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https://github.com/triqs/dft_tools
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99 lines
2.6 KiB
ReStructuredText
99 lines
2.6 KiB
ReStructuredText
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.. highlight:: c
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Clef expressions vs functions
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=====================================================================
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Clef expressions are **NOT** functions. In short,
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* clef expressions are *evaluated* (the order of argument *does not* matter) ::
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eval( expr, x_=1, y_=2, ...);
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* while functions are *called*, as usual (the order of argument *does* matter !) ::
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f(1,2)
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It is however possible to transform expressions into functions, *as soon as you specify the order of the placeholders*,
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and back.
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Function to clef expressions
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-------------------------------------
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This is immediate, if the function accept lazy arguments, cf :ref:`callable_object`::
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auto e1 = f(x_);
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Transforming clef expressions into functions
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----------------------------------------------------
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make_function
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.....................
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Given any expression with placeholder `x_`, `y_`, `z_`, ..., `make_function`
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transform them into a regular function. If we say ::
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auto f = make_function( clef_expression, placeholder_1, placeholder_2, placeholder_3, ...)
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then f is ::
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a function (placeholder_1, placeholder_2, placeholder_3, ...) --> RESULT
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where RESULT is :
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* the result of the complete evaluation of the expression if the list of placeholder exhausts the placeholders of the expression.
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* otherwise a clef_expression of the remaining placeholders, returning a **function**.
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Examples :
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* With one variable::
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auto e1 = 2*x_ + 1;
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auto f = make_function( e1, x_);
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f(3) == 7; // ok
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std::function<double(double)> F(f); // ok
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* With two variables ::
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auto e2 = 2*x_ + y_ + 1;
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auto f = make_function( e2, x_, y_);
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f(3,4) == 11; // ok
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std::function<double(double,double)> F(f); // ok
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* Make a function partially ::
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auto f = make_function( 2*x_ + y_ + 1, x_);
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// f is a lazy expression expression with placeholder y_, returning a function...
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auto f1 = eval (f, y_=1); // f1 is a function x-> 2*x + 2
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f1 (10) == 22;
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* Currifying a function ::
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auto f = make_function ( make_function( 2*x\_ + y\_ + 1, x\_), y\_);
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// f a function y-> x-> 2x+y+1
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// f(y) returns a function x-> 2x+y+1
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Short notation with >> operator
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.....................................
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For function of *one* variable, the make_function notation can be simplified into ::
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// same
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auto f = make_function( 2*x_ + y_ + 1, x_);
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auto f = x_ >> 2*x_ + y_ + 1;
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// same
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auto f = make_function ( make_function( 2*x_ + y_ + 1, y_), x_);
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auto f = x_ >> (y_ >> 2*x_ + y_ + 1) ;
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.. warning::
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The notation ::
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`x_` >> `y_` >> expression
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is banned because it conflicts with the standard priority of >>.
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Use parenthesis.
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