Software

Giuseppe Rodriguez

• blgaussexp: Computation of the subgraph centrality of the nodes of a directed network
• corner.m: Find the corner of a discrete L-curve
• cosereg: Regularization by the Comparison of Solutions Estimator (COSE) method
• drsolve: Solver for linear systems with displacement structure
• ErresTools: Choosing a regularization parameter by error estimation
• FDEMtools3: A MATLAB package for EMI data inversion
• hubauth: Computation of the hub/authority centrality of the nodes of a network
• lbdtik: Tikhonov regularization by Lanczos bidiagonalization
• mngn2: Minimal norm solution of a nonlinear least squares problem
• orthomoms: A Matlab toolbox for the computation of the orthogonal moments of an image
• pqser: A Matlab package for spectral seriation
• ps3d: A Matlab package for photometric stereo 3D reconstruction
• rbc: Recursive computation of the broadcast centrality
• sgcen: Computation of the subgraph centrality of the nodes of an undirected network
• smt: Structured matrices toolbox
• SoftNet: A package for the analysis of complex networks
• specbip: A spectral method for bipartizing a network and detecting a large anti-community
• toms729gw: Fast solver for Toeplitz linear systems
• tpls: Fast least squares solver for Toeplitz linear systems

FDEMtools3

FDEMtools3: a MATLAB package for FDEM data inversion.
Authors: G. P. Deidda, P. Díaz De Alba, C. Fenu, G. Lovicu, F. Pes, and G. Rodriguez
This package provides a set of Matlab functions to solve a non-linear electromagnetic data inversion problem. Starting from electromagnetic data collected by a ground conductivity meter, we reconstruct either the electrical conductivity or the magnetic permeability of the soil with respect to depth by a regularized Gauss-Newton method. The inversion algorithm is based on the low-rank approximation of the Jacobian of the nonlinear model, which depends both on a relaxation parameter and a regularization parameter, chosen by automatic procedures. It also include a module for forward modelling.
The package is described in the papers:

• G. P. Deidda, P. Díaz De Alba, F. Pes, and G. Rodriguez
  Forward electromagnetic induction modelling in a multilayered half-space: An open-source software tool.
  Remote Sens., 15:1772, 2023.
  DOI: 10.3390/rs15071772
• G. P. Deidda, P. Díaz De Alba, C. Fenu, G. Lovicu, and G. Rodriguez
  FDEMtools: a MATLAB package for FDEM data inversion.
  Numer. Algorithms, 84:1313-1327, 2020.
  DOI: 10.1007/s11075-019-00843-2

The algorithms have been developed in the papers:

• G. P. Deidda, C. Fenu, and G. Rodriguez.
  Regularized solution of a nonlinear problem in electromagnetic sounding.
  Inverse Problems, 30:125014 (27 pages), 2014.
  DOI: 10.1088/0266-5611/30/12/125014
• P. Díaz De Alba and G. Rodriguez.
  Regularized inversion of multi-frequency EM data in geophysical applications.
  In F. Ortegón Gallego, M.V. Redondo Neble, and J.R. Rodríguez Galván, editors, Trends in Differential Equations and Applications, volume 8 of SEMA SIMAI Springer Series, pages 357-369. Springer, Switzerland, 2016.
  
• G.P. Deidda, P. Díaz De Alba, and G. Rodriguez.
  Identifying the magnetic permeability in multi-frequency EM data inversion.
  Electron. Trans. Numer. Anal., 47:1-17, 2017.
  

The package requires the Regularization Tools toolbox by P.C. Hansen.
Last updated: January 29, 2023.

