arXiv subjects

Soumyendu Raha

Publications and source records attributed to Soumyendu Raha.

30 records · Page 2Linked to original sources

arXiv2018

Ecologically Sustainable Partitioning of a Metapopulations Network

A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut passing through metapopulations habitat such that populations remain stable. We combine the dynamical system stability analysis with graph partitioning algorithms in our approach to the problem. It finds such a safe construction, when one exists, provided the algebraic connectivity of the graph components is stronger than all the spatially local instabilities in the respective components. The dynamics of the populations on the spatially discrete patches (graph nodes) and their spatial communication with other patches is modeled as a reaction-diffusion system. By reversing the Turing-instability idea the stability conditions of the partitioned system are found to depend on local dynamics of the metapopulations and the Fiedler value of the Laplacian matrix of the graph. This leads to the necessary and sufficient conditions for removal of the graph edges subject to the stability of the partitioned graph networks. An heuristic bisection graph partitioning algorithm has been proposed and examples illustrate the theoretical result.

math.DS↗

arXiv2018

Efficient Realization of Givens Rotation through Algorithm-Architecture Co-design for Acceleration of QR Factorization

We present efficient realization of Generalized Givens Rotation (GGR) based QR factorization that achieves 3-100x better performance in terms of Gflops/watt over state-of-the-art realizations on multicore, and General Purpose Graphics Processing Units (GPGPUs). GGR is an improvement over classical Givens Rotation (GR) operation that can annihilate multiple elements of rows and columns of an input matrix simultaneously. GGR takes 33% lesser multiplications compared to GR. For custom implementation of GGR, we identify macro operations in GGR and realize them on a Reconfigurable Data-path (RDP) tightly coupled to pipeline of a Processing Element (PE). In PE, GGR attains speed-up of 1.1x over Modified Householder Transform (MHT) presented in the literature. For parallel realization of GGR, we use REDEFINE, a scalable massively parallel Coarse-grained Reconfigurable Architecture, and show that the speed-up attained is commensurate with the hardware resources in REDEFINE. GGR also outperforms General Matrix Multiplication (gemm) by 10% in-terms of Gflops/watt which is counter-intuitive.

cs.DC↗

arXiv2018

Achieving Efficient Realization of Kalman Filter on CGRA through Algorithm-Architecture Co-design

In this paper, we present efficient realization of Kalman Filter (KF) that can achieve up to 65% of the theoretical peak performance of underlying architecture platform. KF is realized using Modified Faddeeva Algorithm (MFA) as a basic building block due to its versatility and REDEFINE Coarse Grained Reconfigurable Architecture (CGRA) is used as a platform for experiments since REDEFINE is capable of supporting realization of a set algorithmic compute structures at run-time on a Reconfigurable Data-path (RDP). We perform several hardware and software based optimizations in the realization of KF to achieve 116% improvement in terms of Gflops over the first realization of KF. Overall, with the presented approach for KF, 4-105x performance improvement in terms of Gflops/watt over several academically and commercially available realizations of KF is attained. In REDEFINE, we show that our implementation is scalable and the performance attained is commensurate with the underlying hardware resources

cs.MS↗

arXiv2017

Accelerating BLAS and LAPACK via Efficient Floating Point Architecture Design

Basic Linear Algebra Subprograms (BLAS) and Linear Algebra Package (LAPACK) form basic building blocks for several High Performance Computing (HPC) applications and hence dictate performance of the HPC applications. Performance in such tuned packages is attained through tuning of several algorithmic and architectural parameters such as number of parallel operations in the Directed Acyclic Graph of the BLAS/LAPACK routines, sizes of the memories in the memory hierarchy of the underlying platform, bandwidth of the memory, and structure of the compute resources in the underlying platform. In this paper, we closely investigate the impact of the Floating Point Unit (FPU) micro-architecture for performance tuning of BLAS and LAPACK. We present theoretical analysis for pipeline depth of different floating point operations like multiplier, adder, square root, and divider followed by characterization of BLAS and LAPACK to determine several parameters required in the theoretical framework for deciding optimum pipeline depth of the floating operations. A simple design of a Processing Element (PE) is presented and shown that the PE outperforms the most recent custom realizations of BLAS and LAPACK by 1.1X to 1.5X in Gflops/W, and 1.9X to 2.1X in Gflops/mm^2.

