Inversion Of Large Matrix Research Articles

Unfolding of sparse high-energy γ-ray spectra from LaBr3:Ce detectors

Here we report on the characterization of one of the large-volume LaBr3:Ce detectors for the ELIGANT project at ELI-NP. The main focus of this work is the response function for high-energy γ rays of such detectors. In particular, we compare a selection of unfolding methods to resolve small structures in γ-ray spectra with high-energies. Three methods have been compared using γ-ray spectra with energies up to 12 MeV obtained in an experiment at the 3 MV TandetronTM facility at IFIN-HH. The results show that the iterative unfolding approach gives the best qualitative reproduction of the emitted γ-ray spectrum. Furthermore, the correlation fluctuations in high-energy regime from the iterative method are two orders of magnitude smaller than when using the matrix inversion approach with second derivative regularization. In addition, the iterative method is computationally faster as it does not contain large matrix inversions. The matrix inversion method does, however, give more consistent results over the full energy range and in the low-statistics limit. Our conclusion is that the performance of the iterative approach makes it well suitable for semi-online analysis of experimental data. These results will be important, both for experiments with the ELIGANT setup, and for on-line diagnostics of the energy spread of the γ-ray beam which is under implementation at ELI-NP.

Floating Point versus Fixed point Tradeoffs in FPGA Implementations of QR Decomposition Algorithm

A wide variety of digital communication systems are encountered with high computational tasks. QR decomposition is one of such algorithms that can be implemented on FPGAs as a solution to large complex matrix inversion problems. A flexible vector processing architecture for the fixed and floating point implementations of the QR decomposition is presented. The design is implemented on the StratixIV device with 230K logic elements and verified with the SignalTap II built-in logic analyzer. Throughputs of 2.4M and 2.11M decompositions per second with maximum clock frequency of 340 MHz and 360 MHz are achieved for 4×4 matrices with the fixed and floating point designs respectively. The FPGA resource utilizations of the two data type implementations are also compared for different matrix sizes for the StratixIV and Arria10 devices.

Reliability feedback–aided low‐complexity detection in uplink massive MIMO systems

SummaryMassive multiple‐input multiple‐output (MIMO) plays a crucial role in realizing the demand for higher data rates and improved quality of service for 5G and beyond communication systems. Reliable detection of transmitted information bits from all the users is one of the challenging tasks for practical implementation of massive‐MIMO systems. The conventional linear detectors such as zero forcing (ZF) and minimum mean square error (MMSE) achieve near‐optimal bit error rate (BER) performance. However, ZF and MMSE require large dimensional matrix inversion which induces high computational complexity for symbol detection in such systems. This motivates for devising alternate low‐complexity near‐optimal detection algorithms for uplink massive‐MIMO systems. In this work, we propose an ordered sequential detection algorithm that exploits the concept of reliability feedback for achieving near‐optimal performance in uplink massive‐MIMO systems. In the proposed algorithm, symbol corresponding to each user is detected in an ordered sequence by canceling the interference from all the other users, followed by reliability feedback‐based decision. Incorporation of the sequence ordering and the reliability feedback‐based decision enhances the interference cancellation, which reduces the error propagation in sequential detection, and thus, improves the BER performance. Simulation results show that the proposed algorithm significantly outperforms recently reported massive‐MIMO detection techniques in terms of BER performance. In addition, the computational complexity of the proposed algorithm is substantially lower than that of the existing algorithms for the same BER. This indicates that the proposed algorithm exhibits a desirable trade‐off between the complexity and the performance for massive‐MIMO systems.

A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.

