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Primitive Cholesky Decomposition

Source: R/primitives.R, R/rules-reverse.R
prim_chol.Rd

Computes the Cholesky decomposition of a symmetric positive-definite matrix. Axes before the last two are batch axes.

Usage

prim_chol(x, lower = FALSE)

Arguments

x

(arrayish)
One input, with at least 2 axes, the last two of equal size (a square matrix); any leading axes are batch axes. Can be any float data type. An R value materializes at its default data type.

lower

(logical(1))
If FALSE (default, matching base R's base::chol()), compute the upper triangular factor U such that x = t(U) %*% U. If TRUE, compute the lower triangular factor L such that x = L %*% t(L).

Value

(arrayish)
Has the same shape and data type as the input. The values in the triangle not specified by lower are implementation-defined.

Details

Differentiation is only implemented for a single matrix: the reverse rule errors on a batched input (an input with more than 2 axes).

Implemented Rules

  • stablehlo

  • reverse

StableHLO

Lowers to hlo_cholesky(), specified under cholesky.

References

Murray I (2016). “Differentiation of the Cholesky decomposition.” arXiv preprint arXiv:1602.07527.

Walter S (2012). Structured higher-order algorithmic differentiation in the forward and reverse mode with application in optimum experimental design. Ph.D. thesis, Mathematisch-Naturwissenschaftliche Fakult"at II.

See also

nv_solve()

Examples

# create a positive-definite matrix
x <- nv_matrix(c(4, 2, 2, 3), nrow = 2, dtype = "f32")
prim_chol(x, lower = TRUE)
#> AnvlArray
#>  2.0000 0.0000
#>  1.0000 1.4142
#> [ CPUf32{2,2} ]