## -----------------------------------------------------------------------------
set.seed(1123)


## -----------------------------------------------------------------------------
#N <- matrix( c(1,2,1,3,2,5,1,7,3,6,2,8),
#             nrow = 4, ncol = 3,
#             dimnames = list( c("i1", "i2", "i3", "i4"),
#                              c("v1", "v2", "v3")) )

N <- matrix( c(4, 3, 6, 2, 2, 3, 0, 0, 2, 0,
               2, 4, 4, 0, 5, 3, 0, 2, 1, 1,
               4, 2, 5, 5, 0, 1, 0, 0, 1, 4,
               4, 2, 2, 1, 1, 0, 0,11, 0, 1,
               1, 1, 3, 3, 4, 0, 1, 1, 2, 6,
               2, 1, 1, 3, 1, 3, 4, 3, 4, 0,
               2, 0, 1, 3, 2, 0, 1,10, 0, 3,
               4, 3, 3, 1, 1, 2, 5, 1, 2, 0,
               1, 2, 0, 5, 3, 1, 3, 1, 0, 6),
               nrow = 10, ncol = 9,
               dimnames = list(
                 c("red", "orange", "yellow", "green",
                   "blue", "purple", "white", "black",
                   "pink", "brown"),
                 c("video", "jazz", "country", "rap",
                   "pop", "opera", "low F", "high F",
                   "middle F")) )

n <- sum(sum(N))
print(N, digits=2)
print(n)


## -----------------------------------------------------------------------------
P <- (1/n) * N
print(P, digits=2)


## -----------------------------------------------------------------------------
r <- rowSums(P)
c <- colSums(P)
print(r, digits=2)
print(c, digits=2)


## -----------------------------------------------------------------------------
Dr <- diag(r)
Dc <- diag(c)
print(Dr, digits=2)
print(Dc, digits=2)


## -----------------------------------------------------------------------------
# Pour construire R ou C, il n'est pas nécessaire de construire Dr ou Dc.
# L'utilisation de la fonction sweep est plus efficace.
R <- sweep(P, MARGIN = 1, 1/r, '*')
R <- sweep(P, MARGIN = 1, 1/r, '*')
print(R, digits=2)
print(C, digits=2)


## -----------------------------------------------------------------------------
# On vérifie que la somme des éléments d'une ligne de R ou C est égale à 1.
print(rowSums(R), digits=2)
print(rowSums(C), digits=2)


## -----------------------------------------------------------------------------
scaleR <- 1/sqrt(r)
scaleC <- 1/sqrt(c)
S <- sweep(P - r %*% t(c), 1, scaleR, FUN = "*")
S <- sweep(S, 2, scaleC, FUN = "*")
dec <- svd(S)
Phi <- sweep(dec$u, 1, scaleR, FUN="*")
F <- sweep(Phi, 2, dec$d, FUN="*")
Gam <- sweep(dec$v, 1, scaleC, FUN="*")
G <- sweep(Gam, 2, dec$d, FUN="*")
plot(c(F[,1], G[,1]), c(F[,2], G[,2]), main = "x: d1, y: d2", type = "n",
     xlab="", ylab="", asp = 1, xaxt = "n", yaxt = "n")
text(c(F[,1], G[,1]), c(F[,2], G[,2]), c(rownames(P), colnames(P)),
     adj = 0, cex = 0.6)
points(0, 0, pch = 3)


## -----------------------------------------------------------------------------
plot(c(F[,1], Gam[,1]), c(F[,2], Gam[,2]), main = "x: d1, y: d2", type = "n",
     xlab="", ylab="", asp = 1, xaxt = "n", yaxt = "n")
text(c(F[,1], Gam[,1]), c(F[,2], Gam[,2]), c(rownames(P), colnames(P)),
     adj = 0, cex = 0.6)
points(0, 0, pch = 3)