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/*
* CSRGeneralMatrix.hpp
*
* Created on: May 6, 2015
* Authors: Michael Wegner <michael.wegner@student.kit.edu>
* Eugenio Angriman <angrimae@hu-berlin.de>
*/
#ifndef NETWORKIT_ALGEBRAIC_CSR_GENERAL_MATRIX_HPP_
#define NETWORKIT_ALGEBRAIC_CSR_GENERAL_MATRIX_HPP_
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iostream>
#include <numeric>
#include <omp.h>
#include <stdexcept>
#include <vector>
#include <networkit/Globals.hpp>
#include <networkit/algebraic/AlgebraicGlobals.hpp>
#include <networkit/algebraic/Vector.hpp>
#include <networkit/graph/Graph.hpp>
#include <tlx/unused.hpp>
namespace NetworKit {
template <class ValueType>
class CSRGeneralMatrix {
std::vector<index> rowIdx, columnIdx;
std::vector<ValueType> nonZeros;
count nRows, nCols;
bool isSorted;
ValueType zero;
class IndexProxy {
public:
IndexProxy(CSRGeneralMatrix &mat, index i, index j) : Matrix{mat}, i{i}, j{j} {}
operator const ValueType &() const {
return const_cast<const CSRGeneralMatrix &>(Matrix)(i, j);
}
void operator=(double rhs) { Matrix.setValue(i, j, rhs); }
private:
CSRGeneralMatrix &Matrix;
index i;
index j;
};
public:
CSRGeneralMatrix()
: rowIdx(0), columnIdx(0), nonZeros(0), nRows(0), nCols(0), isSorted(true), zero(0) {}
CSRGeneralMatrix(count dimension, ValueType zero = 0)
: rowIdx(dimension + 1), columnIdx(0), nonZeros(0), nRows(dimension), nCols(dimension),
isSorted(true), zero(zero) {}
CSRGeneralMatrix(count nRows, count nCols, ValueType zero = 0)
: rowIdx(nRows + 1), columnIdx(0), nonZeros(0), nRows(nRows), nCols(nCols), isSorted(true),
zero(zero) {}
CSRGeneralMatrix(count dimension, const std::vector<Triplet> &triplets, ValueType zero = 0,
bool isSorted = false)
: CSRGeneralMatrix(dimension, dimension, triplets, zero, isSorted) {}
CSRGeneralMatrix(count nRows, count nCols, const std::vector<Triplet> &triplets,
ValueType zero = 0, bool isSorted = false)
: rowIdx(nRows + 1), columnIdx(triplets.size()), nonZeros(triplets.size()), nRows(nRows),
nCols(nCols), isSorted(isSorted), zero(zero) {
const count nnz = triplets.size();
for (index i = 0; i < nnz; ++i)
rowIdx[triplets[i].row]++;
for (index i = 0, prefixSum = 0; i < nRows; ++i) {
count nnzInRow = rowIdx[i];
rowIdx[i] = prefixSum;
prefixSum += nnzInRow;
}
rowIdx[nRows] = nnz;
for (index i = 0; i < nnz; ++i) {
index row = triplets[i].row;
index dest = rowIdx[row];
columnIdx[dest] = triplets[i].column;
nonZeros[dest] = triplets[i].value;
rowIdx[row]++;
}
rowIdx.back() = 0;
std::rotate(rowIdx.rbegin(), rowIdx.rbegin() + 1, rowIdx.rend());
}
CSRGeneralMatrix(count nRows, count nCols, const std::vector<std::vector<index>> &columnIdx,
const std::vector<std::vector<ValueType>> &values, ValueType zero = 0,
bool isSorted = false)
: rowIdx(nRows + 1), nRows(nRows), nCols(nCols), isSorted(isSorted), zero(zero) {
count nnz = columnIdx[0].size();
for (index i = 1; i < columnIdx.size(); ++i) {
rowIdx[i] = rowIdx[i - 1] + columnIdx[i - 1].size();
nnz += columnIdx[i].size();
}
rowIdx[nRows] = nnz;
this->columnIdx = std::vector<index>(nnz);
this->nonZeros = std::vector<double>(nnz);
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(nRows); ++i) {
for (index k = 0; k < columnIdx[i].size(); ++k) {
this->columnIdx[rowIdx[i] + k] = columnIdx[i][k];
nonZeros[rowIdx[i] + k] = values[i][k];
}
}
}
