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#include "purify/config.h"
#include "purify/types.h"
#include <iostream>
#include "catch2/catch_all.hpp"
#include "purify/directories.h"
#include "purify/logging.h"
#include "purify/integration.h"
#include "purify/kernels.h"
using namespace purify;
TEST_CASE("integration") {
const t_uint max_evaluations = 1000;
std::function<t_real(Vector<t_real>)> func;
std::function<t_complex(Vector<t_real>)> cfunc;
for (auto int_method : {integration::method::p, integration::method::h}) {
SECTION("1d") {
const t_uint ndim = 1;
const Vector<t_real> xmin = -Vector<t_real>::Ones(ndim);
const Vector<t_real> xmax = Vector<t_real>::Ones(ndim);
func = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x.array() * x.array()).sum();
};
cfunc = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x.array() * x.array()).sum();
};
const t_real result = integration::integrate(xmin, xmax, func, integration::norm_type::l2,
1e-4, 1e-4, max_evaluations, int_method);
const t_complex cresult =
integration::integrate(xmin, xmax, cfunc, integration::norm_type::paired, 1e-4, 1e-4,
max_evaluations, integration::method::p);
CAPTURE(result);
CAPTURE(cresult);
CHECK(std::abs(result - ndim * std::pow(2, ndim - 1) * 2. / 3) < 1e-4);
CHECK(std::abs(cresult - ndim * std::pow(2, ndim - 1) * 2. / 3) < 1e-4);
}
SECTION("2d") {
const t_uint ndim = 2;
const Vector<t_real> xmin = -Vector<t_real>::Ones(ndim);
const Vector<t_real> xmax = Vector<t_real>::Ones(ndim);
func = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x.array() * x.array()).sum();
};
cfunc = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x.array() * x.array()).sum();
};
const t_real result = integration::integrate(xmin, xmax, func, integration::norm_type::l2,
1e-4, 1e-4, max_evaluations, int_method);
const t_complex cresult =
integration::integrate(xmin, xmax, cfunc, integration::norm_type::paired, 1e-4, 1e-4,
max_evaluations, int_method);
CAPTURE(result);
CAPTURE(cresult);
CHECK(std::abs(result - ndim * std::pow(2, ndim - 1) * 2. / 3) < 1e-4);
CHECK(std::abs(cresult - ndim * std::pow(2, ndim - 1) * 2. / 3) < 1e-4);
}
SECTION("3d") {
const t_uint ndim = 3;
const Vector<t_real> xmin = -Vector<t_real>::Ones(ndim);
const Vector<t_real> xmax = Vector<t_real>::Ones(ndim);
func = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x.array() * x.array()).sum();
};
cfunc = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x.array() * x.array()).sum();
};
const t_real result = integration::integrate(xmin, xmax, func, integration::norm_type::l2,
1e-4, 1e-4, max_evaluations, int_method);
const t_complex cresult =
integration::integrate(xmin, xmax, cfunc, integration::norm_type::paired, 1e-4, 1e-4,
max_evaluations, integration::method::p);
CAPTURE(result);
CAPTURE(cresult);
CHECK(std::abs(result - ndim * std::pow(2, ndim - 1) * 2. / 3) < 1e-4);
CHECK(std::abs(cresult - ndim * std::pow(2, ndim - 1) * 2. / 3) < 1e-4);
}
}
}
TEST_CASE("complex") {
const t_uint max_evaluations = 100000;
std::function<t_complex(Vector<t_real>)> cfunc1;
for (auto int_method : {integration::method::p, integration::method::h}) {
SECTION("Fourier Series") {
const t_uint ndim = 1;
const Vector<t_real> xmin = -Vector<t_real>::Ones(ndim) * constant::pi;
const Vector<t_real> xmax = Vector<t_real>::Ones(ndim) * constant::pi;
const t_real n = 1.;
const t_complex I(0., 1.);
cfunc1 = [=](const Vector<t_real> &x) {
assert(x.size() == ndim);
return (x(0) >= 0) ? std::exp(I * n * x(0)) * 1. / 2. : -std::exp(I * n * x(0)) * 1. / 2.;
};
const t_complex cresult = integration::integrate(
xmin, xmax, cfunc1, integration::norm_type::l2, 1e-6, 1e-6, max_evaluations, int_method);
CAPTURE(cresult);
CHECK(std::abs(cresult - t_complex(0., 2.)) / 2. < 1e-4);
}
SECTION("Fourier Series omp") {
const t_uint ndim = 1;
const Vector<t_real> xmin = -Vector<t_real>::Ones(ndim) * constant::pi;
const Vector<t_real> xmax = Vector<t_real>::Ones(ndim) * constant::pi;
const t_real n = 1.;
const t_complex I(0., 1.);
std::vector<std::function<t_complex(Vector<t_real>)>> funcs;
for (int i = 0; i < 4; i++) {
funcs.push_back([=](const Vector<t_real> &x) -> t_complex {
assert(x.size() == ndim);
return ((x(0) >= 0) ? std::exp(I * n * x(0)) * 1. / 2.
: -std::exp(I * n * x(0)) * 1. / 2.) *
(i + 1.);
});
}
#pragma omp parallel for
for (int i = 0; i < funcs.size(); i++) {
const t_complex cresult =
integration::integrate(xmin, xmax, funcs.at(i), integration::norm_type::l2, 1e-6, 1e-6,
max_evaluations, int_method);
CAPTURE(cresult);
CHECK(std::abs(cresult - t_complex(0., 2. * static_cast<t_real>(i + 1))) /
(2. * static_cast<t_real>(i + 1)) <
1e-4);
}
}
}
}
TEST_CASE("Numerical_Fourier_transform") {
const t_uint max_evaluations = 1e7;
const t_uint J = 4;
const t_real w = 10;
const t_real u = 10;
const t_real v = 10;
std::function<t_complex(Vector<t_real>)> cfunc;
const t_uint ndim = 2;
const Vector<t_real> xmin = Vector<t_real>::Zero(ndim);
Vector<t_real> xmax = Vector<t_real>::Ones(ndim);
xmax(0) = 0.99;
xmax(1) = 2 * constant::pi;
t_real width = 1.;
const t_complex I(0., 1.);
t_uint evals = 0;
cfunc = [=, &evals](const Vector<t_real> &x) -> t_complex {
assert(x.size() == ndim);
evals++;
return std::exp(-2 * constant::pi * I *
(x(0) * std::cos(x(1)) * u + x(0) * std::sin(x(1)) * v +
w * (std::sqrt(1 - std::pow(x(0), 2)) - 1))) *
x(0) / std::sqrt(1 - std::pow(x(0), 2)) / (2 * constant::pi);
};
const t_complex cresult =
integration::integrate(xmin, xmax, cfunc, integration::norm_type::paired, 1e-5, 1e-5,
max_evaluations, integration::method::p);
CAPTURE(cresult);
CAPTURE(evals);
CHECK(std::abs(cresult - t_complex(0.007601618963237, -0.003167113583181)) / std::abs(cresult) <
1e-6);
}
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