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katastrofa
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Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 10:16 am

I don't know who "discovered" complex derivatives, but their applications in different disciplines has been popular for a while. I find it strange that any of these is attributed to some 56-year-old sapling.
"Numerical algorithms based on the theory of complex variable", Lyness, 1967 (paywall)
"Numerical Differentiation of Analytic Functions", Lyness & Moler, 1967 (PDF)

Are you pulling my leg? The sensitivity analysis in various fields requires an accurate estimation of derivatives, and hence they use complex step method instead of finite differencing, e.g. "The Complex-Step Derivative Approximation", Martins, et al., 2003 (example of an application and a simple estimation of the error)
 
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Cuchulainn
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Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 10:27 am

I am not disagreeing, But maybe I did not explain well. BTW this is the 1st article
https://pdfs.semanticscholar.org/3de7/e ... 7aaae9.pdf

 I am just amazed that it is used in statistics.. any links?

 56-year-old sapling.
Ouch. Check it out.
Last edited by Cuchulainn on July 27th, 2018, 10:53 am, edited 1 time in total.
 
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Cuchulainn
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Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 10:51 am

C99 doesn't even have a native matrix type......
 
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FaridMoussaoui
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Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 12:46 pm

How to get the article for free (as the author get $0 anyway):
  1. get the DOI reference from the paywall web page. 
  2. go to https://twitter.com/sci_hub
  3. click on the link on the left hand side. It is now: https://sci-hub.tw
  4. done
 
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katastrofa
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Joined: August 16th, 2007, 5:36 am
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Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 1:01 pm

How to get the article for free (as the author get $0 anyway):
  1. get the DOI reference from the paywall web page. 
  2. go to https://twitter.com/sci_hub
  3. click on the link on the left hand side. It is now: https://sci-hub.tw
  4. done
That's cheating! Just kidding :-) Many thanks!
 
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FaridMoussaoui
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Joined: June 20th, 2008, 10:05 am
Location: Genève, Genf, Ginevra, Geneva

Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 1:08 pm

Never understood why paying for a scientic paper (between $10-$30 and it's a pdf file!!!).
When I don't find the paper online (for free), I ask the author.

Sci-Hub is a breath of fresh air for a LOT of scientists around the world who can't afford the predatory prices (and practice) of the editors.
 
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Cuchulainn
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Re: Calculate the derivative of exp(A) over A

July 27th, 2018, 4:44 pm

Of course, the complex step method breaks down for the Hessian, in which case it seems multi-complex step method is a solution.(?)

The real pain is that C++ is miles behind Matlab and Fortran in this respect.
 
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katastrofa
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Re: Calculate the derivative of exp(A) over A

July 28th, 2018, 11:07 am

Never understood why paying for a scientic paper (between $10-$30 and it's a pdf file!!!).
When I don't find the paper online (for free), I ask the author.

Sci-Hub is a breath of fresh air for a LOT of scientists around the world who can't afford the predatory prices (and practice) of the editors.
FaridMoussaoui, IMHO, scientific journals are just a lucrative business marketed on their former prestige. Every scientist (or only those naive or with misplaced ambitions?) dreams about publishing in Nature like a chav about a new iPhone model. Not many succeed, because nepotism and power seem to be the main selection criteria, even if it often entails publishing poor, trivial or even incorrect work - they will juice up the title and fudge the results, et voila! (E.g., there was recently a flashy title about ML application in medicine outperforming the medical diagnosis. I instantly wondered how a standard multinomial regression would perform on the same data. The authors indeed performed such an obvious comparison, but hid the outcome in the supplement - it was as good as their ML model, hence...) I'd better warn you though that I hold a huge grudge against the academia and scientists, so I may be exaggerating :-)
 
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katastrofa
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Re: Calculate the derivative of exp(A) over A

July 28th, 2018, 11:11 am

Of course, the complex step method breaks down for the Hessian, in which case it seems multi-complex step method is a solution.(?)

The real pain is that C++ is miles behind Matlab and Fortran in this respect.
It breaks down - or simply wasn't designed to approximate higher order derivatives. It's indeed naturally extended using multi-complex analysis when one needs to analyse sensitivity or elasticity of non-linear systems, utility functions depending on several factors, uncertainty in the multiple parameter models, etc. (I suppose many people in the forum applied such methods, knowingly or not.)

C99 doesn't even have a native matrix type......
It didn't stop me from solving complex multidimensional Hamiltonians  :-)
 
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Cuchulainn
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Re: Calculate the derivative of exp(A) over A

July 28th, 2018, 12:18 pm

C99 doesn't even have a native matrix type......
It didn't stop me from solving complex multidimensional Hamiltonians  :-)
Indeed. It's just the cognitive distance between maths and C++ that makes it all a nuisance.