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June 24, 2017 15:22
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R function for performing Lagrangian polynomial interpolation
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# Function for performing Lagrangian polynomial interpolation https://en.wikipedia.org/wiki/Lagrange_polynomial. | |
# Requires the package rSymPy https://cran.r-project.org/web/packages/rSymPy/index.html. | |
# Parameters: | |
# x: x values of interpolating points | |
# y: values corresponding to x values | |
# Returns: | |
# Simplified interpolated polynomial that passes through the given x and y points | |
lagrange.poly <- function(x, y) { | |
require(rSymPy) | |
if (length(x) != length(y)) { | |
stop('x and y must be of equal length') | |
} | |
l <- list() # List to store Lagrangian polynomials L_{1,2,3,4} | |
k <- 1 | |
for (i in x) { | |
# Set the numerator and denominator of the Lagrangian polynomials to 1 and build them up | |
num <- 1 | |
denom <- 1 | |
# Remove the current x value from the iterated list | |
p <- x[! x %in% i] | |
# For the remaining points, construct the Lagrangian polynomial by successively | |
# appending each x value | |
for (j in p) { | |
num <- paste(num, "*", "(", 'x', " - ", as.character(j), ")", sep = "", collapse = "") | |
denom <- paste(denom, "*", "(", as.character(i)," - ", as.character(j), ")", sep = "", collapse = "") | |
} | |
# Set each Lagrangian polynomial in rSymPy to simplify later. | |
l[k] <- paste("(", num, ")", "/", "(", denom, ")", sep = "", collapse = "") | |
k <- k + 1 | |
} | |
# Similar to before, we construct the final Lagrangian polynomial by successively building | |
# up the equation by iterating through the polynomials L_{1,2,3,4} and the y values | |
# corresponding to the x values. | |
eq <- 0 | |
for (i in 1:length(y)) { | |
eq <- paste(eq, '+', as.character(y[i]), "*", l[[i]], sep = "", collapse = "") | |
} | |
# Define x variable for rSymPy to simplify | |
x <- Var('x') | |
# Simplify the result with rSymPy and return the polynomial | |
return(sympy(paste("simplify(", eq, ")"))) | |
} |
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I have a value of interval censored lifetable data. I would love to use interpolation to fill in the missing values in R.