Re: Integrate function with arguments using quadrature

From: kila suelika (semeegozy_at_[hidden])
Date: 2020-08-20 05:41:07

In you lambda expression, you have to capture B_local :

    auto f = [&](Real x) { return std::bind(f0, _1, B_local)(x); };

The *[&]* tells the compiler to capture variables by reference
automatically.

On Mon, Aug 17, 2020 at 2:26 AM Anirban Pal via Boost-users <
boost-users_at_[hidden]> wrote:

> 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
>
>
>
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