nifty_gridder.cc 13.6 KB
Newer Older
Martin Reinecke's avatar
import  
Martin Reinecke committed
1
2
3
4
5
#include <pybind11/pybind11.h>
#include <pybind11/numpy.h>
#include <iostream>
#include <algorithm>

Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
6
7
8
9
10
11
#ifdef __GNUC__
#define RESTRICT __restrict__
#else
#define RESTRICT
#endif

Martin Reinecke's avatar
import  
Martin Reinecke committed
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
using namespace std;

namespace py = pybind11;

namespace {

constexpr double pi = 3.141592653589793238462643383279502884197;

static const uint16_t utab[] = {
#define Z(a) 0x##a##0, 0x##a##1, 0x##a##4, 0x##a##5
#define Y(a) Z(a##0), Z(a##1), Z(a##4), Z(a##5)
#define X(a) Y(a##0), Y(a##1), Y(a##4), Y(a##5)
X(0),X(1),X(4),X(5)
#undef X
#undef Y
#undef Z
};

uint32_t coord2morton2D_32 (uint32_t x, uint32_t y)
  {
  typedef uint32_t I;
  return  (I)(utab[x&0xff])     | ((I)(utab[(x>>8)&0xff])<<16)
       | ((I)(utab[y&0xff])<<1) | ((I)(utab[(y>>8)&0xff])<<17);
  }

static const uint8_t m2p2D_1[4][4] = {
{ 4, 1, 11, 2},{0,15, 5, 6},{10,9,3,12},{14,7,13,8}};
static uint8_t m2p2D_3[4][64];
static const uint8_t p2m2D_1[4][4] = {
{ 4, 1, 3, 10},{0,6,7,13},{15,9,8,2},{11,14,12,5}};
static uint8_t p2m2D_3[4][64];
static int peano2d_done=0;

static void init_peano2d (void)
  {
  peano2d_done=1;

  for (int d=0; d<4; ++d)
    for (uint32_t p=0; p<64; ++p)
      {
      unsigned rot = d;
      uint32_t v = p<<26;
      uint32_t res = 0;
      for (int i=0; i<3; ++i)
        {
        unsigned tab=m2p2D_1[rot][v>>30];
        v<<=2;
        res = (res<<2) | (tab&0x3);
        rot = tab>>2;
        }
      m2p2D_3[d][p]=res|(rot<<6);
      }
  for (int d=0; d<4; ++d)
    for (uint32_t p=0; p<64; ++p)
      {
      unsigned rot = d;
      uint32_t v = p<<26;
      uint32_t res = 0;
      for (int i=0; i<3; ++i)
        {
        unsigned tab=p2m2D_1[rot][v>>30];
        v<<=2;
        res = (res<<2) | (tab&0x3);
        rot = tab>>2;
        }
      p2m2D_3[d][p]=res|(rot<<6);
      }
  }

uint32_t morton2peano2D_32(uint32_t v, int bits)
  {
  if (!peano2d_done) init_peano2d();
  unsigned rot = 0;
  uint32_t res = 0;
  v<<=32-(bits<<1);
  int i=0;
  for (; i<bits-2; i+=3)
    {
    unsigned tab=m2p2D_3[rot][v>>26];
    v<<=6;
    res = (res<<6) | (tab&0x3fu);
    rot = tab>>6;
    }
  for (; i<bits; ++i)
    {
    unsigned tab=m2p2D_1[rot][v>>30];
    v<<=2;
    res = (res<<2) | (tab&0x3);
    rot = tab>>2;
    }
  return res;
  }

void myassert(bool cond, const char *msg)
  {
  if (cond) return;
Martin Reinecke's avatar
Martin Reinecke committed
108
  throw runtime_error(msg);
Martin Reinecke's avatar
import  
Martin Reinecke committed
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
  }

template<typename It, typename Comp> class IdxComp__
  {
  private:
    It begin;
    Comp comp;
  public:
    IdxComp__ (It begin_, Comp comp_): begin(begin_), comp(comp_) {}
    bool operator() (std::size_t a, std::size_t b) const
      { return comp(*(begin+a),*(begin+b)); }
  };
/*! Performs an indirect sort on the supplied iterator range and returns in
    \a idx a \a vector containing the indices of the smallest, second smallest,
    third smallest, etc. element, according to \a comp. */
template<typename It, typename T2, typename Comp>
  inline void buildIndex (It begin, It end, std::vector<T2> &idx, Comp comp)
  {
  using namespace std;
  T2 num=end-begin;
  idx.resize(num);
  for (T2 i=0; i<num; ++i) idx[i] = i;
  sort (idx.begin(),idx.end(),IdxComp__<It,Comp>(begin,comp));
  }

