:mod:`memote.support.matrix`
============================

.. py:module:: memote.support.matrix

.. autoapi-nested-parse::

   Supporting functions checking the matrix condition of the model object.

   ..
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Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   memote.support.matrix.absolute_extreme_coefficient_ratio
   memote.support.matrix.number_independent_conservation_relations
   memote.support.matrix.matrix_rank
   memote.support.matrix.degrees_of_freedom


.. data:: LOGGER
   

   

.. function:: absolute_extreme_coefficient_ratio(model)

   Return the maximum and minimum absolute, non-zero coefficients.


   :Parameters:

       **model** : cobra.Model
           The metabolic model under investigation.














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.. function:: number_independent_conservation_relations(model)

   Return the number of conserved metabolite pools.

   This number is given by the left null space of the stoichiometric matrix.

   :Parameters:

       **model** : cobra.Model
           The metabolic model under investigation.














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.. function:: matrix_rank(model)

   Return the rank of the model's stoichiometric matrix.


   :Parameters:

       **model** : cobra.Model
           The metabolic model under investigation.














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.. function:: degrees_of_freedom(model)

   Return the degrees of freedom, i.e., number of "free variables".


   :Parameters:

       **model** : cobra.Model
           The metabolic model under investigation.









   .. rubric:: Notes

   This specifically refers to the dimensionality of the (right) null space
   of the stoichiometric matrix, as dim(Null(S)) corresponds directly to the
   number of free variables in the system [R44cca40782ba-1]_. The formula used calculates
   this using the rank-nullity theorem [R44cca40782ba-2]_.

   .. rubric:: References

   .. [R44cca40782ba-1] Fukuda, K. & Terlaky, T. Criss-cross methods: A fresh view on
      pivot algorithms. Mathematical Programming 79, 369-395 (1997).

   .. [R44cca40782ba-2] Alama, J. The Rank+Nullity Theorem. Formalized Mathematics 15,
      (2007).

   .. only:: latex

      [R44cca40782ba-1]_, [R44cca40782ba-2]_




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