/** \param N1 = number of nodes of type 1
* \param d1 = size of neighborhoods of nodes of type 1
* \param N2 = number of nodes of type 2
* \param d2 = size of neighborhoods of nodes of type 2
* \note asserts that N1 * d1 == N2 * d2
*/
BipartiteGraph createRandomBipartiteGraph( size_t N1, size_t N2, size_t d1, size_t d2 ) {
BipartiteGraph G;
DAI_ASSERT( N1 * d1 == N2 * d2 );
// build lists of degree-repeated vertex numbers
std::vector<size_t> stubs1( N1*d1, 0 );
for( size_t n1 = 0; n1 < N1; n1++ )
for( size_t t = 0; t < d1; t++ )
stubs1[n1*d1 + t] = n1;
// build lists of degree-repeated vertex numbers
std::vector<size_t> stubs2( N2*d2, 0 );
for( size_t n2 = 0; n2 < N2; n2++ )
for( size_t t = 0; t < d2; t++ )
stubs2[n2*d2 + t] = n2;
// shuffle lists
random_shuffle( stubs1.begin(), stubs1.end() );
random_shuffle( stubs2.begin(), stubs2.end() );
// add edges
vector<BipartiteGraph::Edge> edges;
edges.reserve( N1*d1 );
for( size_t e = 0; e < N1*d1; e++ )
edges.push_back( BipartiteGraph::Edge(stubs1[e], stubs2[e]) );
// finish construction
G.construct( N1, N2, edges.begin(), edges.end() );
return G;
}
// N = number of variables
// n = size of variable neighborhoods
// K = number of factors
// k = size of factor neighborhoods
// asserts: N * n == K * k
BipartiteGraph CreateRandomBipartiteGraph( size_t N, size_t K, size_t n, size_t k ) {
BipartiteGraph G;
DAI_ASSERT( N * n == K * k );
// build lists of degree-repeated vertex numbers
std::vector<size_t> stubs1(N*n,0);
for( size_t i = 0; i < N; i++ )
for( size_t t = 0; t < n; t++ )
stubs1[i*n + t] = i;
// build lists of degree-repeated vertex numbers
std::vector<size_t> stubs2(K*k,0);
for( size_t I = 0; I < K; I++ )
for( size_t t = 0; t < k; t++ )
stubs2[I*k + t] = I;
// shuffle lists
random_shuffle( stubs1.begin(), stubs1.end() );
random_shuffle( stubs2.begin(), stubs2.end() );
// add edges
vector<BipartiteGraph::Edge> edges;
edges.reserve( N*n );
for( size_t e = 0; e < N*n; e++ )
edges.push_back( BipartiteGraph::Edge(stubs1[e], stubs2[e]) );
// finish construction
G.construct( N, K, edges.begin(), edges.end() );
return G;
}
void checkAddEdge(unsigned numOfVertices, Edge toBeAdded, Edges existing, Edges missing)
{
g.addEdge(toBeAdded);
ASSERT_EQ(existing.size(), g.numOfEdges());
ASSERT_EQ(numOfVertices, g.numOfVertices());
for (auto elem : existing) ASSERT_TRUE(g.edgeExists(elem));
for (auto elem : missing) ASSERT_FALSE(g.edgeExists(elem));
}
/// Constructs a regular LDPC graph with N=6, j=2, K=4, k=3
BipartiteGraph createSmallLDPCGraph() {
BipartiteGraph G;
size_t N=4, j=3, K=4; // k=3;
typedef BipartiteGraph::Edge Edge;
vector<Edge> edges;
edges.reserve( N*j );
edges.push_back( Edge(0,0) ); edges.push_back( Edge(1,0) ); edges.push_back( Edge(2,0) );
edges.push_back( Edge(0,1) ); edges.push_back( Edge(1,1) ); edges.push_back( Edge(3,1) );
edges.push_back( Edge(0,2) ); edges.push_back( Edge(2,2) ); edges.push_back( Edge(3,2) );
edges.push_back( Edge(1,3) ); edges.push_back( Edge(2,3) ); edges.push_back( Edge(3,3) );
// finish construction
G.construct( N, K, edges.begin(), edges.end() );
return G;
}
void
PlotGraph::PlotAugmentingPath(BipartiteGraph& _bg, vector<EID>& _path){
//get assignment size, assume the sizes of agents and tasks are identical
size_t as_size = _bg.GetNumAgents();
double plx[as_size];
double ply[as_size];
/*
//gnuplot_resetplot(g);
gnuplot_cmd(g, (char*)"unset label");
gnuplot_cmd(g, (char*)"set xrange [-0.25:1.25]");
gnuplot_cmd(g, (char*)"set yrange [-0.25:%f]", as_size-1+.25);
gnuplot_cmd(g, (char*)"set xtics 0");
gnuplot_cmd(g, (char*)"set ytics 0");
gnuplot_cmd(g, (char*)"set nokey");
*/
//gnuplot_cmd(g, (char*)"set style line 2 lt 2 lc rgb \"blue\" lw 3");
// Plot matching
//cout<<endl<<"Set M: "<<endl;
//DisplayData(_M);
bool alter = true;
for (unsigned int i = 0; i < _path.size(); i++){
plx[0] = _path[i].first;
ply[0] = 0.0;
plx[1] = _path[i].second;
ply[1] = 1.0;
//gnuplot_setstyle(g, (char*)"linespoints lc rgb \"#55DD99\" lw 3");
if(alter)
gnuplot_setstyle(g, (char*)"lines lc rgb \"#458B74\" lw 3");
else
gnuplot_setstyle(g, (char*)"lines lc rgb \"#7CCD7C\" lw 3");
alter = !alter;
gnuplot_plot_xy(g, plx, ply, 2, NULL);
}
#ifdef SAVE_PLOTS
stringstream ss;
ss << setw(3) << setfill('0') << Cnt++;
string postfix = ss.str();
string name="save/plot"+postfix+".jpeg";
gnuplot_cmd(g, (char*)"set terminal jpeg");
//gnuplot_cmd(g, (char*)"set terminal jpeg small size 320,240");//bad
gnuplot_cmd(g, (char*)"set output \"%s\"", name.c_str());
printf("saved jpeg: \"%s\"\n", name.c_str());
#endif
gnuplot_cmd(g, (char*)"replot");
sleep(period);
}
void verifyMatching(BipartiteGraph g, unsigned expectedSize)
{
