long nk(long n,long k)
{
if( k>n )return 0;
if( n==0)return 1;
if( k==0)return 1;
return nk( n-1,k) + nk(n-1,k-1);
}
int main()
{
long n;
long k;
while(1)
{
cin >> n >> k;
cout << nk(n,k);
}
return 0;
}
T binomial_coefficient(T n, T k) {
T nk(n-k);
if (k <= nk){
std::swap(k,nk);
}
auto numerator = factors_from_down_to(n,k+T(1));
auto denominator = factorial(nk);
return numerator / denominator;
}
std::string SwordFuncs::lookup(std::string ref) {
std::ostringstream output;
// Set up module specific variables
sword::VerseKey vk;
// Variables related to splitting up the reference for iteration
sword::ListKey refRange = vk.parseVerseList(ref.c_str(), vk, true);
refRange.setPersist(true);
module->setKey(refRange);
try {
int i = 0;
for ((*module) = sword::TOP; !module->popError(); (*module)++) {
i++;
sword::VerseKey nk(module->getKey());
sword::SWBuf buffer = module->renderText();
std::string text = buffer.c_str();
if (versenum) {
output << " " << nk.getVerse();
}
output << " " << trim(text);
}
if (i > 1)
output << std::endl << module->getKey()->getRangeText();
vkey = module->getKey();
} catch (const std::runtime_error &re) {
// speciffic handling for runtime_error
std::cerr << "Runtime error: " << re.what() << std::endl;
} catch (const std::exception &ex) {
// speciffic handling for all exceptions extending std::exception, except
// std::runtime_error which is handled explicitly
std::cerr << "Error occurred: " << ex.what() << std::endl;
} catch (...) {
// catch any other errors (that we have no information about)
std::cerr << "Unknown failure occured. Possible memory corruption"
<< std::endl;
}
return output.str();
}
gaussian_model EMclustering::maximization(MatrixXf x, MatrixXf r)
{
int d = x.rows();
int n = x.cols();
int k = r.cols();
//cerr<<x<<endl;
VectorXf nk(r.rows());
nk = r.colwise().sum();
VectorXf w(nk.size());
w = nk/n;
MatrixXf tmp1(x.rows(),r.cols());
tmp1 = x * r;
VectorXf tmp2(nk.size());
tmp2 = nk.array().inverse();
//cerr<<tmp2<<endl<<endl;
MatrixXf mu(x.rows(),r.cols());
mu = tmp1 * tmp2.asDiagonal() ;
MatrixXf *sigma = new MatrixXf[k];
for(int i=0;i<k;i++)
sigma[i].setZero(d,d);
MatrixXf sqrtr(r.rows(),r.cols());
sqrtr = r.cwiseSqrt();
MatrixXf xo(d,n);
MatrixXf tmp3(d,d);
tmp3.setIdentity(d,d);
for(int i=0;i<k;i++)
{
xo = x.colwise() - mu.col(i);
VectorXf tmp4(sqrtr.rows());
tmp4 = sqrtr.col(i);
tmp4 = tmp4.adjoint();
xo = xo* tmp4.asDiagonal();
sigma[i] = xo*xo.adjoint()/nk(i);
sigma[i] = sigma[i] + tmp3*1e-6;
//cerr<<sigma[i]<<endl<<endl;
}
gaussian_model model;
model.mu = mu;
model.sigma = new MatrixXf[k];
for(int i=0;i<k;i++)
model.sigma[i] = sigma[i];
model.weight = w;
nk.resize(0);
w.resize(0);
tmp1.resize(0,0);
tmp2.resize(0);
tmp3.resize(0,0);
mu.resize(0,0);
for(int i=0;i<k;i++)
sigma[i].resize(0,0);
delete [] sigma;
sqrtr.resize(0,0);
xo.resize(0,0);
tmp3.resize(0,0);
//cerr<<"---"<<endl;
model.weight = model.weight.adjoint();
//cerr<<model.weight<<endl<<endl;
//cerr<<model.mu<<endl<<endl;
//for(int i=0;i<k;i++)
//{
// cerr<<model.sigma[i]<<endl<<endl;
//}
return model;
}
SEXP multitask(SEXP X0, SEXP y0, SEXP nk0, SEXP groups0, SEXP lambda0, SEXP corrfactor0, SEXP model0, SEXP conveps0, SEXP eps0, SEXP maxiter0,SEXP maxitersg0)
{
Rcpp::NumericVector lasso_result;
//convert parameters to Rcpp types
Rcpp::NumericMatrix X(X0);
Rcpp::NumericVector y(y0);
Rcpp::IntegerVector nk(nk0);
int K = nk.size();
Rcpp::IntegerMatrix groups(groups0);
