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Primitive Cholesky Decomposition

Source: R/primitives.R, R/rules-backward.R
nvl_cholesky.Rd

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

Usage

nvl_cholesky(operand, lower)

Arguments

operand

(tensorish)
Tensorish value of data type floating-point with at least 2 dimensions. The last two dimensions must be equal (square matrix); any leading dimensions are batch dimensions.

lower

(logical(1))
If TRUE, compute the lower triangular factor L such that operand = L %*% t(L). If FALSE, compute the upper triangular factor U such that operand = t(U) %*% U.

Value

tensorish
Has the same shape and data type as the input. The values in the triangle not specified by lower are implementation-defined. It is ambiguous if the input is ambiguous.

Implemented Rules

  • stablehlo

  • backward

StableHLO

Lowers to stablehlo::hlo_cholesky().

References

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

Walter, Sebastian (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

jit_eval({
  # Create a positive-definite matrix
  x <- nv_tensor(matrix(c(4, 2, 2, 3), nrow = 2), dtype = "f32")
  nvl_cholesky(x, lower = TRUE)
})
#> AnvilTensor
#>  2.0000 0.0000
#>  1.0000 1.4142
#> [ CPUf32{2,2} ]