double Lasso(size_t m, size_t n) {
std::vector<T> A(m * n);
std::vector<T> b(m);
std::default_random_engine generator;
std::uniform_real_distribution<T> u_dist(static_cast<T>(0),
static_cast<T>(1));
std::normal_distribution<T> n_dist(static_cast<T>(0),
static_cast<T>(1));
for (unsigned int i = 0; i < m * n; ++i)
A[i] = n_dist(generator);
std::vector<T> x_true(n);
for (unsigned int i = 0; i < n; ++i)
x_true[i] = u_dist(generator) < static_cast<T>(0.8)
? static_cast<T>(0) : n_dist(generator) / static_cast<T>(std::sqrt(n));
#ifdef _OPENMP
#pragma omp parallel for
#endif
for (unsigned int i = 0; i < m; ++i)
for (unsigned int j = 0; j < n; ++j)
b[i] += A[i * n + j] * x_true[j];
// b[i] += A[i + j * m] * x_true[j];
for (unsigned int i = 0; i < m; ++i)
b[i] += static_cast<T>(0.5) * n_dist(generator);
T lambda_max = static_cast<T>(0);
#ifdef _OPENMP
#pragma omp parallel for reduction(max : lambda_max)
#endif
for (unsigned int j = 0; j < n; ++j) {
T u = 0;
for (unsigned int i = 0; i < m; ++i)
//u += A[i * n + j] * b[i];
u += A[i + j * m] * b[i];
lambda_max = std::max(lambda_max, std::abs(u));
}
pogs::MatrixDense<T> A_('r', m, n, A.data());
pogs::PogsDirect<T, pogs::MatrixDense<T> > pogs_data(A_);
std::vector<FunctionObj<T> > f;
std::vector<FunctionObj<T> > g;
f.reserve(m);
for (unsigned int i = 0; i < m; ++i)
f.emplace_back(kSquare, static_cast<T>(1), b[i]);
g.reserve(n);
for (unsigned int i = 0; i < n; ++i)
g.emplace_back(kAbs, static_cast<T>(0.2) * lambda_max);
double t = timer<double>();
pogs_data.Solve(f, g);
return timer<double>() - t;
}
double Logistic(size_t m, size_t n) {
std::vector<T> A(m * (n + 1));
std::vector<T> d(m);
std::vector<T> x(n + 1);
std::vector<T> y(m);
std::default_random_engine generator;
std::uniform_real_distribution<T> u_dist(static_cast<T>(0),
static_cast<T>(1));
std::normal_distribution<T> n_dist(static_cast<T>(0),
static_cast<T>(1));
for (unsigned int i = 0; i < m; ++i) {
for (unsigned int j = 0; j < n; ++j)
A[i * (n + 1) + j] = n_dist(generator);
A[i * (n + 1) + n] = 1;
}
std::vector<T> x_true(n + 1);
for (unsigned int i = 0; i < n; ++i)
x_true[i] = u_dist(generator) < 0.8 ? 0 : n_dist(generator) / n;
x_true[n] = n_dist(generator) / n;
#pragma omp parallel for
for (unsigned int i = 0; i < m; ++i) {
d[i] = 0;
for (unsigned int j = 0; j < n + 1; ++j)
// u += A[i + j * m] * x_true[j];
d[i] += A[i * n + j] * x_true[j];
}
for (unsigned int i = 0; i < m; ++i)
d[i] = 1 / (1 + std::exp(-d[i])) > u_dist(generator);
T lambda_max = static_cast<T>(0);
#pragma omp parallel for reduction(max : lambda_max)
for (unsigned int j = 0; j < n; ++j) {
T u = 0;
for (unsigned int i = 0; i < m; ++i)
// u += A[i * n + j] * (static_cast<T>(0.5) - d[i]);
u += A[i + j * m] * (static_cast<T>(0.5) - d[i]);
lambda_max = std::max(lambda_max, std::abs(u));
}
Dense<T, ROW> A_(A.data());
PogsData<T, Dense<T, ROW>> pogs_data(A_, m, n + 1);
pogs_data.x = x.data();
pogs_data.y = y.data();
pogs_data.f.reserve(m);
for (unsigned int i = 0; i < m; ++i)
pogs_data.f.emplace_back(kLogistic, 1, 0, 1, -d[i]);
pogs_data.g.reserve(n + 1);
for (unsigned int i = 0; i < n; ++i)
pogs_data.g.emplace_back(kAbs, static_cast<T>(0.5) * lambda_max);
pogs_data.g.emplace_back(kZero);
double t = timer<double>();
Pogs(&pogs_data);
return timer<double>() - t;
}
