#'
#' Normalize a vector or a matrix (by columns), using euclidian norm
#'
-#' @param X Vector or matrix to be normalized
+#' @param x Vector or matrix to be normalized
#'
-#' @return The normalized matrix (1 column if X is a vector)
+#' @return The normalized matrix (1 column if x is a vector)
#'
+#' @examples
+#' x <- matrix(c(1,2,-1,3), ncol=2)
+#' normalize(x) #column 1 is 1/sqrt(5) (1 2),
+#' #and column 2 is 1/sqrt(10) (-1, 3)
#' @export
-normalize = function(X)
+normalize <- function(x)
{
- X = as.matrix(X)
- norm2 = sqrt( colSums(X^2) )
- sweep(X, 2, norm2, '/')
+ x <- as.matrix(x)
+ norm2 <- sqrt( colSums(x^2) )
+ sweep(x, 2, norm2, '/')
}
# Computes a tensor-vector product
#
# @return Matrix of size dxd
#
-.T_I_I_w = function(Te, w)
+.T_I_I_w <- function(Te, w)
{
- d = length(w)
- Ma = matrix(0,nrow=d,ncol=d)
- for (j in 1:d)
- Ma = Ma + w[j] * Te[,,j]
- Ma
+ d <- length(w)
+ Ma <- matrix(0,nrow=d,ncol=d)
+ for (j in 1:d)
+ Ma <- Ma + w[j] * Te[,,j]
+ Ma
}
# Computes the second-order empirical moment between input X and output Y
#
# @return Matrix of size dxd
#
-.Moments_M2 = function(X, Y)
+.Moments_M2 <- function(X, Y)
{
- n = nrow(X)
- d = ncol(X)
- M2 = matrix(0,nrow=d,ncol=d)
- matrix( .C("Moments_M2", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
- pd=as.integer(d), M2=as.double(M2), PACKAGE="morpheus")$M2, nrow=d, ncol=d)
+ n <- nrow(X)
+ d <- ncol(X)
+ M2 <- matrix(0,nrow=d,ncol=d)
+ matrix( .C("Moments_M2", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
+ pd=as.integer(d), M2=as.double(M2), PACKAGE="morpheus")$M2, nrow=d, ncol=d)
}
# Computes the third-order empirical moment between input X and output Y
#
# @return Array of size dxdxd
#
-.Moments_M3 = function(X, Y)
+.Moments_M3 <- function(X, Y)
{
- n = nrow(X)
- d = ncol(X)
- M3 = array(0,dim=c(d,d,d))
- array( .C("Moments_M3", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
- pd=as.integer(d), M3=as.double(M3), PACKAGE="morpheus")$M3, dim=c(d,d,d) )
+ n <- nrow(X)
+ d <- ncol(X)
+ M3 <- array(0,dim=c(d,d,d))
+ array( .C("Moments_M3", X=as.double(X), Y=as.double(Y), pn=as.integer(n),
+ pd=as.integer(d), M3=as.double(M3), PACKAGE="morpheus")$M3, dim=c(d,d,d) )
}
#' computeMoments
#'
#' @return A list L where L[[i]] is the i-th cross-moment
#'
+#' @examples
+#' X <- matrix(rnorm(100), ncol=2)
+#' Y <- rbinom(100, 1, .5)
+#' M <- computeMoments(X, Y)
+#'
#' @export
computeMoments = function(X, Y)
- list( colMeans(Y * X), .Moments_M2(X,Y), .Moments_M3(X,Y) )
+ list( colMeans(Y * X), .Moments_M2(X,Y), .Moments_M3(X,Y) )
# Find the optimal assignment (permutation) between two sets (minimize cost)
#
-# @param distances The distances matrix, in columns (distances[i,j] is distance between i
-# and j)
+# @param distances The distances matrix, in columns
+# (distances[i,j] is distance between i and j)
#
# @return A permutation minimizing cost
#
-.hungarianAlgorithm = function(distances)
+.hungarianAlgorithm <- function(distances)
{
- n = nrow(distances)
- .C("hungarianAlgorithm", distances=as.double(distances), pn=as.integer(n),
- assignment=integer(n), PACKAGE="morpheus")$assignment
+ n <- nrow(distances)
+ .C("hungarianAlgorithm", distances=as.double(distances), pn=as.integer(n),
+ assignment=integer(n), PACKAGE="morpheus")$assignment
}
#' alignMatrices
#' Align a set of parameters matrices, with potential permutations.
