.. _matrix_aggregating_methods:

Matrix aggregating methods
==========================

SpAbs
-----
.. math::
    {\rm SpAbs} = \sum_{i = 1}^N \left| \lambda_i \right|

where :math:`\lambda_i` is :math:`i`-th eigenvalue.

SpMax
-----
.. math::
    {\rm SpMax} = \max_{i = 1}^N \lambda_i

SpDiam
------
.. math::
    {\rm SpDiam} = {\rm SpMax} - {\rm SpMin}

SpAD
----
.. math::
    {\rm SpAD} = \sum_{i = 1}^N \left| \lambda_i - \bar{\lambda} \right|

SpMAD
-----
.. math::
    {\rm SpMAD} = \frac{\rm SpAD}{A}

where :math:`A` is number of atoms.

LogEE
-----
.. math::
    {\rm LogEE} = \log(\sum_{i = 1}^N \exp(\lambda_i))

SM1
---
.. math::
    {\rm SM1} = \sum_{i = 1}^N \lambda_i

VE1
---
.. math::
    {\rm VE1} = \sum_{i = 1}^N \left| \ell_i \right|

where :math:`\ell_i` is eigenvector elements corresponding to leading eigenvalue.

VE2
---
.. math::
    {\rm VE2} = \frac{\rm VE1}{A}

VE3
---
.. math::
    {\rm VE3} = \log(\frac{A}{10} \cdot {\rm VE1})

NaN when :math:`{\rm VE1} = 0`.

VR1
---
.. math::
    {\rm VR1} = \sum_{(i, j) \in {\rm bonds}} \left( \ell_i \cdot \ell_j \right)^{-1/2}

VR2
---
.. math::
    {\rm VR2} = \frac{\rm VR1}{A}

VR3
---
.. math::
    {\rm VR3} = \log(\frac{A}{10} \cdot {\rm VR1})

NaN when :math:`{\rm VR1} = 0`.
