GaussIndependent: Linearly independent rows and columns by Gaussian elimination

In SSBtools: Statistics Norway's Miscellaneous Tools

Linearly independent rows and columns by Gaussian elimination

Description

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

Details

GaussRank returns the rank

Value

List of logical vectors specifying independent rows and columns

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)
GaussRank(x)
GaussRank(t(x))

## Not run: 
# For comparison, qr-based rank may not work
rankMatrix(x, method = "qr")

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

## End(Not run)

SSBtools documentation built on July 9, 2023, 6:16 p.m.