CSRGeneralMatrix(count nRows, count nCols, const std::vector<index> &rowIdx,
const std::vector<index> &columnIdx, const std::vector<ValueType> &nonZeros,
ValueType zero = 0, bool isSorted = false)
: rowIdx(rowIdx), columnIdx(columnIdx), nonZeros(nonZeros), nRows(nRows), nCols(nCols),
isSorted(isSorted), zero(zero) {}
CSRGeneralMatrix(const CSRGeneralMatrix &other) = default;
CSRGeneralMatrix(CSRGeneralMatrix &&other) noexcept = default;
~CSRGeneralMatrix() = default;
CSRGeneralMatrix &operator=(CSRGeneralMatrix &&other) noexcept = default;
CSRGeneralMatrix &operator=(const CSRGeneralMatrix &other) = default;
IndexProxy operator()(index i, index j) { return IndexProxy(*this, i, j); }
bool operator==(const CSRGeneralMatrix &other) const {
bool equal = nRows == other.nRows && nCols == other.nCols && zero == other.zero
&& nnz() == other.nnz();
if (equal)
forNonZeroElementsInRowOrder([&](index i, index j, ValueType value) {
if (other(i, j) != value) {
equal = false;
return;
}
});
return equal;
}
bool isApprox(const CSRGeneralMatrix &other, const double eps = 0.01) const {
bool equal = nRows == other.nRows && nCols == other.nCols && zero == other.zero
&& nnz() == other.nnz();
if (equal)
forNonZeroElementsInRowOrder([&](index i, index j, ValueType value) {
if (std::abs(other(i, j) - value) > eps) {
equal = false;
return;
}
});
return equal;
}
bool operator!=(const CSRGeneralMatrix &other) const { return !((*this) == other); }
count numberOfRows() const noexcept { return nRows; }
count numberOfColumns() const noexcept { return nCols; }
ValueType getZero() const noexcept { return zero; }
count nnzInRow(const index i) const {
assert(i < nRows);
return rowIdx[i + 1] - rowIdx[i];
}
count nnz() const noexcept { return nonZeros.size(); }
const ValueType &operator()(index i, index j) const {
assert(i < nRows);
assert(j < nCols);
if (rowIdx[i] == rowIdx[i + 1])
return zero; // no non-zero value is present in this row
if (!sorted()) {
for (index k = rowIdx[i]; k < rowIdx[i + 1]; ++k) {
if (columnIdx[k] == j) {
return nonZeros[k];
}
}
} else {
// finding the correct index where j should be inserted
auto it = std::lower_bound(columnIdx.begin() + rowIdx[i],
columnIdx.begin() + rowIdx[i + 1], j);
index colIdx = static_cast<index>(it - columnIdx.begin());
if (it == columnIdx.end())
return zero;
else if (*it == j) {
return nonZeros[colIdx];
}
}
return zero;
}
void setValue(index i, index j, ValueType value) {
assert(i < nRows);
assert(j < nCols);
index colIdx = none;
if (!isSorted) {
for (index k = rowIdx[i]; k < rowIdx[i + 1]; ++k) {
if (columnIdx[k] == j) {
colIdx = k;
}
}
if (colIdx != none) {
if (value != zero) { // update existing value
nonZeros[colIdx] = value;
} else { // remove value if set to zero
columnIdx.erase(columnIdx.begin() + colIdx);
nonZeros.erase(nonZeros.begin() + colIdx);
for (index k = i + 1; k < rowIdx.size(); ++k) {
--rowIdx[k];
}
}
} else if (value != zero) { // don't add zero values
columnIdx.emplace(std::next(columnIdx.begin(), rowIdx[i + 1]), j);
nonZeros.emplace(std::next(nonZeros.begin(), rowIdx[i + 1]), value);
// update rowIdx
for (index k = i + 1; k < rowIdx.size(); ++k) {
++rowIdx[k];
}
}
} else {
// finding the correct index where j should be inserted
auto it = std::lower_bound(columnIdx.begin() + rowIdx[i],
columnIdx.begin() + rowIdx[i + 1], j);
