| // 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) |
| |
| #include "ceres/dense_qr.h" |
| |
| #include <algorithm> |
| #include <memory> |
| #include <string> |
| #ifndef CERES_NO_CUDA |
| #include "ceres/context_impl.h" |
| #include "cublas_v2.h" |
| #include "cusolverDn.h" |
| #endif // CERES_NO_CUDA |
| |
| #ifndef CERES_NO_LAPACK |
| |
| // LAPACK routines for solving a linear least squares problem using QR |
| // factorization. This is done in three stages: |
| // |
| // A * x = b |
| // Q * R * x = b (dgeqrf) |
| // R * x = Q' * b (dormqr) |
| // x = R^{-1} * Q'* b (dtrtrs) |
| |
| // clang-format off |
| |
| // Compute the QR factorization of a. |
| // |
| // a is an m x n column major matrix (Denoted by "A" in the above description) |
| // lda is the leading dimension of a. lda >= max(1, num_rows) |
| // tau is an array of size min(m,n). It contains the scalar factors of the |
| // elementary reflectors. |
| // work is an array of size max(1,lwork). On exit, if info=0, work[0] contains |
| // the optimal size of work. |
| // |
| // if lwork >= 1 it is the size of work. If lwork = -1, then a workspace query is assumed. |
| // dgeqrf computes the optimal size of the work array and returns it as work[0]. |
| // |
| // info = 0, successful exit. |
| // info < 0, if info = -i, then the i^th argument had illegal value. |
| extern "C" void dgeqrf_(const int* m, const int* n, double* a, const int* lda, |
| double* tau, double* work, const int* lwork, int* info); |
| |
| // Apply Q or Q' to b. |
| // |
| // b is a m times n column major matrix. |
| // size = 'L' applies Q or Q' on the left, size = 'R' applies Q or Q' on the right. |
| // trans = 'N', applies Q, trans = 'T', applies Q'. |
| // k is the number of elementary reflectors whose product defines the matrix Q. |
| // If size = 'L', m >= k >= 0 and if side = 'R', n >= k >= 0. |
| // a is an lda x k column major matrix containing the reflectors as returned by dgeqrf. |
| // ldb is the leading dimension of b. |
| // work is an array of size max(1, lwork) |
| // lwork if positive is the size of work. If lwork = -1, then a |
| // workspace query is assumed. |
| // |
| // info = 0, successful exit. |
| // info < 0, if info = -i, then the i^th argument had illegal value. |
| extern "C" void dormqr_(const char* side, const char* trans, const int* m, |
| const int* n ,const int* k, double* a, const int* lda, |
| double* tau, double* b, const int* ldb, double* work, |
| const int* lwork, int* info); |
| |
| // Solve a triangular system of the form A * x = b |
| // |
| // uplo = 'U', A is upper triangular. uplo = 'L' is lower triangular. |
| // trans = 'N', 'T', 'C' specifies the form - A, A^T, A^H. |
| // DIAG = 'N', A is not unit triangular. 'U' is unit triangular. |
| // n is the order of the matrix A. |
| // nrhs number of columns of b. |
| // a is a column major lda x n. |
| // b is a column major matrix of ldb x nrhs |
| // |
| // info = 0 successful. |
| // = -i < 0 i^th argument is an illegal value. |
| // = i > 0, i^th diagonal element of A is zero. |
| extern "C" void dtrtrs_(const char* uplo, const char* trans, const char* diag, |
| const int* n, const int* nrhs, double* a, const int* lda, |
| double* b, const int* ldb, int* info); |
| // clang-format on |
| |
| #endif |
| |
| namespace ceres::internal { |
| |
| DenseQR::~DenseQR() = default; |
| |
| std::unique_ptr<DenseQR> DenseQR::Create(const LinearSolver::Options& options) { |
| std::unique_ptr<DenseQR> dense_qr; |
| |
