bd%e6%95%b0%e5%8a%9f%e8%83%bd","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/116324.html","title":{"rendered":"C++\u4ee3\u7801\u5b9e\u73b0MATLAB\u4e2d\u7684hdphmm\u51fd\u6570\u529f\u80fd"},"content":{"rendered":"

\/\/ ============================================================<\/span>
\n\/\/ HDP-HMM with Sticky Transitions (Fox et al., 2011)<\/span>
\n\/\/ \u5b8c\u5168\u81ea\u5305\u542b (\u4ec5\u4f9d\u8d56 C++ \u6807\u51c6\u5e93, \u65e0\u7b2c\u4e09\u65b9\u4f9d\u8d56)<\/span>
\n\/\/ \u7f16\u8bd1: g++ -std=c++14 -O2 HDPHMM.cpp -o hdpmm_demo<\/span>
\n\/\/ \u8fd0\u884c: .\/hdpmm_demo<\/span>
\n\/\/ ============================================================<\/span><\/p>\n

#<\/span>include<\/span> <vector><\/span><\/span>
\n#<\/span>include<\/span> <cmath><\/span><\/span>
\n#<\/span>include<\/span> <random><\/span><\/span>
\n#<\/span>include<\/span> <algorithm><\/span><\/span>
\n#<\/span>include<\/span> <iostream><\/span><\/span>
\n#<\/span>include<\/span> <iomanip><\/span><\/span>
\n#<\/span>include<\/span> <limits><\/span><\/span><\/p>\n

\/\/ ============================================================<\/span>
\n\/\/ \u7b80\u6613\u77e9\u9635\u7c7b (\u66ff\u4ee3 Eigen)<\/span>
\n\/\/ ============================================================<\/span>
\nclass<\/span> Matrix<\/span> {<\/span>
\npublic<\/span>:<\/span>
\n int<\/span> rows,<\/span> cols;<\/span>
\n std::<\/span>vector<<\/span>double<\/span>><\/span> data;<\/span><\/p>\n

Matrix<\/span>(<\/span>)<\/span> :<\/span> rows<\/span>(<\/span>0<\/span>)<\/span>,<\/span> cols<\/span>(<\/span>0<\/span>)<\/span> {<\/span>}<\/span>
\n Matrix<\/span>(<\/span>int<\/span> r,<\/span> int<\/span> c,<\/span> double<\/span> init =<\/span> 0.0<\/span>)<\/span>
\n :<\/span> rows<\/span>(<\/span>r)<\/span>,<\/span> cols<\/span>(<\/span>c)<\/span>,<\/span> data<\/span>(<\/span>(<\/span>size_t)<\/span>r *<\/span> c,<\/span> init)<\/span> {<\/span>}<\/span><\/p>\n

double<\/span>&<\/span> operator<\/span>(<\/span>)<\/span>(<\/span>int<\/span> i,<\/span> int<\/span> j)<\/span> {<\/span> return<\/span> data[<\/span>(<\/span>size_t)<\/span>i *<\/span> cols +<\/span> j]<\/span>;<\/span> }<\/span>
\n double<\/span> operator<\/span>(<\/span>)<\/span>(<\/span>int<\/span> i,<\/span> int<\/span> j)<\/span> const<\/span> {<\/span> return<\/span> data[<\/span>(<\/span>size_t)<\/span>i *<\/span> cols +<\/span> j]<\/span>;<\/span> }<\/span><\/p>\n

static<\/span> Matrix Zero<\/span>(<\/span>int<\/span> r,<\/span> int<\/span> c)<\/span> {<\/span> return<\/span> Matrix<\/span>(<\/span>r,<\/span> c,<\/span> 0.0<\/span>)<\/span>;<\/span> }<\/span>
\n static<\/span> Matrix Ones<\/span>(<\/span>int<\/span> r,<\/span> int<\/span> c)<\/span> {<\/span> return<\/span> Matrix<\/span>(<\/span>r,<\/span> c,<\/span> 1.0<\/span>)<\/span>;<\/span> }<\/span>
\n static<\/span> Matrix Constant<\/span>(<\/span>int<\/span> r,<\/span> int<\/span> c,<\/span> double<\/span> v)<\/span> {<\/span> return<\/span> Matrix<\/span>(<\/span>r,<\/span> c,<\/span> v)<\/span>;<\/span> }<\/span>
\n static<\/span> Matrix Identity<\/span>(<\/span>int<\/span> n)<\/span> {<\/span>
\n Matrix I<\/span>(<\/span>n,<\/span> n,<\/span> 0.0<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> I<\/span>(<\/span>i,<\/span> i)<\/span> =<\/span> 1.0<\/span>;<\/span>
\n return<\/span> I;<\/span>
\n }<\/span><\/p>\n

Matrix transpose<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n Matrix R<\/span>(<\/span>cols,<\/span> rows)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> rows;<\/span> ++<\/span>i)<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> cols;<\/span> ++<\/span>j)<\/span>
\n R<\/span>(<\/span>j,<\/span> i)<\/span> =<\/span> (<\/span>*<\/span>this<\/span>)<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n return<\/span> R;<\/span>
\n }<\/span><\/p>\n

Matrix operator<\/span>*<\/span>(<\/span>const<\/span> Matrix&<\/span> B)<\/span> const<\/span> {<\/span>
\n Matrix R<\/span>(<\/span>rows,<\/span> B.<\/span>cols,<\/span> 0.0<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> rows;<\/span> ++<\/span>i)<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> cols;<\/span> ++<\/span>k)<\/span> {<\/span>
\n double<\/span> a =<\/span> (<\/span>*<\/span>this<\/span>)<\/span>(<\/span>i,<\/span> k)<\/span>;<\/span>
\n if<\/span> (<\/span>a ==<\/span> 0.0<\/span>)<\/span> continue<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> B.<\/span>cols;<\/span> ++<\/span>j)<\/span>
\n R<\/span>(<\/span>i,<\/span> j)<\/span> +=<\/span> a *<\/span> B<\/span>(<\/span>k,<\/span> j)<\/span>;<\/span>
\n }<\/span>
\n return<\/span> R;<\/span>
\n }<\/span><\/p>\n

