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gf: Work on documentation

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Olivier Parcollet 2013-09-18 15:13:23 +02:00
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23
doc/installation/requirements.rst
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@ -16,28 +16,23 @@ C++ compilers
TRIQS is written in C++, i.e. in the **C++11** standard as defined by the ISO standardization committee.
A recent compiler is therefore mandatory.
There are 3 categories of C++ compilers:
* Standard compliant C++ compilers
* Standard compliant C++ compilers (recommended and supported).
* :ref:`clang 3.3<install_clang>` and higher
* :ref:`clang 3.2<install_clang>` and higher (in particular the default clang on OS X 10.8).
* g++ 4.8.1 and higher
These compilers are recommended and supported.
* The intel icc 14.0 is close to be C++11 compliant, but presents currently too many bugs to be supported
at present. It compiles 99% of TRIQS, but we do not have the ressources to write and
maintains all necessary workarounds.
* Obsolete compilers
* g++ 4.6.3 to 4.8.0
TRIQS can be built with these compilers but because they lack full C++11 support,
TRIQS may be slower (some optimisations are disabled in the library).
These compilers may not be supported in later releases.
Besides, for *our codes*, icc does not provide a significant speed gain (unlike MKL),
so we do not recommend it for TRIQS.
* C++98 compilers
* g++ before 4.6
* Intel icc 12.0 and below
* g++ before 4.8.1
* Intel icc 13.0 and below
Compilers implementing the previous version of the C++ standard (C++98) do not work and
will *not* be supported.

2
doc/reference/c++/arrays/containers/compound_ops.rst
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@ -14,3 +14,5 @@ Compound assignment operators (+=, -=, * =, /=)
The containers and the view have compound operators.
*NB* : These operators make no sense for const views, and result in a compile error.

11
doc/reference/c++/arrays/containers/rebind.rst
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@ -5,13 +5,20 @@
rebind
==================================
* **Synopsis**:
* **Synopsis** for X_view (X=array, matrix, vector):
.. cpp:function:: void rebind(array_view const & a)
* **Synopsis** for X_const_view (X=array, matrix, vector):
.. cpp:function:: void rebind(array_view const & a)
.. cpp:function:: void rebind(array_const_view const & a)
* **Effect** :
Rebinds the view
After this method, the view points to the same as a.
After this method, the view points to the same as *a*.
Following the :ref:`memory management rules <arr_view_memory>`, if nothing else views the
data originally pointed to by the view, this data is destroyed.

26
doc/reference/c++/arrays/containers/view_assign.rst
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@ -7,8 +7,9 @@ Assignment to views
**Synopsis** :
template<typename RHS>
array_view & operator=(RHS const & X);
template<typename RHS> array_view & operator=(RHS const & X);
*NB: The assignment operator is deleted for const_views.*
The `view classes` have a quite general assignment operator.
We will illustrate it on the `array_view` class, it is the same for `matrix` and `vector`.
@ -21,31 +22,30 @@ We will illustrate it on the `array_view` class, it is the same for `matrix` and
e.g. : array, array_view, matrix, matrix_view,
but also formal expression (See , e.g. A+B), or any custom object of your choice.
`Effect` : all the elements viewed by the view are replaced
by the evaluation of RHS.
*Effect* :
Every elements viewed by the view are replaced by the evaluation of RHS.
.. warning::
*Precondition*
The shape of the view and of RHS must match exactly or behaviour is undefined.
If the debug macro, :ref:`TRIQS_ARRAYS_ENFORCE_BOUNDCHECK<arr_debug_macro>` is defined,
this condition is checked at runtime.
.. note::
We could lower this condition, since we don't need a domain here, just the evaluation
on the indices...
NB : We could lower this condition, since we don't need a domain here, just the evaluation on the indices...
* A scalar.
`Effect` : all elements viewed by the view are set to this scalar.
*Effect* :
Every elements viewed by the view are set to this scalar, except for the matrix_view,
where the matrix is set to the identity.
NB : no move assign operator
NB : no move assignment operator
---------------------------------------
Note that **there is no move assign operators for views**.
If RHS is an rvalue reference, the regular operator = is called, that
Note that **there is no move assignment operators for views**.
If RHS is an rvalue reference, the regular operator= (view const &) is called, that
makes a copy of the data of RHS into the elements viewed by the view.
This behaviour is consistent with the fact that views are *not* regular types.

36
doc/reference/c++/arrays/containers/view_constructors.rst
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@ -14,15 +14,6 @@ Constructors of array_view
Views have `view semantics`, i.e. they **never** make a copy of the data.
====================================================================== =====================================================================================================
Constructors of array_view Comments
====================================================================== =====================================================================================================
array_view(const array_view &) Copy construction (makes a shallow copy)
array_view(const T & X) T is any type such that X.indexmap() and X.storage() can be used to construct a view.
REF to concept here ....
====================================================================== =====================================================================================================
+-----------------------------------+---------------------------------------------------------------------------------------+
| Constructors of array_view | Comments |
+===================================+=======================================================================================+
@ -39,7 +30,28 @@ array_view(const T & X) T is any
+-----------------------------------+---------------------------------------------------------------------------------------+
Constructors of matrix_view, vector_view
------------------------------------------------
Constructors of array_const_view
---------------------------------------
Similar to array_view
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
| Constructors of array_const_view<T,R,OptionsFlags, TraversalOrder> | Comments |
+========================================================================+=======================================================================================+
| array_const_view(array_const_view const &) | Create a new view, viewing the same data. Does **not** copy data. (copy constructor) |
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
| array_const_view(array_view<T,R,OptionsFlags, TraversalOrder> const &) | Create a new view, viewing the same data. Does **not** copy data |
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
| array_const_view(const T & X) | T is any type such that X.indexmap() and X.storage() can be used to construct a view. |
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
| array_const_view(array_const_view &&) | Move construction (trivial here, a copy constructor is very quick anyway). |
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
| explicit array_const_view(PyObject * X) | Construct an array_view from the Python object X. Type and rank must match exactly, |
| | or an exception if thrown |
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
| | .. note:: X is a borrowed reference, array does not affect its counting reference. |
+------------------------------------------------------------------------+---------------------------------------------------------------------------------------+
Constructors of matrix_view, vector_view, matrix_const_view, vector_const_view
-------------------------------------------------------------------------------
Similar to array_view, array_const_view

