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POMost efficient way to calculate the exponential of each element of a matrix
 

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  1. POMost efficient way to calculate the exponential of each element of a matrix
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    <p>I'm migrating from Matlab to C + GSL and I would like to know <strong>what's the most efficient way to calculate the matrix B for which:</strong></p> <pre><code>B[i][j] = exp(A[i][j]) </code></pre> <p>where i in [0, Ny] and j in [0, Nx].</p> <p>Notice that this is different from matrix exponential:</p> <pre><code>B = exp(A) </code></pre> <p>which can be accomplished with some unstable/unsupported code in GSL (linalg.h).</p> <p>I've just found the brute force solution (couple of 'for' loops), but <strong>is there any smarter way to do it?</strong></p> <p>EDIT</p> <h2>Results from the solution post of Drew Hall</h2> <p>All the results are from a 1024x1024 <code>for(for)</code> loop in which in each iteration two <code>double</code> values (a complex number) are assigned. <strong>The time is the averaged time over 100 executions</strong>.</p> <ul> <li>Results when taking into account the {Row,Column}-Major mode to store the matrix: <ul> <li>226.56 ms when looping over the row in the inner loop in Row-Major mode (case 1).</li> <li>223.22 ms when looping over the column in the inner loop in Row-Major mode (case 2).</li> <li>224.60 ms when using the <code>gsl_matrix_complex_set</code> function provided by GSL (case 3).</li> </ul></li> </ul> <p><strong>Source code for case 1</strong>:</p> <pre><code>for(i=0; i&lt;Nx; i++) { for(j=0; j&lt;Ny; j++) { /* Operations to obtain c_value (including exponentiation) */ matrix[2*(i*s_tda + j)] = GSL_REAL(c_value); matrix[2*(i*s_tda + j)+1] = GSL_IMAG(c_value); } } </code></pre> <p><strong>Source code for case 2</strong>:</p> <pre><code>for(i=0; i&lt;Nx; i++) { for(j=0; j&lt;Ny; j++) { /* Operations to obtain c_value (including exponentiation) */ matrix-&gt;data[2*(j*s_tda + i)] = GSL_REAL(c_value); matrix-&gt;data[2*(j*s_tda + i)+1] = GSL_IMAG(c_value); } } </code></pre> <p><strong>Source code for case 3</strong>:</p> <pre><code>for(i=0; i&lt;Nx; i++) { for(j=0; j&lt;Ny; j++) { /* Operations to obtain c_value (including exponentiation) */ gsl_matrix_complex_set(matrix, i, j, c_value); } } </code></pre>
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    1. USAlejandro Cámara
    1. USAlejandro Cámara
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    1. COI think you're only thinking it's inefficient/dumb because you're used to MATLAB, where using nested fors is a recipe for disaster. But MATLAB would have done that under the hood, it's just that if you write it out, it sucks. But C doesn't work that way, you always write it out and it'll be just as fast/faster than the MATLAB...
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      1. USScott Stafford
    2. COHmmm...these performance numbers are indistinguishable. I'm surprised--can we see the code you ran in each case? I wonder if your compiler has noticed that the values are independent and automatically reordered & unrolled the loops to maximize performance. Seeing the generated assembly in each case would tell us that.
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      1. POMost efficient way to calculate the exponential of each element of a matrix
      1. USDrew Hall
    3. COYou're using a constant value on the RHS of the assignment in each case (what happened to exp()?)--I suspect the compiler has hoisted that out of the loop and replaced the loop with some sort of memset()-like operation. Try to make the assignment dependent on the data--even just something like matrix[2*(i*s_tda + j)] = sin(matrix[2*(i*s_tda + j)]) would probably defeat that optimization and show cache effects.
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      1. POMost efficient way to calculate the exponential of each element of a matrix
      1. USDrew Hall
 

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