fourier.hpp

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// Copyright 2019 Global Phasing Ltd.
//
// Fourier transform applied to map coefficients.
 
#ifndef GEMMI_FOURIER_HPP_
#define GEMMI_FOURIER_HPP_
 
#include <array>
#include <complex>       // for std::conj
#include "recgrid.hpp"   // for ReciprocalGrid
#include "math.hpp"      // for rad
#include "symmetry.hpp"  // for GroupOps, Op
#include "fail.hpp"      // for fail
 
#ifdef __MINGW32__  // MinGW may have problem with std::mutex etc
# define POCKETFFT_CACHE_SIZE 0
#endif
#define POCKETFFT_NO_MULTITHREADING
#include "third_party/pocketfft_hdronly.h"
 
namespace gemmi {
 
// Returns angle in [0, 360). When it's negative but approximately zero,
// printing 0.00 than 360.00 might be better, hence the second arg.
// The default value is for similar precision as float around 360:
// std::nextafter(360.f, 361.f) - 360.f -> 3.052e-5
template<typename T>
double phase_in_angles(const std::complex<T>& v, double eps=2e-5) {
  double angle = gemmi::deg(std::arg(v));
  if (angle < -eps)
    angle += 360.;
  return std::max(0., angle);  // the order matters when angle is -0.0
}
 
// the first arg is usually Mtz::data
inline void add_asu_f_phi_to_float_vector(std::vector<float>& float_data,
                                          const AsuData<std::complex<float>>& asu_data) {
  float_data.reserve(float_data.size() + asu_data.v.size() * 5);
  for (const auto& item : asu_data.v) {
    for (int i = 0; i != 3; ++i)
      float_data.push_back((float) item.hkl[i]);
    float_data.push_back(std::abs(item.value));
    float_data.push_back((float) gemmi::phase_in_angles(item.value));
  }
}
 
template<typename DataProxy>
std::array<int, 3> get_size_for_hkl(const DataProxy& data,
                                    std::array<int, 3> min_size,
                                    double sample_rate) {
  // adjust min_size by checking Miller indices in the data
  for (size_t i = 0; i < data.size(); i += data.stride()) {
    Miller hkl = data.get_hkl(i);
    for (int j = 0; j != 3; ++j) {
      int v = 2 * std::abs(hkl[j]) + 1;
      if (v > min_size[j])
        min_size[j] = v;
    }
  }
  std::array<double, 3> dsize{{(double)min_size[0],
                               (double)min_size[1],
                               (double)min_size[2]}};
  if (sample_rate > 0) {
    const UnitCell& cell = data.unit_cell();
    double max_1_d2 = 0;
    for (size_t i = 0; i < data.size(); i += data.stride())
      max_1_d2 = std::max(max_1_d2, cell.calculate_1_d2(data.get_hkl(i)));
    double inv_d_min = std::sqrt(max_1_d2);
    std::array<double, 3> cellr = {{cell.ar, cell.br, cell.cr}};
    for (int i = 0; i < 3; ++i)
      dsize[i] = std::max(dsize[i], sample_rate * inv_d_min / cellr[i]);
  }
  return good_grid_size(dsize, GridSizeRounding::Up, data.spacegroup());
}
 
template<typename DataProxy>
bool data_fits_into(const DataProxy& data, std::array<int, 3> size) {
  for (size_t i = 0; i < data.size(); i += data.stride()) {
    Miller hkl = data.get_hkl(i);
    for (int j = 0; j != 3; ++j)
      if (2 * std::abs(hkl[j]) >= size[j])
        return false;
  }
  return true;
}
 