Matrix operator<\/span>+<\/span>(<\/span>const<\/span> Matrix&<\/span> B)<\/span> const<\/span> {<\/span>
\n Matrix R<\/span>(<\/span>rows,<\/span> cols)<\/span>;<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> data.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> R.<\/span>data[<\/span>i]<\/span> =<\/span> data[<\/span>i]<\/span> +<\/span> B.<\/span>data[<\/span>i]<\/span>;<\/span>
\n return<\/span> R;<\/span>
\n }<\/span>
\n Matrix operator<\/span>–<\/span>(<\/span>const<\/span> Matrix&<\/span> B)<\/span> const<\/span> {<\/span>
\n Matrix R<\/span>(<\/span>rows,<\/span> cols)<\/span>;<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> data.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> R.<\/span>data[<\/span>i]<\/span> =<\/span> data[<\/span>i]<\/span> –<\/span> B.<\/span>data[<\/span>i]<\/span>;<\/span>
\n return<\/span> R;<\/span>
\n }<\/span>
\n Matrix operator<\/span>*<\/span>(<\/span>double<\/span> s)<\/span> const<\/span> {<\/span>
\n Matrix R<\/span>(<\/span>rows,<\/span> cols)<\/span>;<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> data.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> R.<\/span>data[<\/span>i]<\/span> =<\/span> data[<\/span>i]<\/span> *<\/span> s;<\/span>
\n return<\/span> R;<\/span>
\n }<\/span>
\n Matrix operator<\/span>\/<\/span>(<\/span>double<\/span> s)<\/span> const<\/span> {<\/span> return<\/span> (<\/span>*<\/span>this<\/span>)<\/span> *<\/span> (<\/span>1.0<\/span> \/<\/span> s)<\/span>;<\/span> }<\/span>
\n Matrix&<\/span> operator<\/span>+=<\/span>(<\/span>const<\/span> Matrix&<\/span> B)<\/span> {<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> data.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span> data[<\/span>i]<\/span> +=<\/span> B.<\/span>data[<\/span>i]<\/span>;<\/span>
\n return<\/span> *<\/span>this<\/span>;<\/span>
\n }<\/span>
\n Matrix&<\/span> operator<\/span>\/=<\/span>(<\/span>double<\/span> s)<\/span> {<\/span>
\n for<\/span> (<\/span>double<\/span>&<\/span> v :<\/span> data)<\/span> v \/=<\/span> s;<\/span>
\n return<\/span> *<\/span>this<\/span>;<\/span>
\n }<\/span><\/p>\n

double<\/span> sum<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n double<\/span> s =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>double<\/span> v :<\/span> data)<\/span> s +=<\/span> v;<\/span>
\n return<\/span> s;<\/span>
\n }<\/span>
\n double<\/span> norm<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n double<\/span> s =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>double<\/span> v :<\/span> data)<\/span> s +=<\/span> v *<\/span> v;<\/span>
\n return<\/span> std::<\/span>sqrt<\/span>(<\/span>s)<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ LU \u5206\u89e3\u6c42\u884c\u5217\u5f0f<\/span>
\n double<\/span> determinant<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n int<\/span> n =<\/span> rows;<\/span>
\n Matrix M =<\/span> *<\/span>this<\/span>;<\/span>
\n double<\/span> det =<\/span> 1.0<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
\n int<\/span> pivot =<\/span> i;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> i +<\/span> 1<\/span>;<\/span> k <<\/span> n;<\/span> ++<\/span>k)<\/span>
\n if<\/span> (<\/span>std::<\/span>fabs<\/span>(<\/span>M<\/span>(<\/span>k,<\/span> i)<\/span>)<\/span> ><\/span> std::<\/span>fabs<\/span>(<\/span>M<\/span>(<\/span>pivot,<\/span> i)<\/span>)<\/span>)<\/span> pivot =<\/span> k;<\/span>
\n if<\/span> (<\/span>std::<\/span>fabs<\/span>(<\/span>M<\/span>(<\/span>pivot,<\/span> i)<\/span>)<\/span> <<\/span> 1e-12<\/span>)<\/span> return<\/span> 0.0<\/span>;<\/span>
\n if<\/span> (<\/span>pivot !=<\/span> i)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> n;<\/span> ++<\/span>j)<\/span> std::<\/span>swap<\/span>(<\/span>M<\/span>(<\/span>i,<\/span> j)<\/span>,<\/span> M<\/span>(<\/span>pivot,<\/span> j)<\/span>)<\/span>;<\/span>
\n det =<\/span> –<\/span>det;<\/span>
\n }<\/span>
\n det *=<\/span> M<\/span>(<\/span>i,<\/span> i)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> i +<\/span> 1<\/span>;<\/span> k <<\/span> n;<\/span> ++<\/span>k)<\/span> {<\/span>
\n double<\/span> f =<\/span> M<\/span>(<\/span>k,<\/span> i)<\/span> \/<\/span> M<\/span>(<\/span>i,<\/span> i)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> i;<\/span> j <<\/span> n;<\/span> ++<\/span>j)<\/span> M<\/span>(<\/span>k,<\/span> j)<\/span> -=<\/span> f *<\/span> M<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> det;<\/span>
\n }<\/span><\/p>\n

