
Re: very specific symmetric matrix
Posted:
Jun 12, 2014 9:53 AM


"Eric " <eric.malitz@gmail.com> wrote in message news:lnavdt$e9i$1@newscl01ah.mathworks.com... > Bear with me as I try to explain what I want. I doubt anyone here will be > able to walk me through this, but I've tried many different things and I'm > all out of options. > > In general, what I'm trying to get is a specific symmetric matrix where > the entries are functions I have, evaluated at a grid of points (using the > i and j corresponding to those grid points). What I first imagined doing > was to try to make a matrix of function handles. Can't do this. The matrix > I want is composed of (M2)x(M2) blocks of (N2)x(N2) entries. I have > functions A, B, D and E. They are functions of 2 variables i,j (these come > from the grid; the functions look like u(i+1,j)2*u(i,j)+... etc). I want > something resembling this: > > E(2,2) D(2,2) 0... B(2,2) A(2,2) > 0.... 0..... > D(2,3) E(2,3) D(2,3) 0... A(2,3) B(2,3) A(2,3) > 0..... 0..... > 0... D(2,4) E(2,4) D(2,4) 0.... A(2,4) > B(2,4) A(2,4) 0..... > 0 0 D(2,5) E(2,5) > > > And this continues on. The main diagonal of the whole MATRIX is a block > with E running down the main diagonal of this BLOCK but evaluated at > (2,2), (2,3), (2,4), etc.. > The 2 off diagonals, next to E, are D, again evaluated at (2,2), (2,3), > etc. as you go down in rows. The blocks to the right and under this block > is the same idea but it's B along main diagonal and A on the 2 off > diagonals. These blocks all continue down in this symmetric fashion, and > the rest of is 0's. Again, (M2)x(M2) blocks of (N2)*(N2) entries. Let > me do a specific example where N=M=5: > > E D 0 B A 0 0 0 0 < evaluated at (2,2) > D E D A B A 0 0 0 <evaluated at (2,3) > 0 D E 0 A B 0 0 0 <evaluated at (2,4)
This line is inconsistent with what you described above. The second 0 should be D(2, 4), shouldn't it? There are similar inconsistencies with other lines.
> B A 0 E D 0 B A 0< evaluated at (3,2) > A B A D E D A B A<evaluated at (3,3) > 0 A B 0 D E 0 A B< evaluated at (3,4) > 0 0 0 B A 0 E D 0<evaluated at (4,2) > 0 0 0 A B A D E D<evaluated at (4,3) > 0 0 0 0 A B 0 D E< evaluated at (4,4) > > I challenge anyone to help me, after hours and hours of getting nowhere > with this.
If your functions are vectorized (can be evaluated for vectors of values, not just scalars) then try the following:
% Define some coordinates [c1, c2] = meshgrid(2:4);
% Define a function E = @(x1, x2) x1+x2;
% Evaluate E to get a vector of data v1 = E(c1(:), c2(:));
% Use v1 to create a matrix with E on the main diagonal and one of the diagonals above the main. % Since the diagonal above the main is shorter, I needed to cut a few elements off the end of v1 % to make the matrix returned by the second DIAG call the same size as the first M = diag(v1, 0)+diag(v1(1:end2), 2);
What you should receive is a 9by9 M matrix whose main diagonal is [4 5 6 5 6 7 6 7 8] and where each of those diagonal elements is duplicated two elements to the right in their row.
This generalizes to multiple functions (not just the one E that I used) and different diagonals.
If the E, D, etc. return values are matrices instead of vectors the same size as the inputs, take a look at the BLKDIAG function, regular concatenation, or (depending on the specific pattern) the CIRCSHIFT function .
E1 = [1 2;3 4]; D1 = [5 6; 7 8]; z = zeros(2); M2 = [E1 D1 z; D1 z E1; z E1 D1]
 Steve Lord slord@mathworks.com To contact Technical Support use the Contact Us link on http://www.mathworks.com

