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tools/cub-1.8.0/experimental/sparse_matrix.h
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/******************************************************************************
* Copyright (c) 2011, Duane Merrill. All rights reserved.
* Copyright (c) 2011-2018, NVIDIA CORPORATION. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the NVIDIA CORPORATION nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL NVIDIA CORPORATION BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
******************************************************************************/
/******************************************************************************
* Matrix data structures and parsing logic
******************************************************************************/
#pragma once
#include <cmath>
#include <cstring>
#include <iterator>
#include <string>
#include <algorithm>
#include <iostream>
#include <queue>
#include <set>
#include <fstream>
#include <stdio.h>
#ifdef CUB_MKL
#include <numa.h>
#include <mkl.h>
#endif
using namespace std;
/******************************************************************************
* COO matrix type
******************************************************************************/
struct GraphStats
{
int num_rows;
int num_cols;
int num_nonzeros;
double diag_dist_mean; // mean
double diag_dist_std_dev; // sample std dev
double pearson_r; // coefficient of variation
double row_length_mean; // mean
double row_length_std_dev; // sample std_dev
double row_length_variation; // coefficient of variation
double row_length_skewness; // skewness
void Display(bool show_labels = true)
{
if (show_labels)
printf("
"
"\t num_rows: %d
"
"\t num_cols: %d
"
"\t num_nonzeros: %d
"
"\t diag_dist_mean: %.2f
"
"\t diag_dist_std_dev: %.2f
"
"\t pearson_r: %f
"
"\t row_length_mean: %.5f
"
"\t row_length_std_dev: %.5f
"
"\t row_length_variation: %.5f
"
"\t row_length_skewness: %.5f
",
num_rows,
num_cols,
num_nonzeros,
diag_dist_mean,
diag_dist_std_dev,
pearson_r,
row_length_mean,
row_length_std_dev,
row_length_variation,
row_length_skewness);
else
printf(
"%d, "
"%d, "
"%d, "
"%.2f, "
"%.2f, "
"%f, "
"%.5f, "
"%.5f, "
"%.5f, "
"%.5f, ",
num_rows,
num_cols,
num_nonzeros,
diag_dist_mean,
diag_dist_std_dev,
pearson_r,
row_length_mean,
row_length_std_dev,
row_length_variation,
row_length_skewness);
}
};
/******************************************************************************
* COO matrix type
******************************************************************************/
/**
* COO matrix type. A COO matrix is just a vector of edge tuples. Tuples are sorted
* first by row, then by column.
*/
template<typename ValueT, typename OffsetT>
struct CooMatrix
{
//---------------------------------------------------------------------
// Type definitions and constants
//---------------------------------------------------------------------
// COO edge tuple
struct CooTuple
{
OffsetT row;
OffsetT col;
ValueT val;
CooTuple() {}
CooTuple(OffsetT row, OffsetT col) : row(row), col(col) {}
CooTuple(OffsetT row, OffsetT col, ValueT val) : row(row), col(col), val(val) {}
/**
* Comparator for sorting COO sparse format num_nonzeros
*/
bool operator<(const CooTuple &other) const
{
if ((row < other.row) || ((row == other.row) && (col < other.col)))
{
return true;
}
return false;
}
};
//---------------------------------------------------------------------
// Data members
//---------------------------------------------------------------------
// Fields
int num_rows;
int num_cols;
int num_nonzeros;
CooTuple* coo_tuples;
//---------------------------------------------------------------------
// Methods
//---------------------------------------------------------------------
// Constructor
CooMatrix() : num_rows(0), num_cols(0), num_nonzeros(0), coo_tuples(NULL) {}
/**
* Clear
*/
void Clear()
{
if (coo_tuples) delete[] coo_tuples;
coo_tuples = NULL;
}
// Destructor
~CooMatrix()
{
Clear();
}
// Display matrix to stdout
void Display()
{
cout << "COO Matrix (" << num_rows << " rows, " << num_cols << " columns, " << num_nonzeros << " non-zeros):
";
cout << "Ordinal, Row, Column, Value
";
for (int i = 0; i < num_nonzeros; i++)
{
cout << '\t' << i << ',' << coo_tuples[i].row << ',' << coo_tuples[i].col << ',' << coo_tuples[i].val << "
";
}
}
/**
* Builds a symmetric COO sparse from an asymmetric CSR matrix.
