forked from bartvdbraak/blender
6fb6a08bf8
Even tho it's currently only used by Libmv we might use it for something else in the future. Plus, it's actually where it logically belongs to.
733 lines
18 KiB
C++
733 lines
18 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 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: sameeragarwal@google.com (Sameer Agarwal)
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#include "ceres/linear_least_squares_problems.h"
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#include <cstdio>
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#include <string>
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#include <vector>
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#include "ceres/block_sparse_matrix.h"
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#include "ceres/block_structure.h"
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#include "ceres/casts.h"
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#include "ceres/file.h"
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#include "ceres/internal/scoped_ptr.h"
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#include "ceres/stringprintf.h"
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#include "ceres/triplet_sparse_matrix.h"
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#include "ceres/types.h"
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#include "glog/logging.h"
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namespace ceres {
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namespace internal {
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using std::string;
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LinearLeastSquaresProblem* CreateLinearLeastSquaresProblemFromId(int id) {
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switch (id) {
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case 0:
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return LinearLeastSquaresProblem0();
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case 1:
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return LinearLeastSquaresProblem1();
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case 2:
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return LinearLeastSquaresProblem2();
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case 3:
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return LinearLeastSquaresProblem3();
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case 4:
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return LinearLeastSquaresProblem4();
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default:
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LOG(FATAL) << "Unknown problem id requested " << id;
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}
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return NULL;
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}
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/*
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A = [1 2]
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[3 4]
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[6 -10]
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b = [ 8
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18
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-18]
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x = [2
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3]
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D = [1
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2]
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x_D = [1.78448275;
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2.82327586;]
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*/
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LinearLeastSquaresProblem* LinearLeastSquaresProblem0() {
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LinearLeastSquaresProblem* problem = new LinearLeastSquaresProblem;
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TripletSparseMatrix* A = new TripletSparseMatrix(3, 2, 6);
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problem->b.reset(new double[3]);
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problem->D.reset(new double[2]);
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problem->x.reset(new double[2]);
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problem->x_D.reset(new double[2]);
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int* Ai = A->mutable_rows();
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int* Aj = A->mutable_cols();
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double* Ax = A->mutable_values();
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int counter = 0;
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for (int i = 0; i < 3; ++i) {
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for (int j = 0; j< 2; ++j) {
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Ai[counter] = i;
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Aj[counter] = j;
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++counter;
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}
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}
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Ax[0] = 1.;
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Ax[1] = 2.;
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Ax[2] = 3.;
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Ax[3] = 4.;
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Ax[4] = 6;
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Ax[5] = -10;
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A->set_num_nonzeros(6);
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problem->A.reset(A);
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problem->b[0] = 8;
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problem->b[1] = 18;
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problem->b[2] = -18;
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problem->x[0] = 2.0;
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problem->x[1] = 3.0;
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problem->D[0] = 1;
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problem->D[1] = 2;
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problem->x_D[0] = 1.78448275;
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problem->x_D[1] = 2.82327586;
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return problem;
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}
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/*
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A = [1 0 | 2 0 0
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3 0 | 0 4 0
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0 5 | 0 0 6
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0 7 | 8 0 0
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0 9 | 1 0 0
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0 0 | 1 1 1]
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b = [0
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1
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2
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3
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4
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5]
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c = A'* b = [ 3
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67
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33
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9
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17]
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A'A = [10 0 2 12 0
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0 155 65 0 30
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2 65 70 1 1
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12 0 1 17 1
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0 30 1 1 37]
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S = [ 42.3419 -1.4000 -11.5806
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-1.4000 2.6000 1.0000
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11.5806 1.0000 31.1935]
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r = [ 4.3032
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5.4000
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5.0323]
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S\r = [ 0.2102
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2.1367
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0.1388]
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A\b = [-2.3061
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0.3172
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0.2102
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2.1367
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0.1388]
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*/
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// The following two functions create a TripletSparseMatrix and a
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// BlockSparseMatrix version of this problem.
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// TripletSparseMatrix version.