Standard multiconfiguration time-dependent Hartree (MCTDH) calculations use a direct product basis and rely on the potential being a sum of products (SOPs). The size of the direct product MCTDH basis scales exponentially with the number of atoms. Accurate potentials may not be SOPs. We introduce an MCTDH approach that uses a pruned basis and a collocation grid. Pruning the basis significantly reduces its size. Collocation makes it possible to do calculations using a potential that is not a SOP. The collocation point set is a Smolyak grid. Strategies using pruned MCTDH bases already exist, but they work only if the potential is a SOP. Strategies for using MCTDH with collocation also exist, but they work only if the MCTDH basis is a direct product. In this paper, we combine a pruned basis with collocation. This makes it possible to mitigate the direct-product basis size problem and do calculations when the potential is not a SOP. Because collocation is used, there are no integrals and no need for quadrature. All required matrix-vector products can be evaluated sequentially. We use nested sets of collocation points and hierarchical basis functions. They permit efficient inversion of the (large) matrix whose elements are basis functions evaluated at points, which is necessary to transform values of functions at points to basis coefficients. The inversion technique could be used outside of chemical physics. We confirm the validity of this new pruned, collocation-based (PC-)MCTDH approach by calculating the first 50 vibrational eigenenergies of CH2NH.

A coordinate descent approach for sparse Bayesian learning in high dimensional QTL mapping and genome-wide association studies.

Genomic scanning approaches that detect one locus at a time are subject to many problems in genome-wide association studies and quantitative trait locus mapping. The problems include large matrix inversion, over-conservativeness for tests after Bonferroni correction and difficulty in evaluation of the total genetic contribution to a trait's variance. Targeting these problems, we take a further step and investigate a multiple locus model that detects all markers simultaneously in a single model. We developed a sparse Bayesian learning (SBL) method for quantitative trait locus mapping and genome-wide association studies. This new method adopts a coordinate descent algorithm to estimate parameters (marker effects) by updating one parameter at a time conditional on current values of all other parameters. It uses an L2 type of penalty that allows the method to handle extremely large sample sizes (>100 000). Simulation studies show that SBL often has higher statistical powers and the simulated true loci are often detected with extremely small P-values, indicating that SBL is insensitive to stringent thresholds in significance testing. An R package (sbl) is available on the comprehensive R archive network (CRAN) and https://github.com/MeiyueComputBio/sbl/tree/master/R%20packge. Supplementary data are available at Bioinformatics online.

A flexible forcing immersed boundary-simplified lattice Boltzmann method for two and three-dimensional fluid-solid interaction problems

In this paper, a novel flexible forcing immersed boundary-simplified lattice Boltzmann method (FFIB-SLBM) is introduced to efficiently simulate two and three-dimensional fluid-solid interaction problems. Here, the simplified lattice Boltzmann method (Chen et al. [1]) with benefits such as lower virtual memories, ease in the implementation of the physical boundary conditions and higher numerical stability over the standard lattice Boltzmann method is coupled with an implicit flexible forcing immersed boundary scheme (Dash et al. [2]) which accurately satisfies the no-slip condition for the unsteady and moving boundary problems. The proposed FFIB-SLBM solver not only avoids the complex mathematics involved in the large banded matrix inversion but also requires lesser computational memory resources compares to the conventional immersed boundary-lattice Boltzmann method. The capabilities and accuracy of the coupled FFIB-SLBM solver are checked with several two and three-dimensional fluid-solid interaction problems. The obtained results from FFIB-SLBM solver are noticed to be in very good agreement with the published literature.

Low complexity and high performance symbol detection scheme for uplink wide‐banded cyclic prefixed filter bank multiple access system without analysis filtering

This Letter proposes a new symbol detection scheme for an uplink wide-banded cyclic prefixed filter bank multiple access system. The feature of the proposed scheme is that it eliminates the analysis filter bank processing that is commonly employed in the existing schemes. By leveraging a particular interleaving structure, the large matrix inversion operation is decomposed into parallel matrices inversions with small sizes. The benefits of the proposed scheme include lower complexity and higher spectral efficiency. In addition, the detection performance is also improved, which is verified by simulations.

