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Osni Marques' Home Page
Interests
Selected Publications
- The Use of Bulk States to Accelerate the Band Edge State Calculation
of a Semiconductor Quantum Dot, with C. Voemel, S. Tomov,
L.-W.-Wang and J. Dongarra. Submitted to the Journal of
Computational Physics.
- Benefits of IEEE-754 Features in Modern Symmetric Tridiagonal
Eigensolvers, with C. Voemel and J. Riedy. To appear
in SIAM SISC.
- Computations of Eigenpair Subsets with the MRRR Algorithm, with C. Voemel and B. Parlett. Numerical Linear
Algebra with Applications, 13:643-653, 2006.
- The Advanced CompuTational Software (ACTS) Collection, with T. Drummond. ACM TOMS, 31:282-301, 2005.
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Building A Software Infrastructure for Computational Science
Applications: Lessons and Solutions, with T. Drummond. Proceedings of the SE-HPCS'05 Conference, Saint Louis, MO, 2005.
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The ACTS Collection, Robust and High-Performance Tools for Scientific Computing: Guidelines for Tool Inclusion and Retirement, with T. Drummond.
Technical Report LBNL/PUB-3175, November 15, 2002.
- A Computational Strategy for the Solution
of Large Linear Inverse Problems in Geophysics, with T. Drummond and D. W.
Vasco. International Parallel and Distributed Processing Symposium (IPDPS), Nice,
France, 2003.
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Resolution, Uncertainty and Whole Earth Tomography, with D. W. Vasco and L. R.
Johnson. Journal of Geophysical Research, Solid Earth, 108, Jan 10, 2003.
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On Computing Givens Rotations Reliably and Efficiently, with D.
Bindel, J. Demmel and W. Kahan. ACM TOMS, 28:206-238, 2002.
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A Building Block Approach for Determining Low-frequency Normal Modes
of Macromolecules, with F. Tama, F. X. Gadea and Y.-H. Sanejouand.
Proteins: Structure, Function and Genetics, 41:1-7, 2000.
Applications
Inverse Problems in Earth Sciences
The problems described here resulted from a collaboration
with Don Vasco,
(LBNL/Earth Sciences Division).
In this collaboration, we investigated tools for the solution of large
inverse problems from applications in Geophysics; namely in the
study of a physical model for the internal structure of the Earth. In this
study, a linear model for the Earth structure is obtained by discretizing
the Earth into layers, and the layers into cells. The velocity of wave
propagation in each cell is represented by a set of parameters that account
for anisotropy, location (and correction) of sources and receivers, etc.
These parameters are written in matrix form and the goal is to fit the
model by means of some known data. Travel times of sound waves generated
by earthquakes are used to construct the model. The validation of the model
requires the computation of an approximate generalized inverse and a (partial)
singular value decomposition (SVD) is used for that purpose. The SVD is
also used to estimate resolution and uncertainties.
The following table lists some of the numerical models that have been studied, where
m is number of travel times (number of rows in the matrix),
n is the number of parameters in the model (number of columns in the matrix)
and nnz is the number of nonzero entries in the corresponding matrix.
A block Lanczos algorithm was used to compute a rank-k SVD approximation
for the models. Although sparse, such problems are difficult to deal with
because several thousand singular values and singular vectors may be required
for a proper estimation of the model parameters and resolution. For details,
see Solving Large Linear Inverse Problems
in Geophysics by means of Eigenvalue Calculations and also
BLZPACK.
----------------------------------------
model m n nnz
----------------------------------------
1 846968 96300 28587210
2 1433102 307134 51506866
3 1433102 307134 47968477
----------------------------------------
Gallery:
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Model 3. Resolution for the mantle using 10,000 Lanczos vectors
for compressional waves. The picture shows the diagonal entries of the
resolution matrix, R=VVT, where V contains
the Lanczos approximations for the left singular vectors. |
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Model 3. Velocity deviation estimates for the mantle using 10,000 Lanczos vectors
for compressional waves. |
Conformational Changes of Proteins
This was a collaboration with Yves-Henri
Sanejouand (Laboratoire de Physique, ENS Lyon). The goal was to study conformational changes of proteins by means of linear combinations
of normal modes coordinates. These coordinates are obtained from solutions of an
eigenvalue problem Ax=µx, where A is a symmetric matrix
computed from the potential energy and the atomic masses of the protein.