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LinearLeastSquaresProblem* LinearLeastSquaresProblem1() {
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int num_rows = 6;
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int num_cols = 5;
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LinearLeastSquaresProblem* problem = new LinearLeastSquaresProblem;
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TripletSparseMatrix* A = new TripletSparseMatrix(num_rows,
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num_cols,
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num_rows * num_cols);
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problem->b.reset(new double[num_rows]);
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problem->D.reset(new double[num_cols]);
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problem->num_eliminate_blocks = 2;
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int* rows = A->mutable_rows();
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int* cols = A->mutable_cols();
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double* values = A->mutable_values();
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int nnz = 0;
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// Row 1
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{
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rows[nnz] = 0;
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cols[nnz] = 0;
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values[nnz++] = 1;
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rows[nnz] = 0;
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cols[nnz] = 2;
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values[nnz++] = 2;
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}
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// Row 2
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{
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rows[nnz] = 1;
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cols[nnz] = 0;
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values[nnz++] = 3;
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rows[nnz] = 1;
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cols[nnz] = 3;
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values[nnz++] = 4;
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}
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// Row 3
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{
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rows[nnz] = 2;
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cols[nnz] = 1;
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values[nnz++] = 5;
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rows[nnz] = 2;
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cols[nnz] = 4;
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values[nnz++] = 6;
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}
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// Row 4
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{
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rows[nnz] = 3;
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cols[nnz] = 1;
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values[nnz++] = 7;
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rows[nnz] = 3;
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cols[nnz] = 2;
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values[nnz++] = 8;
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}
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// Row 5
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{
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rows[nnz] = 4;
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cols[nnz] = 1;
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values[nnz++] = 9;
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rows[nnz] = 4;
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cols[nnz] = 2;
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values[nnz++] = 1;
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}
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// Row 6
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{
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rows[nnz] = 5;
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cols[nnz] = 2;
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values[nnz++] = 1;
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rows[nnz] = 5;
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cols[nnz] = 3;
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values[nnz++] = 1;
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rows[nnz] = 5;
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cols[nnz] = 4;
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values[nnz++] = 1;
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}
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A->set_num_nonzeros(nnz);
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CHECK(A->IsValid());
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problem->A.reset(A);
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for (int i = 0; i < num_cols; ++i) {
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problem->D.get()[i] = 1;
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}
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for (int i = 0; i < num_rows; ++i) {
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problem->b.get()[i] = i;
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}
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return problem;
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}
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// BlockSparseMatrix version
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LinearLeastSquaresProblem* LinearLeastSquaresProblem2() {
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int num_rows = 6;
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int num_cols = 5;
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LinearLeastSquaresProblem* problem = new LinearLeastSquaresProblem;
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problem->b.reset(new double[num_rows]);
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problem->D.reset(new double[num_cols]);
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problem->num_eliminate_blocks = 2;
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CompressedRowBlockStructure* bs = new CompressedRowBlockStructure;
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scoped_array<double> values(new double[num_rows * num_cols]);
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for (int c = 0; c < num_cols; ++c) {
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bs->cols.push_back(Block());
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bs->cols.back().size = 1;
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bs->cols.back().position = c;
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}
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int nnz = 0;
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// Row 1
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{
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values[nnz++] = 1;
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values[nnz++] = 2;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 0;
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row.cells.push_back(Cell(0, 0));
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row.cells.push_back(Cell(2, 1));
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}
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// Row 2
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{
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values[nnz++] = 3;
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values[nnz++] = 4;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 1;
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row.cells.push_back(Cell(0, 2));
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row.cells.push_back(Cell(3, 3));
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}
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// Row 3