| switch (options.dense_linear_algebra_library_type) { |
| case EIGEN: |
| dense_qr = std::make_unique<EigenDenseQR>(); |
| break; |
| |
| case LAPACK: |
| #ifndef CERES_NO_LAPACK |
| dense_qr = std::make_unique<LAPACKDenseQR>(); |
| break; |
| #else |
| LOG(FATAL) << "Ceres was compiled without support for LAPACK."; |
| #endif |
| |
| case CUDA: |
| #ifndef CERES_NO_CUDA |
| dense_qr = CUDADenseQR::Create(options); |
| break; |
| #else |
| LOG(FATAL) << "Ceres was compiled without support for CUDA."; |
| #endif |
| |
| default: |
| LOG(FATAL) << "Unknown dense linear algebra library type : " |
| << DenseLinearAlgebraLibraryTypeToString( |
| options.dense_linear_algebra_library_type); |
| } |
| return dense_qr; |
| } |
| |
| LinearSolverTerminationType DenseQR::FactorAndSolve(int num_rows, |
| int num_cols, |
| double* lhs, |
| const double* rhs, |
| double* solution, |
| std::string* message) { |
| LinearSolverTerminationType termination_type = |
| Factorize(num_rows, num_cols, lhs, message); |
| if (termination_type == LinearSolverTerminationType::SUCCESS) { |
| termination_type = Solve(rhs, solution, message); |
| } |
| return termination_type; |
| } |
| |
| LinearSolverTerminationType EigenDenseQR::Factorize(int num_rows, |
| int num_cols, |
| double* lhs, |
| std::string* message) { |
| Eigen::Map<ColMajorMatrix> m(lhs, num_rows, num_cols); |
| qr_ = std::make_unique<QRType>(m); |
| *message = "Success."; |
| return LinearSolverTerminationType::SUCCESS; |
| } |
| |
| LinearSolverTerminationType EigenDenseQR::Solve(const double* rhs, |
| double* solution, |
| std::string* message) { |
| VectorRef(solution, qr_->cols()) = |
| qr_->solve(ConstVectorRef(rhs, qr_->rows())); |
| *message = "Success."; |
| return LinearSolverTerminationType::SUCCESS; |
| } |
| |
| #ifndef CERES_NO_LAPACK |
| LinearSolverTerminationType LAPACKDenseQR::Factorize(int num_rows, |
| int num_cols, |
| double* lhs, |
| std::string* message) { |
| int lwork = -1; |
| double work_size; |
| int info = 0; |
| |
| // Compute the size of the temporary workspace needed to compute the QR |
| // factorization in the dgeqrf call below. |
| dgeqrf_(&num_rows, |
| &num_cols, |
| lhs_, |
| &num_rows, |
| tau_.data(), |
| &work_size, |
| &lwork, |
| &info); |
| if (info < 0) { |
| LOG(FATAL) << "Congratulations, you found a bug in Ceres." |
| << "Please report it." |
| << "LAPACK::dgels fatal error." |
| << "Argument: " << -info << " is invalid."; |
| } |
| |
| lhs_ = lhs; |
| num_rows_ = num_rows; |
| num_cols_ = num_cols; |
| |
| lwork = static_cast<int>(work_size); |
| |
| if (work_.size() < lwork) { |
| work_.resize(lwork); |
| } |
| if (tau_.size() < num_cols) { |
| tau_.resize(num_cols); |
| } |
| |
| if (q_transpose_rhs_.size() < num_rows) { |
| q_transpose_rhs_.resize(num_rows); |
| } |
| |
| // Factorize the lhs_ using the workspace that we just constructed above. |
| dgeqrf_(&num_rows, |
| &num_cols, |
| lhs_, |
| &num_rows, |
| tau_.data(), |
| work_.data(), |
| &lwork, |
| &info); |
| |
| if (info < 0) { |
| LOG(FATAL) << "Congratulations, you found a bug in Ceres." |
| << "Please report it. dgeqrf fatal error." |
| << "Argument: " << -info << " is invalid."; |
| } |
| |
| termination_type_ = LinearSolverTerminationType::SUCCESS; |
| *message = "Success."; |
| return termination_type_; |
| } |
| |
| LinearSolverTerminationType LAPACKDenseQR::Solve(const double* rhs, |
| double* solution, |
| std::string* message) { |
| if (termination_type_ != LinearSolverTerminationType::SUCCESS) { |
