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+// 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_DENSE_CHOLESKY_H_
+#define CERES_INTERNAL_DENSE_CHOLESKY_H_
+
+// This include must come before any #ifndef check on Ceres compile options.
+// clang-format off
+#include "ceres/internal/config.h"
+// clang-format on
+
+#include <memory>
+#include <vector>
+
+#include "Eigen/Dense"
+#include "ceres/cuda_buffer.h"
+#include "ceres/linear_solver.h"
+#include "glog/logging.h"
+#ifndef CERES_NO_CUDA
+#include "ceres/context_impl.h"
+#include "cuda_runtime.h"
+#include "cusolverDn.h"
+#endif // CERES_NO_CUDA
+
+namespace ceres {
+namespace internal {
+
+// An interface that abstracts away the internal details of various dense linear
+// algebra libraries and offers a simple API for solving dense symmetric
+// positive definite linear systems using a Cholesky factorization.
+class CERES_NO_EXPORT DenseCholesky {
+ public:
+ static std::unique_ptr<DenseCholesky> Create(
+ const LinearSolver::Options& options);
+
+ virtual ~DenseCholesky();
+
+ // Computes the Cholesky factorization of the given matrix.
+ //
+ // The input matrix lhs is assumed to be a column-major num_cols x num_cols
+ // matrix, that is symmetric positive definite with its lower triangular part
+ // containing the left hand side of the linear system being solved.
+ //
+ // The input matrix lhs may be modified by the implementation to store the
+ // factorization, irrespective of whether the factorization succeeds or not.
+ // As a result it is the user's responsibility to ensure that lhs is valid
+ // when Solve is called.
+ virtual LinearSolverTerminationType Factorize(int num_cols,
+ double* lhs,
+ std::string* message) = 0;
+
+ // Computes the solution to the equation
+ //
+ // lhs * solution = rhs
+ //
+ // Calling Solve without calling Factorize is undefined behaviour. It is the
+ // user's responsibility to ensure that the input matrix lhs passed to
+ // Factorize has not been freed/modified when Solve is called.
+ virtual LinearSolverTerminationType Solve(const double* rhs,
+ double* solution,
+ std::string* message) = 0;
+
+ // Convenience method which combines a call to Factorize and Solve. Solve is
+ // only called if Factorize returns LINEAR_SOLVER_SUCCESS.
+ //
+ // The input matrix lhs may be modified by the implementation to store the
+ // factorization, irrespective of whether the method succeeds or not. It is
+ // the user's responsibility to ensure that lhs is valid if and when Solve is
+ // called again after this call.
+ LinearSolverTerminationType FactorAndSolve(int num_cols,
+ double* lhs,
+ const double* rhs,
+ double* solution,
+ std::string* message);
+};
+
+class CERES_NO_EXPORT EigenDenseCholesky final : public DenseCholesky {
+ public:
+ LinearSolverTerminationType Factorize(int num_cols,
+ double* lhs,
+ std::string* message) override;
+ LinearSolverTerminationType Solve(const double* rhs,
+ double* solution,
+ std::string* message) override;
+
+ private:
+ using LLTType = Eigen::LLT<Eigen::Ref<Eigen::MatrixXd>, Eigen::Lower>;
+ std::unique_ptr<LLTType> llt_;
+};
+
+#ifndef CERES_NO_LAPACK
+class CERES_NO_EXPORT LAPACKDenseCholesky final : public DenseCholesky {
+ public:
+ LinearSolverTerminationType Factorize(int num_cols,
+ double* lhs,
+ std::string* message) override;
+ LinearSolverTerminationType Solve(const double* rhs,
+ double* solution,
+ std::string* message) override;
+
+ private:
+ double* lhs_ = nullptr;
+ int num_cols_ = -1;
+ LinearSolverTerminationType termination_type_ = LINEAR_SOLVER_FATAL_ERROR;
+};
+#endif // CERES_NO_LAPACK
+
+#ifndef CERES_NO_CUDA
+// CUDA implementation of DenseCholesky using the cuSolverDN library using the
+// 32-bit legacy interface for maximum compatibility.
+class CERES_NO_EXPORT CUDADenseCholesky final : public DenseCholesky {
+ public:
+ static std::unique_ptr<CUDADenseCholesky> Create(
+ const LinearSolver::Options& options);
+ CUDADenseCholesky(const CUDADenseCholesky&) = delete;
+ CUDADenseCholesky& operator=(const CUDADenseCholesky&) = delete;
+ LinearSolverTerminationType Factorize(int num_cols,
+ double* lhs,
+ std::string* message) override;
+ LinearSolverTerminationType Solve(const double* rhs,
+ double* solution,
+ std::string* message) override;
+
+ private:
+ CUDADenseCholesky() = default;
+ // Picks up the cuSolverDN and cuStream handles from the context. If
+ // the context is unable to initialize CUDA, returns false with a
+ // human-readable message indicating the reason.
+ bool Init(ContextImpl* context, std::string* message);
+
+ // Handle to the cuSOLVER context.
+ cusolverDnHandle_t cusolver_handle_ = nullptr;
+ // CUDA device stream.
+ cudaStream_t stream_ = nullptr;
+ // Number of columns in the A matrix, to be cached between calls to *Factorize
+ // and *Solve.
+ size_t num_cols_ = 0;
+ // GPU memory allocated for the A matrix (lhs matrix).
+ CudaBuffer<double> lhs_;
+ // GPU memory allocated for the B matrix (rhs vector).
+ CudaBuffer<double> rhs_;
+ // Scratch space for cuSOLVER on the GPU.
+ CudaBuffer<double> device_workspace_;
+ // Required for error handling with cuSOLVER.
+ CudaBuffer<int> error_;
+ // Cache the result of Factorize to ensure that when Solve is called, the
+ // factiorization of lhs is valid.
+ LinearSolverTerminationType factorize_result_ = LINEAR_SOLVER_FATAL_ERROR;
+};
+
+#endif // CERES_NO_CUDA
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_INTERNAL_DENSE_CHOLESKY_H_