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https://github.com/triqs/dft_tools
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232 lines
8.0 KiB
ReStructuredText
232 lines
8.0 KiB
ReStructuredText
.. index::
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single: Green's functions; full Green's function
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module: gf.local
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.. _fullgreen:
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The complete Green's function (BlockGf)
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=======================================
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As mentioned in the introduction, due to the symmetry, a local Green's function usually
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has a block structure.
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We refer to this object as the `full` or `complete` Green's function, in contrast to
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the blocks it is made of.
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Most properties of this object can be remembered by the simple sentence:
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`A full Green's function is an ordered dictionary name -> block, or equivalently a list of tuples (name, block).`
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The blocks can be any of the matrix-valued Green's functions described :ref:`above<blockgreen>`.
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The role of this object is to gather them, and simplify the code writing
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by factorizing some simple operations.
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A little example
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--------------------
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To start with an example, imagine that the problem
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that we consider could involve 5 d-bands of a solid that, for symmetry reasons,
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are separated into 2 eg and 3 t2g bands. We therefore first construct the 2
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corresponding block Green's functions (in Matsubara frequencies for example)
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and group these blocks into a full Green's function `G` with::
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from pytriqs.gf.local import *
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g1 = GfImFreq(indices = ['eg1','eg2'], beta = 50, n_points = 1000, name = "egBlock")
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g2 = GfImFreq(indices = ['t2g1','t2g2','t2g3'], beta = 50, n_points = 1000, name = "t2gBlock")
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G = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = False)
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where:
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* `NameList` is the ordered list of the names of the blocks.
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* `BlockList` is the corresponding list of block Green's function.
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* `Copy` lets you specify if the blocks of the full Green's function are **copies** of the blocks given in
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* `BlockList` of if they are **views** of these blocks, see :ref:`below<fullgreencopypolicy>`
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These names will be used when we try to access a particular block, for example ::
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>>> G
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Green's Function composed of 2 blocks at inverse temperature Beta = 50.0:
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GfImFreq eg : Beta = 50.000; IndicesL = ['eg1', 'eg2'], IndicesR = ['eg1', 'eg2']
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GfImFreq t2g : Beta = 50.000; IndicesL = ['t2g1', 't2g2', 't2g3'], IndicesR = ['t2g1', 't2g2', 't2g3']
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>>> G['eg']
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GfImFreq eg : Beta = 50.000; IndicesL = ['eg1', 'eg2'], IndicesR = ['eg1', 'eg2']
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Reference
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----------------
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.. autoclass:: pytriqs.gf.local.BlockGf
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:members: copy, copy_from
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Operations
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---------------
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The full Green's functions support various simple operations, that are simply done block by block.
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.. note::
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All these operations compute the array of data, but also, if present in the object, the high frequency expansion tail automatically.
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* compound operators, `+=`, `-=`, `*=`, `\=` : RHS can be a Green's function of the same type or an expression
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* arithmetic operations : `+`, `-`, `*`, `/`, e.g. ::
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G = G1 + 2*G2
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* inversion, e.g. ::
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inv = inverse(g)
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g2=inverse(inverse( g ) - sigma) # this is a Dyson equation
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Block access
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----------------
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Blocks can be accessed like in a `dict` :
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These names will be used when we try to access a particular block, for example ::
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G['eg']
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The generic way to access a Green's function element :math:`G^a_{i j}` is therefore ::
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G[a][i,j]
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Iterator
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--------------------
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One can iterate on the blocks ::
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for name, g in G:
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do_something()
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In the example above ::
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>>> for name, g in G:
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... print name, g
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eg GfImFreq eg : Beta = 50.000; IndicesL = ['eg1', 'eg2'], IndicesR = ['eg1', 'eg2']
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t2g GfImFreq t2g : Beta = 50.000; IndicesL = ['t2g1', 't2g2', 't2g3'], IndicesR = ['t2g1', 't2g2', 't2g3']
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As a result ::
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BlockGf( name_block_generator= G, copy=False)
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generates a new Green's function `G`, viewing the same blocks.