template<typename T>
void add_friedel_mates(ReciprocalGrid<T>& grid) {
  const T default_val = T(); // initialized to 0 or 0+0i
  if (grid.axis_order == AxisOrder::XYZ) {
    for (int w = 0; w != (grid.half_l ? 1 : grid.nw); ++w) {
      int w_ = w == 0 ? 0 : grid.nw - w;
      for (int v = 0; v != grid.nv; ++v) {
        int v_ = v == 0 ? 0 : grid.nv - v;
        for (int u = 0; u != grid.nu; ++u) {
          size_t idx = grid.index_q(u, v, w);
          if (grid.data[idx] == default_val) {
            int u_ = u == 0 ? 0 : grid.nu - u;
            size_t inv_idx = grid.index_q(u_, v_, w_);
            grid.data[idx] = friedel_mate_value(grid.data[inv_idx]);
          }
        }
      }
    }
  } else { // grid.axis_order == AxisOrder::ZYX
    for (int w = 0; w != grid.nw; ++w) {
      int w_ = w == 0 ? 0 : grid.nw - w;
      for (int v = 0; v != grid.nv; ++v) {
        int v_ = v == 0 ? 0 : grid.nv - v;
        if (grid.half_l) {
          size_t idx = grid.index_q(0, v, w);
          if (grid.data[idx] == default_val) {
            size_t inv_idx = grid.index_q(0, v_, w_);
            grid.data[idx] = friedel_mate_value(grid.data[inv_idx]);
          }
        } else {
          for (int u = 0; u != grid.nu; ++u) {
            size_t idx = grid.index_q(u, v, w);
            if (grid.data[idx] == default_val) {
              int u_ = u == 0 ? 0 : grid.nu - u;
              size_t inv_idx = grid.index_q(u_, v_, w_);
              grid.data[idx] = friedel_mate_value(grid.data[inv_idx]);
            }
          }
        }
      }
    }
  }
}
 
template<typename T, typename DataProxy>
void initialize_hkl_grid(ReciprocalGrid<T>& grid, const DataProxy& data,
                         std::array<int, 3> size, bool half_l,
                         AxisOrder axis_order) {
  if (data.size() == 0)
    fail("No data.");
  if (!data.spacegroup())
    fail("No spacegroup.");
  check_grid_factors(data.spacegroup(), size);
  grid.unit_cell = data.unit_cell();
  grid.half_l = half_l;
  grid.axis_order = axis_order;
  grid.spacegroup = data.spacegroup();
  if (half_l)
    size[2] = size[2] / 2 + 1;
  if (axis_order == AxisOrder::ZYX)
    std::swap(size[0], size[2]);
  grid.set_size_without_checking(size[0], size[1], size[2]);
}
 
template<typename DataProxy>
struct FPhiProxy : DataProxy {
  FPhiProxy(const DataProxy& data_proxy, size_t f_col, size_t phi_col)
      : DataProxy(data_proxy), f_col_(f_col), phi_col_(phi_col) {
    if (f_col >= data_proxy.stride() || phi_col >= data_proxy.stride())
      fail("Map coefficients not found.");
  }
  using real = typename DataProxy::num_type;
  real get_f(size_t offset) const { return this->get_num(offset + f_col_); }
  double get_phi(size_t offset) const { return rad(this->get_num(offset + phi_col_)); }
private:
  size_t f_col_, phi_col_;
};
 
// If half_l is true, grid has only data with l>=0.
// Parameter size can be obtained from get_size_for_hkl().
template<typename T, typename FPhi>
FPhiGrid<T> get_f_phi_on_grid(const FPhi& fphi,
                              std::array<int, 3> size, bool half_l,
                              AxisOrder axis_order=AxisOrder::XYZ) {
  FPhiGrid<T> grid;
  initialize_hkl_grid(grid, fphi, size, half_l, axis_order);
  const std::complex<T> default_val; // initialized to 0+0i
  GroupOps ops = grid.spacegroup->operations();
  for (size_t i = 0; i < fphi.size(); i += fphi.stride()) {
    Miller hkl = fphi.get_hkl(i);
    T f = (T) fphi.get_f(i);
    if (f == 0.f)  // is there enough of F=0 to justify this 'if'?
      continue;
    double phi = fphi.get_phi(i);
    for (const Op& op : ops.sym_ops) {
      auto hklp = op.apply_to_hkl(hkl);
      int lp = hklp[2];
      if (axis_order == AxisOrder::ZYX)
        std::swap(hklp[0], hklp[2]);
      if (!grid.has_index(hklp[0], hklp[1], hklp[2]))
        continue;
      int sign = (!half_l || lp >= 0 ? 1 : -1);
      size_t idx = grid.index_n(sign * hklp[0], sign * hklp[1], sign * hklp[2]);
      if (grid.data[idx] == default_val) {
        T theta = sign * T(phi + op.phase_shift(hkl));
        grid.data[idx] = std::complex<T>(f * std::cos(theta), f * std::sin(theta));
      }
    }
  }
  if (!ops.is_centrosymmetric())
    add_friedel_mates(grid);
  return grid;
}
 
