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POHow to efficiently find and merge duplicate enteries of a vector in MATLAB?
 

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  1. POHow to efficiently find and merge duplicate enteries of a vector in MATLAB?
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    <p>I am writing a MATLAB code to quickly solve the following problem: Let X be a random variable distributed according to P(x), take two independent copies of X, call them X1 and X2 and find the distribution of Y = f(X1,X2) where f(,) is a known function. </p> <p>To solve the above, I start with two vectors <code>x</code> and <code>p</code> such that <code>p(i)</code> = P(<code>x(i)</code>). Suppose they both contain <code>n</code> elements. I can easily compute the <code>n</code>-by-<code>n</code> matrix <code>y</code> such that <code>y(i,j)</code> = f(<code>x(i)</code>, <code>x(j)</code>). Furthermore, I can compute the <code>n</code>-by-<code>n</code> matrix <code>p_out</code> such that <code>p_out(i,j) = p(i) * p(j)</code>. This means P(Y = <code>y(i,j)</code>) = <code>p(i,j)</code>.</p> <p>Now, if all elements of <code>y</code> are distinct we are almost done. It remains just converting the matrices to vectors and perhaps sorting them to have a nice output. Suppose we also do this by setting </p> <pre><code>y = y(:); p_out = p_out(:); [y, idx] = sort(y); p_out = p_out(idx); </code></pre> <p>The problem is, however, the elements of <code>y</code> are not typically unique. I, hence, have to merge the identical elements of <code>y</code> as follows: if <code>y(i) = y(j)</code> (remember now <code>y</code> is converted to a vector) then remove <code>y(j)</code> and set <code>p(i) = p(i) + p(j)</code>. A dirty way of doing this is using a for loop (since <code>y</code> is now sorted we only need to compare each element with its following element). However, I wonder if there exits a nicer way. </p> <p>I know that <code>unique</code> would remove the duplicated elements of a vector (hence if we only needed <code>y</code> it would be sufficient). I also know that it returns two index vectors that somehow indicate the position of duplicated elements. However, I cannot think of any nice way to use its outputs to <strong>appropriately</strong> merge the elements of <code>p</code> as well.</p>
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    1. COMaybe this can help: http://stackoverflow.com/questions/18639518/generate-and-plot-the-empirical-joint-pdf-and-cdf-in-matlab
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    2. CO@LuisMendo Thanks. I guess that is a different problem.
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