Low-complexity Graph Sampling With Noise and Signal Reconstruction via Neumann Series

Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed in high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model, minimizing the expected mean square error (MMSE) leads to the known A-optimality criterion for graph sampling, which is expensive to compute and difficult to optimize. In this paper, we propose an augmented objective based on Neumann series that well approximates the original criterion and is amenable to greedy optimization. Specifically, we show that a shifted A-optimal criterion can be equivalently written as a function of an ideal low-pass (LP) graph filter, which in turn can be approximated efficiently via fast graph Fourier transform (FGFT). Minimizing the new objective, we select nodes greedily without large matrix inversions using a matrix inverse lemma. Further, for the dynamic network case where node availability varies across time, we propose an extended sampling strategy that replaces offline samples one-by-one in the selected set. For signal reconstruction, we propose an accompanied biased signal recovery strategy that reuses the approximated filter from sampling. Experiments show that our reconstruction is more robust to large noise than the least square (LS) solution, and our sampling strategy far outperforms several existing schemes.

3D DDA Based on Variational Inequality Theory and Its Solution Scheme

The advantage of 3D discontinuous deformation analysis (3D DDA) is the rigorous contact conditions on the interaction of 3D blocks. These conditions are enforced by the penalty function convention; however, inappropriate penalty parameters easily generate numerical instability. To avoid the introduction of the penalty parameters, the contact conditions in 3D DDA are described as variational inequalities in this study, and the extra-gradient method is employed to solve this new formulation of 3D DDA. The proposed computation scheme is more flexible and dispenses with large scale matrix inversion. Some practical examples originally designed by Shi are analysed, verifying the effectiveness and precision of the new scheme.

Bayesian sparse signal recovery based on log-Laplacian prior

This paper proposes a Bayesian sparse signal recovery algorithm. To improve performance on sparse representation, the log-Laplacian distribution is first defined. With a narrow main lobe and high tail values, it is used as a prior of the sparse signal to model the sparse characteristic. Note that analytical inference of the posterior of the sparse signal is a challenge, because the proposed log-Laplacian prior is not conjugate to the Gaussian likelihood. A maximum a posterior (MAP) estimation-based sparse signal recovery algorithm is further proposed. During the reconstruction of the sparse signal, MAP and maximum likelihood estimation are utilized to estimate the scaling parameter and noise variance, respectively, so as to avoid manual tuning of parameters. Additionally, with the use of the conjugate-gradient algorithm, large matrix inversion is avoided and computational efficiency is improved. Experimental results based on both simulated and measured data validate the effectiveness of the proposed log-Laplacian prior-based sparse signal recovery algorithm. Further, it is applied to micromotion parameters estimation and inverse synthetic aperture radar imaging to confirm its validity.

A novel low complexity downlink linear precoding algorithm for massive MIMO systems

The tremendous advancements in 4G and beyond 4G wireless standards requires a high demand for the increased data rate, high spectral efficiency and minimal power requirement. Massive MIMO is a key technology that can be used to attain all the above requirements at the cost of increased complexity. The performance of this massive MIMO system can be optimized by simple linear precoding techniques, the complexity of which lies on the inversion of large size matrix. In this paper, we propose a large scale low complexity matrix inversion algorithm which is highly suitable for parallel architecture. The proposed algorithm makes use of Chebyshev polynomial and Weyl’s inequality and named as Weyl’s Chebyshev acceleration (WCA) algorithm. This algorithm is further simplified by exploiting the diagonal dominance property of the positive definite Hermitian Gram matrix that is to be inverted. The specialty of this algorithm is, it is inner product free which makes this highly suitable for parallel computing environment and thus the algorithm becomes speedy. The performance of the proposed algorithm is evaluated in urban micro cell scenario and is proven to be more efficient in terms of BER performance and complexity. Also the proposed WCA based precoding algorithm achieves approximately 50% of complexity saving in the total flop count in comparison with the existing algorithms for the micro cell scenario. The BER performance reaches the near optimal results of ZF algorithm as SNR increases.

Route Choice Analysis in the Tokyo Metropolitan Area Using a Link-based Recursive Logit Model Featuring Link Awareness

Abstract Identification of an appropriate route choice model to understand travel behavior remains challenging. To this end, Fosgerau et al. (2013) have recently developed a link-based route choice model termed the “recursive logit” (RL) model. A decision-maker is assumed to choose the next link recursively that maximizes the sum of instantaneous utility and expected downstream utility at each node. However, in practical application, some computational issues remain, including large (and often ill-defined) matrix inversions. Here, we develop an alternative RL model that considers the probability of awareness of the next link that improves the stability of model estimations. The model was estimated using vehicle trajectory data from the ETC (Electronic Toll Collection) 2.0 dataset of the Tokyo Metropolitan area, and the results were compared to those of a conventional RL model in terms of predictive accuracy and computational efficiency.

