|
12 | 12 | end
|
13 | 13 | @inline LinearAlgebra._chol!(A::StaticMatrix, ::Type{UpperTriangular}) = (cholesky(A).U, 0)
|
14 | 14 |
|
15 |
| - |
16 |
| -@generated function _cholesky(::Size{(1,1)}, A::StaticMatrix) |
17 |
| - @assert size(A) == (1,1) |
18 |
| - |
19 |
| - quote |
20 |
| - $(Expr(:meta, :inline)) |
21 |
| - T = promote_type(typeof(sqrt(one(eltype(A)))), Float32) |
22 |
| - similar_type(A,T)((sqrt(A[1]), )) |
| 15 | +@generated function _cholesky(::Size{S}, A::StaticMatrix{M,M}) where {S,M} |
| 16 | + @assert (M,M) == S |
| 17 | + M > 24 && return :(_cholesky_large(Size{$S}(), :A)) |
| 18 | + q = Expr(:block) |
| 19 | + for n in 1:M |
| 20 | + for m ∈ n:M |
| 21 | + r = Expr(:ref, :A, n, m) |
| 22 | + ln = LineNumberNode(@__LINE__,Symbol(@__FILE__)) |
| 23 | + r = Expr(:macrocall, Symbol("@inbounds"), ln, r) |
| 24 | + push!(q.args, Expr(:(=), Symbol(:L_,m,:_,n), r)) |
| 25 | + end |
| 26 | + for k ∈ 1:n-1, m in n:M |
| 27 | + L_m_n = Symbol(:L_,m,:_,n) |
| 28 | + push!(q.args, Expr(:(=), L_m_n, Expr(:call, :muladd, Expr(:call, :(-), Symbol(:L_,m,:_,k)), Symbol(:L_,n,:_,k), L_m_n))) |
| 29 | + end |
| 30 | + L_n_n = Symbol(:L_,n,:_,n) |
| 31 | + push!(q.args, Expr(:(=), L_n_n, Expr(:call, :sqrt, L_n_n))) |
| 32 | + Linv_n_n = Symbol(:Linv_,n,:_,n) |
| 33 | + push!(q.args, Expr(:(=), Linv_n_n, Expr(:call, :inv, L_n_n))) |
| 34 | + for m ∈ n+1:M |
| 35 | + push!(q.args, Expr(:(*=), Symbol(:L_,m,:_,n), Linv_n_n)) |
| 36 | + end |
23 | 37 | end
|
24 |
| -end |
25 |
| - |
26 |
| -@generated function _cholesky(::Size{(2,2)}, A::StaticMatrix) |
27 |
| - @assert size(A) == (2,2) |
28 |
| - |
29 |
| - quote |
30 |
| - $(Expr(:meta, :inline)) |
31 |
| - @inbounds a = sqrt(A[1]) |
32 |
| - @inbounds b = A[3] / a |
33 |
| - @inbounds c = sqrt(A[4] - b'*b) |
34 |
| - T = promote_type(typeof(sqrt(one(eltype(A)))), Float32) |
35 |
| - similar_type(A,T)((a, zero(T), b, c)) |
| 38 | + push!(q.args, :(T = promote_type(typeof(sqrt(one(eltype(A)))), Float32))) |
| 39 | + ret = Expr(:tuple) |
| 40 | + for n ∈ 1:M |
| 41 | + for m ∈ 1:n |
| 42 | + push!(ret.args, Symbol(:L_,n,:_,m)) |
| 43 | + end |
| 44 | + for m ∈ n+1:M |
| 45 | + push!(ret.args, Expr(:call, :zero, :T)) |
| 46 | + end |
36 | 47 | end
|
| 48 | + push!(q.args, Expr(:call, Expr(:call, :similar_type, :A, :T), ret)) |
| 49 | + Expr(:block, Expr(:meta, :inline), q) |
37 | 50 | end
|
38 | 51 |
|
39 |
| -@generated function _cholesky(::Size{(3,3)}, A::StaticMatrix) |
40 |
| - @assert size(A) == (3,3) |
41 |
| - |
42 |
| - quote |
43 |
| - $(Expr(:meta, :inline)) |
44 |
| - @inbounds a11 = sqrt(A[1]) |
45 |
| - @inbounds a12 = A[4] / a11 |
46 |
| - @inbounds a22 = sqrt(A[5] - a12'*a12) |
47 |
| - @inbounds a13 = A[7] / a11 |
48 |
| - @inbounds a23 = (A[8] - a12'*a13) / a22 |
49 |
| - @inbounds a33 = sqrt(A[9] - a13'*a13 - a23'*a23) |
50 |
| - T = promote_type(typeof(sqrt(one(eltype(A)))), Float32) |
51 |
| - similar_type(A,T)((a11, zero(T), zero(T), a12, a22, zero(T), a13, a23, a33)) |
52 |
| - end |
53 |
| -end |
54 | 52 |
|
55 | 53 | # Otherwise default algorithm returning wrapped SizedArray
|
56 |
| -@inline _cholesky(::Size{S}, A::StaticArray) where {S} = |
| 54 | +@inline _cholesky_large(::Size{S}, A::StaticArray) where {S} = |
57 | 55 | SizedArray{Tuple{S...}}(Matrix(cholesky(Hermitian(Matrix(A))).U))
|
58 | 56 |
|
59 | 57 | LinearAlgebra.hermitian_type(::Type{SA}) where {T, S, SA<:SArray{S,T}} = Hermitian{T,SA}
|
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