#'
#' @param Ms A list of matrices, all of same size DxK
-#' @param ref Either a reference matrix or "mean" to align on empirical mean
+#' @param ref A reference matrix to align other matrices with
#' @param ls_mode How to compute the labels assignment: "exact" for exact algorithm
#' (default, but might be time-consuming, complexity is O(K^3) ), or "approx1", or
#' "approx2" to apply a greedy matching algorithm (heuristic) which for each column in
#'
#' @return The aligned list (of matrices), of same size as Ms
#'
+#' @examples
+#' m1 <- matrix(c(1,1,0,0),ncol=2)
+#' m2 <- matrix(c(0,0,1,1),ncol=2)
+#' ref <- m1
+#' Ms <- list(m1, m2, m1, m2)
+#' a <- alignMatrices(Ms, ref, "exact")
+#' # a[[i]] is expected to contain m1 for all i
+#'
#' @export
-alignMatrices = function(Ms, ref, ls_mode)
+alignMatrices <- function(Ms, ref, ls_mode=c("exact","approx1","approx2"))
{
- if (!is.matrix(ref) && ref != "mean")
- stop("ref: matrix or 'mean'")
- if (!ls_mode %in% c("exact","approx1","approx2"))
- stop("ls_mode in {'exact','approx1','approx2'}")
-
- K <- ncol(Ms[[1]])
- if (is.character(ref)) #ref=="mean"
- m_sum = Ms[[1]]
- L <- length(Ms)
- for (i in ifelse(is.character(ref),2,1):L)
- {
- m_ref = if (is.character(ref)) m_sum / (i-1) else ref
- m = Ms[[i]] #shorthand
+ if (!is.matrix(ref) || any(is.na(ref)))
+ stop("ref: matrix, no NAs")
+ ls_mode <- match.arg(ls_mode)
- if (ls_mode == "exact")
- {
- #distances[i,j] = distance between m column i and ref column j
- distances = apply( m_ref, 2, function(col) ( sqrt(colSums((m-col)^2)) ) )
- assignment = .hungarianAlgorithm(distances)
- col <- m[,assignment]
- if (is.list(Ms)) Ms[[i]] <- col else Ms[,,i] <- col
- }
- else
- {
- # Greedy matching:
- # approx1: li[[i]][,j] is assigned to m[,k] minimizing dist(li[[i]][,j],m[,k'])
- # approx2: m[,j] is assigned to li[[i]][,k] minimizing dist(m[,j],li[[i]][,k'])
- available_indices = 1:K
- for (j in 1:K)
- {
- distances =
- if (ls_mode == "approx1")
- {
- apply(as.matrix(m[,available_indices]), 2,
- function(col) ( sqrt(sum((col - m_ref[,j])^2)) ) )
- }
- else #approx2
- {
- apply(as.matrix(m_ref[,available_indices]), 2,
- function(col) ( sqrt(sum((col - m[,j])^2)) ) )
- }
- indMin = which.min(distances)
- if (ls_mode == "approx1")
- {
- col <- m[ , available_indices[indMin] ]
- if (is.list(Ms)) Ms[[i]][,j] <- col else Ms[,j,i] <- col
- }
- else #approx2
- {
- col <- available_indices[indMin]
- if (is.list(Ms)) Ms[[i]][,col] <- m[,j] else Ms[,col,i] <- m[,j]
- }
- available_indices = available_indices[-indMin]
- }
- }
+ K <- ncol(Ms[[1]])
+ L <- length(Ms)
+ for (i in 1:L)
+ {
+ m <- Ms[[i]] #shorthand
- # Update current sum with "label-switched" li[[i]]
- if (is.character(ref)) #ref=="mean"
- m_sum = m_sum + Ms[[i]]
- }
- Ms
+ if (ls_mode == "exact")
+ {
+ #distances[i,j] = distance between m column i and ref column j
+ distances = apply( ref, 2, function(col) ( sqrt(colSums((m-col)^2)) ) )
+ assignment = .hungarianAlgorithm(distances)
+ col <- m[,assignment]
+ Ms[[i]] <- col
+ }
+ else
+ {
+ # Greedy matching:
+ # approx1: li[[i]][,j] is assigned to m[,k] minimizing dist(li[[i]][,j],m[,k'])
+ # approx2: m[,j] is assigned to li[[i]][,k] minimizing dist(m[,j],li[[i]][,k'])
+ available_indices = 1:K
+ for (j in 1:K)
+ {
+ distances =
+ if (ls_mode == "approx1")
+ {
+ apply(as.matrix(m[,available_indices]), 2,
+ function(col) ( sqrt(sum((col - ref[,j])^2)) ) )
+ }
+ else #approx2
+ {
+ apply(as.matrix(ref[,available_indices]), 2,
+ function(col) ( sqrt(sum((col - m[,j])^2)) ) )
+ }
+ indMin = which.min(distances)
+ if (ls_mode == "approx1")
+ {
+ col <- m[ , available_indices[indMin] ]
+ Ms[[i]][,j] <- col
+ }
+ else #approx2
+ {
+ col <- available_indices[indMin]
+ Ms[[i]][,col] <- m[,j]
+ }
+ available_indices = available_indices[-indMin]
+ }
+ }
+ }
+ Ms
}
projects / morpheus.git / blobdiff