Re: [boost] [math] Does any one interesting in calculating derivative for a expression automatically?

Subject: Re: [boost] [math] Does any one interesting in calculating derivative for a expression automatically?
From: Steven Watanabe (watanabesj_at_[hidden])
Date: 2009-03-03 11:45:15

AMDG

Dongfei Yin wrote:
>    Recently, I am working on some mathematical issues, most of my 
> working time, I am calculating the derivative of function manually, it 
> is such a tedious work that I write a piece of code to do it for me. 
> now I want to share it with others.
>    Let me show it for you. it it something like lambda expression, I 
> mean boost::lambda. but the main purpose is to calculate derivative. 
> As lambda do, I defined some variables like _x, _y in advance. A 
> function named "d" can calculate derivative. then we can use it like 
> this.
>    d(_x * _x , _x)(1.0);                //  f(x)=x*x, f '(x) = 2x. so 
> the result will be f '(1.0) = 2.0.
>    d(d(_x * _x, _x), _x)(4.0);          //  f(x)=x*x, f ''(x) = 2, so 
> the result will be f ''(4.0) = 2.0; this argument is just used to 
> determine the return type.
> of cause it can work with more than one variables, such as,
>    d(_x * _y, _x)(2.0, 1.0);            //  f(x,y)=x*y, f 'x(x,y)=y, 
> so the result will be f 'x(x,y)=1.0;
>                                         //  the first argument will be 
> ignored.
>    d(d(_x * _y, _x), _y)(1.0);          //  f(x,y)=x*y, f ''xy(x,y)=0, 
> so here one or two argument are all OK.
> and it can calculate derivative for some complicated expressions. 
> theoretically, it can calculate high derivative for a expression as 
> high as you want until the expression become zero.
> I want to share it with others, but it is not so perfect now. I need 
> some suggestion to make it better.

Take a look at Proto.  http://www.boost.org/libs/proto

In Christ,
Steven Watanabe