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/*============================================================================
* Hilbert encoding for 2D or 3D coordinates.
*============================================================================*/
/*
This file is part of Code_Saturne, a general-purpose CFD tool.
Copyright (C) 1998-2016 EDF S.A.
This program is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
details.
You should have received a copy of the GNU General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/*----------------------------------------------------------------------------*/
#include "cs_defs.h"
/*----------------------------------------------------------------------------
* Standard C library headers
*----------------------------------------------------------------------------*/
#include <assert.h>
#include <float.h>
#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
/*----------------------------------------------------------------------------
* Local headers
*----------------------------------------------------------------------------*/
#include "bft_mem.h"
#include "bft_printf.h"
/*----------------------------------------------------------------------------
* Header for the current file
*----------------------------------------------------------------------------*/
#include "fvm_hilbert.h"
/*----------------------------------------------------------------------------*/
BEGIN_C_DECLS
/*! \cond DOXYGEN_SHOULD_SKIP_THIS */
/*=============================================================================
* Local Macro definitions
*============================================================================*/
/*=============================================================================
* Static global variables
*============================================================================*/
static const double fvm_hilbert_distrib_tol = 0.10;
/* Max. number of sub-iterations to get a well-balanced distribution */
static const int fvm_hilbert_distrib_n_iter_max = 5;
static const int _sampling_factors[4] = {1, /* OD */
2, /* 1D */
2, /* 2D */
4, /* 3D */};
static const unsigned _imax = ~(0U);
/* 2 dimension to nkey conversion */
static const unsigned _idata2d[]
= {0, 3, 1, 2,
0, 1, 3, 2,
2, 3, 1, 0,
2, 1, 3, 0};
/* 2 dimension to nkey state transitions */
static const unsigned _istate2d[]
= {1, 2, 0, 0,
0, 1, 3, 1,
2, 0, 2, 3,
3, 3, 1, 2};
/* 3 dimension to nkey conversion */
static const unsigned _idata3d[]
= {0, 7, 3, 4, 1, 6, 2, 5,
0, 1, 3, 2, 7, 6, 4, 5,
0, 3, 7, 4, 1, 2, 6, 5,
2, 3, 5, 4, 1, 0, 6, 7,
4, 5, 3, 2, 7, 6, 0, 1,
4, 7, 3, 0, 5, 6, 2, 1,
6, 7, 5, 4, 1, 0, 2, 3,
0, 1, 7, 6, 3, 2, 4, 5,
2, 1, 5, 6, 3, 0, 4, 7,
6, 1, 5, 2, 7, 0, 4, 3,
0, 7, 1, 6, 3, 4, 2, 5,
2, 1, 3, 0, 5, 6, 4, 7,
4, 7, 5, 6, 3, 0, 2, 1,
4, 5, 7, 6, 3, 2, 0, 1,
6, 1, 7, 0, 5, 2, 4, 3,
0, 3, 1, 2, 7, 4, 6, 5,
2, 3, 1, 0, 5, 4, 6, 7,
6, 7, 1, 0, 5, 4, 2, 3,
2, 5, 1, 6, 3, 4, 0, 7,
4, 3, 7, 0, 5, 2, 6, 1,
4, 3, 5, 2, 7, 0, 6, 1,
6, 5, 1, 2, 7, 4, 0, 3,
2, 5, 3, 4, 1, 6, 0, 7,
6, 5, 7, 4, 1, 2, 0, 3};
/* 3 dimension to nkey state transitions */
static const unsigned _istate3d[]
= { 1, 6, 3, 4, 2, 5, 0, 0,
0, 7, 8, 1, 9, 4, 5, 1,
15, 22, 23, 20, 0, 2, 19, 2,
3, 23, 3, 15, 6, 20, 16, 22,
11, 4, 12, 4, 20, 1, 22, 13,
22, 12, 20, 11, 5, 0, 5, 19,
17, 0, 6, 21, 3, 9, 6, 2,
10, 1, 14, 13, 11, 7, 12, 7,
8, 9, 8, 18, 14, 12, 10, 11,
21, 8, 9, 9, 1, 6, 17, 7,
7, 17, 15, 12, 16, 13, 10, 10,
11, 14, 9, 5, 11, 22, 0, 8,
18, 5, 12, 10, 19, 8, 12, 20,
8, 13, 19, 7, 5, 13, 18, 4,
23, 11, 7, 17, 14, 14, 6, 1,
2, 18, 10, 15, 21, 19, 20, 15,
16, 21, 17, 19, 16, 2, 3, 18,
6, 10, 16, 14, 17, 23, 17, 15,
18, 18, 21, 8, 17, 7, 13, 16,
3, 4, 13, 16, 19, 19, 2, 5,
16, 13, 20, 20, 4, 3, 15, 12,
9, 21, 18, 21, 15, 14, 23, 10,
22, 22, 6, 1, 23, 11, 4, 3,
14, 23, 2, 9, 22, 23, 21, 0};
/*============================================================================
* Private function definitions
*============================================================================*/
/*----------------------------------------------------------------------------
* Build a Hilbert key based on a 1-d coordinate in [0, 1].
