real IntegraleDeterministico::gauss()
{
resetIntegral();
real omega1 = ((real)128.)/225;
real omega23 = ((322+13*sqrt((real)70))/900);
real omega45 = ((322-13*sqrt((real)70))/900);
real xi23 = ( ((real)1) /3)*sqrt(5-2*sqrt( (real)(10./7) ));
real xi45 = ( ((real)1) /3)*sqrt(5+2*sqrt( (real)(10./7) ));
for (int i = 0; i < intervalli(); i++) {
real c = (x_i(i+1)+x_i(i))/2.;
real m = (x_i(i+1)-x_i(i))/2.;
// http://mathworld.wolfram.com/Legendre-GaussQuadrature.html
add( m*omega1*f_test(c) ); // root = 0
add( m*omega23*f_test(c - m*xi23) );
add( m*omega23*f_test(c + m*xi23) );
add( m*omega45*f_test(c - m*xi45) );
add( m*omega45*f_test(c + m*xi45) );
}
return getIntegral();
}
real IntegraleDeterministico::simpson()
{
resetIntegral();
for (int i = 0; i < intervalli()-1; i+=2) {
add( h()/3 * (f_test(x_i(i)) + 4*f_test(x_i(i+1)) + f_test(x_i(i+2)) ) );
}
return getIntegral();
}
real IntegraleDeterministico::trapezi()
{
resetIntegral();
for (int i = 0; i < intervalli(); i++) {
add( h()/2 * (f_test(x_i(i)) + f_test(x_i(i+1)) ) );
}
return getIntegral();
}
void CParam::CalculateInitProbA(CData &Data) {
// initial value of Y_out_compact and z_out
int count_out = 0; int count_in = 0;
ColumnVector z_out_large(toolarge_nout);
Matrix Y_out_compact_large(toolarge_nout,n_var_independent);
while ( (count_in < Data.n_sample) && (count_out < toolarge_nout) ) {
int k = rdiscrete_fn(pi);
ColumnVector mu_k = Mu.column(k); // Note that mu_k is Mu.column(k)
ColumnVector y_compact_i = rMVN_fn( mu_k,LSIGMA[k-1] );
ColumnVector x_compact_i = exp_ColumnVector(y_compact_i);
ColumnVector x_i(Data.n_var) ;
Data.UpdateFullVector(x_compact_i, x_i);
Data.update_full_x_for_balance_edit(x_i);
if (Data.PassEdits(x_i)) {
count_in++;
} else {
count_out++;
Y_out_compact_large.row(count_out) = y_compact_i.t();
z_out_large(count_out)=k;
}
}
Matrix Y_out_compact = Y_out_compact_large.rows(1,count_out) ; // cut extra space
ColumnVector z_out = z_out_large.rows(1,count_out) ; // cut extra space
// calculate n_z and Sum_groupX
Matrix Y_aug_compact = Y_in_compact & Y_out_compact;
ColumnVector z_aug = z_in & z_out;
int n_out = z_out.nrows();
Prob_A = (1.0 * Data.n_sample / (Data.n_sample+n_out));
}
TEST(generateExpression, algebra_solver) {
static const bool user_facing = true;
std::stringstream msgs;
stan::lang::algebra_solver so; // null ctor should work and not raise error
std::string system_function_name = "bronzino";
stan::lang::variable y("y_var_name");
y.set_type(stan::lang::vector_type());
stan::lang::variable theta("theta_var_name");
theta.set_type(stan::lang::vector_type());
stan::lang::variable x_r("x_r_r_var_name");
x_r.set_type(stan::lang::bare_array_type(stan::lang::double_type()));
stan::lang::variable x_i("x_i_var_name");
x_i.set_type(stan::lang::bare_array_type(stan::lang::int_type()));
