internal/ceres/parallel_utils.h

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2018 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: wjr@google.com (William Rucklidge)

#ifndef CERES_INTERNAL_PARALLEL_UTILS_H_
#define CERES_INTERNAL_PARALLEL_UTILS_H_

namespace ceres {
namespace internal {

// Converts a linear iteration order into a triangular iteration order.
// Suppose you have nested loops that look like
// for (int i = 0; i < n; i++) {
//   for (int j = i; j < n; j++) {
//     ... use i and j
//   }
// }
// Naively using ParallelFor to parallelise those loops might look like
// ParallelFor(..., 0, n * n, num_threads,
//   [](int thread_id, int k) {
//     int i = k / n, j = k % n;
//     if (j < i) return;
//     ...
//    });
// but these empty work items can lead to very unbalanced threading. Instead,
// do this:
// int actual_work_items = (n * (n + 1)) / 2;
// ParallelFor(..., 0, actual_work_items, num_threads,
//   [](int thread_id, int k) {
//     int i, j;
//     UnfoldIteration(k, n, &i, &j);
//     ...
//    });
// which in each iteration will produce i and j satisfying
// 0 <= i <= j < n
void LinearIndexToUpperTriangularIndex(int k, int n, int* i, int* j);

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_PARALLEL_UTILS_H_