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Unfolding <- function(A, ENV = NULL, TransAbund = "Gaussian Columns", offset = 0.5, weight = "All_1", Constrained = FALSE, TransEnv = "Standardize columns", InitConfig = "SVD",
model = "Ratio", condition = "Columns", Algorithm="SMACOF", OptimMethod="CG", r = 2, maxiter = 100, tolerance = 1e-05, lambda = 1, omega = 0, plot = FALSE) {
# offset is the quantity added to the zeros of the table
models = c("Absolute", "Ratio", "Interval", "Ordinal")
conditions = c("Matrix", "Columns")
InitConfigs = c("SVD", "Random", "Correspondences", "PCAEnvironment")
TransAbunds = c("None", "Gaussian", "Column Percent", "Gaussian Columns", "Inverse Square Root", "Divide by Column Maximum")
weights = c("All_1", "0 absences")
TransEnvs = c("Raw Data", "Column centering", "Standardize columns")
Algorithms=c("SMACOF", "GD")
SiteNames = rownames(A)
SpeciesNames = colnames(A)
# Arguments passed as numbers are converted into strings
if (is.numeric(model))
model = models[model]
if (is.numeric(condition))
condition = conditions[condition]
if (is.numeric(InitConfig))
InitConfig = InitConfigs[InitConfig]
if (is.numeric(TransAbund))
TransAbund = TransAbunds[TransAbund]
if (is.numeric(weight))
weight = weights[weight]
if (is.numeric(TransEnv))
TransEnv = TransEnvs[TransEnv]
if (is.numeric(Algorithm))
Algorithm = Algorithms[Algorithm]
if (is.data.frame(A))
A = as.matrix(A)
rownames(A) <- SiteNames
if (!is.null(ENV)) {
if (is.data.frame(ENV))
ENV = as.matrix(ENV)
#Initial Weighted averages (before transformation of abundances)
c = apply(A, 2, sum)
W1 = diagonal(1/c) %*% t(A) %*% ENV
rownames(W1) = SpeciesNames
VarNames = colnames(ENV)
# Useful Parameters of the environmental variables
Minima_Z = apply(ENV, 2, min)
Maxima_Z = apply(ENV, 2, max)
Medians_Z = apply(ENV, 2, quantile, 0.5)
P25_Z = apply(ENV, 2, quantile, 0.25)
P75_Z = apply(ENV, 2, quantile, 0.75)
Means = apply(ENV, 2, mean)
Deviations = apply(ENV, 2, sd)
ENV = InitialTransform(ENV, transform = TransEnv)$X
rownames(ENV) = SiteNames
colnames(ENV) = VarNames
}
n = dim(A)[1]
m = dim(A)[2]
# Transforming the abundance/preference values
P = TransfUnfold(A, TransAbund, offset)
# Calculating Weights
if (weight == "All_1") {
W = matrix(1, n, m)
} else {
W = matrix(as.numeric(A > 0), n, m)
}
# Calculating Initial Configurations
if (InitConfig == "SVD") {
B = -0.5 * (diag(n) - matrix(1, n, n)/(n)) %*% P^2 %*% (diag(m) - matrix(1, m, m)/(m))
sdec = svd(B)
X0 = sdec$u[, 1:r] %*% diag(sqrt(sdec$d[1:r]))
Y0 = sdec$v[, 1:r] %*% diag(sqrt(sdec$d[1:r]))
}
if (InitConfig == "Random") {
X0 = matrix(rnorm(n * r), n, r)
media = ColMeans(X0)
X0 = X0 - matrix(1, n, 1) %*% media
Y0 = matrix(rnorm(m * r), m, r)
media = ColMeans(Y0)
Y0 = Y0 - matrix(1, m, 1) %*% media
}
if (InitConfig == "Correspondences") {
CAS = CA(P)
X0 = CAS$RowCoordinates
Y0 = CAS$ColCoordinates
}
# Calculating Unfolding coordinates
if (Algorithm=="SMACOF")
Unfold = UnfoldingSMACOF(P, W = W, Constrained = Constrained, ENV = ENV, model = model, condition = condition, r = r, maxiter = maxiter, tolerance = tolerance,
lambda = 1, omega = 0, X0 = X0, Y0 = Y0)
if (Algorithm=="GD")
Unfold = UnfoldingGD(P, W = W, Constrained = Constrained, ENV = ENV, model = model, condition = condition, r = r, maxiter = maxiter, tolerance = tolerance,
lambda = 1, omega = 0, X0 = X0, Y0 = Y0, OptimMethod=OptimMethod)
Unfold$call <- match.call()
Unfold$Abundances = A
Unfold$Offset = offset
if (!is.null(ENV)) {
# Useful Parameters of the environmental variables
Unfold$Minima_Z = Minima_Z
Unfold$Maxima_Z = Maxima_Z
Unfold$Medians_Z = Medians_Z
Unfold$P25_Z = P25_Z
Unfold$P75_Z = P75_Z
Unfold$Means_Z = Means
Unfold$Deviations_Z = Deviations
p = dim(ENV)[2]
Unfold$Weighted_Averages = W1
}
Unfold$Initial = InitConfig
if (!is.null(ENV)) {
# Calculating environmental coordinates
Unfold$InterSet = cor(ENV, Unfold$X)
Unfold$Env_Var_Scores = t(ENV) %*% Unfold$X %*% solve(t(Unfold$X) %*% Unfold$X)
Unfold$nvars = ncol(ENV)
ESP = Unfold$X %*% t(Unfold$Env_Var_Scores)
Unfold$Env_fit = sum(ESP^2)/sum(ENV^2)
Unfold$Var_Fit = matrix(1, p, 1)
rownames(Unfold$Var_Fit) <- VarNames
Unfold$QualityVars=cor(ENV, Unfold$X)^2
for (j in 1:p) Unfold$Var_Fit[j] = sum(ESP[, j]^2)/sum(ENV[, j]^2)
}
if (plot)
plot(Unfold, mode = "s")
return(Unfold)
}
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