*/
template <typename CsrMatrixT>
void InitCsrSymmetric(CsrMatrixT &csr_matrix)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
num_rows = csr_matrix.num_cols;
num_cols = csr_matrix.num_rows;
num_nonzeros = csr_matrix.num_nonzeros * 2;
coo_tuples = new CooTuple[num_nonzeros];
for (OffsetT row = 0; row < csr_matrix.num_rows; ++row)
{
for (OffsetT nonzero = csr_matrix.row_offsets[row]; nonzero < csr_matrix.row_offsets[row + 1]; ++nonzero)
{
coo_tuples[nonzero].row = row;
coo_tuples[nonzero].col = csr_matrix.column_indices[nonzero];
coo_tuples[nonzero].val = csr_matrix.values[nonzero];
coo_tuples[csr_matrix.num_nonzeros + nonzero].row = coo_tuples[nonzero].col;
coo_tuples[csr_matrix.num_nonzeros + nonzero].col = coo_tuples[nonzero].row;
coo_tuples[csr_matrix.num_nonzeros + nonzero].val = csr_matrix.values[nonzero];
}
}
// Sort by rows, then columns
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
}
/**
* Builds a COO sparse from a relabeled CSR matrix.
*/
template <typename CsrMatrixT>
void InitCsrRelabel(CsrMatrixT &csr_matrix, OffsetT* relabel_indices)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
num_rows = csr_matrix.num_rows;
num_cols = csr_matrix.num_cols;
num_nonzeros = csr_matrix.num_nonzeros;
coo_tuples = new CooTuple[num_nonzeros];
for (OffsetT row = 0; row < num_rows; ++row)
{
for (OffsetT nonzero = csr_matrix.row_offsets[row]; nonzero < csr_matrix.row_offsets[row + 1]; ++nonzero)
{
coo_tuples[nonzero].row = relabel_indices[row];
coo_tuples[nonzero].col = relabel_indices[csr_matrix.column_indices[nonzero]];
coo_tuples[nonzero].val = csr_matrix.values[nonzero];
}
}
// Sort by rows, then columns
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
}
/**
* Builds a METIS COO sparse from the given file.
*/
void InitMetis(const string &metis_filename)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
// TODO
}
/**
* Builds a MARKET COO sparse from the given file.
*/
void InitMarket(
const string& market_filename,
ValueT default_value = 1.0,
bool verbose = false)
{
if (verbose) {
printf("Reading... "); fflush(stdout);
}
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
std::ifstream ifs;
ifs.open(market_filename.c_str(), std::ifstream::in);
if (!ifs.good())
{
fprintf(stderr, "Error opening file
");
exit(1);
}
bool array = false;
bool symmetric = false;
bool skew = false;
int current_edge = -1;
char line[1024];
if (verbose) {
printf("Parsing... "); fflush(stdout);
}
while (true)
{
ifs.getline(line, 1024);
if (!ifs.good())
{
// Done
break;
}
if (line[0] == '%')
{
// Comment
if (line[1] == '%')
{
// Banner
symmetric = (strstr(line, "symmetric") != NULL);
skew = (strstr(line, "skew") != NULL);
array = (strstr(line, "array") != NULL);
if (verbose) {
printf("(symmetric: %d, skew: %d, array: %d) ", symmetric, skew, array); fflush(stdout);
}
}
}
else if (current_edge == -1)
{
// Problem description
int nparsed = sscanf(line, "%d %d %d", &num_rows, &num_cols, &num_nonzeros);
if ((!array) && (nparsed == 3))
{
if (symmetric)
num_nonzeros *= 2;
// Allocate coo matrix
coo_tuples = new CooTuple[num_nonzeros];
current_edge = 0;
}
else if (array && (nparsed == 2))
{
// Allocate coo matrix
num_nonzeros = num_rows * num_cols;
coo_tuples = new CooTuple[num_nonzeros];
current_edge = 0;
}
else
{
fprintf(stderr, "Error parsing MARKET matrix: invalid problem description: %s
", line);
exit(1);
}
}
else
{
// Edge
if (current_edge >= num_nonzeros)
{