Matching matching = findMaximumMatching(g);
typedef boost::unordered_set<unsigned> VertexSet;
VertexSet first;
VertexSet second;
for (auto elem : matching)
{
ASSERT_TRUE(first.insert(elem.first).second);
ASSERT_TRUE(second.insert(elem.second).second);
ASSERT_TRUE(g.edgeExists(elem));
}
ASSERT_EQ(expectedSize, matching.size());
}
/** Use construction described in "A Class of Group-Structured LDPC Codes"
* by R. M. Tanner, D. Sridhara and T. Fuja
* Proceedings of ICSTA, 2001
*
* Example parameters: (p,j,k) = (31,3,5)
* (p,j,k) = (37,3,4)
* (p,j,k) = (7,2,4)
* (p,j,k) = (29,2,4)
*
* j and k must be divisors of p-1
*/
BipartiteGraph createGroupStructuredLDPCGraph( size_t p, size_t j, size_t k ) {
BipartiteGraph G;
size_t n = j;
size_t N = p * k;
size_t K = p * j;
size_t a, b;
for( a = 2; a < p; a++ )
if( order(a,p) == k )
break;
DAI_ASSERT( a != p );
for( b = 2; b < p; b++ )
if( order(b,p) == j )
break;
DAI_ASSERT( b != p );
// cout << "# order(a=" << a << ") = " << order(a,p) << endl;
// cout << "# order(b=" << b << ") = " << order(b,p) << endl;
DAI_ASSERT( N * n == K * k );
typedef BipartiteGraph::Edge Edge;
vector<Edge> edges;
edges.reserve( N * n );
for( size_t s = 0; s < j; s++ )
for( size_t t = 0; t < k; t++ ) {
size_t P = (powmod(b,s,p) * powmod(a,t,p)) % p;
for( size_t m = 0; m < p; m++ )
edges.push_back( Edge(t*p + m, s*p + ((m + P) % p)) );
}
// finish construction
G.construct( N, K, edges.begin(), edges.end() );
return G;
}
void
PlotGraph::PlotBipartiteGraph(BipartiteGraph& _bg,
vector<VID>& _S,
vector<VID>& _T,
vector<VID>& _N,
vector<EID>& _EG,
vector<EID>& _M,
int target_task){
//get assignment size, assume the sizes of agents and tasks are identical
size_t as_size = _bg.GetNumAgents();
double plx[as_size];
double ply[as_size];
//g=gnuplot_init();
gnuplot_resetplot(g);
gnuplot_cmd(g, (char*)"unset label");
gnuplot_cmd(g, (char*)"set xrange [-0.25:%f]", as_size-1+.25);
gnuplot_cmd(g, (char*)"set yrange [-0.25:1.25]");
gnuplot_cmd(g, (char*)"set xtics 0");
gnuplot_cmd(g, (char*)"set ytics 0");
gnuplot_cmd(g, (char*)"set nokey");
// Plot matching
//cout<<endl<<"Set M: "<<endl;
//DisplayData(_M);
for (unsigned int i = 0; i < _M.size(); i++){
plx[0] = _M[i].first;
ply[0] = 0.0;
plx[1] = _M[i].second;
ply[1] = 1.0;
gnuplot_setstyle(g, (char*)"lines lc rgb \"red\" lw 3");
gnuplot_plot_xy(g, plx, ply, 2, NULL);
}
// Plot admissible edges (EG)
//cout<<"EG: "<<endl;
//DisplayData(_EG);
for(unsigned int i=0; i<_EG.size(); i++){
plx[0] = _EG[i].first;
ply[0] = 0.0;
plx[1] = _EG[i].second;
ply[1] = 1.0;
gnuplot_setstyle(g, (char*)"lines lc rgb \"gray\"");
gnuplot_plot_xy(g, plx, ply, 2, NULL);
plx[0] = (0.9*plx[0] + 0.1*plx[1]);
ply[0] = 0.11;
gnuplot_setstyle(g, (char*)"points pointsize 2 lc rgb \"#FFFFFF\" pt 7");
gnuplot_plot_xy(g, plx, ply, 1, NULL);
//cout<<"EG "<<i<<": "<<_bg.GetMatrix(_EG[i])->GetWeight()<<endl;
gnuplot_cmd(g, (char*)"set label \"%d\" at %f-0.04,0.1 front tc rgb \"#4682B4\" font \",8\"", int(_bg.GetMatrix(_EG[i])->GetWeight()), plx[0]);
}
// Plot membership of set S
//cout<<"S: "<<endl;
//DisplayData(_S);
for(unsigned int i=0; i<_S.size(); i++){
plx[0] = _S[i];
ply[0] = 0.0;
gnuplot_setstyle(g, (char*)"points pointsize 3 lc rgb \"green\" pt 7");
gnuplot_plot_xy(g, plx, ply, 1, NULL);
}
// Plot membership of the set T
//cout<<"T: "<<endl;
//DisplayData(_T);
for(unsigned int i=0; i<_T.size(); i++){
plx[0] = _T[i];
ply[0] = 1.0;
gnuplot_setstyle(g, (char*)"points pointsize 3 lc rgb \"#00BFFF\" pt 7");
gnuplot_plot_xy(g, plx, ply, 1, NULL);
}
if (target_task != -1) // not yet unioned, but the reversal point for the
{ // alternating path
plx[0] = target_task;
ply[0] = 1.0;
gnuplot_setstyle(g, (char*)"points pointsize 3 lc rgb \"grey\" pt 7");
gnuplot_plot_xy(g, plx, ply, 1, NULL);
}
// Plot nodes
for(unsigned int i = 0; i < as_size; i++)
{
plx[i] = i;
ply[i] = 0.0;
}
gnuplot_setstyle(g, (char*)"points pointsize 2 lc rgb \"#102063\" pt 7");
gnuplot_plot_xy(g, plx, ply, as_size, NULL);
for(unsigned int i = 0; i < as_size; i++)
{
plx[i] = i;
ply[i] = 1.0;
}
gnuplot_setstyle(g, (char*)"points pointsize 2 lc rgb \"#102063\" pt 7");
gnuplot_plot_xy(g, plx, ply, as_size, NULL);
for (unsigned int i = 0; i < as_size; i++)
{
gnuplot_cmd(g, (char*)"set label \"x%d\" at %d-0.025,-0.08 tc rgb \"black\"", i, i);
gnuplot_cmd(g, (char*)"set label \"y%d\" at %d-0.025,1.08 tc rgb \"black\"", i, i);
//cout<<"Label "<<i<<": "<<_bg.GetAgent(i)->GetLabel()<<endl;
//cout<<"Label "<<i<<": "<<_bg.GetTask(i)->GetLabel()<<endl;
gnuplot_cmd(g, (char*)"set label \"%d\" at %d-0.025,-0.15 tc rgb \"#112244\"", int(_bg.GetAgent(i)->GetLabel()), i);
gnuplot_cmd(g, (char*)"set label \"%d\" at %d-0.025,1.15 tc rgb \"#112244\"", int(_bg.GetTask(i)->GetLabel()), i);