/*! Performs an indirect sort on the supplied iterator range and returns in
    \a idx a \a vector containing the indices of the smallest, second smallest,
    third smallest, etc. element. */
template<typename It, typename T2> inline void buildIndex (It begin, It end,
  std::vector<T2> &idx)
  {
  using namespace std;
  typedef typename iterator_traits<It>::value_type T;
  buildIndex(begin,end,idx,less<T>());
  }

145
146
147
148
149
150
151
152
153
154
155
156
/*! Returns the remainder of the division \a v1/v2.
    The result is non-negative.
    \a v1 can be positive or negative; \a v2 must be positive. */
inline double fmodulo (double v1, double v2)
  {
  if (v1>=0)
    return (v1<v2) ? v1 : fmod(v1,v2);
  double tmp=fmod(v1,v2)+v2;
  return (tmp==v2) ? 0. : tmp;
//  return (v1>=0) ? ((v1<v2) ? v1 : fmod(v1,v2)) : (fmod(v1,v2)+v2);
  }

Martin Reinecke's avatar
Martin Reinecke committed
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
static inline double one_minus_x2 (double x)
  { return (fabs(x)>0.1) ? (1.+x)*(1.-x) : 1.-x*x; }

void legendre_prep(int n, vector<double> &x, vector<double> &w)
  {
  constexpr double pi = 3.141592653589793238462643383279502884197;
  constexpr double eps = 3e-14;
  int m = (n+1)>>1;
  x.resize(m);
  w.resize(m);

  double t0 = 1 - (1-1./n) / (8.*n*n);
  double t1 = 1./(4.*n+2.);

#pragma omp parallel
{
  int i;
#pragma omp for schedule(dynamic,100)
  for (i=1; i<=m; ++i)
    {
    double x0 = cos(pi * ((i<<2)-1) * t1) * t0;

    int dobreak=0;
    int j=0;
    double dpdx;
    while(1)
      {
      double P_1 = 1.0;
      double P0 = x0;
      double dx, x1;

      for (int k=2; k<=n; k++)
        {
        double P_2 = P_1;
        P_1 = P0;
//        P0 = ((2*k-1)*x0*P_1-(k-1)*P_2)/k;
        P0 = x0*P_1 + (k-1.)/k * (x0*P_1-P_2);
        }

      dpdx = (P_1 - x0*P0) * n / one_minus_x2(x0);

      /* Newton step */
      x1 = x0 - P0/dpdx;
      dx = x0-x1;
      x0 = x1;
      if (dobreak) break;

      if (abs(dx)<=eps) dobreak=1;
      if (++j>=100) throw runtime_error("convergence problem");
      }

    x[m-i] = x0;
    w[m-i] = 2. / (one_minus_x2(x0) * dpdx * dpdx);
    }
} // end of parallel region
  }

Martin Reinecke's avatar
import  
Martin Reinecke committed
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
using a_i_c = py::array_t<int, py::array::c_style | py::array::forcecast>;
using a_d_c = py::array_t<double, py::array::c_style | py::array::forcecast>;
using a_c_c = py::array_t<complex<double>,
  py::array::c_style | py::array::forcecast>;

a_i_c peanoindex(const a_d_c &uv_, int nu, int nv)
  {
  myassert(uv_.ndim()==2, "uv array must be 2D");
  myassert(uv_.shape(1)==2, "uv.shape[1] must be 2");
  int nvis = uv_.shape(0);
  auto uv = uv_.data();

  int npmax = max(nu, nv);
  int nbits = 0;
  for (int istart = npmax-1; istart!=0; istart>>=1, ++nbits);
  vector<int> ipeano(nvis);
  for (int i=0; i<nvis; ++i)
    {
232
    auto u = fmodulo(uv[2*i], 1.)*nu;
Martin Reinecke's avatar
import  
Martin Reinecke committed
233
    auto iu = min(nu-1, int(u));
234
    auto v = fmodulo(uv[2*i+1], 1.)*nv;
Martin Reinecke's avatar
import  
Martin Reinecke committed
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
    auto iv = min(nv-1, int(v));
    ipeano[i] = morton2peano2D_32(coord2morton2D_32(iu,iv),nbits);
    }
  vector<int> newind;
  buildIndex(ipeano.begin(), ipeano.end(), newind);
  int odim[] = {nvis};
  a_i_c res(odim);
  auto iout = res.mutable_data();
  for (int i=0; i<nvis; ++i)
    iout[i] = newind[i];
  return res;
  }

