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Wolfram Language Optimization

Optimize code with Do Loop?

Sandu Ursu

Posted 9 years ago

If anyone is willing to look.. I'd like to know how can I speed up the attached piece of code? In R, a similar implementation runs 25% faster. Shouldn't mention perhaps, but C++ runs it ~40x faster. Thank you. Attachments:

POSTED BY: Sandu Ursu

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Sandu Ursu

Posted 9 years ago

Sander, I always thought that `Block` is faster (true that only marginally) than `Module`. Do you use it for any particular reason which makes `Block` look unfit?

POSTED BY: Sandu Ursu

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 9 years ago

Somehow, I would have expected more specialized functions such as `ListConvolve` or `MovingAverage` to perform better than `qU Most[#] + qD Rest[#] &`, but it is not true: Do[Nest[qU Most[#] + qD Rest[#] &, call, n], {1000}] // Timing Do[Nest[ListConvolve[{qD, qU}, #] &, call, n], {1000}] // Timing Do[Nest[MovingAverage[#, {qU, qD}] &, call, n], {1000}] // Timing

POSTED BY: Gianluca Gorni

Sandu Ursu

Posted 9 years ago

This is fantastic! Sander, please see the attached file for my C++ code. Compiled with g++ it actually runs in 116 ms. [1000 iterations] If compiled in VS 2015 it employs all the arsenal of SIMD and performs the iterations in ~85 ms. Attachments:

POSTED BY: Sandu Ursu

Sander Huisman

Sander Huisman, University of Twente

Posted 9 years ago

Could you post your c code?

POSTED BY: Sander Huisman

Sander Huisman

Sander Huisman, University of Twente

Posted 9 years ago

POSTED BY: Sander Huisman

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 9 years ago

This version runs faster: S = 100; K = 100; \[Alpha] = 0.07; \[Sigma] = 0.2; T = 1; r = 0.03; n = 252; dt = T/n; R = E^(r dt); u = E^(\[Alpha] dt + \[Sigma] Sqrt[dt]); d = E^(\[Alpha] dt - \[Sigma] Sqrt[dt]); qU = (R - d)/(R (u - d)); qD = (1 - R qU)/R; call = Clip[S u^Range[n, 0, -1] d^Range[0, n] - K, {0, \[Infinity]}]; Do[Nest[qU Most[#] + qD Rest[#] &, call, n], {1000}] // Timing

This version runs faster:

S = 100;
K = 100;
\[Alpha] = 0.07;
\[Sigma] = 0.2;
T = 1;
r = 0.03;
n = 252;
dt = T/n;
R = E^(r dt);
u = E^(\[Alpha] dt + \[Sigma] Sqrt[dt]);
d = E^(\[Alpha] dt - \[Sigma] Sqrt[dt]);
qU = (R - d)/(R (u - d));
qD = (1 - R qU)/R;
call = Clip[S u^Range[n, 0, -1] d^Range[0, n] - K, {0, \[Infinity]}];
Do[Nest[qU Most[#] + qD Rest[#] &, call, n], {1000}] // Timing

POSTED BY: Gianluca Gorni

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