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POAlgorithm to express elements of a matrix as a vector
 

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  1. POAlgorithm to express elements of a matrix as a vector
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    <p><strong>Statement of Problem:</strong></p> <ol> <li><p>I have an array <code>M</code> with <code>m</code> rows and <code>n</code> columns. The array <code>M</code> is filled with non-zero elements. </p></li> <li><p>I also have a vector <code>t</code> with <code>n</code> elements, and a vector <code>omega</code> with <code>m</code> elements.</p></li> <li><p>The elements of <code>t</code> correspond to the columns of matrix <code>M</code>.</p></li> <li><p>The elements of <code>omega</code> correspond to the rows of matrix <code>M</code>.</p></li> </ol> <p><strong>Goal of Algorithm:</strong></p> <p>Define <code>chi</code> as the multiplication of vector <code>t</code> and <code>omega</code>. <em>I need to obtain a 1D vector <code>a</code>, where each element of <code>a</code> is a function of <code>chi</code>.</em></p> <p>Each element of <code>chi</code> is unique (i.e. every element is different).</p> <p>Using mathematics notation, this can be expressed as <code>a(chi)</code></p> <p>Each element of vector <code>a</code> corresponds to an element or elements of <code>M</code>. </p> <p><strong>Matlab code:</strong></p> <p>Here is a code snippet showing how the vectors <code>t</code> and <code>omega</code> are generated. The matrix <code>M</code> is pre-existing.</p> <pre><code>[m,n] = size(M); t = linspace(0,5,n); omega = linspace(0,628,m); </code></pre> <p><strong>Conceptual Diagram:</strong></p> <p><strong>This appears to be a type of integration (if this is the right word for it) along constant chi.</strong></p> <p><img src="https://i.stack.imgur.com/AXkQa.png" alt="Diagram"></p> <p><strong>Reference:</strong></p> <p><a href="http://www.scribd.com/doc/45448335/SEISMIC-INVERSE-q-FILTERING#page=208" rel="nofollow noreferrer">Link to reference</a></p> <p>The algorithm is not explicitly stated in the reference. I only wish that this algorithm was described in a manner reminiscent of computer science textbooks! </p> <p>Looking at Figure 11.5, the matrix M is Figure 11.5(a). The goal is to find an algorithm to convert Figure 11.5(a) into 11.5(b).</p> <p>It appears that the algorithm is a type of integration (averaging, perhaps?) along constant <code>chi</code>.</p>
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    1. COFrom the link you have given, I think that to get from figure 11.5(a) to 11.5(b) you should make something called Gabor Transform. Read the page 190 of the book you shared with us. This algorithm seems to be pretty involved. I suggest you try to understand it, and also to consult related pages in the matlab webpage: (1) search 'gabor transform matlab' in google. (2) check the webpage, http://www.mathworks.com/matlabcentral/fileexchange/5237-2d-gabor-filterver123 . This link from Matlab 'file exchange' is promising (4/5 stars from voters)! I think it could work pretty fast for you! Good luck!
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      1. USjespestana
    2. CO@jespestana: Yes, I've written my own version of the Gabor transform, and I've used it to generate something similar to Figure 11.5(a), which is a 2D matrix as a 2D spectrum. Now that the Gabor transform has been calculated, the 2D spectrum needs to be collapsed into a 1D spectrum as noted on pg. 190. I still don't know if the spectral collapsing can be done with the Gabor transform.
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    3. COI think you should try to find another book. I do not understand why they use A(chi) without describing it... Anyway, if you want to integrate using the trapezoidal rule check the function trapz(t,y). Sorry, but I do not know anything about the Gabor transform, let alone about collapsing the data. If you could give us the exact formula you want to implement, it would be easier for us to suggest a solution.
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