Nothing
stirling.matrix <- function( n )
{
###
### this function constructs the Stirling matrix, a lower triangular matrix containing
### the Stirling numbers of the second kind
###
### argument
### n = a positive integer for the order of the matrix
###
if ( !is.numeric( n ) )
stop( "argument n is not numeric" )
if ( !is.vector( n ) )
stop( "argument n is not of the proper data type" )
if ( length( n ) != 1 )
stop( "argument n is not a scalar integer" )
if ( n < 1 )
stop( "arguemtn n is less than 1" )
if ( n == 1 ) {
return( S )
}
nm1 <- n - 1
np1 <- n + 1
S <- matrix( 0, nrow=np1, ncol=np1 )
for ( i in 0:n ) {
ii <- i + 1
S[ii,ii] <- 1
}
for ( j in 0:n ) {
jj <- j + 1
S[1,jj] <- 0
S[jj,1] <- 0
}
for ( i in 1:nm1 ) {
ii <- i + 1
for ( j in 1:i ) {
jj <- j + 1
S[ii+1,jj] <- S[ii,jj-1] + j * S[ii,jj]
}
}
S[1,1] <- 1
return( S )
}
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