forked from jmbr/libpme6
-
Notifications
You must be signed in to change notification settings - Fork 0
/
pme.cpp
436 lines (346 loc) · 12.5 KB
/
pme.cpp
1
2
3
4
5
6
7
8
9
10
11
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
108
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
145
146
147
148
149
150
151
152
153
154
155
156
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
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <limits>
#include <numeric>
#include <functional>
#include <iostream>
#include <fftw3.h>
#include "cube.cpp"
#include "pme.h"
#include "spline.h"
#include "linear-algebra.h"
namespace ewald {
const spline4 spline;
const int order = spline.order;
const double epsilon = std::numeric_limits<double>::epsilon();
pme::pme(long d0, long d1, long d2,
double const unit_cell[],
size_t N_,
double const* q_,
double cut_off_,
double tolerance,
int num_threads)
: N(N_),
q(q_),
cut_off(cut_off_),
threshold(compute_threshold(cut_off, tolerance)),
threshold2(threshold * threshold),
dim0(d0), dim1(d1), dim2(d2),
Q(d0, d1, d2),
Qhat(d0, d1, d2),
BC(d0, d1, d2),
s(3, N, order),
ds(3, N, order)
{
assert(dim0 > 0 && dim1 > 0 && dim2 > 0);
std::memcpy(L, unit_cell, 3 * 3 * sizeof(double));
volume = determinant(L);
assert(volume > 1e2 * epsilon);
matrix_inverse(L, Linv);
std::memset(K, 0, 3 * 3 * sizeof(double));
K[3*0+0] = dim0;
K[3*1+1] = dim1;
K[3*2+2] = dim2;
matrix_matrix_product(K, Linv, H);
initialize_table();
fftw_init_threads();
fftw_plan_with_nthreads(num_threads);
{
// TODO: Benchmark r2c.
fftw_complex* in = reinterpret_cast<fftw_complex*>(Q.memptr());
fftw_complex* out = reinterpret_cast<fftw_complex*>(Qhat.memptr());
forward_plan = fftw_plan_dft_3d(dim0, dim1, dim2,
in, out,
FFTW_FORWARD, FFTW_MEASURE);
}
{
fftw_complex* in = reinterpret_cast<fftw_complex*>(Qhat.memptr());
fftw_complex* out = reinterpret_cast<fftw_complex*>(Qhat.memptr());
backward_plan = fftw_plan_dft_3d(dim0, dim1, dim2,
in, out,
FFTW_BACKWARD, FFTW_MEASURE);
}
}
pme::~pme() {
fftw_destroy_plan(forward_plan);
fftw_destroy_plan(backward_plan);
fftw_cleanup_threads();
}
void pme::initialize_table() {
long k0, k1, k2;
for (k0 = 0; k0 < dim0; ++k0) {
const double h0 = k0 < dim0 / 2 ? k0 : k0 - dim0;
for (k1 = 0; k1 < dim1; ++k1) {
const double h1 = k1 < dim1 / 2 ? k1 : k1 - dim1;
for (k2 = 0; k2 < dim2; ++k2) {
if (k0 == 0 && k1 == 0 && k2 == 0)
continue;
const double h2 = k2 < dim2 / 2 ? k2 : k2 - dim2;
double LinvTm[] = { h0, h1, h2 };
matrix_vector_product_transpose(Linv, LinvTm);
const double hh = dot_product(LinvTm, LinvTm);
const double nrm = norm(spline.factor(k0, dim0)
* spline.factor(k1, dim1)
* spline.factor(k2, dim2));
BC(k0, k1, k2) = psi(hh) * nrm;
}
}
}
}
static void compute_spline(double u,
double* __restrict__ s,
double* __restrict__ ds,
double& floor_u) {
floor_u = floor(u);
double x = u - floor_u + double(order) - 1.0;
// Compute splines and their derivatives using Horner's method.