*
* parameters:
* coord <-- 1-d coordinate, normalized
*
* returns:
* associated Hilbert encoding
*----------------------------------------------------------------------------*/
static fvm_hilbert_code_t
_hilbert_encode_1d(const double coord[1])
{
return coord[0];
}
/*----------------------------------------------------------------------------
* Build a Hilbert key based on 2-d coordinates in [0, 1].
*
* parameters:
* coord <-- 2-d coordinates, normalized
*
* returns:
* associated Hilbert encoding
*----------------------------------------------------------------------------*/
static fvm_hilbert_code_t
_hilbert_encode_2d(const double coord[2])
{
int level;
unsigned int c[2], temp, state;
unsigned int key[2] = {0, 0};
const int maxlevel = 28; /* 28 bits of significance per dimension */
static const unsigned *d[]
= {_idata2d, _idata2d+4, _idata2d+8, _idata2d+12};
static const unsigned *s[]
={_istate2d, _istate2d+4, _istate2d+8, _istate2d+12};
assert(coord[0] >= 0.0 && coord[0] <= 1.0);
assert(coord[1] >= 0.0 && coord[1] <= 1.0);
/* convert x, y coordinates to integers in range [0, imax] */
c[0] = (unsigned int) (coord[0] * (double) _imax); /* x */
c[1] = (unsigned int) (coord[1] * (double) _imax); /* y */
/* use state tables to convert nested quadrant's coordinates level by level */
state = 0;
for (level = 0; level < maxlevel; level++) {
temp = ( (c[0] >> (30-level)) & 2) /* extract 2 bits at current level */
| ((c[1] >> (31-level)) & 1);
/* treat key[] as long shift register, shift in converted coordinate */
key[0] = (key[0] << 2) | (key[1] >> 30);
key[1] = (key[1] << 2) | *(d[state] + temp);
state = *(s[state] + temp);
}
/* Convert 2 part Hilbert key to double and return;
Note that maxlevel could be increased from 28 to 32
by using long doubles (with a double, we have 56 significant bits,
which allows for 28 bits per coordinate). This could be increased
further by using 64-bit integers in intermediate calculations. */
return ldexp ((double) key[0], -24) + ldexp ((double) key[1], -56);
}
/*----------------------------------------------------------------------------
* Build a Hilbert key based on 3-d coordinates in [0, 1].
*
* parameters:
* coord <-- 3-d coordinates, normalized
*
* returns:
* associated Hilbert encoding
*----------------------------------------------------------------------------*/
static fvm_hilbert_code_t
_hilbert_encode_3d(const double coord[3])
{
int level;
unsigned int c[3], temp, state;
unsigned int key[3] = {0, 0, 0};
const int maxlevel = 19; /* 32 bits of significance per dimension */
static const unsigned int *d[]
= {_idata3d, _idata3d+8, _idata3d+16, _idata3d+24,
_idata3d+32, _idata3d+40, _idata3d+48, _idata3d+56,
_idata3d+64, _idata3d+72, _idata3d+80, _idata3d+88,
_idata3d+96, _idata3d+104, _idata3d+112, _idata3d+120,
_idata3d+128, _idata3d+136, _idata3d+144, _idata3d+152,
_idata3d+160, _idata3d+168, _idata3d+176, _idata3d+184};
static const unsigned int *s[]
= {_istate3d, _istate3d+8, _istate3d+16, _istate3d+24,
_istate3d+32, _istate3d+40, _istate3d+48, _istate3d+56,
_istate3d+64, _istate3d+72, _istate3d+80, _istate3d+88,
_istate3d+96, _istate3d+104, _istate3d+112, _istate3d+120,
_istate3d+128, _istate3d+136, _istate3d+144, _istate3d+152,
_istate3d+160, _istate3d+168, _istate3d+176, _istate3d+184};
assert(coord[0] >= 0.0 && coord[0] <= 1.0);
assert(coord[1] >= 0.0 && coord[1] <= 1.0);
assert(coord[2] >= 0.0 && coord[2] <= 1.0);
/* convert x,y,z coordinates to integers in range [0, _imax] */
c[0] = (unsigned int) (coord[0] * (double) _imax); /* x */
