#' Finds linear combinations
#'
#' Finds linear combinations of columns that make up linearly
#' dependent columns
#'
#' @param mat An input matrix
#' @param prefix Character string. What to prefer the output columns with.
#' @export
#' @examples
#' mat <- matrix(c(1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,1), byrow=TRUE, ncol=5, nrow=4)
#' linFinder(mat)
linFinder <- function(mat, prefix = "Column_"){
# If the matrix is full rank then we're done
if(qr(mat)$rank == ncol(mat)){
print("Matrix is of full rank")
return(invisible(seq(ncol(mat))))
}
m <- ncol(mat)
# cols keeps track of which columns are linearly independent
cols <- 1
for(i in seq(2, m)){
ids <- c(cols, i)
mymat <- mat[, ids]
if(qr(mymat)$rank != length(ids)){
# Regression the column of interest on the previous
# columns to figure out the relationship
o <- lm(mat[,i] ~ mat[,cols] + 0)
# Construct the output message
start <- paste0(prefix, i, " = ")
# Which coefs are nonzero
nz <- (abs(coef(o)) > .Machine$double.eps^0.5)
tmp <- paste(prefix, cols[nz], sep = "")
vals <- paste(coef(o)[nz], tmp, sep = "*", collapse = " + ")
message <- paste0(start, vals)
print(message)
}else{
# If the matrix subset was of full rank
# then the newest column is linearly independent
# so add it to the cols list
cols <- ids
}
}
return(invisible(cols))
}
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