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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// Author: wjr@google.com (William Rucklidge)
#include "ceres/parallel_utils.h"
namespace ceres::internal {
void LinearIndexToUpperTriangularIndex(int k, int n, int* i, int* j) {
// This works by unfolding a rectangle into a triangle.
// Say n is even. 4 is a nice even number. The 10 i,j pairs that we
// want to produce are:
// 0,0 0,1 0,2 0,3
// 1,1 1,2 1,3
// 2,2 2,3
// 3,3
// This triangle can be folded into a 5x2 rectangle:
// 3,3 0,0 0,1 0,2 0,3
// 2,2 2,3 1,1 1,2 1,3
// If N is odd, say 5, then the 15 i,j pairs are:
// 0,0 0,1 0,2 0,3 0,4
// 1,1 1,2 1,3 1,4
// 2,2 2,3 2,3
// 3,3 3,4
// 4,4
// which folds to a 5x3 rectangle:
// 0,0 0,1 0,2 0,3 0,4
// 4,4 1,1 1,2 1,3 1,4
// 3,3 3,4 2,2 2,3 2,4
// All this function does is map the linear iteration position to a
// location in the rectangle and work out the appropriate (i, j) for that
// location.
if (n & 1) {
// Odd n. The tip of the triangle is on row 1.
int w = n; // Width of the rectangle to unfold
int i0 = k / w;
int j0 = k % w;
if (j0 >= i0) {
*i = i0;
*j = j0;
} else {
*i = n - i0;
*j = *i + j0;
}
} else {
// Even n. The tip of the triangle is on row 0, making it one wider.
int w = n + 1;
int i0 = k / w;
int j0 = k % w;
if (j0 > i0) {
*i = i0;
*j = j0 - 1;
} else {
*i = n - 1 - i0;
*j = *i + j0;
}
}
}
} // namespace ceres::internal