c[1] = (unsigned int) (coord[1] * (double) _imax); /* y */
c[2] = (unsigned int) (coord[2] * (double) _imax); /* z */
/* use state tables to convert nested quadrant's coordinates level by level */
key[0] = 0; key[1] = 0; key[2] = 0;
state = 0;
for (level = 0; level < maxlevel; level++) {
temp = ( (c[0] >> (29-level)) & 4) /* extract 3 bits at current level */
| ((c[1] >> (30-level)) & 2)
| ((c[2] >> (31-level)) & 1);
/* treat key[] as long shift register, shift in converted coordinate */
key[0] = (key[0] << 3) | (key[1] >> 29);
key[1] = (key[1] << 3) | *(d[state] + temp);
state = *(s[state] + temp);
}
/* Convert 2 part Hilbert key to double and return;
Note that maxlevel could be increased from 19 to 32 by using
a 3-part key and long doubles (with a double, we have 56 significant
bits, which allows for 19 bits per coordinate). This could be increased
further by using 64-bit integers in intermediate calculations. */
return ldexp ((double) key[0], -25) + ldexp ((double) key[1], -57);
}
#if defined(HAVE_MPI)
/*----------------------------------------------------------------------------
* Transform local extents to global extents.
*
* parameters:
* dim <-- spatial dimension (1, 2, or 3)
* g_extents <-> global extents (size: dim*2)
* comm <-- associated MPI communicator
*---------------------------------------------------------------------------*/
static void
_local_to_global_extents(int dim,
cs_coord_t extents[],
MPI_Comm comm)
{
int i;
cs_coord_t l_min[3], l_max[3];
for (i = 0; i < dim; i++) {
l_min[i] = extents[i];
l_max[i] = extents[i + dim];
}
MPI_Allreduce(l_min, extents, dim, CS_MPI_COORD, MPI_MIN, comm);
MPI_Allreduce(l_max, extents + dim, dim, CS_MPI_COORD, MPI_MAX, comm);
}
#endif /* defined(HAVE_MPI) */
/*----------------------------------------------------------------------------
* Build a heap structure or order a heap structure with a working array
* to save the ordering.
*
* parameters:
* parent <-- parent id in the Hilbert code list
* n_codes <-- number of codes to work with
* hilbert_codes <-- array of Hilbert codes to work with
* order <-> working array to save the ordering
*----------------------------------------------------------------------------*/
static void
_descend_hilbert_heap(cs_gnum_t parent,
cs_lnum_t n_codes,
const fvm_hilbert_code_t hilbert_codes[],
cs_lnum_t *order)
{
cs_lnum_t tmp;
cs_lnum_t child = 2 * parent + 1;
while (child < n_codes) {
if (child + 1 < n_codes) {
if (hilbert_codes[order[child + 1]] > hilbert_codes[order[child]])
child++;
}
if (hilbert_codes[order[parent]] >= hilbert_codes[order[child]])
return;
tmp = order[parent];
order[parent] = order[child];
order[child] = tmp;
parent = child;
child = 2 * parent + 1;
} /* End while */
}
#if defined(HAVE_MPI)
/*----------------------------------------------------------------------------
* Evaluate a distribution array.
*
* parameters:
* n_ranges <-- Number of ranges in the distribution
* distribution <-- Number of elements associated to each range of
* the distribution
* optim <-- Optimal count in each range
*
* returns:
* a fit associated to the distribution. If fit = 0,
* distribution is perfect.
*----------------------------------------------------------------------------*/
static double
_evaluate_distribution(int n_ranges,
cs_gnum_t *distribution,
double optim)
{
int i;
double d_low = 0, d_up = 0, fit = 0;
/*
d_low is the max gap between the distribution count and the optimum when
distribution is lower than optimum.
d_up is the max gap between the distribution count and the optimum when
distribution is greater than optimum.