Sparse Aperture InISAR Imaging via Sequential Multiple Sparse Bayesian Learning.

Interferometric inverse synthetic aperture radar (InISAR) imaging for sparse-aperture (SA) data is still a challenge, because the similarity and matched degree between ISAR images from different channels are destroyed by the SA data. To deal with this problem, this paper proposes a novel SA–InISAR imaging method, which jointly reconstructs 2-dimensional (2-D) ISAR images from different channels through multiple response sparse Bayesian learning (M-SBL), a modification of sparse Bayesian learning (SBL), to achieve sparse recovery for multiple measurement vectors (MMV). We note that M-SBL suffers a heavy computational burden because it involves large matrix inversion. A computationally efficient M-SBL is proposed, which, proceeding in a sequential manner to avoid the time-consuming large matrix inversion, is denoted as sequential multiple sparse Bayesian learning (SM-SBL). Thereafter, SM-SBL is introduced to InISAR imaging to simultaneously reconstruct the ISAR images from different channels. Numerous experimental results validate that the proposed SM-SBL-based InISAR imaging algorithm performs superiorly against the traditional single-channel sparse-signal recovery (SSR)-based InISAR imaging methods in terms of noise suppression, outlier reduction and 3-dimensional (3-D) geometry estimation.

Group Sparse Bayesian Learning Via Exact and Fast Marginal Likelihood Maximization

This paper concerns the sparse Bayesian learning (SBL) problem for group sparse signals. Group sparsity means that the signal coefficients can be divided into groups and that the entries in one group are simultaneously zero or nonzero. In SBL, each group is controlled by a hyperparameter, which is estimated by solving the marginal likelihood maximization (MLM) problem. MLM is used to maximize the marginal likelihood of a given hyper-parameter by fixing all others. The main contribution of this paper is to extend the fast marginal likelihood maximization (FMLM) method to the group sparsity case. The key process of realizing FMLM in the group sparsity case is solved by finding the roots of a polynomial. Hence, the local maximum of the marginal likelihood can be found exactly, and the final estimation is obtained more efficiently. Furthermore, most large matrix inverses involved in MLM are replaced with the eigenvalue decompositions of much smaller matrices, which substantially reduces the computational complexity. Numerical results with both simulated and real data demonstrate the excellent performance and relatively high computational efficiency of the proposed method.

Heterogeneous blocked CPU-GPU accelerate scheme for large scale extreme learning machine

Extreme learning machine (ELM) has been intensively studied during the last decade due to its high efficiency, effectiveness and easy to implement. Recently, a variant of ELM named local receptive fields based ELM (ELM-LRF) has been proposed to reduce the global connections and introduce local receptive fields to the input layer. However, an ELM-LRF model with large number of hidden neurons spend plenty of time on solving large scale Moore-Penrose Matrix Inversion (MPMI) problem which has heavy computational cost and needs much more runtime memory. Moreover, this procedure can not be directly accelerated by GPU platforms due to the limited memory of GPU devices. In this paper, we propose three efficient approaches to perform ELM-LRF on GPU platform. First we propose a novel blocked LU decomposition algorithm, which overcomes the limitation of global memory size so that any size of ELM-LRF models can be trained. Furthermore, an efficient blocked Cholesky decomposition algorithm is presented to accelerate blocked LU decomposition algorithm according to matrix characteristics in the ELM-LRF model. Finally we present a heterogeneous blocked CPU-GPU parallel algorithm to fully exploit resources on a GPU node such as to accelerate blocked Cholesky decomposition algorithm furthermore in the ELM-LRF model.

