Cholesky Decomposition Research Articles

High-Throughput MPSoC Implementation of Sparse Bayesian Learning Algorithm

In the field of sparse signal reconstruction, sparse Bayesian learning (SBL) has excellent performance, which is accompanied by extremely high computational complexity. This paper presents an efficient SBL hardware and software (HW&SW) co-implementation method using the ZYNQ series MPSoC (multiprocessor system-on-chip). Firstly, considering the inherent challenges in parallelizing iterative algorithms like SBL, we propose an architecture based on the iterative calculations implemented on the PL side (FPGA) and the iteration control and input management handled by the PS side (ARM). By adopting this structure, we can take advantage of task-level pipelines on the FPGA side, effectively utilizing time and space resources. Secondly, we utilize LDL decomposition to perform the inversion of the Hermitian matrix, which not only exhibits the lowest computational complexity and requires fewer computational resources but also achieves a higher level in the parallel pipeline mechanism compared with other alternative methods. Furthermore, the algorithm conducts iterations sequentially, utilizing the parameters derived from the previous dataset as prior information for initializing the subsequent dataset’s initial values. This approach helps to reduce the number of iterations required. Finally, with the help of Vitis HLS 2022.2 and Vivado tools, we successfully accomplished the development of a hardware design language and its implementation on the ZYNQ UltraScale+ MPSoC ZCU102 platform. Meanwhile, we have solved a direction of arrival (DOA) estimation problem using horizontal line arrays to verify the practical feasibility of the method.

Acceleration of Environmental Electrostatic Potential Using Cholesky Decomposition with Adaptive Metric (CDAM) for Fragment Molecular Orbital-based Molecular Dynamics (FMO-MD) Simulation

Acceleration of Environmental Electrostatic Potential Using Cholesky Decomposition with Adaptive Metric (CDAM) for Fragment Molecular Orbital-based Molecular Dynamics (FMO-MD) Simulation

Conflict-Free Parallel Data Access Technology for Matrix Calculation in Memory System of ASIP of 5G/6G Macro Base Stations

Among the physical layer baseband algorithms in macro base stations, the matrix processing has the dom-inant computing cost, large data access overhead and com-plicated addressing mode. The existing data access methods are not the best solution for memory system of ASIP (Ap-plication Specific Instruction Set Processor) in 5G/6G macro stations. We hence proposed a parallel conflict-free data access method for matrix. Moreover, we proposed a non-redundant access method for positive definite matrix that stores only trigonometric part, and the corresponding parallel addressing method with low storage overhead. Our method solves the problem of data conflict and minimizes the memory space of ASIP, and supports ASIP to approach the performance limit of architecture to the maximum ex-tent under the constraint of architecture and data parallel-ism. We implemented the proposed method as a static memory optimizer, which provides a tool for the design and optimization of memory system of ASIP in 5G/6G macro base stations with low overhead. Experimental results show that for 64W64 positive definite matrix inversion algorithm based on Cholesky decomposition, our addressing method can save 32% of the execution time, and the cost of memory space is reduced by half.

Round-Off Error Analysis in mMIMO Detector Based on Cholesky Decomposition

Round-Off Error Analysis in mMIMO Detector Based on Cholesky Decomposition

A Real-Time FPGA Implementation of the LCMV Algorithm for Target Classification in Hyperspectral Images Using LDL Decomposition

A Real-Time FPGA Implementation of the LCMV Algorithm for Target Classification in Hyperspectral Images Using LDL Decomposition

A generalized approach for Bayesian Gaussian graphical models

Bayesian Gaussian Graphical Models (BGGMs) are tools of growing popularity and interest in network psychometrics and probabilistic graphical modeling. However, some of the existing models are derived from different modeling principles that do not easily allow for extensions and combinations into new models. More specifically, the implementation of some models may not be flexible enough to test different priors or likelihoods. In this paper, we present a new approach to BGGMs that overcomes this limitation by allowing for the estimation of regularized partial correlations between any type of variables while also having an intuitive approach on how to decide about the priors. Our approach is based on using a transformation of the lower diagonal values of the Cholesky (or LDL) decomposition matrix as the parameters of the models, which can receive any zero-centered symmetric distribution as a prior, as well as to include moderators. We have developed the gbggm R package to implement some models based on this approach, and the potentials of the approach are demonstrated with a toy simulation and an empirical example. This new approach expands the range of applications and enhances the flexibility of BGGMs, making them more useful in a variety of contexts.

The Application of Single-Pass Randomized Algorithm for Cholesky Decomposition in Rank Deficit Least Squares

The Application of Single-Pass Randomized Algorithm for Cholesky Decomposition in Rank Deficit Least Squares

Alternative modified Cholesky decomposition of the precision matrix of longitudinal data

The correlation matrix might be of scientific interest for longitudinal data. However, few studies have focused on both robust estimation of the correlation matrix against model misspecification and robustness to outliers in the data, when the precision matrix possesses a typical structure. In this paper, we propose an alternative modified Cholesky decomposition (AMCD) for the precision matrix of longitudinal data, which results in robust estimation of the correlation matrix against model misspecification of the innovation variances. A joint mean-covariance model with multivariate normal distribution and AMCD is established, the quasi-Fisher scoring algorithm is developed, and the maximum likelihood estimators are proven to be consistent and asymptotically normally distributed. Furthermore, a double-robust joint modeling approach with multivariate Laplace distribution and AMCD is established, and the quasi-Newton algorithm for maximum likelihood estimation is developed. The simulation studies and real data analysis demonstrate the effectiveness of the proposed AMCD method.