The following table lists some cases that have been studied,
where n is the dimension of the matrix A (three times the
number of atoms) and nnz is the number of nonzero entries in the
upper triangle of A. For details, see
Protein Motions through Eigenanalyses:
A Set of Study Cases and also BLZPACK. Later, Yves-Henri and collaborators proposed a simplified method,
RTB (rotations-translations of blocks), to study conformation changes
of proteins. For most cases, this method can significantly speed up the
calculations of the low-frequency normal modes that are usually required
in the analyses, without loss of accuracy. The software can be obtained
from Yves-Henri.
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protein n nnz
----------------------------------------
crambin 1188 134217
lysozyme 3795 490602
ras_p21A 4986 669060
ras_p21B 4998 677832
ras_p21C 4998 698973
ras_p21D 4986 691776
arabinose 8592 1161360
citrate synthase 25584 3691020
----------------------------------------
Gallery:
 |
Simplified model of the maltodextrin binding protein (370 residues)
and animation of the first mode shape
(hinge-bending motion, closure of the binding site) using the RTB method.
The picture shows the "effective residues" (one sphere per amino-acid)
and the corresponding bonds (between neighbors). |
 |
Simplified model of the LAO binding protein (238 residues) and
animation
of
the first mode shape (hinge-bending motion, closure of the binding site)
using the RTB method. The picture shows the "effective residues" (one sphere
per amino-acid) and the corresponding bonds (between neighbors). |
 |
 |
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Three representations of crambin (ball-and-stick, ribbon and
Van der Waals), which is a protein found in some seeds. The model shown
comprises 396 atoms. |
 |
 |
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Original upper triangle, reverse Cuthill-McKee and symmetric minimum
degree ordering of the matrix corresponding to the numerical model used
for crambin. The matrix has dimension 1188 and 134217 non zeros in its
upper triangle, including the diagonal. |
 |
 |
Ribbon representation of ras, which is a protein related with
the transmission of biochemical information between the surface of the
cell and its nucleus (mutations in human ras genes are responsible for
up to one third of all cases of cancer, see Just obeying orders,
by S. Day, New Scientist, 27 May 1995), and the upper triangle of the matrix
corresponding to the numerical model for ras (1662 atoms, dimension 4986
and 669060 non zeros in its upper triangle, including the diagonal). |
|
Information Retrieval
In 1997-1998 I collaborated with Mike Palmer, from Inktomi Inc,
in the investigation of matrix methods for information retrieval on sets
of documents obtained from the World Wide Web. The dimension of one of
the term-document matrices examined was 100,000 (number of terms or words)
by 2,559,430 (number of documents or home pages), which contained 421 million
nonzero entries. One of our eigenvalue solvers (BLZPACK)
was used to compute singular values and singular vectors of this
matrix. To the best of our knowledge, at the time it was the largest matrix for which
a (partial) singular value decomposition had been computed.
The computation of 10 singular values and left singular vector required
710 seconds of wall clock time on 64 processors of a Cray T3E-900 (900
Mflops/PE, 256 MB/PE): 99.5% of that time was spent with matrix-vectors
multiplications (for the generation of Lanczos vectors). For details about information
retrieval and related topics see Michael Berry's LSI
Web Site, the LSA Web Site at
CU Boulder, and also some of the papers written by Jon
Kleinberg and
Inderjit
Dhillon.
Gallery:
 |
Singular value distribution of the 100,000-by-2,559,430 term-document
matrix (54 steps of the Lanczos algorithm). |
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First two singular vectors of he 100,000-by-2,559,430 term-document
matrix (54 steps of the Lanczos algorithm). |
Tools for Spectral Portrait Computations
This work was carried out at in collaboration with the Qualitative
Computing Group (led by Prof. Francoise Chaitin-Chatelin) of the Parallel
Algorithms Project (led by Prof. Iain Duff) at CERFACS.