class Helper
  {
Martin Reinecke's avatar
Martin Reinecke committed
250
251
  protected:
    int nu, nv;
Martin Reinecke's avatar
import  
Martin Reinecke committed
252
  public:
Martin Reinecke's avatar
Martin Reinecke committed
253
254
255
256
257
258
    int w;
  protected:
    double beta;
    int nsafe, su;
  public:
    int sv;
Martin Reinecke's avatar
import  
Martin Reinecke committed
259

Martin Reinecke's avatar
Martin Reinecke committed
260
261
262
263
264
    vector<double> kernel;
    int iu0, iv0; // start index of the current visibility
    int bu0, bv0; // start index of the current buffer

    void update(double u_in, double v_in)
Martin Reinecke's avatar
import  
Martin Reinecke committed
265
      {
266
      auto u = fmodulo(u_in, 1.)*nu;
Martin Reinecke's avatar
Martin Reinecke committed
267
268
      iu0 = int(u-w*0.5 + 1 + nu) - nu;
      if (iu0+w>nu+nsafe) iu0 = nu+nsafe-w;
269
      auto v = fmodulo(v_in, 1.)*nv;
Martin Reinecke's avatar
Martin Reinecke committed
270
271
272
273
      iv0 = int(v-w*0.5 + 1 + nv) - nv;
      if (iv0+w>nv+nsafe) iv0 = nv+nsafe-w;
      double xw=2./w;
      for (int i=0; i<w; ++i)
Martin Reinecke's avatar
import  
Martin Reinecke committed
274
        {
Martin Reinecke's avatar
Martin Reinecke committed
275
276
277
278
279
        kernel[i  ] = xw*(iu0+i-u);
        kernel[i+w] = xw*(iv0+i-v);
        }
      for (int i=0; i<2*w; ++i)
        kernel[i] = exp(beta*(sqrt(1-kernel[i]*kernel[i])-1.));
Martin Reinecke's avatar
import  
Martin Reinecke committed
280
281
      }

Martin Reinecke's avatar
Martin Reinecke committed
282
283
    bool need_to_move() const
      { return (iu0<bu0) || (iv0<bv0) || (iu0+w>bu0+su) || (iv0+w>bv0+sv); }
Martin Reinecke's avatar
import  
Martin Reinecke committed
284

Martin Reinecke's avatar
Martin Reinecke committed
285
    void update_position()
Martin Reinecke's avatar
import  
Martin Reinecke committed
286
      {
Martin Reinecke's avatar
Martin Reinecke committed
287
288
      bu0=max(-nsafe, min(nu+nsafe-su, iu0+nsafe-su/2));
      bv0=max(-nsafe, min(nv+nsafe-sv, iv0+nsafe-sv/2));
Martin Reinecke's avatar
import  
Martin Reinecke committed
289
290
      }

Martin Reinecke's avatar
Martin Reinecke committed
291
292
293
294
295
296
297
  protected:
    Helper(int nu_, int nv_, double epsilon)
      : nu(nu_), nv(nv_),
        w(int(-log10(epsilon)+1.9999)), beta(2.3*w), nsafe((w+1)/2),
        su(min(3*w, nu)), sv(min(3*w, nv)),
        kernel(2*w),
        bu0(-1000000), bv0(-1000000)
Martin Reinecke's avatar
import  
Martin Reinecke committed
298
      {
Martin Reinecke's avatar
Martin Reinecke committed
299
      if (min(nu,nv)<2*nsafe) throw runtime_error("grid dimensions too small");
Martin Reinecke's avatar
import  
Martin Reinecke committed
300
301
302
      }
  };

