Visualize neighborhoods of global minima

This commit is contained in:
Aaron Fenyes 2024-07-09 14:01:30 -07:00
parent 77bc124170
commit f84d475580

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@ -0,0 +1,99 @@
include("Engine.jl")
using LinearAlgebra
using SparseArrays
function sphere_in_tetrahedron_shape()
# initialize the partial gram matrix for a sphere inscribed in a regular
# tetrahedron
J = Int64[]
K = Int64[]
values = BigFloat[]
for j in 1:5
for k in 1:5
push!(J, j)
push!(K, k)
if j == k
push!(values, 1)
elseif (j <= 4 && k <= 4)
push!(values, -1/BigFloat(3))
else
push!(values, -1)
end
end
end
gram = sparse(J, K, values)
# plot loss along a slice
loss_lin = []
loss_sq = []
mesh = range(0.9, 1.1, 101)
for t in mesh
L = hcat(
Engine.plane(normalize(BigFloat[ 1, 1, 1]), BigFloat(1)),
Engine.plane(normalize(BigFloat[ 1, -1, -1]), BigFloat(1)),
Engine.plane(normalize(BigFloat[-1, 1, -1]), BigFloat(1)),
Engine.plane(normalize(BigFloat[-1, -1, 1]), BigFloat(1)),
Engine.sphere(BigFloat[0, 0, 0], BigFloat(t))
)
Δ_proj = Engine.proj_diff(gram, L'*Engine.Q*L)
push!(loss_lin, norm(Δ_proj))
push!(loss_sq, dot(Δ_proj, Δ_proj))
end
mesh, loss_lin, loss_sq
end
function circles_in_triangle_shape()
# initialize the partial gram matrix for a sphere inscribed in a regular
# tetrahedron
J = Int64[]
K = Int64[]
values = BigFloat[]
for j in 1:8
for k in 1:8
filled = false
if j == k
push!(values, 1)
filled = true
elseif (j == 1 || k == 1)
push!(values, 0)
filled = true
elseif (j == 2 || k == 2)
push!(values, -1)
filled = true
end
#=elseif (j <= 5 && j != 2 && k == 9 || k == 9 && k <= 5 && k != 2)
push!(values, 0)
filled = true
end=#
if filled
push!(J, j)
push!(K, k)
end
end
end
append!(J, [6, 4, 6, 5, 7, 5, 7, 3, 8, 3, 8, 4])
append!(K, [4, 6, 5, 6, 5, 7, 3, 7, 3, 8, 4, 8])
append!(values, fill(-1, 12))
# plot loss along a slice
loss_lin = []
loss_sq = []
mesh = range(0.99, 1.01, 101)
for t in mesh
L = hcat(
Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
Engine.sphere(BigFloat[0, 0, 0], BigFloat(t)),
Engine.plane(BigFloat[1, 0, 0], BigFloat(1)),
Engine.plane(BigFloat[cos(2pi/3), sin(2pi/3), 0], BigFloat(1)),
Engine.plane(BigFloat[cos(-2pi/3), sin(-2pi/3), 0], BigFloat(1)),
Engine.sphere(4//3*BigFloat[-1, 0, 0], BigFloat(1//3)),
Engine.sphere(4//3*BigFloat[cos(-pi/3), sin(-pi/3), 0], BigFloat(1//3)),
Engine.sphere(4//3*BigFloat[cos(pi/3), sin(pi/3), 0], BigFloat(1//3))
)
Δ_proj = Engine.proj_diff(gram, L'*Engine.Q*L)
push!(loss_lin, norm(Δ_proj))
push!(loss_sq, dot(Δ_proj, Δ_proj))
end
mesh, loss_lin, loss_sq
end