Investigation on the optimisation of Cholesky decomposition algorithm based on SIMD-DSP

Investigation on the optimisation of Cholesky decomposition algorithm based on SIMD-DSP

Correction to “The versatility of the Cholesky decomposition in electronic structure theory”

Correction to “The versatility of the Cholesky decomposition in electronic structure theory”

The relationship between personality throughout adolescence and social anxiety disorder in young adulthood. A longitudinal twin study.

This study examined the longitudinal relationship between a range of personality related variables measured throughout adolescence, and social anxiety disorder (SAD) in young adulthood. In addition, we examined to what degree the phenotypic associations between personality and SAD could be attributed to shared genetic and environmental factors, respectively. A total of 3394 twins (56% females), consisting of seven national birth cohorts from Norway, participated in the study. Personality was measured with self-report questionnaires at three times throughout adolescence, and SAD was measured with a diagnostic interview in early adulthood (M = 19.1 years, SD = 1.2). Correlation and regression analyses were performed to examine phenotypic associations between personality and SAD. We then created four composite scores of personality, in which the personality variables from four different ages throughout adolescence were weighted relative to their importance for SAD. Finally, a series of Cholesky decomposition models were used to examine the underlying genetic and environmental influences on the phenotypic associations between composite scores of personality and SAD. The results showed that especially higher neuroticism, lower extraversion, higher levels of loneliness, and lower levels of resilience, self-efficacy and sense of coherence, were associated with SAD. The phenotypic correlations between composite scores of personality and SAD increased from 0.42 when personality was measured 6-7 years prior to the assessment of SAD, to 0.52 when personality was measured shortly before the assessment of SAD. These phenotypic associations were mainly due to genetic influences, indicating that personality in adolescence predicts SAD in early adulthood due to shared genetic influences rather than having direct 'causal' effects on SAD.

Investigation on the optimisation of Cholesky decomposition algorithm based on SIMD-DSP

Investigation on the optimisation of Cholesky decomposition algorithm based on SIMD-DSP

\(q\)-Analogue of the Generalized Fibonacci and Lucas Polynomials

In this article, we define \(q\)-generalized Fibonacci polynomials and \(q\)-generalized Lucas polynomials using \(q\)-binomial coefficient and obtain their recursive properties. In addition, we introduce generalized \(q\)-Fibonacci matrix and generalized \(q\)-Lucas matrix, then we derive their basic identities. We define \((k,q,t)\)-symmetric generalized Fibonacci matrix and \((k,q,t)\)-symmetric generalized Lucas matrix, then we give the Cholesky factorization of these matrices. Finally, we give determinantal and permanental representations of these new polynomial sequences.

Matrix factorizations for the generalized Charlier and Meixner orthogonal polynomials

The Cholesky factorization of the moment matrix is considered for the generalized Charlier and generalized Meixner discrete orthogonal polynomials. For the generalized Charlier, we present an alternative derivation of the Laguerre–Freud relations found by Smet and Van Assche. Third-order and second-order nonlinear ordinary differential equations are found for the recursion coefficient γn, that happen to be forms of the Painlevé deg-PV in disguise. New Laguerre–Freud relations are also found for the generalized Meixner case, which are compared with those of Smet and Van Assche.

Research on dynamic robust planning method for active distribution network considering correlation

The universality of load subjects in distribution network brings challenges to the reliability of distribution network planning results. In this paper, a two-stage dynamic robust distribution network planning method considering correlation is proposed. The method evaluates the correlation between random variables using the Spearman rank correlation coefficient, and converts the correlated random variables into mutually independent random variables by Cholesky decomposition and independent transformation; expresses the source-load uncertainty by a bounded interval without distribution, and describes the active distribution network planning as a dynamic zero-sum game problem by combining with the two-phase dynamic robust planning; use the Benders decomposition approach to tackle the issue; mathematical simulation is used to confirm the accuracy and efficacy of the method. The results show that the dynamic robustness planning method of active distribution network taking into account the correlation can accurately simulate the operation of active distribution network with uncertain boundaries, which enhances the reliability and economy of the active distribution network planning results.

