Re: Integrate function with arguments using quadrature

From: Anirban Pal (anirban.pal.iitkgp_at_[hidden])
Date: 2020-08-16 18:25:36

Thank you John and Paul for your responses. Allow me to be more clear.

I’m considering something like the following function *f0*, which depends
on *x* and some additional arguments given by the vector *A*. The vector *A
*is unknown at compile time and computed during execution. The function f0
is to be integrated at a constant value for *A* (computed at runtime) with
a range for *x*. The range is also computed at runtime, but it can be
explicitly passed to the *integrator.integrate* call.

Lambda expressions seem to be the way to go. However, lambda expressions do
not seem to easily capture local variables. In the following code, I've
managed to get a lambda expression for the function f(x) = f0(x,A) and I
can integrate that. However, I can only use the global variable *B_global*
instead of *B_local*.

#include <iostream>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/math/quadrature/tanh_sinh.hpp>
#include <boost/bind/bind.hpp>
#include <functional>

typedef boost::multiprecision::cpp_bin_float_100 Real;

Real B_global[] = {0.0, 0.5, 1.0};

Real f0 (Real x, Real *A)
{
    return x*( A[0]*A[0] + A[1]*A[1] + A[2]*A[2] );
}

int main(int argc, char **argv)
{
    using namespace boost::math::quadrature;
    using namespace std::placeholders;
    tanh_sinh<Real> integrator;

    Real *B_local; B_local = (Real *)malloc(3*sizeof(Real));
    B_local[0] = 0.0; B_local[1] = 0.5, B_local[2] = 1.0;

    auto f = [](Real x) { return std::bind(f0, _1, B_global)(x); };
//If I use B_local, I get the error: ‘B_local’ is not captured
    Real Q = integrator.integrate(f, 0.0, 1.0);

    std::cout << std::setprecision(std::numeric_limits<Real>::max_digits10)
     << "Comp.: " << Q << std::endl;

    return 0;
}

I figured I need to use boost::bind.
Also, I wanted to use boost:bind but I was unsuccessful. So I retreated to
std::bind for now.

Thank you.

On Sun, 16 Aug 2020 at 06:51, John Maddock via Boost-users <
boost-users_at_[hidden]> wrote:

>
> On 14/08/2020 22:56, Anirban Pal via Boost-users wrote:
> > Hello,
> >
> > I'm trying to integrate functions with BOOST quadrature routines. So
> > far they have been extremely impressive accuracy-wise, particularly
> > with multiprecision features.
> >
> > I wish to integrate a function and pass some arguments to it. These
> > arguments can be scalars, matrices, structs or objects. I was
> > wondering if there is an example that explores this. Would I need to
> > use a boost.function? Or would a function pointer work?
>
> To create a reusable single-valued functor that integrates from [a, x]
> for fixed a, then I think some nested lambda expressions would work:
>
>     auto integral = [](double x)
>     {  // Integrates from 0 to x:
>        static tanh_sinh<double> integrator;
>        static auto f = [](double x) { return 5 * x + 7; };
>        return integrator.integrate(f, 0.0, x);
>     };
>     std::cout << integral(2) << std::endl;
>     std::cout << integral(4.5) << std::endl;
>
> I'm not sure what you had in mind with non-scalar arguments, but if you
> need to evaluate the above at multiple x values [x_1, x_2.... x_n] then
> conceivably you could integrate from
>
> [a, x_0]
>
> [x_1, x_2]
>
> ....
>
> [x_n-1, x_n]
>
> and then sum to get the integrals
>
> [a, x_0]
>
> [a, x_1]
>
> ....
>
> [a, x_n]
>
> Which may or may not be more efficient.
>
> HTH, John.
>
> >
> > I currently have an implementation using GSL_functions which
> > explicitly allow the function and parameters to be passed as pointers.
> > I am curious if I can do something similar with boost.
> >
> > Thank you.
> >
> >
> > --
> > Anirban Pal
> >
> >
> >
> >
> > _______________________________________________
> > Boost-users mailing list
> > Boost-users_at_[hidden]
> > https://lists.boost.org/mailman/listinfo.cgi/boost-users
>
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-- 
Anirban Pal