\/\/ \u9ad8\u65af-\u7ea6\u65e6\u6d88\u5143\u6c42\u9006<\/span>
\n Matrix inverse<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n int<\/span> n =<\/span> rows;<\/span>
\n Matrix M =<\/span> *<\/span>this<\/span>;<\/span>
\n Matrix I =<\/span> Matrix<\/span>::<\/span>Identity<\/span>(<\/span>n)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
\n int<\/span> pivot =<\/span> i;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> i +<\/span> 1<\/span>;<\/span> k <<\/span> n;<\/span> ++<\/span>k)<\/span>
\n if<\/span> (<\/span>std::<\/span>fabs<\/span>(<\/span>M<\/span>(<\/span>k,<\/span> i)<\/span>)<\/span> ><\/span> std::<\/span>fabs<\/span>(<\/span>M<\/span>(<\/span>pivot,<\/span> i)<\/span>)<\/span>)<\/span> pivot =<\/span> k;<\/span>
\n if<\/span> (<\/span>pivot !=<\/span> i)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> n;<\/span> ++<\/span>j)<\/span> {<\/span>
\n std::<\/span>swap<\/span>(<\/span>M<\/span>(<\/span>i,<\/span> j)<\/span>,<\/span> M<\/span>(<\/span>pivot,<\/span> j)<\/span>)<\/span>;<\/span>
\n std::<\/span>swap<\/span>(<\/span>I<\/span>(<\/span>i,<\/span> j)<\/span>,<\/span> I<\/span>(<\/span>pivot,<\/span> j)<\/span>)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n double<\/span> pv =<\/span> M<\/span>(<\/span>i,<\/span> i)<\/span>;<\/span>
\n if<\/span> (<\/span>std::<\/span>fabs<\/span>(<\/span>pv)<\/span> <<\/span> 1e-300<\/span>)<\/span> pv =<\/span> 1e-300<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> n;<\/span> ++<\/span>j)<\/span> {<\/span> M<\/span>(<\/span>i,<\/span> j)<\/span> \/=<\/span> pv;<\/span> I<\/span>(<\/span>i,<\/span> j)<\/span> \/=<\/span> pv;<\/span> }<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> n;<\/span> ++<\/span>k)<\/span> {<\/span>
\n if<\/span> (<\/span>k ==<\/span> i)<\/span> continue<\/span>;<\/span>
\n double<\/span> f =<\/span> M<\/span>(<\/span>k,<\/span> i)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> n;<\/span> ++<\/span>j)<\/span> {<\/span>
\n M<\/span>(<\/span>k,<\/span> j)<\/span> -=<\/span> f *<\/span> M<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n I<\/span>(<\/span>k,<\/span> j)<\/span> -=<\/span> f *<\/span> I<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> I;<\/span>
\n }<\/span><\/p>\n

\/\/ Cholesky: \u8fd4\u56de\u4e0b\u4e09\u89d2 L, \u6ee1\u8db3 L * L^T = A<\/span>
\n Matrix cholesky<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n int<\/span> n =<\/span> rows;<\/span>
\n Matrix Lm<\/span>(<\/span>n,<\/span> n,<\/span> 0.0<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <=<\/span> i;<\/span> ++<\/span>j)<\/span> {<\/span>
\n double<\/span> s =<\/span> (<\/span>*<\/span>this<\/span>)<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> j;<\/span> ++<\/span>k)<\/span> s -=<\/span> Lm<\/span>(<\/span>i,<\/span> k)<\/span> *<\/span> Lm<\/span>(<\/span>j,<\/span> k)<\/span>;<\/span>
\n if<\/span> (<\/span>i ==<\/span> j)<\/span> {<\/span>
\n if<\/span> (<\/span>s <<\/span> 1e-12<\/span>)<\/span> s =<\/span> 1e-12<\/span>;<\/span>
\n Lm<\/span>(<\/span>i,<\/span> j)<\/span> =<\/span> std::<\/span>sqrt<\/span>(<\/span>s)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n Lm<\/span>(<\/span>i,<\/span> j)<\/span> =<\/span> s \/<\/span> Lm<\/span>(<\/span>j,<\/span> j)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> Lm;<\/span>
\n }<\/span><\/p>\n

\/\/ \u53d6\u7b2c i \u884c (1 x cols)<\/span>
\n Matrix row<\/span>(<\/span>int<\/span> i)<\/span> const<\/span> {<\/span>
\n Matrix R<\/span>(<\/span>1<\/span>,<\/span> cols)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> cols;<\/span> ++<\/span>j)<\/span> R<\/span>(<\/span>0<\/span>,<\/span> j)<\/span> =<\/span> (<\/span>*<\/span>this<\/span>)<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n return<\/span> R;<\/span>
\n }<\/span>
\n}<\/span>;<\/span><\/p>\n

inline<\/span> Matrix operator<\/span>*<\/span>(<\/span>double<\/span> s,<\/span> const<\/span> Matrix&<\/span> M)<\/span> {<\/span> return<\/span> M *<\/span> s;<\/span> }<\/span><\/p>\n

\/\/ ============================================================<\/span>
\n\/\/ HDP-HMM \u7c7b (Sticky HDP-HMM, Fox et al. 2011)<\/span>
\n\/\/ ============================================================<\/span>
\nclass<\/span> HDPHMM<\/span> {<\/span>
\npublic<\/span>:<\/span>
\n double<\/span> alpha,<\/span> gamma,<\/span> kappa;<\/span>
\n int<\/span> L;<\/span><\/p>\n

Matrix beta;<\/span> \/\/ L x 1 \u5168\u5c40\u8f6c\u79fb\u57fa\u5206\u5e03<\/span>
\n Matrix A;<\/span> \/\/ L x L \u8f6c\u79fb\u77e9\u9635<\/span>
\n std::<\/span>vector<<\/span>Matrix><\/span> theta;<\/span> \/\/ \u6bcf\u4e2a D x 1<\/span>
\n std::<\/span>vector<<\/span>Matrix><\/span> Sigma;<\/span> \/\/ \u6bcf\u4e2a D x D<\/span><\/p>\n

Matrix observations;<\/span> \/\/ T x D<\/span>
\n int<\/span> T,<\/span> D;<\/span>
\n std::<\/span>vector<<\/span>int<\/span>><\/span> z;<\/span><\/p>\n