*/
for (i = 0; i < n_ranges; i++) {
if (distribution[i] > optim)
d_up = CS_MAX(d_up, distribution[i] - optim);
else
d_low = CS_MAX(d_low, optim - distribution[i]);
}
fit = (d_up + d_low) / optim;
#if 0 && defined(DEBUG) && !defined(NDEBUG)
if (cs_glob_rank_id <= 0)
bft_printf("<DISTRIBUTION EVALUATION> optim: %g, fit: %g\n",
optim, fit);
#endif
return fit;
}
/*----------------------------------------------------------------------------
* Define a global distribution associated to a sampling array i.e. count
* the number of elements in each range.
*
* parameters:
* dim <-- 2D or 3D
* n_ranks <-- number of ranks (= number of ranges)
* gsum_weight <-- global sum of all weightings
* n_codes <-- local number of Hilbert codes
* hilbert_codes <-- local list of Hilbert codes to distribute
* weight <-- weighting related to each code
* order <-- ordering array
* sampling <-- sampling array
* c_freq <-> pointer to the cumulative frequency array
* g_distrib <-> pointer to a distribution array
* comm <-- mpi communicator
*----------------------------------------------------------------------------*/
static void
_define_rank_distrib(int dim,
int n_ranks,
cs_gnum_t gsum_weight,
cs_lnum_t n_codes,
const fvm_hilbert_code_t hilbert_codes[],
const cs_lnum_t weight[],
const cs_lnum_t order[],
const fvm_hilbert_code_t sampling[],
double cfreq[],
cs_gnum_t g_distrib[],
MPI_Comm comm)
{
int id, rank_id;
fvm_hilbert_code_t sample_code;
cs_lnum_t i;
int bucket_id = 1;
cs_gnum_t *l_distrib = NULL;
const int sampling_factor = _sampling_factors[dim];
const int n_samples = sampling_factor * n_ranks;
/* Initialization */
BFT_MALLOC(l_distrib, n_samples, cs_gnum_t);
for (id = 0; id < n_samples; id++) {
l_distrib[id] = 0;
g_distrib[id] = 0;
}
/* hilbert_codes are supposed to be ordered */
sample_code = sampling[bucket_id];
for (i = 0; i < n_codes; i++) {
cs_gnum_t o_id = order[i];
if (sample_code >= hilbert_codes[o_id])
l_distrib[bucket_id - 1] += weight[o_id];
else {
while (hilbert_codes[o_id] > sample_code) {
bucket_id++;
assert(bucket_id < n_samples + 1);
sample_code = sampling[bucket_id];
}
l_distrib[bucket_id - 1] += weight[o_id];
}
} /* End of loop on elements */
/* Define the global distribution */
MPI_Allreduce(l_distrib, g_distrib, n_samples, CS_MPI_GNUM, MPI_SUM, comm);
BFT_FREE(l_distrib);
/* Define the cumulative frequency related to g_distribution */
cfreq[0] = 0.;
for (id = 0; id < n_samples; id++)
cfreq[id+1] = cfreq[id] + (double)g_distrib[id]/(double)gsum_weight;
cfreq[n_samples] = 1.0;
#if 0 && defined(DEBUG) && !defined(DEBUG) /* For debugging purpose only */
if (cs_glob_rank_id <= 0) {
FILE *dbg_file = NULL;
char *rfilename = NULL;
int len;
static int loop_id1 = 0;
len = strlen("DistribOutput_l.dat")+1+2;
BFT_MALLOC(rfilename, len, char);
sprintf(rfilename, "DistribOutput_l%02d.dat", loop_id1);
loop_id1++;
dbg_file = fopen(rfilename, "w");
fprintf(dbg_file,
"# Sample_id | OptCfreq | Cfreq | Sampling |"
"Global Distrib\n");
for (i = 0; i < n_samples; i++)
fprintf(dbg_file, "%8d %15.5f %15.10f %15.10f %10u\n",
i, (double)i/(double)n_samples, cfreq[i],
(double)(sampling[i]), distrib[i]);
fprintf(dbg_file, "%8d %15.5f %15.10f %15.10f %10u\n",
i, 1.0, 1.0, 1.0, 0);
fclose(dbg_file);
BFT_FREE(rfilename);
}
#endif /* debugging output */
/* Convert global distribution from n_samples to n_ranks */
for (rank_id = 0; rank_id < n_ranks; rank_id++) {
cs_gnum_t sum = 0;
cs_lnum_t shift = rank_id * sampling_factor;
for (id = 0; id < sampling_factor; id++)
sum += g_distrib[shift + id];
g_distrib[rank_id] = sum;
} /* End of loop on ranks */
#if 0 && defined(DEBUG) && !defined(NDEBUG) /* Sanity check in debug */
{
cs_gnum_t sum = 0;
for (rank_id = 0; rank_id < n_ranks; rank_id++)
sum += g_distrib[rank_id];
if (sum != gsum_weight)
bft_error(__FILE__, __LINE__, 0,
"Error while computing global distribution.\n"
"sum = %u and gsum_weight = %u\n",
sum, gsum_weight);
}
#endif /* sanity check */
}
/*----------------------------------------------------------------------------
* Update a distribution associated to sampling to assume a well-balanced
* distribution of the leaves of the tree.