SoftNet

A package for the analysis of complex networks.
Authors: C. Fenu, L. Reichelm and G. Rodriguez.
The software is described in the paper

• C. Fenu, L. Reichel, and G. Rodriguez
  SoftNet: A package for the analysis of complex networks.
  Algorithms, 15:296, 2022.
  DOI: 10.3390/a15090296

Last updated: June 29, 2022.

mngn2

mngn2: minimal norm solution of a nonlinear least squares problem.
Authors: F. Pes and G. Rodriguez.
This Matlab package implements the algorithms described in the papers:

• F. Pes and G. Rodriguez.
  The minimal norm Gauss-Newton method and some of its regularized variants.
  Electron. Trans. Numer. Anal., 53:459-480, 2020.
  DOI: 10.1553/etna_vol53s459
• F. Pes and G. Rodriguez.
  A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems.
  Appl. Numer. Math., 171:233-248, 2022.
  DOI: 10.1016/j.apnum.2021.09.002

The package requires the routine get_l.m from the Regularization Tools toolbox by P.C. Hansen.
Last updated: December 14, 2021.

ps3d

A Matlab package for photometric stereo 3D reconstruction.
Authors: A. Concas, R. Dessì, C. Fenu, G. Rodriguez, and M. Vanzi.
The software is described in the paper

• A. Concas, R. Dessì, C. Fenu, G. Rodriguez, and M. Vanzi
  Identifying the lights position in photometric stereo under unknown lighting.
  In 2021 21st International Conference on Computational Science and Its Applications (ICCSA), pages 10-20, Cagliari, Italy, September 2021.
  DOI: 10.1109/ICCSA54496.2021.00013.

Last updated: February 9, 2023.

rbc

Recursive computation of the broadcast centrality.
Authors: M. Al Mugahwi, O. De La Cruz Cabrera, C. Fenu, L. Reichel, and G. Rodriguez.
The software is described in the paper

• M. Al Mugahwi, O. De La Cruz Cabrera, C. Fenu, L. Reichel, and G. Rodriguez.
  Block matrix models for dynamic networks.
  Appl. Math. Comput., 402:126121, 2021.
  DOI: 10.1016/j.amc.2021.126121.

Last updated: February 19, 2021.

specbip

specbip: a spectral method for bipartizing a network and detecting a large anti-community.
Authors: A. Concas, S. Noschese, L. Reichel, and G. Rodriguez.
This function approximates a given network by a bipartite one. The algorithm produces a node permutation which makes the possible bipartite nature of the initial adjacency matrix evident, and identifies the two sets of nodes. The same procedure can be used to detect the presence of a large anti-community in a network and to identify it. The toolbox is described in the paper

• A. Concas, S. Noschese, L. Reichel, and G. Rodriguez.
  A spectral method for bipartizing a network and detecting a large anti-community.
  J. Comput. and Appl. Math., 2020.
  DOI: 10.1016/j.cam.2019.06.022

Last updated: June 24, 2019.

pqser

pqser: a Matlab package for spectral seriation.
Authors: A. Concas, C. Fenu, and G. Rodriguez.
This toolbox contains an implementation of an algorithm to solve the seriation problem. It also implements a data structure for PQ trees. The toolbox is described in the paper

• A. Concas, C. Fenu, and G. Rodriguez.
  pqser: a Matlab package for spectral seriation
  Numer. Algorithms, 80(3):879-902, 2019.
  DOI: 10.1007/s11075-018-0510-6

The spectral algorithm has been introduced in the paper

• J. E. Atkins, E. G. Boman, and B. Hendrickson.
  A spectral algorithm for seriation and the consecutive ones problem.
  SIAM J. Comput., 28(1):297-310, 1998.
  

Last updated: September 20, 2018.

cosereg

cosereg: regularization by the Comparison of Solutions Estimator (COSE) method.
Authors: M. E. Hochstenbach, Y. Park, L. Reichel, G. Rodriguez, and X. Yu.
The Comparison of Solution Estimator (COSE) is a strategy for choosing the regularization parameter by comparing the results of different methods. One of the functions in the toolbox is intended for small scale problems, the others are for large scale problems. Both standard and general form can be treated.
The algorithms are described in the papers:

• M. E. Hochstenbach, L. Reichel, and G. Rodriguez.
  Regularization parameter determination for discrete ill-posed problems.
  J. Comput. and Appl. Math., 273:132-149, 2015.
  DOI: 10.1016/j.cam.2014.06.004
• Y. Park, L. Reichel, G. Rodriguez, and X. Yu.
  Parameter determination for Tikhonov regularization problems in general form.
  J. Comput. and Appl. Math., 343:12-25, 2018.
  DOI: 10.1016/j.cam.2018.04.049