}
/* //image setting
set terminal png
{{no}transparent} {{no}interlace}
{tiny | small | medium | large | giant}
{font <face> {<pointsize>}}
{size <x>,<y>} {{no}crop}
{{no}enhanced}
{<color0> <color1> <color2> ...}
*/
#ifdef SAVE_PLOTS
stringstream ss;
ss << setw(3) << setfill('0') << Cnt++;
string postfix = ss.str();
string name="save/plot"+postfix+".jpeg";
gnuplot_cmd(g, (char*)"set terminal jpeg");
//gnuplot_cmd(g, (char*)"set terminal jpeg small size 320,240");//bad
gnuplot_cmd(g, (char*)"set output \"%s\"", name.c_str());
printf("saved jpeg: \"%s\"\n", name.c_str());
#endif
gnuplot_cmd(g, (char*)"replot");
sleep(period);
//gnuplot_close(g);
}
/// Main function
int main( int argc, char *argv[] ) {
try {
// Variables for storing command line arguments
size_t seed;
size_t states = 2;
string type;
size_t d, N, K, k, j, n1, n2, n3, prime;
bool periodic = false;
FactorType ft;
LDPCType ldpc;
Real beta, sigma_w, sigma_th, mean_w, mean_th, noise;
// Declare the supported options.
po::options_description opts("General command line options");
opts.add_options()
("help", "produce help message")
("seed", po::value<size_t>(&seed), "random number seed (tries to read from /dev/urandom if not specified)")
("states", po::value<size_t>(&states), "number of states of each variable (default=2 for binary variables)")
;
// Graph structure options
po::options_description opts_graph("Options for specifying graph structure");
opts_graph.add_options()
("type", po::value<string>(&type), "factor graph type (one of 'FULL', 'DREG', 'LOOP', 'TREE', 'GRID', 'GRID3D', 'HOI', 'LDPC')")
("d", po::value<size_t>(&d), "variable connectivity (only for type=='DREG');\n\t<d><N> should be even")
("N", po::value<size_t>(&N), "number of variables (not for type=='GRID','GRID3D')")
("n1", po::value<size_t>(&n1), "width of grid (only for type=='GRID','GRID3D')")
("n2", po::value<size_t>(&n2), "height of grid (only for type=='GRID','GRID3D')")
("n3", po::value<size_t>(&n3), "length of grid (only for type=='GRID3D')")
("periodic", po::value<bool>(&periodic), "periodic grid? (only for type=='GRID','GRID3D'; default=0)")
("K", po::value<size_t>(&K), "number of factors (only for type=='HOI','LDPC')")
("k", po::value<size_t>(&k), "number of variables per factor (only for type=='HOI','LDPC')")
;
// Factor options
po::options_description opts_factors("Options for specifying factors");
opts_factors.add_options()
("factors", po::value<FactorType>(&ft), "factor type (one of 'EXPGAUSS','POTTS','ISING')")
("beta", po::value<Real>(&beta), "inverse temperature (ignored for factors=='ISING')")
("mean_w", po::value<Real>(&mean_w), "mean of pairwise interactions w_{ij} (only for factors=='ISING')")
("mean_th", po::value<Real>(&mean_th), "mean of unary interactions th_i (only for factors=='ISING')")
("sigma_w", po::value<Real>(&sigma_w), "stddev of pairwise interactions w_{ij} (only for factors=='ISING')")
("sigma_th", po::value<Real>(&sigma_th), "stddev of unary interactions th_i (only for factors=='ISING'")
;
// LDPC options
po::options_description opts_ldpc("Options for specifying LDPC code factor graphs");
opts_ldpc.add_options()
("ldpc", po::value<LDPCType>(&ldpc), "type of LDPC code (one of 'SMALL','GROUP','RANDOM')")
("j", po::value<size_t>(&j), "number of parity checks per bit (only for type=='LDPC')")
("noise", po::value<Real>(&noise), "bitflip probability for binary symmetric channel (only for type=='LDPC')")
("prime", po::value<size_t>(&prime), "prime number for construction of LDPC code (only for type=='LDPC' with ldpc='GROUP'))")
;
// All options
opts.add(opts_graph).add(opts_factors).add(opts_ldpc);
// Parse command line arguments
po::variables_map vm;
po::store(po::parse_command_line(argc, argv, opts), vm);
po::notify(vm);
// Display help message if necessary
if( vm.count("help") || !vm.count("type") ) {
cout << "This program is part of libDAI - http://www.libdai.org/" << endl << endl;
cout << "Usage: ./createfg [options]" << endl << endl;
cout << "Creates a factor graph according to the specified options." << endl << endl;
cout << endl << opts << endl;
cout << "The following factor graph types with pairwise interactions can be created:" << endl;
cout << "\t'FULL': fully connected graph of <N> variables" << endl;
cout << "\t'DREG': random regular graph of <N> variables where each variable is connected with <d> others" << endl;
cout << "\t'LOOP': a single loop of <N> variables" << endl;
cout << "\t'TREE': random tree-structured (acyclic, connected) graph of <N> variables" << endl;
cout << "\t'GRID': 2D grid of <n1>x<n2> variables" << endl;
cout << "\t'GRID3D': 3D grid of <n1>x<n2>x<n3> variables" << endl;