fprintf(stderr, "Error parsing MARKET matrix: encountered more than %d num_nonzeros
", num_nonzeros);
exit(1);
}
int row, col;
double val;
if (array)
{
if (sscanf(line, "%lf", &val) != 1)
{
fprintf(stderr, "Error parsing MARKET matrix: badly formed current_edge: '%s' at edge %d
", line, current_edge);
exit(1);
}
col = (current_edge / num_rows);
row = (current_edge - (num_rows * col));
coo_tuples[current_edge] = CooTuple(row, col, val); // Convert indices to zero-based
}
else
{
// Parse nonzero (note: using strtol and strtod is 2x faster than sscanf or istream parsing)
char *l = line;
char *t = NULL;
// parse row
row = strtol(l, &t, 0);
if (t == l)
{
fprintf(stderr, "Error parsing MARKET matrix: badly formed row at edge %d
", current_edge);
exit(1);
}
l = t;
// parse col
col = strtol(l, &t, 0);
if (t == l)
{
fprintf(stderr, "Error parsing MARKET matrix: badly formed col at edge %d
", current_edge);
exit(1);
}
l = t;
// parse val
val = strtod(l, &t);
if (t == l)
{
val = default_value;
}
/*
int nparsed = sscanf(line, "%d %d %lf", &row, &col, &val);
if (nparsed == 2)
{
// No value specified
val = default_value;
}
else if (nparsed != 3)
{
fprintf(stderr, "Error parsing MARKET matrix 1: badly formed current_edge: %d parsed at edge %d
", nparsed, current_edge);
exit(1);
}
*/
coo_tuples[current_edge] = CooTuple(row - 1, col - 1, val); // Convert indices to zero-based
}
current_edge++;
if (symmetric && (row != col))
{
coo_tuples[current_edge].row = coo_tuples[current_edge - 1].col;
coo_tuples[current_edge].col = coo_tuples[current_edge - 1].row;
coo_tuples[current_edge].val = coo_tuples[current_edge - 1].val * (skew ? -1 : 1);
current_edge++;
}
}
}
// Adjust nonzero count (nonzeros along the diagonal aren't reversed)
num_nonzeros = current_edge;
if (verbose) {
printf("done. Ordering..."); fflush(stdout);
}
// Sort by rows, then columns
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
if (verbose) {
printf("done. "); fflush(stdout);
}
ifs.close();
}
/**
* Builds a dense matrix
*/
int InitDense(
OffsetT num_rows,
OffsetT num_cols,
ValueT default_value = 1.0,
bool verbose = false)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
this->num_rows = num_rows;
this->num_cols = num_cols;
num_nonzeros = num_rows * num_cols;
coo_tuples = new CooTuple[num_nonzeros];
for (OffsetT row = 0; row < num_rows; ++row)
{
for (OffsetT col = 0; col < num_cols; ++col)
{
coo_tuples[(row * num_cols) + col] = CooTuple(row, col, default_value);
}
}
// Sort by rows, then columns
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
return 0;
}
/**
* Builds a wheel COO sparse matrix having spokes spokes.
*/
int InitWheel(
OffsetT spokes,
ValueT default_value = 1.0,
bool verbose = false)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
num_rows = spokes + 1;
num_cols = num_rows;
num_nonzeros = spokes * 2;
coo_tuples = new CooTuple[num_nonzeros];
// Add spoke num_nonzeros
int current_edge = 0;
for (OffsetT i = 0; i < spokes; i++)
{
coo_tuples[current_edge] = CooTuple(0, i + 1, default_value);
current_edge++;
}
// Add rim
for (OffsetT i = 0; i < spokes; i++)
{
OffsetT dest = (i + 1) % spokes;
coo_tuples[current_edge] = CooTuple(i + 1, dest + 1, default_value);
current_edge++;
}
// Sort by rows, then columns
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
return 0;
}
/**
* Builds a square 2D grid CSR matrix. Interior num_vertices have degree 5 when including
* a self-loop.
*
* Returns 0 on success, 1 on failure.
