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-// Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
-// http://code.google.com/p/ceres-solver/
-//
-// 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: keir@google.com (Keir Mierle)
-
-syntax = "proto2";
-
-package ceres.internal;
-
-message BlockProto {
-  // The span of the block.
-  optional int32 size = 1;
-
-  // Position along the row or column (depending on storage orientation).
-  optional int32 position = 2;
-}
-
-message CellProto {
-  // Column or row block id as appropriate.
-  optional int32 block_id = 1;
-
-  // Position in the values array the cell is located. Each cell is stored as a
-  // row-major chunk inside the values array.
-  optional int32 position = 2;
-}
-
-// A single row or column, depending on the matrix type.
-message CompressedRowProto {
-  optional BlockProto block = 2;
-  repeated CellProto cells = 1;
-}
-
-message BlockStructureProto {
-  repeated BlockProto cols = 1;
-  repeated CompressedRowProto rows = 2;
-}
-
-// A block sparse matrix, either in column major or row major format.
-message BlockSparseMatrixProto {
-  optional int64 num_rows = 2;
-  optional int64 num_cols = 3;
-  optional int64 num_nonzeros = 4;
-  repeated double values = 1 [packed=true];
-
-  optional BlockStructureProto block_structure = 5;
-}
-
-message TripletSparseMatrixProto {
-  optional int64 num_rows = 4;
-  optional int64 num_cols = 5;
-  optional int64 num_nonzeros = 6;
-
-  // The data is stored as three arrays. For each i, values(i) is stored at the
-  // location (rows(i), cols(i)). If the there are multiple entries with the
-  // same (rows(i), cols(i)), the values entries corresponding to them are
-  // summed up.
-  repeated int64 rows = 1 [packed=true];
-  repeated int64 cols = 2 [packed=true];
-  repeated double values = 3 [packed=true];
-}
-
-message CompressedRowSparseMatrixProto {
-  optional int64 num_rows = 4;
-  optional int64 num_cols = 5;
-
-  repeated int64 rows = 1 [packed=true];
-  repeated int64 cols = 2 [packed=true];
-  repeated double values = 3 [packed=true];
-}
-
-message DenseSparseMatrixProto {
-  optional int64 num_rows = 1;
-  optional int64 num_cols = 2;
-
-  // Entries are stored in row-major order.
-  repeated double values = 3 [packed=true];
-}
-
-// A sparse matrix. It is a union; only one field is permitted. If new sparse
-// implementations are added, update this proto accordingly.
-message SparseMatrixProto {
-  optional TripletSparseMatrixProto triplet_matrix = 1;
-  optional BlockSparseMatrixProto block_matrix = 2;
-  optional CompressedRowSparseMatrixProto compressed_row_matrix = 3;
-  optional DenseSparseMatrixProto dense_matrix = 4;
-}
-
-// A linear least squares problem.
-//
-// Given a matrix A, an optional diagonal matrix D as a vector, and a vector b,
-// the proto represents the following linear least squares problem.
-//
-//   | A | x = | b |
-//   | D |     | 0 |
-//
-// If D is empty, then the problem is considered to be
-//
-//   A x = b
-//
-// The desired solution for the problem is the vector x that solves the
-// following optimization problem:
-//
-//   arg min_x ||Ax - b||^2 + ||Dx||^2
-//
-// If x is present, then it is the expected solution to the
-// problem. The dimensions of A, b, x, and D should be consistent.
-message LinearLeastSquaresProblemProto {
-  optional SparseMatrixProto a = 1;
-  repeated double b = 2 [packed=true];
-  repeated double d = 3 [packed=true];
-  repeated double x = 4 [packed=true];
-  // If the problem is of SfM type, i.e it has a generalized
-  // bi-partite structure, then num_eliminate_blocks is the number of
-  // column blocks that are to eliminated in the formation of the
-  // Schur complement. For more details see
-  // explicit_schur_complement_solver.h.
-  optional int32 num_eliminate_blocks = 5;
-}