Added C++ implementation for the quantum systems' energy calculations (#476)

Author: rajdakin

contents/quantum_systems/code/c++/energy.cpp

@@ -0,0 +1,57 @@
+#include <vector>
+#include <complex>
+
+#include <fftw3.h>
+
+void fft(std::vector<std::complex<double>> x, bool inverse) {
+    std::vector<std::complex<double>> y(x.size());
+    for (size_t i = 0; i < x.size(); i++) {
+        y.push_back(std::complex(0.0, 0.0));
+    }
+    
+    fftw_plan p;
+
+    p = fftw_plan_dft_1d(x.size(), reinterpret_cast<fftw_complex*>(x.data()),
+                         reinterpret_cast<fftw_complex*>(y.data()),
+                         (inverse ? FFTW_BACKWARD : FFTW_FORWARD), FFTW_ESTIMATE);
+
+    fftw_execute(p);
+    fftw_destroy_plan(p);
+
+    for (size_t i = 0; i < x.size(); ++i) {
+        x[i] = y[i] / sqrt((double)x.size());
+    }
+}
+
+double calculate_energy(std::vector<std::complex<double>> wfc, std::vector<std::complex<double>> h_r,
+                        std::vector<std::complex<double>> h_k, double dx, size_t size) {
+    std::vector<std::complex<double>> wfc_k(wfc);
+    std::vector<std::complex<double>> wfc_c(size);
+    fft(wfc_k, false);
+
+    for (size_t i = 0; i < size; ++i) {
+        wfc_c.push_back(conj(wfc[i]));
+    }
+
+    std::vector<std::complex<double>> energy_k(size);
+    std::vector<std::complex<double>> energy_r(size);
+
+    for (size_t i = 0; i < size; ++i) {
+        energy_k.push_back(wfc_k[i] * h_k[i]);
+    }
+
+    fft(energy_k, true);
+
+    for (size_t i = 0; i < size; ++i) {
+        energy_k[i] *= wfc_c[i];
+        energy_r.push_back(wfc_c[i] * h_r[i] * wfc[i]);
+    }
+
+    double energy_final = 0;
+
+    for (size_t i = 0; i < size; ++i) {
+        energy_final += real(energy_k[i] + energy_r[i]);
+    }
+
+    return energy_final * dx;
+}

contents/quantum_systems/quantum_systems.md

@@ -231,6 +231,8 @@ This ultimately looks like this:
 [import, lang:"haskell"](code/haskell/Energy.hs)
 {% sample lang="c" %}
 [import:29-, lang:"c_cpp"](code/c/energy.c)
+{% sample lang="cpp" %}
+[import:26-57, lang:"c_cpp"](code/c++/energy.cpp)
 {% sample lang="py" %}
 [import:4-17, lang:"python"](code/python/energy.py)
 {% endmethod %}