Linearly independent rows and columns by Gaussian elimination

The function is written primarily for large sparse matrices with integers and even more correctly it is primarily written for dummy matrices (0s and 1s in input matrix).

Usage

GaussIndependent(
  x,
  printInc = FALSE,
  tolGauss = (.Machine$double.eps)^(1/2),
  testMaxInt = 0,
  allNumeric = FALSE
)

GaussRank(x, printInc = FALSE)

Arguments

x

A (sparse) matrix

printInc

Printing "..." to console when TRUE

tolGauss

A tolerance parameter for sparse Gaussian elimination and linear dependency. This parameter is used only in cases where integer calculation cannot be used.

testMaxInt

Parameter for testing: The Integer overflow situation will be forced when testMaxInt is exceeded

allNumeric

Parameter for testing: All calculations use numeric algorithm (as integer overflow) when TRUE

Value

List of logical vectors specifying independent rows and columns

Details

GaussRank returns the rank

Note

The main algorithm is based on integers and exact calculations. When integers cannot be used (because of input or overflow), the algorithm switches. With printInc = TRUE as a parameter, ..... change to ----- when switching to numeric algorithm. With numeric algorithm, a kind of tolerance for linear dependency is included. This tolerance is designed having in mind that the input matrix is a dummy matrix.

Examples

x <- ModelMatrix(SSBtoolsData("z2"), formula = ~fylke + kostragr * hovedint - 1)

GaussIndependent(x)
#> $rows
#>  [1]  TRUE  TRUE  TRUE FALSE  TRUE FALSE  TRUE FALSE  TRUE  TRUE FALSE  TRUE
#> [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE
#> [25] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE  TRUE FALSE FALSE
#> [37] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
#> 
#> $columns
#>  [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE FALSE
#> [13]  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE
#> 
GaussRank(x)
#> [1] 13
GaussRank(t(x))
#> [1] 13

if (FALSE) { # \dontrun{
# For comparison, qr-based rank may not work
rankMatrix(x, method = "qr")

# Dense qr works 
qr(as.matrix(x))$rank
} # }