Skip to main content

numerics - How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?


Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question on StackOverflow and one user mentioned that in Julia, the BLAS/LAPACK implementation can be found by executing versioninfo(). Several users who tried my code there had varying results, with some observing Mathematica to execute faster, and others observing Julia executing faster.


In my case, my Julia installation appears to make use of the OpenBLAS implementation, and it runs between 3 to 6 times slower than Mathematica's Eigensystem for randomly-generated arrays of size $1000\times1000$ to $2000\times2000$.


In the Mathematica documentation's tutorial/SomeNotesOnInternalImplementation, it mentions "For dense arrays, LAPACK algorithms extended for arbitrary precision are used when appropriate" and "BLAS technology is used to optimize for particular machine architectures", but nothing more.


EDIT: So in response to Kuba's comment, apparently one of the Julia devs noted that there is anomalous behavior in Julia with regards to eigenvector computation speed as a function of BLAS thread number. In short, using more threads in Julia's use of OpenBLAS appears to slow things down considerably. For reference, in Mathematica:


SetSystemOptions["MKLThreads" -> 1];

First@Timing@Eigensystem[RandomReal[{-500, 500}, {1000, 1000}]]
SetSystemOptions["MKLThreads" -> 2];
First@Timing@Eigensystem[RandomReal[{-500, 500}, {1000, 1000}]]
SetSystemOptions["MKLThreads" -> 3];
First@Timing@Eigensystem[RandomReal[{-500, 500}, {1000, 1000}]]
SetSystemOptions["MKLThreads" -> 4];
First@Timing@Eigensystem[RandomReal[{-500, 500}, {1000, 1000}]]
(*Out:*)
1.747211
1.466409

1.341609
1.357209

So I guess there's nothing wrong with Mathematica's implementation.




Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

Is there a way to do conditional matrix loop using 'continue'

I have the following: n = 3; m = 5; ww = RandomReal[{0, 0.1}, {n, n}]; uu = RandomReal[{0, 1}, {m, n}]; pp = RandomReal[{0, 1}, {n, n}]; ss = RandomInteger[{0, 5}, {m, n}]; Grid[{{"ww", "uu", "pp", "ss"}, {ww // TableForm, uu // TableForm, pp // TableForm, ss // TableForm}}, Spacings -> {5, 2}, Dividers -> All] where I would like to look at every element of matrix ss and produce a matrix tt , with zeroes at the locations in ss which have zeroes, and in all other positions do the following: tt = (-1/Subscript[ww, m]) Log[(1 - uu)/(Subscript[pp, m - 1])], where Subscript[ww, m] is the value at index of ww matrix and where Subscript[pp, m - 1] is the value at index-1 of pp matrix. So for example if the first value ever read from matrix ss happens to be 2, then value taken from matrix ww would be from the row 2, but from pp would be from row 1. Also how to tell difference between a 0 as a valid value from within the matrix elemen...