McSpatial (version 2.0)

smooth12: Univariate or Bivariate Interpolation

Description

Uses the Akima (1970) method for univariate interpolation and the Modified Shephard Algorithm for bivariate interpolation.

Usage

smooth12(x,y,xout,knum=16,std=TRUE)

Arguments

x

The actual values of the x-variable(s). A simple numeric variable for univariate interpolation and a matrix of locations for bivariate interpolation.

y

The variable to be interpolated.

xout

Points on the x-axis where the function is to be evaluated. A single numeric variable in the case of univariate interpolation and a matrix of locations for bivariate interpolation.

knum

The number of target points used for bivariate interpolation.

std

If TRUE, re-scales the columns of x and xout by dividing by the standard deviation of the columns in x. Not applicable for univariate interpolation.

Value

• The values of y interpolated to the xout locations.

Details

The univariate version of the function is designed as a partial replacement for the aspline function in the akima package. It produces a smooth function that closely resembles the interpolation that would be done by hand. Values of y are averaged across any ties for x. The function does not allow for extrapolation beyond the min(x), max(x) range. The bivariate version of the function uses the modifed Shepard's method for interpolation. The function uses the RANN package to find the nearest knum target points to each location in xout. The following formula is used to interpolate from these target points to the locations given in xout: $$\frac{\sum_{i=1}^{knum} w_i y_i}{\sum_{i=1}^{knum} w_i}$$ where $w_{i} = ((maxd - d_{i})^2)/(maxd*d_{i})$ and $maxd = max(d_{1}, ..., d_{knum})$.

References

Akima, Hiroshi, "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures," Journal of the Association for Computing Machinery 17 (1970), 589-602. Franke, R. and G. Neilson, "Smooth Interpolation of Large Sets of Scatter data," International Journal of Numerical Methods in Engineering 15 (1980), 1691 - 1704.

See Also

maketarget

Examples

set.seed(484849)
n = 1000
x <- runif(n,-2*pi,2*pi)
x <- sort(x)
y <- sin(x) + cos(x) - .5*sin(2*x) - .5*cos(2*x) + sin(3*x)/3 + cos(3*x)/3
x1 <- seq(-2*pi,2*pi,length=100)
y1 <- sin(x1) + cos(x1) - .5*sin(2*x1) - .5*cos(2*x1) + sin(3*x1)/3 + cos(3*x1)/3

yout <- smooth12(x1,y1,x)
plot(x,y,type="l")
lines(x,yout,col="red")

x <- seq(0,10)
xmat <- expand.grid(x,x)
y <- sqrt((xmat[,1]-5)^2 + (xmat[,2]-5)^2)
xout <- cbind(runif(n,0,10),runif(n,0,10))
y1 <- sqrt((xout[,1]-5)^2 + (xout[,2]-5)^2)
y2 <- smooth12(xmat,y,xout)
cor(y1,y2)