Matrix aggregating methods

SpAbs

\[{\rm SpAbs} = \sum_{i = 1}^N \left| \lambda_i \right|\]

where \(\lambda_i\) is \(i\)-th eigenvalue.

SpMax

\[{\rm SpMax} = \max_{i = 1}^N \lambda_i\]

SpDiam

\[{\rm SpDiam} = {\rm SpMax} - {\rm SpMin}\]

SpAD

\[{\rm SpAD} = \sum_{i = 1}^N \left| \lambda_i - \bar{\lambda} \right|\]

SpMAD

\[{\rm SpMAD} = \frac{\rm SpAD}{A}\]

where \(A\) is number of atoms.

LogEE

\[{\rm LogEE} = \log(\sum_{i = 1}^N \exp(\lambda_i))\]

SM1

\[{\rm SM1} = \sum_{i = 1}^N \lambda_i\]

VE1

\[{\rm VE1} = \sum_{i = 1}^N \left| \ell_i \right|\]

where \(\ell_i\) is eigenvector elements corresponding to leading eigenvalue.

VE2

\[{\rm VE2} = \frac{\rm VE1}{A}\]

VE3

\[{\rm VE3} = \log(\frac{A}{10} \cdot {\rm VE1})\]

NaN when \({\rm VE1} = 0\).

VR1

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

VR2

\[{\rm VR2} = \frac{\rm VR1}{A}\]

VR3

\[{\rm VR3} = \log(\frac{A}{10} \cdot {\rm VR1})\]

NaN when \({\rm VR1} = 0\).