Which Matrix Storage Format should I choose for large sparse matrices in MKL

[Tamas]

In our nextnano3 code, most of them are utilizing a sparse matrix format called MRS format which position for customized CRS (compressed row storage) format. It is a row-indexed meager storage mode. It is comparable to a format called Bell Labs format additional than it seems that the Bell Labs' is somehow dissimilar, i.e. Bell Labs stores as primary the diagonal entries, then the upper offdiagonal right of entry and then the lower offdiagonal entries, whereas the superior and lower offdiagonal parts have encompassed the similar length, implying that it stores a symmetric structured matrix (be able to comprise zeros).

[Antonio1]

Theoretically, sparsely be in contact to systems which are insecurely attached. Think regarding a line of balls associated by springs from one to the next; this is a meager system. By contrast, if the similar line of balls had springs concerning every ball to the entire additional balls, the system would be corresponding to by an impenetrable matrix. The concept of sparsity is helpful in combinatorics and submission areas such as network theory, which comprise a low density of important data or connections.

[Carlos16]

As talk regarding on top, it is additional efficient to accumulate merely the non-zero component of a sparse matrix. There is a numeral of ordinary storage formats used for sparse matrices, additional than the majority of them employ the similar essential technique. That is, store the entire non-zero elements of the matrix into a linear selection and make available auxiliary arrays to describe the locations of the non-zero elements in the innovative matrix.

[Deepest BLUE]

The storing the non-zero component of a sparse matrix into a linear selection is completed by walking down every column (column-major format) or across every row (row-major format) in organize and writing the non-zero elements to a linear selection in organize they come into view in the walk. For symmetric matrices, it is essential to store merely the superior triangular half of the matrix (upper triangular format) or the lower triangular half of the matrix (lower triangular format).

[Madhuparna]

The Intel MKL straight sparse solvers to utilize a row-major superior triangular storage format the matrix is compacted row-by-row and for symmetric matrices merely non-zero elements in the superior triangular partially of the matrix are stored. The Intel MKL sparse matrix storage format for uninterrupted sparse solvers is particular by three arrays: values, columns, and row Index. The subsequent table illustrates the arrays in terms of the values, row, and column situations of the non-zero elements in a sparse matrix.

[Wampanoag]

The length of the values and columns collections is equivalent to the numeral of non-zero elements in the matrix. As the row Index collection gives the position of the first non-zero component within a row, and the non-zero elements are accumulated one subsequent to the additional, the numeral of non-zero elements in the I-th row is equal to the dissimilarity of row Index(I) and row Index(I+1). To encompassed this relationship hold for the most recent row of the matrix, an supplementary entry (dummy entry) is added to the end of row Index. Its value is equivalent to the numeral of non-zero elements plus one. This creates the total length of the row Index array one larger than the numeral of rows in the matrix.

[Susquehannock]

The storage format for the meager solver be obliged to be conventional to two significant restrictions the non-zero values in a prearranged row must be placed into the values array in the organize in which they happen in the row (from left to right) no diagonal element be able to be omitted from the values array for several symmetric or structurally symmetric matrix. The subsequent restriction implies with the intention of if symmetric or structurally symmetric matrices encompassed zero diagonal elements, then they are obliged to be unambiguously represented in the values array.