33
doc/reference/c++/arrays/containers/views.rst
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@ -13,19 +13,27 @@ Views
template <typename ValueType, ull_t OptionsFlags=0, ull_t TraversalOrder=0> class matrix_view;
template <typename ValueType, ull_t OptionsFlags=0> class vector_view;
template <typename ValueType, int Rank, ull_t OptionsFlags=0, ull_t TraversalOrder=0> class array_const_view;
template <typename ValueType, ull_t OptionsFlags=0, ull_t TraversalOrder=0> class matrix_const_view;
template <typename ValueType, ull_t OptionsFlags=0> class vector_const_view;
where triqs::ull_t is the type defined by :
.. code-block:: c
typedef unsigned long long ull_t;
* The view type of X (= array, matrix, vector) is called X_view, with the same template parameters as the regular type.
* The view types of X (= array, matrix, vector) are called X_view, and X_const_view, with the same template parameters as the regular type.
* A `view` is give access to a restricted portion of the array, matrix or vector, i.e. a `partial view` of the data.
The view can also be `complete` (i.e. show all the container).
* The views model the :ref:`MutableCuboidArray`, :ref:`MutableMatrix`, :ref:`MutableVector`, like the corresponding regular type.
* The const views are similar to view, except that theirs contents can not be modified.
They model the :ref:`ImmutableCuboidArray`, :ref:`ImmutableMatrix`, :ref:`ImmutableVector`, like the corresponding *const* regular type.
* Views have `view semantics`, i.e. their behave like a reference to the data, they are not regular type.
In particular, they never make copy of the data.
See :ref:`view_vs_regular` for a detailed discussion of the difference between a regular type and its corresponding view.
@ -33,6 +41,8 @@ where triqs::ull_t is the type defined by :
* Views are largely interoperable : it is easy and quick to take a matrix_view of an array, or vice versa.
Cf constructors belows.
* Const views can be constructed from a view, but the reverse is not true (Cf constructors).
* **Memory Management**
Views offers a strong guarantee of the existence of the data, like a std::shared_ptr.
@ -70,15 +80,17 @@ NB: Rank is only present for array, since matrix have rank 2 and vector rank 1.
Member types
--------------------------------------
+--------------+----------------------------------------------------------+
+-----------------+-----------------------------------+
| Member type | Definitions |
+==============+==========================================================+
+=================+===================================+
| value_type | ValueType |
+--------------+----------------------------------------------------------+
| view_type | The corresponding view type, i.e. the view itself |
+--------------+----------------------------------------------------------+
+-----------------+-----------------------------------+
| view_type | The corresponding view type |
+-----------------+-----------------------------------+
| const_view_type | The corresponding const view type |
+-----------------+-----------------------------------+
| regular_type | The corresponding regular type |
+--------------+----------------------------------------------------------+
+-----------------+-----------------------------------+
Member constexpr
--------------------------------------
@ -92,7 +104,7 @@ Member constexpr
+--------+------+-------------------------------+
Member functions
---------------------
------------------
+-------------------------------------------+------------------------------------------+
| Member function | Meaning |
@ -101,12 +113,12 @@ Member functions
+-------------------------------------------+------------------------------------------+
| (destructor) | |
+-------------------------------------------+------------------------------------------+
| :ref:`operator ()<arr_call>` | element of access/views/lazy expressions |
+-------------------------------------------+------------------------------------------+
| :ref:`operator =<arr_view_assign>` | assigns values to the container |
+-------------------------------------------+------------------------------------------+
| :ref:`operator +=,-=,*=,/=<arr_comp_ops>` | compound assignment operators |
+-------------------------------------------+------------------------------------------+
| :ref:`operator ()<arr_call>` | element of access/views/lazy expressions |
+-------------------------------------------+------------------------------------------+
| begin/cbegin | returns iterator to the beginning |
+-------------------------------------------+------------------------------------------+
| end/cend | returns iterator to the end |
@ -133,7 +145,6 @@ Member functions
Non-member functions
------------------------
+---------------------------------+-------------------------------------------+
| Member function | Meaning |
+=================================+===========================================+

9
doc/reference/c++/conventions.rst
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@ -18,14 +18,15 @@ Efficient techniques which were considered before as complex and reserved to pro
are now becoming simple to implement, like e.g. expression templates.
The implementation of most of the TRIQS library (e.g. clef, arrays) would be either impossible or at least
much more complex and time consuming (with a lot of abstruse boost-like construction)
much more complex and time consuming (with a lot of abstruse boost-like constructions)
in previous versions of C++.
Besides, this evolution is not finished.
Besides, this evolution is not finished (in fact it seems to accelerate !).
The new coming standard, C++14, expected to be adopted and implemented very soon,
will still make it a lot better. In particular, the concept support (template constraints)
will still make it a lot better. In particular, the concept support (template constraints TS)
will hopefully solve the most problematic issue with metaprogramming techniques, i.e. the lack of concept
check at compile time, resulting in long and obscur error messages from the compiler when *using* the library.
check at compile time, resulting in long and obscur error messages from the compiler when *using* the library,
which can leave the non-C++-expert user quite clueless...
Hence, TRIQS will move to C++14 as soon as compilers are available.
Notation

2
doc/reference/c++/gf/concepts.rst
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@ -99,7 +99,7 @@ Mesh
It does not really need to be a mesh : e.g. if the function is represented on a polynomial basis,
it is the parameters of this representation (max number of coordinates, e.g.)
* **Refines** : RegularType, HasConstIterator BoostSerializable, H5-serializable.
* **Refines** : RegularType, HasConstIterator BoostSerializable, H5-serializable, Printable.
* **Definition** :

2
doc/reference/c++/gf/contents.rst
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@ -15,6 +15,8 @@ various Green functions.
intro
gf_and_view
gf_part_eval_curry
slicing
concepts
meshes
tail

