(De)symmetrize square binary matrix in various ways.
Usage
symmetrize(mat, rule = c("upper", "lower", "div", "intdiv"))Details
Argument mat is to be a square numeric matrix. The way it is made
symmetric, or asymetric, depends on the value of the rule argument.
If rule is "upper" or "lower" then mat is made symmetric by copying,
respectively, upper triangle onto lower, or lower onto upper. The value of
rule specifies values of which triangle will stay in the returned value.
If rule is "intdiv" then the off-diagonal values are distributed
approximately equally between the lower/upper triangles. If r is the
computed result, then r[i,j] will be equal to
(x[i,j] + x[j,i]) \%/\% 2 if r[i,j] is in the lower triangle.
It will be equal to
(x[i,j] + x[j,i]) \%/\% 2 + 1 if in the upper triangle.
If rule is "div" then the off-diagonal values are distributed equally
between the lower/upper triangles: as with "intdiv" but using normal
/ division.
Examples
m <- matrix(1:16, 4, 4)
# copy upper triangle onto lower symmetrically
symmetrize(m, "upper")
#> [,1] [,2] [,3] [,4]
#> [1,] 1 5 9 13
#> [2,] 5 6 10 14
#> [3,] 9 10 11 15
#> [4,] 13 14 15 16
# copy lower triangle onto upper symmetrically
symmetrize(m, "lower")
#> [,1] [,2] [,3] [,4]
#> [1,] 1 2 3 4
#> [2,] 2 6 7 8
#> [3,] 3 7 11 12
#> [4,] 4 8 12 16
# distribute off-diagonal values exactly
# r[i,j] = (m[i,j] + m[j,i]) / 2
r1 <- symmetrize(m, "div")
r1
#> [,1] [,2] [,3] [,4]
#> [1,] 1.0 3.5 6.0 8.5
#> [2,] 3.5 6.0 8.5 11.0
#> [3,] 6.0 8.5 11.0 13.5
#> [4,] 8.5 11.0 13.5 16.0
all.equal(sum(m), sum(r1))
#> [1] TRUE
# distribute off-diagonal values using integer division
r2 <- symmetrize(m, "intdiv")
r2
#> [,1] [,2] [,3] [,4]
#> [1,] 1 4 6 9
#> [2,] 3 6 9 11
#> [3,] 6 8 11 14
#> [4,] 8 11 13 16
all.equal(sum(m), sum(r2))
#> [1] TRUE