Re: [Boost-users] Integrate function with arguments using quadrature

16 Aug 2020

      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 
#include 
#include 
#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@lists.boost.org> 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
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