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.. include:: ../../global.inc
.. include:: manual_chapter_numbers.inc
.. index::
pair: combinatorics; Tutorial
.. _new_manual.combinatorics:
##################################################################################################################################################################################################################################################
|new_manual.combinatorics.chapter_num|: :ref:`@combinations<decorators.combinations>`, :ref:`@permutations<decorators.permutations>` and all versus all :ref:`@product<decorators.product>`
##################################################################################################################################################################################################################################################
.. seealso::
* :ref:`Manual Table of Contents <new_manual.table_of_contents>`
* :ref:`@combinations_with_replacement <decorators.combinations_with_replacement>`
* :ref:`@combinations <decorators.combinations>`
* :ref:`@permutations <decorators.permutations>`
* :ref:`@product <decorators.product>`
* :ref:`formatter() <decorators.formatter>`
.. note::
Remember to look at the example code:
* :ref:`new_manual.combinatorics.code`
**************************************
Overview
**************************************
A surprising number of computational problems involve some sort of all versus all calculations.
Previously, this would have required all the parameters to be supplied using a custom function
on the fly with :ref:`@files<decorators.files_on_the_fly>`.
From version 2.4, *Ruffus* supports :ref:`@combinations_with_replacement <decorators.combinations_with_replacement>`,
:ref:`@combinations <decorators.combinations>`, :ref:`@permutations <decorators.permutations>`,
:ref:`@product <decorators.product>`.
These provide as far as possible all the functionality of the four combinatorics iterators
from the standard python `itertools <http://docs.python.org/2/library/itertools.html>`__
functions of the same name.
***************************************************************************
Generating output with :ref:`formatter()<decorators.formatter>`
***************************************************************************
String replacement always takes place via :ref:`formatter()<decorators.formatter>`. Unfortunately,
the other *Ruffus* workhorses of :ref:`regex()<decorators.regex>` and :ref:`suffix()<decorators.suffix>`
do not have sufficient syntactic flexibility.
Each combinatorics decorator deals with multiple sets of inputs whether this might be:
* a self-self comparison (such as :ref:`@combinations_with_replacement <decorators.combinations_with_replacement>`,
:ref:`@combinations <decorators.combinations>`, :ref:`@permutations <decorators.permutations>`) or,
* a self-other comparison (:ref:`@product <decorators.product>`)
The replacement strings thus require an extra level of indirection to refer to
parsed components.
#. The first level refers to which *set* of inputs.
#. The second level refers to which input file in any particular *set* of inputs.
For example, if the *inputs* are **[A1,A2],[B1,B2],[C1,C2] vs [P1,P2],[Q1,Q2],[R1,R2] vs [X1,X2],[Y1,Y2],[Z1,Z2]**,
then ``'{basename[2][0]}'`` is the `basename <http://docs.python.org/2/library/os.path.html#os.path.basename>`__ for
* the third set of inputs (**X,Y,Z**) and
* the first file name string in each **Input** of that set (**X1, Y1, Z1**)
.. _new_manual.product:
***************************************************************************
All vs all comparisons with :ref:`@product <decorators.product>`
***************************************************************************
:ref:`@product <decorators.product>` generates the Cartesian **product** between sets of input files,
i.e. all vs all comparisons.
The effect is analogous to a nested for loop.
:ref:`@product <decorators.product>` can be useful, for example, in bioinformatics for finding
the corresponding genes (orthologues) for a set of proteins in multiple species.