Martin Reinecke's avatar
Martin Reinecke committed
303
class WriteHelper: public Helper
Martin Reinecke's avatar
import  
Martin Reinecke committed
304
305
306
307
308
309
310
  {
  private:
    vector<complex<double>> data;
    complex<double> *grid;

    void dump()
      {
Martin Reinecke's avatar
Martin Reinecke committed
311
      if (bu0<-nsafe) return; // nothing written into buffer yet
Martin Reinecke's avatar
import  
Martin Reinecke committed
312
313
#pragma omp critical
{
Martin Reinecke's avatar
Martin Reinecke committed
314
315
316
      int idxu = (bu0+nu)%nu;
      int idxv0 = (bv0+nv)%nv;
      for (int iu=0; iu<su; ++iu)
Martin Reinecke's avatar
import  
Martin Reinecke committed
317
318
        {
        int idxv = idxv0;
Martin Reinecke's avatar
Martin Reinecke committed
319
        for (int iv=0; iv<sv; ++iv)
Martin Reinecke's avatar
import  
Martin Reinecke committed
320
          {
Martin Reinecke's avatar
Martin Reinecke committed
321
          grid[idxu*nv + idxv] += data[iu*sv + iv];
Martin Reinecke's avatar
import  
Martin Reinecke committed
322
323
324
325
326
327
328
329
330
          if (++idxv>=nv) idxv=0;
          }
        if (++idxu>=nu) idxu=0;
        }
}
      }

  public:
    complex<double> *p0;
Martin Reinecke's avatar
Martin Reinecke committed
331
332
333
    WriteHelper(int nu_, int nv_, double epsilon, complex<double> *grid_)
      : Helper(nu_, nv_, epsilon), data(su*sv, 0.), grid(grid_) {}
    ~WriteHelper() { dump(); }
Martin Reinecke's avatar
import  
Martin Reinecke committed
334

Martin Reinecke's avatar
Martin Reinecke committed
335
    void prep_write(double u_in, double v_in)
Martin Reinecke's avatar
import  
Martin Reinecke committed
336
      {
Martin Reinecke's avatar
Martin Reinecke committed
337
338
      update(u_in, v_in);
      if (need_to_move())
Martin Reinecke's avatar
import  
Martin Reinecke committed
339
340
        {
        dump();
Martin Reinecke's avatar
Martin Reinecke committed
341
        update_position();
Martin Reinecke's avatar
import  
Martin Reinecke committed
342
343
        fill(data.begin(), data.end(), 0.);
        }
Martin Reinecke's avatar
Martin Reinecke committed
344
      p0 = data.data() + sv*(iu0-bu0) + iv0-bv0;
Martin Reinecke's avatar
import  
Martin Reinecke committed
345
346
347
      }
  };

Martin Reinecke's avatar
Martin Reinecke committed
348
class ReadHelper: public Helper
Martin Reinecke's avatar
import  
Martin Reinecke committed
349
350
351
352
353
354
355
  {
  private:
    vector<complex<double>> data;
    const complex<double> *grid;

    void load()
      {
Martin Reinecke's avatar
Martin Reinecke committed
356
357
358
      int idxu = (bu0+nu)%nu;
      int idxv0 = (bv0+nv)%nv;
      for (int iu=0; iu<su; ++iu)
Martin Reinecke's avatar
import  
Martin Reinecke committed
359
360
        {
        int idxv = idxv0;
Martin Reinecke's avatar
Martin Reinecke committed
361
        for (int iv=0; iv<sv; ++iv)
Martin Reinecke's avatar
import  
Martin Reinecke committed
362
          {
Martin Reinecke's avatar
Martin Reinecke committed
363
          data[iu*sv + iv] = grid[idxu*nv + idxv];
Martin Reinecke's avatar
import  
Martin Reinecke committed
364
365
366
367
368
369
370
371
          if (++idxv>=nv) idxv=0;
          }
        if (++idxu>=nu) idxu=0;
        }
      }

  public:
    const complex<double> *p0;
Martin Reinecke's avatar
Martin Reinecke committed
372
373
    ReadHelper(int nu_, int nv_, double epsilon, const complex<double> *grid_)
      : Helper(nu_, nv_, epsilon), data(su*sv,0.), grid(grid_), p0(nullptr) {}
Martin Reinecke's avatar
import  
Martin Reinecke committed
374