const double a[] = {
32.0 / 3.0, -8.0, 2.0, -1.0 / 6.0,
-22.0 / 3.0, 10.0, -4.0, 1.0 / 2.0,
2.0 / 3.0, -2.0, 2.0, -1.0 / 2.0,
0.0, 0.0, 0.0, 1.0 / 6.0
};
for (size_t k = 0; k < 4; ++k, --x) {
s[k] = a[4*k] + (a[4*k+1] + (a[4*k+2] + a[4*k+3] * x) * x) * x;
ds[k] = a[4*k+1] + (2.0 * a[4*k+2] + 3.0 * a[4*k+3] * x) * x;
}
}
void pme::interpolate(double const* __restrict__ x,
double const* __restrict__ y,
double const* __restrict__ z) {
for (size_t n = 0; n < N; ++n) {
double u[] = { x[n], y[n], z[n] };
matrix_vector_product(H, u);
const double q_n = q[n];
double floor_u[3];
for (size_t d = 0; d < 3; ++d)
compute_spline(u[d], &s(d, n, 0), &ds(d, n, 0), floor_u[d]);
for (long c0 = 0; c0 < order; ++c0) {
const long l0 = floor_u[0] + c0 - order + 1;
const long k0 = l0 < 0 ? l0 + dim0 : l0;
const double q_n_s0 = q_n * s(0, n, c0);
for (long c1 = 0; c1 < order; ++c1) {
const long l1 = floor_u[1] + c1 - order + 1;
const long k1 = l1 < 0 ? l1 + dim1 : l1;
const double q_n_s0_s1 = q_n_s0 * s(1, n, c1);
for (long c2 = 0; c2 < order; ++c2) {
const long l2 = floor_u[2] + c2 - order + 1;
const long k2 = l2 < 0 ? l2 + dim2 : l2;
Q(k0, k1, k2) += q_n_s0_s1 * s(2, n, c2);
// printf("cube (%s): %d %d %d %d %g\n", __func__, n, k0, k1, k2, std::real(Qhat(k0, k1, k2)));
}
}
}
}
}
double pme::energy(double const* __restrict__ x,
double const* __restrict__ y,
double const* __restrict__ z,
double* __restrict__ force_x,
double* __restrict__ force_y,
double* __restrict__ force_z) {
Q.zeros();
Qhat.zeros();
s.zeros();
ds.zeros();
interpolate(x, y, z);
/*
{
std::complex<double> const* Qptr = Q.memptr();
std::complex<double> total { 0.0, 0.0 };
for (long r = 0; r < dim0 * dim1 * dim2; ++r)
total += Qptr[r];
std::printf("%s: Interpolated a total \"charge\" of %g + %g i\n", __func__, real(total), imag(total));
}
*/
fftw_execute(forward_plan);
Qhat *= BC;
fftw_execute(backward_plan);
double Erecip = 0.0;
for (long k0 = 0; k0 < dim0; ++k0)
for (long k1 = 0; k1 < dim1; ++k1)
for (long k2 = 0; k2 < dim2; ++k2)
Erecip += real(Q(k0, k1, k2)) * real(Qhat(k0, k1, k2));
double Erecip1 = 0.0;
for (size_t n = 0; n < N; ++n) {
double u[] = { x[n], y[n], z[n] };
matrix_vector_product(H, u);
for (long c0 = 0; c0 < order; ++c0) {
const long l0 = floor(u[0]) + c0 - order + 1;
const long k0 = l0 < 0 ? l0 + dim0 : l0;
for (long c1 = 0; c1 < order; ++c1) {
const long l1 = floor(u[1]) + c1 - order + 1;
const long k1 = l1 < 0 ? l1 + dim1 : l1;
const double ds0_s1 = ds(0, n, c0) * s(1, n, c1);
const double s0_ds1 = s(0, n, c0) * ds(1, n, c1);
const double s0_s1 = s(0, n, c0) * s(1, n, c1);
for (long c2 = 0; c2 < order; ++c2) {
const long l2 = floor(u[2]) + c2 - order + 1;
const long k2 = l2 < 0 ? l2 + dim2 : l2;
const double Q_k = std::real(Qhat(k0, k1, k2));
Erecip1 += Q_k * std::real(Q(k0, k1, k2));
double w[] = {
ds0_s1 * s(2, n, c2),
s0_ds1 * s(2, n, c2),
s0_s1 * ds(2, n, c2)
};
matrix_vector_product_transpose(H, w);
// if (n == 1)
// printf("cube (%s): %3d\t%3d\t%3d\t%3d\t%3.6f\t%3.6f\t%3.6f\t%3.6f\t%3.9f\n",
// __func__, n, k0, k1, k2,
// std::real(Q(k0, k1, k2)), std::imag(Q(k0, k1, k2)),
// std::real(Qhat(k0, k1, k2)), std::imag(Qhat(k0, k1, k2)),
// Q_k * std::real(Q(k0, k1, k2)));
const double factor = -2.0 * Q_k * q[n];
force_x[n] += factor * w[0];
force_y[n] += factor * w[1];
force_z[n] += factor * w[2];
}
}
}
}
printf("%s: Erecip = %3.16f vs. %3.16f\n", __func__, Erecip, Erecip1);
return double(Erecip1);
}
double pme::energy_extra() const {
const double sum_q = std::accumulate(q, q + N, 0.0, std::plus<double>());
return 1.0 / 6.0 * pow(M_PI * threshold, 3.0) / volume * sum_q * sum_q;
}
double pme::energy_self() const {
const double q2 = std::inner_product(q, q + N, q, 0.0);
return 1.0 / 12.0 * pow(M_PI, 3.0) * pow(threshold, 6.0) * q2;
}
double pme::psi(double h2) const {
const double b2 = M_PI * h2 / threshold2;
const double b = sqrt(b2);
const double b3 = b2 * b;
const double h = sqrt(h2);
const double h3 = h2 * h;
return pow(M_PI, 9.0 / 2.0) / (3.0 * volume) * h3
* (sqrt(M_PI) * erfc(b) + (1.0 / (2.0 * b3) - 1.0 / b) * exp(-b2));
}
double pme::recip_convergence_term(double h2,
std::complex<double> const& rho) const {
const double norm_rho2 = norm(rho);
return norm_rho2 * psi(h2);
}
static inline double direct_term(double r2, double threshold2, double& fac) {
const double r6 = r2 * r2 * r2;
const double r8 = r6 * r2;
const double a2 = M_PI * threshold2 * r2;
const double a4 = a2 * a2;
const double a6 = a4 * a2;
const double exp_m_a2 = exp(-a2);
fac = -(a6 + 3.0 * a4 + 6.0 * a2 + 6.0) * exp_m_a2 / r8;
return (1.0 + a2 + 0.5 * a4) * exp_m_a2 / r6;
}
double pme::direct_convergence_term(double const* v, double* dv) const {
const double r2 = dot_product(v, v);
double fac;
const double energy = direct_term(r2, threshold2, fac);
for (size_t k = 0; k < 3; ++k)
dv[k] = fac * v[k];
return energy;
}
static double diff_direct_term(double threshold, double cut_off) {
// Computes the derivative of direct_term() with respect to the
// variable threshold. Note that the input is threshold, not
// threshold squared (threshold2).
