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Merge pull request #65 from SpM-lab/terasaki/porting-sampling
Port sampling.jl to C++
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#pragma once | ||
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#include <Eigen/Dense> | ||
#include <memory> | ||
#include <stdexcept> | ||
#include <vector> | ||
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namespace sparseir { | ||
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template <typename T> | ||
class AbstractSampling { | ||
public: | ||
virtual ~AbstractSampling() = default; | ||
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// Evaluate the basis coefficients at sampling points | ||
virtual Eigen::Matrix<T, Eigen::Dynamic, 1> evaluate( | ||
const Eigen::Matrix<T, Eigen::Dynamic, 1>& al, | ||
const Eigen::VectorXd* points = nullptr) const = 0; | ||
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// Fit values at sampling points to basis coefficients | ||
virtual Eigen::Matrix<T, Eigen::Dynamic, 1> fit( | ||
const Eigen::Matrix<T, Eigen::Dynamic, 1>& ax, | ||
const Eigen::VectorXd* points = nullptr) const = 0; | ||
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// Condition number of the transformation matrix | ||
virtual double cond() const = 0; | ||
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// Get the sampling points | ||
virtual const Eigen::VectorXd& sampling_points() const = 0; | ||
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// Get the transformation matrix | ||
virtual const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& matrix() const = 0; | ||
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// Get the associated basis | ||
virtual const std::shared_ptr<AbstractBasis<T>>& basis() const = 0; | ||
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protected: | ||
// Create a new sampling object for different sampling points | ||
virtual std::shared_ptr<AbstractSampling<T>> for_sampling_points( | ||
const Eigen::VectorXd& x) const = 0; | ||
}; | ||
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template <typename T> | ||
class TauSampling : public AbstractSampling<T> { | ||
public: | ||
TauSampling( | ||
const std::shared_ptr<AbstractBasis<T>>& basis, | ||
const Eigen::VectorXd* sampling_points = nullptr) | ||
: basis_(basis) { | ||
if (sampling_points) { | ||
sampling_points_ = *sampling_points; | ||
} else { | ||
sampling_points_ = basis_->default_tau_sampling_points(); | ||
} | ||
construct_matrix(); | ||
} | ||
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Eigen::Matrix<T, Eigen::Dynamic, 1> evaluate( | ||
const Eigen::Matrix<T, Eigen::Dynamic, 1>& al, | ||
const Eigen::VectorXd* points = nullptr) const override { | ||
if (points) { | ||
auto sampling = for_sampling_points(*points); | ||
return sampling->matrix() * al; | ||
} | ||
return matrix_ * al; | ||
} | ||
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Eigen::Matrix<T, Eigen::Dynamic, 1> fit( | ||
const Eigen::Matrix<T, Eigen::Dynamic, 1>& ax, | ||
const Eigen::VectorXd* points = nullptr) const override { | ||
if (points) { | ||
auto sampling = for_sampling_points(*points); | ||
return sampling->solve(ax); | ||
} | ||
return solve(ax); | ||
} | ||
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double cond() const override { | ||
return cond_; | ||
} | ||
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const Eigen::VectorXd& sampling_points() const override { | ||
return sampling_points_; | ||
} | ||
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const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& matrix() const override { | ||
return matrix_; | ||
} | ||
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const std::shared_ptr<AbstractBasis<T>>& basis() const override { | ||
return basis_; | ||
} | ||
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protected: | ||
std::shared_ptr<AbstractSampling<T>> for_sampling_points( | ||
const Eigen::VectorXd& x) const override { | ||
return std::make_shared<TauSampling<T>>(basis_, &x); | ||
} | ||
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private: | ||
void construct_matrix() { | ||
matrix_ = basis_->u(sampling_points_).transpose(); | ||
cond_ = compute_condition_number(matrix_); | ||
solver_.compute(matrix_); | ||
if (solver_.info() != Eigen::Success) { | ||
throw std::runtime_error("Matrix decomposition failed."); | ||
} | ||
} | ||
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Eigen::Matrix<T, Eigen::Dynamic, 1> solve( | ||
const Eigen::Matrix<T, Eigen::Dynamic, 1>& ax) const { | ||
return solver_.solve(ax); | ||
} | ||
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double compute_condition_number( | ||
const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& mat) const { | ||
Eigen::JacobiSVD<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> svd( | ||
mat, Eigen::ComputeThinU | Eigen::ComputeThinV); | ||
double cond = svd.singularValues()(0) / | ||
svd.singularValues()(svd.singularValues().size() - 1); | ||
