weightsLinearInterp1D: Weights for linear interpolation in 1D and 2D

In sdetorus: Statistical Tools for Toroidal Diffusions

Weights for linear interpolation in 1D and 2D

Description

Computation of weights for linear interpolation in 1D and 2D.

Usage

weightsLinearInterp1D(x, g1, g2, circular = FALSE)

weightsLinearInterp2D(x, y, gx1, gx2, gy1, gy2, circular = FALSE)

Arguments

x, y	vectors of length n containing the points where the weights should be computed.
g1, g2, gx1, gx2, gy1, gy2	vectors of length n such that g1 <= x <= g2 for 1D and gx1 <= x <= gx2 and gy1 <= y <= gy2 for 2D.
circular	flag to indicate whether the differences should be circularly wrapped.

Details

See the examples for how to use the weights for linear binning.

Value

• For 1D, a matrix of size c(n, 2) containing the weights for lower (g1) and upper (g1) bins.

• For 2D, a matrix of size c(n, 4) containing the weights for lower-lower (g1x, g1y), upper-lower (g2x, g1y), lower-upper (g1x, g2y) and upper-upper (g2x, g2y) bins. cbind(g1x, g1y), cbind(g1x, g1y), cbind(g1x, g1y) and cbind(g2x, g2y).

Examples

# 1D, linear
x <- seq(-4, 4, by = 0.5)
g1 <- x - 0.25
g2 <- x + 0.5
w <- weightsLinearInterp1D(x = x, g1 = g1, g2 = g2)
f <- function(x) 2 * x + 1
rowSums(w * cbind(f(g1), f(g2)))
f(x)

# 1D, circular
x <- seq(-pi, pi, by = 0.5)
g1 <- toPiInt(x - 0.25)
g2 <- toPiInt(x + 0.5)
w <- weightsLinearInterp1D(x = x, g1 = g1, g2 = g2, circular = TRUE)
f <- function(x) 2 * sin(x) + 1
rowSums(w * cbind(f(g1), f(g2)))
f(x)

# 2D, linear
x <- seq(-4, 4, by = 0.5)
y <- 2 * x
gx1 <- x - 0.25
gx2 <- x + 0.5
gy1 <- y - 0.75
gy2 <- y + 0.25
w <- weightsLinearInterp2D(x = x, y = y, gx1 = gx1, gx2 = gx2,
                           gy1 = gy1, gy2 = gy2)
f <- function(x, y) 2 * x + 3 * y + 1
rowSums(w * cbind(f(gx1, gy1), f(gx2, gy1), f(gx1, gy2), f(gx2, gy2)))
f(x, y)

# 2D, circular
x <- seq(-pi, pi, by = 0.5)
y <- toPiInt(2 * x)
gx1 <- toPiInt(x - 0.25)
gx2 <- toPiInt(x + 0.5)
gy1 <- toPiInt(y - 0.75)
gy2 <- toPiInt(y + 0.25)
w <- weightsLinearInterp2D(x = x, y = y, gx1 = gx1, gx2 = gx2,
                           gy1 = gy1, gy2 = gy2, circular = TRUE)
f <- function(x, y) 2 * sin(x) + 3 * cos(y) + 1
rowSums(w * cbind(f(gx1, gy1), f(gx2, gy1), f(gx1, gy2), f(gx2, gy2)))
f(x, y)

sdetorus documentation built on June 22, 2024, 6:58 p.m.