An example of outer product in R -

i reading textbook named "an introduction r" , gives me example totally cannot understand.

the examples states

as artificial cute example, consider determinants of 2 2 matrices [a, b; c, d] each entry non-negative integer in range 0, 1, . . . , 9, digit. problem find determinants, ad − bc, of possible matrices of form , represent frequency each value occurs high density plot. amounts finding probability distribution of determinant if each digit chosen independently , uniformly @ random.

and provides code:

d <- outer(0:9, 0:9) fr <- table(outer(d, d, "-")) plot(as.numeric(names(fr)), fr, type="h", xlab="determinant", ylab="frequency")  

i know first line doing have no idea "-" sign in outer() function , table() in case. also, why use name() function in last plot() function

perhaps should explain small example first. let's suppose want find distribution of determinant ad - bc, a, b, c, d either 0 or 1.

the first line

product <- outer(0:1, 0:1, "*") #     [,1] [,2] #[1,]    0    0 #[2,]    0    1 

computes possible outcomes of paired product, i.e.,

0 * 0 = 0 0 * 1 = 0 1 * 0 = 0 1 * 1 = 1 

this maps possible outcomes of ad , bc in ad - bc.

the second line:

minus <- outer(product, product, "-")     , , 1, 1        [,1] [,2] [1,]    0    0 [2,]    0    1  , , 2, 1       [,1] [,2] [1,]    0    0 [2,]    0    1  , , 1, 2       [,1] [,2] [1,]    0    0 [2,]    0    1  , , 2, 2       [,1] [,2] [1,]   -1   -1 [2,]   -1    0 

computes possible outcomes of ad - bc. perhaps not easy read 4d array. how about:

minus <- as.numeric(minus) #[1]  0  0  0  1  0  0  0  1  0  0  0  1 -1 -1 -1  0 

then time make contingency table of possible outcomes:

fr <- table(minus) #-1  0  1  # 3 10  3  

finally, example code plot table.

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what if solve problem

you felt difficult read result of outer, every time apply outer, dimension grows. example, applying outer 2 1d vectors results in 2d matrix, while further applying outer 2 2d matrices results in 4d array.

for easy-to-understand purpose, use as.numeric() flatten result of outer every time. use this:

product <- as.numeric(outer(0:1,0:1,"*")) #[1] 0 0 0 1  minus <- as.numeric(outer(product, product, "-")) #[1]  0  0  0  1  0  0  0  1  0  0  0  1 -1 -1 -1  0  plot(table(minus)) 

with original problem, do:

product <- as.numeric(outer(0:9,0:9,"*")) minus <- as.numeric(outer(product, product, "-")) plot(table(minus))