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PO
 

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  1. PO
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    <p>This a job where Rcpp excels. Nested loops are straight forward to implement and you don't need much C++ experience. (I like RcppEigen, but you don't really need it for this. You could use "pure" Rcpp.)</p> <pre><code>library(RcppEigen) library(inline) incl &lt;- ' using Eigen::Map; using Eigen::MatrixXd; typedef Map&lt;MatrixXd&gt; MapMatd; ' body &lt;- ' const MapMatd A(as&lt;MapMatd&gt;(AA)), B(as&lt;MapMatd&gt;(BB)); const int nA(A.rows()), mA(A.cols()), mB(B.cols()); MatrixXd R = MatrixXd::Ones(nA,mB); for (int i = 0; i &lt; nA; ++i) { for (int j = 0; j &lt; mB; ++j) { for (int k = 0; k &lt; mA; ++k) { R(i,j) *= (1 - A(i,k) * B(k,j)); } R(i,j) = 1 - R(i,j); } } return wrap(R); ' funRcpp &lt;- cxxfunction(signature(AA = "matrix", BB ="matrix"), body, "RcppEigen", incl) </code></pre> <p>Now, lets put your code in an R function:</p> <pre><code>doupleApply &lt;- function(A, B) t(apply(A,1, function(x) apply(B,2,function(y) 1-prod(1-x*y)))) </code></pre> <p>Compare the results:</p> <pre><code>all.equal(doupleApply(A,B), funRcpp(A,B)) #[1] TRUE </code></pre> <p>Benchmarks:</p> <pre><code>library(microbenchmark) microbenchmark(doupleApply(A,B), funRcpp(A,B)) # Unit: microseconds # expr min lq median uq max neval #doupleApply(A, B) 169.699 179.2165 184.4785 194.9290 280.011 100 # funRcpp(A, B) 1.738 2.3560 4.6885 4.9055 11.293 100 set.seed(42) A &lt;- matrix(rnorm(3*1e3), ncol=3) B &lt;- matrix(rnorm(3*1e3), nrow=3) all.equal(doupleApply(A,B), funRcpp(A,B)) #[1] TRUE microbenchmark(doupleApply(A,B), funRcpp(A,B), times=5) # Unit: milliseconds # expr min lq median uq max neval # doupleApply(A, B) 4483.46298 4585.18196 4587.71539 4672.01518 4712.92597 5 # funRcpp(A, B) 24.05247 24.08028 24.48494 26.32971 28.38075 5 </code></pre>
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    1. POsimplifying a computation, so it could be done using matrix operations
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    1. USRoland
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      1. VTUpMod
    1. COThanks for this. I know that C++ is faster. but in essence tey are the same - both requires O(N^3) calculations. matrix multiplication, however, requires less than that. This is why I'm looking at transformations rather than implementation optimizations
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    2. COI don't agree. Matrix multiplication does not require less calculations.
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    3. COmatrix multiplication has long been studied. I think in the late 1960s or early 1970s there was an algorithm to multiply matrices at O(n^2.7) or so. Since then, there were a few more improvements, and I think that now you get it with less than O(n^2.4)
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