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PODetect non-uniform direction in a Matrix
 

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  1. PODetect non-uniform direction in a Matrix
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    <p><strong>Background</strong></p> <p>Given a matrix like this:</p> <pre><code>X = [1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] </code></pre> <p>We can see that each number is increasing both to the right and down. However the direction doesn't matter, as long as the direction/slope is uniform.</p> <p>This can be tested by:</p> <pre><code>&gt; gradient(X) &gt;= 0; ans = [1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1] </code></pre> <p>and</p> <pre><code>&gt; gradient(X') &gt;= 0 % transpose of X ans = [1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1] </code></pre> <p>In this example I am assuming that the data is increasing right/down, it would not be a complicated task to extend to any uniform direction.</p> <p>This can be combined into the full test:</p> <pre><code>&gt; all(all(gradient(X) &gt; 0)) &amp;&amp; all(all(gradient(X') &gt; 0)) ans = 1 </code></pre> <p><strong>Question:</strong></p> <p>How can I detect any deviation from this uniform direction and "fix" it. The fix should involve interpolating a value from the surrounding points.</p> <p><strong>Note:</strong></p> <p>In practice these matrices are quite large and contain values which might only differ by tiny amounts. I am assuming at the moment that there will only be one deviation at a time, they won't be grouped together: <code>[1 2 3 2 4 5] (2 is an error)</code> for example, rather than <code>[1 2 3 2 1 4] ([2 1] is an error)</code></p> <p><strong>Edit:</strong></p> <p><code>[1 2 3 2 4 5]</code> should become <code>[1 2 3 3.5 4 5]</code> Where 3.5 is the interpolated value of the surrounding points (in this case the average of 3 and 4).</p> <p><strong>Edit2:</strong></p> <p>Ignore the interpolation part, I will work that out later.</p> <p>Given </p> <pre><code> X = 1 2 3 4 5 2 3 2 5 6 3 4 5 6 7 4 5 6 7 8 </code></pre> <p>2 is obviously the "error". I would like the following as output:</p> <pre><code>2 3 4 3 2 5 4 5 6 </code></pre> <p>Which is the error value and the surrounding points. From these points I will do a 2D interpolation to replace 2 with (hopefully) 4, using 3, 3, 5, and 5 (ignoring the corners 2, 4, 4, and 6).</p>
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    1. USSamuel O'Malley
    1. USSamuel O'Malley
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    1. COWhat is the correct output for `[1 2 3 2 4 5]`?
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      1. USDan
    2. COThe 2 should be removed and replaced with the average of 3 and 4 to get 3.5: `[1 2 3 3.5 4 5]`
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      1. USSamuel O'Malley
    3. COOnly one deviation by rows or also by columns? Because it can happen that while you fix a value in one direction (e.g. the row) you spoil the other direction (i.e. the column).
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