ndims(A::Cholesky)

Extends ndims to return 2 if passed a Cholesky object

assert_positive(vars...)

Examples

julia> GPLinearODEMaker.assert_positive([1,2,3,4])

julia> GPLinearODEMaker.assert_positive([-1,2,3,4])
ERROR: AssertionError: passed a negative/0 variable that needs to be positive
[...]

auto_addprocs(;add_procs=0)

Adds either as many workers as there are CPU threads minus 2 if none are active or the amount specified by add_procs

log_laplace_approximation(H, g, logh; λ=1)

Compute the logarithm of the Laplace approxmation for the integral of a function of the following form ∫ exp(-λ g(y)) h(y) dy ≈ exp(-λ g(y)) h(y) (2π/λ)^(d/2) |H(y)|^(-1/2) where y is the value of y at the global mode and H is the (Hessian) matrix of second order partial derivatives of g(y) (see slide 10 of http://www.stats.ox.ac.uk/~steffen/teaching/bs2HT9/laplace.pdf). When used to calculate evidences, one can set λ = 1, g(y) = -log-likelihood, h(y) = model prior, and H(y) = the Fisher information matrix (FIM) or the Hessian matrix of the negative log-likelihood. Could possiblly improve with methods from Ruli et al. 2016 (https://arxiv.org/pdf/1502.06440.pdf)?

powers_of_negative_one(power)

Finds -1 ^ power without calling ^

Examples

julia> GPLinearODEMaker.powers_of_negative_one(0) == GPLinearODEMaker.powers_of_negative_one(2) == 1
true
julia> GPLinearODEMaker.powers_of_negative_one(1) == GPLinearODEMaker.powers_of_negative_one(3) == -1
true

reconstruct_array(non_zero_entries, template_A)

Fill a matrix with non_zero_entries at the locations of the non-zero entries in template_A

Examples

julia> template_A = [4. 0;5 0];

julia> non_zero_entries = [2., 3];

julia> GPLinearODEMaker.reconstruct_array(non_zero_entries, template_A)
2×2 Array{Float64,2}:
 2.0  0.0
 3.0  0.0

remove_zeros(V)

Return the a version of the passed vector after removing all zero entries. Could possibly be replaced with a view-based version.

Examples

julia> V = [1, 2, 0, 3, 0, 4, 5];

julia> GPLinearODEMaker.remove_zeros(V)
5-element Array{Int64,1}:
 1
 2
 3
 4
 5

ridge_chol(A)

Perform a Cholesky factorization on A, adding a small ridge when necessary

Examples

julia> A = [4. 2;2 10];

julia> GPLinearODEMaker.ridge_chol(A)
LinearAlgebra.Cholesky{Float64,Array{Float64,2}}
U factor:
2×2 LinearAlgebra.UpperTriangular{Float64,Array{Float64,2}}:
 2.0  1.0
  ⋅   3.0

sendto(workers; args...)

Send the args to the workers specified by thier number IDs. Stolen shamelessly from ParallelDataTransfer.jl

Examples

julia> sendto([1, 2], x=100, y=rand(2, 3));

julia> z = randn(10, 10); sendto(workers(), z=z);

symmetric_A(A; ignore_asymmetry=false, chol=false)

Check if A is approximately symmetric and then return a symmetrized version or, optionally, the Cholesky factorization

Examples

julia> A = [1. 1; 0 1];

julia> GPLinearODEMaker.symmetric_A(A; ignore_asymmetry=true)
2×2 LinearAlgebra.Symmetric{Float64,Array{Float64,2}}:
 1.0  0.5
 0.5  1.0

symmetrize_A(A)

Symmetrize A (i.e. add its transpose and divide by 2)

Examples

julia> A = [1. 1; 0 1];

julia> GPLinearODEMaker.symmetrize_A(A)
2×2 LinearAlgebra.Symmetric{Float64,Array{Float64,2}}:
 1.0  0.5
 0.5  1.0