colIdx = static_cast<index>(it - columnIdx.begin());
if (colIdx < rowIdx[i + 1] && columnIdx[colIdx] == j) {
if (value != zero) { // update existing value
nonZeros[colIdx] = value;
} else { // remove value if set to zero
columnIdx.erase(columnIdx.begin() + colIdx);
nonZeros.erase(nonZeros.begin() + colIdx);
for (index k = i + 1; k < rowIdx.size(); ++k) {
--rowIdx[k];
}
}
} else if (value != zero) { // don't add zero values
columnIdx.emplace(std::next(columnIdx.begin(), colIdx), j);
nonZeros.emplace(std::next(nonZeros.begin(), colIdx), value);
// update rowIdx
for (index k = i + 1; k < rowIdx.size(); ++k) {
++rowIdx[k];
}
}
}
assert(this->operator()(i, j) == value);
}
void sort() {
#pragma omp parallel
{
std::vector<index> permutation(nCols);
#pragma omp for schedule(guided)
for (omp_index i = 0; i < static_cast<omp_index>(nRows); ++i) {
const index startOfRow = rowIdx[i], endOfRow = rowIdx[i + 1];
const count nonZerosInRow = endOfRow - startOfRow;
if (nonZerosInRow <= 1
|| std::is_sorted(columnIdx.begin() + startOfRow, columnIdx.begin() + endOfRow))
continue;
permutation.resize(nonZerosInRow);
std::iota(permutation.begin(), permutation.end(), index{0});
std::sort(permutation.begin(), permutation.end(), [&](index x, index y) {
return columnIdx[startOfRow + x] < columnIdx[startOfRow + y];
});
Aux::ArrayTools::applyPermutation(columnIdx.begin() + startOfRow,
columnIdx.begin() + endOfRow,
permutation.begin());
Aux::ArrayTools::applyPermutation(nonZeros.begin() + startOfRow,
nonZeros.begin() + endOfRow, permutation.begin());
}
}
isSorted = true;
#ifdef NETWORKIT_SANITY_CHECKS
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(nRows); ++i)
assert(
std::is_sorted(columnIdx.begin() + rowIdx[i], columnIdx.begin() + rowIdx[i + 1]));
#endif // NETWORKIT_SANITY_CHECKS
}
bool sorted() const noexcept { return isSorted; }
Vector row(index i) const {
assert(i < nRows);
Vector row(numberOfColumns(), zero, true);
parallelForNonZeroElementsInRow(i, [&row](index j, double value) { row[j] = value; });
return row;
}
Vector column(index j) const {
assert(j < nCols);
Vector column(numberOfRows(), getZero());
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(numberOfRows()); ++i)
column[i] = (*this)(i, j);
return column;
}
Vector diagonal() const {
Vector diag(std::min(nRows, nCols), zero);
if (sorted()) {
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(diag.getDimension()); ++i) {
const auto it = std::lower_bound(columnIdx.begin() + rowIdx[i],
columnIdx.begin() + rowIdx[i + 1], i);
if (it != columnIdx.end() && *it == static_cast<index>(i))
diag[i] = nonZeros[it - columnIdx.begin()];
}
} else {
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(diag.getDimension()); ++i) {
diag[i] = (*this)(i, i);
}
}
return diag;
}
CSRGeneralMatrix operator+(const CSRGeneralMatrix &other) const {
assert(nRows == other.nRows && nCols == other.nCols);
return CSRGeneralMatrix<ValueType>::binaryOperator(
*this, other, [](double val1, double val2) { return val1 + val2; });
}
CSRGeneralMatrix &operator+=(const CSRGeneralMatrix &other) {
assert(nRows == other.nRows && nCols == other.nCols);
*this = CSRGeneralMatrix<ValueType>::binaryOperator(
*this, other, [](double val1, double val2) { return val1 + val2; });
return *this;
}
CSRGeneralMatrix operator-(const CSRGeneralMatrix &other) const {
assert(nRows == other.nRows && nCols == other.nCols);
