Rank: 486 based on 217 downloads (last 30 days) and 9 files submitted
photo

Matthew Harker, Paul O'Leary,

E-mail
Company/University
University of Leoben, Austria

Personal Profile:

Matthew Harker and Paul O'Leary we work on discrete mathematics for inverse problems and machine vision. Discrete orthogonal basis functions and matrix algebraic approached to solving ODEs and PDEs are central to our research.

Professional Interests:
matrix algebraic solutions to ODEs and PDEs

 

Watch this Author's files

 

Files Posted by Matthew Harker, View all
Updated   File Tags Downloads
(last 30 days)
Comments Rating
24 Jun 2014 Screenshot figure2eps: version 1.3 Combine vector graphics, e.g. text, axis etc. with bitmap graphics for surfaces in one eps file. Author: Matthew Harker, Paul O'Leary, eps, bitmap, opengl, zbuffer, painters, renderer 22 0
  • 4.0
4.0 | 1 rating
19 Mar 2014 Screenshot Solving Inverse IVPs and BVPs real-time solution of inverse problems for embedded systems Author: Matthew Harker, Paul O'Leary, ivp, bvp, inverse problems, embedded systems, realtime 12 0
04 Mar 2014 Screenshot Discrete Orthogonal Polynomial Toolbox: DOPBox Version 1.8 A toolbox for discrete orthogonal polynomials and their applications to fitting, ODEs etc. Author: Matthew Harker, Paul O'Leary, discrete orthogonal p..., polynomial approximat..., fitting, local polynomial appr..., bvps, ivps 40 0
  • 5.0
5.0 | 2 ratings
20 Aug 2013 Screenshot Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0 This toolbox is for the regularized reconstruction of a surface from its measured gradient field. Author: Matthew Harker, Paul O'Leary, gradient field, surface reconstructio..., inverse problems, discrete orthogonal p..., tikhonov regularizati..., spectral methods 45 3
31 Jul 2013 Screenshot publish2latex Using full Latex markup in m-files to generate high quality documentation. Version 1.3 Author: Matthew Harker, Paul O'Leary, latex, pdf, publish, documentation 12 0
Comments and Ratings by Matthew Harker, View all
Updated File Comments Rating
02 Sep 2013 Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0 This toolbox is for the regularized reconstruction of a surface from its measured gradient field. Author: Matthew Harker, Paul O'Leary,

Indeed there was an error in dopDiffLocal which was a result of a change made in Version 1.6. We have deposited a corrected version of the library (Version 1.7).

26 Aug 2013 Pseudospectral Differentiation on an Arbitrary Grid Numerically differentiates a function on an arbitrary grid. Author: Greg von Winckel

It is important to point out that this approach only workd for a very small number of points (nodes). The differentiating matrix D should be rank one deficient. However running the following simple test shows that even for a very small problem D has additional nullspaces. Already with 20 nodes and quadratically spaced point the method generates a degenerate differentiating matrix.
%
n = 20;
% Generate a seto of linearly spaced nodes 0 <= x <= 1
x1 = linspace( 0, 1, n )';
% generate quadratically spaced nodes as an example of arbitrary
% nodes.
x2 = x1.^2;
%
%% Compute the Differentiating Matrices
%
D1 = collocD( x1 );
D2 = collocD( x2 );
%
%% Compute the Rank of the Matrices
% The following test shows that the matrices do not have a consistent
% rank. It may be concluded that the method, although theoritically
% sound, is serioudly deficient in its numerical behavious.
%
disp('Rank of the differentiating matrices');
rD1 = rank( D1 )
rD2 = rank( D2 )
%
% Rank deficiency
%
disp('Rank deficiency of the differentiating matrices');
disp('All shound be rank-1 deficient.');
%
rdD1 = length(x1) - rD1
rdD2 = length(x2) - rD2

14 Aug 2013 DMSUITE MATLAB Differentiation Matrix Suite Author: J.A.C Weideman

There algorith behind the function poldif.m is numerically unstable. Consider the following code

N = 30;
x0 = linspace( 0, 1, N)';
x1 = x0.^2;
x2 = x1.*x0;
%
D0 = poldif( x0, 1 );
D1 = poldif( x1, 1 );
D2 = poldif( x2, 1 );

These are simply three different distributions of nodes 0 <= x <= 1.
Given N points each of the differentiating matrices should be rank N - 1, a differentiating has the constant vector as its null space.
Computing

%
rD0 = rank( D0 )
rD1 = rank( D1 )
rD2 = rank( D2 )
%
reveals ranks of 29, 6, and 3 respectivly! Firstly this indicates tha the algorithm has failed, even for the modest number of 30 nodes. Now if we compute D times a constant vector it should yield the zero vector.
%
vnD0 = D0 * ones( N, 1);
vnD1 = D1 * ones( N, 1);
vnD2 = D2 * ones( N, 1);
%
It does not. This is a more serious error. Since the errors are concentrated at the ends of the support. Exactly where we need precision if initial and boundary value problems are to be solved accurately.

Despite this problem, the package as a whole is an important contribution.

Comments and Ratings on Matthew Harker,'s Files View all
Updated File Comment by Comments Rating
10 Sep 2013 figure2eps: version 1.3 Combine vector graphics, e.g. text, axis etc. with bitmap graphics for surfaces in one eps file. Author: Matthew Harker, Paul O'Leary, MERCIER, David

02 Sep 2013 Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0 This toolbox is for the regularized reconstruction of a surface from its measured gradient field. Author: Matthew Harker, Paul O'Leary, Paul O'Leary,, Matthew Harker,

Indeed there was an error in dopDiffLocal which was a result of a change made in Version 1.6. We have deposited a corrected version of the library (Version 1.7).

29 Aug 2013 Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0 This toolbox is for the regularized reconstruction of a surface from its measured gradient field. Author: Matthew Harker, Paul O'Leary, E

Hello again,

I just got the code working by replacing line 157 in the m-file "dopDiffLocal.m" from

rS = rank( S );

to

rS = sprank( S );

since the error I was getting before seemed to have been generated by the fact that the matrix S is sparse, and the function rank does not work with sparse matrices.

Please let me know your take on this modification (i.e., if this was your intended meaning in the context).

Thanks again,

E.

29 Aug 2013 Surface Reconstruction from Gradient Fields: grad2Surf Version 1.0 This toolbox is for the regularized reconstruction of a surface from its measured gradient field. Author: Matthew Harker, Paul O'Leary, E

Dear authors,

I have downloaded your code for surface reconstruction from gradient for comparison purposes. I am in the early testing stages, and I tried generating a test surface using the function provided "g2sTestSurf.m". Specifically, I tried:

[Z,Zx,Zy,x,y] = g2sTestSurf(121,121,'even',1);

This works, and I can see the test surface as well as its gradient components, but when I try to reconstruct the surface from the gradient, by typing in the command:

Zr = g2s( Zx, Zy, x, y );

I get the following error message:

Error using svd
Use svds for sparse singular values and vectors.

Error in rank (line 15)
s = svd(A);

Error in dopDiffLocal (line 157)
rS = rank( S );

Error in g2s (line 82)
Dx = dopDiffLocal( x, N, N, 'sparse' ) ;

Could you please let me know what it is that I am doing wrong?

Thank you in advance,

E.

05 Jun 2013 Discrete Orthogonal Polynomial Toolbox: DOPBox Version 1.8 A toolbox for discrete orthogonal polynomials and their applications to fitting, ODEs etc. Author: Matthew Harker, Paul O'Leary, Arghad

Contact us