Determinant in modulus/sign form

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(operand, logarithm = TRUE)

# S3 method for class 'AnvlArray'
determinant(x, logarithm = TRUE, ...)

Arguments

operand

(arrayish)
Square matrix of floating-point data type.

logarithm

(logical(1))
If TRUE (default), return the log of the absolute determinant.

x

(arrayish)
Same as operand; this is the name used by the base R S3 generic.

...

No additional arguments.

Value

Named list with elements modulus and sign, both scalar arrayish with the same dtype as operand. 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 (\(\prod_i |U_{ii}|\)).

See also

nv_det(), nv_solve(), prim_lu()

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{} ] 
#>