template<typename T, typename DataProxy>
ReciprocalGrid<T> get_value_on_grid(const DataProxy& data, size_t column,
                                    std::array<int, 3> size, bool half_l,
                                    AxisOrder axis_order=AxisOrder::XYZ) {
  ReciprocalGrid<T> grid;
  initialize_hkl_grid(grid, data, size, half_l, axis_order);
 
  if (column >= data.stride())
    fail("Map coefficients not found.");
  GroupOps ops = grid.spacegroup->operations();
  for (size_t i = 0; i < data.size(); i += data.stride()) {
    Miller hkl = data.get_hkl(i);
    T val = (T) data.get_num(i + column);
    if (val != 0.) {
      for (const Op& op : ops.sym_ops) {
        auto hklp = op.apply_to_hkl(hkl);
        int lp = hklp[2];
        if (axis_order == AxisOrder::ZYX)
          std::swap(hklp[0], hklp[2]);
        if (!grid.has_index(hklp[0], hklp[1], hklp[2]))
          continue;
        int sign = (!half_l || lp >= 0 ? 1 : -1);
        size_t idx = grid.index_n(sign * hklp[0], sign * hklp[1], sign * hklp[2]);
        if (grid.data[idx] == 0.)  // 0 is the default value
          grid.data[idx] = val;
      }
    }
  }
  if (!ops.is_centrosymmetric())
    add_friedel_mates(grid);
  return grid;
}
 
 
template<typename T>
void transform_f_phi_grid_to_map_(FPhiGrid<T>&& hkl, Grid<T>& map) {
  // NaNs are not good for FFT, so we change them to 0.
  // x -> conj(x) is equivalent to changing axis direction before FFT.
  for (std::complex<T>& x : hkl.data)
    if (std::isnan(x.imag()))
      x = 0;
    else
      x.imag(-x.imag());
  map.spacegroup = hkl.spacegroup;
  map.unit_cell = hkl.unit_cell;
  map.axis_order = hkl.axis_order;
  if (hkl.axis_order == AxisOrder::XYZ) {
    int nw = hkl.half_l ? 2 * (hkl.nw - 1) : hkl.nw;
    map.set_size(hkl.nu, hkl.nv, nw);
  } else { // hkl.axis_order == AxisOrder::ZYX
    int nu = hkl.half_l ? 2 * (hkl.nu - 1) : hkl.nu;
    check_grid_factors(map.spacegroup, {{hkl.nw, hkl.nv, nu}});
    map.set_size_without_checking(nu, hkl.nv, hkl.nw);
  }
  // FIXME set_size_without_checking is changing axis_order - bad
  map.axis_order = hkl.axis_order;
  pocketfft::shape_t shape{(size_t)hkl.nw, (size_t)hkl.nv, (size_t)hkl.nu};
  std::ptrdiff_t s = sizeof(T);
  pocketfft::stride_t stride{2*s * hkl.nv * hkl.nu, 2*s * hkl.nu, 2*s};
  pocketfft::shape_t axes{2, 1, 0};
  if (hkl.axis_order == AxisOrder::ZYX)
    std::swap(axes[0], axes[2]);
  T norm = T(1.0 / hkl.unit_cell.volume);
  if (hkl.half_l) {
    size_t last_axis = axes.back();
    axes.pop_back();
    pocketfft::c2c<T>(shape, stride, stride, axes, pocketfft::BACKWARD,
                      &hkl.data[0], &hkl.data[0], norm);
    pocketfft::stride_t stride_out{s * map.nu * map.nv, s * map.nu, s};
    shape[0] = (size_t) map.nw;
    shape[2] = (size_t) map.nu;
    pocketfft::c2r<T>(shape, stride, stride_out, last_axis, pocketfft::BACKWARD,
                      &hkl.data[0], &map.data[0], 1.0f);
  } else {
    pocketfft::c2c<T>(shape, stride, stride, axes, pocketfft::BACKWARD,
                      &hkl.data[0], &hkl.data[0], norm);
    assert(map.data.size() == hkl.data.size());
    for (size_t i = 0; i != map.data.size(); ++i)
      map.data[i] = hkl.data[i].real();
  }
}
 