158
doc/reference/c++/gf/gf_and_view.rst
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@ -5,30 +5,37 @@
gf and gf_view
=================
gf is the Green function container, with its view gf_view, defined as ::
**Synopsis**:
template<typename Variable, typename Target=matrix_valued, typename Opt=void> class gf; // regular type
template<typename Variable, typename Target=matrix_valued, typename Opt=void> class gf_view; // view type
.. code-block:: c
In this section, we describe all common properties of gf.
In practice, one works with one of the specialization described below (:ref:`gf_special`),
with their specific aspects (domains, interpolation methods, ....).
template<typename Variable, typename Target=matrix_valued, typename Opt=void> class gf;
template<typename Variable, typename Target=matrix_valued, typename Opt=void> class gf_view;
template<typename Variable, typename Target=matrix_valued, typename Opt=void> class gf_const_view;
Hereafter, we describe the containers, the views.
Properties specific to each :ref:`specializations<gf_special>` are described in a specific page, linked in the table below.
Template parameters
----------------------------
* **Variable** determines the domain of the Green function
* **Target** determines the value of the Green function
* **Opt** is currently not used [default to void]. It may be used to differentiate different Green functions
with the same Variable, Target but different behaviour (e.g. interpolation, ...).
+-----------------------------------------+-------------------------------+-------------------------------+--------------------------------------+
| Template parameter | Accepted type | Access in the class | Meaning |
+=========================================+===============================+===============================+======================================+
| Variable | Cf table below | variable_t | The domain of definition of the |
| | | | Green function |
+-----------------------------------------+-------------------------------+-------------------------------+--------------------------------------+
| Target | Cf Table below | target_t | The target space of the function |
+-----------------------------------------+-------------------------------+-------------------------------+--------------------------------------+
| Opt | void | option_t | Currently unused |
+-----------------------------------------+-------------------------------+-------------------------------+--------------------------------------+
They can have the following values :
The *Variable* template parameter can take the following values :
+--------------------------+--------------------------------------------+
| Variable | Meaning |
+==========================+============================================+
| gf_imfreq | Imaginary Matsubara frequency |
| imfreq | Imaginary Matsubara frequency |
+--------------------------+--------------------------------------------+
| imtime | Imaginary Matsubara time |
+--------------------------+--------------------------------------------+
@ -43,14 +50,16 @@ They can have the following values :
| cartesian_product<Gs...> | Cartesian product of gf<Gs> ... functions. |
+--------------------------+--------------------------------------------+
and
The *Target* template parameter can take the following values :
+-------------------------+-----------------------------------------------------+
| Target | Meaning |
+=========================+=====================================================+
| scalar_valued | The function is scalar valued (double, complex...). |
+-------------------------+-----------------------------------------------------+
| matrix_valued [default] | The function is matrix valued. |
+-------------------------+-----------------------------------------------------+
| scalar_valued | The function is scalar valued (double, complex...). |
| tensor_valued<R> | The function is tensor valued with rank |
+-------------------------+-----------------------------------------------------+
.. _gf_special:
@ -58,19 +67,21 @@ and
Specializations
-------------------
+-----------------+------------------+--------------------+----------------------------+
| Variable\Target | matrix_valued | scalar_valued | G (another Green function) |
+=================+==================+====================+============================+
+-------------------------+-------------------------------+-------------------------------+---------------------------+
| Variable/Target | matrix_valued | scalar_valued | gf_valued |
+=========================+===============================+===============================+===========================+
| imfreq | :doc:`gf_imfreq` | :doc:`gf_imfreq_s` | |
+-----------------+------------------+--------------------+----------------------------+
+-------------------------+-------------------------------+-------------------------------+---------------------------+
| imtime | :doc:`gf_imtime` | :doc:`gf_imtime_s` | |
+-----------------+------------------+--------------------+----------------------------+
+-------------------------+-------------------------------+-------------------------------+---------------------------+
| refreq | :doc:`gf_refreq` | :doc:`gf_refreq_s` | |
+-----------------+------------------+--------------------+----------------------------+
+-------------------------+-------------------------------+-------------------------------+---------------------------+
| retime | :doc:`gf_retime` | :doc:`gf_retime_s` | |
+-----------------+------------------+--------------------+----------------------------+
+-------------------------+-------------------------------+-------------------------------+---------------------------+
| block_index | | | :doc:`block_gf<gf_block>` |
+-----------------+------------------+--------------------+----------------------------+
+-------------------------+-------------------------------+-------------------------------+---------------------------+
| cartesian_product<M...> | :doc:`gf_product<gf_product>` | :doc:`gf_product<gf_product>` | |
+-------------------------+-------------------------------+-------------------------------+---------------------------+
.. toctree::
:hidden:
@ -82,32 +93,103 @@ Specializations
gf_imtime
gf_retime
gf_block
gf_prod
Construction/factories
-------------------------------
gf/gf_view have very basic constructors :
default, copy, move, and one constructor from the data used by the functions (reserved for advanced users).
Various specializations however provides several factories, adapted to each case, of the form ::
auto g= make_gf<Variable, Target, Opt> ( ....) ;
This is the recommended way to construct `gf` objects.
Cf examples in various specializations.
gf_product
Member types
-----------------
--------------------------------------
+----------------+-------------------------------------------------------------+
| Member type | Definitions |
+================+=============================================================+
| view_type | The corresponding view type |
+----------------+-------------------------------------------------------------+
| regular_type | The corresponding regular type i.e. the container itself |
+----------------+-------------------------------------------------------------+
| mesh_t | The mesh |
+----------------+-------------------------------------------------------------+
| target_shape_t | Type storing the information to construct the target space, |
| | Depends on the specialisation (a shape for matrix_valued |
| | gf, empty for a scalar valued, ... Cf Specialisations) |
+----------------+-------------------------------------------------------------+
| data_t | Type of the data array |
+----------------+-------------------------------------------------------------+
| singularity_t | Type of the singularity (tail, nothing...) |
+----------------+-------------------------------------------------------------+
| symmetry_t | Symmetry (unused at this stage). |
+----------------+-------------------------------------------------------------+
Member functions
---------------------
+-------------------------------------------+------------------------------------------+
| Member function | Meaning |
+===========================================+==========================================+
| :ref:`(constructor)<gf_constr>` | |
+-------------------------------------------+------------------------------------------+
| (destructor) | |
+-------------------------------------------+------------------------------------------+
| :ref:`operator ()<gf_call>` | Evaluation on a point of the domain |
+-------------------------------------------+------------------------------------------+
| :ref:`operator []<gf_subscript>` | Access to the value on the mesh |
+-------------------------------------------+------------------------------------------+
| :ref:`mesh<gf_data>` | Access to the mesh |
+-------------------------------------------+------------------------------------------+
| :ref:`singularity<gf_data>` | Access to the singularity |
+-------------------------------------------+------------------------------------------+
| :ref:`symmetry<gf_data>` | Access to the symmetry |
+-------------------------------------------+------------------------------------------+
| :ref:`data<gf_data>` | Direct view of the data [Advanced] |
+-------------------------------------------+------------------------------------------+
| :ref:`operator =<gf_reg_assign>` | Assigns values to the container |
+-------------------------------------------+------------------------------------------+
| :ref:`operator +=,-=,*=,/=<gf_comp_ops>` | compound assignment operators |
+-------------------------------------------+------------------------------------------+
.. toctree::
:hidden:
gf_constructors
gf_data
gf_assign
gf_call
gf_subcript
compound_ops
call
resize
STL
Non-member functions
------------------------
+---------------------------------+-------------------------------------------+
| Member function | Meaning |
+=================================+===========================================+
| :ref:`swap<gf_swap>` | Swap of 2 containers |
+---------------------------------+-------------------------------------------+
| :ref:`operator\<\<<gf_stream>` | Writing to stream |
+---------------------------------+-------------------------------------------+
.. toctree::
:hidden:
stream
swap
Interaction with CLEF expressions
-------------------------------------
The gf containers and their view classes can be :doc:`used with the CLEF Library <clef>`.
.. toctree::
:hidden:
clef

