randLS contains a C++ implementation of a randomized mixed precision
preconditioner for the LSQR solver.
This work was published under the title, "A Mixed Precision Randomized
Preconditioner for the LSQR solver on GPUs" at ISC23; It is an attempt to
investigate the effect that mixed precision computations have on randomized
preconditioners for least squares solvers, while at the same time attaining
modest runtime savings.
Latest developments that use mixed precision sparse sketching to solve regularized
least squares can be found in the "dev" branch.
MAGMA[1] is used for performing BLAS on the GPU, cudaRand[2] for
generating random samples and custom cuda kernels for conversions between
precisions.
A simple configuration of the project can be achieved by running the following
script at the root directory of the project:
cmake \
-DMAGMA_INC="path-to-magma-include" \
-DCUDA_INC="path-to-cuda-include" \
-DMAKE_CUDA_ARCHITECTURES=80 \ # gpu architecture is set to AMPERE
-DMAGMA_LIB="path-to-magma-lib" \
-DRANDLS_LIB="path-to-magma-lib" \
-G "Unix Makefiles" \
-S -B build
then build with:
cd build; make
The experiments with matrices HGDP_1, HGDP_2, CIFAR_1, CIFAR_2.
cd build;
./run_lsqr ${tol} \
${precond_precision} \
${precond_precision_in} \
${solver_precision} \
${solver_precision_in} \
${in_mtx_filename} \
${in_rhs_filehaname} \
precond \
${sampling_coeff} \
${out_file} \
${warmup_iters} \
${runtime_iters}
tol: LSQR tolerance
precond_precision: high precision used for preconditioner.
precond_precision_in: low precision used for preconditioner.
solver_precision: high precision used for solver.
solver_precision_in: low precision used for solver.
in_mtx_filename: filename of input matrix
in_rhs_filename: filename of input rhs
precond: use this to run lsqr with preconditioner
samples: signifies the rows of the sketch matrix as sampling_coeff * num_cols_A
out_file: filename of output file, containing the runtimes.
warmup_iters: number of iterations used for warmup.
runtime_iters: numer of iterations used for measuring runtime.
CUDA 11.4.4, gcc 11.3.0 and MAGMA 2.6.2 and cmake 3.25.1 were used.
[1]. Tomov, S., Dongarra, J., Baboulin, M.: Towards dense linear algebra for
hybrid GPU accelerated manycore systems. Parallel Computing 36(5-6), 232–240
(Jun 2010), 10.1016/j.parco.2009.12.005
[2]. cuRand: https://docs.nvidia.com/cuda/curand/index.html