*/
int InitGrid2d(OffsetT width, bool self_loop, ValueT default_value = 1.0)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
exit(1);
}
int interior_nodes = (width - 2) * (width - 2);
int edge_nodes = (width - 2) * 4;
int corner_nodes = 4;
num_rows = width * width;
num_cols = num_rows;
num_nonzeros = (interior_nodes * 4) + (edge_nodes * 3) + (corner_nodes * 2);
if (self_loop)
num_nonzeros += num_rows;
coo_tuples = new CooTuple[num_nonzeros];
int current_edge = 0;
for (OffsetT j = 0; j < width; j++)
{
for (OffsetT k = 0; k < width; k++)
{
OffsetT me = (j * width) + k;
// West
OffsetT neighbor = (j * width) + (k - 1);
if (k - 1 >= 0) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// East
neighbor = (j * width) + (k + 1);
if (k + 1 < width) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// North
neighbor = ((j - 1) * width) + k;
if (j - 1 >= 0) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// South
neighbor = ((j + 1) * width) + k;
if (j + 1 < width) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
if (self_loop)
{
neighbor = me;
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
}
}
// Sort by rows, then columns, update dims
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
return 0;
}
/**
* Builds a square 3D grid COO sparse matrix. Interior num_vertices have degree 7 when including
* a self-loop. Values are unintialized, coo_tuples are sorted.
*/
int InitGrid3d(OffsetT width, bool self_loop, ValueT default_value = 1.0)
{
if (coo_tuples)
{
fprintf(stderr, "Matrix already constructed
");
return -1;
}
OffsetT interior_nodes = (width - 2) * (width - 2) * (width - 2);
OffsetT face_nodes = (width - 2) * (width - 2) * 6;
OffsetT edge_nodes = (width - 2) * 12;
OffsetT corner_nodes = 8;
num_cols = width * width * width;
num_rows = num_cols;
num_nonzeros = (interior_nodes * 6) + (face_nodes * 5) + (edge_nodes * 4) + (corner_nodes * 3);
if (self_loop)
num_nonzeros += num_rows;
coo_tuples = new CooTuple[num_nonzeros];
int current_edge = 0;
for (OffsetT i = 0; i < width; i++)
{
for (OffsetT j = 0; j < width; j++)
{
for (OffsetT k = 0; k < width; k++)
{
OffsetT me = (i * width * width) + (j * width) + k;
// Up
OffsetT neighbor = (i * width * width) + (j * width) + (k - 1);
if (k - 1 >= 0) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// Down
neighbor = (i * width * width) + (j * width) + (k + 1);
if (k + 1 < width) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// West
neighbor = (i * width * width) + ((j - 1) * width) + k;
if (j - 1 >= 0) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// East
neighbor = (i * width * width) + ((j + 1) * width) + k;
if (j + 1 < width) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// North
neighbor = ((i - 1) * width * width) + (j * width) + k;
if (i - 1 >= 0) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
// South
neighbor = ((i + 1) * width * width) + (j * width) + k;
if (i + 1 < width) {
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
if (self_loop)
{
neighbor = me;
coo_tuples[current_edge] = CooTuple(me, neighbor, default_value);
current_edge++;
}
}
}
}
// Sort by rows, then columns, update dims
std::stable_sort(coo_tuples, coo_tuples + num_nonzeros);
return 0;
}
};
/******************************************************************************
* COO matrix type
******************************************************************************/
/**
* CSR sparse format matrix
*/
template<
typename ValueT,
typename OffsetT>
struct CsrMatrix
{
int num_rows;
int num_cols;
int num_nonzeros;
OffsetT* row_offsets;
OffsetT* column_indices;
ValueT* values;
bool numa_malloc;
