Nothing
monic.polynomial.recurrences <- function( recurrences )
{
###
### This function returns a data frame with parameters
### required to construct monic orthogonal polynomials
### based on the standard recurrence relation for
### the non-monic polynomials
###
### Parameter
### recurrences = the data frame of recurrence parameters c, d, e and f
###
np1 <- nrow( recurrences )
n <- np1 - 1
monic.recurrences <- data.frame( matrix( nrow=np1, ncol=2 ) )
names( monic.recurrences ) <- c( "a", "b" )
c <- recurrences$c
d <- recurrences$d
e <- recurrences$e
f <- recurrences$f
j <- 0
k <- 1
while( j <= n ) {
if ( e[k] == 0 )
monic.recurrences[k,"a"] <- 0
else
monic.recurrences[k,"a"] <- - ( d[k] / e[k] )
if ( j == 0 )
monic.recurrences[k,"b"] <- 0
else {
if ( e[k-1] == 0 || e[k] == 0 )
monic.recurrences[k,"b"] <- 0
else
monic.recurrences[k,"b"] <- ( c[k-1] * f[k] ) / ( e[k-1] * e[k] )
}
j <- j + 1
k <- k + 1
}
return( monic.recurrences )
}
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