robinhankin / magic Goto Github PK

create and investigate magic squares and magic hypercubes

Home Page: https://robinhankin.github.io/magic/

R 98.08% TeX 1.92%

magic's Introduction

Manipulation of high-dimensional arrays in R with the magic package

Overview

The magic package implements functionality for manipulating high-dimensional arrays using efficient vectorised methods. The original application was high-dimensional magic hypercubes. This README shows some of the more useful functions in the package.

Installation

You can install the released version of magic from CRAN with:

# install.packages("magic")  # uncomment this to install the package
library("magic")

Package highlights

Function adiag() binds arbitrarily-dimensioned arrays corner-to-corner
Function apad() pads arbitrarily-dimensioned arrays
Function apldrop() is a replacement for APL’s drop
Function aplus() superimposes two arrays of different dimensions and returns the sum of overlapping elements
Function arev() is a multidimensional generalization of rev()
Function arot() is a generalization of matlab’s rotdim
Function fnsd() returns the first nonsingleton dimension of an arbitrary dimensioned array
Function ashift() shifts the origin of arbitrary dimensioned arrays

Much of the package functionality is vectorised in array dimension.

Further information

For more detail, see the package vignette

vignette("magic")

magic's People

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kunju-pitt jianguozhou3 noissee

magic's Issues

poor documentation in latin.Rd

Tim Hesterberg writes:

Thank you for writing the magic package.

library(magic)
help(latin)

brings up a help file that does not include 'latin' in the usage section
(though latin.Rd includes alias{latin}

no README

Trenckler hypercubes

Trenckler hypercubes are not implemented but:

trenckler.2np1 <- function(m,d){  # n = 2m+1
    n <- 2*m+1
    eg <- as.matrix(cbind(expand.grid(rep(list(seq_len(n)),d)),1))
    
    f <- function(k){
        eg %*% 
            c(
                (-1)^(seq_len(k)-1), rep((-1)^k,d-k),   
                (-1)^(k+1) * (d-k-(k+1)%%2)*((n+1)/2)-1 # C_k
              ) %% n
    }
    
    dm <- seq_len(d)-1  # 0:(d-1)
    out <-  1 + sapply(dm,f) %*% n^dm
    dim(out) <- rep(n,d)
    return(force.integer(out))
}

trenckler.4n <- function(m,d){  # n = 4*m
    n <- 4*m
    eg <- as.matrix(expand.grid(rep(list(seq_len(n)),d)))
    f <- function(x){ # condition on top line
       ( sum(x + floor((2*(x-1)/n))) %%2) == 1
    }
    crit <- apply(eg,1,f) 
    eg[crit,] <- n+1-eg[crit,]  # defn on p1
    out <- 1 + (eg-1) %*% n^(seq_len(d)-1)
    dim(out) <- rep(n,d)
    return(force.integer(out))
}

magic.prime exception

magic.prime says "Claimed to work for prime order," but:

> is.magic(magic.prime(2))
[1] FALSE
> magic.prime(2)
     [,1] [,2]
[1,]    1    4
[2,]    2    3
>

and of course 2 is prime!

use mathjax in the Rd files

magic squares web site is gone

The web site linked in the help pages,

http://www.magic-squares.de/general/general.html

is now a domain holding page with no content :(

adiag

I would find it useful if adiag

also took a list as input like Matrix::bdiag does.
accepted all numeric data frames in addition to matrices.

magic rectangles and magic hyperrectangles

Magic rectangles and hyperrectangles are well-defined and here is a little function I wrote a couple of years ago to test for this:

`is.magichyperrectangle` <- function(a, ndim, give.answers = FALSE, func = sum, boolean = FALSE) 
{
    n <- dim(a)[1]
    d <- length(dim(a))
    jj <- d - ndim
    out <- apply(combn(d, jj), 2, function(i){apply(a, i, func)})

    if(boolean){
        answer <- all(out)
    } else {
        answer <- minmax(out)
    }
    
    if (give.answers) {
        dim(out) <- c(rep(n, jj), ncol(out))
        return(list(answer = answer, alice.sums = out))
    } else {
        return(answer)
    }
}