Home  Forums  Reviews  Guides  Newsgroups  Register  Search 
Thread Tools 
pauldepstein@att.net 


 
KaiUwe Bux
Guest
Posts: n/a

http://www.velocityreviews.com/forums/(EMail Removed) wrote:
> Let double NR( double x, double(*)(const double&) f ) be the > signature of a NewtonRaphson function NR. > > Here, f is a function which returns a double and accepts a const > double&. The aim of the game is to find a zero of this function f > (the point at which f crosses the xaxis). This zerooff which > solves our problem is the double which NR returns. It remains to > explain what the "double x" represents. This is the startingguess > that is required in NewtonRaphson implementations. > > In my case, I have the following amended NewtonRaphson situation. I > have a function of the form > > double MyFunc(double x1, double x2, double x3, double x4, double x5) > > I want to solve the following problem: Fix x1, x2, x3, and x4. Then > use Newton Raphson to return the double y such that MyFunc(x1, x2, x3, > x4, y) = 0. > > I was unable to find a way of using the readymade function NR because > it assumes f accepts 1 double and returns 1 double, whereas My Func > accepts 5 doubles and returns 1 double. > > My veryinelegant solution was to copypaste the NR code and adapt it > so that the pointertofunction parameter was of the type I needed. > > Is there a more elegant approach that calls on the NR function already > present? I would change NR into a template: template < typename Float, typename Func > Float find_zero ( Float initial_guess, Func f ); Then, you could use bind() from c++0x or Boost to fix the first four arguments and pass the resulting function object into the template. Best KaiUwe Bux 




KaiUwe Bux 


 
James Kanze
Guest
Posts: n/a

On Nov 15, 9:53*am, (EMail Removed) wrote:
> Let double NR( double x, double(*)(const double&) f ) *be the > signature of a NewtonRaphson function NR. > Here, f is a function which returns a double and accepts a > const double&. The aim of the game is to find a zero of > this function f (the point at which f crosses the xaxis). > This zerooff which solves our problem is the double which NR > returns. It remains to explain what the *"double x" > represents. This is the startingguess that is required in > NewtonRaphson implementations. > In my case, I have the following amended NewtonRaphson > situation. *I have a function of the form > double MyFunc(double x1, double x2, double x3, double x4, double x5) > I want to solve the following problem: *Fix x1, x2, x3, and > x4. *Then use Newton Raphson to return the double y such that > MyFunc(x1, x2, x3, x4, y) = 0. > I was unable to find a way of using the readymade function NR > because it assumes f accepts 1 double and returns 1 double, > whereas My Func accepts 5 doubles and returns 1 double. That's because the interface to the existing NR function is very poorly designed. In C++, the "standard" solution for any callback would be: class NRCallBack { public: virtual ~NRCallBack() {} virtual double operator()( double ) const = 0 ; } ; So the signature of NR would be: double NR( double x, NRCallBack const& f ) ; Rather than providing a function, you then derive from NRCallBack, and define the appropriate operator. In your precise case, it's probably a bit wordy, because we don't have lambda classes, and you'd have to do something like: double NRforMyFunc( double x1, double x2, double x3, double x4 ) { class F : public NRCallBack { public: NRCallBack( double x1, double x2, double x3, double x4 ) : x1( x1 ) , x2( x2 ) , x3( x3 ) , x4( x4 ) { } virtual double operator()( double x ) const { return MyFunc( x1, x2, x3, x4, x ) ; } private: double x1 ; double x2 ; double x3 ; double x4 ; } ; return NR( 0.0, F() ) ; } If (as may be the case), NR is in fact a C function, and must be callable from C, the established convention is to pass an additional void* with user data, i.e.: double NR( double x, double (*f)( double, void* ), void* ) ; Again, you have to write a wrapper function which takes the additional, fixed values as a void*, move these values into an array, and pass the address of the array to NR. > My veryinelegant solution was to copypaste the NR code and > adapt it so that the pointertofunction parameter was of the > type I needed. You may end up having to do this, if it's interface is broken. > Is there a more elegant approach that calls on the NR function > already present? Depending on the context of what you're doing, you may be able to use static variables and a wrapper function. IMHO, it's playing with fire, however, and you'd be better off rewriting the function to use one of the above interfaces, depending on whether it is pure C++, or it must be callable from C as well.  James Kanze (GABI Software) email:(EMail Removed) Conseils en informatique orientée objet/ Beratung in objektorientierter Datenverarbeitung 9 place Sémard, 78210 St.Cyrl'École, France, +33 (0)1 30 23 00 34 