| *message = "QR factorization failed and solve called."; |
| return termination_type_; |
| } |
| |
| std::copy_n(rhs, num_rows_, q_transpose_rhs_.data()); |
| |
| const char side = 'L'; |
| char trans = 'T'; |
| const int num_c_cols = 1; |
| const int lwork = work_.size(); |
| int info = 0; |
| dormqr_(&side, |
| &trans, |
| &num_rows_, |
| &num_c_cols, |
| &num_cols_, |
| lhs_, |
| &num_rows_, |
| tau_.data(), |
| q_transpose_rhs_.data(), |
| &num_rows_, |
| work_.data(), |
| &lwork, |
| &info); |
| if (info < 0) { |
| LOG(FATAL) << "Congratulations, you found a bug in Ceres." |
| << "Please report it. dormr fatal error." |
| << "Argument: " << -info << " is invalid."; |
| } |
| |
| const char uplo = 'U'; |
| trans = 'N'; |
| const char diag = 'N'; |
| dtrtrs_(&uplo, |
| &trans, |
| &diag, |
| &num_cols_, |
| &num_c_cols, |
| lhs_, |
| &num_rows_, |
| q_transpose_rhs_.data(), |
| &num_rows_, |
| &info); |
| |
| if (info < 0) { |
| LOG(FATAL) << "Congratulations, you found a bug in Ceres." |
| << "Please report it. dormr fatal error." |
| << "Argument: " << -info << " is invalid."; |
| } else if (info > 0) { |
| *message = |
| "QR factorization failure. The factorization is not full rank. R has " |
| "zeros on the diagonal."; |
| termination_type_ = LinearSolverTerminationType::FAILURE; |
| } else { |
| std::copy_n(q_transpose_rhs_.data(), num_cols_, solution); |
| termination_type_ = LinearSolverTerminationType::SUCCESS; |
| } |
| |
| return termination_type_; |
| } |
| |
| #endif // CERES_NO_LAPACK |
| |
| #ifndef CERES_NO_CUDA |
| |
| bool CUDADenseQR::Init(ContextImpl* context, std::string* message) { |
| if (!context->InitCUDA(message)) { |
| return false; |
| } |
| cublas_handle_ = context->cublas_handle_; |
| cusolver_handle_ = context->cusolver_handle_; |
| stream_ = context->stream_; |
| error_.Reserve(1); |
| *message = "CUDADenseQR::Init Success."; |
| return true; |
| } |
| |
| LinearSolverTerminationType CUDADenseQR::Factorize(int num_rows, |
| int num_cols, |
| double* lhs, |
| std::string* message) { |
| factorize_result_ = LinearSolverTerminationType::FATAL_ERROR; |
| lhs_.Reserve(num_rows * num_cols); |
| tau_.Reserve(std::min(num_rows, num_cols)); |
| num_rows_ = num_rows; |
| num_cols_ = num_cols; |
| lhs_.CopyToGpuAsync(lhs, num_rows * num_cols, stream_); |
| int device_workspace_size = 0; |
| if (cusolverDnDgeqrf_bufferSize(cusolver_handle_, |
| num_rows, |
| num_cols, |
| lhs_.data(), |
| num_rows, |
| &device_workspace_size) != |
| CUSOLVER_STATUS_SUCCESS) { |
| *message = "cuSolverDN::cusolverDnDgeqrf_bufferSize failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| device_workspace_.Reserve(device_workspace_size); |
| if (cusolverDnDgeqrf(cusolver_handle_, |
| num_rows, |
| num_cols, |
| lhs_.data(), |
| num_rows, |
| tau_.data(), |
| reinterpret_cast<double*>(device_workspace_.data()), |
| device_workspace_.size(), |
| error_.data()) != CUSOLVER_STATUS_SUCCESS) { |
| *message = "cuSolverDN::cusolverDnDgeqrf failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| if (cudaDeviceSynchronize() != cudaSuccess || |
| cudaStreamSynchronize(stream_) != cudaSuccess) { |
| *message = "Cuda device synchronization failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| int error = 0; |
| error_.CopyToHost(&error, 1); |
| if (error < 0) { |
| LOG(FATAL) << "Congratulations, you found a bug in Ceres - " |
| << "please report it. " |
| << "cuSolverDN::cusolverDnDgeqrf fatal error. " |
| << "Argument: " << -error << " is invalid."; |