stan::lang::algebra_solver so2(system_function_name, y, theta, x_r, x_i);
stan::lang::expression e1 = so2;
generate_expression(e1, user_facing, msgs);
EXPECT_EQ(msgs.str(),
"algebra_solver(bronzino_functor__(), y_var_name, "
"theta_var_name, x_r_r_var_name, x_i_var_name, pstream__)");
}
void SolveSystem (
Vector<double, int>& x_local,
const MatrixDense<double, int>& K_local,
const Vector<double, int>& b_local,
const int numb_node_i,
const int* list_node_i,
const int* l2i,
int numb_node_p,
const int* list_node_p,
const int* l2p,
const int numb_global_node,
const int numb_l2g,
const int* l2g,
const MPI_Comm& mpi_comm ) {
// -- number of processors
int numb_procs;
// -- process number (process rank)
int proc_numb;
// -- get number of processes
MPI_Comm_size( mpi_comm, &numb_procs );
// -- get current process rank
MPI_Comm_rank( mpi_comm, &proc_numb );
MatrixDense<double,int> Kii;
MatrixDense<double,int> Kip;
MatrixDense<double,int> Kpi;
MatrixDense<double,int> Kpp;
Schur::SplitMatrixToBlock(Kii, Kip, Kpi, Kpp, K_local,
list_node_i, numb_node_i,
list_node_p, numb_node_p);
// Check transpose
//CheckTranspose(Kip, Kpi);
// Reconstruct K
//std::string gmatrix_filename = "../output/cube-125_2/cube-125_g_2.csv";
//ReconstructK(K_local, l2g, numb_global_node, gmatrix_filename, mpi_comm);
// LU factorization of Kii
MatrixDense<double, int> Kii_lu;
Factor::LU(Kii_lu, Kii);
MatrixDense<double, int> Uii_inv,Lii_inv;
Lii_inv.Allocate(numb_node_i, numb_node_i);
Uii_inv.Allocate(numb_node_i, numb_node_i);
Vector<double, int> x,rhs;
rhs.Allocate(numb_node_i);
for(int i = 0;i < numb_node_i;++i)
rhs(i) = 0;
// invert Lii and Uii
for(int i = 0;i < numb_node_i;++i){
if(i > 0) rhs(i - 1) = 0;
rhs(i) = 1;
DirectSolver::Forward(x, Kii_lu, rhs);
for(int j = 0;j < numb_node_i;++j)
Lii_inv(j,i) = x(j);
DirectSolver::Backward(x,Kii_lu, rhs);
for(int j = 0;j < numb_node_i;++j)
Uii_inv(j,i) = x(j);
}
// calculate S_local
MatrixDense<double, int> Lpi,Uip,prod;
Kpi.MatrixMatrixProduct(Lpi, Uii_inv);
Lii_inv.MatrixMatrixProduct(Uip, Kip);
Lpi.MatrixMatrixProduct(prod, Uip);
MatrixDense<double, int> S_local;
Kpp.MatrixMatrixSubstraction(S_local, prod);
// merge all numb_node_p in one list
int length_list_p[numb_procs];
MPI_Allgather(&numb_node_p, 1, MPI_INT, length_list_p, 1, MPI_INT, mpi_comm);
/*std::stringstream out_length_list;
for(int i = 0;i < numb_procs;++i){
out_length_list << length_list_p[i] << " ";
}
out_length_list << "\n";*/
int all_list_global_p[numb_procs][numb_global_node];
for(int i = 0;i < numb_procs;++i){
if(proc_numb == i){
for(int j = 0;j < numb_node_p;++j){
all_list_global_p[i][j] = l2g[ list_node_p[j] ];
}
}
MPI_Bcast(all_list_global_p[i], length_list_p[i], MPI_INT, i, mpi_comm);
}
/*for(int i = 0;i < numb_procs;++i){