Matrix Nmat;<\/span> \/\/ L x L<\/span>
\n Matrix Ni;<\/span> \/\/ L x 1<\/span><\/p>\n

std::<\/span>mt19937 rng;<\/span><\/p>\n

HDPHMM<\/span>(<\/span>int<\/span> L_,<\/span> double<\/span> a_,<\/span> double<\/span> g_,<\/span> double<\/span> k_,<\/span> unsigned<\/span> seed =<\/span> 42u<\/span>)<\/span>
\n :<\/span> alpha<\/span>(<\/span>a_)<\/span>,<\/span> gamma<\/span>(<\/span>g_)<\/span>,<\/span> kappa<\/span>(<\/span>k_)<\/span>,<\/span> L<\/span>(<\/span>L_)<\/span>,<\/span> rng<\/span>(<\/span>seed)<\/span> {<\/span>}<\/span><\/p>\n

void<\/span> initialize<\/span>(<\/span>const<\/span> Matrix&<\/span> data)<\/span> {<\/span>
\n observations =<\/span> data;<\/span>
\n T =<\/span> data.<\/span>rows;<\/span>
\n D =<\/span> data.<\/span>cols;<\/span><\/p>\n

z.<\/span>resize<\/span>(<\/span>T)<\/span>;<\/span>
\n std::<\/span>uniform_int_distribution<<\/span>int<\/span>><\/span> dist<\/span>(<\/span>0<\/span>,<\/span> L –<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> t =<\/span> 0<\/span>;<\/span> t <<\/span> T;<\/span> ++<\/span>t)<\/span> z[<\/span>t]<\/span> =<\/span> dist<\/span>(<\/span>rng)<\/span>;<\/span><\/p>\n

beta =<\/span> Matrix<\/span>::<\/span>Constant<\/span>(<\/span>L,<\/span> 1<\/span>,<\/span> 1.0<\/span> \/<\/span> L)<\/span>;<\/span>
\n A =<\/span> Matrix<\/span>::<\/span>Constant<\/span>(<\/span>L,<\/span> L,<\/span> 1.0<\/span> \/<\/span> L)<\/span>;<\/span>
\n Nmat =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>L,<\/span> L)<\/span>;<\/span>
\n Ni =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>L,<\/span> 1<\/span>)<\/span>;<\/span><\/p>\n

theta.<\/span>resize<\/span>(<\/span>L)<\/span>;<\/span>
\n Sigma.<\/span>resize<\/span>(<\/span>L)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n theta[<\/span>k]<\/span> =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>D,<\/span> 1<\/span>)<\/span>;<\/span>
\n Sigma[<\/span>k]<\/span> =<\/span> Matrix<\/span>::<\/span>Identity<\/span>(<\/span>D)<\/span>;<\/span>
\n }<\/span>
\n updateCounts<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> updateCounts<\/span>(<\/span>)<\/span> {<\/span>
\n Nmat =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>L,<\/span> L)<\/span>;<\/span>
\n Ni =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>L,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> t =<\/span> 0<\/span>;<\/span> t <<\/span> T –<\/span> 1<\/span>;<\/span> ++<\/span>t)<\/span> {<\/span>
\n int<\/span> i =<\/span> z[<\/span>t]<\/span>,<\/span> j =<\/span> z[<\/span>t +<\/span> 1<\/span>]<\/span>;<\/span>
\n Nmat<\/span>(<\/span>i,<\/span> j)<\/span> +=<\/span> 1<\/span>;<\/span>
\n Ni<\/span>(<\/span>i,<\/span> 0<\/span>)<\/span> +=<\/span> 1<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

\/\/ —– \u91c7\u6837\u8f6c\u79fb\u77e9\u9635 A \u548c\u5168\u5c40 beta —–<\/span>
\n void<\/span> sampleTransitions<\/span>(<\/span>)<\/span> {<\/span>
\n std::<\/span>vector<<\/span>std::<\/span>vector<<\/span>int<\/span>>><\/span> m<\/span>(<\/span>L,<\/span> std::<\/span>vector<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>L,<\/span> 0<\/span>)<\/span>)<\/span>;<\/span>
\n std::<\/span>uniform_real_distribution<<\/span>double<\/span>><\/span> u01<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> L;<\/span> ++<\/span>i)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span> {<\/span>
\n double<\/span> p =<\/span> (<\/span>Nmat<\/span>(<\/span>i,<\/span> j)<\/span> *<\/span> beta<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span>)<\/span> \/<\/span>
\n (<\/span>Nmat<\/span>(<\/span>i,<\/span> j)<\/span> +<\/span> alpha *<\/span> beta<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span>
\n +<\/span> (<\/span>i ==<\/span> j ?<\/span> kappa :<\/span> 0.0<\/span>)<\/span> +<\/span> 1e-300<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>u01<\/span>(<\/span>rng)<\/span> <<\/span> p)<\/span> m[<\/span>i]<\/span>[<\/span>j]<\/span> =<\/span> 1<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

Matrix beta_post<\/span>(<\/span>L,<\/span> 1<\/span>,<\/span> gamma \/<\/span> L)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> L;<\/span> ++<\/span>i)<\/span>
\n beta_post<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span> +=<\/span> m[<\/span>i]<\/span>[<\/span>j]<\/span>;<\/span>
\n beta =<\/span> sampleDirichlet<\/span>(<\/span>beta_post)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> L;<\/span> ++<\/span>i)<\/span> {<\/span>
\n Matrix alpha_post<\/span>(<\/span>L,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span>
\n alpha_post<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span> =<\/span> alpha *<\/span> beta<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span>;<\/span>
\n alpha_post<\/span>(<\/span>i,<\/span> 0<\/span>)<\/span> +=<\/span> kappa;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span>
\n alpha_post<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span> +=<\/span> Nmat<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span><\/p>\n

Matrix row_probs =<\/span> sampleDirichlet<\/span>(<\/span>alpha_post)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span>
\n A<\/span>(<\/span>i,<\/span> j)<\/span> =<\/span> row_probs<\/span>(<\/span>j,<\/span> 0<\/span>)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

\/\/ —– \u524d\u5411-\u540e\u5411\u91c7\u6837\u9690\u72b6\u6001 —–<\/span>
\n void<\/span> sampleStates<\/span>(<\/span>)<\/span> {<\/span>
\n Matrix logLik<\/span>(<\/span>T,<\/span> L)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> t =<\/span> 0<\/span>;<\/span> t <<\/span> T;<\/span> ++<\/span>t)<\/span> {<\/span>
\n Matrix xrow =<\/span> observations.<\/span>row<\/span>(<\/span>t)<\/span>;<\/span> \/\/ 1 x D<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span>
\n logLik<\/span>(<\/span>t,<\/span> k)<\/span> =<\/span> logEmissionProb<\/span>(<\/span>xrow,<\/span> k)<\/span>;<\/span>
\n }<\/span><\/p>\n

