Skip to contents

Cholesky Decomposition

Source: R/api.R, R/api-generics.R
nv_chol.Rd

Computes the Cholesky decomposition of a symmetric positive-definite matrix. Supports batched inputs: axes before the last two are batch axes.

Usage

nv_chol(x, lower = FALSE)

# S3 method for class 'AnvlArray'
chol(x, ..., lower = FALSE)

Arguments

x

(arrayish)
One input, a symmetric positive-definite matrix with at least 2 axes, the last two forming the square matrix and any leading ones batch axes. Can be any numeric data type: a float keeps its own, and an integer one is converted to the default float data type (see default_dtypes()). An R value materializes at its default data type and is converted in the same way.

lower

(logical(1))
If TRUE, return the lower-triangular factor.

...

No additional arguments.

Value

(arrayish)
Triangular matrix with the input's shape, and its data type – or the default float data type (see default_dtypes()) where the input was an integer one. The values in the triangle not selected by lower are implementation-defined.

Details

Differentiation is only implemented for a single matrix: a gradient() of a batched decomposition errors.

See also

nv_solve(), prim_chol()

Examples

# the factor has the matrix's shape and data type
a <- nv_matrix(c(4, 2, 2, 3), nrow = 2, dtype = "f32")
nv_chol(a)
#> AnvlArray
#>  2.0000 1.0000
#>  0.0000 1.4142
#> [ CPUf32{2,2} ] 

# an integer matrix is factored at the default float data type
nv_chol(nv_matrix(c(4L, 2L, 2L, 3L), nrow = 2))
#> AnvlArray
#>  2.0000 1.0000
#>  0.0000 1.4142
#> [ CPUf32{2,2} ]