pcinterpolate: Interpolate a monotone function (via piecewise cubic Hermite)
In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description Usage Arguments Details Value References See Also Examples

Interpolate a monotone function from a two-column table

1 2	pcderiv(x,fn) pcinterpolate(x,fn,deriv,xnew)

`x`	vector of x values
`fn`	function values corresponding to each value in x
`deriv`	vector of (estimated) derivative values assuming monotonicity, output of pcderiv and input to pcinterpolate
`xnew`	vector of new x values to interpolate values of the function.

The monotone piecewise cubic interpolation algorithm is from the references given below.

`deriv`	for pcderiv, estimated derivatives at x values
`y`	for pcinterpolate, length(xnew) x 2 matrix of interpolated fn values and derivatives

Fritsch FN and Carlson RE (1980), Monotone piecewise cubic interpolation. Siam J Numerical Analysis, 17, 238-246.

Kahaner D, Moler CB and Nash S (1989). Numerical Methods and Software Prentice Hall.

makedeptable

n=21
x=seq(0,pi/2,length=n)
fn=sin(x)
der=pcderiv(x,fn)
print(cbind(der,cos(x)))
xnew=seq(.05,1.,.05)
out=pcinterpolate(x,fn,der,xnew)
fval=sin(xnew)
print(cbind(out[,1],fval,abs(out[,1]-fval)))
cat("max err in deriv : ", max(abs(der-cos(x))), "\n")
cat("max err in interp : ", max(abs(out[,1]-fval)), "\n")