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| 1 | +#include <sirius.hpp> |
| 2 | +#include <testing.hpp> |
| 3 | + |
| 4 | +using namespace sirius; |
| 5 | + |
| 6 | +using f_type = double; |
| 7 | + |
| 8 | +int test_vector_calculus(cmd_args const& args__) |
| 9 | +{ |
| 10 | + /* matrix of reciprocal vectors */ |
| 11 | + r3::matrix<double> M({{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}); |
| 12 | + M = M * twopi; |
| 13 | + |
| 14 | + double pw_cutoff = args__.value<double>("pw_cutoff", 10.0); |
| 15 | + |
| 16 | + /* list of G-vectors distributed over MPI ranks */ |
| 17 | + fft::Gvec gvec(M, pw_cutoff, mpi::Communicator::world(), true); |
| 18 | + |
| 19 | + /* this is how G-vetors need to be arranged for FFT transforms */ |
| 20 | + auto gvp = std::make_shared<fft::Gvec_fft>(gvec, mpi::Communicator::world(), mpi::Communicator::self()); |
| 21 | + |
| 22 | + /* get some estimation of the FFT grid */ |
| 23 | + auto fft_grid = fft::get_min_grid(pw_cutoff, M); |
| 24 | + |
| 25 | + std::cout << "fft_grid: " << fft_grid[0] << " " << fft_grid[1] << " " << fft_grid[2] << std::endl; |
| 26 | + |
| 27 | + /* for SpFFT: we need to provide local size of z-dimension in real space */ |
| 28 | + auto spl_z = fft::split_z_dimension(fft_grid[2], mpi::Communicator::world()); |
| 29 | + |
| 30 | + /* select the device */ |
| 31 | + auto spfft_pu = SPFFT_PU_HOST; //(pu__ == device_t::CPU) ? SPFFT_PU_HOST : SPFFT_PU_GPU; |
| 32 | + |
| 33 | + /* create SpFFT grid object */ |
| 34 | + int const maxNumThreads{-1}; |
| 35 | + spfft::Grid spfft_grid(fft_grid[0], fft_grid[1], fft_grid[2], gvp->zcol_count(), |
| 36 | + spl_z.local_size(), spfft_pu, maxNumThreads, mpi::Communicator::world().native(), SPFFT_EXCH_DEFAULT); |
| 37 | + |
| 38 | + //fft::spfft_grid_type<f_type> spfft_grid(fft_grid[0], fft_grid[1], fft_grid[2], gvp->zcol_count(), |
| 39 | + // spl_z.local_size(), spfft_pu, maxNumThreads, mpi::Communicator::world().native(), SPFFT_EXCH_DEFAULT); |
| 40 | + |
| 41 | + /* transform type: complex to real */ |
| 42 | + const auto fft_type = SPFFT_TRANS_R2C; |
| 43 | + |
| 44 | + /* G-vector triplets in the FFT storage format */ |
| 45 | + auto const& gv = gvp->gvec_array(); |
| 46 | + /* create the FFT transform object */ |
| 47 | + auto spfft = spfft_grid.create_transform(spfft_pu, fft_type, fft_grid[0], fft_grid[1], |
| 48 | + fft_grid[2], spl_z.local_size(), gvp->count(), |
| 49 | + SPFFT_INDEX_TRIPLETS, gv.at(memory_t::host)); |
| 50 | + //fft::spfft_transform_type<f_type> spfft(spfft_grid.create_transform(spfft_pu, fft_type, fft_grid[0], fft_grid[1], |
| 51 | + // fft_grid[2], spl_z.local_size(), gvp->count(), |
| 52 | + // SPFFT_INDEX_TRIPLETS, gv.at(memory_t::host))); |
| 53 | + |
| 54 | + int num_points = spfft.local_slice_size(); |
| 55 | + |
| 56 | + //mdarray<std::complex<double>, 1> fpw({gvp->count()}); |
| 57 | + //mdarray<std::complex<double>, 1> frg({num_points}); |
| 58 | + //mdarray<std::complex<double>, 1> gpw({gvp->count()}); |
| 59 | + //mdarray<std::complex<double>, 1> grg({num_points}); |
| 60 | + |