James Kanze 
James Kanze
Guest
Posts: n/a

On Nov 15, 10:26*am, KaiUwe Bux <(EMail Removed)> wrote:
> (EMail Removed) wrote: > > Let double NR( double x, double(*)(const double&) f ) *be the > > signature of a NewtonRaphson function NR. > > Here, f is a function which returns a double and accepts a > > const double&. * * *The aim of the game is to find a zero of > > this function f (the point at which f crosses the xaxis). > > *This zerooff which solves our problem is the double which > > NR returns. * It remains to explain what the *"double x" > > represents. * This is the startingguess that is required in > > NewtonRaphson implementations. > > In my case, I have the following amended NewtonRaphson situation. *I > > have a function of the form > > double MyFunc(double x1, double x2, double x3, double x4, double x5) > > I want to solve the following problem: *Fix x1, x2, x3, and x4. *Then > > use Newton Raphson to return the double y such that MyFunc(x1, x2, x3, > > x4, y) = 0. > > I was unable to find a way of using the readymade function NR because > > it assumes f accepts 1 double and returns 1 double, whereas My Func > > accepts 5 doubles and returns 1 double. > > My veryinelegant solution was to copypaste the NR code and adapt it > > so that the pointertofunction parameter was of the type I needed. > > Is there a more elegant approach that calls on the NR function already > > present? > I would change NR into a template: > * template < typename Float, typename Func > > * Float find_zero ( Float initial_guess, Func f ); > Then, you could use bind() from c++0x or Boost to fix the > first four arguments and pass the resulting function object > into the template. This is a very elegant solution for a few special cases, but it results in an infection template; if the call to this function is in a function which receives the callback function as an argument, that function must be a template as well. And so on, add infitum; depending on the use pattern, you can very quickly end up with an unmanageable mess, where all of your functions are templates. (This might be workable if your compiler supports export, but not many do.)  James Kanze (GABI Software) email:(EMail Removed) Conseils en informatique orientée objet/ Beratung in objektorientierter Datenverarbeitung 9 place Sémard, 78210 St.Cyrl'École, France, +33 (0)1 30 23 00 34 




James Kanze 
KaiUwe Bux
Guest
Posts: n/a

James Kanze wrote:
> On Nov 15, 10:26*am, KaiUwe Bux <(EMail Removed)> wrote: >> (EMail Removed) wrote: >> > Let double NR( double x, double(*)(const double&) f ) *be the >> > signature of a NewtonRaphson function NR. > >> > Here, f is a function which returns a double and accepts a >> > const double&. * * *The aim of the game is to find a zero of >> > this function f (the point at which f crosses the xaxis). >> > This zerooff which solves our problem is the double which >> > NR returns. * It remains to explain what the *"double x" >> > represents. * This is the startingguess that is required in >> > NewtonRaphson implementations. > >> > In my case, I have the following amended NewtonRaphson situation. *I >> > have a function of the form > >> > double MyFunc(double x1, double x2, double x3, double x4, double x5) > >> > I want to solve the following problem: *Fix x1, x2, x3, and x4. *Then >> > use Newton Raphson to return the double y such that MyFunc(x1, x2, x3, >> > x4, y) = 0. > >> > I was unable to find a way of using the readymade function NR because >> > it assumes f accepts 1 double and returns 1 double, whereas My Func >> > accepts 5 doubles and returns 1 double. > >> > My veryinelegant solution was to copypaste the NR code and adapt it >> > so that the pointertofunction parameter was of the type I needed. > >> > Is there a more elegant approach that calls on the NR function already >> > present? > >> I would change NR into a template: > >> template < typename Float, typename Func > >> Float find_zero ( Float initial_guess, Func f ); > >> Then, you could use bind() from c++0x or Boost to fix the >> first four arguments and pass the resulting function object >> into the template. > > This is a very elegant solution for a few special cases, but it > results in an infection template; if the call to this function > is in a function which receives the callback function as an > argument, that function must be a template as well. Huh? I admit that this sentence has too many "this" and "that" for me to get references straight. So, I do not really understand what you mean. Anyway, I also do not see any reason why this template could not be called from ordinary functions: template < typename Float, typename Func > Float find_zero ( Float initial_guess, Func f ) { return ( 1 ); } double caller ( double x, double(*f)(double) ) { return ( find_zero( x, f ) ); } double id ( double x ) { return (x); } #include <iostream> #include <ostream> int main ( void ) { std::cout << caller( 1.0, &id ) << '\n'; } (BTW: a Google search for "infection template" only yield medical stuff.) > And so on, > add infitum; depending on the use pattern, you can very quickly > end up with an unmanageable mess, where all of your functions > are templates. (This might be workable if your compiler > supports export, but not many do.) I don't see that. Could you please elaborate? Best KaiUwe Bux 