return CSRGeneralMatrix<ValueType>::binaryOperator(
*this, other, [](double val1, double val2) { return val1 - val2; });
}
CSRGeneralMatrix &operator-=(const CSRGeneralMatrix &other) {
assert(nRows == other.nRows && nCols == other.nCols);
*this = CSRGeneralMatrix<ValueType>::binaryOperator(
*this, other, [](double val1, double val2) { return val1 - val2; });
return *this;
}
CSRGeneralMatrix operator*(const ValueType &scalar) const {
return CSRGeneralMatrix(*this) *= scalar;
}
CSRGeneralMatrix &operator*=(const ValueType &scalar) {
#pragma omp parallel for
for (omp_index k = 0; k < static_cast<omp_index>(nonZeros.size()); ++k)
nonZeros[k] *= scalar;
return *this;
}
Vector operator*(const Vector &vector) const {
assert(!vector.isTransposed());
assert(nCols == vector.getDimension());
Vector result(nRows, zero);
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(numberOfRows()); ++i) {
double sum = zero;
for (index cIdx = rowIdx[i]; cIdx < rowIdx[i + 1]; ++cIdx) {
sum += nonZeros[cIdx] * vector[columnIdx[cIdx]];
}
result[i] = sum;
}
return result;
}
CSRGeneralMatrix operator*(const CSRGeneralMatrix &other) const {
assert(nCols == other.nRows);
std::vector<index> rowIdx(numberOfRows() + 1, 0);
std::vector<index> columnIdx;
std::vector<double> nonZeros;
#pragma omp parallel
{
std::vector<int64_t> marker(other.numberOfColumns(), -1);
count numThreads = omp_get_num_threads();
index threadId = omp_get_thread_num();
count chunkSize = (numberOfRows() + numThreads - 1) / numThreads;
index chunkStart = threadId * chunkSize;
index chunkEnd = std::min(numberOfRows(), chunkStart + chunkSize);
for (index i = chunkStart; i < chunkEnd; ++i) {
for (index jA = this->rowIdx[i]; jA < this->rowIdx[i + 1]; ++jA) {
index k = this->columnIdx[jA];
for (index jB = other.rowIdx[k]; jB < other.rowIdx[k + 1]; ++jB) {
index j = other.columnIdx[jB];
if (marker[j] != (int64_t)i) {
marker[j] = i;
++rowIdx[i + 1];
}
}
}
}
std::fill(marker.begin(), marker.end(), -1);
#pragma omp barrier
#pragma omp single
{
for (index i = 0; i < numberOfRows(); ++i)
rowIdx[i + 1] += rowIdx[i];
columnIdx = std::vector<index>(rowIdx[numberOfRows()]);
nonZeros = std::vector<double>(rowIdx[numberOfRows()]);
}
for (index i = chunkStart; i < chunkEnd; ++i) {
index rowBegin = rowIdx[i];
index rowEnd = rowBegin;
for (index jA = this->rowIdx[i]; jA < this->rowIdx[i + 1]; ++jA) {
index k = this->columnIdx[jA];
double valA = this->nonZeros[jA];
for (index jB = other.rowIdx[k]; jB < other.rowIdx[k + 1]; ++jB) {
index j = other.columnIdx[jB];
double valB = other.nonZeros[jB];
if (marker[j] < (int64_t)rowBegin) {
marker[j] = rowEnd;
columnIdx[rowEnd] = j;
nonZeros[rowEnd] = valA * valB;
++rowEnd;
} else {
nonZeros[marker[j]] += valA * valB;
}
}
}
}
}
CSRGeneralMatrix result(numberOfRows(), other.numberOfColumns(), rowIdx, columnIdx,
nonZeros);
if (sorted() && other.sorted())
result.sort();
return result;
}
CSRGeneralMatrix operator/(const ValueType &divisor) const {
return CSRGeneralMatrix(*this) /= divisor;
}
CSRGeneralMatrix &operator/=(const ValueType &divisor) { return *this *= 1.0 / divisor; }
template <typename L>
static CSRGeneralMatrix binaryOperator(const CSRGeneralMatrix &A, const CSRGeneralMatrix &B,
L binaryOp);
static CSRGeneralMatrix mTmMultiply(const CSRGeneralMatrix &A, const CSRGeneralMatrix &B) {