| 61 | + //double* fft_buf = spfft.space_domain_data(SPFFT_PU_HOST); |
| 62 | + |
| 63 | + //for (int iv = 0; iv < 10; iv++) { |
| 64 | + // fpw.zero(); |
| 65 | + // fpw(iv) = std::complex<double>(1, 0); |
| 66 | + // spfft.backward(reinterpret_cast<double const*>(fpw.at(memory_t::host)), SPFFT_PU_HOST); |
| 67 | + // fft::spfft_output(spfft, frg.at(memory_t::host)); |
| 68 | + |
| 69 | + // double* ptr = reinterpret_cast<double*>(frg.at(memory_t::host)); |
| 70 | + // for (int i = 0; i < 2 * num_points; i++) { |
| 71 | + // if (ptr[i] != fft_buf[i]) { |
| 72 | + // std::cout << "wrong value" << std::endl; |
| 73 | + // } |
| 74 | + // } |
| 75 | + |
| 76 | + // copy(frg, grg); |
| 77 | + |
| 78 | + // fft::spfft_input(spfft, grg.at(memory_t::host)); |
| 79 | + // double* ptr1 = reinterpret_cast<double*>(grg.at(memory_t::host)); |
| 80 | + // //for (int i = 0; i < 2 * num_points; i++) { |
| 81 | + // // if (ptr1[i] != fft_buf[i]) { |
| 82 | + // // std::cout << "wrong value after spfft_input" << std::endl; |
| 83 | + // // } |
| 84 | + // //} |
| 85 | + // spfft.forward(SPFFT_PU_HOST, reinterpret_cast<double*>(gpw.at(memory_t::host)), SPFFT_FULL_SCALING); |
| 86 | + |
| 87 | + // double d1{0}; |
| 88 | + // for (int ig = 0; ig < gvec.count(); ig++) { |
| 89 | + // d1 += std::abs(gpw[ig] - fpw[ig]); |
| 90 | + // } |
| 91 | + // std::cout << "iv: " << iv << " diff: " << d1 << std::endl; |
| 92 | + |
| 93 | + // for (int ig = 0; ig < 20; ig++) { |
| 94 | + // std::cout << "ig: " << ig << " fpw: " << fpw[ig] << " gpw: " << gpw[ig] << std::endl; |
| 95 | + // } |
| 96 | + |
| 97 | + //} |
| 98 | + |
| 99 | + |
| 100 | + |
| 101 | + for (int iv = 0; iv < 10; iv++) { //gvec.count(); iv++) { |
| 102 | + std::cout << "Gvec: lattice: " << gvec.gvec<index_domain_t::local>(iv) |
| 103 | + <<" Cartesian: " << gvec.gvec_cart<index_domain_t::local>(iv) |
| 104 | + << std::endl; |
| 105 | + |
| 106 | + Smooth_periodic_function<f_type> f(spfft, gvp); |
| 107 | + Smooth_periodic_function<f_type> g(spfft, gvp); |
| 108 | + f.zero(); |
| 109 | + f.f_pw_local(iv) = std::complex<double>(1, 0); |
| 110 | + //for (int ig = 0; ig < 10; ig++) { |
| 111 | + // f.f_pw_local(ig) = random<std::complex<double>>() / std::pow(gvec.gvec_len<index_domain_t::local>(ig) + 1, 2); |
| 112 | + //} |
| 113 | + f.fft_transform(1); |
| 114 | + if (true) { |
| 115 | + std::cout << " testing ∇(∇f) == ∆f identity;"; |
| 116 | + auto lapl_f = laplacian(f); |
| 117 | + auto grad_f = gradient(f); |
| 118 | + lapl_f.fft_transform(1); |
| 119 | + auto div_grad_f = divergence(grad_f); |
| 120 | + div_grad_f.fft_transform(1); |
| 121 | + double diff{0}; |
| 122 | + for (int i = 0; i < num_points; i++) { |
| 123 | + diff += std::abs(lapl_f.value(i) - div_grad_f.value(i)); |
| 124 | + } |
| 125 | + std::cout << " difference: " << diff << std::endl; |
| 126 | + } |
| 127 | + |
| 128 | + g.zero(); |
| 129 | + for (int i = 0; i < num_points; i++) { |
| 130 | + g.value(i) = f.value(i); |
| 131 | + } |
| 132 | + /* transform to reciprocal space */ |
| 133 | + g.fft_transform(-1); |