cout << "The following higher-order interactions factor graphs can be created:" << endl;
cout << "\t'HOI': random factor graph consisting of <N> variables and <K> factors," << endl;
cout << "\t each factor being an interaction of <k> variables." << endl;
cout << "The following LDPC code factor graphs can be created:" << endl;
cout << "\t'LDPC': simulates LDPC decoding problem, using an LDPC code of <N> bits and <K>" << endl;
cout << "\t parity checks, with <k> bits per check and <j> checks per bit, transmitted" << endl;
cout << "\t on a binary symmetric channel with probability <noise> of flipping a bit." << endl;
cout << "\t The transmitted codeword has all bits set to zero. The argument 'ldpc'" << endl;
cout << "\t determines how the LDPC code is constructed: either using a group structure," << endl;
cout << "\t or randomly, or a fixed small code with (N,K,k,j) = (4,4,3,3)." << endl << endl;
cout << "For all types except type=='LDPC', the factors have to be specified as well." << endl << endl;
cout << "EXPGAUSS factors (the default) are created by drawing all log-factor entries" << endl;
cout << "independently from a Gaussian with mean 0 and standard deviation <beta>." << endl << endl;
cout << "In case of pairwise interactions, one can also choose POTTS factors, for which" << endl;
cout << "the log-factors are simply delta functions multiplied by the strength <beta>." << endl << endl;
cout << "For pairwise interactions and binary variables, one can also use ISING factors." << endl;
cout << "Here variables x1...xN are assumed to be +1/-1--valued, and unary interactions" << endl;
cout << "are of the form exp(th*xi) with th drawn from a Gaussian distribution with mean" << endl;
cout << "<mean_th> and standard deviation <sigma_th>, and pairwise interactions are of the" << endl;
cout << "form exp(w*xi*xj) with w drawn from a Gaussian distribution with mean <mean_w>" << endl;
cout << "and standard deviation <sigma_w>." << endl;
return 1;
}
// Set default number of states
if( !vm.count("states") )
states = 2;
// Set default factor type
if( !vm.count("factors") )
ft = FactorType::EXPGAUSS;
// Check validness of factor type
if( ft == FactorType::POTTS )
if( type == HOI_TYPE )
throw "For factors=='POTTS', interactions should be pairwise (type!='HOI')";
if( ft == FactorType::ISING )
if( ((states != 2) || (type == HOI_TYPE)) )
throw "For factors=='ISING', variables should be binary (states==2) and interactions should be pairwise (type!='HOI')";
// Read random seed
if( !vm.count("seed") ) {
ifstream infile;
bool success;
infile.open( "/dev/urandom" );
success = infile.is_open();
if( success ) {
infile.read( (char *)&seed, sizeof(size_t) / sizeof(char) );
success = infile.good();
infile.close();
}
if( !success )
throw "Please specify random number seed.";
}
rnd_seed( seed );
// Set default periodicity
if( !vm.count("periodic") )
periodic = false;
// Store some options in a PropertySet object
PropertySet options;
if( vm.count("mean_th") )
options.Set("mean_th", mean_th);
if( vm.count("sigma_th") )
options.Set("sigma_th", sigma_th);
if( vm.count("mean_w") )
options.Set("mean_w", mean_w);
if( vm.count("sigma_w") )
options.Set("sigma_w", sigma_w);
if( vm.count("beta") )
options.Set("beta", beta);
// Output some comments
cout << "# Factor graph made by " << argv[0] << endl;
cout << "# type = " << type << endl;
cout << "# states = " << states << endl;
// The factor graph to be constructed
FactorGraph fg;
#define NEED_ARG(name, desc) do { if(!vm.count(name)) throw "Please specify " desc " with --" name; } while(0);
if( type == FULL_TYPE || type == DREG_TYPE || type == LOOP_TYPE || type == TREE_TYPE || type == GRID_TYPE || type == GRID3D_TYPE ) {
// Pairwise interactions
// Check command line options
if( type == GRID_TYPE ) {
NEED_ARG("n1", "width of grid");
NEED_ARG("n2", "height of grid");
N = n1 * n2;
} else if( type == GRID3D_TYPE ) {
NEED_ARG("n1", "width of grid");
NEED_ARG("n2", "height of grid");
NEED_ARG("n3", "depth of grid");
N = n1 * n2 * n3;
} else
NEED_ARG("N", "number of variables");
if( states > 2 || ft == FactorType::POTTS ) {
NEED_ARG("beta", "stddev of log-factor entries");
} else {
NEED_ARG("mean_w", "mean of pairwise interactions");
NEED_ARG("mean_th", "mean of unary interactions");
NEED_ARG("sigma_w", "stddev of pairwise interactions");
NEED_ARG("sigma_th", "stddev of unary interactions");
}
if( type == DREG_TYPE )
NEED_ARG("d", "connectivity (number of neighboring variables of each variable)");
// Build pairwise interaction graph
GraphAL G;
if( type == FULL_TYPE )
G = createGraphFull( N );
else if( type == DREG_TYPE )
G = createGraphRegular( N, d );
