is.magic {magic}R Documentation

Various tests for the magicness of a square

Description

Returns TRUE if the square is magic, semimagic, panmagic, associative, normal. If argument give.answers is TRUE, also returns additional information about the sums.

Usage

is.magic(m, give.answers = FALSE, FUN=sum, boolean=FALSE) 
is.panmagic(m, give.answers = FALSE, FUN=sum, boolean=FALSE) 
is.pandiagonal(m, give.answers = FALSE, FUN=sum, boolean=FALSE) 
is.semimagic(m, give.answers = FALSE, FUN=sum, boolean=FALSE) 
is.semimagic.default(m)
is.associative(m)
is.normal(m)
is.sparse(m)
is.mostperfect(m,give.answers=FALSE)
is.2x2.correct(m,give.answers=FALSE)
is.bree.correct(m,give.answers=FALSE)
is.latin(m,give.answers=FALSE)
is.antimagic(m, give.answers = FALSE, FUN=sum) 
is.totally.antimagic(m, give.answers = FALSE, FUN=sum)
is.sam(m)
is.stam(m)

Arguments

m The square to be tested
give.answers Boolean, with TRUE meaning return additional information about the sums (see details)
FUN A function that is evaluated for each row, column, and unbroken diagonal
boolean Boolean, with TRUE meaning that the square is deemed magic, semimagic, etc, if all applications of FUN evaluate to TRUE. If boolean is FALSE, square m is magic etc if all applications of FUN are identical

Details

Value

Returns TRUE if the square is semimagic, etc. and FALSE if not.
If give.answers is taken as an argument and is TRUE, return a list of at least five elements. The first element of the list is the answer: it is TRUE if the square is (semimagic, magic, panmagic) and FALSE otherwise. Elements 2-5 give the result of a call to allsums(), viz: rowwise and columnwise sums; and broken major (ie NW-SE) and minor (ie NE-SW) diagonal sums.
Function is.bree.correct() also returns the sums of elements distant n/2 along a major diagonal (diag.sums); and function is.2x2.correct() returns the sum of each 2x2 submatrix (tbt.sums); for other size windows use subsums() directly. Function is.mostperfect() returns both of these.
Function is.semimagic.default() returns TRUE if the argument is semimagic [with respect to sum()] using a faster method than is.semimagic().

Note

Functions that take a FUN argument apply that function to each row, column, and diagonal as necessary. If FUN takes its default value of sum(), the sum will be returned; if prod(), the product will be returned, and so on. There are many choices for this argument that produce interesting tests; consider FUN=max, for example. With this, a “magic” square is one whose row, sum and (leading) diagonals have identical maxima. Thus diag(5) is magic with respect to max(), but diag(6) isn't.

Function is.magic() is vectorized; if a list is supplied, the defaults are assumed.

Author(s)

Robin K. S. Hankin

References

http://mathworld.wolfram.com/MagicSquare.html

See Also

minmax,is.perfect,is.semimagichypercube

Examples

is.magic(magic(4))

is.magic(diag(9),FUN=max)  #should be TRUE

stopifnot(is.magic(magic(3:8)))

is.panmagic(panmagic.4())
is.panmagic(panmagic.8())

data(Ollerenshaw)
is.mostperfect(Ollerenshaw)

proper.magic <- function(m){is.magic(m) & is.normal(m)}
proper.magic(magic(20))

[Package magic version 1.4-4 Index]