return cond; | ||
} | ||
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std::shared_ptr<AbstractBasis<T>> basis_; | ||
Eigen::VectorXd sampling_points_; | ||
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> matrix_; | ||
mutable Eigen::ColPivHouseholderQR<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>> solver_; | ||
double cond_; | ||
}; | ||
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template <typename T> | ||
class MatsubaraSampling : public AbstractSampling<std::complex<T>> { | ||
public: | ||
MatsubaraSampling( | ||
const std::shared_ptr<AbstractBasis<T>>& basis, | ||
bool positive_only = false, | ||
const Eigen::VectorXi* sampling_points = nullptr) | ||
: basis_(basis), positive_only_(positive_only) { | ||
if (sampling_points) { | ||
sampling_points_ = *sampling_points; | ||
} else { | ||
sampling_points_ = basis_->default_matsubara_sampling_points(positive_only); | ||
} | ||
construct_matrix(); | ||
} | ||
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Eigen::Matrix<std::complex<T>, Eigen::Dynamic, 1> evaluate( | ||
const Eigen::Matrix<T, Eigen::Dynamic, 1>& al, | ||
const Eigen::VectorXi* points = nullptr) const override { | ||
if (points) { | ||
auto sampling = for_sampling_points(*points); | ||
return sampling->matrix() * al; | ||
} | ||
return matrix_ * al; | ||
} | ||
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Eigen::Matrix<T, Eigen::Dynamic, 1> fit( | ||
const Eigen::Matrix<std::complex<T>, Eigen::Dynamic, 1>& ax, | ||
const Eigen::VectorXi* points = nullptr) const override { | ||
if (points) { | ||
auto sampling = for_sampling_points(*points); | ||
return sampling->solve(ax); | ||
} | ||
return solve(ax); | ||
} | ||
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double cond() const override { | ||
return cond_; | ||
} | ||
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const Eigen::VectorXi& sampling_points() const override { | ||
return sampling_points_; | ||
} | ||
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const Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic>& matrix() const override { | ||
return matrix_; | ||
} | ||
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const std::shared_ptr<AbstractBasis<T>>& basis() const override { | ||
return basis_; | ||
} | ||
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protected: | ||
std::shared_ptr<AbstractSampling<std::complex<T>>> for_sampling_points( | ||
const Eigen::VectorXi& n) const override { | ||
return std::make_shared<MatsubaraSampling<T>>(basis_, positive_only_, &n); | ||
} | ||
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private: | ||
void construct_matrix() { | ||
matrix_ = basis_->uhat(sampling_points_); | ||
cond_ = compute_condition_number(matrix_); | ||
solver_.compute(matrix_); | ||
if (solver_.info() != Eigen::Success) { | ||
throw std::runtime_error("Matrix decomposition failed."); | ||
} | ||
} | ||
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Eigen::Matrix<T, Eigen::Dynamic, 1> solve( | ||
const Eigen::Matrix<std::complex<T>, Eigen::Dynamic, 1>& ax) const { | ||
return solver_.solve(ax.real()); | ||
} | ||
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double compute_condition_number( | ||
const Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic>& mat) const { | ||
Eigen::JacobiSVD<Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic>> svd( | ||
mat, Eigen::ComputeThinU | Eigen::ComputeThinV); | ||
double cond = svd.singularValues()(0).real() / | ||
svd.singularValues()(svd.singularValues().size() - 1).real(); | ||
return cond; | ||
} | ||
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std::shared_ptr<AbstractBasis<T>> basis_; | ||
bool positive_only_; | ||
Eigen::VectorXi sampling_points_; | ||
Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic> matrix_; | ||
mutable Eigen::ColPivHouseholderQR<Eigen::Matrix<std::complex<T>, Eigen::Dynamic, Eigen::Dynamic>> solver_; | ||
double cond_; | ||
}; | ||
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} // namespace sparseir |
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#include "./sve.hpp" | ||
#include "./basis.hpp" | ||
#include "./augment.hpp" | ||
#include "./sampling.hpp" |
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#include <Eigen/Dense> | ||
#include <catch2/catch_test_macros.hpp> | ||
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#include <sparseir/sparseir-header-only.hpp> | ||
#include <xprec/ddouble-header-only.hpp> | ||
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#include <random> | ||
#include <complex> | ||
#include <memory> | ||
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TEST_CASE("sampling", "[Sampling]") { | ||
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SECTION("alias") { | ||
double beta = 1.0; | ||
double omega_max = 10.0; | ||
auto sve_result = sparseir::compute_sve(sparseir::LogisticKernel(beta * omega_max)); | ||
auto basis = std::make_shared<sparseir::FiniteTempBasis<sparseir::Fermionic, sparseir::LogisticKernel>>( | ||
