James Baglama


Dr. James Baglama James Baglama
Chair of Mathematics
Department of Mathematics and Applied Mathematical Sciences
University of Rhode Island
Kingston, Rhode Island 02881
Office: Lippitt Hall 200D
Phone: 401.874.2709
Fax: 401.874.4454


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All computer codes are illustrations of methods developed in the Papers listed below. They are not optimized for performance or set up for commercial use. Any use beyond illustrative or public use requires consent of the code author(s) - James Baglama.


EIGENVALUES
Symmetric
The program irbleigs.m is a MATLAB program for computing a few eigenvalues and associated eigenvectors located anywhere in spectrum of a large sparse Hermitian matrix. The irbleigs.m program is matrix-free, i.e., the matrix is accessed only through the evaluation of matrix-vector products. The code can also compute the generalized eigenpairs of certain generalized eigenvalue problems.
Click here to download the MATLAB code irbleigs.m.
The program trreigs.m is a MATLAB program for computing a few extreme eigenvalues and associated eigenvectors of a large sparse symmetric matrix. The trreigs.m program is matrix-free, i.e., the matrix is accessed only through the evaluation of matrix-vector products. This MATLAB code trreigs.m is provided to illustrate Algorithm 6.1 in the paper: Baglama, J., Bella, T. and Picucci, J., Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix SIAM Journal on Scientific Computing, 43(5), (2021), pp.S200-S224. pdf file
Click here to download the MATLAB code trreigs.m.
   
Non-Symmetric
The program ahbeigs.m is a MATLAB program for computing a few eigenvalues and associated eigenvectors located anywhere in spectrum of a large sparse non-symmetric matrix. The program ahbeigs.m is based on a block Arnoldi method that makes use of Householder reflections to maintain orthogonality and restarting is accomplished by augmentation of the Krylov subspace with Schur vectors. No factorization is required in order to find extreme eigenvalues, however factorization is performed when searching for non-extreme eigenvalues. The program can solve the standard or the generalized eigenvalue problem. Research supported by NSF grant DMS-0311786. Reference paper: Baglama, J., Augmented block householder Arnoldi method Linear algebra and its applications, 429(10), (2008), pp.2315-2334. pdf file pdf file
Click here to download the MATLAB code ahbeigs.m.


SINGULAR VALUES
The routine irblsvds.m is a MATLAB program for computing a few singular values and singular vectors of a m x n matrix A. irblsvds.m uses the (m+n) x (m+n) Hermitian matrix Z = [0 A; A' 0] and calls irbleigs.m to find a few eigenvalues and eigenvectors of the matrix Z. The singular values of A are the positive eigenvalues of Z, the "right" singular vectors V, correspond to the last n elements of the eigenvectors of Z, and the "left" singular vectors U, correspond to the first m elements of the eigenvectors of Z.References (papers) 1, 2, 3, 9, and 10.
Click here to download the MATLAB code irblsvds.m.
The routines irlba.m and irlbablk.m are MATLAB programs for computing a few singular values and singular vectors of a m x n matrix A. irlba.m is a restarted Lanczos bidiagonalization method and irlbablk.m is a restarted block Lanczos bidiagonalization method. Restarting is carried out by augmentation of Krylov subspaces with either Ritz vectors or harmonic Ritz vectors. Reference papers: Augmented Implicitly Restarted Lanczos Bidiagonalization Methods paper14.pdf and Restarted Block Lanczos Bidiagonalization Methods paper17.pdf
Click here to download the MATLAB code irlba.m.
Click here to download the block MATLAB code irlbablk.m.
The code irlba has also been written in the language R by Bryan Lewis. Click here for the video and slides.
Click here for the R package on CRAN for the code irlba. Code is maintained by Bryan Lewis.
Click here for the Python package of irlba. Code is maintained by Bryan Lewis.
The routines rd2svds.m and trrsvds.m are MATLAB programs for computing a few singular values and singular vectors of a m x n matrix A. trrsvds.m is a hybrid restarted Lanczos bidiagonalization method using thick-restarting and restarting with linear combination to compute the k largest (or smallest) singular values and associated vectors. Implements Algorithm 4 the paper Hybrid Iterative Refined Restarted Lanczos Bidiagonalization Method rd2svds.m is a restarted Lanczos bidiagonalization method using deflation to compute the k largest singular values and associated vectors. Implements Algorithm 5 the paper Hybrid Iterative Refined Restarted Lanczos Bidiagonalization Method paper34.pdf
Click here to download the readme file readme.txt.
Click here to download the MATLAB driver code driver_trrsvds_rd2svds.m.
Click here to download the MATLAB code trrsvds.m.
Click here to download the MATLAB code rd2svds.m.