Penyusunan Program Komputasi Pengidentifikasi Parameter Dinamik Balok Ditumpu Jepit-Bebas

Operational Modal Analysis (OMA) is a new procedure to identify a structural vibrating system. In this paper, the operational modal analysis based on Ibrahim Time Domain Method. This method requires some displacement data from free vibration response of structure model. Here, a beam with clamped-free condition is used as a test model. Based on Finite Element Method, this beam is divided into 3 elements that consist of 6 degree of freedoms for each element (3 translations and 3 rotations). In this case, a fixed lumped mass is added to each translation node. The beam is excited in its clamped support by sinusoidal displacement during 0.1 s. After 0.1 s, the excitation is stopped and then the displacement data is recorded. Therefore, this condition could be assumed that recorded data represents free vibration response. For this purpose, some computation program was developed to predict the response of free vibration system. First, we make a program SINUS.FOR to produce a sinus displacement function. This function as a support motion is used as an input for program BALKEN.FOR that consist of various program, like Guyan Condensation, Cholesky Decomposition, Jacobi Method, Matrix Iteration Method, Phase Plane Method, Finite Difference Method, Houbolt Method, etc. This entire program is compiled by FORTRAN programming language. Next, the output of BALKEN.FOR that called matrix [A] become an input of program EIGENWERT-ITD.MW which is written in MAPLE programming languages. In this research, it is assumed that only the displacement of x1(t), x2(t) and x3(t) is known. It is known that to identify a system with 6 degrees of freedom, The Ibrahim Time Domain Method requires displacement responses. To fulfill this condition, we need 9 pseudo measurement stations. It means that each station with known displacement response has to be manipulated in such way so that it can produce 3 pseudo displacement response groups. The Result shows that the common error is below 5 %. Except, the damping ratio of mode number 5 is more than 10 %. While the other result can be identified better, especially for the natural frequency is identified very well.

Clinamen2: Functional-style evolutionary optimization in Python for atomistic structure searches

Clinamen2 is a versatile functional-style Python implementation of the covariance matrix adaptation evolution strategy (CMA-ES) utilizing Cholesky decomposition. On top of a problem-agnostic core algorithm, the software package offers a suite of utilities and library code enabling applications to important atomistic structure searches. Features include massively distributed computation and the BI-Population restart scheme. This article details the general code structure and introduces examples that illustrate some relevant applications for the materials science and chemistry worlds, including interfacing to density-functional-theory codes and machine-learned surrogate models. The functional design renders the code modular and adaptable, and makes the creation of interfaces to other atomistic software straightforward. Program summaryProgram Title: Clinamen2CPC Library link to program files:https://doi.org/10.17632/x7syr2txsd.1Developer's repository link:https://github.com/Madsen-s-research-group/clinamen2-public-releasesCode Ocean capsule:https://codeocean.com/capsule/4950229Licensing provisions: Apache-2.0Programming language: PythonSupplementary material:Nature of problem: Find optimal atomistic structures retaining full flexibility in the choice of the optimization target, the methodological approach and its implementation (e.g. CPU- vs. GPU-heavy calculations). Enable interfacing with relevant software, including but not limited to density-functional-theory (DFT) codes and machine-learning (ML) solutions.Solution method: The covariance matrix adaptation evolution strategy (CMA-ES) algorithm is implemented using Cholesky decompositions for efficiency. The core algorithm and application examples for specific problems are implemented in functional-style Python free of side effects, with data classes to keep track of the state of the evolution. Dask is used for job control to enable highly distributed workflows. Advanced strategies like BI-Population CMA-ES are easy to implement and illustrated in the examples.

An adaptive support domain for the in-compressible fluid flow based on the localized radial basis function collocation method

In this paper, an adaptive support domain scheme is proposed to the in-compressible fluid flow based on the localized radial basis function collocation method (LRBFCM). The idea of the adaptive support domain avoids complex mathematical derivations of the finite difference method (FDM). Unlike other upwind schemes in the LRBFCM, the support domain uses the sampling nodes similar to different finite difference schemes, and the improved LRBFCM is further applied to the in-compressible fluid flows. Considering the Kronecker tensor product and Cholesky decomposition techniques, the improved LRBFCM can be easily used to the lid-driven problems with Reynolds numbers up to 100,000 by a simple mathematical derivation. The proposed LRBFCM has an adaptive support domain similar to the finite difference schemes with much less CPU time costs.

AN EFFICIENT METHOD TO SIMULATE THE VARYING STATIC RECEPTANCE OF A THIN-WALLED WORKPIECE

A new method to simulate the varying static receptance of a thin-walled workpiece based on the Cholesky decomposition is presented in this paper. In this method, the system stiffness matrix is updated by subtracting the elemental stiffness matrices of the removed elements from the initial system stiffness matrix. The updated system stiffness matrix is permuted by using a novel method based on element removing sequence and considering fill-in reduction. The Cholesky factor of the permuted system stiffness matrix is reused to compute the static receptance of the workpiece for multiple cutter locations. The reduction of computation time by using this new method is proved by a numerical test and the accuracy of the simulation is demonstrated with a machining test.

Regularized estimation of Kronecker structured covariance matrix using modified Cholesky decomposition

In this paper, we study a Kronecker structured model for covariance matrices when data are matrix-valued. Using the modified Cholesky decomposition for Kronecker structured covariance matrix, we propose a regularized covariance estimator by imposing shrinkage and smoothing penalties on the Cholesky factors. A regularized flip-flop (RFF) algorithm is developed to produce a statistically efficient estimator for a large covariance matrix of matrix-valued data. Asymptotic properties are investigated and the performance of the estimator is evaluated by simulations. The results presented are applied to real data example.