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91 lines
3.1 KiB
91 lines
3.1 KiB
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2018 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: wjr@google.com (William Rucklidge)
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#include "ceres/parallel_utils.h"
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namespace ceres {
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namespace internal {
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void LinearIndexToUpperTriangularIndex(int k, int n, int* i, int* j) {
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// This works by unfolding a rectangle into a triangle.
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// Say n is even. 4 is a nice even number. The 10 i,j pairs that we
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// want to produce are:
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// 0,0 0,1 0,2 0,3
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// 1,1 1,2 1,3
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// 2,2 2,3
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// 3,3
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// This triangle can be folded into a 5x2 rectangle:
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// 3,3 0,0 0,1 0,2 0,3
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// 2,2 2,3 1,1 1,2 1,3
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// If N is odd, say 5, then the 15 i,j pairs are:
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// 0,0 0,1 0,2 0,3 0,4
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// 1,1 1,2 1,3 1,4
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// 2,2 2,3 2,3
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// 3,3 3,4
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// 4,4
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// which folds to a 5x3 rectangle:
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// 0,0 0,1 0,2 0,3 0,4
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// 4,4 1,1 1,2 1,3 1,4
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// 3,3 3,4 2,2 2,3 2,4
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// All this function does is map the linear iteration position to a
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// location in the rectangle and work out the appropriate (i, j) for that
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// location.
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if (n & 1) {
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// Odd n. The tip of the triangle is on row 1.
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int w = n; // Width of the rectangle to unfold
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int i0 = k / w;
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int j0 = k % w;
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if (j0 >= i0) {
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*i = i0;
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*j = j0;
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} else {
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*i = n - i0;
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*j = *i + j0;
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}
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} else {
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// Even n. The tip of the triangle is on row 0, making it one wider.
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int w = n + 1;
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int i0 = k / w;
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int j0 = k % w;
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if (j0 > i0) {
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*i = i0;
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*j = j0 - 1;
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} else {
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*i = n - 1 - i0;
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*j = *i + j0;
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}
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}
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}
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} // namespace internal
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} // namespace ceres
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