Dense Matrix Format#

A dense matrix can be stored in both row-major and column-major memory layout (ordering) and it is represented by the following parameters.

  • The number of rows in the matrix.

  • The number of columns in the matrix.

  • The leading dimension, which must be

    • Greater than or equal to the number of columns in the row-major layout

    • Greater than or equal to the number of rows in the column-major layout

  • The pointers to the values array of length

    • \(rows \times leading\; dimension\) in the row-major layout

    • \(columns \times leading\; dimension\) in the column-major layout

The following figure represents a \(5 \times 2\) dense matrix with both memory layouts

../_images/dense_matrix.png

Dense matrix representations#

The indices within the matrix represents the contiguous locations in memory.

The leading dimension is useful to represent a sub-matrix within the original one:

../_images/sub_matrix.png

Sub-matrix representations#