Matrix logAlpha<\/span>(<\/span>T,<\/span> L)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span>
\n logAlpha<\/span>(<\/span>0<\/span>,<\/span> k)<\/span> =<\/span> std::<\/span>log<\/span>(<\/span>beta<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span> +<\/span> 1e-300<\/span>)<\/span> +<\/span> logLik<\/span>(<\/span>0<\/span>,<\/span> k)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> t =<\/span> 1<\/span>;<\/span> t <<\/span> T;<\/span> ++<\/span>t)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n double<\/span> mx =<\/span> –<\/span>std::<\/span>numeric_limits<\/span><<\/span>double<\/span>><\/span>::<\/span>infinity<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span> {<\/span>
\n double<\/span> v =<\/span> logAlpha<\/span>(<\/span>t –<\/span> 1<\/span>,<\/span> j)<\/span> +<\/span> std::<\/span>log<\/span>(<\/span>A<\/span>(<\/span>j,<\/span> k)<\/span> +<\/span> 1e-300<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>v ><\/span> mx)<\/span> mx =<\/span> v;<\/span>
\n }<\/span>
\n logAlpha<\/span>(<\/span>t,<\/span> k)<\/span> =<\/span> mx +<\/span> logLik<\/span>(<\/span>t,<\/span> k)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

std::<\/span>vector<<\/span>int<\/span>><\/span> z_new<\/span>(<\/span>T)<\/span>;<\/span><\/p>\n

\/\/ \u91c7\u6837\u6700\u540e\u4e00\u4e2a\u72b6\u6001<\/span>
\n Matrix probs_last<\/span>(<\/span>L,<\/span> 1<\/span>)<\/span>;<\/span>
\n double<\/span> pmax =<\/span> –<\/span>std::<\/span>numeric_limits<\/span><<\/span>double<\/span>><\/span>::<\/span>infinity<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span>
\n if<\/span> (<\/span>logAlpha<\/span>(<\/span>T –<\/span> 1<\/span>,<\/span> k)<\/span> ><\/span> pmax)<\/span> pmax =<\/span> logAlpha<\/span>(<\/span>T –<\/span> 1<\/span>,<\/span> k)<\/span>;<\/span>
\n double<\/span> psum =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n probs_last<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span> =<\/span> std::<\/span>exp<\/span>(<\/span>logAlpha<\/span>(<\/span>T –<\/span> 1<\/span>,<\/span> k)<\/span> –<\/span> pmax)<\/span>;<\/span>
\n psum +=<\/span> probs_last<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span>;<\/span>
\n }<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> probs_last<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span> \/=<\/span> psum;<\/span>
\n z_new[<\/span>T –<\/span> 1<\/span>]<\/span> =<\/span> sampleDiscrete<\/span>(<\/span>probs_last)<\/span>;<\/span><\/p>\n

\/\/ \u540e\u5411\u91c7\u6837<\/span>
\n for<\/span> (<\/span>int<\/span> t =<\/span> T –<\/span> 2<\/span>;<\/span> t >=<\/span> 0<\/span>;<\/span> —<\/span>t)<\/span> {<\/span>
\n int<\/span> nxt =<\/span> z_new[<\/span>t +<\/span> 1<\/span>]<\/span>;<\/span>
\n Matrix probs<\/span>(<\/span>L,<\/span> 1<\/span>)<\/span>;<\/span>
\n double<\/span> pmx =<\/span> –<\/span>std::<\/span>numeric_limits<\/span><<\/span>double<\/span>><\/span>::<\/span>infinity<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n double<\/span> v =<\/span> logAlpha<\/span>(<\/span>t,<\/span> k)<\/span> +<\/span> std::<\/span>log<\/span>(<\/span>A<\/span>(<\/span>k,<\/span> nxt)<\/span> +<\/span> 1e-300<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>v ><\/span> pmx)<\/span> pmx =<\/span> v;<\/span>
\n }<\/span>
\n double<\/span> ps =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n double<\/span> v =<\/span> logAlpha<\/span>(<\/span>t,<\/span> k)<\/span> +<\/span> std::<\/span>log<\/span>(<\/span>A<\/span>(<\/span>k,<\/span> nxt)<\/span> +<\/span> 1e-300<\/span>)<\/span>;<\/span>
\n probs<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span> =<\/span> std::<\/span>exp<\/span>(<\/span>v –<\/span> pmx)<\/span>;<\/span>
\n ps +=<\/span> probs<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span>;<\/span>
\n }<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> probs<\/span>(<\/span>k,<\/span> 0<\/span>)<\/span> \/=<\/span> ps;<\/span>
\n z_new[<\/span>t]<\/span> =<\/span> sampleDiscrete<\/span>(<\/span>probs)<\/span>;<\/span>
\n }<\/span><\/p>\n

z =<\/span> z_new;<\/span>
\n updateCounts<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ —– \u91c7\u6837\u53d1\u5c04\u53c2\u6570 (\u9ad8\u65af\u5206\u5e03) —–<\/span>
\n void<\/span> sampleEmissions<\/span>(<\/span>)<\/span> {<\/span>
\n double<\/span> nu0 =<\/span> D +<\/span> 2<\/span>;<\/span>
\n Matrix Psi0 =<\/span> Matrix<\/span>::<\/span>Identity<\/span>(<\/span>D)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n std::<\/span>vector<<\/span>int<\/span>><\/span> idx;<\/span>
\n for<\/span> (<\/span>int<\/span> t =<\/span> 0<\/span>;<\/span> t <<\/span> T;<\/span> ++<\/span>t)<\/span>
\n if<\/span> (<\/span>z[<\/span>t]<\/span> ==<\/span> k)<\/span> idx.<\/span>push_back<\/span>(<\/span>t)<\/span>;<\/span><\/p>\n

int<\/span> nk =<\/span> (<\/span>int<\/span>)<\/span>idx.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>nk ==<\/span> 0<\/span>)<\/span> {<\/span>
\n theta[<\/span>k]<\/span> =<\/span> sampleGaussian<\/span>(<\/span>Matrix<\/span>::<\/span>Zero<\/span>(<\/span>D,<\/span> 1<\/span>)<\/span>,<\/span> Matrix<\/span>::<\/span>Identity<\/span>(<\/span>D)<\/span>)<\/span>;<\/span>
\n Sigma[<\/span>k]<\/span> =<\/span> sampleInvWishart<\/span>(<\/span>nu0,<\/span> Psi0)<\/span>;<\/span>
\n continue<\/span>;<\/span>
\n }<\/span><\/p>\n

