MATLAB in Physics - Matrices by Matt McDonnell

The third lecture in a series on using MATLAB® in undergraduate physics courses. (matrices, demo, physics)

rrefexample(A)

rrefmovie(A,tol)

vectorExamples

LINFACTOR: uses LU or CHOL to factorize a matrix, or previously computed factors to solve Ax=b by Tim Davis

A simple M-file to solve Ax=b using LU or CHOL. (inv, lu, linsolve)

linfactor (arg1, arg2)

lintest (A,b)

lintests

n-Mode Tensor - Matrix Product by Fabian Schneiter

Calculates the n-mode product between a tensor and a matrix. (nmode, matrix, tensor)

nmodeproduct(A,M,n)

subspace.m by Andrew Knyazev

Angle between subspaces. (angle, subspaces, linear algebra)

subspace(A,B)

ortha.m by Andrew Knyazev

Orthonormalization Relative to matrix A (linear algebra, orthonormalization, relative)

[Q,varargout]=ortha(A,X)

Multiple-root polynomial solved by partial fraction expansion by Feng Cheng Chang

To find poles/residues of the rational function, instead of roots/multiplicities of the polynomial (mathematics, communications, control design)

polyroots(p)

Polynomial coefficient vector derived from sub-polynomial factors by Feng Cheng Chang

A polynomial coefficient vector is derived from several powered polynomial factors. (linear algebra, polynomial roots, polynomial division)

polyget(A)

Factorization of a polynomial with multiple roots by Feng Cheng Chang

By a novel effective approach "Monic polynomial subtraction" for computing GCD polynomial. (linear algebra, polynomial roots, greatest common divis...)

polyfct(p)

drawLA - Draw Toolbox for Linear Algebra. by Vladimir Bondarenko

Plot 2D/3D of vectors, planes, lines, spheres, and... display matrix equations. (visualization, plotting, linear algebra)

Introduction to the drawLA Toolbox

dispMEq(eq, varargin)

drawAxes(d, colr, labels)

Triangular and diagonal indexing by Bruno Luong

A collection of functions to index diagonal and triangular parts of the matrix (indexing, diagonal, matrix)

DiagM(n)

DuplicationM(n, option)

EliminationM(n, varargin)

Sum benchmark by Alain Barraud

Compute set of real values to be summed with an a priori known sum and specified condition number (linear algebra, sum computation, full precision comput...)

[sfp,se]=ExactSum(x)

[x,cdv,sv]=SumBench(n,cdref,sth)

test.m

Global to Local Coordinate Transformation Matrix by Paulo J. Paupitz Goncalves

T = trans_matrix_beam3d(x0,y0,z0,x1,y1,z1,alpha) (transformation, coordinate, global)

trans_matrix_beam3d(varargin)

Vector algebra for arrays of any size, with array expansion enabled by Paolo de Leva

Multiple dot, cross, and outer products, cross divisions, norms, normalizations, projections, etc. (linear algebra, projection, algebra)

cross2(a, b, idA, idB)

crossdiv(varargin)

dot2(a, b, idA, idB)

CIRCULANT (v2.0, feb 2009) by Jos (10584)

(yet another, but fast) Circulent Matrix (matrix, matrix manipulation, matrices)

circulant(A,d)

Linearly spaced multidimensional matrix without loop by Steeve AMBROISE

Generates a N-dimensional matrix of linearly equally spaced points between the matrices d1 and d2. (kronecker tensor prod..., linearly spaced, multidimensional matr...)

linspaceNDim(d1, d2, n)

Conjugate Gradient Method by Yi Cao

Conjugate Gradient Method to solve a system of linear equations (linear algebra, linear equation, mathematics)

conjgrad(A,b,tol)

h_trid by Matt Fig

Uses the Householder method to tridiagonalize a matrix. (linear algebra, tridiagonalize househ..., symmetric)

h_trid(A)

shift by John T. McCarthy

SHIFT a row or column RELATIVE to the other elements in a MATRIX. (matrices, shift, matrix)

shiftd(A,column,shift,type)

shiftl(A,row,shift,type)

shiftr(A,row,shift,type)

spok: checks if a MATLAB sparse matrix is OK by Tim Davis

Useful for mexFunction authors only (linear algebra, sparse, mex)

spok (A) ...

spok_install

spok_test

EliminateConstraints by Andrew Jackson

Eliminates variables from a problem with linear equality constraints to give an unconstrained proble (linear algebra, contraint, linear)

[C,d]=eliminateConstraints(A,b)

LCP / MCP solver (Newton-based) by Yuval

Solve the Linear Complementarity Problem. (lcp, mixed complementarity..., mathematics)

LCP(M,q,l,u,x0,display)

Vandermonde matrix by Siqing Wu

Creating matrix with terms of geometric progression in each row (geometric progression, linear algebra, vandermonde matrix)

vanderm(v,c)

Create orthonormal vectors by Calvin Price

Creates a random set of orthonormal vectors (linear algebra, orthonormal vectors, orthogonal vectors)

get_orthonormal(m,n)

UDFactor by Dmitry Savransky

Performs the U-D factorization of a symmetric matrix. (linear algebra, ud factorization, ud filter)

UDFactor(P,uflag)

Std Example by Bo Dai

according to the example in paper 'A note on standard deviation', which was written by Harley Weston (linear algebra, standard derivation, denominator)