else if( type == LOOP_TYPE )
G = createGraphLoop( N );
else if( type == TREE_TYPE )
G = createGraphTree( N );
else if( type == GRID_TYPE )
G = createGraphGrid( n1, n2, periodic );
else if( type == GRID3D_TYPE )
G = createGraphGrid3D( n1, n2, n3, periodic );
// Construct factor graph from pairwise interaction graph
fg = createFG( G, ft, states, options );
// Output some additional comments
if( type == GRID_TYPE || type == GRID3D_TYPE ) {
cout << "# n1 = " << n1 << endl;
cout << "# n2 = " << n2 << endl;
if( type == GRID3D_TYPE )
cout << "# n3 = " << n3 << endl;
}
if( type == DREG_TYPE )
cout << "# d = " << d << endl;
cout << "# options = " << options << endl;
} else if( type == HOI_TYPE ) {
// Higher order interactions
// Check command line arguments
NEED_ARG("N", "number of variables");
NEED_ARG("K", "number of factors");
NEED_ARG("k", "number of variables per factor");
NEED_ARG("beta", "stddev of log-factor entries");
// Create higher-order interactions factor graph
do {
fg = createHOIFG( N, K, k, beta );
} while( !fg.isConnected() );
// Output some additional comments
cout << "# K = " << K << endl;
cout << "# k = " << k << endl;
cout << "# beta = " << beta << endl;
} else if( type == LDPC_TYPE ) {
// LDPC codes
// Check command line arguments
NEED_ARG("ldpc", "type of LDPC code");
NEED_ARG("noise", "bitflip probability for binary symmetric channel");
// Check more command line arguments (seperately for each LDPC type)
if( ldpc == LDPCType::RANDOM ) {
NEED_ARG("N", "number of variables");
NEED_ARG("K", "number of factors");
NEED_ARG("k", "number of variables per factor");
NEED_ARG("j", "number of parity checks per bit");
if( N * j != K * k )
throw "Parameters should satisfy N * j == K * k";
} else if( ldpc == LDPCType::GROUP ) {
NEED_ARG("prime", "prime number");
NEED_ARG("k", "number of variables per factor");
NEED_ARG("j", "number of parity checks per bit");
if( !isPrime(prime) )
throw "Parameter <prime> should be prime";
if( !((prime-1) % j == 0 ) )
throw "Parameters should satisfy (prime-1) % j == 0";
if( !((prime-1) % k == 0 ) )
throw "Parameters should satisfy (prime-1) % k == 0";
N = prime * k;
K = prime * j;
} else if( ldpc == LDPCType::SMALL ) {
N = 4;
K = 4;
j = 3;
k = 3;
}
// Output some additional comments
cout << "# N = " << N << endl;
cout << "# K = " << K << endl;
cout << "# j = " << j << endl;
cout << "# k = " << k << endl;
if( ldpc == LDPCType::GROUP )
cout << "# prime = " << prime << endl;
cout << "# noise = " << noise << endl;
// Construct likelihood and paritycheck factors
Real likelihood[4] = {1.0 - noise, noise, noise, 1.0 - noise};
Real *paritycheck = new Real[1 << k];
createParityCheck(paritycheck, k, 0.0);
// Create LDPC structure
BipartiteGraph ldpcG;
bool regular;
do {
if( ldpc == LDPCType::GROUP )
ldpcG = createGroupStructuredLDPCGraph( prime, j, k );
else if( ldpc == LDPCType::RANDOM )
ldpcG = createRandomBipartiteGraph( N, K, j, k );
else if( ldpc == LDPCType::SMALL )
ldpcG = createSmallLDPCGraph();
regular = true;
for( size_t i = 0; i < N; i++ )
if( ldpcG.nb1(i).size() != j )
regular = false;
for( size_t I = 0; I < K; I++ )
if( ldpcG.nb2(I).size() != k )
regular = false;
} while( !regular && !ldpcG.isConnected() );
// Convert to FactorGraph
vector<Factor> factors;
for( size_t I = 0; I < K; I++ ) {
VarSet vs;
for( size_t _i = 0; _i < k; _i++ ) {
size_t i = ldpcG.nb2(I)[_i];
vs |= Var( i, 2 );
}
factors.push_back( Factor( vs, paritycheck ) );
}
delete paritycheck;
// Generate noise vector
vector<char> noisebits(N,0);
size_t bitflips = 0;
for( size_t i = 0; i < N; i++ ) {
if( rnd_uniform() < noise ) {
noisebits[i] = 1;
bitflips++;
}
}
cout << "# bitflips = " << bitflips << endl;
// Simulate transmission of all-zero codeword
vector<char> input(N,0);
vector<char> output(N,0);
for( size_t i = 0; i < N; i++ )
output[i] = (input[i] + noisebits[i]) & 1;
// Add likelihoods
for( size_t i = 0; i < N; i++ )
factors.push_back( Factor(Var(i,2), likelihood + output[i]*2) );
// Construct Factor Graph
fg = FactorGraph( factors );
} else
throw "Invalid type";
// Output additional comments
cout << "# N = " << fg.nrVars() << endl;
cout << "# seed = " << seed << endl;
// Output factor graph
cout << fg;
} catch( const char *e ) {
/// Display error message
cerr << "Error: " << e << endl;
return 1;
}
return 0;
}
void checkMatching(unsigned matchingSize, Edges edgesToAdd)
{
for (auto edge : edgesToAdd) g.addEdge(edge);
verifyMatching(g, matchingSize);
}
int main( int argc, char *argv[] ) {
try {
size_t N, K, k, d, j, n1, n2, n3;
size_t prime;
size_t seed;
Real beta, sigma_w, sigma_th, noise, mean_w, mean_th;
string type;
size_t states = 2;
// Declare the supported options.