39
doc/reference/c++/gf/gf_assign.rst Normal file
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@ -0,0 +1,39 @@
.. highlight:: c
.. _gf_reg_assign:
Assignment
=========================
**Synopsis** ::
gf & operator=(gf const & X); (1)
template<??? RHS> gf & operator=(RHS const & X); (2)
The container have a quite general assignment operator.
* (1) just make a copy of X into *\*this*.
* (2) **RHS** can be anything that models the :ref:`???` concept
.. warning::
In both cases, if needed, the container is resized.
Hence **assignment invalidates all pointers and views to it**.
Move assign operator
---------------------------
**Synopsis** ::
gf & operator=(gf && X);
Standard move assign operator.
Move the data of X as data of `*this`.

138
doc/reference/c++/gf/gf_block.rst
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@ -2,35 +2,165 @@
.. _gf_block:
gf<block_index, G> or block_gf<G>
block_gf<G> (alias of gf<block_index, G>)
===================================================
This is a specialisation of :ref:`gf_and_view` for block functions.
A block Green function is nothing but Green function on a discrete domain representing the
block indices, and whose value is a Green function itself.
For convenience, for following aliases are provided ::
template<typename ... T> using block_gf = gf <block_index, gf<T...>>;
template<typename ... T> using block_gf_view = gf_view <block_index, gf<T...>>;
template<typename ... T> using block_gf_const_view = gf_const_view<block_index, gf<T...>>;
Constructors
--------------
The constructors of the gf.
target_shape_t = {}
Factories
-------------
Also several factories are provided for these block Green functions.
Factories for the regular type
.....................................
The factories for the regular type *gf* are ::
// From a number and a gf to be copied
template <typename Variable, typename Target, typename Opt>
block_gf<Variable, Target, Opt>
make_block_gf(int n, gf<Variable, Target, Opt> const & g);
// From a vector of gf (moving directly)
template <typename Variable, typename Target, typename Opt>
block_gf<Variable, Target, Opt>
make_block_gf(std::vector<gf<Variable, Target, Opt>> &&V);
// From a vector of gf or views (a gf must be contructible from GF2)
template <typename Variable, typename Target, typename Opt, typename GF2>
block_gf<Variable, Target, Opt>
make_block_gf(std::vector<GF2> const &V);
// From a init list of GF with the correct type
template <typename Variable, typename Target, typename Opt>
block_gf<Variable, Target, Opt>
make_block_gf(std::initializer_list<gf<Variable, Target, Opt>> const &V);
// From vector<string> and a gf to be copied
template <typename Variable, typename Target, typename Opt>
block_gf<Variable, Target, Opt>
make_block_gf(std::vector<std::string> const &block_names,
gf<Variable, Target, Opt> const &g);
// From vector<string>, vector<gf>
template <typename Variable, typename Target, typename Opt>
block_gf<Variable, Target, Opt>
make_block_gf(std::vector<std::string> const &block_names,
std::vector<gf<Variable, Target, Opt>> V);
// From vector<string>, init_list<GF>
template <typename Variable, typename Target, typename Opt>
block_gf<Variable, Target, Opt>
make_block_gf(std::vector<std::string> const &block_names,
std::initializer_list<gf<Variable, Target, Opt>> const &V);
Factories for the view type
.....................................
The factories for the view type *gf_view*, *gf_const_view* are ::
// Build a view of the gf.
// 1- All Green functions must have the same type
// 2- [Expert only] This is a simplified version of the code.
// In the real code, the reference is of stripped from G in the type deduction.
template<typename ... G>
gf_view<block_index, G>
make_block_gf_view(G && ... g);
// Make a view from a vector of gf
template<typename GF>
gf_view<block_index,GF>
make_block_gf_view_from_vector (std::vector<GF> V);
Domain & mesh
----------------
The domain is a discrete domain ...
Singularity
-------------
Factories
-------------
None.
Interpolation method
---------------------
None.
Data storage
---------------
Not exposed to user.
HDF5 storage convention
---------------------------
TO BE WRITTEN.
Iterators
-----------
TO BE COMPLETED.
Block gf have a natural iterator, e.g. ::
// if a BG is block function
for (auto & g : BG) ....
Examples
---------
.. compileblock::
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main() {
double beta =1;
// Make a block gf of 3 gf, which are empty (default constructed).
auto Bg0 = block_gf<imfreq> (3);
// make a few gf<imfreq> ...
auto g1 = gf<imfreq> ({beta, Fermion}, {2,2});
// ... and construct some block function out of them.
auto Bg1 = make_block_gf<imfreq> (3, g1);
auto Bg2 = make_block_gf<imfreq> ({g1,g1,g1});
auto Bg3 = make_block_gf<imfreq> ({"a","b","c"}, {g1,g1,g1});
// do something on all blocks
for (auto const &g : Bg1) {
std::cout<< g.mesh() << std::endl;
}
// multiply them by 1,2,3 ...
auto i = 1;
for (auto & g : Bg1) g = g * i++;
// a little save in an hdf5 file ?
H5::H5File file("test_block_gf.h5", H5F_ACC_TRUNC );
h5_write(file, "B3", Bg3);
}

