interpBarycentric: Barycentric interpolation

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Barycentric interpolation

Description

interpBarycentric(x, fun, xNew, options) evaluates (interpolates) function values funNew at given points xNew by barycentric interpolation from function values fun given at chebpoints x.

Usage

interpBarycentric(x, fun, xNew, w, options)

Arguments

x	points in which is fun given (for more accuracy use chebpoints).
fun	function values of fun given at points x.
xNew	point in which fun will be estimated.
options	optional parameter, set the ChebPoints TRUE or FALSE by options$isChebPts <- TRUE.

Value

This function returns a list consisting of values funNew of function fun evaluated at points xNew.

Note

Ver.: 16-Sep-2018 21:16:14 (consistent with Matlab CharFunTool v1.3.0, 24-Jul-2017 10:06:48).

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Barycentric_coordinate_system.

Other Utility Function: ChebCoefficients(), ChebPoints(), ChebPolyValues(), ChebPoly(), ChebValues(), GammaLog(), GammaMultiLog(), GammaMulti(), GammaZX(), Hypergeom1F1MatApprox(), Hypergeom1F1Mat(), Hypergeom2F1Mat(), Hypergeom2F1(), HypergeompFqMat(), InterpChebValues(), hypergeom1F1()

Examples

## EXAMPLE 1
# Barycentric interpolant of the Sine function on (-pi,pi)
x <- ChebPoints(32, c(-pi, pi))[[1]]
f <- sin(x)
xNew <- seq(from = -pi,
            to = pi,
            length.out = 201)
fNew <- interpBarycentric(x, f, xNew)
plot(
        x,
        f,
        type = "p",
        xlab = "",
        ylab = "",
        main = "",
        pch = 20,
        col = "red",
        cex = 1.5
)
lines(xNew, fNew[[2]], col = "blue",  lwd = 2)
print(list(
        "xNew" = xNew,
        "fNew" = fNew[[2]],
        "sin(xNew)" = sin(xNew)
))

## EXAMPLE 2
# Barycentric interpolant of the Normal CDF
x <- ChebPoints(21, c(-8, 8))
f <- pnorm(x[[1]])
xNew <- seq(from = -5,
            to = 5,
            length.out = 201)
fNew <- interpBarycentric(x[[1]], f, xNew)[[2]]
plot(
        xNew,
        fNew,
        type = "p",
        xlim = c(-8 , 8),
        xlab = "",
        ylab = "",
        main = "",
        pch = 20,
        col = "red",
        cex = 1
)
lines(x[[1]], f, col = "blue",  lwd = 2)
print(list(
        "xNew" = xNew,
        "fNew" = fNew,
        "pnorm(xNew)" = pnorm(xNew)
))

## EXAMPLE 3
# Barycentric interpolant of the Normal quantile function
x <- ChebPoints(2 ^ 7, c(-8, 8))
cdf <- pnorm(x[[1]])
prob <- seq(from = 1e-4,
            to = 1 - 1e-4,
            length.out = 101)
qf <- interpBarycentric(cdf, x[[1]], prob)[[2]]
plot(
        cdf,
        x[[1]],
        type = "p",
        xlim = c(0, 1),
        xlab = "",
        ylab = "",
        main = "",
        pch = 20,
        col = "red",
        cex = 1
)
lines(prob, qf, col = "blue",  lwd = 2)
print(list(prob, qf, qnorm(prob)))

## EXAMPLE 4
# Barycentric interpolant of the Compound distribution
cfX <- function(t)
        cfX_Exponential(t, 5)
cf <- function(t)
        cfN_Poisson(t, 10, cfX)
x <- ChebPoints(2 ^ 9, c(0, 10))
prob <- c(0.9, 0.95, 0.99)
options <- list()
options$isCompound <- TRUE
result <- cf2DistGP(cf, x[[1]], prob, options)
CDF <- function(x)
        interpBarycentric(result$x, result$cdf, x)[[2]]
PDF <- function(x)
        interpBarycentric(result$x, result$pdf, x)[[2]]
QF <- function(p)
        interpBarycentric(result$cdf, result$x, p)[[2]]
prob <- seq(from = 1e-4,
            to = 1 - 1e-4,
            length.out = 201)
plot(
        prob,
        QF(prob),
        type = "p",
        xlim = c(0, 1),
        xlab = "",
        ylab = "",
        main = "",
        pch = 20,
        col = "red",
        cex = 1
)
lines(result$cdf, result$x, col = "blue",  lwd = 2)

gajdosandrej/CharFunToolR documentation built on June 3, 2024, 7:46 p.m.