cs.AR↗

arXiv2017

A Geometric Approach to Rotor Failure Tolerant Trajectory Tracking Control Design for a Quadrotor

This paper addresses the problem of designing a trajectory tracking control law for a quadrotor UAV, subsequent to complete failure of a single rotor. The control design problem considers the reduced state space which excludes the angular velocity and orientation about the vertical body axis. The proposed controller enables the quadrotor to track the orientation of this axis, and consequently any prescribed position trajectory using only three rotors. The control design is carried out in two stages. First, in order to track the reduced attitude dynamics, a geometric controller with two input torques is designed on the Lie-Group $SO(3)$. This is then extended to $SE(3)$ by designing a saturation based feedback law, in order to track the center of mass position with bounded thrust. The control law for the complete dynamics achieves exponential tracking for all initial conditions lying in an open-dense subset. The novelty of the geometric control design is in its ability to effectively execute aggressive, global maneuvers despite complete loss of a rotor. Numerical simulations on models of a variable pitch and a conventional quadrotor have been presented to demonstrate the practical applicability of the control design.

math.OC↗

arXiv2016

Efficient Realization of Householder Transform through Algorithm-Architecture Co-design for Acceleration of QR Factorization

We present efficient realization of Householder Transform (HT) based QR factorization through algorithm-architecture co-design where we achieve performance improvement of 3-90x in-terms of Gflops/watt over state-of-the-art multicore, General Purpose Graphics Processing Units (GPGPUs), Field Programmable Gate Arrays (FPGAs), and ClearSpeed CSX700. Theoretical and experimental analysis of classical HT is performed for opportunities to exhibit higher degree of parallelism where parallelism is quantified as a number of parallel operations per level in the Directed Acyclic Graph (DAG) of the transform. Based on theoretical analysis of classical HT, an opportunity re-arrange computations in the classical HT is identified that results in Modified HT (MHT) where it is shown that MHT exhibits 1.33x times higher parallelism than classical HT. Experiments in off-the-shelf multicore and General Purpose Graphics Processing Units (GPGPUs) for HT and MHT suggest that MHT is capable of achieving slightly better or equal performance compared to classical HT based QR factorization realizations in the optimized software packages for Dense Linear Algebra (DLA). We implement MHT on a customized platform for Dense Linear Algebra (DLA) and show that MHT achieves 1.3x better performance than native implementation of classical HT on the same accelerator. For custom realization of HT and MHT based QR factorization, we also identify macro operations in the DAGs of HT and MHT that are realized on a Reconfigurable Data-path (RDP). We also observe that due to re-arrangement in the computations in MHT, custom realization of MHT is capable of achieving 12% better performance improvement over multicore and GPGPUs than the performance improvement reported by General Matrix Multiplication (GEMM) over highly tuned DLA software packages for multicore and GPGPUs which is counter-intuitive.

cs.PF↗

arXiv2016

Accelerating BLAS on Custom Architecture through Algorithm-Architecture Co-design

Basic Linear Algebra Subprograms (BLAS) play key role in high performance and scientific computing applications. Experimentally, yesteryear multicore and General Purpose Graphics Processing Units (GPGPUs) are capable of achieving up to 15 to 57% of the theoretical peak performance at 65W to 240W respectively for compute bound operations like Double/Single Precision General Matrix Multiplication (XGEMM). For bandwidth bound operations like Single/Double precision Matrix-vector Multiplication (XGEMV) the performance is merely 5 to 7% of the theoretical peak performance in multicores and GPGPUs respectively. Achieving performance in BLAS requires moving away from conventional wisdom and evolving towards customized accelerator tailored for BLAS through algorithm-architecture co-design. In this paper, we present acceleration of Level-1 (vector operations), Level-2 (matrix-vector operations), and Level-3 (matrix-matrix operations) BLAS through algorithm architecture co-design on a Coarse-grained Reconfigurable Architecture (CGRA). We choose REDEFINE CGRA as a platform for our experiments since REDEFINE can be adapted to support domain of interest through tailor-made Custom Function Units (CFUs). For efficient sequential realization of BLAS, we present design of a Processing Element (PE) and perform micro-architectural enhancements in the PE to achieve up-to 74% of the theoretical peak performance of PE in DGEMM, 40% in DGEMV and 20% in double precision inner product (DDOT). We attach this PE to REDEFINE CGRA as a CFU and show the scalability of our solution. Finally, we show performance improvement of 3-140x in PE over commercially available Intel micro-architectures, ClearSpeed CSX700, FPGA, and Nvidia GPGPUs.