A new approximate fast method of computing the scattering from multilayer rough surfaces based on the Kirchhoff approximation

AbstractIn this paper a new approximate fast method of calculating the bistatic‐scattering coefficients of a multilayer structure with random rough interfaces was presented based on the Kirchhoff Approximation (KA) and the electromagnetic theory of stratified media. First, the electromagnetic scattering from a Gauss rough metal or dielectric surface was calculated by KA method and method of moment (MOM), and the effectiveness of KA method was confirmed and verified. Second, a new approximate fast method was presented to calculate electromagnetic scattering from a multilayer‐random‐rough surface based on electromagnetic reflection from multilayer parallel surfaces and KA. The calculated results by the new method were in good agreements with those by MOM, especially near the specular point. Finally, a comparison of the new method and MOM was carried out in consuming computing time, memory resources, and complexity. The comparison indicated that the new approximate method was faster by about 30–150 times than MOM. The new approximate fast method could avoid a large matrix inversion and greatly reduce the computation time and memory resources and thus improve the computational efficiency. It was an effective approximation fast analyzing method of electromagnetic scattering from multilayer rough surfaces.

Coordinated multicell beamforming for massive multiple‐input multiple‐output systems based on uplink–downlink duality

This paper studies joint beamforming and power allocation for multicell multiuser multi-antenna systems with the objective of maximising the minimum signal-to-interference-plus-noise ratio (max-min SINR). The authors first consider developing an iterative algorithm to achieve the optimal performance by extending the uplink-downlink duality for finite-scale wireless communication systems. The solution is then generalised to achieve the asymptotically optimal multicell beamforming with the aim to reduce the overhead of signalling exchange between coordinated base stations based on large dimension random matrix theory. Based on that, an efficient multicell beamforming algorithm is proposed to asymptotically achieve the max-min SINR. To further solve the complexity issue of large dimensional matrix inversion involved in the calculation of beamforming vectors, they propose a low-complexity beamforming calculator based on truncated polynomial expansion approach. Numerical results validate the effectiveness of the authors' proposed algorithms and show that they can achieve the optimal or asymptotically optimal performance in a massive multi-input multi-output system with low complexity and small backhaul overhead.

An incremental approach for springback analysis of elasto-plastic beam undergoing contact driven large deflection

In this article the solution methodology for a beam on a vee-die undergoing large elasto-plastic deflection along with nonlinear contact development with the die is discussed. A bi-linear stress strain material model is converted into an incremental moment- curvature based constitutive law to ease formulation. The one dimensional governing equation obtained, is highly nonlinear owing to material and geometry and involve boundary condition change. The entire problem is solved in three steps: solving an end loaded cantilever under non-conservative force, followed by choosing the solutions which satisfy the configurational constraint and finally reanalyzing the contact data for springback analysis. The end loaded cantilever problem is solved by an incremental procedure coupled with Runge–Kutta fourth-order explicit initial value solver. Suitable normalization of the pertinent variables of the governing equation paved the way to identify dependence of the responses on a unique non-dimensional parameter. The presented methodology doesn't involve large matrix inversion and so is computationally economic. It may be used in sheet metal manufacturing control facilities to predict springback and reduce the expensive experimental iterations.

Obtaining Arbitrary Prescribed Mean Field Dynamics for Recurrently Coupled Networks of Type-I Spiking Neurons with Analytically Determined Weights.

A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks.

Low-complexity soft-output detection for massive MIMO using SCBiCG and Lanczos methods

Massive MIMO is a promising technology to improve spectral efficiency, cell coverage, and system capacity for 5G. However, these benefits take place at great cost of computational complexity, especially in systems with hundreds of antennas at the base station. This paper aims to address the minimum mean square error (MMSE) detection in uplink massive MIMO systems utilizing the symmetric complex bi-conjugate gradients (SCBiCG) and the Lanczos method. Both the proposed methods can avoid the large scale matrix inversion which is necessary for MMSE, thus, reducing the computational complexity by an order of magnitude with respect to the number of user equipment. To enable the proposed methods for soft-output detection, we also derive an approximating calculation scheme for the log-likelihood ratios (LLRs), which further reduces the complexity. We compare the proposed methods with existing exact and approximate detection methods. Simulation results demonstrate that the proposed methods can achieve near-optimal performance of MMSE detection with relatively low computational complexity.