Sum of Maple to MATLAB

Question

Bibha 2011-5-14

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Hi All,

There is a saying "A pee to an ant is flooding".... I guess my question appears simple but being new to MATLAB, couldn't find my way. Seeking some help...

Lm = [1 2 3]';
Um = [4 5 6]';

Maple:

sum(Lm[p,1] * sum(Lm[q,1] * (Um[p,1] - Um[q,1]),q=1..3), p=1..3)

What will be the equivalent MATLAB for the above?

Thank you.

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Matt Fig 2011-5-14

I would have to know what that Maple command did first! Since this is a MATLAB site, it is possible that nobody on here knows what that Maple command does...

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Answer 1

Walter Roberson 2011-5-14

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The most direct equivalent would be

Lm(1,1) * (Lm(2,1) * (Um(1,1) - Um(2,1)) + Lm(3,1) * (Um(1,1) - Um(3,1))) + Lm(2,1) * (Lm(1,1) * (Um(2,1) - Um(1,1)) + Lm(3,1) * (Um(2,1) - Um(3,1))) + Lm(3,1) * (Lm(1,1) * (Um(3,1) - Um(1,1)) + Lm(2,1) * (Um(3,1) - Um(2,1)))

Which works out to be 0

If we generalize to

sum(Lm[p,1] * sum(Lm[q,1] * (Um[p,1] - Um[q,1]),q=1..N), p=1..N) %MAPLE

where N is the length of Um and Lm, then:

breaking it down,

T(p) := sum(Lm[q,1] * (Um[p,1] - Um[q,1]),q=1..N) %Maple

would be

T(p) = sum(Lm .* (Um(p)-Um)) %MATLAB

and when Lm and Um are column vectors, that could be written

T(p) = Lm.' * (Um(p)-Um) %MATLAB

Then,

sum(Lm[p,1] * T[p,1],p=1..N) %Maple

would be

T = zeros(length(Lm),1);  %MATLAB
for p=1:T
  T(p) = Lm.' * (Um(p)-Um)
end
sum(Lm .* T)

but the sum(Lm .* T) could also be written as Lm.' * T leading to

T = zeros(length(Lm),1);  %MATLAB
for p=1:T
  T(p) = Lm.' * (Um(p)-Um)
end
Lm.' * T

In turn, in MATLAB that could be written as

Lm.' * arrayfun(@(p) Lm.' * (Um(p)-Um),1:length(Lm)).'

Note here that arrayfun is returning a row vector instead of a column vector, so the .' after the arrayfun is needed to switch back to a column vector for the array multiplication.

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Answer 2

Andrei Bobrov 2011-5-14

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more variant

Lm.'*bsxfun(@minus,Um,Um.')*Lm

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Walter Roberson 2011-5-14

Nice compaction!

Bibha 2011-5-14

Thank you again!

Just phenomenal.

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Answer 3

Matt Fig 2011-5-14

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It would help, for those of us who do not have Maple and consequently do not know what the result of that Maple command is, if you would show the expected output. Even if you have to make a simple example and create the output by hand, show inputs and expected outputs.

The best I can guess would be:

S = 0;  % This is the result you want at the end.
for p = 1:3
    tmp = 0;
    for q = 1:3
        tmp = tmp + Lm(q) * (Um(p)-Um(q));
    end
    S = S + tmp*Lm(p);
end
S  % Look at the final result...

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Answer 4

Bibha 2011-5-14

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Thanks for all the answers!

I wish I could select all the answers but I am selecting the one where an educated person is trying to educate other rather than giving the answer right away.

Well, no doubt, I learned more functions from all of you guys but I am giving credit to the hard worker.

Quite amazed by the one line of code that did the trick! Thank you andrei.