LEAST SQUARES
The routines alsqr.m and irlsqr.m are MATLAB programs for computing the solution of min ||Ax-b|| where A is an (m x n) matrix, b an (m x 1) vector, and x is an (n x 1) vector. b is not assumed to be in span(Col(A)). The routine alsqr.m is an augmented preconditioned LSQR method. The preconditioner is computed via an augmented Lanczos bidiagonalization method with harmonic Ritz vectors. The program then runs LSQR on the preconditioned system. The routine irlsqr.m is a preconditioned implictly restarted LSQR method, that is mathematically equivalent to< i>alsqr.m . The preconditioner is computed via implicitly restarted Lanczos bidiagonalization method with harmonic Ritz values. The program then runs LSQR on the preconditioned system. References: An Augmented LSQR Method http://link.springer.com/article/10.1007%2Fs11075-012-9665-8 and Implicitly Restarting the LSQR Algorithm http://etna.mcs.kent.edu/vol.42.2014/pp85-105.dir/pp85-105.pdf
Click here to download the MATLAB code alsqr.m.
Click here to download the MATLAB code irlsqr.m.


DIRECT SOLVER FOR BANDED LINEAR SYSTEMS
The following are the MATLAB and FORTRAN 95 codes associated with the paper, An asynchronous direct solver for banded linear systems. This package provides a set of functions to solve linear systems that do not require row echelon form. The functions are (i) Algorithm_21_TMFS.m, a MATLAB function to solve tridiagonal linear systems without exponential growth using a modified forward substitution technique, and (ii) Algorithm_22_TMFBS.m, a MATLAB function to solve tridiagonal linear systems without exponential growth using a modified forward and backward substitution technique, and (iii) Algorithm_31_BMFS.m, a MATLAB and FORTRAN function to solve banded systems using a forward substitution technique. Note that the current implementation in Fortran requires the ISML add-on. In MATLAB, one can see a demonstration of the algorithms compared to the built-in backslash solver by running the associated driver.m functions. Reference: An Asynchronous Direct Solver for Banded Linear Systems http://link.springer.com/article/10.1007/s11075-016-0251-3
Click here to download the README file README.txt.
Click here to download the MATLAB code Algorithm_21_TMFS_Driver.m.
Click here to download the MATLAB code Algorithm_21_TMFS.m.
Click here to download the MATLAB code Algorithm_22_TMFBS_Driver.m.
Click here to download the MATLAB code Algorithm_22_TMFBS.m.
Click here to download the MATLAB code Algorithm_31_BMFS.m.
Click here to download the MATLAB code Algorithm_31_BMFS_Driver.m.
Click here to download the FORTRAN 95 code Algorithm_31_BMFS.f90.