Matrix mean =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>D,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> t :<\/span> idx)<\/span>
\n for<\/span> (<\/span>int<\/span> d =<\/span> 0<\/span>;<\/span> d <<\/span> D;<\/span> ++<\/span>d)<\/span>
\n mean<\/span>(<\/span>d,<\/span> 0<\/span>)<\/span> +=<\/span> observations<\/span>(<\/span>t,<\/span> d)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> d =<\/span> 0<\/span>;<\/span> d <<\/span> D;<\/span> ++<\/span>d)<\/span> mean<\/span>(<\/span>d,<\/span> 0<\/span>)<\/span> \/=<\/span> nk;<\/span><\/p>\n

Matrix scatter =<\/span> Matrix<\/span>::<\/span>Zero<\/span>(<\/span>D,<\/span> D)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> t :<\/span> idx)<\/span> {<\/span>
\n Matrix diff<\/span>(<\/span>D,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> d =<\/span> 0<\/span>;<\/span> d <<\/span> D;<\/span> ++<\/span>d)<\/span>
\n diff<\/span>(<\/span>d,<\/span> 0<\/span>)<\/span> =<\/span> observations<\/span>(<\/span>t,<\/span> d)<\/span> –<\/span> mean<\/span>(<\/span>d,<\/span> 0<\/span>)<\/span>;<\/span>
\n scatter +=<\/span> diff *<\/span> diff.<\/span>transpose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

Matrix Psi_n =<\/span> Psi0 +<\/span> scatter
\n +<\/span> (<\/span>mean *<\/span> mean.<\/span>transpose<\/span>(<\/span>)<\/span>)<\/span> *<\/span> (<\/span>(<\/span>double<\/span>)<\/span>nk \/<\/span> (<\/span>nk +<\/span> 1.0<\/span>)<\/span>)<\/span>;<\/span>
\n double<\/span> nu_n =<\/span> nu0 +<\/span> nk;<\/span>
\n Sigma[<\/span>k]<\/span> =<\/span> sampleInvWishart<\/span>(<\/span>nu_n,<\/span> Psi_n)<\/span>;<\/span><\/p>\n

Matrix cov_theta =<\/span> Sigma[<\/span>k]<\/span> \/<\/span> (<\/span>double<\/span>)<\/span>nk;<\/span>
\n theta[<\/span>k]<\/span> =<\/span> sampleGaussian<\/span>(<\/span>mean,<\/span> cov_theta)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

void<\/span> gibbsStep<\/span>(<\/span>)<\/span> {<\/span>
\n sampleTransitions<\/span>(<\/span>)<\/span>;<\/span>
\n sampleStates<\/span>(<\/span>)<\/span>;<\/span>
\n sampleEmissions<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> run<\/span>(<\/span>int<\/span> nIter)<\/span> {<\/span>
\n for<\/span> (<\/span>int<\/span> iter =<\/span> 0<\/span>;<\/span> iter <<\/span> nIter;<\/span> ++<\/span>iter)<\/span> {<\/span>
\n gibbsStep<\/span>(<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>iter %<\/span> 50<\/span> ==<\/span> 0<\/span>)<\/span> {<\/span>
\n std::<\/span>cout <<<\/span> "Iter "<\/span> <<<\/span> std::<\/span>setw<\/span>(<\/span>3<\/span>)<\/span> <<<\/span> iter
\n <<<\/span> " | active states: "<\/span> <<<\/span> countActiveStates<\/span>(<\/span>)<\/span>
\n <<<\/span> std::<\/span>endl;<\/span>
\n }<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

int<\/span> countActiveStates<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n std::<\/span>vector<<\/span>bool<\/span>><\/span> used<\/span>(<\/span>L,<\/span> false<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> s :<\/span> z)<\/span> used[<\/span>s]<\/span> =<\/span> true<\/span>;<\/span>
\n int<\/span> cnt =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>bool<\/span> b :<\/span> used)<\/span> if<\/span> (<\/span>b)<\/span> cnt++<\/span>;<\/span>
\n return<\/span> cnt;<\/span>
\n }<\/span><\/p>\n

void<\/span> printTransitionMatrix<\/span>(<\/span>)<\/span> const<\/span> {<\/span>
\n std::<\/span>cout <<<\/span> "Transition Matrix A:"<\/span> <<<\/span> std::<\/span>endl;<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>fixed <<<\/span> std::<\/span>setprecision<\/span>(<\/span>4<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> L;<\/span> ++<\/span>i)<\/span> {<\/span>
\n std::<\/span>cout <<<\/span> " "<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> L;<\/span> ++<\/span>j)<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>setw<\/span>(<\/span>8<\/span>)<\/span> <<<\/span> A<\/span>(<\/span>i,<\/span> j)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>endl;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

private<\/span>:<\/span>
\n double<\/span> logEmissionProb<\/span>(<\/span>const<\/span> Matrix&<\/span> x_row,<\/span> int<\/span> k)<\/span> const<\/span> {<\/span>
\n Matrix x =<\/span> x_row.<\/span>transpose<\/span>(<\/span>)<\/span>;<\/span> \/\/ D x 1<\/span>
\n Matrix diff =<\/span> x –<\/span> theta[<\/span>k]<\/span>;<\/span>
\n double<\/span> logDet =<\/span> std::<\/span>log<\/span>(<\/span>Sigma[<\/span>k]<\/span>.<\/span>determinant<\/span>(<\/span>)<\/span> +<\/span> 1e-300<\/span>)<\/span>;<\/span>
\n Matrix quad =<\/span> diff.<\/span>transpose<\/span>(<\/span>)<\/span> *<\/span> Sigma[<\/span>k]<\/span>.<\/span>inverse<\/span>(<\/span>)<\/span> *<\/span> diff;<\/span>
\n return<\/span> –<\/span>0.5<\/span> *<\/span> (<\/span>D *<\/span> std::<\/span>log<\/span>(<\/span>2<\/span> *<\/span> M_PI)<\/span> +<\/span> logDet +<\/span> quad<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