*
* parameters:
* dim <-- 1D, 2D or 3D
* n_ranks <-- number of ranks (= number of ranges)
* c_freq <-> cumulative frequency array
* sampling <-> pointer to pointer to a sampling array
* comm <-- mpi communicator
*----------------------------------------------------------------------------*/
static void
_update_sampling(int dim,
int n_ranks,
double c_freq[],
fvm_hilbert_code_t *sampling[])
{
int i, j, next_id;
double target_freq, f_high, f_low, delta;
double s_low, s_high;
fvm_hilbert_code_t *new_sampling = NULL, *_sampling = *sampling;
const int sampling_factor = _sampling_factors[dim];
const int n_samples = sampling_factor * n_ranks;
const double unit = 1/(double)n_samples;
/* Compute new_sampling */
BFT_MALLOC(new_sampling, n_samples + 1, fvm_hilbert_code_t);
new_sampling[0] = _sampling[0];
next_id = 1;
for (i = 0; i < n_samples; i++) {
target_freq = (i+1)*unit;
/* Find the next id such as c_freq[next_id] >= target_freq */
for (j = next_id; j < n_samples + 1; j++) {
if (c_freq[j] >= target_freq) {
next_id = j;
break;
}
}
/* Find new s such as new_s is equal to target_freq by
a linear interpolation */
f_low = c_freq[next_id-1];
f_high = c_freq[next_id];
s_low = _sampling[next_id-1];
s_high = _sampling[next_id];
if (f_high - f_low > 0) {
delta = (target_freq - f_low) * (s_high - s_low) / (f_high - f_low);
new_sampling[i+1] = s_low + delta;
}
else /* f_high = f_low */
new_sampling[i+1] = s_low + 0.5 * (s_low + s_high);
#if 0 && defined(DEBUG) && !defined(NDEBUG)
bft_printf(" <_update_distrib> (rank: %d) delta: %g, target: %g,"
" next_id: %d, f_low: %g, f_high: %g, s_low: %g, s_high: %g\n"
"\t => new_sampling: %g\n",
cs_glob_rank_id, delta, target_freq, next_id,
f_low, f_high, s_low, s_high, new_sampling[i+1]);
#endif
} /* End of loop on samples */
new_sampling[n_samples] = 1.0;
BFT_FREE(_sampling);
/* Return pointers */
*sampling = new_sampling;
}
/*----------------------------------------------------------------------------
* Compute a sampling array which assumes a well-balanced distribution of
* leaves of the tree among the ranks.
