3,063 research outputs found
Fast, Dense Feature SDM on an iPhone
In this paper, we present our method for enabling dense SDM to run at over 90
FPS on a mobile device. Our contributions are two-fold. Drawing inspiration
from the FFT, we propose a Sparse Compositional Regression (SCR) framework,
which enables a significant speed up over classical dense regressors. Second,
we propose a binary approximation to SIFT features. Binary Approximated SIFT
(BASIFT) features, which are a computationally efficient approximation to SIFT,
a commonly used feature with SDM. We demonstrate the performance of our
algorithm on an iPhone 7, and show that we achieve similar accuracy to SDM
Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs
Many problems in geophysical and atmospheric modelling require the fast
solution of elliptic partial differential equations (PDEs) in "flat" three
dimensional geometries. In particular, an anisotropic elliptic PDE for the
pressure correction has to be solved at every time step in the dynamical core
of many numerical weather prediction models, and equations of a very similar
structure arise in global ocean models, subsurface flow simulations and gas and
oil reservoir modelling. The elliptic solve is often the bottleneck of the
forecast, and an algorithmically optimal method has to be used and implemented
efficiently. Graphics Processing Units have been shown to be highly efficient
for a wide range of applications in scientific computing, and recently
iterative solvers have been parallelised on these architectures. We describe
the GPU implementation and optimisation of a Preconditioned Conjugate Gradient
(PCG) algorithm for the solution of a three dimensional anisotropic elliptic
PDE for the pressure correction in NWP. Our implementation exploits the strong
vertical anisotropy of the elliptic operator in the construction of a suitable
preconditioner. As the algorithm is memory bound, performance can be improved
significantly by reducing the amount of global memory access. We achieve this
by using a matrix-free implementation which does not require explicit storage
of the matrix and instead recalculates the local stencil. Global memory access
can also be reduced by rewriting the algorithm using loop fusion and we show
that this further reduces the runtime on the GPU. We demonstrate the
performance of our matrix-free GPU code by comparing it to a sequential CPU
implementation and to a matrix-explicit GPU code which uses existing libraries.
The absolute performance of the algorithm for different problem sizes is
quantified in terms of floating point throughput and global memory bandwidth.Comment: 18 pages, 7 figure
Parallel structurally-symmetric sparse matrix-vector products on multi-core processors
We consider the problem of developing an efficient multi-threaded
implementation of the matrix-vector multiplication algorithm for sparse
matrices with structural symmetry. Matrices are stored using the compressed
sparse row-column format (CSRC), designed for profiting from the symmetric
non-zero pattern observed in global finite element matrices. Unlike classical
compressed storage formats, performing the sparse matrix-vector product using
the CSRC requires thread-safe access to the destination vector. To avoid race
conditions, we have implemented two partitioning strategies. In the first one,
each thread allocates an array for storing its contributions, which are later
combined in an accumulation step. We analyze how to perform this accumulation
in four different ways. The second strategy employs a coloring algorithm for
grouping rows that can be concurrently processed by threads. Our results
indicate that, although incurring an increase in the working set size, the
former approach leads to the best performance improvements for most matrices.Comment: 17 pages, 17 figures, reviewed related work section, fixed typo
Devito: Towards a generic Finite Difference DSL using Symbolic Python
Domain specific languages (DSL) have been used in a variety of fields to
express complex scientific problems in a concise manner and provide automated
performance optimization for a range of computational architectures. As such
DSLs provide a powerful mechanism to speed up scientific Python computation
that goes beyond traditional vectorization and pre-compilation approaches,
while allowing domain scientists to build applications within the comforts of
the Python software ecosystem. In this paper we present Devito, a new finite
difference DSL that provides optimized stencil computation from high-level
problem specifications based on symbolic Python expressions. We demonstrate
Devito's symbolic API and performance advantages over traditional Python
acceleration methods before highlighting its use in the scientific context of
seismic inversion problems.Comment: pyHPC 2016 conference submissio
- …