Papers
  1. Baglama, J., Calvetti, D. and Reichel, L., Iterative methods for the computation of a few eigenvalues of a large symmetric matrix. BIT Numerical Mathematics, 36, (1996), pp.400-421. pdf file
     
  2. Baglama, J., Calvetti, D., Reichel, L. and Ruttan, A., Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling. Journal of Computational Physics, 146(1), (1998), pp.203-226. pdf file
     
  3. Baglama, J., Calvetti, D. and Reichel, L., Fast leja points. Electron. Trans. Numer. Anal, 7(124-140), (1998), pp.119-120. pdf file
     
  4. Baglama, J., Calvetti, D., Golub, G.H. and Reichel, L., Adaptively preconditioned GMRES algorithms. SIAM Journal on Scientific Computing, 20(1), (1998), pp.243-269. pdf file
     
  5. Jang, S.J. and Baglama, J., Qualitative behavior of a variable-yield simple food chain with an inhibiting nutrient. Mathematical biosciences, 164(1), (2000), pp.65-80. pdf file
     
  6. Allen, E.J., Baglama, J. and Boyd, S.K., Numerical approximation of the product of the square root of a matrix with a vector. Linear Algebra and its Applications, 310(1-3), (2000), pp.167-181. pdf file
       
  7. Baglama, J., Dealing with linear dependence during the iterations of the restarted block Lanczos methods. Numerical Algorithms, 25, (2000), pp.23-36. pdf file
       
  8. Jang, S.J. and Baglama, J., A nutrient-prey-predator model with intratrophic predation. Applied mathematics and computation, 129(2-3), (2002), pp.517-536. pdf file
       
  9. Baglama, J., Calvetti, D. and Reichel, L., IRBL: An implicitly restarted block-Lanczos method for large-scale Hermitian eigenproblems. SIAM Journal on Scientific Computing, 24(5), (2003), pp.1650-1677. pdf file
       
  10. Baglama, J., Calvetti, D. and Reichel, L., Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix. ACM Transactions on Mathematical Software (TOMS), 29(3), (2003), pp.337-348. pdf file
       
  11. Jang, S.J. and Baglama, J., Persistence in variable-yield nutrient-plankton models. Mathematical and computer modelling, 38(3-4), (2003), pp.281-298. pdf file
       
  12. Jang, S.R.J., Baglama, J. and Seshaiyer, P., Intratrophic predation in a simple food chain with fluctuating nutrient. Discrete Contin. Dyn. Syst. Ser. B, 5(2), (2005), pp.335-352. pdf file
       
  13. Jang, S.J. and Baglama, J., Nutrient-plankton models with nutrient recycling. Computers and Mathematics with Applications, 49(2-3), (2005), pp.375-387. pdf file
       
  14. Baglama, J. and Reichel, L., Augmented implicitly restarted Lanczos bidiagonalization methods. SIAM Journal on Scientific Computing, 27(1), (2005), pp.19-42. pdf file
       
  15. Jang, S.J. and Baglama, J., Droop models of nutrient-plankton interaction with intratrophic predation. Applied mathematics and computation, 169(2), (2005), pp.1106-1128. pdf file
       
  16. Jang, S.J., Baglama, J. and Rick, J., Nutrient-phytoplankton-zooplankton models with a toxin. Mathematical and Computer Modelling, 43(1-2), (2006), pp.105-118. pdf file
       
  17. Baglama, J. and Reichel, L., Restarted block Lanczos bidiagonalization methods. Numerical Algorithms, 43(3), (2006), pp.251-272. pdf file
       
  18. Jang, S.R.J. and Baglama, J., Nutrient-plankton interaction with a toxin in a variable input nutrient environment. In Current Developments In Mathematical Biology (2007), pp. 131-147. pdf file
       
  19. Baglama, J. and Reichel, L., Decomposition methods for large linear discrete ill-posed problems. Journal of computational and applied mathematics, 198(2),(2007), pp.332-343. pdf file
       
  20. Baglama, J. and Reichel, L., Augmented GMRES-type methods. Numerical Linear Algebra with Applications, 14(4), (2007), pp.337-350. pdf file
       
  21. Baglama, J., Augmented block householder Arnoldi method. Linear algebra and its applications, 429(10), (2008), pp.2315-2334. pdf file
       
