I would like to take the inverse of this subsetted diagonal matrix (I hope I have created a dput in the right way):
dput(DMIdiag[1:20,1:20])
structure(c(581.166666666667, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 5397.42, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1254652.485, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15164.7616666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3721176.8,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1805.11333333333,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 266406189.456667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 478590.468333333,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508510.586666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 348034.096666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 945785.841666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1056505.53666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1389813.64166667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28585.2133333333,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 713675.006666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 661456.686666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53533.9066666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7291.31666666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49375.4466666667,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 807758.686666667
), .Dim = c(20L, 20L))
My code:
DMI <- p + rowSums(Z, na.rm = TRUE)*1 #p is a vector and Z is a matrix
DMIdiag <- diag(DMI) #produces the matrix above
DMIinv <- solve(DMIdiag)
Running the last line gives me:
Error in solve.default(DMIdiag) :
Lapack routine dgesv: system is exactly singular: U[173,173] = 0
I don't really understand how this matrix be singular, if this is even the problem?
You can get the inverse of a diagonal matrix by replacing its diagonal components by their reciprocals. Therefore if you do
DMIinv <- DMIDiag
diag(DMIinv) <- 1/diag(DMIDiag)
Then DMIinv will be the inverse of DMIDiag, as we can show by doing:
DMIDiag %*% DMIinv
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20]
#> [1,] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [2,] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [3,] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [6,] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
#> [9,] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
#> [10,] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
#> [11,] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
#> [12,] 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
#> [13,] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
#> [14,] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
#> [15,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
#> [16,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
#> [17,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
#> [18,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
#> [19,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
#> [20,] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Which is the 20 x 20 identity matrix.