Martin Reinecke's avatar
Martin Reinecke committed
375
    void prep_read(double u_in, double v_in)
Martin Reinecke's avatar
import  
Martin Reinecke committed
376
      {
Martin Reinecke's avatar
Martin Reinecke committed
377
378
      update(u_in, v_in);
      if (need_to_move())
Martin Reinecke's avatar
import  
Martin Reinecke committed
379
        {
Martin Reinecke's avatar
Martin Reinecke committed
380
        update_position();
Martin Reinecke's avatar
import  
Martin Reinecke committed
381
382
        load();
        }
Martin Reinecke's avatar
Martin Reinecke committed
383
      p0 = data.data() + sv*(iu0-bu0) + iv0-bv0;
Martin Reinecke's avatar
import  
Martin Reinecke committed
384
385
386
387
      }
  };

a_c_c to_grid (const a_d_c &uv_, const a_c_c &vis_,
Martin Reinecke's avatar
Martin Reinecke committed
388
               int nu, int nv, double epsilon)
Martin Reinecke's avatar
import  
Martin Reinecke committed
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
  {
  myassert(uv_.ndim()==2, "uv array must be 2D");
  myassert(uv_.shape(1)==2, "uv.shape[1] must be 2");
  int nvis = uv_.shape(0);
  myassert(vis_.ndim()==1, "vis array must be 1D");
  myassert(vis_.shape(0)==nvis, "array size mismatch");
  auto uv = uv_.data();
  auto vis = vis_.data();

  int odim[] = {nu,nv};
  a_c_c res(odim);
  auto grid = res.mutable_data();
  for (int i=0; i<nu*nv; ++i) grid[i] = 0.;

#pragma omp parallel
{
Martin Reinecke's avatar
Martin Reinecke committed
405
  WriteHelper hlp(nu, nv, epsilon, grid);
Martin Reinecke's avatar
import  
Martin Reinecke committed
406
407
408
409
410

  // Loop over sampling points
#pragma omp for schedule(dynamic,10000)
  for (int ipart=0; ipart<nvis; ++ipart)
    {
Martin Reinecke's avatar
Martin Reinecke committed
411
    hlp.prep_write(uv[2*ipart], uv[2*ipart+1]);
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
412
413
414
415
416
417
    auto * RESTRICT ptr = hlp.p0;
    int w = hlp.w;
    auto v = vis[ipart];
    const double * RESTRICT ku = hlp.kernel.data();
    const double * RESTRICT kv = hlp.kernel.data()+hlp.w;
    for (int cu=0; cu<w; ++cu)
Martin Reinecke's avatar
import  
Martin Reinecke committed
418
      {
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
419
420
421
422
      complex<double> tmp = v*ku[cu];
      for (int cv=0; cv<w; ++cv)
        ptr[cv] += tmp*kv[cv];
      ptr+=hlp.sv;
Martin Reinecke's avatar
import  
Martin Reinecke committed
423
424
425
426
427
428
      }
    }
} // end of parallel region
  return res;
  }

Martin Reinecke's avatar
Martin Reinecke committed
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
a_d_c to_grid_post (const a_c_c &grid_)
  {
  myassert(grid_.ndim()==2, "grid array must be 2D");
  int nu = grid_.shape(0), nv = grid_.shape(1);
  auto grid = grid_.data();

  int odim[] = {nu,nv};
  a_d_c res(odim);
  auto grid2 = res.mutable_data();
  for (int u=0; u<nu; ++u)
    {
    int xu = (u==0) ? 0 : nu-u;
    for (int v=0; v<nv; ++v)
      {
      int xv = (v==0) ? 0 : nv-v;
      int i1 = u*nv+v;
      int i2 = xu*nv+xv;
      grid2[i1] = 0.5*(grid[i1].real()+grid[i1].imag()+
                       grid[i2].real()-grid[i2].imag());
      }
    }
  return res;
  }

Martin Reinecke's avatar
import  
Martin Reinecke committed
453
a_c_c from_grid (const a_d_c &uv_, const a_c_c &grid_,
Martin Reinecke's avatar
Martin Reinecke committed
454
  int nu, int nv, double epsilon)
Martin Reinecke's avatar
import  
Martin Reinecke committed
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
  {
  myassert(uv_.ndim()==2, "uv array must be 2D");
  myassert(uv_.shape(1)==2, "uv.shape[1] must be 2");
  myassert(grid_.ndim()==2, "grid array must be 2D");
  int nvis = uv_.shape(0);
  auto uv = uv_.data();
  auto grid = grid_.data();

  myassert(nu==grid_.shape(0), "oops");
  myassert(nv==grid_.shape(1), "oops");

  int odim[] = {nvis};
  a_c_c res(odim);
  auto vis = res.mutable_data();

  // Loop over sampling points
#pragma omp parallel
{
Martin Reinecke's avatar
Martin Reinecke committed
473
  ReadHelper hlp(nu, nv, epsilon, grid);
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
474