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More interestingly ::
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BlockGf( name_block_generator= [ (index,g) for (index,g) in G if Test(index), copy=False)]
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makes a partial view of some of the blocks selected by the `Test` condition.
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.. warning::
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The order in which the blocks appear is guaranteed to be the same as in the constructor.
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This is why the Green's function is similar to an **ordered** dictionary, not a simple dict.
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View or copies ?
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---------------------
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.. _fullgreencopypolicy:
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The Green's function is to be thought like a dict, hence accessing the
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block returns references. When constructing the Green's function BlockGf,
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the parameter `Copy` tells whether a copy of the block must be made before
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putting them in the Green function or not.
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.. note::
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This is the standard behaviour in python for a list of a dict.
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Example:
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* If you define a Green's function with::
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G = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = False)
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.. note::
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Copy is optional, False is the default value. We keep it here for clarity.
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The ``Copy = False`` implies that the blocks of ``G`` are *references* ``g1`` and ``g2``.
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So, if you modify ``g1``, say by putting it to zero with ``g1.zero()``, then the
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first block of G will also be put to zero. Similarly, imagine you define two
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Green's functions like this::
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G1 = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = False)
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G2 = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = False)
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Here G1 and G2 are exactly the same object, because they both have blocks
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which are views of ``g1`` and ``g2``.
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* Instead, if you write::
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G = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = True)
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The ``Copy = True`` ensures that the blocks of G are new copies of ``g1``
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and ``g2``. If you then modify ``g1`` it will not have any effect on G.
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Clearly if you define::
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G1 = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = True)
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G2 = BlockGf(name_list = ('eg','t2g'), block_list = (g1,g2), make_copies = True)
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Here ``G1`` and ``G2`` are different objects, both having made copies
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of ``g1`` and ``g2`` for their blocks.
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An equivalent writing is ::
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G1 = BlockGf(name_list = ('eg','t2g'), block_list = (g1.copy(),g2.copy()))
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G2 = BlockGf(name_list = ('eg','t2g'), block_list = (g1.copy(),g2.copy()))
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shelve / pickle
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---------------------
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Green's functions are `pickable`, i.e. they support the standard python serialization techniques.
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* It can be used with the `shelve <http://docs.python.org/library/shelve.html>`_ and `pickle <http://docs.python.org/library/pickle.html>`_ module::
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import shelve
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s = shelve.open('myfile','w')
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s['G'] = G # G is stored in the file.
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* It can be sent/broadcasted/reduced over mpi ::
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from pytriqs.utility import MPI
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mpi.send (G, destination)
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.. warning::
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Shelve is not a portable format, it may change from python version to another (and it does).
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For portability, we recommend using the HDF5 interface for storing data on disks.
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HDF5
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--------
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BlockGf are hdf-compatible with the following HDF5 data scheme
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The BlockGf(TRIQS_HDF5_data_scheme = "BlockGf") is decomposed in the following objects :
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========================= =========================== ===========================================================================
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Name Type Meaning
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========================= =========================== ===========================================================================
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__BlockIndicesList string The python repr of the list of blocks, e.g. ('up', 'down')
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__Name string Name of the Green's function block
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__Note string Note
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For each block name type of the block The Block Green's function
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========================= =========================== ===========================================================================
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Example::
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/Gtau Group
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/Gtau/__BlockIndicesList Dataset {SCALAR}
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/Gtau/__Name Dataset {SCALAR}
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/Gtau/__Note Dataset {SCALAR}
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/Gtau/down Group
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/Gtau/down/Data Dataset {1, 1, 1000}
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/Gtau/down/ ...
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...
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/Gtau/up Group
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/Gtau/up/Data Dataset {1, 1, 1000}
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/Gtau/up/ ...
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