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{
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values[nnz++] = 5;
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values[nnz++] = 6;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 2;
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row.cells.push_back(Cell(1, 4));
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row.cells.push_back(Cell(4, 5));
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}
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// Row 4
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{
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values[nnz++] = 7;
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values[nnz++] = 8;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 3;
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row.cells.push_back(Cell(1, 6));
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row.cells.push_back(Cell(2, 7));
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}
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// Row 5
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{
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values[nnz++] = 9;
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values[nnz++] = 1;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 4;
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row.cells.push_back(Cell(1, 8));
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row.cells.push_back(Cell(2, 9));
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}
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// Row 6
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{
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values[nnz++] = 1;
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values[nnz++] = 1;
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values[nnz++] = 1;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 5;
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row.cells.push_back(Cell(2, 10));
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row.cells.push_back(Cell(3, 11));
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row.cells.push_back(Cell(4, 12));
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}
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BlockSparseMatrix* A = new BlockSparseMatrix(bs);
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memcpy(A->mutable_values(), values.get(), nnz * sizeof(*A->values()));
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for (int i = 0; i < num_cols; ++i) {
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problem->D.get()[i] = 1;
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}
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for (int i = 0; i < num_rows; ++i) {
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problem->b.get()[i] = i;
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}
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problem->A.reset(A);
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return problem;
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}
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/*
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A = [1 0
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3 0
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0 5
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0 7
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0 9
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0 0]
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b = [0
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1
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2
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3
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4
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5]
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*/
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// BlockSparseMatrix version
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LinearLeastSquaresProblem* LinearLeastSquaresProblem3() {
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int num_rows = 5;
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int num_cols = 2;
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LinearLeastSquaresProblem* problem = new LinearLeastSquaresProblem;
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problem->b.reset(new double[num_rows]);
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problem->D.reset(new double[num_cols]);
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problem->num_eliminate_blocks = 2;
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CompressedRowBlockStructure* bs = new CompressedRowBlockStructure;
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scoped_array<double> values(new double[num_rows * num_cols]);
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for (int c = 0; c < num_cols; ++c) {
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bs->cols.push_back(Block());
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bs->cols.back().size = 1;
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bs->cols.back().position = c;
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}
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int nnz = 0;
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// Row 1
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{
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values[nnz++] = 1;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 0;
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row.cells.push_back(Cell(0, 0));
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}
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// Row 2
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{
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values[nnz++] = 3;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 1;
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row.cells.push_back(Cell(0, 1));
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}
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// Row 3
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{
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values[nnz++] = 5;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 2;
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row.cells.push_back(Cell(1, 2));
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}
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// Row 4
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{
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values[nnz++] = 7;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 3;
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row.cells.push_back(Cell(1, 3));
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}
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// Row 5
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{
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values[nnz++] = 9;
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 1;
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row.block.position = 4;
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row.cells.push_back(Cell(1, 4));
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}
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BlockSparseMatrix* A = new BlockSparseMatrix(bs);
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memcpy(A->mutable_values(), values.get(), nnz * sizeof(*A->values()));
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for (int i = 0; i < num_cols; ++i) {
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problem->D.get()[i] = 1;
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}
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for (int i = 0; i < num_rows; ++i) {
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problem->b.get()[i] = i;
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}
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problem->A.reset(A);
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return problem;
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}
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/*
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A = [1 2 0 0 0 1 1
