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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2018 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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 Google Inc. 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 THE COPYRIGHT OWNER OR CONTRIBUTORS 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.
//
// Author: wjr@google.com (William Rucklidge)
#include "ceres/parallel_utils.h"
namespace ceres {
namespace 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 internal
} // namespace ceres
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