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##############################################################################################################################
#
# The R-squared calculation based on two numeric vectors of equal length
#
#
#' R-squared
#'
#' Calculates R-squared given vectors for x and y
#'
#' @param x1 a vector or matrix of real numbers
#' @param y1 a vector or matrix of real numbers
#'
#' @return a vector of numbers with length equal to the number of trials (N)
#'
#' @examples
#' R2(c(1,2,3,4,5),c(1,2,3,4,4))
#' R2(matrix(runif(10000),ncol=5),matrix(runif(10000),ncol=5))
#'
#' @export
#' R2()
R2 <- function(x1, y1){
mlist <- fitmetric_check(x1,y1)
x <- mlist[[1]]
y <- mlist[[2]]
N <- mlist[[3]]
dof <- mlist[[4]]
#define R2 components x and y
xb <- rowSums(x)/dof #xbar (mean of x)
xd <- x-xb #xdelta (x-xbar)
yb <- rowSums(y)/dof #ybar (mean of y)
yd <- y-yb #ydelta (y-ybar)
#calculate R2 numerator
n1 <- xd*yd
n1s <- rowSums(n1)
num <- n1s*n1s #numerator
#calculate R2 denominator
d1 <- xd^2
d2 <- yd^2
d1s <- rowSums(d1)
d2s <- rowSums(d2)
den <- d1s*d2s #denominator
#calculate R2 (this is an array of R2 calculations based on noise)
out <- num/den #R2
return(out)
}
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