*
* parameters:
* dim <-- 2D or 3D
* n_ranks <-- number of ranks
* gmax_level <-- level on which Hilbert encoding is build
* n_codes <-- local number of Hilbert ids
* hilbert_codes <-- local list of Hilbert ids to distribute
* weight <-- weighting related to each code
* order <-- ordering array
* sampling <-> pointer to pointer to a sampling array
* comm <-- mpi communicator
*
* returns:
* fit associated to the returned sampling array
*----------------------------------------------------------------------------*/
static double
_bucket_sampling(int dim,
int n_ranks,
cs_lnum_t n_codes,
const fvm_hilbert_code_t hilbert_codes[],
const cs_lnum_t weight[],
const cs_lnum_t order[],
fvm_hilbert_code_t *sampling[],
MPI_Comm comm)
{
int i, n_iters;
cs_lnum_t j;
double fit, best_fit, optim;
cs_gnum_t lsum_weight = 0, gsum_weight = 0;
cs_gnum_t *distrib = NULL;
double *cfreq = NULL;
fvm_hilbert_code_t *best_sampling = NULL;
fvm_hilbert_code_t *_sampling = *sampling;
const int sampling_factor = _sampling_factors[dim];
const int n_samples = sampling_factor * n_ranks;
const double unit = 1/(double)n_samples;
/* Compute the global number of elements and the optimal number of elements
on each rank */
for (j = 0; j < n_codes; j++)
lsum_weight += weight[j];
MPI_Allreduce(&lsum_weight, &gsum_weight, 1, CS_MPI_GNUM, MPI_SUM, comm);
optim = (double)gsum_weight / (double)n_ranks;
/* Define a naive sampling (uniform distribution) */
for (i = 0; i < n_samples + 1; i++)
_sampling[i] = i*unit;
/* Define the distribution associated to the current sampling array */
BFT_MALLOC(distrib, n_samples, cs_gnum_t);
BFT_MALLOC(cfreq, n_samples + 1, double);
_define_rank_distrib(dim,
n_ranks,
gsum_weight,
n_codes,
hilbert_codes,
weight,
order,
_sampling,
cfreq,
distrib,
comm);
/* Initialize best choice */
fit = _evaluate_distribution(n_ranks, distrib, optim);
best_fit = fit;
BFT_MALLOC(best_sampling, n_samples + 1, fvm_hilbert_code_t);
for (i = 0; i < (n_samples + 1); i++)
best_sampling[i] = _sampling[i];
/* Loop to get a better sampling array */
for (n_iters = 0;
( n_iters < fvm_hilbert_distrib_n_iter_max
&& fit > fvm_hilbert_distrib_tol);
n_iters++) {
_update_sampling(dim, n_ranks, cfreq, &_sampling);
/* Compute the new distribution associated to the new sampling */
_define_rank_distrib(dim,
n_ranks,
gsum_weight,
n_codes,
hilbert_codes,
weight,
order,
_sampling,
cfreq,
distrib,
comm);
fit = _evaluate_distribution(n_ranks, distrib, optim);
/* Save the best sampling array and its fit */
if (fit < best_fit) {
best_fit = fit;
for (i = 0; i < (n_samples + 1); i++)
best_sampling[i] = _sampling[i];
}
} /* End of while */
#if 0 && defined(DEBUG) && !defined(NDEBUG)
if (cs_glob_rank_id <= 0) {
bft_printf("\n <_bucket_sampling> n_iter: %d, opt: %g, best_fit: %g\n",
n_iters, optim, best_fit);
#endif
/* Free memory */
BFT_FREE(cfreq);
BFT_FREE(distrib);
BFT_FREE(_sampling);
*sampling = best_sampling;
return best_fit;
}
#endif /* FM_HAVE_MPI */
/*! (DOXYGEN_SHOULD_SKIP_THIS) \endcond */
/*============================================================================
* Public function definitions
*============================================================================*/
/*----------------------------------------------------------------------------
* Determine the global extents associated with a set of coordinates
*
* parameters:
* dim <-- spatial dimension
* n_coords <-- local number of coordinates
* coords <-- entity coordinates; size: n_entities*dim (interlaced)
* g_extents --> global extents (size: dim*2)
* comm <-- associated MPI communicator
*---------------------------------------------------------------------------*/
#if defined(HAVE_MPI)
void
fvm_hilbert_get_coord_extents(int dim,
size_t n_coords,
const cs_coord_t coords[],
cs_coord_t g_extents[],
MPI_Comm comm)
#else
void
fvm_hilbert_get_coord_extents(int dim,
size_t n_coords,
const cs_coord_t coords[],
cs_coord_t g_extents[])
#endif
{
size_t i, j;
/* Get global min/max coordinates */
for (j = 0; j < (size_t)dim; j++) {
g_extents[j] = DBL_MAX;
g_extents[j + dim] = -DBL_MAX;
}
for (i = 0; i < n_coords; i++) {
for (j = 0; j < (size_t)dim; j++) {
if (coords[i*dim + j] < g_extents[j])
g_extents[j] = coords[i*dim + j];
else if (coords[i*dim + j] > g_extents[j + dim])
g_extents[j + dim] = coords[i*dim + j];
}
}
#if defined(HAVE_MPI)
if (comm != MPI_COMM_NULL)
_local_to_global_extents(dim, g_extents, comm);
#endif
}
/*----------------------------------------------------------------------------
* Encode an array of coordinates.
*
* The caller is responsible for freeing the returned array once it is
* no longer useful.
