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https://github.com/triqs/dft_tools
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58 lines
1.6 KiB
ReStructuredText
58 lines
1.6 KiB
ReStructuredText
.. highlight:: c
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Functional construct (II) : map
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========================================================
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* **Purpose** :
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fold implements the folding (or reduction) on the array.
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* **Syntax** :
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If `f` is a function, or a function object of synopsis (T, R being 2 types) ::
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R f ( T, R )
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then ::
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auto F = fold(f);
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is a callable object which can fold any array of value_type T.
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So, if
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* A is a type which models the :ref:`HasImmutableArrayInterface` concept
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(e.g. an array , a matrix, a vector, an expression, ...)
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* A::value_type is T
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then ::
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fold (f) ( A, R init = R() ) = f( f( f( ... f( a(0,1), f(a(0,0), init)))))
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Note that :
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* The order of traversal is the same as foreach.
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* The precise return type of fold is an implementation detail, depending on the precise type of f,
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use auto to keep it.
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* The function f will be inlined if possible, leading to efficient algorithms.
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* fold is implemented using a foreach loop, hence it is efficient.
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* **Example** :
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Many algorithms can be written in form of map/fold.
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The function *sum* which returns the sum of all the elements of the array is implemented approximately like this
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(this function already exists in the lib, cf ???) ::
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template <class A>
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typename A::value_type sum(A const & a) { return fold ( std::plus<typename A::value_type>()) (a); }
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Note in this example :
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* the simplicity of the code
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* the genericity : it is valid for any dimension of array.
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* internally, the library will rewrite it as a series of for loop, ordered in the TraversalOrder of the array
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and inline the plus operator.
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