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## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are
## met:
##
## Redistributions of source code must retain the above copyright
## notice, this list of conditions and the following disclaimer.
##
## Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in
## the documentation and/or other materials provided with the
## distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
## "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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#' @title Polynomial interpolation
#'
#' @description
#' Finds a polynomial function interpolating the given points
#'
#' @param x a vector of x values
#' @param y a vector of y values
#'
#' @details
#' \code{polyinterp} finds a polynomial that interpolates the given points.
#'
#' @return a polynomial equation's coefficients
#'
#' @family interp
#' @family algebra
#'
#' @examples
#' x <- c(1, 2, 3)
#' y <- x^2 + 5 * x - 3
#' f <- polyinterp(x, y)
#'
#' @export
polyinterp <- function(x, y) {
if(length(x) != length(y))
stop("Length of x and y vectors must be the same")
n <- length(x) - 1
vandermonde <- rep(1, length(x))
for(i in 1:n) {
xi <- x^i
vandermonde <- cbind(vandermonde, xi)
}
beta <- solve(vandermonde, y)
names(beta) <- NULL
return(beta)
}
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