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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 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: sameeragarwal@google.com (Sameer Agarwal)
+
+#include "ceres/compressed_row_sparse_matrix.h"
+
+namespace ceres {
+namespace internal {
+
+// Incomplete LQ factorization as described in
+//
+// Preconditioning techniques for indefinite and nonsymmetric linear
+// systems. Yousef Saad, Preprint RIACS-ILQ-TR, RIACS, NASA Ames
+// Research Center, Moffett Field, CA, 1987.
+//
+// An incomplete LQ factorization of a matrix A is a decomposition
+//
+//   A = LQ + E
+//
+// Where L is a lower triangular matrix, and Q is a near orthonormal
+// matrix. The extent of orthonormality depends on E. E is the "drop"
+// matrix. Each row of L has a maximum of l_level_of_fill entries, and
+// all non-zero entries are within l_drop_tolerance of the largest
+// entry. Each row of Q has a maximum of q_level_of_fill entries and
+// all non-zero entries are within q_drop_tolerance of the largest
+// entry.
+//
+// E is the error of the incomplete factorization.
+//
+// The purpose of incomplete factorizations is preconditioning and
+// there one only needs the L matrix, therefore this function just
+// returns L.
+//
+// Caller owns the result.
+CompressedRowSparseMatrix* IncompleteLQFactorization(
+    const CompressedRowSparseMatrix& matrix,
+    const int l_level_of_fill,
+    const double l_drop_tolerance,
+    const int q_level_of_fill,
+    const double q_drop_tolerance);
+
+// In the row vector dense_row(0:num_cols), drop values smaller than
+// the max_value * drop_tolerance. Of the remaining non-zero values,
+// choose at most level_of_fill values and then add the resulting row
+// vector to matrix.
+//
+// scratch is used to prevent allocations inside this function. It is
+// assumed that scratch is of size matrix->num_cols().
+void DropEntriesAndAddRow(const Vector& dense_row,
+                          const int num_entries,
+                          const int level_of_fill,
+                          const double drop_tolerance,
+                          vector<pair<int, double> >* scratch,
+                          CompressedRowSparseMatrix* matrix);
+
+}  // namespace internal
+}  // namespace ceres