assert(A.nRows == B.nRows);
std::vector<std::vector<index>> columnIdx(A.numberOfColumns());
std::vector<std::vector<double>> values(A.numberOfColumns());
for (index k = 0; k < A.numberOfRows(); ++k) {
A.forNonZeroElementsInRow(k, [&](index i, double vA) {
B.forNonZeroElementsInRow(k, [&](index j, double vB) {
bool found = false;
for (index l = 0; l < columnIdx[i].size(); ++l) {
if (columnIdx[i][l] == j) {
values[i][l] += vA * vB;
found = true;
break;
}
}
if (!found) {
columnIdx[i].push_back(j);
values[i].push_back(vA * vB);
}
});
});
}
return CSRGeneralMatrix(A.nCols, B.nCols, columnIdx, values);
}
static CSRGeneralMatrix mmTMultiply(const CSRGeneralMatrix &A, const CSRGeneralMatrix &B) {
assert(A.nCols == B.nCols);
std::vector<std::vector<index>> columnIdx(A.numberOfRows());
std::vector<std::vector<double>> values(A.numberOfRows());
for (index i = 0; i < A.numberOfRows(); ++i) {
A.forNonZeroElementsInRow(i, [&](index k, double vA) {
for (index j = 0; j < B.numberOfRows(); ++j) {
double vB = B(j, k);
if (vB != A.zero) {
bool found = false;
for (index l = 0; l < columnIdx[i].size(); ++l) {
if (columnIdx[i][l] == j) {
values[i][l] += vA * vB;
found = true;
break;
}
}
if (!found) {
columnIdx[i].push_back(j);
values[i].push_back(vA * vB);
}
}
}
});
}
return CSRGeneralMatrix(A.nRows, B.nRows, columnIdx, values);
}
static Vector mTvMultiply(const CSRGeneralMatrix &matrix, const Vector &vector) {
assert(matrix.nRows == vector.getDimension() && !vector.isTransposed());
Vector result(matrix.numberOfColumns(), 0);
for (index k = 0; k < matrix.numberOfRows(); ++k) {
matrix.forNonZeroElementsInRow(
k, [&](index j, double value) { result[j] += value * vector[k]; });
}
return result;
}
CSRGeneralMatrix transpose() const {
std::vector<index> rowIdx(numberOfColumns() + 1);
for (index i = 0; i < nnz(); ++i)
++rowIdx[columnIdx[i] + 1];
for (index i = 0; i < numberOfColumns(); ++i)
rowIdx[i + 1] += rowIdx[i];
std::vector<index> columnIdx(rowIdx[numberOfColumns()]);
std::vector<double> nonZeros(rowIdx[numberOfColumns()]);
for (index i = 0; i < numberOfRows(); ++i) {
for (index j = this->rowIdx[i]; j < this->rowIdx[i + 1]; ++j) {
index colIdx = this->columnIdx[j];
columnIdx[rowIdx[colIdx]] = i;
nonZeros[rowIdx[colIdx]] = this->nonZeros[j];
++rowIdx[colIdx];
}
}
index shift = 0;
for (index i = 0; i < numberOfColumns(); ++i) {
index temp = rowIdx[i];
rowIdx[i] = shift;
shift = temp;
}
rowIdx[numberOfColumns()] = nonZeros.size();
return CSRGeneralMatrix(nCols, nRows, rowIdx, columnIdx, nonZeros, getZero());
}
CSRGeneralMatrix extract(const std::vector<index> &rowIndices,
const std::vector<index> &columnIndices) const {
std::vector<Triplet> triplets;
std::vector<std::vector<index>> columnMapping(numberOfColumns());
for (index j = 0; j < columnIndices.size(); ++j)
columnMapping[columnIndices[j]].push_back(j);
bool sorted = true;
for (index i = 0; i < rowIndices.size(); ++i) {
Triplet last = {i, 0, 0};
(*this).forNonZeroElementsInRow(rowIndices[i], [&](index k, double value) {
if (!columnMapping[k].empty()) {
for (index j : columnMapping[k]) {
if (last.row == i && last.column > j)
sorted = false;
last = {i, j, value};
triplets.push_back(last);
}
}
});
}
return CSRGeneralMatrix(rowIndices.size(), columnIndices.size(), triplets, getZero(),
sorted);
}
void assign(const std::vector<index> &rowIndices, const std::vector<index> &columnIndices,