/**
* Constructor
*/
CsrMatrix() : num_rows(0), num_cols(0), num_nonzeros(0), row_offsets(NULL), column_indices(NULL), values(NULL)
{
#ifdef CUB_MKL
numa_malloc = ((numa_available() >= 0) && (numa_num_task_nodes() > 1));
#else
numa_malloc = false;
#endif
}
/**
* Clear
*/
void Clear()
{
#ifdef CUB_MKL
if (numa_malloc)
{
numa_free(row_offsets, sizeof(OffsetT) * (num_rows + 1));
numa_free(values, sizeof(ValueT) * num_nonzeros);
numa_free(column_indices, sizeof(OffsetT) * num_nonzeros);
}
else
{
if (row_offsets) mkl_free(row_offsets);
if (column_indices) mkl_free(column_indices);
if (values) mkl_free(values);
}
#else
if (row_offsets) delete[] row_offsets;
if (column_indices) delete[] column_indices;
if (values) delete[] values;
#endif
row_offsets = NULL;
column_indices = NULL;
values = NULL;
}
/**
* Destructor
*/
~CsrMatrix()
{
Clear();
}
GraphStats Stats()
{
GraphStats stats;
stats.num_rows = num_rows;
stats.num_cols = num_cols;
stats.num_nonzeros = num_nonzeros;
//
// Compute diag-distance statistics
//
OffsetT samples = 0;
double mean = 0.0;
double ss_tot = 0.0;
for (OffsetT row = 0; row < num_rows; ++row)
{
OffsetT nz_idx_start = row_offsets[row];
OffsetT nz_idx_end = row_offsets[row + 1];
for (int nz_idx = nz_idx_start; nz_idx < nz_idx_end; ++nz_idx)
{
OffsetT col = column_indices[nz_idx];
double x = (col > row) ? col - row : row - col;
samples++;
double delta = x - mean;
mean = mean + (delta / samples);
ss_tot += delta * (x - mean);
}
}
stats.diag_dist_mean = mean;
double variance = ss_tot / samples;
stats.diag_dist_std_dev = sqrt(variance);
//
// Compute deming statistics
//
samples = 0;
double mean_x = 0.0;
double mean_y = 0.0;
double ss_x = 0.0;
double ss_y = 0.0;
for (OffsetT row = 0; row < num_rows; ++row)
{
OffsetT nz_idx_start = row_offsets[row];
OffsetT nz_idx_end = row_offsets[row + 1];
for (int nz_idx = nz_idx_start; nz_idx < nz_idx_end; ++nz_idx)
{
OffsetT col = column_indices[nz_idx];
samples++;
double x = col;
double y = row;
double delta;
delta = x - mean_x;
mean_x = mean_x + (delta / samples);
ss_x += delta * (x - mean_x);
delta = y - mean_y;
mean_y = mean_y + (delta / samples);
ss_y += delta * (y - mean_y);
}
}
samples = 0;
double s_xy = 0.0;
double s_xxy = 0.0;
double s_xyy = 0.0;
for (OffsetT row = 0; row < num_rows; ++row)
{
OffsetT nz_idx_start = row_offsets[row];
OffsetT nz_idx_end = row_offsets[row + 1];
for (int nz_idx = nz_idx_start; nz_idx < nz_idx_end; ++nz_idx)
{
OffsetT col = column_indices[nz_idx];
samples++;
double x = col;
double y = row;
double xy = (x - mean_x) * (y - mean_y);
double xxy = (x - mean_x) * (x - mean_x) * (y - mean_y);
double xyy = (x - mean_x) * (y - mean_y) * (y - mean_y);
double delta;
delta = xy - s_xy;
s_xy = s_xy + (delta / samples);
delta = xxy - s_xxy;
s_xxy = s_xxy + (delta / samples);
delta = xyy - s_xyy;
s_xyy = s_xyy + (delta / samples);
}
}
double s_xx = ss_x / num_nonzeros;
double s_yy = ss_y / num_nonzeros;
double deming_slope = (s_yy - s_xx + sqrt(((s_yy - s_xx) * (s_yy - s_xx)) + (4 * s_xy * s_xy))) / (2 * s_xy);
stats.pearson_r = (num_nonzeros * s_xy) / (sqrt(ss_x) * sqrt(ss_y));
//
// Compute row-length statistics
//
// Sample mean
stats.row_length_mean = double(num_nonzeros) / num_rows;
variance = 0.0;
stats.row_length_skewness = 0.0;
for (OffsetT row = 0; row < num_rows; ++row)
{
OffsetT length = row_offsets[row + 1] - row_offsets[row];
double delta = double(length) - stats.row_length_mean;
variance += (delta * delta);
stats.row_length_skewness += (delta * delta * delta);
}
variance /= num_rows;
stats.row_length_std_dev = sqrt(variance);
