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#define DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN
#include <doctest/doctest.h>
#include <cstdlib> // for rand
#include <climits> // for INT_MIN, INT_MAX
#include <vector>
#include <gemmi/atox.hpp>
#include <gemmi/math.hpp>
#include <gemmi/it92.hpp>
#include <gemmi/util.hpp> // for is_in_list
#include <gemmi/asudata.hpp> // for ComplexCorrelation
#include <linalg.h>
static double draw() { return 10.0 * std::rand() / RAND_MAX - 5; }
static gemmi::Transform random_transform() {
gemmi::Transform a;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j)
a.mat[i][j] = draw();
a.vec.at(i) = draw();
}
return a;
}
TEST_CASE("Transform::inverse") {
std::srand(12345);
gemmi::Transform tr = random_transform();
linalg::mat<double,4,4> m44 = linalg::identity;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j)
m44[i][j] = tr.mat[i][j];
m44[i][3] = tr.vec.at(i);
}
linalg::mat<double,4,4> inv_m44 = linalg::inverse(m44);
gemmi::Transform inv_tr = tr.inverse();
CHECK_EQ(inv_m44[3][3], doctest::Approx(1.0));
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j)
CHECK_EQ(inv_tr.mat[i][j], doctest::Approx(inv_m44[i][j]));
CHECK_EQ(inv_tr.vec.at(i), doctest::Approx(inv_m44[i][3]));
CHECK_EQ(inv_m44[3][i], 0);
}
}
TEST_CASE("SMat33::inverse") {
gemmi::SMat33<double> sm{draw(), draw(), draw(), draw(), draw(), draw()};
gemmi::Mat33 m = sm.as_mat33();
CHECK_EQ(sm.determinant(), m.determinant());
gemmi::Mat33 inv1 = m.inverse();
gemmi::Mat33 inv2 = sm.inverse().as_mat33();
for (int i = 0; i < 3; ++i)
for (int j = 0; j < 3; ++j)
CHECK(std::abs(inv1.a[i][j] - inv2.a[i][j]) < 1e-16);
}
TEST_CASE("Transform::combine") {
std::srand(12345);
gemmi::Transform a = random_transform();
gemmi::Transform b = random_transform();
gemmi::Vec3 v;
for (int i = 0; i < 3; ++i)
v.at(i) = draw();
gemmi::Vec3 result1 = a.combine(b).apply(v);
gemmi::Vec3 result2 = a.apply(b.apply(v));
for (int i = 0; i < 3; ++i)
CHECK_EQ(result1.at(i), doctest::Approx(result2.at(i)));
}
TEST_CASE("SMat33::smallest_eigenvalue") {
auto ev = gemmi::SMat33<double>{3, 0, 3, 2, 4, 2}.calculate_eigenvalues();
CHECK_EQ(ev[0], doctest::Approx(8));
CHECK_EQ(ev[1], doctest::Approx(-1));
CHECK_EQ(ev[2], doctest::Approx(-1));
gemmi::SMat33<double> m2{3, 3, 5, 1, -1, -1};
auto ev2 = m2.calculate_eigenvalues();
CHECK_EQ(ev2[0], doctest::Approx(6));
CHECK_EQ(ev2[1], doctest::Approx(3));
CHECK_EQ(ev2[2], doctest::Approx(2));
}
TEST_CASE("Variance") {
gemmi::Variance v;
for (double x : {0.14, 0.08, 0.16, 0.12, 0.04})
v.add_point(x);
CHECK_EQ(v.for_sample(), 0.00232);
CHECK_EQ(v.n, 5);
CHECK_EQ(v.mean_x, 0.108);
}
TEST_CASE("Covariance") {
gemmi::Covariance cov;
cov.add_point(2.1, 8);
cov.add_point(2.5, 12);
cov.add_point(4.0, 14);
cov.add_point(3.6, 10);
CHECK_EQ(cov.n, 4);
CHECK_EQ(cov.mean_x, 3.05);
CHECK_EQ(cov.mean_y, 11);
CHECK_EQ(cov.for_population(), doctest::Approx(1.15));
CHECK_EQ(cov.for_sample(), doctest::Approx(1.53333));
}
TEST_CASE("Correlation") {
gemmi::Correlation cor;