cs.AR↗

arXiv2015

Performance metrics in a hybrid MPI-OpenMP based molecular dynamics simulation with short-range interactions

We discuss the computational bottlenecks in molecular dynamics (MD) and describe the challenges in parallelizing the computation intensive tasks. We present a hybrid algorithm using MPI (Message Passing Interface) with OpenMP threads for parallelizing a generalized MD computation scheme for systems with short range interatomic interactions. The algorithm is discussed in the context of nanoindentation of Chromium films with carbon indenters using the Embedded Atom Method potential for Cr Cr interaction and the Morse potential for Cr C interactions. We study the performance of our algorithm for a range of MPIthread combinations and find the performance to depend strongly on the computational task and load sharing in the multicore processor. The algorithm scaled poorly with MPI and our hybrid schemes were observed to outperform the pure message passing scheme, despite utilizing the same number of processors or cores in the cluster. Speed-up achieved by our algorithm compared favourably with that achieved by standard MD packages.

physics.comp-ph↗

arXiv2014

The Exponentially Faster Stick-Slip Dynamics of the Peeling of an Adhesive Tape

The stick-slip dynamics is considered from the nonlinear differential-algebraic equation (DAE) point of view and the peeling dynamics is shown to be a switching differential index DAE model. In the stick-slip regime with bifurcations, the differential index can be arbitrarily high. The time scale of the peeling velocity, the algebraic variable, in this regime is shown to be exponentially faster compared to the angular velocity of the spool and/or the stretch rate of the tape. A homogenization scheme for the peeling velocity which is characterized by the bifurcations is discussed and is illustrated with numerical examples.

nlin.CD↗

arXiv2013

Rollover Preventive Force Synthesis at Active Suspensions in a Vehicle Performing a Severe Maneuver with Wheels Lifted off

Among the intelligent safety technologies for road vehicles, active suspensions controlled by embedded computing elements for preventing rollover have received a lot of attention. The existing models for synthesizing and allocating forces in such suspensions are conservatively based on the constraint that no wheels lift off the ground. However, in practice, smart/active suspensions are more necessary in the situation where the wheels have just lifted off the ground. The difficulty in computing control in the last situation is that the problem requires satisfying disjunctive constraints on the dynamics. To the authors',knowledge, no efficient solution method is available for the simulation of dynamics with disjunctive constraints and thus hardware realizable and accurate force allocation in an active suspension tends to be a difficulty. In this work we give an algorithm for and simulate numerical solutions of the force allocation problem as an optimal control problem constrained by dynamics with disjunctive constraints. In particular we study the allocation and synthesis of time-dependent active suspension forces in terms of sensor output data in order to stabilize the roll motion of the road vehicle. An equivalent constraint in the form of a convex combination (hull) is proposed to satisfy the disjunctive constraints. The validated numerical simulations show that it is possible to allocate and synthesize control forces at the active suspensions from sensor output data such that the forces stabilize the roll moment of the vehicle with its wheels just lifted off the ground during arbitrary fish-hook maneuvers.

eess.SY↗

arXiv2011

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such systems which appears in astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity into the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved nonnormal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this enlightens the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of origin of turbulence therein.

astro-ph.HE↗

arXiv2008

The Stochastic Logarithmic Norm for Stability Analysis of Stochastic Differential Equations

To analyze the stability of Itô stochastic differential equations with multiplicative noise, we introduce the stochastic logarithmic norm. The logarithmic norm was originally introduced by G. Dahlquist in 1958 as a tool to study the growth of solutions to ordinary differential equations and for estimating the error growth in discretization methods for their approximate solutions. We extend the concept to the stability analysis of Itô stochastic differential equations with multiplicative noise. Stability estimates for linear Itô SDEs using the one, two and $\infty$-norms in the $l$-th mean, where $1 \leq l < \infty $, are derived and the application of the stochastic logarithmic norm is illustrated with examples.

math.NA↗