63
doc/reference/c++/gf/gf_call.rst Normal file
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@ -0,0 +1,63 @@
.. highlight:: c
.. _gf_call:
Operator()
==================================
**Synopsis** ::
value_type const & operator()(mesh_t::domain_t::point_t) const (1)
view_type operator()() const (2)
ClefExpression operator()(ClefExpression) const (3)
The operator () is in charge of evaluating the Green function on its domain,
by any means (e.g. interpolation) that the specialization define.
For example, g(t) for a Green function in time would return some interpolation of
the value of g between the closest mesh point.
Hence, this operator is only const : it would make no sense to modify g(t).
(to modify the Green function, cf operator []).
However, the Clef automatic assignment method (cf...) *is* written
with the () operator, in order have a better syntax for multivariable function.
It would be more logical to use [], but a strange, old and extremely inconvenient limitation of C++
forbids to overload [] for multiple variables...
NB : This is valid for both the container (e.g. gf), and the view (e.g. gf_view).
.. _gf_element_access:
(1) Evaluation
---------------------------------
Evaluation at one point of the domain.
NB : Specialization may provide other overloads.
.. _gf_making_view:
(2) Building a view
---------------------------------
The special case (2) (no argument) returns a complete view of the object
(equivalent to view_type(* this)).
.. _gf_lazy:
(3) Interaction with clef expressions
-------------------------------------------------
* gf and gf_view can be used with the triqs::clef library

54
doc/reference/c++/gf/gf_constructors.rst Normal file
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@ -0,0 +1,54 @@
.. highlight:: c
.. _gf_constr:
Constructors
====================
Constructors of gf
---------------------------
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| Constructors | Comments |
+================================+===================================================================================================================+
| gf() | Empty gf |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| gf(gf const &) | Copy construction |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| gf(gf &&) | Move construction |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| gf(gf_view & g) | Make a clone of the view. |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| gf(gf_const_view & g) | Make a clone of the const view. |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| gf(mesh_t m, target_shape_t s) | Constructs a gf with mesh m and a target shape s. s depends on the specialization: it is the information needed |
| | to construct the gf, aside from the mesh itself : typically the size of the matrix for a matrix_valued gf. |
| | target_shape_t is described in the specialization section. section XXX). The function is initialized to 0 |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
| gf(mesh_t m, data_t dat, | *[Advanced]* Construct a gf from its elements (a mesh, a data array, a singularity, a symmetry, and an evaluator. |
| singularity_view_t const & si, | Normally should be reserved for lib purposes...(remove from the doc ?). |
| symmetry_t const & s, | |
| evaluator_t const & eval) | |
+--------------------------------+-------------------------------------------------------------------------------------------------------------------+
Examples
------------
There are more examples for each specializations in the corresponding pages.
.. compileblock::
#include <triqs/gfs.hpp>
using namespace triqs::gfs;
int main(){
auto beta = 10;
gf<imfreq> gf { {beta, Fermion}, {1,1}};
}

49
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@ -0,0 +1,49 @@
.. highlight:: c
.. _gf_data:
Data access
====================
mesh
------------
* **Synopsis**:
.. cpp:function:: mesh_t const & () const
Access to the mesh of the green function.
data
------------
* **Synopsis**:
.. cpp:function:: data_t const & () const
.. cpp:function:: data_t & ()
Access to the data array where the value of the gf is stored on the mesh points.
singularity
------------
* **Synopsis**:
.. cpp:function:: singularity_t const & () const
.. cpp:function:: singularity & ()
Access to the singularity type
symmetry
------------
* **Synopsis**:
.. cpp:function:: symmetry_t const & () const
Access to the symmetry type. Can not be modifed after construction. *(why ?)*.

46
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@ -5,27 +5,18 @@
gf<imfreq>
==========================================================
This is a specialisation of :ref:`gf_and_view` for imaginary Matsubara frequencies.
Domain & mesh
----------------
Singularity
-------------
:ref:`gf_tail`.
Factories
-------------
The factories are ::
make_gf(gf_mesh<imfreq,Opt> m, matrix_shape_t shape, local::tail_view t = local::tail(shape) )
make_gf(double beta, statistic_enum S, matrix_shape_t shape, size_t Nmax = 1025, local::tail_view t = local::tail(shape) )
Interpolation method
---------------------
@ -51,30 +42,25 @@ Examples
.. compileblock::
#include <triqs/gfs/imfreq.hpp>
using namespace triqs::gfs;
int main() {
double beta=1; // inverse temperature
size_t n_freq=5; // we will have 5 points including iw=0 and iw=beta
auto GF = make_gf<imfreq>(beta, Fermion, make_shape(1,1), n_freq);
};
An alternative declaration with an explicit construction of the underlying mesh:
.. compileblock::
#include <triqs/gfs/imfreq.hpp>
using namespace triqs::gfs;
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main(){
double beta=10;
int Nfreq =100;
auto GF = make_gf<imfreq>(gf_mesh<imfreq>{beta,Fermion,Nfreq}, make_shape(1,1), local::tail(1,1));
// or even simpler
auto GF2 = make_gf<imfreq>({beta,Fermion,Nfreq}, make_shape(1,1), local::tail(1,1));
// First give information to build the mesh, second to build the target
auto GF1 = gf<imfreq> { {beta,Fermion,Nfreq}, {1,1} };
// or a more verbose/explicit form ...
auto GF2 = gf<imfreq> { gf_mesh<imfreq>{beta,Fermion,Nfreq}, make_shape(1,1) };
// Filling the gf with something...
placeholder<0> wn_;
GF1(wn_) << 1/ (wn_ + 2);
// evaluation at n=3
std::cout << GF1(3) << " == "<< 1/ ( 1_j * std::acos(-1) / beta * (2*3+1) + 2) << std::endl;
// the high frequency expansion was automatically computed.
std::cout << GF1.singularity() << std::endl;
}