The goal was to develop tools for the computation of pseudospectra of linear
operators. For details, see Spectral Portrait Computation by a Lanczos
Method (augmented and
normal matrix versions). See also
Pseudospectra of Linear Operators by Nick
Trefethen, SIAM Review, 39:383-406, 1997, and the
Matrix
Market page on spectral portraits.
Gallery:
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Spectral portrait of the La Rose matrix (65536 grid points). |
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Spectral portrait of the Tolosa matrix (18225 grid points). |
Structural Engineering Problems
In my Ph.D. work at COPPE, Federal
University of Rio de Janeiro, Brazil, I studied reduced basis techniques
for the solution of systems of partial differential equations, and algorithms
for the solution of large sparse eigenvalue problems. These problems arise
very often in Structural Engineering Finite Element analyses. During the
thesis I was a Research Associate with PETROBRAS
(The Brazilian Petroleum Company) and also worked as a consultant for INPE
(Brazilian Institute for Spatial Research), using the MSC/NASTRAN
code.
Gallery:
 |
Double-cross with frequencies distributed in clusters (see Selected
Results from the NAFEMS, Dynamics Working Group Free Vibrations, Benchmarks,
Part 1, by A. Morris, Benchmarks, April 1987). The finite element model
used comprises 321 nodes, 320 2D beam elements and 947 degrees of freedom.
|
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Self-elevating drilling unit designed for operation up to 100m
water depth. The finite element model used comprises 90 nodes, 96 3D beam
elements and 531 degrees of freedom.
|
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Steel jacket platform designed for 170m water depth.
The finite element model comprises 437 nodes, 1097 3D beam elements and
2463 degrees of freedom.
|
Software
The development of the software listed below was required in the context of the
problems I have worked on. The codes are stored in gzipped tar files and also winzip files.
In case of download problems or questions about the codes just send me an e-mail. The release date is given as a
reference since I may update the codes from time to time.
- STETESTER (for Symmetric
Tridiagonal Eigensolver Tester) is a Fortran 90 implementation of a testing infrastructure for LAPACK's symmetric tridiagonal eigensolvers, which is available upon request. Difficult test matrices and performance results obtained on a variety of platforms are also provided.
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BLZPACK (for Block LancZos PACKage, release 04/00)
is a standard Fortran 77 implementation of the block Lanczos algorithm intended
for the solution of the standard eigenvalue problem Ax=µx or the
generalized eigenvalue problem Ax=µBx,
where A and B are real, sparse symmetric matrices, µ
an eigenvalue and x an eigenvector. The development of this eigensolver
was motivated by the need to solve large, sparse, generalized problems
from free vibration analyses in structural engineering. Several upgrades
were performed afterwards aiming at the solution of eigenvalues problems
from a wider range of applications. Documentation: user's guide,
technical report and comprehensive bibliography. Source code: blzpack.tgz,
blzpack.zip.
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HLZPACK (for Hermitian LancZos PACKage, release 04/00)
is a standard Fortran 77 implementation of the Lanczos algorithm intended for
the solution of the problem Hx=µx, where H is a complex
Hermitian matrix, µ an eigenvalue and x an eigenvector. The development
of this eigensolver began at CERFACS and was motivated mainly by the need to compute spectral portraits. Documentation: user's guide,
technical report and comprehensive bibliography. Source code: hlzpack.tgz,
hlzpack.zip.
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SKYPACK (for SKYline PACKage, release 04/00) is a
standard Fortran 77 implementation of a set of subroutines intended for computations
(factorization, matrix-vector product) with matrices stored in a skyline (profile)
form. The development
of this package began at CERFACS and was motivated by finite element applications. Documentation: user's guide,
technical report and comprehensive bibliography. Source code: skypack.tgz,
skypack.zip.
Other