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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 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: moll.markus@arcor.de (Markus Moll)
+
+#ifndef CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
+#define CERES_INTERNAL_POLYNOMIAL_SOLVER_H_
+
+#include "ceres/internal/eigen.h"
+
+namespace ceres {
+namespace internal {
+
+// Use the companion matrix eigenvalues to determine the roots of the polynomial
+//
+//   sum_{i=0}^N polynomial(i) x^{N-i}.
+//
+// This function returns true on success, false otherwise.
+// Failure indicates that the polynomial is invalid (of size 0) or
+// that the eigenvalues of the companion matrix could not be computed.
+// On failure, a more detailed message will be written to LOG(ERROR).
+// If real is not NULL, the real parts of the roots will be returned in it.
+// Likewise, if imaginary is not NULL, imaginary parts will be returned in it.
+bool FindPolynomialRoots(const Vector& polynomial,
+                         Vector* real,
+                         Vector* imaginary);
+
+// Evaluate the polynomial at x using the Horner scheme.
+inline double EvaluatePolynomial(const Vector& polynomial, double x) {
+  double v = 0.0;
+  for (int i = 0; i < polynomial.size(); ++i) {
+    v = v * x + polynomial(i);
+  }
+  return v;
+}
+
+}  // namespace internal
+}  // namespace ceres
+
+#endif  // CERES_INTERNAL_POLYNOMIAL_SOLVER_H_