# Types of Numeric Tables¶

## Heterogeneous Numeric Tables¶

Heterogeneous numeric tables enable you to deal with data structures that are of different data types by nature. oneDAL provides two ways to represent non-homogeneous numeric tables: AOS and SOA.

### AOS Numeric Table¶

AOS Numeric Table provides access to observations (feature vectors) that are laid out in a contiguous memory block:

### SOA Numeric Table¶

SOA Numeric Table provides access to data sets where observations for each feature are laid out contiguously in memory:

## Homogeneous Numeric Tables¶

Use homogeneous numeric tables, that is, objects of the HomogenNumericTable class, and matrices, that is, objects of the Matrix, PackedTriangularMatrix, and PackedSymmetricMatrix classes, when all the features are of the same basic data type. Values of the features are laid out in memory as one contiguous block in the row-major order, that is, Observation 1, Observation 2, and so on. In oneDAL, Matrix is a homogeneous numeric table most suitable for matrix algebra operations.

For triangular and symmetric matrices with reduced memory footprint, special classes are available: PackedTriangularMatrix and PackedSymmetricMatrix. Use the DataLayout enumeration to choose between representations of triangular and symmetric matrices:

• Lower packed: lowerPackedSymetricMatrix or lowerPackedTriangularMatrix

• Upper packed: upperPackedTriangularMatrix or upperPackedSymetricMatrix

## CSR Numeric Table¶

oneDAL offers the CSRNumericTable class for a special version of a homogeneous numeric table that encodes sparse data, that is, the data with a significant number of zero elements. The library uses the Condensed Sparse Row (CSR) format for encoding:

Three arrays describe the sparse matrix M as follows:

• The array values contains non-zero elements of the matrix row-by-row.

• The j-th element of the array columns encodes the column index in the matrix M for the j-th element of the array values.

• The i-th element of the array rowIndex encodes the index in the array values corresponding to the first non-zero element in rows indexed i or greater. The last element in the array rowIndex encodes the number of non-zero elements in the matrix M.

The library supports 1-based CSR encoding only. In C++ you can specify it by providingoneBased value through the indexing parameter of type CSRIndexing in the constructor of CSRNumericTable.

## Merged Numeric Table¶

oneDAL offers the MergedNumericTable class for tables that provides access to data sets comprising several logical components, such as a set of feature vectors and corresponding labels. This type of tables enables you to read those data components from one data source. This special type of numeric tables can hold several numeric tables of any type but CSRNumericTable. In a merged numeric table, arrays are joined by columns and therefore can have different numbers of columns. In the case of different numbers of rows in input matrices, the number of rows in a merged table equals $$min(r_1, r_2, \ldots, r_m)$$, where $$r_i$$ is the number of rows in the i-th matrix, $$i = 1, 2, 3, \ldots, m$$.