mirror of
https://github.com/triqs/dft_tools
synced 2024-12-27 06:43:40 +01:00
135 lines
3.5 KiB
ReStructuredText
135 lines
3.5 KiB
ReStructuredText
.. highlight:: c
|
|
|
|
Functional constructs : map & fold
|
|
###########################################
|
|
|
|
Two standard functional constructs are provided :
|
|
|
|
* *map* that promotes a function of the array element to a function of the array,
|
|
element by element.
|
|
|
|
* *fold* is the reduction of a function on the array.
|
|
|
|
.. _map:
|
|
|
|
map
|
|
========================================================
|
|
* **Purpose** :
|
|
|
|
map promotes any function into an `array function`, acting term by term.
|
|
|
|
* **Synopsis** ::
|
|
|
|
template<class F> auto map (F f);
|
|
|
|
If `f` is a function, or a function object ::
|
|
|
|
ValueType2 f(ValueType1)
|
|
|
|
Then map(f) is a function::
|
|
|
|
ReturnType map(f) ( ArrayType const & A)
|
|
|
|
where ArrayType models the :ref:`ImmutableCuboidArray` concept
|
|
|
|
* with value_type == ValueType1
|
|
|
|
and ReturnType models the :ref:`ImmutableCuboidArray` concept
|
|
|
|
* with the same domain as ArrayType
|
|
* with value_type == ValueType2
|
|
|
|
* N.B. : Some cases require explicit cast, e.g. for the standard abs function (already defined in arrays/mapped_function.hpp) ,
|
|
or the compiler does not know which std::abs you are talking about ::
|
|
|
|
auto Abs = map( std::function<double(double)>(static_cast< double (*)(double)> (std::abs)) );
|
|
|
|
* TO DO : clarify the F f or F const & : check code and put an example with std::ref.
|
|
|
|
* **Example** :
|
|
|
|
.. compileblock::
|
|
|
|
#include <triqs/arrays.hpp>
|
|
using triqs::arrays::matrix; using triqs::clef::placeholder;
|
|
int main() {
|
|
// declare and init a matrix
|
|
placeholder<0> i_; placeholder<1> j_;
|
|
matrix<int> A (2,2); A(i_,j_) << i_ + j_ ;
|
|
|
|
// the mapped function
|
|
auto F = triqs::arrays::map([](int i) { return i*2.5;});
|
|
|
|
matrix<double> B;
|
|
B = F(A);
|
|
std::cout<< A << B<< std::endl;
|
|
|
|
// works also with expressions of course
|
|
B = F( 2*A );
|
|
B = B + 3* F(2*A); // ok that is just an example...
|
|
std::cout<< A << B<< std::endl;
|
|
}
|
|
|
|
|
|
fold
|
|
========================================================
|
|
|
|
* **Purpose** :
|
|
fold implements the folding (or reduction) on the array.
|
|
|
|
* **Syntax** :
|
|
|
|
If `f` is a function, or a function object of synopsis (T, R being 2 types) ::
|
|
|
|
R f ( T, R )
|
|
|
|
then ::
|
|
|
|
auto F = fold(f);
|
|
|
|
is a callable object which can fold any array of value_type T.
|
|
|
|
So, if
|
|
|
|
* A is a type which models the :ref:`ImmutableCuboidArray` concept
|
|
(e.g. an array , a matrix, a vector, an expression, ...)
|
|
|
|
* A::value_type is T
|
|
|
|
then ::
|
|
|
|
fold (f) ( A, R init = R() ) = f( f( f( ... f( a(0,1), f(a(0,0), init)))))
|
|
|
|
Note that :
|
|
|
|
* The order of traversal is the same as foreach.
|
|
* The precise return type of fold is an implementation detail, depending on the precise type of f,
|
|
use auto to keep it.
|
|
* The function f will be inlined if possible, leading to efficient algorithms.
|
|
* fold is implemented using a foreach loop, hence it is efficient.
|
|
|
|
* **Example** :
|
|
|
|
Many algorithms can be written in form of map/fold.
|
|
|
|
The function *sum* which returns the sum of all the elements of the array is implemented approximately like this
|
|
(this function already exists in the lib, cf ???) ::
|
|
|
|
template <class A>
|
|
typename A::value_type sum(A const & a) { return fold ( std::plus<typename A::value_type>()) (a); }
|
|
|
|
Note in this example :
|
|
|
|
* the simplicity of the code
|
|
* the genericity : it is valid for any dimension of array.
|
|
* internally, the library will rewrite it as a series of for loop, ordered in the TraversalOrder of the array
|
|
and inline the plus operator.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|