43
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@ -16,15 +16,6 @@ Singularity
:ref:`gf_tail`.
Factories
-------------
The factories are ::
make_gf(mesh<imfreq,Opt> m, local::tail_view t = local::tail({1,1}) )
make_gf(double beta, statistic_enum S, size_t Nmax = 1025, local::tail_view t = local::tail({1,1}) )
Interpolation method
---------------------
@ -50,29 +41,25 @@ Examples
.. compileblock::
#include <triqs/gfs/imfreq.hpp>
using namespace triqs::gfs;
int main() {
double beta=1; // inverse temperature
size_t n_freq=5; // we will have 5 points including iw=0 and iw=beta
auto GF = make_gf<imfreq,scalar_valued>(beta, Fermion, n_freq);
};
An alternative declaration with an explicit construction of the underlying mesh:
.. compileblock::
#include <triqs/gfs/imfreq.hpp>
using namespace triqs::gfs;
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main(){
double beta=10;
int Nfreq =100;
auto GF = make_gf<imfreq,scalar_valued>(gf_mesh<imfreq>{beta,Fermion,Nfreq});
// auto GF2 = make_gf<imfreq,scalar_valued>({beta,Fermion,Nfreq});
// First give information to build the mesh, second to build the target
auto GF1 = gf<imfreq,scalar_valued> { {beta,Fermion,Nfreq} };
// or a more verbose/explicit form ...
auto GF2 = gf<imfreq,scalar_valued> { gf_mesh<imfreq>{beta,Fermion,Nfreq} };
// Filling the gf with something...
placeholder<0> wn_;
GF1(wn_) << 1/ (wn_ + 2);
// evaluation at n=3
std::cout << GF1(3) << " == "<< 1/ ( 1_j * std::acos(-1) / beta * (2*3+1) + 2) << std::endl;
// the high frequency expansion was automatically computed.
std::cout << GF1.singularity() << std::endl;
}

46
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@ -10,31 +10,26 @@ This is a specialisation of :ref:`gf_and_view` for imaginary Matsubara time.
Domain & mesh
----------------
Singularity
-------------
Factories
-------------
Code ::
make_gf(MeshType && m, tqa::mini_vector<size_t,2> shape, local::tail_view const & t)
make_gf(double beta, statistic_enum S, tqa::mini_vector<size_t,2> shape, size_t Nmax=1025, mesh_kind mk= half_bins)
make_gf(double beta, statistic_enum S, tqa::mini_vector<size_t,2> shape, size_t Nmax, mesh_kind mk, local::tail_view const & t)
Interpolation method
---------------------
None.
Data storage
---------------
* `data_t` : 3d array (C ordered) of complex<double>.
* g.data()(i, range(), range()) is the value of g for the i-th point of the mesh.
HDF5 storage convention
---------------------------
h5 tag : `ImTime`
Examples
@ -42,16 +37,25 @@ Examples
.. compileblock::
#include <triqs/gfs/imtime.hpp>
using namespace triqs::gfs;
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main(){
double beta=10, a = 1;
int n_times=5;
// First give information to build the mesh, second to build the target
auto GF1 = gf<imtime> { {beta,Fermion,n_times}, {1,1} };
// or a more verbose/explicit form ...
auto GF2 = gf<imtime> { gf_mesh<imtime>{beta,Fermion,n_times}, make_shape(1,1) };
// Filling the gf with something...
placeholder<0> tau_;
//GF1(tau_) << exp ( - a * tau_) / (1 + exp(- beta * a));
// evaluation at n=3
std::cout << make_matrix(GF1(3)) << " == "<< exp ( - a * 3) / (1 + exp(- beta * a)) << std::endl;
}
int main() {
double beta=1; //inverse temperature
triqs::gfs::statistic_enum stat=triqs::gfs::Fermion;
size_t n_times=5;
auto shape = triqs::arrays::make_shape(1,1);
auto GF=make_gf<imtime>(beta, stat, shape, n_times);
};

