## A random matrix
dummy_matrix <- matrix(rnorm(90), 9, 10)
## ancestral.dist
## A random tree with node labels
rand_tree <- rtree(5) ; rand_tree$node.label <- paste0("n", 1:4)
## Adding the tip and node names to the matris
rownames(dummy_matrix) <- c(rand_tree$tip.label, rand_tree$node.label)
## Calculating the distances to the ancestors
ancestral.dist(dummy_matrix, tree = rand_tree)
## Calculating the manhattan distances to the root
ancestral.dist(dummy_matrix, tree = rand_tree,
to.root = TRUE, method = "manhattan")
## angles
## The angles in degrees of each axis
angles(dummy_matrix)
## The angles in slope from the 1:1 slope (Beta = 1)
angles(dummy_matrix, unit = "slope", base = 1)
## centroids
## Distances between each row and centroid of the matrix
centroids(dummy_matrix)
## Distances between each row and an arbitrary point
centroids(dummy_matrix, centroid = c(1,2,3,4,5,6,7,8,9,10))
## Distances between each row and the origin
centroids(dummy_matrix, centroid = 0)
## convhull.surface
## Making a matrix with more elements than dimensions (for convhull)
thinner_matrix <- matrix(rnorm(90), 18, 5)
## Convex hull hypersurface of a matrix
convhull.surface(thinner_matrix)
## convhull.volume
## Convex hull volume of a matrix
convhull.volume(thinner_matrix)
## deviations
## The deviations from the least square hyperplane
deviations(dummy_matrix)
## The deviations from the plane between the x and y axis
deviations(dummy_matrix, hyperplane = c(0,1,1,0,0,0,0,0,0,0,0))
## diagonal
## Matrix diagonal
diagonal(dummy_matrix) # WARNING: only valid if the dimensions are orthogonal
## disalignment
## Two dummy matrices
matrix_1 <- matrix(rnorm(16), 4, 4)
matrix_2 <- matrix(rnorm(16), 4, 4)
## Measuring the disalignment of matrix_1 from matrix_2
disalignment(matrix_1, matrix_2)
## Same but using the 2nd major axis of the 0.75 CI ellipse
## from matrix_2 and the first point from matrix_1.
disalignment(matrix_1, matrix_2,
axis = 2, level = 0.75,
point.to.reject = 1)
## displacements
## displacement ratios (from the centre)
displacements(dummy_matrix)
## displacement ratios (from an arbitrary point)
displacements(dummy_matrix, reference = c(1,2,3,4,5,6,7,8,9,10))
## displacement ratios from the centre (manhattan distance)
displacements(dummy_matrix, method = "manhattan")
## edge.length.tree
## Making a dummy tree with node labels
dummy_tree <- makeNodeLabel(rtree((nrow(dummy_matrix)/2)+1))
## Naming the elements in the matrix
named_matrix <- dummy_matrix
rownames(named_matrix) <- c(dummy_tree$tip.label,
dummy_tree$node.label)
## The total edge length of each element in the matrix (to the root)
edge.length.tree(named_matrix, tree = dummy_tree)
## The edge lengths for each edge leading to the elements in the matrix
edge.length.tree(named_matrix, tree = dummy_tree, to.root = FALSE)
## ellipsoid.volume
## Ellipsoid volume of a matrix
ellipsoid.volume(dummy_matrix)
## Calculating the same volume with provided eigen values
ordination <- prcomp(dummy_matrix)
## Calculating the ellipsoid volume by providing your own eigen values
ellipsoid.volume(ordination$x, method = ordination$sdev^2)
## func.div
## Functional divergence
func.div(dummy_matrix)
## func.eve
## Functional evenness
func.eve(dummy_matrix)
## Functional evenness (based on manhattan distances)
func.eve(dummy_matrix, method = "manhattan")
## group.dist
## The distance between groups
dummy_matrix2 <- matrix(runif(40, min = 2, max = 4), 4, 10)
## The minimum distance between both groups
group.dist(dummy_matrix, dummy_matrix2)
## The distance between both groups' centroids
group.dist(dummy_matrix, dummy_matrix2, probs = 0.5)
## The minimum distance between the 50% CI of each group
group.dist(dummy_matrix, dummy_matrix2, probs = c(0.25, 0.75))
## mode.val
## Modal value of a vector
mode.val(dummy_matrix)
## neighbours
## The nearest neighbour euclidean distances
neighbours(dummy_matrix)
