How do I create such matrix ? (please look at the thread for further details)

Hi,

Let say I have a matrix [ X1 X2 X3 .... Xm]

I need to use a method base on X1, X2 and X3 to get my X4, X5 till Xm.

The method in order to find X4 is X4=(X1+X2+X3)/3. Once X4 is calculated, we use the X4 to calculate X5 which now the it will turn out to be X5=(X2+X3+X4)/3 and find X6 using the found X5 and X4, X6=(X3+X4+X5)/3 and so on until we find Xm.

My question is, how do we come out with such matrix ?

Answer 1

[Walter Roberson]

X = rand(1,3);
for K = 4 : m
  X(K) = mean(X(K-3:K-1));
end

[Derick Wong]

That is useful,thanks. But what if now that there is an occasion where a matrix eg. [ 1 2 3 4 5 ; 1 2 3 4 5 ; 1 2 3 4 5] is to be the variable X u declared ? Given that matrix, I will have to recalculate X4 and X5 which is 4 and 5 in this case for all rows.

[Walter Roberson]

Do you mean the case where X4 and X5 have already been found, so you want to continue on from X6 ? But 4 is not (1 + 2 + 3)/3 ?

If it is the question of how to do this for several rows simultaneously, then

X = rand(2,3);   %example 2 rows
for K = 4 : m
  X(:,K) = mean(X(:,K-3:K-1),2);
end

Answer 2

[Andrei Bobrov]

X = randi(25,1,10);

n = 3;
X = X(:);
X = [X(1:n);conv2(X(1:end-n+2),ones(n,1)/n,'valid')];

on Deric's comment

X = randi(1500,93,343);

n = 3;
X = [X(:,1:n), conv2(X(:,1:end-n+2),ones(1,n)/n,'valid')];

[Derick Wong]

Hi,

May I ask what if that the matrix has 343 columns and 93 rows ?

[Andrei Bobrov]

see in my answer code after row with "on Deric ..."

Answer 3

[Roger Stafford]

In case it is of interest to you, Derick, here is an explicit formula for individual elements of your vector X in terms of its first three elements. That is, it doesn't involve iteration - one can find the n-th element without evaluating others.

Let x1, x2, and x3 be the first three elements.

 a = (x1+2*x2+3*x3)/6;
 b = (-x1+4*x2-3*x3)/6;
 c = (-2*x1-x2+3*x3)/3/sqrt(2);
 t = atan2(sqrt(2),-1);
 X(n) = a+3^(-(n-2)/2)*(b*cos((n-2)*t)+c*sin((n-2)*t));

This shows that X consists of rather widely-spaced points in an exponentially decaying sine function.