.. code-block:: pycon
:emphasize-lines: 2
>>> from itertools import product
>>> # product('ABC', 'XYZ') --> AX AY AZ BX BY BZ CX CY CZ
>>> [ "".join(a) for a in product('ABC', 'XYZ')]
['AX', 'AY', 'AZ', 'BX', 'BY', 'BZ', 'CX', 'CY', 'CZ']
This example Calculates the **@product** of **A,B** and **P,Q** and **X,Y** files
.. code-block:: python
:emphasize-lines: 4,17,19,22,25,27,28,29,30,32,34,35,36
from ruffus import *
from ruffus.combinatorics import *
# Three sets of initial files
@originate([ 'a.start', 'b.start'])
def create_initial_files_ab(output_file):
with open(output_file, "w") as oo: pass
@originate([ 'p.start', 'q.start'])
def create_initial_files_pq(output_file):
with open(output_file, "w") as oo: pass
@originate([ ['x.1_start', 'x.2_start'],
['y.1_start', 'y.2_start'] ])
def create_initial_files_xy(output_file):
with open(output_file, "w") as oo: pass
# @product
@product( create_initial_files_ab, # Input
formatter("(.start)$"), # match input file set # 1
create_initial_files_pq, # Input
formatter("(.start)$"), # match input file set # 2
create_initial_files_xy, # Input
formatter("(.start)$"), # match input file set # 3
"{path[0][0]}/" # Output Replacement string
"{basename[0][0]}_vs_" #
"{basename[1][0]}_vs_" #
"{basename[2][0]}.product", #
"{path[0][0]}", # Extra parameter: path for 1st set of files, 1st file name
["{basename[0][0]}", # Extra parameter: basename for 1st set of files, 1st file name
"{basename[1][0]}", # 2nd
"{basename[2][0]}", # 3rd
])
def product_task(input_file, output_parameter, shared_path, basenames):
print "# basenames = ", " ".join(basenames)
print "input_parameter = ", input_file
print "output_parameter = ", output_parameter, "\n"
#
# Run
#
pipeline_run(verbose=0)
This results in:
.. code-block:: pycon
:emphasize-lines: 2,6,10,14,18,22,26,30
>>> pipeline_run(verbose=0)
# basenames = a p x
input_parameter = ('a.start', 'p.start', 'x.start')
output_parameter = /home/lg/temp/a_vs_p_vs_x.product
# basenames = a p y
input_parameter = ('a.start', 'p.start', 'y.start')
output_parameter = /home/lg/temp/a_vs_p_vs_y.product
# basenames = a q x
input_parameter = ('a.start', 'q.start', 'x.start')
output_parameter = /home/lg/temp/a_vs_q_vs_x.product
# basenames = a q y
input_parameter = ('a.start', 'q.start', 'y.start')
output_parameter = /home/lg/temp/a_vs_q_vs_y.product
# basenames = b p x
input_parameter = ('b.start', 'p.start', 'x.start')
output_parameter = /home/lg/temp/b_vs_p_vs_x.product
# basenames = b p y
input_parameter = ('b.start', 'p.start', 'y.start')
output_parameter = /home/lg/temp/b_vs_p_vs_y.product
# basenames = b q x
input_parameter = ('b.start', 'q.start', 'x.start')
output_parameter = /home/lg/temp/b_vs_q_vs_x.product
# basenames = b q y
input_parameter = ('b.start', 'q.start', 'y.start')
output_parameter = /home/lg/temp/b_vs_q_vs_y.product
.. _new_manual.permutations:
******************************************************************************************************************************************************
Permute all k-tuple orderings of inputs without repeats using :ref:`@permutations <decorators.permutations>`
******************************************************************************************************************************************************
Generates the **permutations** for all the elements of a set of **Input** (e.g. **A B C D**),
* r-length tuples of *input* elements
* excluding repeated elements (**A A**)
* and order of the tuples is significant (both **A B** and **B A**).
.. code-block:: pycon
:emphasize-lines: 2
>>> from itertools import permutations
>>> # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
>>> [ "".join(a) for a in permutations("ABCD", 2)]
['AB', 'AC', 'AD', 'BA', 'BC', 'BD', 'CA', 'CB', 'CD', 'DA', 'DB', 'DC']
This following example calculates the **@permutations** of **A,B,C,D** files
.. code-block:: python
:emphasize-lines: 13,17,20,25,28-30
from ruffus import *
from ruffus.combinatorics import *
# initial file pairs
@originate([ ['A.1_start', 'A.2_start'],
['B.1_start', 'B.2_start'],
['C.1_start', 'C.2_start'],
['D.1_start', 'D.2_start']])
def create_initial_files_ABCD(output_files):
for output_file in output_files:
with open(output_file, "w") as oo: pass
# @permutations
@permutations(create_initial_files_ABCD, # Input
formatter(), # match input files
# tuple of 2 at a time
2,
# Output Replacement string
"{path[0][0]}/"
"{basename[0][1]}_vs_"
"{basename[1][1]}.permutations",
# Extra parameter: path for 1st set of files, 1st file name
"{path[0][0]}",
# Extra parameter
["{basename[0][0]}", # basename for 1st set of files, 1st file name
"{basename[1][0]}", # 2nd
])
def permutations_task(input_file, output_parameter, shared_path, basenames):
print " - ".join(basenames)
#
# Run
#
pipeline_run(verbose=0)
This results in:
.. code-block:: pycon
>>> pipeline_run(verbose=0)
A - B
A - C
A - D
B - A
B - C
B - D
C - A
C - B
C - D
D - A
D - B
D - C
.. _new_manual.combinations:
********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************
Select unordered k-tuples within inputs excluding repeated elements using :ref:`@combinations <decorators.combinations>`
********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************
Generates the **combinations** for all the elements of a set of **Input** (e.g. **A B C D**),
* r-length tuples of *input* elements
* without repeated elements (**A A**)
* where order of the tuples is irrelevant (either **A B** or **B A**, not both).