po::options_description desc("Allowed options");
desc.add_options()
("help", "produce help message")
("type", po::value<string>(&type), "factor graph type:\n\t'full', 'grid', 'grid_torus', 'dreg', 'loop', 'tree', 'hoi', 'ldpc_random', 'ldpc_group', 'ldpc_small', 'potts3d'")
("seed", po::value<size_t>(&seed), "random number seed (tries to read from /dev/urandom if not specified)")
("N", po::value<size_t>(&N), "number of variables (not for type=='ldpc_small')")
("n1", po::value<size_t>(&n1), "width of 3D grid (only for type=='potts3d')")
("n2", po::value<size_t>(&n2), "height of 3D grid (only for type=='potts3d')")
("n3", po::value<size_t>(&n3), "length of 3D grid (only for type=='potts3d')")
("K", po::value<size_t>(&K), "number of factors\n\t(only for type=='hoi' and 'type=='ldpc_{random,group}')")
("k", po::value<size_t>(&k), "number of variables per factor\n\t(only for type=='hoi' and type=='ldpc_{random,group}')")
("d", po::value<size_t>(&d), "variable connectivity\n\t(only for type=='dreg')")
("j", po::value<size_t>(&j), "number of parity checks per bit\n\t(only for type=='ldpc_{random,group}')")
("prime", po::value<size_t>(&prime), "prime number for construction of LDPC code\n\t(only for type=='ldpc_group')")
("beta", po::value<Real>(&beta), "stddev of log-factor entries\n\t(only for type=='hoi', 'potts3d', 'grid' if states>2)")
("mean_w", po::value<Real>(&mean_w), "mean of pairwise interactions w_{ij}\n\t(not for type=='hoi', 'ldpc_*', 'potts3d')")
("mean_th", po::value<Real>(&mean_th), "mean of singleton interactions th_i\n\t(not for type=='hoi', 'ldpc_*', 'potts3d')")
("sigma_w", po::value<Real>(&sigma_w), "stddev of pairwise interactions w_{ij}\n\t(not for type=='hoi', 'ldpc_*', 'potts3d')")
("sigma_th", po::value<Real>(&sigma_th), "stddev of singleton interactions th_i\n\t(not for type=='hoi', 'ldpc_*', 'potts3d'")
("noise", po::value<Real>(&noise), "bitflip probability for binary symmetric channel (only for type=='ldpc')")
("states", po::value<size_t>(&states), "number of states of each variable (should be 2 for all but type=='grid', 'grid_torus', 'loop', 'potts3d')")
;
po::variables_map vm;
po::store(po::parse_command_line(argc, argv, desc), vm);
po::notify(vm);
if( vm.count("help") || !vm.count("type") ) {
if( vm.count("type") ) {
if( type == FULL_TYPE ) {
cout << "Creates fully connected pairwise graphical model of <N> binary variables;" << endl;
} else if( type == GRID_TYPE ) {
cout << "Creates (non-periodic) 2D Ising grid of (approx.) <N> variables (which need not be binary);" << endl;
} else if( type == GRID_TORUS_TYPE ) {
cout << "Creates periodic 2D Ising grid of (approx.) <N> variables (which need not be binary);" << endl;
} else if( type == DREG_TYPE ) {
cout << "Creates random d-regular graph of <N> binary variables with uniform degree <d>" << endl;
cout << "(where <d><N> should be even);" << endl;
} else if( type == LOOP_TYPE ) {
cout << "Creates a pairwise graphical model consisting of a single loop of" << endl;
cout << "<N> variables (which need not be binary);" << endl;
} else if( type == TREE_TYPE ) {
cout << "Creates a pairwise, connected graphical model without cycles (i.e., a tree)" << endl;
cout << "of <N> binary variables;" << endl;
} else if( type == HOI_TYPE ) {
cout << "Creates a random factor graph of <N> binary variables and" << endl;
cout << "<K> factors, each factor being an interaction of <k> variables." << endl;
cout << "The entries of the factors are exponentials of i.i.d. Gaussian" << endl;
cout << "variables with mean 0 and standard deviation <beta>." << endl;
} else if( type == LDPC_RANDOM_TYPE ) {
cout << "Simulates LDPC decoding problem, using a LDPC code of <N> bits and <K> parity" << endl;
cout << "checks, with <k> bits per check and <j> checks per bit, transmitted on a binary" << endl;
cout << "symmetric channel with probability <noise> of flipping a bit. The transmitted" << endl;
cout << "codeword has all bits set to zero. The LDPC code is randomly generated." << endl;
} else if( type == LDPC_GROUP_TYPE ) {
cout << "Simulates LDPC decoding problem, using a LDPC code of <N> bits and <K> parity" << endl;
cout << "checks, with <k> bits per check and <j> checks per bit, transmitted on a binary" << endl;
cout << "symmetric channel with probability <noise> of flipping a bit. The transmitted" << endl;
cout << "codeword has all bits set to zero. The LDPC code is constructed (using group" << endl;
