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111
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 536 (17 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.
Building rome in a day.
 In Proc. Int. Conf. on Computer Vision.
, 2009
"... We present a system that can reconstruct 3D geometry from large, unorganized collections of photographs such as those found by searching for a given city (e.g., Rome) on Internet photosharing sites. Our system is built on a set of new, distributed computer vision algorithms for image matching and ..."
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Cited by 285 (30 self)
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We present a system that can reconstruct 3D geometry from large, unorganized collections of photographs such as those found by searching for a given city (e.g., Rome) on Internet photosharing sites. Our system is built on a set of new, distributed computer vision algorithms for image matching and 3D reconstruction, designed to maximize parallelism at each stage of the pipeline and to scale gracefully with both the size of the problem and the amount of available computation. Our experimental results demonstrate that it is now possible to reconstruct cityscale image collections with more than a hundred thousand images in less than a day. intRoDuction Amateur photography was once largely a personal endeavor. Traditionally, a photographer would capture a moment on film and share it with a small number of friends and family members, perhaps storing a few hundred of them in a shoebox. The advent of digital photography, and the recent growth of photosharing Web sites such as Flickr.com, have brought about a seismic change in photography and the use of photo collections. Today, a photograph shared online can potentially be seen by millions of people. As a result, we now have access to a vast, evergrowing collection of photographs the world over capturing its cities and landmarks innumerable times. For instance, a search for the term "Rome" on Flickr returns nearly 3 million photographs. This collection represents an increasingly complete photographic record of the city, capturing every popular site, façade, interior, fountain, sculpture, painting, and café. Virtually anything that people find interesting in Rome has been captured from thousands of viewpoints and under myriad illumination and weather conditions. For example, the Trevi Fountain appears in over 50,000 of these photographs. How much of the city of Rome can be reconstructed in 3D from this photo collection? In principle, the photos of Rome on Flickr represent an ideal data set for 3D modeling research, as they capture the highlights of the city in exquisite detail and from a broad range of viewpoints. However, extracting high quality 3D models from such a collection is challenging for several reasons. First, the photos are unstructuredthey are taken in no particular order and we have no control over the distribution of camera viewpoints. Second, they are uncalibratedthe photos are taken by thousands of different photographers and we know very little about the camera settings. Third, the scale of the problem is
iSAM2: Incremental Smoothing and Mapping Using the Bayes Tree
"... We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probabili ..."
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Cited by 71 (26 self)
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We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable reordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.
Multicore bundle adjustment
 In IEEE Conference on Computer Vision and Pattern Recognition (CVPR
, 2011
"... We present the design and implementation of new inexact Newton type Bundle Adjustment algorithms that exploit hardware parallelism for efficiently solving large scale 3D scene reconstruction problems. We explore the use of multicore CPU as well as multicore GPUs for this purpose. We show that overco ..."
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Cited by 61 (4 self)
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We present the design and implementation of new inexact Newton type Bundle Adjustment algorithms that exploit hardware parallelism for efficiently solving large scale 3D scene reconstruction problems. We explore the use of multicore CPU as well as multicore GPUs for this purpose. We show that overcoming the severe memory and bandwidth limitations of current generation GPUs not only leads to more space efficient algorithms, but also to surprising savings in runtime. Our CPU based system is up to ten times and our GPU based system is up to thirty times faster than the current state of the art methods [1], while maintaining comparable convergence behavior. The code and additional results are available at
DOLFIN: Automated finite element computing
, 2009
"... We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms ..."
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Cited by 57 (6 self)
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We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which lowlevel code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and highperformance linear algebra. Easytouse objectoriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.
Informationbased compact Pose SLAM
 IEEE Trans. Robot
, 2010
"... Abstract—Pose SLAM is the variant of simultaneous localization and map building (SLAM) is the variant of SLAM, in which only the robot trajectory is estimated and where landmarks are only used to produce relative constraints between robot poses. To reduce the computational cost of the information fi ..."