:ref:`@combinations <decorators.combinations>` can be useful, for example, in calculating a transition probability matrix
for a set of states. The diagonals are meaningless "self-self" transitions which are excluded.
.. code-block:: pycon
:emphasize-lines: 2
>>> from itertools import combinations
>>> # combinations('ABCD', 3) --> ABC ABD ACD BCD
>>> [ "".join(a) for a in combinations("ABCD", 3)]
['ABC', 'ABD', 'ACD', 'BCD']
This example calculates the **@combinations** of **A,B,C,D** files
.. code-block:: python
:emphasize-lines: 13,17,20,25,28-30
from ruffus import *
from ruffus.combinatorics import *
# initial file pairs
@originate([ ['A.1_start', 'A.2_start'],
['B.1_start', 'B.2_start'],
['C.1_start', 'C.2_start'],
['D.1_start', 'D.2_start']])
def create_initial_files_ABCD(output_files):
for output_file in output_files:
with open(output_file, "w") as oo: pass
# @combinations
@combinations(create_initial_files_ABCD, # Input
formatter(), # match input files
# tuple of 3 at a time
3,
# Output Replacement string
"{path[0][0]}/"
"{basename[0][1]}_vs_"
"{basename[1][1]}_vs_"
"{basename[2][1]}.combinations",
# Extra parameter: path for 1st set of files, 1st file name
"{path[0][0]}",
# Extra parameter
["{basename[0][0]}", # basename for 1st set of files, 1st file name
"{basename[1][0]}", # 2nd
"{basename[2][0]}", # 3rd
])
def combinations_task(input_file, output_parameter, shared_path, basenames):
print " - ".join(basenames)
#
# Run
#
pipeline_run(verbose=0)
This results in:
.. code-block:: pycon
>>> pipeline_run(verbose=0)
A - B - C
A - B - D
A - C - D
B - C - D
.. _new_manual.combinations_with_replacement:
********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************
Select unordered k-tuples within inputs *including* repeated elements with :ref:`@combinations_with_replacement <decorators.combinations_with_replacement>`
********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************
Generates the **combinations_with_replacement** for all the elements of a set of **Input** (e.g. **A B C D**),
* r-length tuples of *input* elements
* including repeated elements (**A A**)
* where order of the tuples is irrelevant (either **A B** or **B A**, not both).
:ref:`@combinations_with_replacement <decorators.combinations_with_replacement>` can be useful,
for example, in bioinformatics for finding evolutionary relationships between genetic elements such as proteins
and genes. Self-self comparisons can be used a baseline for scaling similarity scores.
.. code-block:: pycon
:emphasize-lines: 2
>>> from itertools import combinations_with_replacement
>>> # combinations_with_replacement('ABCD', 2) --> AA AB AC AD BB BC BD CC CD DD
>>> [ "".join(a) for a in combinations_with_replacement('ABCD', 2)]
['AA', 'AB', 'AC', 'AD', 'BB', 'BC', 'BD', 'CC', 'CD', 'DD']
This example calculates the **@combinations_with_replacement** of **A,B,C,D** files
.. code-block:: python
:emphasize-lines: 13,17,20,25,28-30
from ruffus import *
from ruffus.combinatorics import *
# initial file pairs
@originate([ ['A.1_start', 'A.2_start'],
['B.1_start', 'B.2_start'],
['C.1_start', 'C.2_start'],
['D.1_start', 'D.2_start']])
def create_initial_files_ABCD(output_files):
for output_file in output_files:
with open(output_file, "w") as oo: pass
# @combinations_with_replacement
@combinations_with_replacement(create_initial_files_ABCD, # Input
formatter(), # match input files
# tuple of 2 at a time
2,
# Output Replacement string
"{path[0][0]}/"
"{basename[0][1]}_vs_"
"{basename[1][1]}.combinations_with_replacement",
# Extra parameter: path for 1st set of files, 1st file name
"{path[0][0]}",
# Extra parameter
["{basename[0][0]}", # basename for 1st set of files, 1st file name
"{basename[1][0]}", # 2rd
])
def combinations_with_replacement_task(input_file, output_parameter, shared_path, basenames):
print " - ".join(basenames)
#
# Run
#
pipeline_run(verbose=0)
This results in:
.. code-block:: pycon
>>> pipeline_run(verbose=0)
A - A
A - B
A - C
A - D
B - B
B - C
B - D
C - C
C - D
D - D
|
