## ----eval=FALSE-------------------------------------------------------------------------
# B <- matrix(c(50, 67, 90, 98, 120,
#              55, 71, 93, 102, 129,
#              65, 76, 95, 105, 134,
#              50, 80, 102, 130, 138,
#              60, 82, 97, 135, 151,
#              65, 89, 106, 137, 153,
#              75, 95, 117, 133, 155), ncol=5, byrow=TRUE)
# rownames(B) <- c("G1","G2","G3","G4","G5","G6","G7")
# colnames(B) <- c("E1","E2","E3","E4","E5")
# 
# B2 = B
# B2[1,1] = B2[2,1] = NA
# B2 <- as.matrix(B2)
# 
# same <- function(a,b, tol=1e-3){
#   all.equal( abs(a), abs(b), tol=tol, check.attributes=FALSE)
# }

## ----eval=FALSE-------------------------------------------------------------------------
# library(ade4)
# made <- ade4::nipals(B2, nf=5, rec=TRUE, niter=500, tol=1e-9)
# 
# B2a <- apply(B2, 2, function(x) {
#   n <- sum(!is.na(x))
#   x <- x - mean(x, na.rm=TRUE)
#   x <- x / ( sd(x, na.rm=TRUE) * sqrt((n-1) / n ))
# })
# 
# mnip <- nipals::nipals(B2a, ncomp=5, center=FALSE, scale=FALSE,
#                        fitted=TRUE, maxiter=500, tol=1e-9, gramschmidt=FALSE)

## ----eval=FALSE-------------------------------------------------------------------------
# # data
# same(B2a, as.matrix(made$tab))
# # TRUE
# 
# # eigenvalues, ade4 uses squared singular values / n-1
# mnip$eig
# # [1] 5.2913781 2.2555596 1.1651281 0.2590878 0.1563175
# made$eig
# # [1] 4.666454778 0.847924398 0.226254436 0.011187921 0.004072542
# same(mnip$eig ^ 2 / (nrow(B2a)-1), made$eig)
# # TRUE
# 
# # P loadings
# same(mnip$loadings, made$c1)
# # TRUE
# 
# # T scores. For nipals, sweep IN the eigenvalues
# same( sweep(mnip$scores, 2, mnip$eig, "*"), made$li)
# # TRUE
# 

## ----eval=FALSE-------------------------------------------------------------------------
# library(plsdepot)
# mpls <- plsdepot::nipals(B2, comps=5)
# library(nipals)
# mnip <- nipals::nipals(B2a, ncomp=5, maxiter=100, tol=1e-6, gramschmidt=FALSE)

## ----eval=FALSE-------------------------------------------------------------------------
# # eigenvalues
# mnip$eig
# # [1] 4.8762167 2.0442757 1.0728055 0.2369607 0.1432779
# mpls$values[,1]
# # [1] 3.963172007 0.696484184 0.191839875 0.009366425 0.003421661
# same(mnip$eig, sqrt(mpls$values[,1] * 6) )
# # TRUE
# 
# # P loadings
# mnip$loadings
# mpls$loadings
# same(mnip$loadings, mpls$loadings, tol=1e-2 )
# # TRUE
# 
# # T scores
# mnip$scores
# mpls$scores
# same( sweep(mnip$scores, 2, mnip$eig, "*"), mpls$scores)
# # TRUE

## ----eval=FALSE-------------------------------------------------------------------------
# library(mixOmics)
# library(nipals)
# mnip <- nipals::nipals(B2, gramschmidt=FALSE)
# mmix <- mixOmics::nipals(scale(B2), ncomp=5)

## ----eval=FALSE-------------------------------------------------------------------------
# # eigenvalues
# mnip$eig
# mmix$eig
# same(mnip$eig, mmix$eig)
# # TRUE
# 
# # P loadings
# mnip$loadings
# mmix$p
# same(mnip$loadings, mmix$p, tol=1e-2)
# # TRUE
# 
# # T scores
# mnip$scores
# mmix$t
# same(mnip$scores, mmix$t, tol=1e-2)
# # TRUE

## ----eval=FALSE-------------------------------------------------------------------------
# set.seed(43)
# Bbig <- matrix(rnorm(100*100), nrow=100)
# Bbig2 <- Bbig
# Bbig2[1,1] <- NA

## ----eval=FALSE-------------------------------------------------------------------------
# system.time(ade4::nipals(Bbig2, nf=1)) # Only 1 PC!
# ##  user  system elapsed
# ## 42.09    0.00   42.14

## ----eval=FALSE-------------------------------------------------------------------------
# system.time(plsdepot::nipals(Bbig2, comps=1)) # Only 1 PC !
# #   user  system elapsed
# #    0.5     0.0     0.5
# system.time(plsdepot::nipals(Bbig2, comps=100)) # 100 PCs
# #   user  system elapsed
# #  30.19    0.00   30.18

## ----eval=FALSE-------------------------------------------------------------------------
# system.time(mixOmics::nipals(scale(Bbig2), ncomp=100)) # 100 PCs
# #   user  system elapsed
# #  20.70    0.00   20.81

## ----eval=FALSE-------------------------------------------------------------------------
# system.time(nipals::nipals(Bbig2, ncomp=100, gramschmidt=FALSE)) # 100 PCs
# #   user  system elapsed
# #   2.93    0.00    2.93

## ----eval=FALSE-------------------------------------------------------------------------
# system.time(nipals::nipals(Bbig2, ncomp=100, gramschmidt=TRUE)) # 100 PCs
# #   user  system elapsed
# #    3.6     0.0     3.6

## ----eval=FALSE-------------------------------------------------------------------------
# system.time(empca(Bbig2, ncomp=100, gramschmidt=FALSE)) # 100 PCs
# #   user  system elapsed
# #   1.03    0.00    1.03
# system.time(empca(Bbig2, ncomp=100, gramschmidt=TRUE)) # 100 PCs
# #   user  system elapsed
# #  10.44    0.00   10.45