const CSRGeneralMatrix &source) {
assert(rowIndices.size() == source.numberOfRows());
assert(columnIndices.size() == source.numberOfColumns());
for (index i = 0; i < rowIndices.size(); ++i)
source.forElementsInRow(i, [&](index j, double value) {
setValue(rowIndices[i], columnIndices[j], value);
});
}
template <typename F>
void apply(F unaryElementFunction);
static CSRGeneralMatrix adjacencyMatrix(const Graph &graph, ValueType zero = 0) {
count nonZeros = graph.isDirected() ? graph.numberOfEdges() : graph.numberOfEdges() * 2;
std::vector<Triplet> triplets(nonZeros);
index idx = 0;
graph.forEdges([&](node i, node j, double val) {
triplets[idx++] = {i, j, val};
if (!graph.isDirected() && i != j)
triplets[idx++] = {j, i, val};
});
return CSRGeneralMatrix(graph.upperNodeIdBound(), triplets, zero);
}
static CSRGeneralMatrix diagonalMatrix(const Vector &diagonalElements, ValueType zero = 0) {
count nRows = diagonalElements.getDimension();
count nCols = diagonalElements.getDimension();
std::vector<index> rowIdx(nRows + 1, 0);
std::iota(rowIdx.begin(), rowIdx.end(), 0);
std::vector<index> columnIdx(nCols);
std::vector<double> nonZeros(nCols);
#pragma omp parallel for
for (omp_index j = 0; j < static_cast<omp_index>(nCols); ++j) {
columnIdx[j] = j;
nonZeros[j] = diagonalElements[j];
}
return CSRGeneralMatrix(nRows, nCols, rowIdx, columnIdx, nonZeros, zero);
}
static CSRGeneralMatrix incidenceMatrix(const Graph &graph, ValueType zero = 0) {
if (!graph.hasEdgeIds())
throw std::runtime_error("Graph has no edge Ids. Index edges first by "
"calling graph.indexEdges()");
std::vector<Triplet> triplets;
if (graph.isDirected()) {
graph.forEdges([&](node u, node v, edgeweight weight, edgeid edgeId) {
if (u != v) {
edgeweight w = std::sqrt(weight);
triplets.push_back({u, edgeId, w});
triplets.push_back({v, edgeId, -w});
}
});
} else {
graph.forEdges([&](node u, node v, edgeweight weight, edgeid edgeId) {
if (u != v) {
edgeweight w = std::sqrt(weight);
if (u < v) { // orientation: small node number -> great node number
triplets.push_back({u, edgeId, w});
triplets.push_back({v, edgeId, -w});
} else {
triplets.push_back({u, edgeId, -w});
triplets.push_back({v, edgeId, w});
}
}
});
}
return CSRGeneralMatrix(graph.upperNodeIdBound(), graph.upperEdgeIdBound(), triplets, zero);
}
static CSRGeneralMatrix laplacianMatrix(const Graph &graph, ValueType zero = 0) {
std::vector<Triplet> triples;
graph.forNodes([&](const index i) {
double weightedDegree = 0;
graph.forNeighborsOf(i, [&](const index j, double weight) { // - adjacency matrix
if (i != j) // exclude diagonal since this would be subtracted by
// the adjacency weight
weightedDegree += weight;
triples.push_back({i, j, -weight});
});
if (weightedDegree != 0)
triples.push_back({i, i, weightedDegree}); // degree matrix
});
return CSRGeneralMatrix(graph.numberOfNodes(), triples, zero);
}
static CSRGeneralMatrix normalizedLaplacianMatrix(const Graph &graph, ValueType zero = 0) {
std::vector<Triplet> triples;
std::vector<double> weightedDegrees(graph.upperNodeIdBound(), 0);
graph.parallelForNodes([&](const node u) { weightedDegrees[u] = graph.weightedDegree(u); });
graph.forNodes([&](const node i) {
graph.forNeighborsOf(i, [&](const node j, double weight) {
if (i != j)
triples.push_back(
{i, j, -weight / std::sqrt(weightedDegrees[i] * weightedDegrees[j])});
