MATLAB | EPFL Graph Search

MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on

The Neutron Scattering Structure Factor

Jérôme Egger

In the experience of neutron scattering, the structure factor is a value that can be almost directly measured (through the differential inelastic neutron scattering cross section). Thus it can be interesting to have a calculation which could give a theoretical point of view, even if the system used in the calculation cannot be as complex as in the real case. Although this calculation (of a simplified system) could be a bad representation of the real system, it is already a point of comparison which yields finally to a better understanding. The present work has the aim to provide a useful matlab code for the computation of the structure factor of small magnetic cluster in “spin-only” scattering. A concrete exemple and the result for a special configuration will be also given.

2010

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and

\|E\|_{2}

are finite. These properties allow to approximate any QT-matrix, within any given precision,by means of a finite number of parameters.QT-matrices, equipped with the norm

\|A\|_{\mathcal{QT}} = \alpha\|a\|_{\mathcal{W}} + \|E\|_{2}, for

\alpha \geq (1 + \sqrt{5})/2$,are a Banach algebra with the standard arithmetic operations. We provide an algorithmicdescription of these operations on the finite parametrization of QT-matrices, and we developa MATLAB toolbox implementing them in a transparent way. The toolbox is then extended toperform arithmetic operations on matrices of finite size that have a Toeplitz plus low-rankstructure. This enables the development of algorithms for Toeplitz and quasi-Toeplitz matriceswhose cost does not necessarily increase with the dimension of the problem.Some examples of applications to computing matrix functions and to solving matrix equa-tions are presented, and confirm the effectiveness of the approach.

MATHICSE2018

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off- diagonal blocks. This comprises problems with banded data, recently studied in [22, 32], which often arise in the discretization of elliptic PDEs. We show that, under suitable assumptions, the quasiseparable structure is guaranteed to be numerically present in the solution, and explicit novel estimates of the numerical rank of the off-diagonal blocks are provided. Efficient solution schemes that rely on the technology of hierarchical matrices are described, and several numerical experiments confirm the applicability and efficiency of the approaches. We develop a MATLAB toolbox that allows easy replication of the experiments and a ready-to-use interface for the solvers. The performances of the different approaches are compared, and we show that the new methods described are efficient on several classes of relevant problems.

MATHICSE2017

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and

\|E\|_{2}

are finite. These properties allow to approximate any QT-matrix, within any given precision,by means of a finite number of parameters.QT-matrices, equipped with the norm

\|A\|_{\mathcal{QT}} = \alpha\|a\|_{\mathcal{W}} + \|E\|_{2}, for

MATHICSE2018