stats.row_length_skewness = (stats.row_length_skewness / num_rows) / pow(stats.row_length_std_dev, 3.0);
stats.row_length_variation = stats.row_length_std_dev / stats.row_length_mean;
return stats;
}
/**
* Build CSR matrix from sorted COO matrix
*/
void FromCoo(const CooMatrix<ValueT, OffsetT> &coo_matrix)
{
num_rows = coo_matrix.num_rows;
num_cols = coo_matrix.num_cols;
num_nonzeros = coo_matrix.num_nonzeros;
#ifdef CUB_MKL
if (numa_malloc)
{
numa_set_strict(1);
// numa_set_bind_policy(1);
// values = (ValueT*) numa_alloc_interleaved(sizeof(ValueT) * num_nonzeros);
// row_offsets = (OffsetT*) numa_alloc_interleaved(sizeof(OffsetT) * (num_rows + 1));
// column_indices = (OffsetT*) numa_alloc_interleaved(sizeof(OffsetT) * num_nonzeros);
row_offsets = (OffsetT*) numa_alloc_onnode(sizeof(OffsetT) * (num_rows + 1), 0);
column_indices = (OffsetT*) numa_alloc_onnode(sizeof(OffsetT) * num_nonzeros, 0);
values = (ValueT*) numa_alloc_onnode(sizeof(ValueT) * num_nonzeros, 1);
}
else
{
values = (ValueT*) mkl_malloc(sizeof(ValueT) * num_nonzeros, 4096);
row_offsets = (OffsetT*) mkl_malloc(sizeof(OffsetT) * (num_rows + 1), 4096);
column_indices = (OffsetT*) mkl_malloc(sizeof(OffsetT) * num_nonzeros, 4096);
}
#else
row_offsets = new OffsetT[num_rows + 1];
column_indices = new OffsetT[num_nonzeros];
values = new ValueT[num_nonzeros];
#endif
OffsetT prev_row = -1;
for (OffsetT current_edge = 0; current_edge < num_nonzeros; current_edge++)
{
OffsetT current_row = coo_matrix.coo_tuples[current_edge].row;
// Fill in rows up to and including the current row
for (OffsetT row = prev_row + 1; row <= current_row; row++)
{
row_offsets[row] = current_edge;
}
prev_row = current_row;
column_indices[current_edge] = coo_matrix.coo_tuples[current_edge].col;
values[current_edge] = coo_matrix.coo_tuples[current_edge].val;
}
// Fill out any trailing edgeless vertices (and the end-of-list element)
for (OffsetT row = prev_row + 1; row <= num_rows; row++)
{
row_offsets[row] = num_nonzeros;
}
}
/**
* Display log-histogram to stdout
*/
void DisplayHistogram()
{
// Initialize
int log_counts[9];
for (int i = 0; i < 9; i++)
{
log_counts[i] = 0;
}
// Scan
int max_log_length = -1;
for (OffsetT row = 0; row < num_rows; row++)
{
OffsetT length = row_offsets[row + 1] - row_offsets[row];
int log_length = -1;
while (length > 0)
{
length /= 10;
log_length++;
}
if (log_length > max_log_length)
{
max_log_length = log_length;
}
log_counts[log_length + 1]++;
}
printf("CSR matrix (%d rows, %d columns, %d non-zeros):
", (int) num_rows, (int) num_cols, (int) num_nonzeros);
for (int i = -1; i < max_log_length + 1; i++)
{
printf("\tDegree 1e%d: \t%d (%.2f%%)
", i, log_counts[i + 1], (float) log_counts[i + 1] * 100.0 / num_cols);
}
fflush(stdout);
}
/**
* Display matrix to stdout
*/
void Display()
{
printf("Input Matrix:
");
for (OffsetT row = 0; row < num_rows; row++)
{
printf("%d [@%d, #%d]: ", row, row_offsets[row], row_offsets[row + 1] - row_offsets[row]);
for (OffsetT current_edge = row_offsets[row]; current_edge < row_offsets[row + 1]; current_edge++)
{
printf("%d (%f), ", column_indices[current_edge], values[current_edge]);
}
printf("
");
}
fflush(stdout);
}
};
/******************************************************************************
* Matrix transformations
******************************************************************************/
// Comparator for ordering rows by degree (lowest first), then by row-id (lowest first)
template <typename OffsetT>
struct OrderByLow
{
OffsetT* row_degrees;
OrderByLow(OffsetT* row_degrees) : row_degrees(row_degrees) {}
bool operator()(const OffsetT &a, const OffsetT &b)
{