Martin Reinecke's avatar
import  
Martin Reinecke committed
475
476
477
#pragma omp for schedule(dynamic,10000)
  for (int ipart=0; ipart<nvis; ++ipart)
    {
Martin Reinecke's avatar
Martin Reinecke committed
478
    hlp.prep_read(uv[2*ipart], uv[2*ipart+1]);
Martin Reinecke's avatar
import  
Martin Reinecke committed
479
    complex<double> r = 0.;
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
480
481
482
483
484
    auto * RESTRICT ptr = hlp.p0;
    int w = hlp.w;
    const double * RESTRICT ku = hlp.kernel.data();
    const double * RESTRICT kv = hlp.kernel.data()+hlp.w;
    for (int cu=0; cu<w; ++cu)
Martin Reinecke's avatar
import  
Martin Reinecke committed
485
486
      {
      complex<double> tmp = 0.;
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
487
488
489
490
      for (int cv=0; cv<w; ++cv)
        tmp += ptr[cv] * kv[cv];
      r += tmp*ku[cu];
      ptr += hlp.sv;
Martin Reinecke's avatar
import  
Martin Reinecke committed
491
      }
Martin Reinecke's avatar
Martin Reinecke committed
492
    vis[ipart] = r;
Martin Reinecke's avatar
import  
Martin Reinecke committed
493
494
495
496
497
    }
}
  return res;
  }

Martin Reinecke's avatar
Martin Reinecke committed
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
a_c_c from_grid_pre (const a_d_c &grid_)
  {
  myassert(grid_.ndim()==2, "grid array must be 2D");
  int nu = grid_.shape(0), nv = grid_.shape(1);
  auto grid = grid_.data();

  int odim[] = {nu,nv};
  a_c_c res(odim);
  auto grid2 = res.mutable_data();
  for (int u=0; u<nu; ++u)
    {
    int xu = (u==0) ? 0 : nu-u;
    for (int v=0; v<nv; ++v)
      {
      int xv = (v==0) ? 0 : nv-v;
      int i1 = u*nv+v;
      int i2 = xu*nv+xv;
      double v1 = 0.5*grid[i1];
      double v2 = 0.5*grid[i2];
      grid2[i1] = complex<double>(v1+v2, v1-v2);
      }
    }
  return res;
  }

Martin Reinecke's avatar
Martin Reinecke committed
523
524
525
526
527
528
529
530
531
532
533
a_d_c correction_factors (size_t n, size_t nval, double epsilon)
  {
  auto w = int(-log10(epsilon)+1.9999);
  auto beta = 2.3*w;
  auto p = int(1.5*w+2);
  double alpha = pi*w/n;
  vector<double> x, wgt;
  legendre_prep(2*p,x,wgt);
  auto psi = x;
  for (auto &v:psi)
    v = exp(beta*(sqrt(1-v*v)-1.));
Martin Reinecke's avatar
tweaks    
Martin Reinecke committed
534
  int odim[] = {int(nval)};
Martin Reinecke's avatar
Martin Reinecke committed
535
536
537
538
539
540
541
542
543
544
545
546
  a_d_c res(odim);
  auto val = res.mutable_data();
  for (size_t k=0; k<nval; ++k)
    {
    double tmp=0;
    for (int i=0; i<p; ++i)
      tmp += wgt[i]*psi[i]*cos(alpha*k*x[i]);
    val[k] = 1./(w*tmp);
    }
  return res;
  }

Martin Reinecke's avatar
import  
Martin Reinecke committed
547
548
549
550
551
552
553
554
} // unnamed namespace

PYBIND11_MODULE(nifty_gridder, m)
  {
  using namespace pybind11::literals;

  m.def("peanoindex",&peanoindex);
  m.def("to_grid",&to_grid);
Martin Reinecke's avatar
Martin Reinecke committed
555
  m.def("to_grid_post",&to_grid_post);
Martin Reinecke's avatar
import  
Martin Reinecke committed
556
  m.def("from_grid",&from_grid);
Martin Reinecke's avatar
Martin Reinecke committed
557
  m.def("from_grid_pre",&from_grid_pre);
Martin Reinecke's avatar
Martin Reinecke committed
558
  m.def("correction_factors",&correction_factors);
Martin Reinecke's avatar
import  
Martin Reinecke committed
559
  }