cout << "theory) using a parameter <prime>; <j> and <k> should both be divisors of <prime>-1." << endl;
} else if( type == LDPC_SMALL_TYPE ) {
cout << "Simulates LDPC decoding problem, using a LDPC code of 4 bits and 4 parity" << endl;
cout << "checks, with 3 bits per check and 3 checks per bit, transmitted on a binary" << endl;
cout << "symmetric channel with probability <noise> of flipping a bit. The transmitted" << endl;
cout << "codeword has all bits set to zero. The LDPC code is fixed." << endl;
} else if( type == POTTS3D_TYPE ) {
cout << "Builds 3D Potts model of size <n1>x<n2>x<n3> with nearest-neighbour Potts" << endl;
cout << "interactions with <states> states and inverse temperature <beta>." << endl;
} else
cerr << "Unknown type (should be one of 'full', 'grid', 'grid_torus', 'dreg', 'loop', 'tree', 'hoi', 'ldpc_random', 'ldpc_group', 'ldpc_small', 'potts3d')" << endl;
if( type == FULL_TYPE || type == GRID_TYPE || type == GRID_TORUS_TYPE || type == DREG_TYPE || type == LOOP_TYPE || type == TREE_TYPE ) {
if( type == GRID_TYPE || type == GRID_TORUS_TYPE || type == LOOP_TYPE ) {
cout << "if <states> > 2: factor entries are exponents of Gaussians with mean 0 and standard deviation beta; otherwise," << endl;
}
cout << "singleton interactions are Gaussian with mean <mean_th> and standard" << endl;
cout << "deviation <sigma_th>; pairwise interactions are Gaussian with mean" << endl;
cout << "<mean_w> and standard deviation <sigma_w>." << endl;
}
}
cout << endl << desc << endl;
return 1;
}
if( !vm.count("states") )
states = 2;
if( !vm.count("seed") ) {
ifstream infile;
bool success;
infile.open( "/dev/urandom" );
success = infile.is_open();
if( success ) {
infile.read( (char *)&seed, sizeof(size_t) / sizeof(char) );
success = infile.good();
infile.close();
}
if( !success )
throw "Please specify random number seed.";
}
rnd_seed( seed );
FactorGraph fg;
cout << "# Factor graph made by " << argv[0] << endl;
cout << "# type = " << type << endl;
if( type == FULL_TYPE ) {
if( !vm.count("N") || !vm.count("mean_w") || !vm.count("mean_th") || !vm.count("sigma_w") || !vm.count("sigma_th") )
throw "Please specify all required arguments";
MakeFullFG( N, mean_w, mean_th, sigma_w, sigma_th, fg );
cout << "# N = " << N << endl;
cout << "# mean_w = " << mean_w << endl;
cout << "# mean_th = " << mean_th << endl;
cout << "# sigma_w = " << sigma_w << endl;
cout << "# sigma_th = " << sigma_th << endl;
} else if( type == GRID_TYPE || type == GRID_TORUS_TYPE ) {
#define NEED_ARG(name, desc) do { if(!vm.count(name)) throw "Please specify " desc " with --" name; } while(0);
if( states > 2 ) {
NEED_ARG("N", "number of nodes");
NEED_ARG("beta", "stddev of log-factor entries");
} else {
NEED_ARG("N", "number of nodes");
NEED_ARG("mean_w", "mean of pairwise interactions");
NEED_ARG("mean_th", "mean of singleton interactions");
NEED_ARG("sigma_w", "stddev of pairwise interactions");
NEED_ARG("sigma_th", "stddev of singleton interactions");
}
size_t n = (size_t)sqrt((long double)N);
N = n * n;
bool periodic = false;
if( type == GRID_TYPE )
periodic = false;
else
periodic = true;
if( states > 2 )
MakeGridNonbinaryFG( periodic, n, states, beta, fg );
else
MakeGridFG( periodic, n, mean_w, mean_th, sigma_w, sigma_th, fg );
cout << "# n = " << n << endl;
cout << "# N = " << N << endl;
if( states > 2 )
cout << "# beta = " << beta << endl;
else {
cout << "# mean_w = " << mean_w << endl;
cout << "# mean_th = " << mean_th << endl;
cout << "# sigma_w = " << sigma_w << endl;
cout << "# sigma_th = " << sigma_th << endl;
}
} else if( type == DREG_TYPE ) {
if( !vm.count("N") || !vm.count("mean_w") || !vm.count("mean_th") || !vm.count("sigma_w") || !vm.count("sigma_th") || !vm.count("d") )
throw "Please specify all required arguments";
MakeDRegFG( N, d, mean_w, mean_th, sigma_w, sigma_th, fg );
cout << "# N = " << N << endl;
cout << "# d = " << d << endl;
cout << "# mean_w = " << mean_w << endl;
cout << "# mean_th = " << mean_th << endl;
cout << "# sigma_w = " << sigma_w << endl;
cout << "# sigma_th = " << sigma_th << endl;
} else if( type == LOOP_TYPE ) {
if( states > 2 ) {
if( !vm.count("N") || !vm.count("beta") )
throw "Please specify all required arguments";
} else {
if( !vm.count("N") || !vm.count("mean_w") || !vm.count("mean_th") || !vm.count("sigma_w") || !vm.count("sigma_th") )
throw "Please specify all required arguments";
}
if( states > 2 )
MakeLoopNonbinaryFG( N, states, beta, fg );
else
