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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 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
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// 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/context_impl.h"
#include "ceres/cuda_buffer.h"
#include "ceres/linear_solver.h"
#ifndef CERES_NO_CUDA
#include "ceres/context_impl.h"
#include "cuda_runtime.h"
#include "cusolverDn.h"
#endif // CERES_NO_CUDA
namespace ceres::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 LinearSolverTerminationType::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_;
};
class CERES_NO_EXPORT FloatEigenDenseCholesky 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:
Eigen::MatrixXf lhs_;
Eigen::VectorXf rhs_;
Eigen::VectorXf solution_;
using LLTType = Eigen::LLT<Eigen::MatrixXf, 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_ =
LinearSolverTerminationType::FATAL_ERROR;
};
class CERES_NO_EXPORT FloatLAPACKDenseCholesky 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:
Eigen::MatrixXf lhs_;
Eigen::VectorXf rhs_and_solution_;
int num_cols_ = -1;
LinearSolverTerminationType termination_type_ =
LinearSolverTerminationType::FATAL_ERROR;
};
#endif // CERES_NO_LAPACK
class DenseIterativeRefiner;
// Computes an initial solution using the given instance of
// DenseCholesky, and then refines it using the DenseIterativeRefiner.
class CERES_NO_EXPORT RefinedDenseCholesky final : public DenseCholesky {
public:
RefinedDenseCholesky(
std::unique_ptr<DenseCholesky> dense_cholesky,
std::unique_ptr<DenseIterativeRefiner> iterative_refiner);
~RefinedDenseCholesky() override;
LinearSolverTerminationType Factorize(int num_cols,
double* lhs,
std::string* message) override;
LinearSolverTerminationType Solve(const double* rhs,
double* solution,
std::string* message) override;
private:
std::unique_ptr<DenseCholesky> dense_cholesky_;
std::unique_ptr<DenseIterativeRefiner> iterative_refiner_;
double* lhs_ = nullptr;
int num_cols_;
};
#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:
explicit CUDADenseCholesky(ContextImpl* context);
ContextImpl* context_ = 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
// factorization of lhs is valid.
LinearSolverTerminationType factorize_result_ =
LinearSolverTerminationType::FATAL_ERROR;
};
// A mixed-precision iterative refinement dense Cholesky solver using FP32 CUDA
// Dense Cholesky for inner iterations, and FP64 outer refinements.
// This class implements a modified version of the "Classical iterative
// refinement" (Algorithm 4.1) from the following paper:
// Haidar, Azzam, Harun Bayraktar, Stanimire Tomov, Jack Dongarra, and Nicholas
// J. Higham. "Mixed-precision iterative refinement using tensor cores on GPUs
// to accelerate solution of linear systems." Proceedings of the Royal Society A
// 476, no. 2243 (2020): 20200110.
//
// The three key modifications from Algorithm 4.1 in the paper are:
// 1. We use Cholesky factorization instead of LU factorization since our A is
// symmetric positive definite.
// 2. During the solution update, the up-cast and accumulation is performed in
// one step with a custom kernel.
class CERES_NO_EXPORT CUDADenseCholeskyMixedPrecision final
: public DenseCholesky {
public:
static std::unique_ptr<CUDADenseCholeskyMixedPrecision> Create(
const LinearSolver::Options& options);
CUDADenseCholeskyMixedPrecision(const CUDADenseCholeskyMixedPrecision&) =
delete;
CUDADenseCholeskyMixedPrecision& operator=(
const CUDADenseCholeskyMixedPrecision&) = delete;
LinearSolverTerminationType Factorize(int num_cols,
double* lhs,
std::string* message) override;
LinearSolverTerminationType Solve(const double* rhs,
double* solution,
std::string* message) override;
private:
CUDADenseCholeskyMixedPrecision(ContextImpl* context,
int max_num_refinement_iterations);
// Helper function to wrap Cuda boilerplate needed to call Spotrf.
LinearSolverTerminationType CudaCholeskyFactorize(std::string* message);
// Helper function to wrap Cuda boilerplate needed to call Spotrs.
LinearSolverTerminationType CudaCholeskySolve(std::string* message);
// Picks up the cuSolverDN and cuStream handles from the context in the
// options, and the number of refinement iterations from the options. If
// the context is unable to initialize CUDA, returns false with a
// human-readable message indicating the reason.
bool Init(const LinearSolver::Options& options, std::string* message);
ContextImpl* context_ = nullptr;
// Number of columns in the A matrix, to be cached between calls to *Factorize
// and *Solve.
size_t num_cols_ = 0;
CudaBuffer<double> lhs_fp64_;
CudaBuffer<double> rhs_fp64_;
CudaBuffer<float> lhs_fp32_;
// Scratch space for cuSOLVER on the GPU.
CudaBuffer<float> device_workspace_;
// Required for error handling with cuSOLVER.
CudaBuffer<int> error_;
// Solution to lhs * x = rhs.
CudaBuffer<double> x_fp64_;
// Incremental correction to x.
CudaBuffer<float> correction_fp32_;
// Residual to iterative refinement.
CudaBuffer<float> residual_fp32_;
CudaBuffer<double> residual_fp64_;
// Number of inner refinement iterations to perform.
int max_num_refinement_iterations_ = 0;
// Cache the result of Factorize to ensure that when Solve is called, the
// factorization of lhs is valid.
LinearSolverTerminationType factorize_result_ =
LinearSolverTerminationType::FATAL_ERROR;
};
#endif // CERES_NO_CUDA
} // namespace ceres::internal
#endif // CERES_INTERNAL_DENSE_CHOLESKY_H_