| // The following line is unreachable, but return failure just to be |
| // pedantic, since the compiler does not know that. |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| |
| *message = "Success"; |
| factorize_result_ = LinearSolverTerminationType::SUCCESS; |
| return LinearSolverTerminationType::SUCCESS; |
| } |
| |
| LinearSolverTerminationType CUDADenseQR::Solve(const double* rhs, |
| double* solution, |
| std::string* message) { |
| if (factorize_result_ != LinearSolverTerminationType::SUCCESS) { |
| *message = "Factorize did not complete successfully previously."; |
| return factorize_result_; |
| } |
| rhs_.CopyToGpuAsync(rhs, num_rows_, stream_); |
| int device_workspace_size = 0; |
| if (cusolverDnDormqr_bufferSize(cusolver_handle_, |
| CUBLAS_SIDE_LEFT, |
| CUBLAS_OP_T, |
| num_rows_, |
| 1, |
| num_cols_, |
| lhs_.data(), |
| num_rows_, |
| tau_.data(), |
| rhs_.data(), |
| num_rows_, |
| &device_workspace_size) != |
| CUSOLVER_STATUS_SUCCESS) { |
| *message = "cuSolverDN::cusolverDnDormqr_bufferSize failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| device_workspace_.Reserve(device_workspace_size); |
| // Compute rhs = Q^T * rhs, assuming that lhs has already been factorized. |
| // The result of factorization would have stored Q in a packed form in lhs_. |
| if (cusolverDnDormqr(cusolver_handle_, |
| CUBLAS_SIDE_LEFT, |
| CUBLAS_OP_T, |
| num_rows_, |
| 1, |
| num_cols_, |
| lhs_.data(), |
| num_rows_, |
| tau_.data(), |
| rhs_.data(), |
| num_rows_, |
| reinterpret_cast<double*>(device_workspace_.data()), |
| device_workspace_.size(), |
| error_.data()) != CUSOLVER_STATUS_SUCCESS) { |
| *message = "cuSolverDN::cusolverDnDormqr failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| int error = 0; |
| error_.CopyToHost(&error, 1); |
| if (error < 0) { |
| LOG(FATAL) << "Congratulations, you found a bug in Ceres. " |
| << "Please report it." |
| << "cuSolverDN::cusolverDnDormqr fatal error. " |
| << "Argument: " << -error << " is invalid."; |
| } |
| // Compute the solution vector as x = R \ (Q^T * rhs). Since the previous step |
| // replaced rhs by (Q^T * rhs), this is just x = R \ rhs. |
| if (cublasDtrsv(cublas_handle_, |
| CUBLAS_FILL_MODE_UPPER, |
| CUBLAS_OP_N, |
| CUBLAS_DIAG_NON_UNIT, |
| num_cols_, |
| lhs_.data(), |
| num_rows_, |
| rhs_.data(), |
| 1) != CUBLAS_STATUS_SUCCESS) { |
| *message = "cuBLAS::cublasDtrsv failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| if (cudaDeviceSynchronize() != cudaSuccess || |
| cudaStreamSynchronize(stream_) != cudaSuccess) { |
| *message = "Cuda device synchronization failed."; |
| return LinearSolverTerminationType::FATAL_ERROR; |
| } |
| rhs_.CopyToHost(solution, num_cols_); |
| *message = "Success"; |
| return LinearSolverTerminationType::SUCCESS; |
| } |
| |
| std::unique_ptr<CUDADenseQR> CUDADenseQR::Create( |
| const LinearSolver::Options& options) { |
| if (options.dense_linear_algebra_library_type != CUDA) { |
| // The user called the wrong factory method. |
| return nullptr; |
| } |
| auto cuda_dense_qr = std::unique_ptr<CUDADenseQR>(new CUDADenseQR()); |
| std::string cuda_error; |
| if (cuda_dense_qr->Init(options.context, &cuda_error)) { |
| return cuda_dense_qr; |
| } |
| // Initialization failed, destroy the object (done automatically) and return a |
| // nullptr. |
| LOG(ERROR) << "CUDADenseQR::Init failed: " << cuda_error; |
| return nullptr; |
| } |
| |
| CUDADenseQR::CUDADenseQR() = default; |
| |
| #endif // CERES_NO_CUDA |
| |
| } // namespace ceres::internal |
