Cholesky promotes Float16 to Float32 #912
Description
I found this anomaly and the discussion on
https://discourse.julialang.org/t/cholseky-promotes-float16/76772
with @artkuo seems to conclude that it is a bug.
I'm seeing Cholesky promote half precision to single on its own. Is this
supposed to happen? lu does not do this.
julia> R=rand(Float16,3,3)
3×3 Matrix{Float16}:
4.00391e-01 8.24219e-01 2.50000e-01
2.34375e-02 2.90527e-01 1.09375e-01
7.85156e-01 9.42383e-01 3.76465e-01
julia> P=R'*R
3×3 Matrix{Float16}:
7.77344e-01 1.07617e+00 3.98438e-01
1.07617e+00 1.65234e+00 5.92773e-01
3.98438e-01 5.92773e-01 2.16187e-:q
julia> PF=lu(P)
LU{Float16, Matrix{Float16}}
L factor:
3×3 Matrix{Float16}:
1.00000e+00 0.00000e+00 0.00000e+00
7.22168e-01 1.00000e+00 0.00000e+00
3.70117e-01 1.58325e-01 1.00000e+00
U factor:
3×3 Matrix{Float16}:
1.07617e+00 1.65234e+00 5.92773e-01
0.00000e+00 -1.17188e-01 -2.95410e-02
0.00000e+00 0.00000e+00 1.50299e-03
julia> QF=cholesky(P)
Cholesky{Float32, Matrix{Float32}}
U factor:
3×3 UpperTriangular{Float32, Matrix{Float32}}:
8.81671e-01 1.22060e+00 4.51912e-01
⋅ 4.03073e-01 1.02135e-01
⋅ ⋅ 3.91250e-02