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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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)
+//
+// Utility routines for validating arrays.
+//
+// These are useful for detecting two common class of errors.
+//
+// 1. Uninitialized memory - where the user for some reason did not
+// compute part of an array, but the code expects it.
+//
+// 2. Numerical failure while computing the cost/residual/jacobian,
+// e.g. NaN, infinities etc. This is particularly useful since the
+// automatic differentiation code does computations that are not
+// evident to the user and can silently generate hard to debug errors.
+
+#ifndef CERES_INTERNAL_ARRAY_UTILS_H_
+#define CERES_INTERNAL_ARRAY_UTILS_H_
+
+#include <string>
+#include "ceres/internal/port.h"
+
+namespace ceres {
+namespace internal {
+
+// Fill the array x with an impossible value that the user code is
+// never expected to compute.
+void InvalidateArray(int size, double* x);
+
+// Check if all the entries of the array x are valid, i.e. all the
+// values in the array should be finite and none of them should be
+// equal to the "impossible" value used by InvalidateArray.
+bool IsArrayValid(int size, const double* x);
+
+// If the array contains an invalid value, return the index for it,
+// otherwise return size.
+int FindInvalidValue(const int size, const double* x);
+
+// Utility routine to print an array of doubles to a string. If the
+// array pointer is NULL, it is treated as an array of zeros.
+void AppendArrayToString(const int size, const double* x, std::string* result);
+
+// This routine takes an array of integer values, sorts and uniques
+// them and then maps each value in the array to its position in the
+// sorted+uniqued array. By doing this, if there are k unique
+// values in the array, each value is replaced by an integer in the
+// range [0, k-1], while preserving their relative order.
+//
+// For example
+//
+// [1 0 3 5 0 1 5]
+//
+// gets mapped to
+//
+// [1 0 2 3 0 1 3]
+void MapValuesToContiguousRange(int size, int* array);
+
+}  // namespace internal
+}  // namespace ceres
+
+#endif  // CERES_INTERNAL_ARRAY_UTILS_H_