#  Prediction Problems

library(MASS)
zlrs = file.choose()
source(zlrs)

# Connectedness problem for group work
(1,1,1) (1,1,3) (1,2,1) (1,3,2) (1,3,5) (2,1,3)
(2,1,4) (2,2,1) (2,2,2) (2,2,5) (2,3,1) (3,1,4)
(3,1,5) (3,3,1) (3,3,3) (4,1,2) (4,2,2) (4,3,4)

# 1)Determine the number of disconnected groups of the
# above filled subclasses.
# 2)Which subclasses (minimum number) are needed in 
# order to connect all of these groups?


# small prediction problem
y = matrix(data=c(128,150,90,110,120),ncol=1)
X = matrix(data=c(1,1,1,1,1),ncol=1)
herds = c(1,1,2,2,2)
sires = c(1,2,1,2,3)
Zh = desgn(herds,0)
Zs = desgn(sires,0)
Z = cbind(Zh,Zs)
Gh = id(2)*(1/6)
Gs = id(3)*(1/15)
G = block(Gh,Gs)
dd = c(5,4,5,20,2)
RI=diag(dd)

#  Pigs in litters
Litter
1         1,  2,  3,  4,  5
         13, 10,  9, 16,  8

2         6,  7,  8,  9
         15, 12,  7, 18

3        10, 11, 12, 13, 14, 15
         20, 11,  9, 17, 10, 14
----------------------------------
y = mu + litter + pig + e     e = 10 l = 3 p

lits = c(1,1,1,1,1,2,2,2,2,3,3,3,3,3,3)
pigs = c(1:15)
oval = rep(1,length(lits))
y = matrix(c(13,10,9,16,8,15,12,7,18,20,11,9,17,10,14),ncol=1)
Xm = desgn(oval,0)
Zl = desgn(lits,0)
Zp = desgn(pigs,0)
Gl = id(3)*10
G2 = id(15)*3
GI = block(G1,G2)

# Evaluation of pigs = lits + pigs solutions, SEP of these 
# pigs unrelated between litters
# put in full-sib relationships - compare models



#Homework Problem, plant heights
y = matrix(data=c(25.3,17.8,20.1,26.1,19.2,24.6,23.7,24.5,26.0,28.4,22.9,25.8),
ncol=1)
dd = c(40,39,37,35,40,40,33,38,40,30,28,34)
RI=diag(dd)
FB=c(1,1,1,2,2,2,3,3,3,4,4,4)
X =desgn(FB,0)
LL=c(1,2,3,1,2,3,1,2,3,1,2,3)
Z = desgn(LL,0)
dd = c(10,10,10)
GI=diag(dd)