How to plot six concentric circles using meshgrid and plot?

2013 3 27
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I am trying to plot six concentric circles using meshgrid() and plot(). The circles' radii vary between 0.5 and 1.75 (with intervals of 0.25). I am wondering whether the code below is sufficiently efficient and whether indeed it should be performed as delineated below:
theta = linspace(0, 2*pi, 50);
[X, Y] = meshgrid(0.5:0.25:1.75, theta);
plot(a+cos(Y).*X, b+sin(Y).*X);
?

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Matt J
Matt J 2013-3-27

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You could conserve a little memory if you did it this way, but I don't know anyone who cares about efficiency for such a small plotting task,
theta = linspace(0, 2*pi, 50).';
R=0.5:0.25:1.75;
plot(a+cos(theta)*R, b+sin(theta)*R);

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Yuval
Yuval 2013-3-27
Should there be a dot after the closed parenthesis, viz. theta = linspace(0, 2*pi, 50)*.'*; What is its purpose?
Matt J
Matt J 2013-3-27
编辑：Matt J 2013-3-27
.' transposes a vector or matrix. If you tried my code, you should have seen that it works.
Yuval
Yuval 2013-3-27
Thanks Matt! Just one thing - I realise it works. However, why would the transpose of theta be requisite in this case? To what end?
Matt J
Matt J 2013-3-27
编辑：Matt J 2013-3-27
If a is a column vector and b is a row vector then the entries of a*b will consist of all combinations of products a(i)*b(j). That is what we want to do with a=cos(theta) and b=R. But LINSPACE always outputs a row vector, so the transpose is needed to make it into a column vector.
Yuval
Yuval 2013-3-27
But is that truly necessary ("needed", as you put it)? I mean, as I have tried I am able to confirm that the required plotting gets done even without that minor emendation. How is that "needed" then? Please care to clarify.
Matt J
Matt J 2013-3-27
编辑：Matt J 2013-3-27
You mean you ran my code exactly, but with the transpose omitted and everything worked fine? I don't think so. You should have gotten a dimension mismatch error as I do below
Error using *
Inner matrix dimensions must agree.
Error in test (line 6)
plot(a+cos(theta)*R, b+sin(theta)*R);
And it's perfectly clear why this happens. Matrix multiplication between 2 row vectors together like cos(theta) and R or sin(theta) and R is undefined.
Yuval
Yuval 2013-3-27
编辑：Yuval 2013-3-27
I mean I ran mine, the original one I posted here, in which the transpose was clearly omitted, and yet the plot was just as that generated by your own code, with the transpose. Is that still impossible? Did you mean to suggest that that is strictly mandatory if R is defined as you proposed? Please allow me to re-post what works perfectly fine on this machine:
theta = linspace(0, 2*pi, 50); R = 0.5: 0.25: 1.75; [X, Y] = meshgrid(R, theta); plot(a+cos(Y).*X, b+sin(Y).*X);
Matt J
Matt J 2013-3-27
编辑：Matt J 2013-3-27
Yes, the transposition of theta was only relevant to my proposed approach -- the one that does not use meshgrid. Notice that you use elementwise .* multiplication whereas I use pure matrix multiplication '*'. Matrix multiplication requires the operands to be appropriately shaped.

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