README.md

In mdgordo/flatlandr: Interpolation functions for multiple dimensional data

flatlandr

This package provides functions for interpolation in multiple dimensions. Currently under development.

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("mdgordo/flatlandr")

Example

library(flatlandr)

## function for interpolation:
fxy <- function(x, y) {
  r = log(x) + x^2*y - y^3
  return(r)
}

### create 10 chebyshev nodes in each dimension on (0,10) and (5,15)
lb = c(1,5)
ub = c(10,15)
ss = chebstatespace(10, lb, ub)

### apply function
y = mapply(fxy, ss$x, ss$y)
y = matrix(y, ncol = 10)

### find coefficient matrix
cmat = chebcoefs(y, degree = 5)

### interpolate
chebpred(2.5, 10.3, cmat, lb, ub)
#> [1] -1027.437
fxy(2.5, 10.3)
#> [1] -1027.436

Test and plot interpolations vs true value

library(tidyverse)
#> ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
#> ✓ ggplot2 3.3.5     ✓ purrr   0.3.4
#> ✓ tibble  3.1.6     ✓ dplyr   1.0.7
#> ✓ tidyr   1.1.4     ✓ stringr 1.4.0
#> ✓ readr   1.4.0     ✓ forcats 0.5.1
#> ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
#> x dplyr::filter() masks stats::filter()
#> x dplyr::lag()    masks stats::lag()

x = seq(1,10,.1); y = seq(5,15,.1)
df.test <- crossing("x" = x, "y" = y)

df.test$ytrue <- mapply(fxy, df.test$x, df.test$y)
df.test$yinterp <- mapply(chebpred, x = df.test$x, y = df.test$y, coefmat = list(cmat), lb = list(lb), ub = list(ub))

ggplot(df.test) + 
  geom_tile(aes(x = x, y = y, fill = ytrue)) + scale_fill_viridis_c()

ggplot(df.test) + 
  geom_tile(aes(x = x, y = y, fill = yinterp)) + scale_fill_viridis_c()

Simplical and Bilinear Interpolation

x <- c(200, 300)
y <- c(40, 45)
df.test2 <- crossing(x, y)
df.test2$vfx <- mapply(fxy, df.test2$x, df.test2$y)

df.interp <- crossing(x = seq(200, 300, 1), y = seq(40, 45, .05))

df.interp$pred_bi <- mapply(simplr, x0 = df.interp$x, y0 = df.interp$y, 
                            x = list(df.test2$x), y = list(df.test2$y), vfx = list(df.test2$vfx), method = "bilinear")

ggplot(df.interp) + 
  geom_tile(aes(x = x, y = y, fill = pred_bi)) + scale_fill_viridis_c()

Reference: Judd, Kenneth. (1998). “Numerical Methods in Economics.” MIT Press. ch6.

mdgordo/flatlandr documentation built on Feb. 13, 2022, 11:31 a.m.