*
* parameters:
* dim <-- 1D, 2D or 3D
* extents <-- coordinate extents for normalization (size: dim*2)
* n_coords <-- nomber of coordinates in array
* coords <-- coordinates in the grid (interlaced, not normalized)
* h_code --> array of corresponding Hilbert codes (size: n_coords)
*----------------------------------------------------------------------------*/
void
fvm_hilbert_encode_coords(int dim,
const cs_coord_t extents[],
cs_lnum_t n_coords,
const cs_coord_t coords[],
fvm_hilbert_code_t h_code[])
{
cs_lnum_t i, j, k;
cs_coord_t s[3], d[3], n[3];
int e_dim = 0;
int dim_map[3] = {-1, -1, -1};
cs_coord_t d_max = 0.0;
const double epsilon = 1e-4;
for (i = 0; i < dim; i++) {
s[i] = extents[i];
d[i] = extents[i+dim] - extents[i];
}
/* Check if box is not flat */
for (i = 0; i < dim; i++) {
d[i] = extents[i+dim] - extents[i];
d_max = CS_MAX(d_max, d[i]);
}
for (i = 0; i < dim; i++) {
if (d[i] >= d_max * epsilon) {
dim_map[e_dim] = i;
e_dim += 1;
}
}
switch(dim) {
case 3:
{
if (e_dim == 3) {
for (i = 0; i < n_coords; i++) {
for (j = 0; j < 3; j++)
n[j] = (coords[i*3 + j] - s[j]) / d[j];
h_code[i] = _hilbert_encode_3d(n);
}
}
else if (e_dim == 2) {
for (i = 0; i < n_coords; i++) {
for (j = 0; j < 2; j++) {
k = dim_map[j];
n[j] = (coords[i*3 + k] - s[k]) / d[k];
}
h_code[i] = _hilbert_encode_2d(n);
}
}
else if (e_dim == 1) {
for (i = 0; i < n_coords; i++) {
k = dim_map[0];
n[0] = (coords[i*3 + k] - s[k]) / d[k];
h_code[i] = _hilbert_encode_1d(n);
}
}
}
break;
case 2:
{
if (e_dim == 2) {
for (i = 0; i < n_coords; i++) {
for (j = 0; j < 2; j++)
n[j] = (coords[i*2 + j] - s[j]) / d[j];
h_code[i] = _hilbert_encode_2d(n);
}
}
else if (e_dim == 1) {
for (i = 0; i < n_coords; i++) {
k = dim_map[0];
n[0] = (coords[i*3 + k] - s[k]) / d[k];
h_code[i] = _hilbert_encode_1d(n);
}
}
}
break;
case 1:
{
for (i = 0; i < n_coords; i++) {
n[0] = (coords[i] - s[0]) / d[0];
h_code[i] = _hilbert_encode_1d(n);
}
}
break;
default:
assert(dim > 0 && dim < 4);
break;
}
}
/*----------------------------------------------------------------------------
* Locally order a list of Hilbert ids.
*
* parameters:
* n_codes <-- number of Hilbert ids to order
* hilbert_codes <-- array of Hilbert ids to order
* order --> pointer to pre-allocated ordering table
*----------------------------------------------------------------------------*/
void
fvm_hilbert_local_order(cs_lnum_t n_codes,
const fvm_hilbert_code_t hilbert_codes[],
cs_lnum_t order[])
{
cs_lnum_t i, tmp;
assert(n_codes == 0 || hilbert_codes != NULL);
assert(n_codes == 0 || order != NULL);
for (i = 0; i < n_codes; i++)
order[i] = i;
/* Build heap */
for (i = n_codes/2 - 1; (int)i >= 0; i--)
_descend_hilbert_heap(i, n_codes, hilbert_codes, order);
/* Sort array */
for (i = n_codes - 1; (int)i >= 0; i--) {
tmp = order[0];
order[0] = order[i];
order[i] = tmp;
_descend_hilbert_heap(0, i, hilbert_codes, order);
}
}
/*----------------------------------------------------------------------------
* Locally order a list of coordinates based on their Hilbert code.
*
* This variant may use a maximum depth of 32 levels, and switches
* to lexicographical ordering if this is not enough.
