Test: add unit test for lebedev quadrature

source/module_base/test/CMakeLists.txt

@@ -230,6 +230,11 @@ AddTest(
   SOURCES formatter_test.cpp
 )
 
+AddTest(
+  TARGET lebedev_laikov
+  SOURCES test_lebedev_laikov.cpp ../ylm.cpp ../math_lebedev_laikov.cpp
+)
+
 if(ENABLE_GOOGLEBENCH)
   AddTest(
     TARGET perf_sphbes

source/module_base/test/test_lebedev_laikov.cpp

@@ -0,0 +1,152 @@
+#include "module_base/math_lebedev_laikov.h"
+#include "module_base/ylm.h"
+
+#include "gtest/gtest.h"
+#include <random>
+#ifdef __MPI
+#include <mpi.h>
+#endif
+
+using ModuleBase::Lebedev_laikov_grid;
+
+// mock the function to prevent unnecessary dependency
+namespace ModuleBase {
+void WARNING_QUIT(const std::string&, const std::string&) {}
+}
+
+class LebedevLaikovTest: public ::testing::Test {
+protected:
+    void randgen(int lmax, std::vector<double>& coef);
+    const double tol = 1e-12;
+};
+
+
+void LebedevLaikovTest::randgen(int lmax, std::vector<double>& coef) {
+    coef.resize((lmax + 1) * (lmax + 1));
+
+    // fill coef with uniformly distributed random numbers
+    std::random_device rd;
+    std::mt19937 gen(rd());
+    std::uniform_real_distribution<double> dis(0.0, 1.0);
+    for (size_t i = 0; i < coef.size(); ++i) {
+        coef[i] = dis(gen);
+    }
+
+    // normalize the coefficients
+    double fac = 0.0;
+    for (size_t i = 0; i < coef.size(); ++i) {
+        fac += coef[i] * coef[i];
+    }
+
+    fac = 1.0 / std::sqrt(fac);
+    for (size_t i = 0; i < coef.size(); ++i) {
+        coef[i] *= fac;
+    }
+}
+
+
+TEST_F(LebedevLaikovTest, Accuracy) {
+    /* 
+     * Given
+     *
+     *      f = c[0]*Y00 + c[1]*Y10 + c[2]*Y11 + ...,
+     *
+     * where c[0], c[1], c[2], ... are some random numbers, the integration
+     * of |f|^2 on the unit sphere
+     *
+     *      \int |f|^2 d\Omega = c[0]^2 + c[1]^2 + c[2]^2 + ... .
+     *
+     * This test verifies with the above integral that quadrature with
+     * Lebedev grid is exact up to floating point errors.
+     *
+     */
+
+    // (ngrid, lmax)
+    std::set<std::pair<int, int>> supported = {
+        {6, 3},
+        {14, 5},
+        {26, 7},
+        {38, 9},
+        {50, 11},
+        {74, 13},
+        {86, 15},
+        {110, 17},
+        {146, 19},
+        {170, 21},
+        {194, 23},
+        {230, 25},
+        {266, 27},
+        {302, 29},
+        {350, 31},
+        {434, 35},
+        {590, 41},
+        {770, 47},
+        {974, 53},
+        {1202, 59},
+        {1454, 65},
+        {1730, 71},
+        {2030, 77},
+        {2354, 83},
+        {2702, 89},
+        {3074, 95},
+        {3470, 101},
+        {3890, 107},
+        {4334, 113},
+        {4802, 119},
+        {5294, 125},
+        {5810, 131},
+    };
+
+    std::vector<double> coef;
+
+    for (auto& grid_info: supported) {
+        int ngrid = grid_info.first;
+        int grid_lmax = grid_info.second;
+
+        Lebedev_laikov_grid lebgrid(ngrid);
+        lebgrid.generate_grid_points();
+
+        const double* weight = lebgrid.get_weight();
+        const ModuleBase::Vector3<double>* grid = lebgrid.get_grid_coor();
+
+        int func_lmax = grid_lmax / 2;
+        randgen(func_lmax, coef);
+
+        double val = 0.0;
+        std::vector<double> ylm_real;
+        for (int i = 0; i < ngrid; i++) {
+            ModuleBase::Ylm::sph_harm(func_lmax,
+                    grid[i].x, grid[i].y, grid[i].z, ylm_real);
+            double tmp = 0.0;
+            for (size_t j = 0; j < coef.size(); ++j) {
+                tmp += coef[j] * ylm_real[j];
+            }
+            val += weight[i] * tmp * tmp;
+        }
+
+        double val_ref = 0.0;
+        for (size_t i = 0; i < coef.size(); ++i) {
+            val_ref += coef[i] * coef[i];
+        }
+
+        double abs_diff = std::abs(val - val_ref);
+        EXPECT_LT(abs_diff, tol);
+    }
+}
+
+
+int main(int argc, char** argv)
+{
+#ifdef __MPI
+    MPI_Init(&argc, &argv);
+#endif
+
+    testing::InitGoogleTest(&argc, argv);
+    int result = RUN_ALL_TESTS();
+
+#ifdef __MPI
+    MPI_Finalize();
+#endif
+
+    return result;
+}