cor.add_point(2.1, 8);
cor.add_point(2.5, 12);
CHECK_EQ(cor.n, 2);
CHECK_EQ(cor.coefficient(), 1.0);
cor.add_point(4.0, 14);
cor.add_point(3.6, 10);
CHECK_EQ(cor.n, 4);
CHECK_EQ(cor.mean_x, 3.05);
CHECK_EQ(cor.mean_y, 11);
CHECK_EQ(cor.coefficient(), doctest::Approx(0.66257388));
CHECK_EQ(cor.covariance(), doctest::Approx(1.15));
CHECK_EQ(cor.x_variance(), doctest::Approx(0.6025));
CHECK_EQ(cor.y_variance(), doctest::Approx(5));
// scipy.stats.linregress([2.1, 2.5, 4.0, 3.6], [8, 12, 14, 10])
CHECK_EQ(cor.slope(), doctest::Approx(1.9087136929460577));
CHECK_EQ(cor.intercept(), doctest::Approx(5.178423236514524));
}
TEST_CASE("ComplexCorrelation") {
gemmi::ComplexCorrelation cor;
cor.add_point(std::complex<double>{1., 2.}, std::complex<double>{2., 2.});
cor.add_point(std::complex<double>{2., 0.}, std::complex<double>{4., 0.});
cor.add_point(std::complex<double>{3., -0.3}, std::complex<double>{7., -0.1});
std::complex<double> cc = cor.coefficient();
// compare with value from numpy.corrcoef
CHECK(std::fabs(cc.real() - 0.8929758288830972) < 1e-15);
CHECK(std::fabs(cc.imag() - -0.37799898875604704) < 1e-15);
}
TEST_CASE("string_to_int") {
CHECK_EQ(gemmi::string_to_int(std::to_string(INT_MAX), true), INT_MAX);
CHECK_EQ(gemmi::string_to_int(std::to_string(INT_MIN), true), INT_MIN);
CHECK_EQ(gemmi::string_to_int("", false), 0);
}
TEST_CASE("is_in_list") {
CHECK(gemmi::is_in_list("abc", "abc"));
CHECK(gemmi::is_in_list("abc", "a,abc"));
CHECK(gemmi::is_in_list("abc", "xyz,ab,abc,"));
CHECK(!gemmi::is_in_list("abc", ",abcd"));
CHECK(!gemmi::is_in_list("abc", "abc , abc"));
CHECK(!gemmi::is_in_list("abc", "a,"));
}
TEST_CASE("IT92") {
using Table = gemmi::IT92<double>;
const Table::Coef& coef = Table::get(gemmi::El::Mg, 0);
double B = 23.4;
double r = 1.5;
double dens1 = coef.calculate_density_iso(r*r, B);
double dens2 = coef.precalculate_density_iso(B).calculate(r*r);
CHECK_EQ(dens1, doctest::Approx(dens2));
double U = B / (8 * gemmi::pi() * gemmi::pi());
gemmi::SMat33<float> mat{(float)U, (float)U, (float)U, 0, 0, 0};
gemmi::Vec3 v1(r, 0, 0);
double dens3 = coef.calculate_density_aniso(v1, mat);
CHECK_EQ(dens1, doctest::Approx(dens3));
double dens4 = coef.precalculate_density_aniso_u(mat).calculate(v1);
CHECK_EQ(dens1, doctest::Approx(dens4));
double xr = r * std::sqrt(1./3);
gemmi::Vec3 v2(xr, xr, xr);
double dens5 = coef.calculate_density_aniso(v2, mat);
CHECK_EQ(dens1, doctest::Approx(dens5));
double dens6 = coef.precalculate_density_aniso_u(mat).calculate(v2);
CHECK_EQ(dens1, doctest::Approx(dens6));
double dens_a = coef.precalculate_density_iso(B, 0.8).calculate(r*r);
double dens_b = coef.precalculate_density_aniso_u(mat, 0.8).calculate(v2);
CHECK_EQ(dens_a, doctest::Approx(dens_b));
}
TEST_CASE("vector_Vec3") {
// superpose_positions depends on the memory layout of Vec3/Position array.
std::vector<gemmi::Vec3> vec(5);
const double* x0 = &vec[0].x;
const double* x1 = &vec[1].x;
auto offset = x1 - x0;
CHECK_EQ(offset, 3);
}
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