In this case, each column's values are double the values in the column before it. So the first step is to figure out the pattern. And we want to produce the following matrix. This time, we'll start with this column vector.
And since we left the statement unsuppressed, we can see each iteration as well. As we can see, we get the matrix we were expecting. Now, let's see what happens when we hit Run. And we'll continue to iterate through the loop until we've gone through all the index variables. The result will be that A is a 3-by-5 matrix.
#MATRIX MATLAB PLUS#
We index into all of the columns in the third row and set those values equal to 1 plus the row above it. So after one iteration, A is now a 2 by 5 matrix.
And the second part, equals A of I minus 1 comma colon plus 1 means that we are setting the second row equal to 1 plus the values in the row before it, in this case row 1, and then end. A of I comma colon means we are indexing into all of the columns in row I, which in this case is row 2. Then inside the loop, I'll write the following command: A of I comma colon equals A of I minus 1 comma colon plus 1, and then end. I'll go ahead and create an index variable for i equals 2 through 5. So this means we're going to need four iterations in the loop. We know that we need to append four rows to our current vector. So now that we have our vector, we need to think about creating our matrix in a loop. And I'll show you why at the end of the video. I'm not going to suppress the outputs in this example. So now that we found the pattern, the question is, how do we create this matrix in a loop? Well, the first step is going to be to create the initial vector. And the second column reads 3, 4, 5, 6, 7, et cetera, et cetera. See, this first column reads 1, 2, 3, 4, 5.
The values in each row are equal to 1 plus the values above it. If we look closely at this matrix, we can see a pattern. And I want to make the following matrix from it, this one right here. We're going to do this by answering a few questions. Today, we're going to talk about creating a matrix in a loop. The function can also connect nodes further than radius = 1.Hello, and welcome back to another MATLAB video. 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?
#MATRIX MATLAB CODE#
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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