feat(linear-static-3d-euler-beam): step 18 - sparse-assembly
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KOKO\Mimi
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#include "fesa/math/sparse_matrix.hpp"
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#include "fesa/fem/dof_manager.hpp"
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#include <algorithm>
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#include <cmath>
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#include <limits>
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#include <stdexcept>
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#include <string>
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#include <tuple>
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#include <utility>
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namespace fesa {
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namespace {
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Status sparseFailure(
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const std::string& code,
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const std::string& identity,
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const std::string& message) {
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return Status::failure(
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FailureCategory::model,
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{{Severity::error,
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code,
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{{}, 0U},
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"SPARSE_MATRIX",
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identity,
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message}});
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}
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Status validateCsr(
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const std::size_t rows,
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const std::size_t columns,
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const std::vector<std::size_t>& rowOffsets,
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const std::vector<std::size_t>& columnIndices,
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const std::vector<double>* const values) {
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if (rows == (std::numeric_limits<std::size_t>::max)() ||
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rowOffsets.size() != rows + 1U) {
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return sparseFailure(
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"invalid-sparse-shape",
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"row-offset-count",
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"CSR row offsets must contain exactly rows plus one entries.");
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}
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if (rowOffsets.empty() || rowOffsets.front() != 0U ||
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rowOffsets.back() != columnIndices.size()) {
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return sparseFailure(
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"invalid-sparse-pattern",
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"row-offset-range",
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"CSR row offsets must start at zero and end at the column count.");
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}
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if (values != nullptr && values->size() != columnIndices.size()) {
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return sparseFailure(
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"invalid-sparse-shape",
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"value-count",
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"CSR column and value arrays must have equal sizes.");
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}
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for (std::size_t row = 0U; row < rows; ++row) {
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const std::size_t begin = rowOffsets[row];
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const std::size_t end = rowOffsets[row + 1U];
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if (begin > end || end > columnIndices.size()) {
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return sparseFailure(
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"invalid-sparse-pattern",
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std::to_string(row),
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"CSR row offsets must be nondecreasing and remain in range.");
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}
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for (std::size_t position = begin; position < end; ++position) {
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if (columnIndices[position] >= columns) {
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return sparseFailure(
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"invalid-sparse-index",
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std::to_string(position),
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"CSR column index is outside the matrix dimensions.");
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}
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if (position > begin &&
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columnIndices[position - 1U] >= columnIndices[position]) {
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return sparseFailure(
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"invalid-sparse-pattern",
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std::to_string(row),
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"CSR columns must be sorted and unique within each row.");
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}
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if (values != nullptr && !std::isfinite((*values)[position])) {
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return sparseFailure(
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"nonfinite-sparse-value",
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std::to_string(position),
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"CSR values must be finite.");
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}
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}
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}
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return Status::ok();
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}
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} // namespace
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Result<SparseMatrix> SparseMatrix::fromCoo(
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const std::size_t rows,
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const std::size_t columns,
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std::vector<CooContribution> contributions,
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const SparsePattern& expectedPattern) {
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const Status patternStatus = validateCsr(
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rows,
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columns,
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expectedPattern.rowOffsets,
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expectedPattern.columnIndices,
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nullptr);
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if (!patternStatus.isOk()) {
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return Result<SparseMatrix>::failure(patternStatus);
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}
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for (const auto& contribution : contributions) {
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if (contribution.row >= rows || contribution.column >= columns) {
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return Result<SparseMatrix>::failure(sparseFailure(
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"invalid-sparse-index",
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std::to_string(contribution.row) + ":" +
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std::to_string(contribution.column),
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"COO contribution index is outside the matrix dimensions."));
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}
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if (!std::isfinite(contribution.value)) {
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return Result<SparseMatrix>::failure(sparseFailure(
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"nonfinite-sparse-value",
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std::to_string(contribution.elementOrder) + ":" +
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std::to_string(contribution.localOrder),
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"COO contribution values must be finite."));
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}
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}
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// The complete tuple fixes duplicate summation order independently of
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// worker completion order. stable_sort also preserves exact tuple ties.
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std::stable_sort(
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contributions.begin(),
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contributions.end(),
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[](const CooContribution& left, const CooContribution& right) {
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return std::tie(
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left.row,
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left.column,
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left.elementOrder,
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left.localOrder) <
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std::tie(
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right.row,
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right.column,
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right.elementOrder,
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right.localOrder);
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});
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std::vector<double> values(expectedPattern.columnIndices.size(), 0.0);
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for (const auto& contribution : contributions) {
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const std::size_t begin = expectedPattern.rowOffsets[contribution.row];
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const std::size_t end = expectedPattern.rowOffsets[contribution.row + 1U];
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const auto first = expectedPattern.columnIndices.begin() + begin;
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const auto last = expectedPattern.columnIndices.begin() + end;
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const auto found = std::lower_bound(first, last, contribution.column);
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if (found == last || *found != contribution.column) {
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return Result<SparseMatrix>::failure(sparseFailure(
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"sparse-pattern-mismatch",
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std::to_string(contribution.row) + ":" +
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std::to_string(contribution.column),
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"COO contribution is absent from the expected sparse pattern."));
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}
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const std::size_t position = static_cast<std::size_t>(
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std::distance(expectedPattern.columnIndices.begin(), found));
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values[position] += contribution.value;
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if (!std::isfinite(values[position])) {
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return Result<SparseMatrix>::failure(sparseFailure(
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"nonfinite-sparse-value",
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std::to_string(contribution.row) + ":" +
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std::to_string(contribution.column),
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"Ordered COO duplicate summation produced a nonfinite value."));
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}
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}
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SparseMatrix matrix{
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rows,
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columns,
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expectedPattern.rowOffsets,
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expectedPattern.columnIndices,
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std::move(values)};
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const Status status = matrix.validate();
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if (!status.isOk()) {
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return Result<SparseMatrix>::failure(status);
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}
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return Result<SparseMatrix>::success(std::move(matrix));
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}
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std::size_t SparseMatrix::rows() const noexcept {
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return rows_;
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}
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std::size_t SparseMatrix::columns() const noexcept {
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return columns_;
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}
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const std::vector<std::size_t>& SparseMatrix::rowOffsets() const noexcept {
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return rowOffsets_;
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}
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const std::vector<std::size_t>& SparseMatrix::columnIndices() const noexcept {
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return columnIndices_;
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}
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const std::vector<double>& SparseMatrix::values() const noexcept {
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return values_;
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}
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Vector SparseMatrix::multiply(const Vector& rhs) const {
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if (columns_ != rhs.size()) {
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throw std::invalid_argument{
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"Sparse matrix-vector multiplication has incompatible dimensions."};
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}
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Vector result{rows_};
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for (std::size_t row = 0U; row < rows_; ++row) {
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double value = 0.0;
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for (std::size_t position = rowOffsets_[row];
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position < rowOffsets_[row + 1U];
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++position) {
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value += values_[position] * rhs[columnIndices_[position]];
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}
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result[row] = value;
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}
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return result;
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}
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Status SparseMatrix::validate() const {
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return validateCsr(
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rows_, columns_, rowOffsets_, columnIndices_, &values_);
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}
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SparseMatrix::SparseMatrix(
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const std::size_t rows,
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const std::size_t columns,
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std::vector<std::size_t> rowOffsets,
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std::vector<std::size_t> columnIndices,
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std::vector<double> values)
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: rows_{rows},
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columns_{columns},
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rowOffsets_{std::move(rowOffsets)},
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columnIndices_{std::move(columnIndices)},
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values_{std::move(values)} {}
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} // namespace fesa
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