How to plot x(i+1,j+1) with respect to i,j from the given data ,code shown in the body?

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Abhay 2014-10-12

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评论： Abhay 2014-10-16

clc;
close all;
clear all;
A1=[0 -.75;-1 0];
A2=[.27 0;0 0];
A3=[0 -.001;0 0];
x(1,1)=1
x(1,2)=2
x(2,1)=1
for i=1:2
    for j=1
    z=x(i+1,j+1)==A1.*x(i,j+1)+A2.*x(i+1,j)+A3.*x(i,j)
    end 
end
[i,j]=meshgrid(2:3,2)
surf(i,j,z)

[EDITED, Jan, please format your code]

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Abhay 2014-10-12

The problem is as follows: x(i+1,j+1)=A1*x(i,j+1)+A2*x(i+1,j)+A3*x(i,j) where x(i+1,j+1),x(i,j+1) and x(i+1,j) and x(i,j) , is a state vector of 2x1 dimension and A1,A2 and A3 are constant system matrices of 2x2 dimension, initial conditions is x(1,1)=1;x(1,2)=2;x(2,1)=1 Problem is to plot x(i+1,j+1) with respect to i and j. Values of A1=[0 -.75;-1 0] , A2=[.27 0;0 0], A3=[0 -.001;0 0]

Sir the code which I had tried is not working.

Jan 2014-10-12

"Is not working" is not useful. Please explain any details.

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Answer 1

SK 2014-10-12

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Hi Abhay,

The problem as you as you have stated it is under-determined. What you additionally need are boundary conditions. For example if you knew the boundary values:

x(1, j) for all j
and
x(i, 1) for all i

Then you could easily generate all the values. Maybe you need to assume that the boundaries are zero?

Also since this is a 2-D to 2-D function, how do you plan to visualize it in a plot?

By the way, to type code, just start the code line with two spaces.

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SK 2014-10-12

编辑：SK 2014-10-12

在 MATLAB Online 中打开

I just posted code but deleted it subsequently because I just read you edited first post.

It seems there is some confusion about the actual problem at hand. You may need to give a clearer statement of the problem. Your code has some puzzling errors. For example:

== checks for equality and returns boolean values. z will therefore only contain true/false values and will be overwritten on each loop. If in case you meant:

x(i+1,j+1) = A1.*x(i,j+1)+A2.*x(i+1,j)+A3.*x(i,j)

then that is not valid code since you are trying to assign a matrix to a scalar.

In Matlab, x(i,j) cannot be vector or array. x(i,j) has to be a scalar (either a number or a cell or a user defined object). Do you need x(i,j) to be a vector? In that case you need to reformulate the problem.

Also note that if A is a (k x k) matrix, and y is a scalar, then:

A.*y
and
A*y

both do the same thing, ie: multiply every element of A with y. On the other hand if y is a (k x 1) vector and A is a (k x k) matrix, then:

A*y

does matrix multiplication of A with y.

SK 2014-10-15

编辑：SK 2014-10-15

在 MATLAB Online 中打开

If you look at the documentation for the surf() funstion in Matlab, you will see that you are using 2 different functions:

surf([X1; X2])

Here you have written [X1; X2] - which is a single matrix formed by concatenating X1 and X2 vertically. Similarly in

surf([X1, X2])

[X1, X2] is also a single matrix formed by concatenating X1 and X2 horizontally.

So in both these you are using the 1-argument form of surf where the (x y) grid is taken to be (1:n) x (1:n). But because [X1; X2] is a different matrix from [X1, X2], the result is different

On the other hand in:

surf(X1, X2)

the first argument is X1 and the second X2. You are using the two argument form of surf(). The second argument specifies only the color shading. So you are only plotting X1.

X is a 2 x N x N matrix, so when you reshape, the result should also have 2*N*N elements. But in your reshape() line it has only N*N elements. For example you could reshape as:

reshape(X, [2*N, N]).

But be very careful when you reshape. In fact the above command is probably not what you want because of the order in which the elements are placed. When Matlab reshapes, it takes the elements, counting along each dimension starting from the first in turn. You have to reshape in such a way that your elements don't get mixed up. In your case you may need to use the permute() function before you reshape.

_________

In addition, let me offer you some unsolicited advice. If you are planning to use Matlab for at least some period of time for your work, it would be worth it to invest some of your time learning the basic syntax and getting familiar with it. It is not exactly my favorite language, but it is very widely used and is relatively easy to learn.

You could start by going to:

cody

about cody

The suggested exercises there can help you get comfortable with with Matlab syntax. Then you would not be so dependent on others for these basic language issues. There are also a lot of online tutorials and short documents that give you information about Matlab. Of course you need to be willing to invest some time experimenting with it.

Abhay 2014-10-16

Dear sir, Thanks for the clarification and your kind advice. Now if will try to tune myself more towards, in learning the cody which in my opinion is the base of this matlab programme, thanks for providing a link for cody,as a beginner it helps me a lot.

With Thanks and Regards, Abhay

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Answer 2

Abhay 2014-10-12

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{clc; clear all; }

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Abhay 2014-10-12

Dear all No any answer at my end.That happened by mistake.

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Answer 3

Abhay 2014-10-15

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Dear all; Regarding my earlier question of 3D plot of 2-D discrete system which was wonderfully solved by SK, I had posted one query,Kindly put your expert comment over that.Thanks

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Abhay 2014-10-15

Dear all; Regarding my earlier question of 3D plot of 2-D discrete system which was wonderfully solved by SK, I had posted one query,Kindly put your expert comment over that.Thanks

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