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30
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
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Cited by 538 (19 self)
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The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, networks and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificiallygenerated matrices cannot meet, and is widely used by the sparse matrix algorithms community for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.
Algorithm 887: Cholmod, supernodal sparse cholesky factorization and update/downdate
 ACM Transactions on Mathematical Software
, 2008
"... CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or A A T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for b ..."
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Cited by 109 (8 self)
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CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or A A T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB TM interfaces. It appears in MATLAB 7.2 as x=A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions.
Algorithm 8xx: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate
, 2006
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Multifrontal multithreaded rankrevealing sparse QR factorization
"... SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading ..."
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Cited by 16 (2 self)
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SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase preeliminates singletons by permuting the input matrix into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fillreducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of A T A. Rankdetection is performed within each frontal matrix using Heath’s method, which does not require column pivoting. The resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a multicore computer.
Interactive Vector Field Feature Identification
"... Fig. 1. Above is a sequence of interactions performed during an exploration session in our system (also demonstrated in our accompanying video). Our interactive framework allows the user to specify representative control points (insets) of desired feature types. These control points guide a mapping ..."
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Cited by 10 (1 self)
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Fig. 1. Above is a sequence of interactions performed during an exploration session in our system (also demonstrated in our accompanying video). Our interactive framework allows the user to specify representative control points (insets) of desired feature types. These control points guide a mapping of the vector field points to the interactive texture canvas, where distances between the projected points encode similarities between their localized neighborhoods. Featurebased visualizations are generated through a painting interface, performed on this canvas. Abstract— We introduce a flexible technique for interactive exploration of vector field data through classification derived from userspecified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate featurebased visualizations by interactively highlighting wellaccepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types. Index Terms—Vector field, data clustering, feature classification, highdimensional data, user interaction 1
User Guide for CHOLMOD: a sparse Cholesky factorization and modification package
, 2009
"... CHOLMOD 1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for ..."
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Cited by 7 (0 self)
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CHOLMOD 1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. It also includes a nonsupernodal LDL T factorization method that can factorize symmetric indefinite matrices if all of their leading submatrices are wellconditioned (D is diagonal). CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. CHOLMOD Copyright c○20052009 by Timothy A. Davis. Portions are also copyrighted by William W. Hager (the Modify Module), and the University of Florida (the Partition and Core Modules). All Rights Reserved. Some of CHOLMOD’s Modules are distributed under the GNU General Public License, and others under the GNU Lesser General Public License. Refer to each Module for details. CHOLMOD is also available under other licenses that permit its use in proprietary applications; contact the authors for details. See
Updated Sparse Cholesky Factors for Corotational Elastodynamics
 TO APPEAR IN ACM TRANSACTIONS ON GRAPHICS
, 2012
"... We present warpcanceling corotation, a nonlinear finite element formulation for elastodynamic simulation that achieves fast performance by making only partial or delayed changes to the simulation’s linearized system matrices. Coupled with an algorithm for incremental updates to a sparse Cholesky fa ..."
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Cited by 6 (1 self)
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We present warpcanceling corotation, a nonlinear finite element formulation for elastodynamic simulation that achieves fast performance by making only partial or delayed changes to the simulation’s linearized system matrices. Coupled with an algorithm for incremental updates to a sparse Cholesky factorization, the method realizes the stability and scalability of a sparse direct method without the need for expensive refactorization at each time step. This finite element formulation combines the widely used corotational method with stiffness warping so that changes in the perelement rotations are initially approximated by inexpensive pernode rotations. When the errors of this approximation grow too large, the perelement rotations are selectively corrected by updating parts of the matrix chosen according to locally measured errors. These changes to the system matrix are propagated to its Cholesky factor by incremental updates that are much faster than refactoring the matrix from scratch. A nested dissection ordering of the system matrix gives rise to a hierarchical factorization in which changes to the system matrix cause limited, wellstructured changes to the Cholesky factor. We show examples of simulations that demonstrate that the proposed formulation produces results that are visually comparable to those produced by a standard corotational formulation. Because our method requires computing only partial updates of the Cholesky factor, it is substantially faster than full refactorization and outperforms widely used iterative methods such as preconditioned conjugate gradients. Our method supports a controlled tradeoff between accuracy and speed, and unlike most iterative methods its performance does not slow for stiffer materials but rather it actually improves.
A computational study of the use of an optimizationbased method for simulating large multibody systems
 OPTIMIZATION METHODS AND SOFTWARE
, 2008
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Interactive Quadrangulation with Reeb Atlases and Connectivity Textures
, 2010
"... Creating highquality quad meshes from triangulated surfaces is a highly non trivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjectiv ..."
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Cited by 4 (1 self)
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Creating highquality quad meshes from triangulated surfaces is a highly non trivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the highfrequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high quality statistics, while meeting the users
Efficient implementations of the generalized lasso dual path algorithm
 In preparation
, 2013
"... We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani & Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the specia ..."
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Cited by 4 (4 self)
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We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani & Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the special cases of trend filtering problems, fused lasso problems, and sparse fused lasso problems, both with X = I and a general matrix X. These specialized implementations offer a considerable improvement over the generic implementation, both in terms of numerical stability and efficiency of the solution path computation. These algorithms are all available for use in the genlasso R package, which can be found in the CRAN repository.