## The furthest neighbour manhattan distances
neighbours(dummy_matrix, which = max, method = "manhattan")
## pairwise.dist
## The pairwise distance
pairwise.dist(dummy_matrix)
## The average squared pairwise distance
mean(pairwise.dist(dummy_matrix)^2)
## equal to:
# geiger::disparity(data = dummy_matrix)
## point.dist
## The distances from the rows dummy_matrix
## to the centroids of dummy_matrix2
point.dist(dummy_matrix, dummy_matrix2)
## The average distances from dummy_matrix
## to the centroids of dummy_matrix2
mean(point.dist(dummy_matrix, dummy_matrix2))
## The manhattan distance from the rows dummy_matrix
## to the standard deviation of dummy_matrix2
point.dist(dummy_matrix, dummy_matrix2, point = sd, method = "manhattan")
## projections
## The distances on the vector defined from the centre of
## the matrix to its centroid (default)
projections(dummy_matrix)
## The distances from the vector defined from the third
## element of the matrix to the point of coordinated
## c(1,1,1, ...) the matrix to its centroid (default)
projections(dummy_matrix, measure = "distance",
point1 = dummy_matrix[3, ],
point2 = 1)
## projections.tree
## Making a dummy tree with node labels
dummy_tree <- makeNodeLabel(rtree((nrow(dummy_matrix)/2)+1))
## Naming the elements in the matrix
named_matrix <- dummy_matrix
rownames(named_matrix) <- c(dummy_tree$tip.label,
dummy_tree$node.label)
## The projection on the vector defined from the root of
## the tree to the ancestor of each element in the matrix
projections.tree(named_matrix, dummy_tree,
type = c("root", "ancestor"))
## The rejection from the vector defined from the centroid
## of the nodes to the centroids of the tips
projections.tree(named_matrix, dummy_tree,
type = c("nodes", "tips"),
measure = "distance")
## A user function that define coordinates based on the
## centroid of the three first nodes
user.fun <- function(matrix, tree, row = NULL) {
return(colMeans(matrix[tree$node.label[1:3], ]))
}
## The projection on the vector defined by the coordinates
## 0,0,0 and a user defined function
projections.tree(named_matrix, dummy_tree,
type = c(0, user.fun))
## projections.between
## Two dummy matrices
matrix_1 <- matrix(rnorm(16), 4, 4)
matrix_2 <- matrix(rnorm(16), 4, 4)
## Projecting the major axis of matrix_2 onto the one from matrix_1
projections.between(matrix_1, matrix_2)
## Projecting both second major 0.75 axes
## and getting the rejections (see projections() for option details)
projections.between(matrix_1, matrix_2,
measure = "distance",
axis = 2, level = 0.75)
## quantiles
## The 95 quantiles
quantiles(dummy_matrix)
## The 100 quantiles (which are equal to the ranges)
quantiles(dummy_matrix, quantile = 100) == ranges(dummy_matrix) # All TRUE
## radius
## The maximal radius of each axis (maximum distance from centre of each axis)
radius(dummy_matrix)
## ranges
## ranges of each column in a matrix
ranges(dummy_matrix)
## ranges of each column in the matrix corrected using the kth root
ranges(dummy_matrix, k.root = TRUE)
## roundness
## calculating the variance-covariance of the dummy_matrix
vcv <- var(dummy_matrix)
## calculating the roundness of it
roundness(vcv)
## calculating the roundness of the dummy matrix by calculating the vcv
roundness(dummy_matrix, vcv = TRUE)
## span.tree.length
## Minimum spanning tree length (default)
span.tree.length(dummy_matrix)
## Minimum spanning tree length from a distance matrix (faster)
distance <- as.matrix(dist(dummy_matrix))
span.tree.length(distance)
## Minimum spanning tree length based on Manhattan distance
span.tree.length(dummy_matrix, method = "manhattan")
span.tree.length(as.matrix(dist(dummy_matrix, method = "manhattan"))) # Same
## variances
## variances of a each column in the matrix
variances(dummy_matrix)
## variances of a each column in the matrix corrected using the kth root
variances(dummy_matrix, k.root = TRUE)
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