Sparse Matrices in MATLAB: Design and Implementation

Gilbert, John R.; Moler, Cleve B.; Schreiber, Robert

doi:10.1137/0613024

Cited by 459 publications

(272 citation statements)

References 17 publications

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“…Spatial EIS combines the original EIS principle developed by Richard and Zhang (2007) for high-dimensional MC integration with sparse matrix algebra, which allows for fast computation on the large sparse precision matrices typically found in high-dimensional spatial applications. In fact, sparse matrix operations signicantly reduce operation counts and memory requirements relative to the corresponding operations on dense matrices (see, e.g., Gilbert et al, 1992, LeSage and Pace, 2009, Pace and LeSage, 2011. This combination of EIS with sparse matrix algebra ensures that accurate MC likelihood evaluations remain computationally feasible even in high-dimensional latent spatial Gaussian models.…”

Section: Model Specicationmentioning

confidence: 99%

Likelihood Based Inference and Prediction in Spatio-Temporal Panel Count Models for Urban Crimes

2015

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. recently developed ecient importance sampling techniques applicable to high-dimensional spatial models with sparse precision matrices. Our estimation results conrm socio-economic explanations for crime and, foremost, the broken-windows hypothesis, whereby less severe crimes in a region is a leading indicator for severe crimes. In addition to ML parameter estimates, we compute several other statistics of interest for law enforcement such as elasticities (idiosyncratic, total, short-term as well as long-term) of severe crimes w.r.t. less severe crimes, one-month-ahead out-of-sample forecasts, predictive cumulative distribution functions and validation test statistics based on these cdf's. Terms of use: Documents inJEL classication: C15; C23; C25; C51; C53; K42; R15.

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Section: Model Specicationmentioning

confidence: 99%

Likelihood Based Inference and Prediction in Spatio-Temporal Panel Count Models for Urban Crimes

2015

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“…This corresponds to Matlab's convention that explicit zeros are never stored in sparse matrices [13], and differs from the convention in the CSparse sparse matrix package [9]. Note that SAID need not be "zero": for example, in the min-plus semiring used for shortest path computations, SAID is ∞.…”

Section: B Kdt Filters In Pythonmentioning

confidence: 99%

High-Productivity and High-Performance Analysis of Filtered Semantic Graphs

Buluç

Duriakova

Fox

et al. 2013

2013 IEEE 27th International Symposium on Parallel and Distributed Processing

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Abstract-High performance is a crucial consideration when executing a complex analytic query on a massive semantic graph. In a semantic graph, vertices and edges carry attributes of various types. Analytic queries on semantic graphs typically depend on the values of these attributes; thus, the computation must view the graph through a filter that passes only those individual vertices and edges of interest.Knowledge Discovery Toolbox (KDT), a Python library for parallel graph computations, is customizable in two ways. First, the user can write custom graph algorithms by specifying operations between edges and vertices. These programmer-specified operations are called semiring operations due to KDT's underlying linear-algebraic abstractions. Second, the user can customize existing graph algorithms by writing filters that return true for those vertices and edges the user wants to retain during algorithm execution. For high productivity, both semiring operations and filters are written in a high-level language, resulting in relatively low performance due to the bottleneck of having to call into the Python virtual machine for each vertex and edge.In this work, we use the Selective Embedded JIT Specialization (SEJITS) approach to automatically translate semiring operations and filters defined by programmers into a lower-level efficiency language, bypassing the upcall into Python. We evaluate our approach by comparing it with the high-performance Combinatorial BLAS engine, and show our approach enables users to write in high-level languages and still obtain the high performance of low-level code. We also present a new roofline model for graph traversals, and show that our high-performance implementations do not significantly deviate from the roofline. Overall, we demonstrate the first known solution to the problem of obtaining high performance from a productivity language when applying graph algorithms selectively on semantic graphs.

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“…Both A and R T are stored by a simple compressed column scheme, because we are going to access them by columns and thus we can take advantage of the locality of reference (see Stewart [37, p. 110]) in Matlab 5 sparse packed storage scheme [16]. As pointed out by Davis & Hager [10, §7.1], in Matlab every change in the structure of a sparse matrix would entail a new copy of the entire matrix.…”

Section: Initial Factorization and Sparse Issuesmentioning

confidence: 99%

Updating and downdating an upper trapezoidal sparse orthogonal factorization†

Santos-Palomo¹,

Guerrero-Garcı́a²

2006

IMA Journal of Numerical Analysis

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We describe how to update and downdate an upper trapezoidal sparse orthogonal factorization, namely the sparse QR factorization of A T k , where A k is a "tall and thin" full column rank matrix formed with a subset of the columns of a fixed matrix A. In order to do that, we have adapted to rectangular matrices (with fewer columns than rows) Saunders' techniques of early 70s for square matrices, by using the static data structure of George and Heath of early 80s but allowing row downdating on it. An implicitly determined column permutation allow us to dispense with computing a new ordering after each update/downdate; it fits well into the Linpack downdating algorithm and ensures that the updated trapezoidal factor will remain sparse. We give all the necessary formulae even if the orthogonal factor is not available, and we comment on our implementation using the sparse toolbox of Matlab 5. Aims, difficulties and related workIn certain non-simplex active-set methods (also currently known as basisdeficiency-allowing simplex variations) for linear programming we need to solve a sequence of sparse compatible systems of the form:where b and c are iteration-dependent vectors, and x, y, and d are unknown vectors. Furthermore, the matrix A k ∈ R n×m k is a "tall and thin" iterationdependent full column rank matrix with m k ≤ n and rank(A k ) = m k . Such

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Sparse Matrices in MATLAB: Design and Implementation

Cited by 459 publications

References 17 publications

Likelihood Based Inference and Prediction in Spatio-Temporal Panel Count Models for Urban Crimes

Likelihood Based Inference and Prediction in Spatio-Temporal Panel Count Models for Urban Crimes

High-Productivity and High-Performance Analysis of Filtered Semantic Graphs

Updating and downdating an upper trapezoidal sparse orthogonal factorization†

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