Nothing
schebyshev.u.quadrature <- function( functn, rule, lower=0, upper=1, weighted=TRUE, ... )
{
###
### This function evaluates the integral of the function functn
### between lower and upper using the weight and abscissa values specified
### in the rule data frame. The rule corresponds to an order n shifted
### Chebyshev polynomial of the second kind, U_n(x), weight function and interval [0,1]
### Lower bound is finite and upper bound is finite.
###
### Parameters
### functn = an R function which should take a numeric argument x and
### possibly some parameters. The function returns a
### numerical vector value for the given argument x.
### rule = a data frame containing the order n quadrature rule
### lower = a scalar lower bound of the integral
### upper = a scalar lower found of the integral.
### weighted = a boolean value which if true includes the weight function in the integrand
### ... = other arguments passed to the function functn.
###
if ( !is.function( functn ) )
stop( "functn argument is not an R function" )
if ( !is.data.frame( rule ) )
stop( "rule argument is not a data frame" )
if ( is.infinite( lower ) )
stop( "lower bound is infinite" )
if ( is.infinite( upper ) )
stop( "lower bound is infinite" )
if ( weighted ) {
ff <-
if ( length( list( ... ) ) && length( formals( functn ) ) > 1 )
function( x ) functn( x, ... )
else
functn
}
else {
ff <-
if ( length( list( ... ) ) && length( formals( functn ) ) > 1 )
function( x ) { functn( x, ... ) / schebyshev.u.weight( x ) }
else
function( x ) { functn( x ) / schebyshev.u.weight( x ) }
}
lambda <- upper - lower
mu <- lower
y <- lambda * rule$x + mu
w <- rule$w
return( lambda * sum( w * ff(y) ) )
}
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