| Title: | combinatorics utilities |
|---|---|
| Description: | routines for combinatorics |
| Authors: | Scott Chasalow |
| Maintainer: | Vince Carey <[email protected]> |
| License: | GPL-2 |
| Version: | 0.0-8 |
| Built: | 2024-08-18 06:29:04 UTC |
| Source: | CRAN |
Generate all combinations of the elements of x taken m at a time. If x is a positive integer, returns all combinations of the elements of seq(x) taken m at a time. If argument "fun" is not null, applies a function given by the argument to each point. If simplify is FALSE, returns a list; else returns a vector or an array. "..." are passed unchanged to function given by argument fun, if any.
combn2:Generate all combinations of the elements of x taken two at a time. If x is missing, generate all combinations of 1:n taken two at a time (that is, the indices of x that would give all combinations of the elements of x if x with length n had been given). Exactly one of arguments "x" and "n" should be given; no provisions for function evaluation.
nCm: Compute the binomial coefficient ("n choose m"), where n is any real number and m is any integer. Arguments n and m may be vectors; they will be replicated as necessary to have the same length. Argument tol controls rounding of results to integers. If the difference between a value and its nearest integer is less than tol, the value returned will be rounded to its nearest integer. To turn off rounding, use tol = 0. Values of tol greater than the default should be used only with great caution, unless you are certain only integer values should be returned.
combn(x, m, fun=NULL, simplify=TRUE, ...)combn(x, m, fun=NULL, simplify=TRUE, ...)
x |
vector source for combinations |
m |
number of elements |
fun |
function to be applied to each combination (may be null) |
simplify |
logical, if FALSE, returns a list, otherwise returns vector or array |
... |
args to fun |
Nijenhuis, A. and Wilf, H.S. (1978) Combinatorial Algorithms for Computers and Calculators. NY: Academic Press.
see simplify argument
Code by Scott Chasalow, R package and doc prep by Vince Carey, [email protected]
~put references to the literature/web site here ~
combn(letters[1:4], 2) combn(10, 5, min) # minimum value in each combination # Different way of encoding points: combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins = 4) #Compute support points and (scaled) probabilities for a #Multivariate-Hypergeometric(n = 3, N = c(4,3,2,1)) p.f.: # table.mat(t(combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate,nbins=4)))combn(letters[1:4], 2) combn(10, 5, min) # minimum value in each combination # Different way of encoding points: combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins = 4) #Compute support points and (scaled) probabilities for a #Multivariate-Hypergeometric(n = 3, N = c(4,3,2,1)) p.f.: # table.mat(t(combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate,nbins=4)))
density of multinomial
dmnom(x, size=sum(x), prob=stop("no prob arg"))dmnom(x, size=sum(x), prob=stop("no prob arg"))
x |
vector |
size |
total |
prob |
parameter vector (sums to 1) |
code by Scott Chasalow, R pack and maint by VJ Carey <[email protected]>
dmnom(c(1,1,4,4),10,c(.2,.2,.3,.3))dmnom(c(1,1,4,4),10,c(.2,.2,.3,.3))
Generate all points on a hypercuboid lattice.
hcube(x, scale, translation)hcube(x, scale, translation)
x |
Argument x is an integer vector giving the extent of each dimension; the number of dimensions is length(x). |
scale |
Argument scale is a vector of real numbers giving an amount by which to multiply the points in each dimension; it will be replicated as necessary to have the same length as x. |
translation |
Argument translate is a vector of real numbers giving an amount to translate (from the "origin", rep(1,length(x))) the points in each dimension; it will be replicated as necessary to have the same length as x. To use rep(0,length(x)) as the origin, use translation = -1. Scaling, if any, is done BEFORE translation. |
A prod(x) by length(x) numeric matrix; element (i,j) gives the location of point i in the jth dimension. The first column (dimension) varies most rapidly.
code by Scott Chasalow, R pack and maint by VJ Carey <[email protected]>
~put references to the literature/web site here ~
fac.design, expand.grid
Computes the number of points on a (p, n)-simplex lattice; that is, the number of p-part compositions of n. This gives the number of points in the support space of a Multinomial(n, q) distribution, where p == length(q).
