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Use the RCM algorithm to permute to banded matrix

Source: R/rcm.R
rcm.Rd

The RCM stands for the reverse Cuthill McKee (RCM) algorithm which is used to permute the matrix to a banded matrix.

Usage

rcm(x)

Arguments

x

A symmetric matrix

Value

A permuted matrix that should be banded

Examples


m <- lotri({
 a + b + c + d + e + f + g + h + i + j + k + l + m + n + o +
 p ~ c(0.4, 0, 0.3, 0, 0, 0, -0.1, 0, 0, 0.2, 0, 0, 0,
       0, 0.5, 0, 0, 0, 0, 0, 1.3, 0, 0, 0, 0, 0, -0.6, 0.8,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0.9, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0.9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.2, 0, 0.3,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.1, 0.2, 0, 0, 0.2,
       0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4, 0, 0, 0, 0, 0, -1.1,
       0.9, 0, 0, 0, 0, 0, 0, 0, 4.7, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0.5, 0, 0.2, 0, 0, 0, 1.9)
})

rcm(m)
#>     p    l    j    o    g    f   n    d    a   m   k   i   e   b h c
#> p 1.9  0.2  0.5  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> l 0.2  0.3 -0.2  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> j 0.5 -0.2  0.9  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> o 0.0  0.0  0.0  4.7  0.9 -1.1 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> g 0.0  0.0  0.0  0.9  0.8 -0.6 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> f 0.0  0.0  0.0 -1.1 -0.6  1.3 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> n 0.0  0.0  0.0  0.0  0.0  0.0 0.4  0.2  0.2 0.0 0.0 0.0 0.0 0.0 0 0
#> d 0.0  0.0  0.0  0.0  0.0  0.0 0.2  0.2 -0.1 0.0 0.0 0.0 0.0 0.0 0 0
#> a 0.0  0.0  0.0  0.0  0.0  0.0 0.2 -0.1  0.4 0.0 0.0 0.0 0.0 0.0 0 0
#> m 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 2.1 0.0 0.0 0.0 0.0 0 0
#> k 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.9 0.0 0.0 0.0 0 0
#> i 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.2 0.0 0.0 0 0
#> e 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.5 0.0 0 0
#> b 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.3 0 0
#> h 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0
#> c 0.0  0.0  0.0  0.0  0.0  0.0 0.0  0.0  0.0 0.0 0.0 0.0 0.0 0.0 0 0