KaiUwe Bux 
James Kanze
Guest
Posts: n/a

On Nov 15, 11:48*am, KaiUwe Bux <(EMail Removed)> wrote:
> James Kanze wrote: > > On Nov 15, 10:26*am, KaiUwe Bux <(EMail Removed)> wrote: > >> (EMail Removed) wrote: > >> > Let double NR( double x, double(*)(const double&) f ) *be the > >> > signature of a NewtonRaphson function NR. > >> > Here, f is a function which returns a double and accepts > >> > a const double&. * * *The aim of the game is to find a > >> > zero of this function f (the point at which f crosses the > >> > xaxis). This zerooff which solves our problem is the > >> > double which NR returns. * It remains to explain what the > >> > *"double x" represents. * This is the startingguess that > >> > is required in NewtonRaphson implementations. > >> > In my case, I have the following amended NewtonRaphson > >> > situation. *I have a function of the form > >> > double MyFunc(double x1, double x2, double x3, double x4, double x5) > >> > I want to solve the following problem: *Fix x1, x2, x3, > >> > and x4. *Then use Newton Raphson to return the double y > >> > such that MyFunc(x1, x2, x3, x4, y) = 0. > >> > I was unable to find a way of using the readymade > >> > function NR because it assumes f accepts 1 double and > >> > returns 1 double, whereas My Func accepts 5 doubles and > >> > returns 1 double. > >> > My veryinelegant solution was to copypaste the NR code > >> > and adapt it so that the pointertofunction parameter > >> > was of the type I needed. > >> > Is there a more elegant approach that calls on the NR > >> > function already present? > >> I would change NR into a template: > >> template < typename Float, typename Func > > >> Float find_zero ( Float initial_guess, Func f ); > >> Then, you could use bind() from c++0x or Boost to fix the > >> first four arguments and pass the resulting function object > >> into the template. > > This is a very elegant solution for a few special cases, but > > it results in an infection template; if the call to this > > function is in a function which receives the callback > > function as an argument, that function must be a template as > > well. > Huh? I admit that this sentence has too many "this" and "that" > for me to get references straight. So, I do not really > understand what you mean. Anyway, I also do not see any reason > why this template could not be called from ordinary functions: The problem is that the fact that it is a template, and is not resolved dynamically, propagates. If the ordinary function calls it with a known callback, fine; the propagation stops there. But if the ordinary function calls it with a functor that is passed in, then if templates are used, the ordinary function has to be a template too. And so on; imagine what would happen if iostream used templates, rather than virtual functions, in streambuf. > template < typename Float, typename Func > > Float find_zero ( Float initial_guess, Func f ) { > * return ( 1 ); > } > double caller ( double x, double(*f)(double) ) { > * return ( find_zero( x, f ) ); > } In this case, I fail to see what you've gained with respect to the initial problem. > double id ( double x ) { > * return (x); > } > #include <iostream> > #include <ostream> > int main ( void ) { > * std::cout << caller( 1.0, &id ) << '\n'; > } > (BTW: a Google search for "infection template" only yield > medical stuff.) Yes. I'm not really sure what the appropriate word should be. The closest analogy I can think of is the GNU license, but of course, templates aren't that infectious. The fact remains that any time you implement genericity with a template, it means that any client code which wants to maintain that genericity neads to be a template as well. Anytime you have a real choice, you should prefer inheritance with virtual functions to templates. (Of course, most of the time you don't have a real choice; templates are designed to solve a different set of problems than virtual functions.)  James Kanze (GABI Software) email:(EMail Removed) Conseils en informatique orientée objet/ Beratung in objektorientierter Datenverarbeitung 9 place Sémard, 78210 St.Cyrl'École, France, +33 (0)1 30 23 00 34 




