Carlos, Sim! a função "eigen" é para decomposição espectral de matrizes quadradas (geralmente de covariâncias ou correlações). A função "svd" generaliza a decomposição. Ou seja, podendo ser aplicada também em matrizes não quadradas. No pacote bpca () ela é a principal função usada no biplot. `bpca.default` <- function(x, lambda.ini=1, lambda.end=2, var.position=2, var.center=TRUE, var.scale=TRUE, method=c('hj', 'sqrt', 'jk', 'gh'), var.rb=FALSE, var.rd=FALSE, limit=10, ...) { stopifnot(is.matrix(x) || is.data.frame(x)) n.lambdas <- (lambda.end - lambda.ini + 1) if(n.lambdas < 2 || n.lambdas > 3) stop('Please, check the parameters: lambda.ini and lambda.end:\n', 'It should be 2 (to bpca.2d) or 3 (to bpca.3d).\n\n') if(!any(var.position == 1:2)) stop('Please, check the parameters: var.position:\n', 'It should be 1 (rows) or 2 (columns).\n\n') x <- as.matrix(x) if(var.position == 1) x <- as.matrix(t(x)) obj.names <- rownames(x) var.names <- colnames(x) x.scaled <- scale(x, center=var.center, scale=var.scale) # scalle variables svdx.scaled <- svd(x.scaled) # svd of variables # variables rownames(svdx.scaled$u) <- obj.names rownames(svdx.scaled$v) <- var.names colnames(svdx.scaled$v) <- paste('PC', 1:length(svdx.scaled$d), sep='') # variables scaled s2.var.scaled <- diag(svdx.scaled$d[lambda.ini:lambda.end]) switch(match.arg(method), hj = { g.var.scaled <- svdx.scaled$u[ ,lambda.ini:lambda.end] %*% s2.var.scaled h.var.scaled <- s2.var.scaled %*% t(svdx.scaled$v[ ,lambda.ini:lambda.end]) hl.var.scaled <- t(h.var.scaled) }, sqrt = { g.var.scaled <- svdx.scaled$u[ ,lambda.ini:lambda.end] %*% sqrt(s2.var.scaled) h.var.scaled <- sqrt(s2.var.scaled) %*% t(svdx.scaled$v[ ,lambda.ini:lambda.end]) hl.var.scaled <- t(h.var.scaled) }, jk = { g.var.scaled <- svdx.scaled$u[ ,lambda.ini:lambda.end] %*% s2.var.scaled h.var.scaled <- t(svdx.scaled$v[ ,lambda.ini:lambda.end]) hl.var.scaled <- t(h.var.scaled) }, gh = { g.var.scaled <- sqrt(nrow(x)-1) * svdx.scaled$u[,lambda.ini:lambda.end] h.var.scaled <- 1/sqrt(nrow(x)-1) * s2.var.scaled %*% t(svdx.scaled$v[,lambda.ini:lambda.end]) hl.var.scaled <- t(h.var.scaled) }) if(is.null(rownames(x.scaled))) row.names <- 1:nrow(x.scaled) else row.names <- rownames(x.scaled) if(is.null(colnames(x.scaled))) col.names <- paste('V', 1:ncol(x.scaled), sep='') else col.names <- colnames(x.scaled) pc.names <- paste('PC', lambda.ini:lambda.end, sep='') rownames(g.var.scaled) <- row.names colnames(g.var.scaled) <- pc.names rownames(hl.var.scaled) <- col.names colnames(hl.var.scaled) <- pc.names # variables if(var.rb) var.rb.res <- var.rbf(hl.var.scaled) else var.rb.res <- NA if(var.rb & var.rd) var.rd.res <- var.rdf(x.scaled, var.rb.res, limit) else var.rd.res <- NA res <- list(call=match.call(), eigenvalues=svdx.scaled$d, eigenvectors=svdx.scaled$v, number=seq(lambda.ini, lambda.end, 1), importance=rbind(general=round(sum(svdx.scaled$d[lambda.ini:lambda.end]^2) / sum(svdx.scaled$d^2), 3), partial=round(sum(svdx.scaled$d[lambda.ini:lambda.end]^2) / sum(svdx.scaled$d[lambda.ini:length(svdx.scaled$d)]^2), 3)), coord=list(objects=g.var.scaled, variables=hl.var.scaled), var.rb=var.rb.res, var.rd=var.rd.res) colnames(res$importance) <- 'explained' if(ncol(g.var.scaled) == 2) class(res) <- c('bpca.2d', 'bpca', 'list') else if(ncol(g.var.scaled) == 3) class(res) <- c('bpca.3d', 'bpca', 'list') invisible(res) } Abs, -- ///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\ Jose Claudio Faria Estatistica - Prof. Pleno UESC/DCET/Brasil joseclaudio.faria at gmail.com ///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\