Matrix sampleDirichlet<\/span>(<\/span>const<\/span> Matrix&<\/span> alpha)<\/span> {<\/span>
\n int<\/span> K =<\/span> alpha.<\/span>rows;<\/span>
\n Matrix samples<\/span>(<\/span>K,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> K;<\/span> ++<\/span>i)<\/span> {<\/span>
\n std::<\/span>gamma_distribution<<\/span>double<\/span>><\/span> g<\/span>(<\/span>alpha<\/span>(<\/span>i,<\/span> 0<\/span>)<\/span>,<\/span> 1.0<\/span>)<\/span>;<\/span>
\n samples<\/span>(<\/span>i,<\/span> 0<\/span>)<\/span> =<\/span> g<\/span>(<\/span>rng)<\/span>;<\/span>
\n }<\/span>
\n double<\/span> s =<\/span> samples.<\/span>sum<\/span>(<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>s <<\/span> 1e-300<\/span>)<\/span> s =<\/span> 1e-300<\/span>;<\/span>
\n samples \/=<\/span> s;<\/span>
\n return<\/span> samples;<\/span>
\n }<\/span><\/p>\n

int<\/span> sampleDiscrete<\/span>(<\/span>const<\/span> Matrix&<\/span> probs)<\/span> {<\/span>
\n double<\/span> total =<\/span> probs.<\/span>sum<\/span>(<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>total <=<\/span> 0.0<\/span>)<\/span> total =<\/span> 1e-300<\/span>;<\/span>
\n std::<\/span>uniform_real_distribution<<\/span>double<\/span>><\/span> u<\/span>(<\/span>0<\/span>,<\/span> total)<\/span>;<\/span>
\n double<\/span> r =<\/span> u<\/span>(<\/span>rng)<\/span>;<\/span>
\n double<\/span> c =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> probs.<\/span>rows;<\/span> ++<\/span>i)<\/span> {<\/span>
\n c +=<\/span> probs<\/span>(<\/span>i,<\/span> 0<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>r <=<\/span> c)<\/span> return<\/span> i;<\/span>
\n }<\/span>
\n return<\/span> probs.<\/span>rows –<\/span> 1<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u4ece N(mean, cov) \u91c7\u6837 (Cholesky \u6cd5)<\/span>
\n Matrix sampleGaussian<\/span>(<\/span>const<\/span> Matrix&<\/span> mean,<\/span> const<\/span> Matrix&<\/span> cov)<\/span> {<\/span>
\n int<\/span> d =<\/span> mean.<\/span>rows;<\/span>
\n Matrix zvec<\/span>(<\/span>d,<\/span> 1<\/span>)<\/span>;<\/span>
\n std::<\/span>normal_distribution<<\/span>double<\/span>><\/span> nd<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> d;<\/span> ++<\/span>i)<\/span> zvec<\/span>(<\/span>i,<\/span> 0<\/span>)<\/span> =<\/span> nd<\/span>(<\/span>rng)<\/span>;<\/span>
\n Matrix Lm =<\/span> cov.<\/span>cholesky<\/span>(<\/span>)<\/span>;<\/span>
\n return<\/span> mean +<\/span> Lm *<\/span> zvec;<\/span>
\n }<\/span><\/p>\n

\/\/ InvWishart(nu, Psi) \u91c7\u6837 (Bartlett \u5206\u89e3)<\/span>
\n Matrix sampleInvWishart<\/span>(<\/span>double<\/span> nu,<\/span> const<\/span> Matrix&<\/span> Psi)<\/span> {<\/span>
\n int<\/span> d =<\/span> Psi.<\/span>rows;<\/span>
\n Matrix S<\/span>(<\/span>d,<\/span> d,<\/span> 0.0<\/span>)<\/span>;<\/span>
\n std::<\/span>normal_distribution<<\/span>double<\/span>><\/span> nd<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> d;<\/span> ++<\/span>i)<\/span> {<\/span>
\n std::<\/span>chi_squared_distribution<<\/span>double<\/span>><\/span> chi<\/span>(<\/span>nu –<\/span> i)<\/span>;<\/span>
\n S<\/span>(<\/span>i,<\/span> i)<\/span> =<\/span> std::<\/span>sqrt<\/span>(<\/span>chi<\/span>(<\/span>rng)<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> j =<\/span> 0<\/span>;<\/span> j <<\/span> i;<\/span> ++<\/span>j)<\/span>
\n S<\/span>(<\/span>i,<\/span> j)<\/span> =<\/span> nd<\/span>(<\/span>rng)<\/span>;<\/span>
\n }<\/span>
\n Matrix W =<\/span> S *<\/span> S.<\/span>transpose<\/span>(<\/span>)<\/span>;<\/span> \/\/ ~ Wishart(nu, I)<\/span>
\n Matrix Lm =<\/span> Psi.<\/span>cholesky<\/span>(<\/span>)<\/span>;<\/span> \/\/ Psi = Lm * Lm^T<\/span>
\n \/\/ X ~ InvWishart(nu, Psi) => X = Lm * W^{-1} * Lm^T<\/span>
\n return<\/span> Lm *<\/span> W.<\/span>inverse<\/span>(<\/span>)<\/span> *<\/span> Lm.<\/span>transpose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span>
\n}<\/span>;<\/span><\/p>\n

\/\/ ============================================================<\/span>
\n\/\/ main<\/span>
\n\/\/ ============================================================<\/span>
\nint<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\n int<\/span> T =<\/span> 1000<\/span>,<\/span> D =<\/span> 2<\/span>,<\/span> trueK =<\/span> 3<\/span>;<\/span>
\n Matrix data<\/span>(<\/span>T,<\/span> D)<\/span>;<\/span><\/p>\n

std::<\/span>vector<<\/span>std::<\/span>vector<<\/span>double<\/span>>><\/span> trueMeans =<\/span> {<\/span>
\n {<\/span> 0.0<\/span>,<\/span> 0.0<\/span>}<\/span>,<\/span>
\n {<\/span> 5.0<\/span>,<\/span> 5.0<\/span>}<\/span>,<\/span>
\n {<\/span>–<\/span>5.0<\/span>,<\/span> 5.0<\/span>}<\/span>
\n }<\/span>;<\/span><\/p>\n

