MATLAB: Writing matrix for 2D plane of atoms

2dmatrix

Hello all

I have a row of 100 atoms and i am considering nearest neighbour interaction. What that means is that each atom has an interaction with itself (self interaction) of magnitude 2; and each atom interacts with its two nearest neighbour atoms from each side of magnitude 1. This 1D problem is represented in matrix as

 2  1  0 0 0 0 ...
-1  2  1 0 0 0 ...
 0 -1  2 1 0 0 ...
 0  0 -1 2 1 0 ...
 .............
 .............

Now, my problem is that i dont know how to write this matrix when instead of a 1D problem, i have a 2D plane of atoms with the same nearest neighbour interaction condition. Can someone please help me ???

Thanks in advance.

Sazzad

Best Answer

a = [-1 2 1];
n = 100;
m = numel(a)-1;
out = full(spdiags(ones(n,1)*[-1 2 1],-m:m,n,n));

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MATLAB: Distance between one point and the next of a list of points

Try this:

XY = [0  0;
	1  0;
	2  0;
	3  0;
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	1 -1;
	2 -1;
	3 -1]
consecutiveDistances = sqrt((x(2:end) - x(1:end-1)) .^ 2 + (y(2:end) - y(1:end-1)) .^ 2)

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consecutiveDistances =

3.1623

Another nice function you might want to know about, if you have the Statistics and Machine Learning Toolbox, is pdist2(). You can use pdist2(XY, XY) tol give distances between every point and every point in a 2-D array:

XY = [0  0;
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	2  0;
	3  0;
	0 -1;
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	2 -1;
	3 -1]
distances = pdist2(XY, XY)

You'll see:

distances =

0 1 2 3 1 1.4142 2.2361 3.1623

1 0 1 2 1.4142 1 1.4142 2.2361

2 1 0 1 2.2361 1.4142 1 1.4142

3 2 1 0 3.1623 2.2361 1.4142 1

1 1.4142 2.2361 3.1623 0 1 2 3

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The columns and row numbers refer to the row in your XY list. So for example, the element at Row 2, Column 3 of distances corresponds to the distance between point (row) 2 of your XY, and point (row) 3 of your XY. So you'd want to look at the diagonal one above the main upper left-to-lower right diagonal. You'll see it is the same list of numbers as consecutiveDistances.

Best Answer

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