MakeLoopFG( N, mean_w, mean_th, sigma_w, sigma_th, fg );
cout << "# N = " << N << endl;
if( states > 2 )
cout << "# beta = " << beta << endl;
else {
cout << "# mean_w = " << mean_w << endl;
cout << "# mean_th = " << mean_th << endl;
cout << "# sigma_w = " << sigma_w << endl;
cout << "# sigma_th = " << sigma_th << endl;
}
} else if( type == TREE_TYPE ) {
if( !vm.count("N") || !vm.count("mean_w") || !vm.count("mean_th") || !vm.count("sigma_w") || !vm.count("sigma_th") )
throw "Please specify all required arguments";
MakeTreeFG( N, mean_w, mean_th, sigma_w, sigma_th, fg );
cout << "# N = " << N << endl;
cout << "# mean_w = " << mean_w << endl;
cout << "# mean_th = " << mean_th << endl;
cout << "# sigma_w = " << sigma_w << endl;
cout << "# sigma_th = " << sigma_th << endl;
} else if( type == HOI_TYPE ) {
if( !vm.count("N") || !vm.count("K") || !vm.count("k") || !vm.count("beta") )
throw "Please specify all required arguments";
do {
MakeHOIFG( N, K, k, beta, fg );
} while( !fg.isConnected() );
cout << "# N = " << N << endl;
cout << "# K = " << K << endl;
cout << "# k = " << k << endl;
cout << "# beta = " << beta << endl;
} else if( type == LDPC_RANDOM_TYPE || type == LDPC_GROUP_TYPE || type == LDPC_SMALL_TYPE ) {
if( !vm.count("noise") )
throw "Please specify all required arguments";
if( type == LDPC_RANDOM_TYPE ) {
if( !vm.count("N") || !vm.count("K") || !vm.count("j") || !vm.count("k") )
throw "Please specify all required arguments";
if( N * j != K * k )
throw "Parameters should satisfy N * j == K * k";
} else if( type == LDPC_GROUP_TYPE ) {
if( !vm.count("prime") || !vm.count("j") || !vm.count("k") )
throw "Please specify all required arguments";
if( !isPrime(prime) )
throw "Parameter <prime> should be prime";
if( !((prime-1) % j == 0 ) )
throw "Parameters should satisfy (prime-1) % j == 0";
if( !((prime-1) % k == 0 ) )
throw "Parameters should satisfy (prime-1) % k == 0";
N = prime * k;
K = prime * j;
} else if( type == LDPC_SMALL_TYPE ) {
N = 4;
K = 4;
j = 3;
k = 3;
}
cout << "# N = " << N << endl;
cout << "# K = " << K << endl;
cout << "# j = " << j << endl;
cout << "# k = " << k << endl;
if( type == LDPC_GROUP_TYPE )
cout << "# prime = " << prime << endl;
cout << "# noise = " << noise << endl;
// p = 31, j = 3, k = 5
// p = 37, j = 3, k = 4
// p = 7 , j = 2, k = 3
// p = 29, j = 2, k = 4
// Construct likelihood and paritycheck factors
Real likelihood[4] = {1.0 - noise, noise, noise, 1.0 - noise};
Real *paritycheck = new Real[1 << k];
MakeParityCheck(paritycheck, k, 0.0);
// Create LDPC structure
BipartiteGraph ldpcG;
bool regular;
do {
if( type == LDPC_GROUP_TYPE )
ldpcG = CreateGroupStructuredLDPCGraph( prime, j, k );
else if( type == LDPC_RANDOM_TYPE )
ldpcG = CreateRandomBipartiteGraph( N, K, j, k );
else if( type == LDPC_SMALL_TYPE )
ldpcG = CreateSmallLDPCGraph();
regular = true;
for( size_t i = 0; i < N; i++ )
if( ldpcG.nb1(i).size() != j )
regular = false;
for( size_t I = 0; I < K; I++ )
if( ldpcG.nb2(I).size() != k )
regular = false;
} while( !regular && !ldpcG.isConnected() );
// Convert to FactorGraph
vector<Factor> factors;
for( size_t I = 0; I < K; I++ ) {
VarSet vs;
for( size_t _i = 0; _i < k; _i++ ) {
size_t i = ldpcG.nb2(I)[_i];
vs |= Var( i, 2 );
}
factors.push_back( Factor( vs, paritycheck ) );
}
delete paritycheck;
// Generate noise vector
vector<char> noisebits(N,0);
size_t bitflips = 0;
for( size_t i = 0; i < N; i++ ) {
if( rnd_uniform() < noise ) {
noisebits[i] = 1;
bitflips++;
}
}
cout << "# bitflips = " << bitflips << endl;
// Simulate transmission of all-zero codeword
vector<char> input(N,0);
vector<char> output(N,0);
for( size_t i = 0; i < N; i++ )
output[i] = (input[i] + noisebits[i]) & 1;
// Add likelihoods
for( size_t i = 0; i < N; i++ )
factors.push_back( Factor(Var(i,2), likelihood + output[i]*2) );
// Construct Factor Graph
fg = FactorGraph( factors );
} else if( type == POTTS3D_TYPE ) {
if( !vm.count("n1") || !vm.count("n2") || !vm.count("n3") || !vm.count("beta") || !vm.count("states") )
throw "Please specify all required arguments";
Make3DPotts( n1, n2, n3, states, beta, fg );
cout << "# N = " << n1*n2*n3 << endl;
cout << "# n1 = " << n1 << endl;
cout << "# n2 = " << n2 << endl;
cout << "# n3 = " << n3 << endl;
cout << "# beta = " << beta << endl;
cout << "# states = " << states << endl;
} else {
throw "Invalid type";
}
cout << "# seed = " << seed << endl;
cout << fg;
} catch( const char *e ) {
cerr << "Error: " << e << endl;
return 1;
}
return 0;
}