Arguments p and n are replicated as necessary to have the length of the longer of them.
nsimplex(p, n)nsimplex(p, n)
p |
vector of integers |
n |
vector of integers |
integer
nsimplex(3,5)nsimplex(3,5)
Generates all permutations of the elements of x, in a minimal- change order. If x is a positive integer, returns all permutations of the elements of seq(x). If argument "fun" is not null, applies a function given by the argument to each point. "..." are passed unchanged to the function given by argument fun, if any.
permn(x, fun=NULL, ...)permn(x, fun=NULL, ...)
x |
vector |
fun |
if non.null, applied at each perm |
... |
args passed to fun |
list: each component is either a permutation, or the results of applying fun to a permutation
Reingold, E.M., Nievergelt, J., Deo, N. (1977) Combinatorial Algorithms: Theory and Practice. NJ: Prentice-Hall. pg. 170.
sample, fact, combn, hcube, xsimplex
# Convert output to a matrix of dim c(6, 720) t(array(unlist(permn(6)), dim = c(6, gamma(7)))) # A check that every element occurs the same number of times in each # position apply(t(array(unlist(permn(6)), dim = c(6, gamma(7)))), 2, tabulate, nbins = 6) # Apply, on the fly, the diff function to every permutation t(array(unlist(permn(6, diff)), dim = c(5, gamma(7))))# Convert output to a matrix of dim c(6, 720) t(array(unlist(permn(6)), dim = c(6, gamma(7)))) # A check that every element occurs the same number of times in each # position apply(t(array(unlist(permn(6)), dim = c(6, gamma(7)))), 2, tabulate, nbins = 6) # Apply, on the fly, the diff function to every permutation t(array(unlist(permn(6, diff)), dim = c(5, gamma(7))))
rmultinomial: Generate random samples from multinomial distributions, where both n and p may vary among distributions
rmultz2: fixed p case
rmultinomial(n, p, rows=max(c(length(n), nrow(p)))) rmultz2(n, p, draws=length(n))rmultinomial(n, p, rows=max(c(length(n), nrow(p)))) rmultz2(n, p, draws=length(n))
n |
vector of sizes |
p |
vector or probs |
rows |
numeric giving desired number rows to be output |
draws |
number samples required |
a matrix of rows rows delivering specified samples
John Wallace, 17 Feb 1997 S-news , mods by Chasalow
n <- c(100,20,10) p <- matrix(c(.3,.1,.5,.1,.1,.2,.6,.8,.3),3) rmultinomial(n,p)n <- c(100,20,10) p <- matrix(c(.3,.1,.5,.1,.1,.2,.6,.8,.3),3) rmultinomial(n,p)
Convert an x-encoded simplex-lattice point to a u-encoded simplex-lattice point (equivalently, "untabulate" bin counts)
x2u(x, labels=seq(along = x))x2u(x, labels=seq(along = x))
x |
x: A numeric vector. x[i] is interpreted as the count in bin i. |
labels |
A vector. Interpreted as the bin labels; default value is seq(along = x), which causes return of a u-encoded simplex-lattice point. Other values of labels cause return of the result of subscripting labels with the u-encoded simplex-lattice point that would have been obtained if the default value of labels were used. |
rep(labels, x), a vector of length sum(x). If labels = seq(along = x) (the default), value is the u-encoded translation of the simplex lattice point, x. Equivalently, value gives the bin numbers, in lexicographic order, for the objects represented by the counts in x. For other values of argument "labels", value gives the bin labels for the objects represented by the counts in x (equivalent to labels[x2u(x)]).
tabulate, rep
Generates all points on a p,n simplex lattice (i.e. a p-part composition of n). Each point is represented as x, a p-dimensional vector of nonnegative integers that sum to n. If argument "fun" is not null, applies a function given by the argument to each point. If simplify is FALSE, returns a list; else returns a vector or an array. "..." are passed unchanged to function given by argument fun, if any.
xsimplex(p, n, fun=NULL, simplify=TRUE, ...)xsimplex(p, n, fun=NULL, simplify=TRUE, ...)
p |
first parameter of lattice description |
n |
second parameter of lattice description |
fun |
function to be applied pointwise |
simplify |
logical: if FALSE, value is a list, otherwise a vector or array |
... |
parameters to be passed to |
#Compute Multinomial(n = 4, pi = rep(1/3, 3)) p.f.: xsimplex(3, 4, dmnom, prob=1/3)#Compute Multinomial(n = 4, pi = rep(1/3, 3)) p.f.: xsimplex(3, 4, dmnom, prob=1/3)