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Cited by 39 (17 self)
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Abstract—Pose SLAM is the variant of simultaneous localization and map building (SLAM) is the variant of SLAM, in which only the robot trajectory is estimated and where landmarks are only used to produce relative constraints between robot poses. To reduce the computational cost of the information filter form of Pose SLAM and, at the same time, to delay inconsistency as much as possible, we introduce an approach that takes into account only highly informative loopclosure links and nonredundant poses. This approach includes constant time procedures to compute the distance between poses, the expected information gain for each potential link, and the exact marginal covariances while moving in open loop, as well as a procedure to recover the state after a loop closure that, in practical situations, scales linearly in terms of both time and memory. Using these procedures, the robot operates most of the time in open loop, and the cost of the loop closure is amortized over long trajectories. This way, the computational bottleneck shifts to data association, which is the search over the set of previously visited poses to determine good candidates for sensor registration. To speed up data association, we introduce a method to search for neighboring poses whose complexity ranges from logarithmic in the usual case to linear in degenerate situations. The method is based on organizing the pose information in a balanced tree whose internal levels are defined using interval arithmetic. The proposed PoseSLAM approach is validated through simulations, real mapping sessions, and experiments using standard SLAM data sets. Index Terms—Information filter, information gain, interval arithmetic, Pose SLAM, state recovery, treebased data association. I.
Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
 ACM Trans. Math. Software
, 2006
"... The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorizatio ..."
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Cited by 30 (10 self)
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The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a lowrank change to A (an update/downdate, A = A±WW T). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLASbased) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package, which forms the basis of x=A\b in MATLAB when A is sparse and symmetric positive definite. 1
A Riemannian optimization approach for computing lowrank solutions of Lyapunov equations
, 2009
"... We propose a new framework based on optimization on manifolds to approximate the solution of a Lyapunov matrix equation by a lowrank matrix. The method minimizes the error on the Riemannian manifold of symmetric positive semidefinite matrices of fixed rank. We detail how objects from differential ..."
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Cited by 26 (4 self)
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We propose a new framework based on optimization on manifolds to approximate the solution of a Lyapunov matrix equation by a lowrank matrix. The method minimizes the error on the Riemannian manifold of symmetric positive semidefinite matrices of fixed rank. We detail how objects from differential geometry, like the Riemannian gradient and Hessian, can be efficiently computed for this manifold. As minimization algorithm we use the Riemannian TrustRegion method of [Found. Comput. Math., 7 (2007), pp. 303–330] based on a secondorder model of the objective function on the manifold. Together with an efficient preconditioner this method can find lowrank solutions with very little memory. We illustrate our results with numerical examples.
Geodesic Patterns
"... Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which d ..."
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Cited by 16 (6 self)
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Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend sideways. Likewise a geodesic is the favored shape of timber support elements in freeform architecture, for reasons of manufacturing and statics. Both problem areas are fundamental in freeform architecture, but so far only experimental solutions have been available. This paper provides a systematic treatment and shows how to design geodesic patterns in different ways: The evolution of geodesic curves is good for local studies and simple patterns; the level set formulation can deal with the global layout of multiple patterns of geodesics; finally geodesic vector fields allow us to interactively model geodesic patterns and perform surface segmentation into panelizable parts.
Design of multicore sparse Cholesky factorization using DAGs
, 2010
"... The rapid emergence of multicore machines has led to the need to design new algorithms that are efficient on these architectures. Here, we consider the solution of sparse symmetric positivedefinite linear systems by Cholesky factorization. We were motivated by the successful division of the comput ..."
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Cited by 16 (8 self)
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The rapid emergence of multicore machines has led to the need to design new algorithms that are efficient on these architectures. Here, we consider the solution of sparse symmetric positivedefinite linear systems by Cholesky factorization. We were motivated by the successful division of the computation in the dense case into tasks on blocks and use of a task manager to exploit all the parallelism that is available between these tasks, whose dependencies may be represented by a directed acyclic graph (DAG). Our sparse algorithm is built on the assembly tree and subdivides the work at each node into tasks on blocks of the Cholesky factor. The dependencies between these tasks may again be represented by a DAG. To limit memory requirements, blocks are updated directly rather than through generatedelement matrices. Our algorithm is implemented within a new efficient and portable solver HSL MA87. It is written in Fortran 95 plus OpenMP and is available as part of the software library HSL. Using problems arising from a range of applications, we present experimental results that support our design choices and demonstrate that HSL MA87 obtains good serial and parallel times on our 8core test machines. Comparisons are made with existing modern solvers and show that HSL MA87 performs well, particularly in the case of very large problems.