ceres-solver/internal/ceres/matrix.proto

// 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.
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//   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
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// 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;
}