Why This Vectorization of my Code Does Not Work?

Question

Kareem Elgindy 2020-7-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/564842-why-this-vectorization-of-my-code-does-not-work

编辑： Kareem Elgindy 2020-7-14

Consider the following two codes:

n = 4;
% Code 1:
c1 = zeros(floor(n/2)+1,n+1); c1(1,1) = 1; c1(1,2:n+1) = 2.^(0:n-1);
for k = 2:n
    for l = 1:floor(k/2), c1(l+1,k+1) = -((k - 2*l + 2)/(4*l*(k - l)))*(k - 2*l + 1)*c1(l,k+1); end
end
c1
% Code 2:
c2 = zeros(floor(n/2)+1,n+1); c2(1,1) = 1; c2(1,2:n+1) = 2.^(0:n-1);
for k = 2:n
    lend = floor(k/2); c2(2:lend+1,k+1) = -((k-2*(1:lend)+2)./(4*(1:lend).*(k-(1:lend)))).*(k-2*(1:lend)+ 1).*c2(1:lend,k+1)';
end
c2

The first code gives

while the second gives

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Answer 1

KSSV 2020-7-14

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https://ww2.mathworks.cn/matlabcentral/answers/564842-why-this-vectorization-of-my-code-does-not-work#answer_465575

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Might be some problem with indexing. Try this:

clc; clear all ;
n = 4;
% Code 1:
c1 = zeros(floor(n/2)+1,n+1); 
c1(1,1) = 1; 
c1(1,2:n+1) = 2.^(0:n-1);
for k = 2:n
    for l = 1:floor(k/2) 
      c1(l+1,k+1) = -((k - 2*l + 2)/(4*l*(k - l)))*(k - 2*l + 1)*c1(l,k+1); 
    end
end
c1
% Code 2:
c2 = zeros(floor(n/2)+1,n+1); 
c2(1,1) = 1; 
c2(1,2:n+1) = 2.^(0:n-1);
for k = 2:n
    lend = floor(k/2); 
    %  c2(2:lend+1,k+1) = -((k-2*(1:lend)+2)./(4*(1:lend).*(k-(1:lend)))).*(k-2*(1:lend)+ 1).*c2(1:lend,k+1)';
    l = 1:lend ; 
    c2(2:lend+1,k+1) = -((k - 2*l + 2)./(4*l.*(k - l))).*(k - 2*l + 1).*c1(l,k+1)'; 
end
c2

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Kareem Elgindy 2020-7-14

编辑：Kareem Elgindy 2020-7-14

Works like a charm :-). But what is wrong in indexing in the previous code?... I still don't get it!! One more thing. In your 2nd code you used c1. In fact, c2 is calculated using previous values of c2 only not c1.

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