97
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@ -0,0 +1,97 @@
.. highlight:: c
.. _gf_eval_curry:
Partial evaluation and Currying
================================
.. warning::
This part of the library is still in alpha, in development.
Multivariable Green function are be both partially evalued, and "curried".
Partial evaluation
--------------------------
**Purpose** :
Having a function (x,y) -> f(x,y), fix x = x0 in order to obtain a function of y only.
**Synopsis** ::
template<int ... pos, typename Opt, typename Target, bool B, bool IsConst, typename IT, typename ... Ms>
gf_view< sliced_domain_t<cartesian_product<Ms...>> ,Target, Opt, IsConst>
partial_eval(gf_impl< cartesian_product<Ms...>, Target,Opt,B,IsConst> const & g, IT index) {
Probably an example would help here ... :
.. compileblock::
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main(){
double beta =1, tmin=0, tmax=1.0;
int n_re_time=100, n_im_time=100;
using g_t_tau_s = gf<cartesian_product<retime,imtime>, scalar_valued>;
// a scalar valued function
auto g= g_t_tau_s { { {tmin, tmax, n_re_time}, {beta, Fermion, n_im_time}} };
// evaluation of the second variable to 3 : 3 is the **index** of the point !
auto g_sliced = partial_eval<1>(g(), 3);
// g_sliced is now a gf_view/gf_const_view<retime> seeing the value at the index 3
std::cout<< g_sliced<< std::endl;
}
Currying
-------------
**Purpose** :
Having a function (x,y) -> f(x,y), rewrite it as x-> y-> f(x,y)
**Synopsis** ::
template <int... pos, typename Target, typename Opt, bool IsConst, typename... Ms>
gf_view<cart_prod<triqs::tuple::filter_t<std::tuple<Ms...>, pos...>>,
lambda_valued<curry_polymorphic_lambda<gf_view<cartesian_product<Ms...>, Target, Opt,IsConst>, pos...>>, Opt, IsConst>
curry(gf_view<cartesian_product<Ms...>, Target, Opt, IsConst> g);
.. compileblock::
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main(){
double beta =1, wmin=0, wmax=1.0;
int n_re_freq=100, n_im_freq=100;
using g_w_wn_s = gf<cartesian_product<refreq,imfreq>, scalar_valued>;
// a scalar valued function
auto g= g_w_wn_s{ { {wmin, wmax, n_re_freq}, {beta, Fermion, n_im_freq}} };
// put expression in it
triqs::clef::placeholder<0> w_;
triqs::clef::placeholder<1> wn_;
g (w_,wn_)<<1/(wn_-1)/( w_ + 3_j );
// Currying by selecting the first variable, i.e. t -> tau -> g(t,tau)
auto g1 = curry<0>(g);
// Currying by selecting the second variable, i.e. tau -> t -> g(t,tau)
auto g2 = curry<1>(g);
//std::cout << g << g1[1]<< g2 [2] << std::endl;
std::cout<< g1[1][2] << g2 [2][1] << g [{1,2}] << std::endl;
}

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@ -1,36 +0,0 @@
.. highlight:: c
.. _gf_prod:
gf<cartesian_product<M...>, T>
===================================================
This is a specialisation of :ref:`gf_and_view` for many variables Green functions.
Domain & mesh
----------------
Singularity
-------------
Factories
-------------
Interpolation method
---------------------
Data storage
---------------
HDF5 storage convention
---------------------------
Examples
---------

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@ -0,0 +1,89 @@
.. highlight:: c
.. _gf_product:
Green functions on cartesian product domains
===================================================
.. warning::
This part of the library is still in alpha, in development.
Domain & mesh
----------------
The domain is a cartesian product of domains.
The mesh is a cartesian product of the corresponding meshes.
Singularity
-------------
None.
Interpolation method
---------------------
A multidimensional linear interpolation is automatically
built from the linear interpolation of the domains.
Data storage
---------------
Like single variables gf, the first index of the array is a flattening
of the indices of the composite mesh.
HDF5 storage convention
---------------------------
For convenience, in hdf5 files, the arrays has higher dimension,
so that the first indices are *not* flatten. EXPLAIN.
Examples
---------
.. compileblock::
#include <triqs/gfs.hpp>
using namespace triqs::gfs; using triqs::clef::placeholder;
int main(){
double beta =1, tmin=0, tmax=1.0;
int n_re_time=100, n_im_time=100;
using g_t_tau_s = gf<cartesian_product<retime,imtime>, scalar_valued>;
using g_t_tau_m = gf<cartesian_product<retime,imtime>, matrix_valued>;
using g_t_tau_t = gf<cartesian_product<retime,imtime>, tensor_valued<3>>;
// a scalar valued function
auto m1 = gf_mesh<retime>{tmin, tmax, n_re_time};
auto m2 = gf_mesh<imtime>{beta, Fermion, n_im_time};
auto g= g_t_tau_s { {m1,m2} };
// a more compact notation
auto g2= g_t_tau_s { { {tmin, tmax, n_re_time}, {beta, Fermion, n_im_time}} };
// a matrix_valued_version
auto gm= g_t_tau_m { { {tmin, tmax, n_re_time}, {beta, Fermion, n_im_time}} , {2,2} };
// a tensor_valued_version
auto gt= g_t_tau_t { { {tmin, tmax, n_re_time}, {beta, Fermion, n_im_time}} , {2,2,2} };
// a little save in an hdf5 file ?
H5::H5File file("test_product_gf.h5", H5F_ACC_TRUNC );
h5_write(file, "g", g);
}
See also :
.. toctree::
:maxdepth: 1
gf_part_eval_curry

36
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@ -14,47 +14,37 @@ Domain & mesh
Singularity
-------------
Factories
-------------
code ::
make_gf(MeshType && m, tqa::mini_vector<size_t,2> shape, local::tail_view const & t)
make_gf(double wmin, double wmax, size_t n_freq, tqa::mini_vector<size_t,2> shape)
make_gf(double wmin, double wmax, size_t n_freq, tqa::mini_vector<size_t,2> shape, mesh_kind mk)
Interpolation method
---------------------
Linear interpolation on the mesh.
Data storage
---------------
* `data_t` : 3d array (C ordered) of complex<double>.
* g.data()(i, range(), range()) is the value of g for the i-th point of the mesh.
HDF5 storage convention
---------------------------
h5 tag : `ReFreq`
Examples
---------
.. compileblock::
#include <triqs/gfs/retime.hpp>
#include <triqs/gfs/refreq.hpp>
using namespace triqs::gfs;
int main() {
double tmin=0;
double tmax=10;
//we will have 5 points
size_t n_times=5;
//we want a Green function whose values are complex numbers
auto shape = triqs::arrays::make_shape(1,1);
// the type of GF is triqs::gfs::gf<triqs::gfs::retime>
auto GF=make_gf<retime>(tmin, tmax, n_times, shape);
double wmin=0, wmax=10; // Frequencies interval
auto n_freq=100; // Number of points
// We want a 2x2 matrix valued function on this mesh...
auto g = gf<refreq> { {wmin, wmax, n_freq}, {2,2} };
};

