Extract Sparse Matrix Notation from a Dense Matrix

Converts a dense matrix to a sparse representation by extracting its non-zero entries and their indices. Entries with absolute value less than or equal to tol are treated as zeros.

Usage

sparse_matrix_notation(M, zero_based = TRUE, tol = 1e-04)

Arguments

M

A numeric matrix or object coercible to a matrix.

zero_based

Logical; if TRUE (default), the returned row and column indices are zero-based (starting at 0). If FALSE, indices are one-based (as in standard R matrices).

tol

Numeric tolerance (default 1e-4). Entries with absolute value less than or equal to tol are treated as zero.

Value

A named list with components:

row_index

Integer vector of row indices for non-zero entries (adjusted by zero_based).

col_index

Integer vector of column indices for non-zero entries (adjusted by zero_based).

values

Numeric vector of the non-zero entries.

M

The original input matrix, coerced to a dense matrix.

Msparse

A copy of M with near-zero entries (as determined by tol) replaced by exact zeros.

Examples

M <- matrix(c(5, 0, 0,
              0, 0, 3,
              0, 2, 0), nrow = 3, byrow = TRUE)
sparse_matrix_notation(M)
#> $row_index
#> [1] 0 1 2
#> 
#> $col_index
#> [1] 0 2 1
#> 
#> $values
#> [1] 5 3 2
#> 
#> $M
#>      [,1] [,2] [,3]
#> [1,]    5    0    0
#> [2,]    0    0    3
#> [3,]    0    2    0
#> 
#> $Msparse
#>      [,1] [,2] [,3]
#> [1,]    5    0    0
#> [2,]    0    0    3
#> [3,]    0    2    0
#>