On 10/29/15 11:35 AM, John Maddock wrote:
On 29/10/2015 15:04, Robert Ramey wrote:
On 10/29/15 3:22 AM, John Maddock wrote:
I think there is a place for polynomial manipulation within Boost, but
I'm not sure that this class is the best basis. As we say in the docs,
it's a braindead implementation that's good enough for what I needed at
the time to implement Boost.Math, but not really suitable for heavy duty
polynomial manipulation.
While you're at it, How about a constexpr/tmp version which would do
polynomial manipulation at compile time?
Interesting idea, what kind of manipulation did you have in mind -
arithmetic? Might be possible in C++14 but certainly not in C++11.
Probably a whole different library actually,
Right
since the order would have
to be a compile time parameter?
I'm thinking it would be a variadic tuple.
here's what I had in mind:
// define a polynomial with coefficients of type T (int, float, etc)
template<typename T>
using polynomial = std::tuple
// now define some operators on these polynomials
template<typename T>j
// polynomial addition - easy to implement
operator+(polynomial<T>lhs, polynomial<T>rhs);
// other ops ... easy to implement
// polynomial division - aaaa - more compilicated to implement
operator/(polynomial<T>lhs, polynomial<T>rhs);
// very cool functions
template<typename T>
constexpr polynomial<T> derivative(polynomial<T> p);
template<typename T>
constexpr polynomial<T> integrate(polynomial<T> p);
// and of course we could evaluate any polynomial at
// specific point at either compile and/or run time
constexpr T evaluate(const polynomial<T> & p);
// a taylor series has the last two terms reserved for a rational
// representation of an error term
template<typename T>
using taylor_series = polynomial<T>;
// evaluate
T value(taylor_series<T>, T x);
// get error value
T error(taylor_series<T>, T x);
// given a sequence of derivatives of F at point x
// calculate a taylor series
template
constexpr taylor_series::taylor_series(x = 0);
// now I can replace my clunky quadrature of function
// F with
// return value and error
template
const expr std::pair fast_integral(
const T & start,
const T & finish
){
using f = integrate(taylor_series<F>(3.233));
T value = evaluate(f, finish) - evaluate(f, start);
T error_value = abs(error(f, finish)) + abs(error(f, start));
return std::pair
};
This would be pretty useful as it stands. Of course it
brings to mind a few more ideas
a) T above is presumed to be a scalar variable - but it
doesn't have to be. What I really need is to permit T
to be a tuble itself so I could handle complex and
and n dimensional space situations.
b) The creating of F is problematic and tedious. For this we need
TMP expression template driven automatic differentiation.
I'm thinking you could put this together in a couple of days
Robert Ramey
