// Ceres Solver - A fast non-linear least squares minimizer
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// http://code.google.com/p/ceres-solver/
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// Author: kushalav@google.com (Avanish Kushal)
//         sameeragarwal@google.com (Sameer Agarwal)
//
// Functions to manipulate visibility information from the block
// structure of sparse matrices.

#ifndef CERES_INTERNAL_VISIBILITY_H_
#define CERES_INTERNAL_VISIBILITY_H_

#include <set>
#include <vector>
#include "ceres/graph.h"

namespace ceres {
namespace internal {

class CompressedRowBlockStructure;

// Given a compressed row block structure, computes the set of
// e_blocks "visible" to each f_block. If an e_block co-occurs with an
// f_block in a residual block, it is visible to the f_block. The
// first num_eliminate_blocks columns blocks are e_blocks and the rest
// f_blocks.
//
// In a structure from motion problem, e_blocks correspond to 3D
// points and f_blocks correspond to cameras.
void ComputeVisibility(const CompressedRowBlockStructure& block_structure,
                       int num_eliminate_blocks,
                       vector<set<int> >* visibility);

// Given f_block visibility as computed by the ComputeVisibility
// function above, construct and return a graph whose vertices are
// f_blocks and an edge connects two vertices if they have atleast one
// e_block in common. The weight of this edge is normalized dot
// product between the visibility vectors of the two
// vertices/f_blocks.
//
// This graph reflects the sparsity structure of reduced camera
// matrix/Schur complement matrix obtained by eliminating the e_blocks
// from the normal equations.
//
// Caller acquires ownership of the returned Graph pointer
// (heap-allocated).
Graph<int>* CreateSchurComplementGraph(const vector<set<int> >& visibility);

}  // namespace internal
}  // namespace ceres

#endif  // CERES_INTERNAL_VISIBILITY_H_