```
## This r script is code for basic principal components analysis.
## translated from the psuedo code.
## variants here is integer indicating which variant are using.
# 1. grandmean center; 2 column center 3 row center 4 column standardized 5 row standardized
# 6. AMMI 7. Correspondence anlaysis
PCA<-function(C,variants,name){
# NEED CALL FROM PREVIOUS FUNCTION INSTEAD OF RE-EXTRACT FROM MATRICE C.
NR = dim(C)[1]
NC = dim(C)[2]
#STEST = 10^(-9)/sqrt(NR)
STEST = 1e-8
#initialized matrix PR, PC, vector EV.
# determine the limit for the number of components.
NXL = min(NR-1, NC-1,7)
#NXL = 1
PR = matrix(0, nrow = NR, ncol = NXL)
PC = matrix(0, nrow =NXL, ncol = NC)
EV = rep(0, 7)
#store temporary information NX ITER STEST SFT
temp = matrix(0, ncol = 4, nrow = NXL)
colnames(temp) = c("NX","ITER","STEST","SFT")
if(variants == 7){
CA.P = ca(C)
PR = CA.P$rowcoord[,1:7]
PC = t(CA.P$colcoord[,1:7])
EV = CA.P$sv[1:7]
}
else{
for(NX in 1:NXL){
SFT = 1
ITER = 0
# initialized the VR with uniform random function
VR = runif(NR, min = -0.5, max = 0.5)
SR = VR
while(ITER<100 & SFT>STEST){
ITER = ITER + 1
#compute VC from VR
VC = t(VR)%*%C
EVP = sum(VC^2)
SVP = sqrt(EVP)
VC = VC/SVP
# recalculate VR from VC by reverse sum
VR = C%*%t(VC)
EVP = sum(VR^2)
SVP = sqrt(EVP)
VR = VR/SVP
SFT = max(abs(VR-SR))
# retain VR as SR
SR = VR
}
print(ITER)
#Store Eigenvalue first
EV[NX] = EVP
SQVP = sqrt(SVP)
VR = VR*SQVP
VC = VC*SQVP
PR[,NX] = VR
PC[NX,] = VC
# write NX, ITER, STEST, SFT into a matrix
temp[NX,] = c(NX, ITER, STEST, SFT)
# remove NX from data copy
C = C - VR%*%VC
}
}
return(list(PC = PC,PR = PR, EV = EV))
}
```

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