if (row_degrees[a] < row_degrees[b])
return true;
else if (row_degrees[a] > row_degrees[b])
return false;
else
return (a < b);
}
};
// Comparator for ordering rows by degree (highest first), then by row-id (lowest first)
template <typename OffsetT>
struct OrderByHigh
{
OffsetT* row_degrees;
OrderByHigh(OffsetT* row_degrees) : row_degrees(row_degrees) {}
bool operator()(const OffsetT &a, const OffsetT &b)
{
if (row_degrees[a] > row_degrees[b])
return true;
else if (row_degrees[a] < row_degrees[b])
return false;
else
return (a < b);
}
};
/**
* Reverse Cuthill-McKee
*/
template <typename ValueT, typename OffsetT>
void RcmRelabel(
CsrMatrix<ValueT, OffsetT>& matrix,
OffsetT* relabel_indices)
{
// Initialize row degrees
OffsetT* row_degrees_in = new OffsetT[matrix.num_rows];
OffsetT* row_degrees_out = new OffsetT[matrix.num_rows];
for (OffsetT row = 0; row < matrix.num_rows; ++row)
{
row_degrees_in[row] = 0;
row_degrees_out[row] = matrix.row_offsets[row + 1] - matrix.row_offsets[row];
}
for (OffsetT nonzero = 0; nonzero < matrix.num_nonzeros; ++nonzero)
{
row_degrees_in[matrix.column_indices[nonzero]]++;
}
// Initialize unlabeled set
typedef std::set<OffsetT, OrderByLow<OffsetT> > UnlabeledSet;
typename UnlabeledSet::key_compare unlabeled_comp(row_degrees_in);
UnlabeledSet unlabeled(unlabeled_comp);
for (OffsetT row = 0; row < matrix.num_rows; ++row)
{
relabel_indices[row] = -1;
unlabeled.insert(row);
}
// Initialize queue set
std::deque<OffsetT> q;
// Process unlabeled vertices (traverse connected components)
OffsetT relabel_idx = 0;
while (!unlabeled.empty())
{
// Seed the unvisited frontier queue with the unlabeled vertex of lowest-degree
OffsetT vertex = *unlabeled.begin();
q.push_back(vertex);
while (!q.empty())
{
vertex = q.front();
q.pop_front();
if (relabel_indices[vertex] == -1)
{
// Update this vertex
unlabeled.erase(vertex);
relabel_indices[vertex] = relabel_idx;
relabel_idx++;
// Sort neighbors by degree
OrderByLow<OffsetT> neighbor_comp(row_degrees_in);
std::sort(
matrix.column_indices + matrix.row_offsets[vertex],
matrix.column_indices + matrix.row_offsets[vertex + 1],
neighbor_comp);
// Inspect neighbors, adding to the out frontier if unlabeled
for (OffsetT neighbor_idx = matrix.row_offsets[vertex];
neighbor_idx < matrix.row_offsets[vertex + 1];
++neighbor_idx)
{
OffsetT neighbor = matrix.column_indices[neighbor_idx];
q.push_back(neighbor);
}
}
}
}
/*
// Reverse labels
for (int row = 0; row < matrix.num_rows; ++row)
{
relabel_indices[row] = matrix.num_rows - relabel_indices[row] - 1;
}
*/
// Cleanup
if (row_degrees_in) delete[] row_degrees_in;
if (row_degrees_out) delete[] row_degrees_out;
}
/**
* Reverse Cuthill-McKee
*/
template <typename ValueT, typename OffsetT>
void RcmRelabel(
CsrMatrix<ValueT, OffsetT>& matrix,
bool verbose = false)
{
// Do not process if not square
if (matrix.num_cols != matrix.num_rows)
{
if (verbose) {
printf("RCM transformation ignored (not square)
"); fflush(stdout);
}
return;
}
// Initialize relabel indices
OffsetT* relabel_indices = new OffsetT[matrix.num_rows];
if (verbose) {
printf("RCM relabeling... "); fflush(stdout);
}
RcmRelabel(matrix, relabel_indices);
if (verbose) {
printf("done. Reconstituting... "); fflush(stdout);
}
// Create a COO matrix from the relabel indices
CooMatrix<ValueT, OffsetT> coo_matrix;
coo_matrix.InitCsrRelabel(matrix, relabel_indices);
// Reconstitute the CSR matrix from the sorted COO tuples
if (relabel_indices) delete[] relabel_indices;
matrix.Clear();
matrix.FromCoo(coo_matrix);
if (verbose) {
printf("done. "); fflush(stdout);
}
}
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