Refactor ConjugateGradientsSolver

1. Convert it from a class to a template function. Where the
   template parameter is "DenseVectorType". This allows us
   to have a single implementation of Conjugate Gradients
   without worrying about where the matrix and the vectors
   are stored or what their internal representation is.

   For the case of CPU based vectors, we abstract operations
   on Eigen vectors using eigen_vector_ops.
2. Introduce ConjugateGradientsLinearOperator which is
   templated on DenseVectorType. It is the matrix vector
   multiplication abstraction.
3. Port the tests and all usages of ConjugateGradientsSolver
   to this new implementation.
4. Introduce Eigen::Vector based RightMultiply and LeftMultiply
   methods into LinearOperator which by default delete to the
   bare pointer based interfaces.
5. Add an identity preconditioner.

These changes are being made in preparation for adding a CUDA
based CGNR solver.

Change-Id: I9da36dc6c131856dd1a4aa7e645aaf12d25dd79b

internal/ceres/eigen_vector_ops.h

@@ -0,0 +1,52 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2022 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)
+
+#ifndef CERES_INTERNAL_EIGEN_VECTOR_OPS_H_
+#define CERES_INTERNAL_EIGEN_VECTOR_OPS_H_
+
+#include "ceres/internal/eigen.h"
+
+namespace ceres::internal {
+
+// Blas1 operations on Eigen vectors. These functions are needed as an
+// abstraction layer so that we can use different versions of a vector style
+// object in the conjugate gradients linear solver.
+inline double Norm(const Vector& x) { return x.norm(); }
+inline void SetZero(Vector& x) { x.setZero(); }
+inline void Axpby(
+    double a, const Vector& x, double b, const Vector& y, Vector& z) {
+  z = a * x + b * y;
+}
+inline double Dot(const Vector& x, const Vector& y) { return x.dot(y); }
+inline void Copy(const Vector& from, Vector& to) { to = from; }
+
+}  // namespace ceres::internal
+
+#endif  // CERES_INTERNAL_EIGEN_VECTOR_OPS_H_