*
* parameters:
* dim <-- 1D, 2D or 3D
* extents <-- coordinate extents for normalization (size: dim*2)
* n_coords <-- nomber of coordinates in array
* coords <-- coordinates in the grid (interlaced, not normalized)
* order --> pointer to pre-allocated ordering table
*----------------------------------------------------------------------------*/
void
fvm_hilbert_local_order_coords(int dim,
const cs_coord_t extents[],
cs_lnum_t n_coords,
const cs_coord_t coords[],
cs_lnum_t order[])
{
fvm_hilbert_code_t *h_code = NULL;
BFT_MALLOC(h_code, n_coords, fvm_hilbert_code_t);
fvm_hilbert_encode_coords(dim, extents, n_coords, coords, h_code);
fvm_hilbert_local_order(n_coords, h_code, order);
BFT_FREE(h_code);
}
/*----------------------------------------------------------------------------
* Get the quantile associated to a Hilbert code using a binary search.
*
* No check is done to ensure that the code is present in the quantiles.
*
* parameters:
* n_quantiles <-- number of quantiles
* code <-- code we are searching for
* quantile_start <-- first Hilbert code in each quantile (size: n_quantiles)
*
* returns:
* id associated to the given code in the codes array.
*----------------------------------------------------------------------------*/
size_t
fvm_hilbert_quantile_search(size_t n_quantiles,
fvm_hilbert_code_t code,
fvm_hilbert_code_t quantile_start[])
{
size_t mid_id = 0;
size_t start_id = 0;
size_t end_id = n_quantiles;
/* use binary search */
while (start_id + 1 < end_id) {
mid_id = start_id + ((end_id -start_id) / 2);
if (quantile_start[mid_id] > code)
end_id = mid_id;
else
start_id = mid_id;
}
/* We may have stopped short of the required value,
or have multiple occurences of a quantile start
(in case of empty quantiles), of which we want to
find the find highest one */
while ( start_id < n_quantiles - 1
&& code >= quantile_start[start_id+1])
start_id++;
return start_id;
}
#if defined(HAVE_MPI)
/*----------------------------------------------------------------------------
* Build a global Hilbert encoding rank index.
*
* The rank_index[i] contains the first Hilbert code assigned to rank [i].
*
* parameters:
* dim <-- 1D, 2D or 3D
* n_codes <-- number of Hilbert codes to be indexed
* hilbert_code <-- array of Hilbert codes to be indexed
* weight <-- weighting related to each code
* order <-- ordering array
* rank_index <-> pointer to the global Hilbert encoding rank index
* comm <-- MPI communicator on which we build the global index
*
* returns:
* the fit related to the Hilbert encoding distribution (lower is better).
*----------------------------------------------------------------------------*/
double
fvm_hilbert_build_rank_index(int dim,
cs_lnum_t n_codes,
const fvm_hilbert_code_t hilbert_code[],
const cs_lnum_t weight[],
const cs_lnum_t order[],
fvm_hilbert_code_t rank_index[],
MPI_Comm comm)
{
int i, id, rank_id, n_ranks, n_samples;
double best_fit;
fvm_hilbert_code_t *sampling = NULL;
const int sampling_factor = _sampling_factors[dim];
/* Allocations and Initialization */
MPI_Comm_size(comm, &n_ranks);
n_samples = sampling_factor * n_ranks;
BFT_MALLOC(sampling, n_samples + 1, fvm_hilbert_code_t);
for (i = 0; i < (n_samples + 1); i++)
sampling[i] = 0;
best_fit = _bucket_sampling(dim,
n_ranks,
n_codes,
hilbert_code,
weight,
order,
&sampling,
comm);
/* Define Hilbert index */
for (rank_id = 0; rank_id < n_ranks + 1; rank_id++) {
id = rank_id * sampling_factor;
rank_index[rank_id] = sampling[id];
}
#if 0 && defined(DEBUG) && !defined(NDEBUG)
{ /* Dump Hilbert index and associated sampling on rank 0 */
bft_printf("\nHilbert rank index:\n\n");
for (rank_id = 0; rank_id < n_ranks + 1; rank_id++) {
id = sampling_factor * rank_id;
bft_printf("rank: %5d (sampling: %f)\n"
" rank_index: %f\n",
rank_id,
(double)sampling[id], (double)rank_index[rank_id]);
}
bft_printf("\n");
bft_printf_flush();
}
#endif
/* Free memory */
BFT_FREE(sampling);
return best_fit;
}
#endif /* HAVE_MPI */
/*----------------------------------------------------------------------------*/
END_C_DECLS
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