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1 4 0 0 0 5 6
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0 0 9 0 0 3 1]
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b = [0
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1
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2]
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*/
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// BlockSparseMatrix version
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//
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// This problem has the unique property that it has two different
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// sized f-blocks, but only one of them occurs in the rows involving
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// the one e-block. So performing Schur elimination on this problem
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// tests the Schur Eliminator's ability to handle non-e-block rows
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// correctly when their structure does not conform to the static
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// structure determined by DetectStructure.
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//
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// NOTE: This problem is too small and rank deficient to be solved without
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// the diagonal regularization.
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LinearLeastSquaresProblem* LinearLeastSquaresProblem4() {
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int num_rows = 3;
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int num_cols = 7;
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LinearLeastSquaresProblem* problem = new LinearLeastSquaresProblem;
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problem->b.reset(new double[num_rows]);
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problem->D.reset(new double[num_cols]);
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problem->num_eliminate_blocks = 1;
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CompressedRowBlockStructure* bs = new CompressedRowBlockStructure;
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scoped_array<double> values(new double[num_rows * num_cols]);
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// Column block structure
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bs->cols.push_back(Block());
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bs->cols.back().size = 2;
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bs->cols.back().position = 0;
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bs->cols.push_back(Block());
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bs->cols.back().size = 3;
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bs->cols.back().position = 2;
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bs->cols.push_back(Block());
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bs->cols.back().size = 2;
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bs->cols.back().position = 5;
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int nnz = 0;
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// Row 1 & 2
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{
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bs->rows.push_back(CompressedRow());
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CompressedRow& row = bs->rows.back();
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row.block.size = 2;
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row.block.position = 0;
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row.cells.push_back(Cell(0, nnz));
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values[nnz++] = 1;
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values[nnz++] = 2;
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|
values[nnz++] = 1;
|
|
values[nnz++] = 4;
|
|
|
|
row.cells.push_back(Cell(2, nnz));
|
|
values[nnz++] = 1;
|
|
values[nnz++] = 1;
|
|
values[nnz++] = 5;
|
|
values[nnz++] = 6;
|
|
}
|
|
|
|
// Row 3
|
|
{
|
|
bs->rows.push_back(CompressedRow());
|
|
CompressedRow& row = bs->rows.back();
|
|
row.block.size = 1;
|
|
row.block.position = 2;
|
|
|
|
row.cells.push_back(Cell(1, nnz));
|
|
values[nnz++] = 9;
|
|
values[nnz++] = 0;
|
|
values[nnz++] = 0;
|
|
|
|
row.cells.push_back(Cell(2, nnz));
|
|
values[nnz++] = 3;
|
|
values[nnz++] = 1;
|
|
}
|
|
|
|
BlockSparseMatrix* A = new BlockSparseMatrix(bs);
|
|
memcpy(A->mutable_values(), values.get(), nnz * sizeof(*A->values()));
|
|
|
|
for (int i = 0; i < num_cols; ++i) {
|
|
problem->D.get()[i] = (i + 1) * 100;
|
|
}
|
|
|
|
for (int i = 0; i < num_rows; ++i) {
|
|
problem->b.get()[i] = i;
|
|
}
|
|
|
|
problem->A.reset(A);
|
|
return problem;
|
|
}
|
|
|
|
namespace {
|
|
bool DumpLinearLeastSquaresProblemToConsole(const SparseMatrix* A,
|
|
const double* D,
|
|
const double* b,
|
|
const double* x,
|
|
int num_eliminate_blocks) {
|
|
CHECK_NOTNULL(A);
|
|
Matrix AA;
|
|
A->ToDenseMatrix(&AA);
|
|
LOG(INFO) << "A^T: \n" << AA.transpose();
|
|
|
|
if (D != NULL) {
|
|
LOG(INFO) << "A's appended diagonal:\n"
|
|
<< ConstVectorRef(D, A->num_cols());
|
|
}
|
|
|
|
if (b != NULL) {
|
|
LOG(INFO) << "b: \n" << ConstVectorRef(b, A->num_rows());
|
|
}
|
|
|
|
if (x != NULL) {
|
|
LOG(INFO) << "x: \n" << ConstVectorRef(x, A->num_cols());
|
|
}
|
|
return true;
|
|
}
|
|
|
|
void WriteArrayToFileOrDie(const string& filename,
|
|
const double* x,
|
|
const int size) {
|
|
CHECK_NOTNULL(x);
|
|
VLOG(2) << "Writing array to: " << filename;
|
|
FILE* fptr = fopen(filename.c_str(), "w");
|
|
CHECK_NOTNULL(fptr);
|
|
for (int i = 0; i < size; ++i) {
|
|
fprintf(fptr, "%17f\n", x[i]);
|
|
}
|
|
fclose(fptr);
|
|
}
|
|
|
|
bool DumpLinearLeastSquaresProblemToTextFile(const string& filename_base,
|
|
const SparseMatrix* A,
|
|
const double* D,
|
|
const double* b,
|
|
const double* x,
|
|
int num_eliminate_blocks) {
|
|
CHECK_NOTNULL(A);
|
|
LOG(INFO) << "writing to: " << filename_base << "*";
|
|
|
|
string matlab_script;
|
|
StringAppendF(&matlab_script,
|
|
"function lsqp = load_trust_region_problem()\n");
|
|
StringAppendF(&matlab_script,
|
|
"lsqp.num_rows = %d;\n", A->num_rows());
|
|
StringAppendF(&matlab_script,
|
|
"lsqp.num_cols = %d;\n", A->num_cols());
|
|
|
|
{
|
|
string filename = filename_base + "_A.txt";
|
|
FILE* fptr = fopen(filename.c_str(), "w");
|
|
CHECK_NOTNULL(fptr);
|
|
A->ToTextFile(fptr);
|
|
fclose(fptr);
|
|
StringAppendF(&matlab_script,
|
|
"tmp = load('%s', '-ascii');\n", filename.c_str());
|
|
StringAppendF(
|
|
&matlab_script,
|
|
"lsqp.A = sparse(tmp(:, 1) + 1, tmp(:, 2) + 1, tmp(:, 3), %d, %d);\n",
|
|
A->num_rows(),
|
|
A->num_cols());
|
|
}
|
|
|
|
|
|
if (D != NULL) {
|
|
string filename = filename_base + "_D.txt";
|
|
WriteArrayToFileOrDie(filename, D, A->num_cols());
|
|
StringAppendF(&matlab_script,
|
|
"lsqp.D = load('%s', '-ascii');\n", filename.c_str());
|
|
}
|
|
|
|
if (b != NULL) {
|
|
string filename = filename_base + "_b.txt";
|
|
WriteArrayToFileOrDie(filename, b, A->num_rows());
|
|
StringAppendF(&matlab_script,
|
|
"lsqp.b = load('%s', '-ascii');\n", filename.c_str());
|
|
}
|
|
|
|
if (x != NULL) {
|
|
string filename = filename_base + "_x.txt";
|
|
WriteArrayToFileOrDie(filename, x, A->num_cols());
|
|
StringAppendF(&matlab_script,
|
|
"lsqp.x = load('%s', '-ascii');\n", filename.c_str());
|
|
}
|
|
|
|
string matlab_filename = filename_base + ".m";
|
|
WriteStringToFileOrDie(matlab_script, matlab_filename);
|
|
return true;
|
|
}
|
|
} // namespace
|
|
|
|
bool DumpLinearLeastSquaresProblem(const string& filename_base,
|
|
DumpFormatType dump_format_type,
|
|
const SparseMatrix* A,
|
|
const double* D,
|
|
const double* b,
|
|
const double* x,
|
|
int num_eliminate_blocks) {
|
|
switch (dump_format_type) {
|
|
case CONSOLE:
|
|
return DumpLinearLeastSquaresProblemToConsole(A, D, b, x,
|
|
num_eliminate_blocks);
|
|
case TEXTFILE:
|
|
return DumpLinearLeastSquaresProblemToTextFile(filename_base,
|
|
A, D, b, x,
|
|
num_eliminate_blocks);
|
|
default:
|
|
LOG(FATAL) << "Unknown DumpFormatType " << dump_format_type;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
} // namespace internal
|
|
} // namespace ceres
|