The symbol between matrix A and vector b is a “backslash”. You can also solve the same system in MATLAB using command You now need to use command “rref”, in order to reduce the augmented matrix to its reduced row echelon form and solve your system:Ĭan you identify the solution of the system after you calculated matrix C? You have now generated augmented matrix Aaug (you can call it a different name if you wish). In order to solve the system Ax=b using Gauss-Jordan elimination, you first need to generate the augmented matrix, consisting of the coefficient matrix A and the right hand side b: To generate a column vector b (make sure you include the prime ’ at the end of the command). The function can also connect nodes further than radius = 1.This command generates a 3x3 matrix, which is displayed on your screen.
It can also support 3D (and arbitrarily higher domensional grids). It can handle 4-connect grid (radius 1 according to L1 norm), 8-connect grid (radius 1 according to L_infty norm). I have a nice working m-function (link: sparse_adj_matrix.m) that is quite general. = size(mat) % Get the matrix sizeĭiagVec1 = repmat(, r, 1) % Make the first diagonal vectorĭiagVec1 = diagVec1(1:end-1) % Remove the last valueĭiagVec2 = ones(c*(r-1), 1) % Make the second diagonal vectorĪdj = diag(diagVec1, 1)+diag(diagVec2, c) % Add the diagonals to a zero matrixĪdj = adj+adj.' % Add the matrix to a transposed copy ofĪnd you'll get the following matrix: adj =Ĩ-connected neighbors: mat = % Sample matrixĭiagVec2 = % Make the second diagonal vectorĭiagVec3 = ones(c*(r-1), 1) % Make the third diagonal vectorĭiagVec4 = diagVec2(2:end-1) % Make the fourth diagonal vectorĪdj = diag(diagVec1, 1)+. Here is how you can create the adjacency matrix for each case, using your sample matrix above as an example: 4-connected neighbors: mat = % Sample matrix You can take advantage of this fact to easily create your matrices using the diag function (or the spdiags function if you want to make a sparse matrix). Specifically, they are symmetric and banded. If you notice, there is a distinct pattern to the adjacency matrices you are creating. How can this improved to avoid all the looping? This the code that I have so far: N = 3 M = 3 +-+-+Īs a bonus, the solution should work for both 4- and 8-connected neighboring points, that is: o o o o We should have the corresponding adjacency matrix: +-+-+ I am trying to build the adjacency matrix such thatįor example, in a 3x3 grid with a graph: 1-2-3 Consider a set of points arranged on a grid of size N-by-M.
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