for(int j = 0;j < length_list_p[i];++j){
out_length_list << all_list_global_p[i][j] << " ";
}
out_length_list << "\n";
}
iomrg::printf("%s\n", out_length_list.str().c_str());*/
// create array pos_S : from global position to position in S
int pos_S[numb_global_node];
for(int i = 0;i < numb_global_node;++i){
pos_S[i] = -1;
}
std::vector<int> S_indices;
for(int i = 0;i < numb_procs;++i){
for(int j = 0;j < length_list_p[i];++j){
S_indices.push_back(all_list_global_p[i][j]);
}
}
std::sort(S_indices.begin(), S_indices.end());
S_indices.erase(std::unique(S_indices.begin(), S_indices.end()), S_indices.end());
int size_S = S_indices.size();
for(int i = 0;i < size_S;++i){
pos_S[ S_indices[i] ] = i;
}
// Assemble S
MatrixDense<double, int> S;
S.Allocate(size_S, size_S);
S.Initialize(0);
double aux_coef[size_S];
iomrg::printf("size_S = %d\n",size_S);
for(int i = 0;i < numb_procs;++i){
int size_local_S = length_list_p[i];
for(int j = 0;j < size_local_S;++j){
if(proc_numb == i){
for(int k = 0;k < size_local_S;++k){
aux_coef[k] = S_local(j,k);
}
}
MPI_Bcast(aux_coef, size_local_S, MPI_DOUBLE, i, mpi_comm);
int r = pos_S[ all_list_global_p[i][j] ];
for(int k = 0;k < size_local_S;++k){
S(r, pos_S[ all_list_global_p[i][k] ]) += aux_coef[k];
}
}
}
// Separate b_local
Vector<double, int> b_i,b_p;
b_i.Allocate(numb_node_i);
b_p.Allocate(numb_node_p);
for(int i = 0;i < numb_l2g;++i){
if(l2p[i] == -1){
b_i( l2i[i] ) = b_local(i);
}else{
b_p( l2p[i] ) = b_local(i);
}
}
// Calculate y_p_local
Vector<double, int> z;
DirectSolver::Forward(z, Kii_lu, b_i);
Vector<double, int> aux_prod;
Lpi.MatrixVectorProduct(aux_prod, z);
Vector<double, int> y_p_local;
y_p_local.Allocate(numb_node_p);
for(int i = 0;i < numb_node_p;++i){
y_p_local(i) = b_p(i) - aux_prod(i);
}
// Calculate y_p
Vector<double, int> y_p(size_S);
for(int i = 0;i < size_S;++i){
aux_coef[i] = 0;
}
for(int i = 0;i < numb_node_p;++i){
aux_coef[ pos_S[ l2g[ list_node_p[i] ] ] ] += y_p_local(i);
}
MPI_Allreduce(aux_coef, y_p.GetCoef(), size_S, MPI_DOUBLE, MPI_SUM,mpi_comm);
// Calculate x_p
Vector<double, int> x_p;
DirectSolver::SolveLU(x_p, S, y_p);
// Calculate y_i
Vector<double, int> aux_prod_2;
aux_prod_2.Allocate(numb_node_i);
aux_prod_2.Assign(0, numb_node_i - 1, 0);
for(int i = 0;i < numb_node_i;++i){
for(int j = 0;j < numb_node_p;++j){
int id_S = pos_S[ l2g[ list_node_p[j] ] ];
aux_prod_2(i) += Uip(i,j) * x_p(id_S);
}
}
Vector<double, int> y_i;
y_i.Allocate(numb_node_i);
for(int i = 0;i < numb_node_i;++i){
y_i(i) = z(i) - aux_prod_2(i);
}
// Calculate x_i
Vector<double, int> x_i;
DirectSolver::Backward(x_i, Kii_lu, y_i);
// Assemble x_local
for(int i = 0;i < numb_node_i;++i){
x_local(list_node_i[i]) = x_i(i);
}
for(int i = 0;i < numb_node_p;++i){
x_local(list_node_p[i]) = x_p(i);
}
}