Rcpp::NumericVector corrfactor(corrfactor0);
double lambda = Rcpp::as<double>(lambda0);
int model = Rcpp::as<int>(model0);
double eps = Rcpp::as<double>(eps0);
double conveps = Rcpp::as<double>(conveps0);
int maxiter = Rcpp::as<int>(maxiter0);
int maxitersg = Rcpp::as<int>(maxitersg0);
assert(K > 0);
assert(lambda >= 0.0);
assert(model >= 0);
assert(model < MULTITASK_MODEL_COUNT);
assert(eps > 0.0);
assert(maxiter > 0);
assert(maxitersg > 0);
int p = groups.nrow();
int L = groups.ncol();
//initialize start values
Rcpp::NumericMatrix alpha_cur(p, K);
for (int i = 0; i < p * K; i++) {
alpha_cur[i] = random(-0.1, 0.1);
}
Rcpp::NumericMatrix beta_cur = alpha_cur;
Rcpp::NumericVector d_cur(L);
std::fill(d_cur.begin(), d_cur.end(), 1.0);
Rcpp::NumericMatrix eta_cur(L, K);
std::fill(eta_cur.begin(), eta_cur.end(), 1.0);
Rcpp::IntegerVector nz_cur(p*K + L*K + L);
std::fill(nz_cur.begin(), nz_cur.end(), 1);
Rcpp::NumericMatrix beta_new;
bool converged = false;
int iterations = 0;
do {
++iterations;
if (iterations >= maxiter && maxiter > 0) {
break;
}
//update alpha
Rcpp::NumericMatrix alpha_new(p, K);
Rcpp::NumericMatrix Xtilde = x_tilde(X, nk, groups, d_cur, eta_cur);
int idx = 0; int n;
for(int k=0; k < K; k++){
n = nk[k];
lasso_result = lasso(Xtilde(Rcpp::Range(idx,idx+n-1), Rcpp::Range(p*k, p*(k+1)-1)), y[Rcpp::Range(idx,idx+n-1)], lambda*corrfactor[k], model, false, eps, maxitersg);
assert(lasso_result.size() == p);
for (int j = 0; j < p; j++) {
alpha_new(j,k) = lasso_result[j];
}
idx += n;
}
//update d
Rcpp::NumericMatrix Xtilde2 = x_tilde_2(X, nk, groups, alpha_new, eta_cur);
lasso_result = lasso(Xtilde2, y, 1.0, model, true, eps, maxitersg);
assert(lasso_result.size() == L);
Rcpp::NumericVector d_new(L);
for (int i = 0; i < L; i++) {
d_new[i] = lasso_result[i]/max(lasso_result);
if(std::isnan(d_new[i])) d_new[i] = 0;
}
//update eta
Rcpp::NumericMatrix eta_new(L, K);
Rcpp::NumericMatrix Xtilde3 = x_tilde_3(X, nk, groups, alpha_new, d_new);
idx = 0;
for(int k=0; k < K; k++){
n = nk[k];
lasso_result = lasso(Xtilde3(Rcpp::Range(idx,idx+n-1),Rcpp::Range(L*k, L*(k+1)-1)), y[Rcpp::Range(idx,idx+n-1)], 1.0, model, true, eps, maxitersg);
assert(lasso_result.size() == L);
for (int l = 0; l < L; l++) {
eta_new(l,k) = lasso_result[l];
}
idx += n;
}
//update beta
beta_new = next_beta(nk, groups, alpha_new, d_new, eta_new);
assert(beta_new.nrow() == p);
assert(beta_new.ncol() == K);
//check structure convergence
Rcpp::IntegerVector nz_new = nz_vec(alpha_new,eta_new,d_new,eps);
int nz_diff = 0;
for (int i = 0; i < nz_new.length(); i++) {
nz_diff += nz_cur[i] - nz_new[i];
}
double max_diff = 0.0;
for (int i = 0; i < p * K; i++) {
double diff = fabs(beta_new[i] - beta_cur[i]);
if (diff > max_diff) {
max_diff = diff;
}
}
if (max_diff < conveps && nz_diff==0) {
converged = true;
}
alpha_cur = alpha_new;
d_cur = d_new;
eta_cur = eta_new;
beta_cur = beta_new;
nz_cur = nz_new;
} while (converged != true);
Rcpp::NumericMatrix beta_refit = refit_model(X, y,beta_new, nk, model, eps, maxitersg);
Rcpp::List result;
result["beta"] = beta_refit;
result["d"] = nz(d_cur,eps);
result["eta"] = nz(eta_cur,eps);
switch (model) {
case MULTITASK_LINEAR:
result["bic"] = bic_linear(X, y, beta_refit, eps, nk);
break;
case MULTITASK_LOGISTIC:
result["bic"] = bic_logistic(X, y, beta_refit, eps, nk);
break;
default:
assert(0);
}
result["converged"] = converged;
return result;
}