Matlab Programs

A Basic Introduction to Matlab:     pdf

Matlab Programs for Image Processing

• Routines for 3D jigsaw puzzle generation and assembly written by Anna Grim:  zip     
  
  • Based on a work at http://math.umn.edu/~olver/vi_/goosst.pdf.

• Routines for automatic planar jigsaw puzzle assembly written by Daniel Hoff:  zip     
  
  • Automatic Jigsaw Puzzle Solver by Daniel Hoff and Peter J. Olver is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
        
    
  • Note: designed to work in Matlab R2011a and later versions.
        Earlier versions may require deleting or modifying the line rng('shuffle'), which only introduces some randomness in order to make the code more robust.
  • Based on a work at http://math.umn.edu/~olver/vi_/puzzles.pdf.

• Routines for recognition of planar curves based on extended signatures written by Daniel Hoff:  zip
  • Based on a work at http://math.umn.edu/~olver/vi_/hoffo.pdf.

Matlab Programs for Math 4457

• dspr.m — normal modes of oscillation of linear mass & spring system
• gspr.m — graph oscillations of linear mass & spring system
• cspr.m — show oscillations of linear mass & spring system
• mspr.m — show oscillations and normal components of linear mass & spring system
• dyst.m — dynamical modes of oscillation of 2D or 3D structure
• network.m — finds potentials and currents in electrical networks
• strut.m — graphs a structure in two or three dimensions, and determines its stability
• graph.m — finds incidence matrix and plots a graph
• quasi.m — plot quasi—periodic function (2 modes)
• quasi3.m — plot quasi—periodic function (3 modes)

Computational subroutines

• incidence.m — computes incidence matrix from edge matrix
• ngon.m — finds coordinates for unit polygon
• solids.m — edge matrices and vertices for regular solids
• house.m — edge matrices and vertices for houses
• tr3.m — linear transformations of multiple points

Graphics subroutines

• button.m — sets up buttons for interacting with dynamical graphics
• circle.m — draws circles
• triangle.m — draws triangles
• linevec.m — draws lines using vector coordinates
• arrowvec.m — draws directed lines using vector coordinates
• textvec.m — writes text at specified coordinates

Matlab Programs for Math 5457

• Qplot.m — for graphing quadratic functions
• ellipse.m — graphs ellipses and their principal axes
• ellipsoid.m — graphs ellipsoids and their principal axes
• network.m — finds potentials and currents in electrical networks
• strut.m — graphs a structure in two or three dimensions, and determines its stability
• graph.m — finds incidence matrix and plots a graph
• cgraph.m — finds incidence matrix and plots complete graph
• ograph.m — finds incidence matrix and plots circular graph

Computational subroutines

• incidence.m — computes incidence matrix from edge matrix
• cedge.m — finds edge matrix for complete graph
• oedge.m — finds edge matrix for circular graph
• cgon.m — finds edge matrix and vertex coordinates for complete graph
• ogon.m — finds edge matrix and vertex coordinates for circular graph
• ngon.m — finds coordinates for unit polygon
• solids.m — edge matrices and vertices for regular solids
• house.m — edge matrices and vertices for houses
• tr3.m — linear transformations of multiple points

Graphics subroutines

• circle.m — draws circles
• triangle.m — draws triangles
• linevec.m — draws lines using vector coordinates
• arrowvec.m — draws directed lines using vector coordinates
• textvec.m — writes text at specified coordinates

Matlab Programs for Math 5458

• phase3.m — phase portrait of 3D ordinary differential equation
• heat.m — numerical solution of 1D heat equation (Crank—Nicholson method)
• wave.m — numerical solution of 1D wave equation (finite difference method)
• go2.m — graph solutions to planar linear o.d.e.'s
• go3.m — graph solutions to three—dimensional linear o.d.e.'s
• dspr.m — normal modes of oscillation of linear mass & spring system
• gspr.m — graph oscillations of linear mass & spring system
• cspr.m — show oscillations of linear mass & spring system
• mspr.m — show oscillations and normal components of linear mass & spring system
• dyst.m — dynamical modes of oscillation of 2D or 3D structure
• phase.m — phase portrait of 2D ordinary differential equation
• phaseg.m — phase portrait plus graph of second order ordinary differential equation
• phasem.m — phase portrait plus movie of pendulum motion

Computational subroutines

• o3.m — a simple 3D differential equation
• fset.m — set up for Fourier sine series
• fsine.m — plot Fourier sine series
• fset2.m — set up for Fourier series
• fouri.m — plot Fourier series
• lo2.m — general planar linear first order o.d.e.
• lo3.m — general three—dimensional linear first order o.d.e.
• button.m — sets up buttons for interacting with dynamical graphics
• quasi.m — plot quasi—periodic function (2 modes)
• quasi3.m — plot quasi—periodic function (3 modes)
• pendulum.m — nonlinear pendulum differential equations
• dpendulum.m — damped nonlinear pendulum differential equations
• fpendulum.m — forced nonlinear pendulum differential equations
• fdpendulum.m — forced damped nonlinear pendulum differential equations

Matlab Programs for Math 5485

• rn.m — rounding function
• iter.m — function iteration
• secant.m — secant method
• newton.m — Newton's method
• gauss.m — regular Gaussian elimination
• gaussr.m — alternative regular Gaussian elimination
• back.m — back substitution
• trid.m — generate tridiagonal matrices
• specr.m — compute spectral radius of a matrix
• miter.m — matrix iteration
• jacobi.m — Jacobi iteration
• gs.m — Gauss—Seidel iteration
• sor.m — SOR iteration
• sorw.m — optimal SOR parameter
• sorad.m — compute SOR spectral radius
• newton3.m — solve z^3 = 1 by Newton's method
• robot.m — position robot arms by Newton's method
• lagrangep.m — Lagrange interpolating polynomial
• lagrangeplot.m — Plot Lagrange interpolating polynomial
• ix2.m — the function 1/(1+x^2)

Matlab Programs for Math 5486

• numode.m — general—purpose numerical ordinary differential equation solver and grapher
• Euler method:  neuler.m    neulerf.m
• Improved Euler method:  ieuler.m    ieulerf.m
• Midpoint method:  midp.m    midpf.m
• Fourth Order Runge—Kutta:  rk4.m    rk4f.m
• Sample Differential Equations:
  • Scalar ode du/dt = (1 — 4t/3)u:   gv.m  Solution:  gvs.m
  • Undamped pendulum:   upend.m
  • Damped pendulum:   dpend.m
  • Van der Pol oscillator:   vpd.m
  • Predator–prey model:   pp.m

e-mail:   olver@umn.edu
http://www.math.umn.edu/~olver