const double threshold2 = threshold * threshold;
const double threshold4 = threshold2 * threshold2;
const double threshold5 = threshold4 * threshold;
const double cut_off2 = cut_off * cut_off;
return -threshold5 * exp(-threshold2 * cut_off2);
}
/** Obtains a suitable value of the threshold parameter. The threshold
* parameter (beta) is obtained by solving the non-linear equation
* direct_term(beta) = tol for a given tolerance tol.
*
* \param cut_off Cut off distance.
*
* \param tol Maximum value of the real space contribution for the
* distance given by cut_off.
*
* \return The solution beta of the non-linear equation.
*/
double pme::compute_threshold(double cut_off, double tol) const {
// XXX Maybe throw exception rather than return an integer status flag.
const double r2 = cut_off * cut_off;
double aux;
// Our initial guess comes from imposing that the value of exp(-a2)
// in direct_term should be greater than or equal to machine
// epsilon.
double beta_init = sqrt(-log(epsilon) / M_PI) / cut_off;
double beta = beta_init;
double beta2 = beta * beta;
double val = direct_term(r2, beta2, aux);
std::clog << "Starting non-linear solver with beta = " << beta << std::endl;
size_t iter;
const size_t max_iters = size_t(1e6);
for (iter = 0; iter < max_iters; ++iter) {
beta -= (direct_term(r2, beta2, aux) - tol) / diff_direct_term(beta, cut_off);
beta2 = beta * beta;
if (std::isinf(beta) || std::isnan(beta)) {
beta_init /= 2.0;
beta = beta_init;
if (beta_init == 0.0) {
std::clog << "Non-linear solver failed to find a suitable value of beta."
<< std::endl;
// Red alert. XXX This should fail more gracefully.
beta = NAN;
break;
}
}
val = direct_term(r2, beta2, aux);
if (fabs(val - tol) < epsilon)
break;
}
std::clog << "Solver stopped after " << iter << " iterations.\n"
<< "Using beta = " << beta << " with value = " << val << "\n";
if (iter == max_iters)
std::clog << "Warning: Non-linear solver did not converge."
<< std::endl;
return beta;
}
double pme::excluded(exclusion_vector const& exclusions,
double const* __restrict__ x,
double const* __restrict__ y,
double const* __restrict__ z,
double* __restrict__ force_x,
double* __restrict__ force_y,
double* __restrict__ force_z) const {
double excluded_energy = 0.0;
for (size_t i = 0; i < N; ++i) {
const double q_i = q[i];
index_vector const& excl = exclusions[i];
for (size_t r = 0; r < excl.size(); ++r) {
const size_t j = excl[r];
if (j <= i)
continue;
const double v[] = { x[i] - x[j], y[i] - y[j], z[i] - z[j] };
const double r2 = dot_product(v, v);
// Note that we must NOT enforce a cut off here. We are
// compensating a masked contribution to the reciprocal part,
// and that contribution does not involve cut offs.
const double r6 = r2 * r2 * r2;
const double invr6 = 1.0 / (r2 * r2 * r2);
const double invr8 = 1.0 / (r6 * r2);
double term;
double f[3];
const double qi_qj = q_i * q[j];
excluded_energy += qi_qj * (invr6 - direct_term(r2, threshold2, term));
const double factor = qi_qj * (6.0 * invr8 + term);
for (size_t k = 0; k < 3; ++k)
f[k] = factor * v[k];
force_x[i] += f[0];
force_y[i] += f[1];
force_z[i] += f[2];
force_x[j] -= f[0];
force_y[j] -= f[1];
force_z[j] -= f[2];
}
}
return excluded_energy;
}
}