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@ -14,44 +14,36 @@ Domain & mesh
Singularity
-------------
Factories
-------------
Code ::
make_gf(double tmin, double tmax, size_t n_points, tqa::mini_vector<size_t,2> shape)
make_gf(double tmin, double tmax, size_t n_points, tqa::mini_vector<size_t,2> shape, mesh_kind mk)
Interpolation method
---------------------
Linear interpolation on the mesh.
Data storage
---------------
* `data_t` : 3d array (C ordered) of complex<double>.
* g.data()(i, range(), range()) is the value of g for the i-th point of the mesh.
HDF5 storage convention
---------------------------
h5 tag : `ReTime`
Examples
---------
.. compileblock::
#include <triqs/gfs/refreq.hpp>
#include <triqs/gfs/retime.hpp>
using namespace triqs::gfs;
int main() {
double wmin=0;
double wmax=10;
size_t n_freq=5;
//we want a Green function whose values are 2*2 matrices of complex numbers
auto shape = triqs::arrays::make_shape(2,2);
auto GF=make_gf<refreq>(wmin, wmax, n_freq, shape);
double tmin=0, tmax=10; // the time interval
auto n_times=100; // we will have 100 points
//we want a 2x2 matrix-valued Green function
auto g=gf<retime>{ {tmin, tmax, n_times} , {2,2} };
};

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@ -0,0 +1,63 @@
.. highlight:: c
.. _gf_subscript:
Operator []
==================================
**Synopsis** ::
value_type const & operator[](mesh_t::index_t const &) const (1a)
value_type & operator[](mesh_t::index_t const &) (1b)
value_type const & operator[](closest_mesh_pt_t const &) const (2a)
value_type & operator[](closest_mesh_pt_t const &) (2b)
ClefExpression operator[](ClefExpression expr) const (3)
The operator [] is in charge of accessing the data of the Green function
on the mesh. This is therefore a way to modify the Green function.
NB : This is valid for both the container (e.g. gf), and the view (e.g. gf_view).
.. _gf_subscript_index:
(1) Use the linear index of the mesh
-----------------------------------------
.. _gf_subscript_closest:
..
(2) Find the closest mesh point from a domain point
---------------------------------------------------------
* May or may not be provided by the specialisation. Cf specialization.
* This is normally used with the helper function::
closest_mesh_point_t closest_mesh_point(Anything x)
closest_mesh_point_t is just a little "vehicle" that can contain anything (by copy or ref ???),
and carry it through the [].
* Usage ::
g [ closest_mesh_point(x) ] += y;
.. _gf_subscript_lazy:
(3) Interaction with clef expressions
-------------------------------------------------
Like (), [] can be called with a ClefExpression.

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@ -3,73 +3,4 @@
Implementation notes
===========================
This part describes how to create a new green function....
.. _Concept_HasConstIterator:
Mesh
-------------------------------------------------
* **Purpose** : An object which has a const_iterator and corresponding functions.
* **Refines** :
* **Definition** :
+--------------------------------------------------------------+-------------------------------------------------------------------------------+
| Elements | Comment |
+==============================================================+===============================================================================+
| mesh_pt_generator<mesh_t> const_iterator | A generator of all the mesh points. |
+--------------------------------------------------------------+-------------------------------------------------------------------------------+
| const_iterator begin()/end() const | Standard access to iterator on the mesh |
| const_iterator cbegin()/cend() const | Standard access to iterator on the mesh |
+--------------------------------------------------------------+-------------------------------------------------------------------------------+
Doxygen documentation
-------------------------------------------------
The :doxy:`full C++ documentation<triqs::gf::gf>` is available here.
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| Elements | Comment |
+====================================================================================+===============================================================================+
| struct tag {}; | A tag for the gf |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| mesh_t | Mesh for the gf, modeling Mesh concept |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| storage_t | The type of the storage of the data (array, vector, etc....) |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| singularity_t | Type of object storing the singularities of the gf. It is used e.g. in the |
| | Fourier transformation, density computation, etc... For a simple g(omega), |
| | g(t), it is typically a high frequency tail. For a more complex function |
| | g(nu,nu'), it can be different. |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| symmetry_t | Type of the object storing the symmetry property of the Green function. It is |
| | *nothing* by default. This type must be a value (DefaultConstructible, |
| | CopyConstructible, Assignable) |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| target_indices_t | Type of the indices of the gf, typically array<std::string,arity> |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| static const int arity | Number of variable authorized in calling the gf (just for compile time check |
| | and nice error message, it is not really necessary) |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| struct evaluator { auto operator()( mesh_t const &, DATA_t const &, S_t const &, | All the permitted const call of the gf ! (DATA_t defined below) with the |
| Args&&... args) .... as many overload as necessary } | parenthesis operator The gf<...> function create such a struct, so it can |
| | hold some data ... |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
| static std::string h5_name() | Name for hdf5 naming (attribute of the tree in which the gf is stored). |
+------------------------------------------------------------------------------------+-------------------------------------------------------------------------------+
* **Values vs Views**
target_t, singularity_t, indices_t are expected to be *values*.
The corresponding views, i.e., target_view_t, singularity_view_t, indices_view_t will be deduced from the value type, and
replaced by the value_type if no view is available.
* S_t is singularity_t or its corresponding view type (if it exists).

27
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@ -5,15 +5,13 @@
Introduction
=================
The TRIQS library provides a generic container `gf` and its view `gf_view`, to store and manipulate
various Green functions.
Several specific green functions are implemented :
The `gf` container and its views `gf_view` and `gf_const_view` allows to store and manipulate
various Green functions, on various meshes, e.g. :
* Matsubara frequency(ies),
* Matsubara time(s),
* real time(s),
* real frequency(ies),
* Matsubara time(s),
* Matsubara frequency(ies),
* Legendre representation.
* Block of other green functions.
* Cartesian product of green functions.
@ -21,23 +19,8 @@ Several specific green functions are implemented :
Various free functions are also provided to handle transformations between various representation of a Green function,
such as Fourier transforms.
More generally, the variable is a point of a ``domain``
The value of the Green function on a point of the domain can be a scalar, a matrix or whatever you want (this type is called type ``target_t``).
You can group several green functions into *blocks* (for example, one block per orbital, or per wave vector...).
Fourier transforms are implemented for these Green functions:
real time <-> real frequency
Matsubara time <-> Matsubara frequency
This section is organized as follows :
* the concepts related to Green functions, their domain, their representation on a grid.
* the container `gf` and its view `gf_view`, which represent various Green functions.
TO BE WRITTEN