James Kanze 
KaiUwe Bux
Guest
Posts: n/a

James Kanze wrote:
> On Nov 15, 11:48*am, KaiUwe Bux <(EMail Removed)> wrote: >> James Kanze wrote: >> > On Nov 15, 10:26*am, KaiUwe Bux <(EMail Removed)> wrote: >> >> (EMail Removed) wrote: >> >> > Let double NR( double x, double(*)(const double&) f ) *be the >> >> > signature of a NewtonRaphson function NR. > >> >> > Here, f is a function which returns a double and accepts >> >> > a const double&. * * *The aim of the game is to find a >> >> > zero of this function f (the point at which f crosses the >> >> > xaxis). This zerooff which solves our problem is the >> >> > double which NR returns. * It remains to explain what the >> >> > "double x" represents. * This is the startingguess that >> >> > is required in NewtonRaphson implementations. > >> >> > In my case, I have the following amended NewtonRaphson >> >> > situation. *I have a function of the form > >> >> > double MyFunc(double x1, double x2, double x3, double x4, double x5) > >> >> > I want to solve the following problem: *Fix x1, x2, x3, >> >> > and x4. *Then use Newton Raphson to return the double y >> >> > such that MyFunc(x1, x2, x3, x4, y) = 0. > >> >> > I was unable to find a way of using the readymade >> >> > function NR because it assumes f accepts 1 double and >> >> > returns 1 double, whereas My Func accepts 5 doubles and >> >> > returns 1 double. > >> >> > My veryinelegant solution was to copypaste the NR code >> >> > and adapt it so that the pointertofunction parameter >> >> > was of the type I needed. > >> >> > Is there a more elegant approach that calls on the NR >> >> > function already present? > >> >> I would change NR into a template: > >> >> template < typename Float, typename Func > >> >> Float find_zero ( Float initial_guess, Func f ); > >> >> Then, you could use bind() from c++0x or Boost to fix the >> >> first four arguments and pass the resulting function object >> >> into the template. > >> > This is a very elegant solution for a few special cases, but >> > it results in an infection template; if the call to this >> > function is in a function which receives the callback >> > function as an argument, that function must be a template as >> > well. > >> Huh? I admit that this sentence has too many "this" and "that" >> for me to get references straight. So, I do not really >> understand what you mean. Anyway, I also do not see any reason >> why this template could not be called from ordinary functions: > > The problem is that the fact that it is a template, and is not > resolved dynamically, propagates. If the ordinary function > calls it with a known callback, fine; the propagation stops > there. But if the ordinary function calls it with a functor > that is passed in, then if templates are used, the ordinary > function has to be a template too. And so on; imagine what > would happen if iostream used templates, rather than virtual > functions, in streambuf. You keep using pronouns and terms like "ordinary function" whose reference is not clear to me. Maybe, I am just dense. So for concreteness, here is a simple template implementation of find_zero using the Newton method: template < typename Float, typename Func > Float find_zero ( Func f, Float initial_guess, Float eps = std::numeric_limits<Float>::epsilon() * 1000, Float h = std::numeric_limits<Float>::epsilon() * 1000, unsigned int iteration_limit = 50 ) { Float x = initial_guess; for ( unsigned int n = 0; n < iteration_limit; ++n ) { Float y = f(x); if ( std::abs(y) < eps ) { return (x); } x = x  y * h / ( f(x+h/2)  f(xh/2) ); } throw( std::invalid_argument( "iteration limit exceeded" ) ); } I fail to see any problem with that. Clearly, there is no requirement that the call back function f has to be a template or that this function can only be called from templates. If one uses the signature template < typename Float, typename Func > Float find_zero ( Func const & f, Float initial_guess, Float eps = std::numeric_limits<Float>::epsilon() * 1000, Float h = std::numeric_limits<Float>::epsilon() * 1000, unsigned int iteration_limit = 50 ); one can even support the inheritance based solution you suggested elsethread. If you could provide code that illustrates the propagation of templates with this example, it would be highly appreciated. >> template < typename Float, typename Func > >> Float find_zero ( Float initial_guess, Func f ) { >> return ( 1 ); >> } > >> double caller ( double x, double(*f)(double) ) { >> return ( find_zero( x, f ) ); >> } > > In this case, I fail to see what you've gained with respect to > the initial problem. Nothing: the code is just meant to illustrate why I don't see that something propagates. That why the function is called "caller". Clearly, I am still missing your point. >> double id ( double x ) { >> return (x); >> } > >> #include <iostream> >> #include <ostream> > >> int main ( void ) { >> std::cout << caller( 1.0, &id ) << '\n'; >> } > >> (BTW: a Google search for "infection template" only yield >> medical stuff.) > > Yes. I'm not really sure what the appropriate word should be. > The closest analogy I can think of is the GNU license, but of > course, templates aren't that infectious. The fact remains that > any time you implement genericity with a template, it means that > any client code which wants to maintain that genericity neads to > be a template as well. Here the key phrase is "wants to maintain that genericity". There is no reason for client code to always be like that. All algorithms is the standard library are templates and they are used in nontemplated code. I do not see the infectious trait you mention. > Anytime you have a real choice, you > should prefer inheritance with virtual functions to templates. I disagree. In my codebase, that would be utterly inappropriate. More to the point: finding roots of functions clearly seems like a task for a template and forcing clients to inherit from some call back just to fit the interface is clearly wrong. > (Of course, most of the time you don't have a real choice; > templates are designed to solve a different set of problems than > virtual functions.) Agreed. Best KaiUwe Bux 




KaiUwe Bux 


 
Thread Tools  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Problem problem problem :( Need Help  Mike  ASP General  2  05112004 08:36 AM 
Powered by vBulletin®. Copyright ©2000  2014, vBulletin Solutions, Inc..
SEO by vBSEO ©2010, Crawlability, Inc. 