Computes the determinant of a square matrix in the modulus / sign
decomposition matching base R's base::determinant(). For the plain
scalar determinant, use nv_det().
Usage
nv_determinant(x, logarithm = TRUE)
# S3 method for class 'AnvlArray'
determinant(x, logarithm = TRUE, ...)Arguments
- x
(
arrayish)
Square matrix of floating-point data type.- logarithm
(
logical(1))
IfTRUE(default), return the log of the absolute determinant.- ...
No additional arguments.
Value
Named list with elements modulus and sign, both scalar
arrayish with the same dtype as x. The full determinant
is sign * exp(modulus) (with logarithm = TRUE) or
sign * modulus (with logarithm = FALSE).
Details
For computing the determinant, we use: $$P A = L U$$ $$\det(L) = 1$$ $$\det(A) = \det(U) / \det(P) = \mathrm{sign}(P^{-1}) \, \prod_i U_{ii} = \mathrm{sign}(P) \, \prod_i U_{ii}$$
Matching base R's det_ge_real, the magnitude is computed in log
space when logarithm = TRUE (\(\sum_i \log|U_{ii}|\)) and as a
direct product when logarithm = FALSE (\(\prod_i |U_{ii}|\)).
Examples
a <- nv_matrix(c(4, 3, 6, 3), nrow = 2, dtype = "f64")
nv_determinant(a)
#> $modulus
#> AnvlArray
#> 1.7918
#> [ CPUf64{} ]
#>
#> $sign
#> AnvlArray
#> -1
#> [ CPUf64{} ]
#>
nv_determinant(a, logarithm = FALSE)
#> $modulus
#> AnvlArray
#> 6
#> [ CPUf64{} ]
#>
#> $sign
#> AnvlArray
#> -1
#> [ CPUf64{} ]
#>