The package requires the Regularization Tools toolbox by P.C. Hansen.
Last updated: May 6, 2018.

orthomoms

orthomoms: a Matlab toolbox for the computation of the orthogonal moments of an image.
Authors: C. Di Ruberto, L. Putzu, and G. Rodriguez.
The functions in this package allow the computation of the moments of an image with respect to Legendre, discrete Chebyshev, and second kind Chebyshev orthogonal polynomials. The orthogonal moments are intended to be used as descriptors for image classification. The toolbox is described in the paper

• C. Di Ruberto, L. Putzu, and G. Rodriguez.
  Fast and accurate computation of orthogonal moments for texture analysis.
  Pattern Recongnit., 83:498-510, 2018.
  DOI: 10.1016/j.patcog.2018.06.012

Last updated: March 5, 2018.

blgaussexp

Computation of the subgraph centrality of the nodes of a directed network.
Authors: C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.
This set of functions allows the computation of the subgraph communicabilities between the nodes of a network, either undirected or directed, as well as the starting/ending convenience. The computation of is performed by block Gauss/Anti-Gauss quadrature. The functions were developed for Matlab, but they are compatible with Octave. They are described in the paper

• C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.
  Block Gauss and anti-Gauss quadrature with application to networks.
  SIAM J. Matrix Anal. Appl.,, 34(4):1655-1684, 2013.
  DOI: 10.1137/120886261

Last updated: October 27, 2014.

hubauth

Computation of the hub/authority centrality of the nodes of a network.
Authors: J. Baglama, C. Fenu, L. Reichel, and G. Rodriguez.
This set of functions allows the computation of the hub/authority centrality of the nodes of a network by three different algorithms: Gauss quadrature, low-rank approximation, and a hybrid method. The functions were developed for Matlab, but they are compatible with Octave. They are described in the paper

• J. Baglama, C. Fenu, L. Reichel, and G. Rodriguez.
  Analysis of directed networks via partial singular value decomposition and Gauss quadrature.
  Linear Algebra Appl., 456:93-121, 2014.
  DOI: 10.1016/j.laa.2014.05.018

The package contains a modified version of the routine irlba described in the paper

• J. Baglama and L. Reichel.
  Augmented implicitly restarted Lanczos bidiagonalization methods.
  SIAM J. Sci. Comput., 27:19-42, 2005.

We also use the routine irblsvds_leja, from

• J. Baglama and L. Reichel.
  An implicitly restarted block Lanczos bidiagonalization method using Leja shifts.
  BIT, 53:285-310, 2013.

We include a copy of both routines in the package, for user's convenience.
Last updated: July 4, 2014.

sgcen

Computation of the subgraph centrality of the nodes of an undirected network.
Authors: C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.
This set of functions allows the computation of the subgraph centrality of the nodes of a network. The functions were developed for Matlab, but they are compatible with Octave. They are described in the paper

• C. Fenu, D. Martin, L. Reichel, and G. Rodriguez.
  Network analysis via partial spectral factorization and Gauss quadrature.
  SIAM J. Sci. Comput., 35(4):A2046-A2068, 2013.
  DOI: 10.1137/130911123

The package contains a copy of the routine irbleigs from

• J. Baglama, D. Calvetti, and L. Reichel.
  Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix.
  ACM Trans. Math. Software, 29:337-348, 2012.