});
if (weightedDegrees[i] != 0) {
if (graph.isWeighted())
triples.push_back({i, i, 1 - (graph.weight(i, i)) / weightedDegrees[i]});
else
triples.push_back({i, i, 1});
}
});
return CSRGeneralMatrix(graph.upperNodeIdBound(), triples, zero);
}
template <typename L>
void forNonZeroElementsInRow(index row, L handle) const {
for (index k = rowIdx[row]; k < rowIdx[row + 1]; ++k)
handle(columnIdx[k], nonZeros[k]);
}
template <typename L>
void parallelForNonZeroElementsInRow(index row, L handle) const;
template <typename L>
void forElementsInRow(index i, L handle) const;
template <typename L>
void parallelForElementsInRow(index row, L handle) const;
template <typename L>
void forElementsInRowOrder(L handle) const;
template <typename L>
void parallelForElementsInRowOrder(L handle) const;
template <typename L>
void forNonZeroElementsInRowOrder(L handle) const;
template <typename L>
void parallelForNonZeroElementsInRowOrder(L handle) const;
};
template <typename ValueType>
template <typename L>
inline CSRGeneralMatrix<ValueType>
CSRGeneralMatrix<ValueType>::binaryOperator(const CSRGeneralMatrix<ValueType> &A,
const CSRGeneralMatrix<ValueType> &B, L binaryOp) {
assert(A.nRows == B.nRows && A.nCols == B.nCols);
if (A.sorted() && B.sorted()) {
std::vector<index> rowIdx(A.nRows + 1);
std::vector<std::vector<index>> columns(A.nRows);
rowIdx[0] = 0;
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(A.nRows); ++i) {
index k = A.rowIdx[i];
index l = B.rowIdx[i];
while (k < A.rowIdx[i + 1] && l < B.rowIdx[i + 1]) {
if (A.columnIdx[k] < B.columnIdx[l]) {
columns[i].push_back(A.columnIdx[k]);
++k;
} else if (A.columnIdx[k] > B.columnIdx[l]) {
columns[i].push_back(B.columnIdx[l]);
++l;
} else { // A.columnIdx[k] == B.columnIdx[l]
columns[i].push_back(A.columnIdx[k]);
++k;
++l;
}
++rowIdx[i + 1];
}
while (k < A.rowIdx[i + 1]) {
columns[i].push_back(A.columnIdx[k]);
++k;
++rowIdx[i + 1];
}
while (l < B.rowIdx[i + 1]) {
columns[i].push_back(B.columnIdx[l]);
++l;
++rowIdx[i + 1];
}
}
for (index i = 0; i < A.nRows; ++i)
rowIdx[i + 1] += rowIdx[i];
count nnz = rowIdx[A.nRows];
std::vector<index> columnIdx(nnz);
std::vector<ValueType> nonZeros(nnz, A.zero);
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(A.nRows); ++i) {
for (index cIdx = rowIdx[i], j = 0; cIdx < rowIdx[i + 1]; ++cIdx, ++j)
columnIdx[cIdx] = columns[i][j];
columns[i].clear();
columns[i].resize(0);
columns[i].shrink_to_fit();
}
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(A.nRows); ++i) {
index k = A.rowIdx[i];
index l = B.rowIdx[i];
for (index cIdx = rowIdx[i]; cIdx < rowIdx[i + 1]; ++cIdx) {
if (k < A.rowIdx[i + 1] && columnIdx[cIdx] == A.columnIdx[k]) {
nonZeros[cIdx] = A.nonZeros[k];
++k;
}
if (l < B.rowIdx[i + 1] && columnIdx[cIdx] == B.columnIdx[l]) {
nonZeros[cIdx] = binaryOp(nonZeros[cIdx], B.nonZeros[l]);
++l;
}
}
}
return CSRGeneralMatrix(A.nRows, A.nCols, rowIdx, columnIdx, nonZeros, A.zero, true);
} else { // A or B not sorted
std::vector<int64_t> columnPointer(A.nCols, -1);
std::vector<ValueType> Arow(A.nCols, A.zero);
std::vector<ValueType> Brow(A.nCols, B.zero);
std::vector<Triplet> triplets;
for (index i = 0; i < A.nRows; ++i) {
index listHead = 0;
count nnz = 0;
// search for nonZeros in our own matrix
for (index k = A.rowIdx[i]; k < A.rowIdx[i + 1]; ++k) {