[w,b]=Select()

STDTest.m

simulink matrix element by Nassim Khaled

This block outputs a given element of a matrix defined by the raw and the column indices of the elem (column, matrix element, raw)

matrix_element

Factoring a multiple-root polynomial by Feng Cheng Chang

A multiple-root polynomial is factored into lower-degree distict-root polynomials, then solved. (linear algebra, polynomial multiple r..., great common divisor)

PolyFct(p)

UFget: MATLAB interface to the UF sparse matrix collection by Tim Davis

Downloads sparse matrices from the web directly into the MATLAB workspace, from a vast range of real (linear algebra, sparse, matrix)

UFget (matrix, UF_Index)

UFget_defaults

UFget_lookup (matrix, UF_Index)

regtools by Per Christian Hansen

Analysis and Solution of Discrete Ill-Posed Problems. (discrete, illposed, regularization)

app_hh(A,beta,v)

art(A,b,k)

baart(n)

successive under/over relaxation by Daniel Cortes

solves the linear system Au=F using successive over/under relaxation. WhereA is diagonally dominant (linear algebra, gauss seidel, successive)

sor(A,F,w,u0,dtol,itmax)

POINTS2CIRCLE by Jos (10584)

determine the circle through 3 points (v2.0) (linear algebra, fit, circle)

points2circle(P,P2,P3)

Gram-Schmidt Process by Anthony Russo

Implements the Gram-Schmidt Process (basis, gram, orthogonal)

Gram_Schmidt_process(A)

basis_col(A)

basis_row(A)

Sort Eigenvectors & Eigenvalues by Calvin Price

Sort a set of eigenvectors and corresponding eigenvalues (eigenvectors, linear algebra, sort)

[P2,D2]=sortem(P,D)

Partial Least-Squares and Discriminant Analysis by Yi Cao

A tutorial and tool using PLS for discriminant analysis. (pca, pls, linear algebra)

Principal Component Analysis and Partial Least Squares

pls (X,Y,tol2)

Pseudo-Inverse Update by Yi Cao

Two rank-one pseudo-inverse update functions. (linear algebra, incremental pseudoinv..., pseudoinverse)

M=pinvupdateapp(A,B,x)

M=pinvupdatered(A,B,c)

Update Inverse Matrix by Yi Cao

update inverse of matrix after appending or reducing one coulmn and one row. (inverse matrix, linear algebra, incremental inverse)

M=invupdateapp(A,x,y,r)

M=invupdatered(A,r,c)

Faddeev-Leverrier Algorithm by Yi Cao

An iterative approach to generate characteristic polynomial coefficients (linear algebra, characteristic polyno..., inverse)

Faddeev-Leverrier Algorithm

[p,Ainv,B]=fadlev(A)

Row Echelon Form by Muhammad Rafiullah Arain

Method for row echelon form of matrix (linear algebra, solution, upper triangular matr...)

ref(a)

detp by Reinaldo Mauricio do Nascimento

Linear algebra with pivoting (linear algebra, determinant, linear equations syst...)

d=detp(A,op)

Totally unimodular by Ed Scheinerman

Checks if a matrix is totally unimodular (linear algebra, totally unimodular, square)

tum(A)

determinant of a 3 by 3 matrix in simulink by Nassim Khaled

This code evaluates the determinant of a 3 by 3 matrix in simulink (linear algebra, determinant, 3 by 3)

Determinant_sim

PCAtool by Guillaume MAZE

Compute everything you need for EOF,EEOF,CEOF,SVD,lagged SVD (empirical orthogonal, compute, pcatool)

calCeof(M,N,METHOD)

calEeof(M,N,METHOD,NLAG,DT)

caleof(M,N,method);

MESHND by Tim Davis

creation and nested dissection of regular 2D and 3D meshes (linear algebra, sparse, nested dissection)

meshnd (arg1,n,k)

meshnd_example

meshnd_quality (do_metis)

conjorth by Joshua Carmichael

Constructs conjugate-orthogonal basis from matrix (linear algebra, conjugate gradient, aconjugate)

[U]=conjorth(W,A)

Linear equation system 'Ax=r' by Gauss elimination method by Sobhan Rostami

Solve N-equation (gauss elimination, matlab, linear algebra)

Nequation.m

andop by Antonio Trujillo-Ortiz

Angle of the scalar product of two vectors. (angle, dop product, linear algebra)

andop(A,B,s)

triangulationVolume by Jeroen Verbunt

Compute volume and area of triangulation using divergence theorem of Gauss (triangulation, volume, area)

testTriangulationVolume(TRI,X,Y,Z)

triangulationVolume(TRI,X,Y,Z)

Hamiltonian operation on Lattice by Yuma Lim

Hamiltonian operation on square Lattices (matrix) (linear algebra, hamilton, hamiltonian)

HamiltonianLattice(a)

OLS by Marco Cococcioni

This functions implements the algorithm of Orthogonal Least Squares. It can be used to rank regresso (ols, functions, linear algebra)

ols(A,b,r,threshold)

Gerschgorin's disk Thm (a test) by Summit Suen

plot eigenvalue on complex plane show that all these points located in such circles. (linear algebra, gerschgorin eigenvalu..., test)

testGerschgorin(A)