Re: c++ Newton-Raphson problem

From:
James Kanze <james.kanze@gmail.com>
Newsgroups:
comp.lang.c++
Date:
Sat, 15 Nov 2008 15:37:16 -0800 (PST)
Message-ID:
<9c61d9c7-303f-41b3-8ce2-2175315d007f@q30g2000prq.googlegroups.com>
On Nov 15, 11:48 am, Kai-Uwe Bux <jkherci...@gmx.net> wrote:

James Kanze wrote:

On Nov 15, 10:26 am, Kai-Uwe Bux <jkherci...@gmx.net> wrote:

pauldepst...@att.net wrote:

Let double NR( double x, double(*)(const double&) f ) be the
signature of a Newton-Raphson 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
x-axis). This zero-of-f which solves our problem is the
double which NR returns. It remains to explain what the
 "double x" represents. This is the starting-guess that
is required in Newton-Raphson implementations.

In my case, I have the following amended Newton-Raphson
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 ready-made
function NR because it assumes f accepts 1 double and
returns 1 double, whereas My Func accepts 5 doubles and
returns 1 double.

My very-inelegant solution was to copy-paste the NR code
and adapt it so that the pointer-to-function 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:james.kanze@gmail.com
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