template<typename T>
Grid<T> transform_f_phi_grid_to_map(FPhiGrid<T>&& hkl) {
  Grid<T> map;
  transform_f_phi_grid_to_map_(std::forward<FPhiGrid<T>>(hkl), map);
  return map;
}
 
template<typename T, typename FPhi>
Grid<T> transform_f_phi_to_map(const FPhi& fphi,
                               std::array<int, 3> size,
                               double sample_rate,
                               bool exact_size=false,
                               AxisOrder order=AxisOrder::XYZ) {
  if (exact_size) {
    gemmi::check_grid_factors(fphi.spacegroup(), size);
  } else {
    size = get_size_for_hkl(fphi, size, sample_rate);
  }
  return transform_f_phi_grid_to_map(get_f_phi_on_grid<T>(fphi, size, true, order));
}
 
template<typename T, typename FPhi>
Grid<T> transform_f_phi_to_map2(const FPhi& fphi,
                                std::array<int, 3> min_size,
                                double sample_rate,
                                std::array<int, 3> exact_size,
                                AxisOrder order=AxisOrder::XYZ) {
  bool exact = (exact_size[0] != 0 || exact_size[1] != 0 || exact_size[2] != 0);
  return transform_f_phi_to_map<float>(fphi, exact ? exact_size : min_size,
                                       sample_rate, exact, order);
}
 
template<typename T>
FPhiGrid<T> transform_map_to_f_phi(const Grid<T>& map, bool half_l, bool use_scale=true) {
  if (half_l && map.axis_order == AxisOrder::ZYX)
    fail("transform_map_to_f_phi(): half_l + ZYX order are not supported yet");
  FPhiGrid<T> hkl;
  hkl.unit_cell = map.unit_cell;
  hkl.spacegroup = map.spacegroup;
  hkl.axis_order = map.axis_order;
  hkl.half_l = half_l;
  int half_nw = map.nw / 2 + 1;
  hkl.set_size_without_checking(map.nu, map.nv, half_l ? half_nw : map.nw);
  T norm = use_scale ? T(map.unit_cell.volume / map.point_count()) : 1;
  pocketfft::shape_t shape{(size_t)map.nw, (size_t)map.nv, (size_t)map.nu};
  std::ptrdiff_t s = sizeof(T);
  pocketfft::stride_t stride_in{s * hkl.nv * hkl.nu, s * hkl.nu, s};
  pocketfft::stride_t stride{2*s * hkl.nv * hkl.nu, 2*s * hkl.nu, 2*s};
  pocketfft::r2c<T>(shape, stride_in, stride, /*axis=*/0, pocketfft::FORWARD,
                    &map.data[0], &hkl.data[0], norm);
  shape[0] = half_nw;
  pocketfft::c2c<T>(shape, stride, stride, {1, 2}, pocketfft::FORWARD,
                    &hkl.data[0], &hkl.data[0], 1.0f);
  if (!half_l)  // add Friedel pairs
    for (int w = half_nw; w != hkl.nw; ++w) {
      int w_ = hkl.nw - w;
      for (int v = 0; v != hkl.nv; ++v) {
        int v_ = v == 0 ? 0 : hkl.nv - v;
        for (int u = 0; u != hkl.nu; ++u) {
          int u_ = u == 0 ? 0 : hkl.nu - u;
          size_t idx = hkl.index_q(u, v, w);
          size_t inv_idx = hkl.index_q(u_, v_, w_);
          hkl.data[idx] = hkl.data[inv_idx];  // conj() is called later
        }
      }
    }
  for (int i = 0; i != hkl.nu * hkl.nv * half_nw; ++i)
    hkl.data[i].imag(-hkl.data[i].imag());
  return hkl;
}
 
} // namespace gemmi
#endif