How to increment a v value to an i position in a vector every n iterations ?

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Hello,
In the context of meshing for a 1D finite elements method, I have a vector with 1 row and n columns (nodes). I divide it into E elements of L nodes, which means that every last node of an element is the first node of the following element.
I would like to create a second vector for which every L iteration I double the L value and shift my whole vector to the right. Example:
E = 3
L = 4
A = [1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4]
( l 1st E l 2nd E l 3rd E l etc... )
B = [1 2 3 4 1 1 2 3 4 1 1 2 3 4 1 1 2 3 4 1 1 2 3 4 1]
( l 1st E l l 2nd E l l 3rd E etc.... (the "l" are just delimiters))
To verify that B was correctly constructed I know that length(B) must be equal to E * (L + 1).
So far I had two leads. Let global_vector be A, and local_vector B (the vector I want to change):
%%1st lead:
Total_Element = 1; %Size of the global element
L = 9; %Number of nodes per element -1
E = 100; %Number of Elements
num_nodes = E * L + 1; %Number of nodes
nodes = linspace(0,L,num_nodes); %Position of the nodes on the global element
global_vector = nodes;
local_vector = [];
for i = L:1:length(global_vector)-L % I stop the loop before the last vector to avoid doubling it at the end
if mod(i,L) == 0
added_value = global_vector (1,i);
local_vector = [local_vector,added_value,added_value];
else
local_vector = [local_vector,global_vector(i)];
end
end
local_vector = [local_vector, global_vector(:,end-L:end)]; % Add the last element to local_vector
%%% 2nd Lead: my local_vector is already constructed, and every L iteration I increment the local_vector on the i + 1 column with the value global_vector(i) without deleting the value local_vector(i), and shifting the local_vector to the right:
Total_Element = 1; %Size of the global element
L = 9; %Number of nodes per element -1
E = 100; %Number of Elements
num_nodes = E * L + 1; %Number of nodes
nodes = linspace(0,L,num_nodes); %Position of the nodes on the global element
global_vector = nodes;
local_vector = global_vector;
j = 0;
for i = L:L:length(global_vector)-L %To double the Lth value of the vector
j = j + 1; %Count of the shift created for every loop
added_value = global_vector(1,i);
local_vector = [local_vector(1,1:i),added_value,global_vector(1,i+j)] %I try to fit the value by addind a row between i and i + 1
end
local_vector = [local_vector, global_vector(:,end-L:end)]; % Same reason as the first lead
But I am stuck since J exceeds quickly the array bounds. Maybe there is a function to do this or a way to make 2 loops run in parallel, but I can't find anything.
I did it for a simpler problem and it works:
Total_Element = 1; %Size of the global element
E = 150;
L = 2;
num_nodes = E * L + 1; %Number of nodes
nodes = linspace(0,L,num_nodes); %Position of the nodes on the global element
global_vector = nodes;
local_vector = global_vector(:,1);
for i = 2:1:length(global_vector)-2
if mod(i,2) == 0
local_vector = [local_vector,global_vector(i)];
else
added_value = global_vector (1,i);
local_vector = [local_vector,added_value,added_value];
end
end
local_vector = [local_vector, global_vector(:,end-1:end)];
Does anyone have a solution for this kind of problem ? Because I can't really find anything similar I don't know if the solution is just way more complicated or if it is something totally different.
Thank you !!
  2 Comments
V.D-C
V.D-C on 10 Jan 2020
In short I want to implement a value from a vector to a second vector every L column, without deleting the value of the second vector on the corresponding column.
Take it in other words: select a value from a vector, take another vector, split it open, add the value, and stick it together again. And do that several times.

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Answers (1)

Guillaume
Guillaume on 10 Jan 2020
I don't really understand your example, particularly the E which doesn't appear to have any meaning (shouldn't the A in your example have E*L elements == 12 ?).
Transforming your example A into your example B by duplicating the first element of each run of length L at the end is trivially done:
L = 4;
A = 1:12; %actually numbers don't matter
assert(mod(numel(A), L) == 0, 'The numbers of elements in A must be a multiple of L');
Btemp = reshape(A, L, []); %reshape A into 2D matrix with L rows.
B = reshape([Btemp; Btemp(1, :)], 1, []) %duplicate 1st row (start of each L run) as last row, and reshape back into vector
No idea if that's what you're really after. If not please clarify with a better example.
  3 Comments
V.D-C
V.D-C on 10 Jan 2020
Sorry for the inconvenience, it's a tricky subject to explain !
Yes I misunderstood you. E is used only at the beginning.
The input is A, and the desired output is B verifying length(B) = E * (L + 1), and Q.
And yes for you example your code work, thank you for that. I will try to implement it in my code with my parameters and see how it works. Thank you for having taking time to reply !!

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