| 134 | + if (true) { |
| 135 | + std::cout << " testing backward transformation;"; |
| 136 | + double d1{0}; |
| 137 | + for (int ig = 0; ig < gvec.count(); ig++) { |
| 138 | + d1 += std::abs(f.f_pw_local(ig) - g.f_pw_local(ig)); |
| 139 | + } |
| 140 | + std::cout << " difference: " << d1 << std::endl; |
| 141 | + } |
| 142 | + |
| 143 | + std::cout << " testing ∇(f * ∇g) == ∇f * ∇g + f ∆g identity;"; |
| 144 | + auto grad_g = gradient(g); |
| 145 | + /* transform to real space */ |
| 146 | + for (int x : {0, 1, 2}) { |
| 147 | + grad_g[x].fft_transform(1); |
| 148 | + } |
| 149 | + |
| 150 | + Smooth_periodic_vector_function<f_type> f_grad_g(spfft, gvp); |
| 151 | + for (int x : {0, 1, 2}) { |
| 152 | + for (int i = 0; i < num_points; i++) { |
| 153 | + f_grad_g[x].value(i) = grad_g[x].value(i) * f.value(i); |
| 154 | + } |
| 155 | + /* transform to reciprocal space */ |
| 156 | + f_grad_g[x].fft_transform(-1); |
| 157 | + } |
| 158 | + auto div_f_grad_g = divergence(f_grad_g); |
| 159 | + /* transform to real space */ |
| 160 | + div_f_grad_g.fft_transform(1); |
| 161 | + |
| 162 | + auto grad_f = gradient(f); |
| 163 | + for (int x : {0, 1, 2}) { |
| 164 | + /* transform to real space */ |
| 165 | + grad_f[x].fft_transform(1); |
| 166 | + } |
| 167 | + |
| 168 | + auto grad_f_grad_g = dot(grad_f, grad_g); |
| 169 | + auto lapl_g = laplacian(g); |
| 170 | + lapl_g.fft_transform(1); |
| 171 | + |
| 172 | + double abs_diff{0}; |
| 173 | + double s1{0}; |
| 174 | + double s2{0}; |
| 175 | + for (int i = 0; i < num_points; i++) { |
| 176 | + auto v1 = div_f_grad_g.value(i); |
| 177 | + auto v2 = grad_f_grad_g.value(i) + f.value(i) * lapl_g.value(i); |
| 178 | + s1 += std::abs(v1); |
| 179 | + s2 += std::abs(v2); |
| 180 | + abs_diff += std::abs(v1 - v2); |
| 181 | + } |
| 182 | + std::cout << " difference: " << abs_diff << std::endl; |
| 183 | + |
| 184 | + std::cout << "values along z" << std::endl; |
| 185 | + for (int z = 0; z < fft_grid[2]; z++) { |
| 186 | + int idx = fft_grid.index_by_coord(0, 0, z); |
| 187 | + std::cout << "z: " << static_cast<double>(z) / fft_grid[2] |
| 188 | + << " ∇(f * ∇g) = " << div_f_grad_g.value(idx) |
| 189 | + << " ∇f * ∇g + f ∆g = " << grad_f_grad_g.value(idx) + f.value(idx) * lapl_g.value(idx) |
| 190 | + << std::endl; |
| 191 | + } |
| 192 | + //if (abs_diff > 1e-6) { |
| 193 | + // //std::cout << "pw=" << iv <<" ∇(f * ∇g) = " << v1 << " ∇f * ∇g + f ∆g = " << v2 << " diff=" << abs_diff << std::endl; |
| 194 | + // std::cout << "pw=" << iv <<" diff=" << abs_diff << std::endl; |
| 195 | + //} |
| 196 | + } |
| 197 | + |
| 198 | + return 0; |
| 199 | +} |
| 200 | + |
| 201 | +int main(int argn, char** argv) |
| 202 | +{ |
| 203 | + cmd_args args(argn, argv, |
| 204 | + { |
| 205 | + {"pw_cutoff=", "(double) plane-wave cutoff"}, |
| 206 | + }); |
| 207 | + |
| 208 | + sirius::initialize(1); |
| 209 | + |
| 210 | + call_test("test_vector_calculus", test_vector_calculus, args); |
| 211 | + |
| 212 | + sirius::finalize(1); |
| 213 | +} |
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