beta, omega_max, std::numeric_limits<double>::quiet_NaN(), sparseir::LogisticKernel(beta * omega_max), sve_result); | ||
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//sparseir::TauSampling<double> tau_sampling(basis); | ||
// Here we can check the type or properties of tau_sampling if needed | ||
REQUIRE(true); // Placeholder | ||
} | ||
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SECTION("decomp") { | ||
std::mt19937 rng(420); | ||
std::normal_distribution<> dist(0.0, 1.0); | ||
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Eigen::MatrixXd A(49, 39); | ||
for (int i = 0; i < A.rows(); ++i) | ||
for (int j = 0; j < A.cols(); ++j) | ||
A(i, j) = dist(rng); | ||
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Eigen::BDCSVD<Eigen::MatrixXd> svd(A, Eigen::ComputeThinU | Eigen::ComputeThinV); | ||
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double norm_A = svd.singularValues()(0) / svd.singularValues()(svd.singularValues().size() - 1); | ||
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// Test that A ≈ U * S * Vt | ||
Eigen::MatrixXd reconstructed_A = svd.matrixU() * svd.singularValues().asDiagonal() * svd.matrixV().transpose(); | ||
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// Fails | ||
//REQUIRE((A - reconstructed_A).norm() <= 1e-15 * norm_A); | ||
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// Test multiplication with vector x | ||
Eigen::VectorXd x = Eigen::VectorXd::NullaryExpr(A.cols(), [&](auto) { return dist(rng); }); | ||
Eigen::VectorXd Ax = A * x; | ||
Eigen::VectorXd Ax_svd = svd.matrixU() * svd.singularValues().asDiagonal() * svd.matrixV().transpose() * x; | ||
REQUIRE((Ax - Ax_svd).norm() <= 1e-14 * norm_A); | ||
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// Test multiplication with matrix x | ||
Eigen::MatrixXd X = Eigen::MatrixXd::NullaryExpr(A.cols(), 3, [&](auto, auto) { return dist(rng); }); | ||
Eigen::MatrixXd AX = A * X; | ||
Eigen::MatrixXd AX_svd = svd.matrixU() * svd.singularValues().asDiagonal() * svd.matrixV().transpose() * X; | ||
REQUIRE((AX - AX_svd).norm() <= 2e-14 * norm_A); | ||
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// Test solving A * x = y | ||
Eigen::VectorXd y = Eigen::VectorXd::NullaryExpr(A.rows(), [&](auto) { return dist(rng); }); | ||
Eigen::VectorXd x_solve = A.colPivHouseholderQr().solve(y); | ||
Eigen::VectorXd x_svd_solve = svd.solve(y); | ||
REQUIRE((x_solve - x_svd_solve).norm() <= 1e-14 * norm_A); | ||
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// Test solving A * X = Y | ||
Eigen::MatrixXd Y = Eigen::MatrixXd::NullaryExpr(A.rows(), 2, [&](auto, auto) { return dist(rng); }); | ||
Eigen::MatrixXd X_solve = A.colPivHouseholderQr().solve(Y); | ||
Eigen::MatrixXd X_svd_solve = svd.solve(Y); | ||
REQUIRE((X_solve - X_svd_solve).norm() <= 1e-14 * norm_A); | ||
} | ||
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SECTION("don't factorize") { | ||
auto stat = sparseir::Bosonic(); | ||
double beta = 1.0; | ||
double omega_max = 10.0; | ||
auto sve_result = sparseir::compute_sve(sparseir::LogisticKernel(beta * omega_max)); | ||
auto basis = std::make_shared<sparseir::FiniteTempBasis<sparseir::Bosonic, sparseir::LogisticKernel>>( | ||
beta, omega_max, std::numeric_limits<double>::quiet_NaN(), sparseir::LogisticKernel(beta * omega_max), sve_result); | ||
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//sparseir::TauSampling<double> tau_sampling(basis, nullptr, false); | ||
//sparseir::MatsubaraSampling<double> matsubara_sampling(basis, false); | ||
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// Since we don't factorize, we might check if the factorization is skipped | ||
// Adjust this check according to your implementation details | ||
REQUIRE(true); // Placeholder | ||
} | ||
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/* | ||
SECTION("fit from tau") { | ||
std::vector<std::shared_ptr<sparseir::Statistics>> stats = {std::make_shared<sparseir::Bosonic>(), std::make_shared<sparseir::Fermionic>()}; | ||
std::vector<double> omegas = {10.0, 42.0}; | ||
for (auto& stat_ptr : stats) { | ||
auto stat = *stat_ptr; | ||
for (auto& omega_max : omegas) { | ||
double beta = 1.0; | ||
auto sve_result = sparseir::compute_sve(sparseir::LogisticKernel(beta * omega_max)); | ||
auto basis = std::make_shared<sparseir::FiniteTempBasis<decltype(stat), sparseir::LogisticKernel>>( | ||
beta, omega_max, std::numeric_limits<double>::quiet_NaN(), sparseir::LogisticKernel(beta * omega_max), sve_result); | ||
sparseir::TauSampling<double> tau_sampling(basis); | ||
// Generate random coefficients al | ||
Eigen::VectorXd al(basis->size()); | ||
std::mt19937 rng(12345); | ||
std::normal_distribution<> dist(0.0, 1.0); | ||
for (int i = 0; i < al.size(); ++i) | ||
al(i) = dist(rng); | ||
auto ax = tau_sampling.evaluate(al); | ||
// Fit to get coefficients | ||
auto al_fit = tau_sampling.fit(ax); | ||
REQUIRE((al - al_fit).norm() <= 1e-10 * al.norm()); | ||
} | ||
} | ||
} | ||
*/ | ||
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} |