Added C++ lang implementation of the split operator

contents/split-operator_method/code/c++/split_op.cpp

@@ -0,0 +1,191 @@
+#include <complex>
+#include <vector>
+#include <iostream>
+#include <cstring>
+#include <fstream>
+
+// Using fftw3 library.
+#include <fftw3.h>
+
+struct Params {
+ Params(double _xmax, unsigned int _res, double _dt, unsigned int _timesteps, bool im) {
+ xmax = _xmax;
+ res = _res;
+ dt = _dt;
+ timesteps = _timesteps;
+ dx = 2.0 * xmax / res;
+ x.reserve(res);
+ dk = M_PI / xmax;
+ k.reserve(res);
+ im_time = im;
+
+ for (size_t i = 0; i < res; ++i) {
+ x.push_back(xmax / res - xmax + i * (2.0 * xmax / res));
+ if (i < res / 2) {
+ k.push_back(i * M_PI / xmax);
+ } else {
+ k.push_back((static_cast<double>(i) - res) * M_PI / xmax);
+ }
+ }
+ }
+
+ double xmax;
+ unsigned int res;
+ double dt;
+ unsigned int timesteps;
+ double dx;
+ std::vector<double> x;
+ double dk;
+ std::vector<double> k;
+ bool im_time;
+};
+
+struct Operators {
+public:
+ Operators(Params &par, double voffset,
+ double wfcoffset) {
+ size = par.res;
+ v.reserve(size);
+ pe.reserve(size);
+ ke.reserve(size);
+ wfc.reserve(size);
+
+ for (size_t i = 0; i < size; ++i) {
+ v.emplace_back(0.5 * pow(par.x[i] - voffset, 2));
+ wfc.emplace_back(exp(-pow(par.x[i] - wfcoffset, 2) / 2.0));
+
+ if (par.im_time) {
+ ke.emplace_back(exp(-0.5 * par.dt * pow(par.k[i], 2)));
+ pe.emplace_back(exp(-0.5 * par.dt * v[i]));
+ } else {
+ ke.emplace_back(exp(-0.5 * par.dt * pow(par.k[i], 2) * std::complex<double>(0.0, 1.0)));
+ pe.emplace_back(exp(-0.5 * par.dt * v[i] * std::complex<double>(0.0, 1.0)));
+ }
+ }
+ }
+
+ size_t size;
+ std::vector<std::complex<double>> v;
+ std::vector<std::complex<double>> pe;
+ std::vector<std::complex<double>> ke;
+ std::vector<std::complex<double>> wfc;
+};
+
+void fft(std::vector<std::complex<double>> x, int n, bool inverse) {
+ std::complex<double> y[n];
+ memset(y, 0, sizeof(y));
+ fftw_plan p;
+
+ p = fftw_plan_dft_1d(n, reinterpret_cast<fftw_complex*>(x.data()), reinterpret_cast<fftw_complex*>(y),
+ (inverse ? FFTW_BACKWARD : FFTW_FORWARD), FFTW_ESTIMATE);
+
+ fftw_execute(p);
+ fftw_destroy_plan(p);
+
+ for (size_t i = 0; i < n; ++i) {
+ x[i] = y[i] / sqrt(static_cast<double>(n));
+ }
+}
+
+void split_op(Params &par, Operators &opr) {
+ double density[opr.size];
+
+ for (size_t i = 0; i < par.timesteps; ++i) {
+ for (size_t j = 0; j < opr.size; ++j) {
+ opr.wfc[j] *= opr.pe[j];
+ }
+
+ fft(opr.wfc, opr.size, false);
+
+ for (size_t j = 0; j < opr.size; ++j) {
+ opr.wfc[j] *= opr.ke[j];
+ }
+
+ fft(opr.wfc, opr.size, true);
+
+ for (size_t j = 0; j < opr.size; ++j) {
+ opr.wfc[j] *= opr.pe[j];
+ }
+
+ for (size_t j = 0; j < opr.size; ++j) {
+ density[j] = pow(abs(opr.wfc[j]), 2);
+ }
+
+ if (par.im_time) {
+ double sum = 0;
+
+ for (size_t j = 0; j < opr.size; ++j) {
+ sum += density[j];
+ }
+
+ sum *= par.dx;
+
+ for (size_t j = 0; j < opr.size; ++j) {
+ opr.wfc[j] /= sqrt(sum);
+ }
+ }
+
+ // Writing data into a file in the format of:
+ // index, density, real potential.
+ std::stringstream filename_stream;
+ filename_stream << "output" << i << ".dat";
+
+ std::ofstream fstream = std::ofstream(filename_stream.str());
+
+ if (fstream) {
+ for (int i = 0; i < opr.size; ++i) {
+ std::stringstream data_stream;
+
+ data_stream << i << "\t" << density[i] << "\t" << real(opr.v[i]) << "\n";
+
+ fstream.write(data_stream.str().c_str(), data_stream.str().length());
+ }
+ }
+
+ fstream.close();
+ }
+}
+
+double calculate_energy(Params par, Operators opr) {
+ std::vector<std::complex<double>> wfc_r(opr.wfc);
+ std::vector<std::complex<double>> wfc_k(opr.wfc);
+ std::vector<std::complex<double>> wfc_c(opr.size);
+ fft(wfc_k, opr.size, false);
+
+ for (size_t i = 0; i < opr.size; ++i) {
+ wfc_c.push_back(conj(wfc_r[i]));
+ }
+
+ std::vector<std::complex<double>> energy_k(opr.size);
+ std::vector<std::complex<double>> energy_r(opr.size);
+
+ for (size_t i = 0; i < opr.size; ++i) {
+ energy_k.push_back(wfc_k[i] * pow(std::complex<double>(par.k[i], 0.0), 2));
+ }
+
+ fft(energy_k, opr.size, true);
+
+ for (size_t i = 0; i < opr.size; ++i) {
+ energy_k[i] *= 0.5 * wfc_c[i];
+ energy_r.push_back(wfc_c[i] * opr.v[i] * wfc_r[i]);
+ }
+
+ double energy_final = 0;
+
+ for (size_t i = 0; i < opr.size; ++i) {
+ energy_final += real(energy_k[i] + energy_r[i]);
+ }
+
+ return energy_final * par.dx;
+}
+
+int main() {
+ Params par = Params(5.0, 256, 0.05, 100, true);
+ Operators opr = Operators(par, 0.0, -1.0);
+
+ split_op(par, opr);
+
+ std::cout << "The energy is " << calculate_energy(par, opr) << "\n";
+
+ return 0;
+}