Last updated: Jun 16, 2014.

smt

Structured matrices toolbox.
Authors: M. Redivo-Zaglia and G. Rodriguez.
smt is a Matlab toolbox for structured matrix computation.
For documentation, see

• M. Redivo-Zaglia and G. Rodriguez.
  smt: a Matlab structured matrices toolbox.
  Numer. Algorithms, 59(4):639-659, 2012.
  DOI: 10.1007/s11075-011-9527-9

Last updated: January 20, 2011.

drsolve

Solver for linear systems with displacement structure.
Authors: A. Aricò and G. Rodriguez.
This package provides a set of Matlab functions to solve linear systems whose matrix belongs to the following classes: Cauchy-like, Toeplitz-like, Toeplitz+Hankel-like and Vandermonde-like. The solvers have a computational cost O(rn²), and use O(rn) memory locations, where n is the size and r is the displacement rank of the matrix.
See

• A. Aricò and G. Rodriguez.
  A fast solver for linear systems with displacement structure.
  Numer. Algorithms, 55(4):529-556, 2010.
  DOI: 10.1007/s11075-010-9421-x

Last updated: May 9, 2011.

ErresTools

Choosing a regularization parameter by error estimation.
Authors: G. Rodriguez.
This small Matlab toolbox contains some functions for determining a suitable value of the regularization parameter in TSVD and Tikhonov regularization by employing the error estimates described in the papers

• C. Brezinski, G. Rodriguez, and S. Seatzu.
  Error estimates for linear systems with applications to regularization.
  Numer. Algorithms, 49(1-4):85-104, 2008.
  DOI: 10.1007/s11075-008-9163-1
• C. Brezinski, G. Rodriguez, and S. Seatzu.
  Error estimates for the regularization of least squares problems.
  Numer. Algorithms, 51(1):61-76, 2009.
  DOI: 10.1007/s11075-008-9243-2

Some of the functions require the toolbox Regularization Tools by P.C. Hansen.
Last updated: March 10, 2010.

toms729gw

Fast solver for Toeplitz linear systems.
Authors: A. Aricò and G. Rodriguez (for the Matlab MEX gateway).
Authors: P.C. Hansen and T. Chan (for the computational routines).
This is a Matlab (Fortran) MEX gateway for TOMS Algorithm 729 by P.C Hansen and T. Chan, which implements a look-ahead Levinson method for the solution of Toeplitz linear systems. The algorithm is described in the paper

• P.C. Hansen and T. Chan.
  FORTRAN subroutines for general Toeplitz systems
  ACM Trans. Math. Software, 18(3):256-273, 1992.

Last updated: February 27, 2010.

lbdtik

Tikhonov regularization by Lanczos bidiagonalization.
Authors: L. Reichel and G. Rodriguez.
This Matlab function computes the Tikhonov regularized solution a linear system, choosing the regularization parameter by minimizing an estimate of the error. A test driver, (which requires the Regularization Tools) is included. The algorithm is described in the paper

• L. Reichel, G. Rodriguez, and S. Seatzu.
  Error estimates for large-scale ill-posed problems.
  Numer. Algorithms, 51(3):341-361, 2009.
  DOI: 10.1007/s11075-008-9244-1

Last updated: October 6, 2009.

tpls

Fast least squares solver for Toeplitz linear systems.
Author: G. Rodriguez.
This Matlab functions compute the least squares solution of an overdetermined, full-rank, Toeplitz linear system, by a fast algorithm. The method is based on the computation of the Schur complement of an augmented matrix, and is described in the paper

• G. Rodriguez.
  Fast solution of Toeplitz- and Cauchy-like least squares problems.
  SIAM J. Matrix Anal. Appl.,, 28(3):724-748, 2006.
  DOI: 10.1137/050629148

Last updated: August 4, 2007.

corner.m

Find the corner of a discrete L-curve.
Authors: P.C. Hansen, T.K. Jensen, and G. Rodriguez.
This Matlab function implements an adaptive algorithm for computing the corner of a discrete L-curve. The L-curve is a technique used in regularization methods for estimating the regularization parameter. The algorithm is described in the paper

• P.C. Hansen, T.K. Jensen, and G. Rodriguez.
  An adaptive pruning algorithm for the discrete L-curve criterion.
  J. Comput. and Appl. Math., 198(2):483-492, 2007.
  DOI: 10.1016/j.cam.2005.09.026

This function is included in Version 4 of the Regularization Tools by P.C. Hansen.
Last updated: January 11, 2007.