\/\/ \u751f\u6210\u5408\u6210\u6570\u636e (3 \u72b6\u6001\u9ad8\u65af HMM, \u81ea\u8f6c\u79fb 0.9) – \u56fa\u5b9a\u79cd\u5b50\u4fdd\u8bc1\u53ef\u590d\u73b0<\/span>
\n std::<\/span>mt19937 rng<\/span>(<\/span>42<\/span>)<\/span>;<\/span>
\n std::<\/span>normal_distribution<<\/span>double<\/span>><\/span> noise<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\n std::<\/span>uniform_real_distribution<<\/span>double<\/span>><\/span> u01<\/span>(<\/span>0<\/span>,<\/span> 1<\/span>)<\/span>;<\/span>
\n int<\/span> state =<\/span> 0<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> t =<\/span> 0<\/span>;<\/span> t <<\/span> T;<\/span> ++<\/span>t)<\/span> {<\/span>
\n if<\/span> (<\/span>u01<\/span>(<\/span>rng)<\/span> <<\/span> 0.1<\/span>)<\/span> state =<\/span> (<\/span>state +<\/span> 1<\/span>)<\/span> %<\/span> trueK;<\/span>
\n for<\/span> (<\/span>int<\/span> d =<\/span> 0<\/span>;<\/span> d <<\/span> D;<\/span> ++<\/span>d)<\/span>
\n data<\/span>(<\/span>t,<\/span> d)<\/span> =<\/span> trueMeans[<\/span>state]<\/span>[<\/span>d]<\/span> +<\/span> noise<\/span>(<\/span>rng)<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u6784\u9020 HDP-HMM (\u56fa\u5b9a\u79cd\u5b50, \u4fbf\u4e8e\u590d\u73b0)<\/span>
\n HDPHMM model<\/span>(<\/span>\/*L=*\/<\/span>10<\/span>,<\/span> \/*alpha=*\/<\/span>1.0<\/span>,<\/span> \/*gamma=*\/<\/span>1.0<\/span>,<\/span> \/*kappa=*\/<\/span>10.0<\/span>,<\/span>
\n \/*seed=*\/<\/span>42u<\/span>)<\/span>;<\/span>
\n model.<\/span>initialize<\/span>(<\/span>data)<\/span>;<\/span><\/p>\n

std::<\/span>cout <<<\/span> "=== HDP-HMM Gibbs Sampling ==="<\/span> <<<\/span> std::<\/span>endl;<\/span>
\n model.<\/span>run<\/span>(<\/span>\/*nIter=*\/<\/span>500<\/span>)<\/span>;<\/span><\/p>\n

std::<\/span>cout <<<\/span> "\\\\nFinal active states: "<\/span>
\n <<<\/span> model.<\/span>countActiveStates<\/span>(<\/span>)<\/span> <<<\/span> std::<\/span>endl;<\/span>
\n model.<\/span>printTransitionMatrix<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

std::<\/span>cout <<<\/span> "\\\\nEstimated emission means:"<\/span> <<<\/span> std::<\/span>endl;<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>fixed <<<\/span> std::<\/span>setprecision<\/span>(<\/span>4<\/span>)<\/span>;<\/span>
\n std::<\/span>vector<<\/span>bool<\/span>><\/span> used<\/span>(<\/span>model.<\/span>L,<\/span> false<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> s :<\/span> model.<\/span>z)<\/span> used[<\/span>s]<\/span> =<\/span> true<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> k =<\/span> 0<\/span>;<\/span> k <<\/span> model.<\/span>L;<\/span> ++<\/span>k)<\/span> {<\/span>
\n if<\/span> (<\/span>used[<\/span>k]<\/span>)<\/span> {<\/span>
\n std::<\/span>cout <<<\/span> "State "<\/span> <<<\/span> k <<<\/span> ": "<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> d =<\/span> 0<\/span>;<\/span> d <<\/span> model.<\/span>D;<\/span> ++<\/span>d)<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>setw<\/span>(<\/span>9<\/span>)<\/span> <<<\/span> model.<\/span>theta[<\/span>k]<\/span>(<\/span>d,<\/span> 0<\/span>)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>endl;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

return<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\/\/
\n\/\/ HDP-HMM with Sticky Transitions (Fox et al., 2011)
\n\/\/ \u5b8c\u5168\u81ea\u5305\u542b (\u4ec5\u4f9d\u8d56 C \u6807\u51c6\u5e93, \u65e0\u7b2c\u4e09\u65b9\u4f9d\u8d56)
\n\/\/ \u7f16\u8bd1: g -stdc14 -O2 HDPHMM.cpp -o hdpmm_demo
\n\/\/ \u8fd0\u884c: .\/hdpmm_demo
\n\/\/ #include
\n#include
\n#include
\n#include
\n#include <<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,1284,190,427],"topic":[],"class_list":["post-116324","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-matlab","tag-190","tag-427"],"yoast_head":"\nC++\u4ee3\u7801\u5b9e\u73b0MATLAB\u4e2d\u7684hdphmm\u51fd\u6570\u529f\u80fd - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/116324.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"C++\u4ee3\u7801\u5b9e\u73b0MATLAB\u4e2d\u7684hdphmm\u51fd\u6570\u529f\u80fd - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\/\/ \/\/ HDP-HMM with Sticky Transitions (Fox et al., 2011) \/\/ \u5b8c\u5168\u81ea\u5305\u542b (\u4ec5\u4f9d\u8d56 C \u6807\u51c6\u5e93, \u65e0\u7b2c\u4e09\u65b9\u4f9d\u8d56) \/\/ \u7f16\u8bd1: g -stdc14 -O2 HDPHMM.cpp -o hdpmm_demo \/\/ \u8fd0\u884c: .\/hdpmm_demo \/\/ #include #include #include #include #include <\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/116324.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-20T23:25:16+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/116324.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/116324.html\",\"name\":\"C++\u4ee3\u7801\u5b9e\u73b0MATLAB\u4e2d\u7684hdphmm\u51fd\u6570\u529f\u80fd - 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