index j = A.columnIdx[k];
Arow[j] = A.nonZeros[k];
columnPointer[j] = listHead;
listHead = j;
nnz++;
}
// search for nonZeros in the other matrix
for (index k = B.rowIdx[i]; k < B.rowIdx[i + 1]; ++k) {
index j = B.columnIdx[k];
Brow[j] = B.nonZeros[k];
if (columnPointer[j]
== -1) { // our own matrix does not have a nonZero entry in column j
columnPointer[j] = listHead;
listHead = j;
nnz++;
}
}
// apply operator on the found nonZeros in A and B
for (count k = 0; k < nnz; ++k) {
ValueType value = binaryOp(Arow[listHead], Brow[listHead]);
if (value != A.zero)
triplets.push_back({i, listHead, value});
index temp = listHead;
listHead = columnPointer[listHead];
// reset for next row
columnPointer[temp] = -1;
Arow[temp] = A.zero;
Brow[temp] = B.zero;
}
nnz = 0;
}
return CSRGeneralMatrix(A.numberOfRows(), A.numberOfColumns(), triplets);
}
}
template <typename ValueType>
template <typename F>
void CSRGeneralMatrix<ValueType>::apply(const F unaryElementFunction) {
#pragma omp parallel for
for (omp_index k = 0; k < static_cast<omp_index>(nonZeros.size()); ++k)
nonZeros[k] = unaryElementFunction(nonZeros[k]);
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::parallelForNonZeroElementsInRow(index i, L handle) const {
#pragma omp parallel for
for (omp_index k = rowIdx[i]; k < static_cast<omp_index>(rowIdx[i + 1]); ++k)
handle(columnIdx[k], nonZeros[k]);
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::forElementsInRow(index i, L handle) const {
Vector rowVector = row(i);
index j = 0;
rowVector.forElements([&](ValueType val) { handle(j++, val); });
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::parallelForElementsInRow(index i, L handle) const {
row(i).parallelForElements(handle);
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::forElementsInRowOrder(L handle) const {
for (index i = 0; i < nRows; ++i) {
index col = 0;
for (index k = rowIdx[i]; k < rowIdx[i + 1]; ++k) {
while (col < columnIdx[k]) {
handle(i, col, getZero());
++col;
}
handle(i, col, nonZeros[k]);
++col;
}
}
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::parallelForElementsInRowOrder(L handle) const {
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(nRows); ++i) {
index col = 0;
for (index k = rowIdx[i]; k < rowIdx[i + 1]; ++k) {
while (col < columnIdx[k]) {
handle(i, col, getZero());
++col;
}
handle(i, col, nonZeros[k]);
++col;
}
}
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::forNonZeroElementsInRowOrder(L handle) const {
for (index i = 0; i < nRows; ++i)
for (index k = rowIdx[i]; k < rowIdx[i + 1]; ++k)
handle(i, columnIdx[k], nonZeros[k]);
}
template <typename ValueType>
template <typename L>
inline void CSRGeneralMatrix<ValueType>::parallelForNonZeroElementsInRowOrder(L handle) const {
#pragma omp parallel for
for (omp_index i = 0; i < static_cast<omp_index>(nRows); ++i)
for (index k = rowIdx[i]; k < rowIdx[i + 1]; ++k)
handle(i, columnIdx[k], nonZeros[k]);
}
// print functions for test debugging / output
template <typename T>
inline std::ostream &operator<<(std::ostream &os, const CSRGeneralMatrix<T> &M) {
for (index row = 0; row < M.numberOfRows(); ++row) {
if (row != 0)
os << std::endl;
for (index col = 0; col < M.numberOfColumns(); ++col) {
if (col != 0)
os << ", ";
os << M(row, col);
}
}
return os;
}
} /* namespace NetworKit */
#endif // NETWORKIT_ALGEBRAIC_CSR_GENERAL_MATRIX_HPP_