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Merge pull request #10 from seshasaibehara/DiffClex
Gradients of correlations
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| Copyright (C) 1996-2006 Ole Stauning ([email protected]) | ||
| All rights reserved. | ||
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| This code is provided "as is", without any warranty of any kind, | ||
| either expressed or implied, including but not limited to, any implied | ||
| warranty of merchantibility or fitness for any purpose. In no event | ||
| will any party who distributed the code be liable for damages or for | ||
| any claim(s) by any other party, including but not limited to, any | ||
| lost profits, lost monies, lost data or data rendered inaccurate, | ||
| losses sustained by third parties, or any other special, incidental or | ||
| consequential damages arising out of the use or inability to use the | ||
| program, even if the possibility of such damages has been advised | ||
| against. The entire risk as to the quality, the performance, and the | ||
| fitness of the program for any particular purpose lies with the party | ||
| using the code. | ||
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| This code, and any derivative of this code, may not be used in a | ||
| commercial package without the prior explicit written permission of | ||
| the authors. Verbatim copies of this code may be made and distributed | ||
| in any medium, provided that this copyright notice is not removed or | ||
| altered in any way. No fees may be charged for distribution of the | ||
| codes, other than a fee to cover the cost of the media and a | ||
| reasonable handling fee. | ||
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| *************************************************************** | ||
| ANY USE OF THIS CODE CONSTITUTES ACCEPTANCE OF THE TERMS OF THE | ||
| COPYRIGHT NOTICE | ||
| *************************************************************** |
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| FADBAD++ Templates for Automatic Differentiation | ||
| ================================================ | ||
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| FADBAD++ defines C++ templates for performing automatic differentiation | ||
| of functions implemented as C/C++ programs. Three types of automatic | ||
| differentiation has been implemented. The forward and the backward methods | ||
| are implemented to compute first order derivatives and the Taylor expansion | ||
| method is implemented to compute Taylor series expansion. | ||
| All templates are flexible in the way that the arithmetic used in as | ||
| template-arguments can be chosen by the user. This way differentiation of | ||
| programs, based on any arithmetic such as: double, interval, multiprecision | ||
| etc. is possible. This flexibility also makes it possible to perform automatic | ||
| differentiation on a program which itself uses automatic differentiation. | ||
| All three methods can be mixed in an application and the user can obtain | ||
| derivatives using the most optimal combination of methods for the application. | ||
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| APPLICATIONS: | ||
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| * Forward automatic differentiation on a function f : R^n->R^n, evaluated | ||
| in interval arithmetics, using the BIAS/PROFIL package, to obtain function | ||
| values and derivatives. Used with the interval Newton method to obtain | ||
| guarenteed enlosures of all solutions to the nonlinear equation f(x)=0. | ||
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| * Forward-Backward automatic differentiation on a function f : R^n->R, | ||
| evaluated in interval arithmetics, using the BIAS/PROFIL package and the | ||
| backward method to obtain first order derivatives (the gradient) and the | ||
| forward method to differentiate the first order derivatives to obtain the | ||
| second order derivatives (the Hessian). Used with the interval Krawczyk | ||
| method to perform global optimization obtaining a guarenteed enclosure of | ||
| the global minimum. | ||
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| * Numerical integration of a function f : RxR^n->R, using a | ||
| three-point-two-derivative formula. The Backward method has been used to | ||
| differentiate the Numerical integration program obtaining the n partial | ||
| derivatives of the integral with respect to the n parameters in the | ||
| function. | ||
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| * Taylor expansion of the solution to an ordinary differential equation, | ||
| used to solve initial value problems. The Forward method has been used to | ||
| differentiate the initial value problem solver to obtain the solution of | ||
| the variational problem. | ||
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| * Taylor expansion of the solution to an ordinary differential equation | ||
| using interval arithmetics and using the Forward method to obtain | ||
| derivatives of the Taylor coefficients with respect to the point of | ||
| expansion, which are the values of the Taylor coefficients for the | ||
| solution of the variational problem. Used in a method which solves initial | ||
| value problems with guaranteed enclosures. | ||
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| LICENSING: | ||
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| FADBAD++ is distributed under the dual licensing business model similer to the | ||
| model used by MySQL, Trolltech and Sleepycat. In return for the advantages you | ||
| realize from using FADBAD++ in your application, we require that you do one of | ||
| the following: | ||
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| * Either: Contribute to the continued development of the product by | ||
| purchasing commercial licenses from the authors. This option secures you | ||
| the right to distribute your application under the license terms of your | ||
| choice. | ||
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| * Or: Contribute to the Open Source community by placing your application | ||
| under an Open Source license (e.g. the GPL). This option secures all users | ||
| the rights to obtain the application's full source code, modify it, and | ||
| redistribute it. | ||
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| Contact the authors if you want to obtain a commercial licence or if you are | ||
| unsure about what license to use <[email protected]>. | ||
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| More information about automatic differentiation in general and source code | ||
| for FADBAD++ with documentation can be obtained from the FADBAD++ homepage: | ||
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| http://www.fadbad.com | ||
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