HBF format

Harwell Boeing Form [Saa91] is a format which facilites the storage of sparse matrix. Instead of store all the values, the idea is to only store the non-zero values.
So, to have a efficient data storage, we must be able to provide three vectors, admitting two delimiters : the number of non-zero values ('nz_number') and the number of rows and columns of the matrix ('dimension')

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Val : array of reals of size 'nz_number', containing the non-zero values.

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Col : array of integers of size 'nz_number', containing the column indexes.

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Row : array of integers of size 'dimension' +1, containing the beginning index of each row.

Example 1 (HBF format)  

$$\mathbf{M}= \left(\begin{array}{cccc} 10 & -4 & 3 & 6 \\ 5 & 2 & 1 & 0 \\ 0 & 3 & 0 & -2 \\ 0 & -4 & 0 & 0 \\ \end{array} \right)$$

$\mathbf{M}$ matrix can be stored by :

$$\begin{array}{\vert c\vert\vert c\vert c\vert c\vert c\vert\vert ... ... \hline \emph{Col} & 0 & 2 & 1 & 3 & 2 & 1 & 0 & 1 & 3 & 1 \hline \end{array}$$

$$\begin{array}{\vert c\vert\vert c\vert c\vert c\vert c\vert}\hline \emph{Row} & 0 & 4 & 7 & 9 \hline \end{array}$$

Note that the order of the non-zero elements of a row is not important. Moreover, PSI accepts HBF format with 'column' storage (PEPS models by example) and indifferently states numerotation from 0 to $dimension-1$ and from $1$ to $dimension$.