  22. Jang, S.R.J., Baglama, J. and Rick, J., Plankton-toxin interaction with a variable input nutrient. Journal of Biological Dynamics, 2(1), (2008), pp.14-30. pdf file
       
  23. Jang, S.R.J. and Baglama, J., Continuous-time predator–prey models with parasites. Journal of Biological Dynamics, 3(1), (2009), pp.87-98. pdf file
       
  24. Jang, S.R.J., Baglama, J. and Wu, L., Random dispersal in a predator-prey-parasite system. Journal of Biological Systems, 18(04), (2010), pp.825-845. pdf file
       
  25. Baglama, J. and Reichel, L., An implicitly restarted block Lanczos bidiagonalization method using Leja shifts. BIT Numerical Mathematics, 53, (2013), pp.285-310. Journal Link
       
  26. Baglama, J., Reichel, L. and Richmond, D., An augmented LSQR method. Numerical Algorithms, 64, (2013), pp.263-293. Journal Link
       
  27. Jang, S., Baglama, J. and Wu, L., Dynamics of phytoplankton-zooplankton systems with toxin producing phytoplankton. Applied Mathematics and Computation, 227, (2014), pp.717-740. Journal Link
       
  28. Baglama, J. and Richmond, D.J., Implicitly restarting the LSQR algorithm. Electronic Transactions on Numerical Analysis, 42, (2014), pp.85-105. pdf file
       
  29. Baglama, J., Fenu, C., Reichel, L. and Rodriguez, G., Analysis of directed networks via partial singular value decomposition and Gauss quadrature. Linear Algebra and its Applications, 456, (2014), pp.93-121. Journal Link
       
  30. Baglama, J., Kane, M., Lewis, B. and Poliakov, A., Efficient thresholded correlation using truncated singular value decomposition. arXiv preprint arXiv:1512.07246 (2015). Arxiv Link
       
  31. Baglama, J., IRLBA: Fast Partial Singular Value Decomposition Method, Chapter in Handbook of Big Data (2016), pp.125-136.
       
  32. Jandron, M.A., Ruffa, A.A. and Baglama, J., An asynchronous direct solver for banded linear systems. Numerical Algorithms, 76, (2017), pp.211-235. Journal Link
       
  33. Baglama, J., Bella, T. and Picucci, J., Hybrid iterative refined method for computing a few extreme eigenpairs of a symmetric matrix. SIAM Journal on Scientific Computing, 43(5), (2021), pp.S200-S224. pdf file
       
  34. Baglama, J., Perovic, V. and Picucci, J., Hybrid iterative refined restarted Lanczos bidiagonalization methods. Numerical Algorithms, Vol. 92, (2023), pp. 1183-1212. Journal Link
       


Quotes


"Experience is what you get when you didn't get what you wanted"
- Randy Pausch


"Don't waste time calculating your chances of success and failure. Just fix your aim and begin"
- Guan Yin Tzu


"An invisible red thread connects those who are destined to meet, regardless of time, place, or circumstance. The thread may stretch or tangle, but will never break."
- An ancient Chinese belief


"The most exciting phrase to hear in science, the one that heralds new discoveries, is not `Eureka!' but `That's funny...' "
- Isaac Asmiov


"Time and space are modes by which we think and not conditions in which we live."
- Albert Einstein


"It is a miracle that curiosity survives formal education."
- Albert Einstein


" It is the supreme art of the teacher to awaken joy in creative expression and knowledge."
- Albert Einstein


"I am not a teacher, I am an awakener."
- Robert Frost


"If nothing's fair, why can't it ever be unfair in *my* favor?"
- Calvin and Hobbes, "Calvin and Hobbes"



NOTICE: The information presented on this page represents the personal views, ideas, and opinions of the author. This is not an official University of Rhode Island web page. Links contained at this web site to other organizations, are presented as a service and neither constitute nor imply university endorsement or warranty.


James Baglama