## Given the MME, iteratively solve for the solutions by Successive Over Relaxation.

## Arguments
## LHS: left hand side of MME
## RHS: right hand side of MME
## inits: a vecotr of initial values for the solutions
## w: a vector of relaxation factor
## disp: a logical value. If true, show the solutions at each iteration

## Note: When 'w' is all one, Gauss Seidel method will be performed.

## Literature1 : Mrode, R.A. 2005. Linear Models for the Prediction of Animal Breeding Values. CAB International, Oxon, UK.
## Literature 2: Misztal, I. 2008. Computational Techniques in Animal Breeding. Course Notes. University of Georgia.

## Author: Gota Morota <morota at wisc dot edu>
## Create: 9-Apr-2010
## Last-Modified: 11-Apr-2010
## License: GPLv3 or later

`sor` <-
function(LHS, RHS, inits, w, disp){
	
	D <- diag(diag(LHS))
	R <- LHS
	diag(R) <- 0
	Dinv <- solve(D)
	x <- matrix(inits)
	
	diff <- 1
	i = 0
	while (diff > 10E-9){
		i = i + 1
		oldx <- x
		for (j in 1:dim(LHS)[1]){
			x[j] <- (1-w[j])*x[j] + w[j]*(1/LHS[j,j])*(RHS[j] - sum(LHS[j,][-j]*x[-j]))
		}
		
		if (disp == TRUE){
			cat('\n')
			cat("iteration ", i, '\n')
			print(x)
		}
		diff <-  (  sum((x - oldx)^2) ) /sum(x^2)
	}
	
	cat('\n')
	cat("Final solutions after",  i, "th iteration"  )
	return(x)

}