contents/split-operator_method/split-operator_method.md

@@ -102,6 +102,8 @@ Regardless, we first need to set all the initial parameters, including the initi
 {% sample lang="c" %}
 [import:11-21, lang:"c_cpp"](code/c/split_op.c)
 [import:52-73, lang:"c_cpp"](code/c/split_op.c)
+{% sample lang="cpp" %}
+[import:10-41, lang:"c_cpp"](code/c++/split_op.cpp)
 {% sample lang="py" %}
 [import:11-30, lang:"python"](code/python/split_op.py)
 {% sample lang="hs" %}
@@ -121,6 +123,8 @@ Afterwards, we turn them into operators:
 {% sample lang="c" %}
 [import:23-29, lang:"c_cpp"](code/c/split_op.c)
 [import:75-96, lang:"c_cpp"](code/c/split_op.c)
+{% sample lang="cpp" %}
+[import:43-72, lang:"c_cpp"](code/c++/split_op.cpp)
 {% sample lang="py" %}
 [import:33-54, lang:"python"](code/python/split_op.py)
 {% sample lang="hs" %}
@@ -140,6 +144,8 @@ The final step is to do the iteration, itself.
 [import:65-112, lang:"julia"](code/julia/split_op.jl)
 {% sample lang="c" %}
 [import:98-148, lang:"c_cpp"](code/c/split_op.c)
+{% sample lang="cpp" %}
+[import:74-183, lang:"c_cpp"](code/c++/split_op.cpp)
 {% sample lang="py" %}
 [import:57-95, lang:"python"](code/python/split_op.py)
 {% sample lang="hs" %}
@@ -165,6 +171,8 @@ Checking to make sure your code can output the correct energy for a harmonic tra
 [import, lang:"julia"](code/julia/split_op.jl)
 {% sample lang="c" %}
 [import, lang:"c_cpp"](code/c/split_op.c)
+{% sample lang="cpp" %}
+[import, lang:"c_cpp"](code/c++/split_op.cpp)
 {% sample lang="py" %}
 [import:5-127, lang:"python"](code/python/split_op.py)
 {% sample lang="hs" %}