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Sketch backtracking Newton's method

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This code is a mess, but I'm committing it to record a working state
before I start trying to clean up.
This commit is contained in:
Aaron Fenyes 2024-07-15 11:32:04 -07:00
parent 3910b9f740
commit 25b09ebf92
4 changed files with 254 additions and 8 deletions
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11
engine-proto/gram-test/overlapping-pyramids.jl
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@ -47,17 +47,25 @@ guess = hcat(
Engine.rand_on_shell(fill(BigFloat(-1), 2))
)
# complete the gram matrix using gradient descent followed by Newton's method
# complete the gram matrix
#=
L, history = Engine.realize_gram_gradient(gram, guess, scaled_tol = 0.01)
L_pol, history_pol = Engine.realize_gram_newton(gram, L)
=#
L, history = Engine.realize_gram(Float64.(gram), Float64.(guess))
completed_gram = L'*Engine.Q*L
println("Completed Gram matrix:\n")
display(completed_gram)
#=
println("\nSteps: ", size(history.scaled_loss, 1), " + ", size(history_pol.scaled_loss, 1))
println("Loss: ", history_pol.scaled_loss[end], "\n")
=#
println("\nSteps: ", size(history.scaled_loss, 1))
println("Loss: ", history.scaled_loss[end], "\n")
# === algebraic check ===
#=
R, gens = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
x = gens[1]
t = gens[2:4]
@ -85,3 +93,4 @@ x_constraint = 25//16 * to_univariate(S, evaluate(rank_constraints[1], [2], [ind
t₂_constraint = 25//16 * to_univariate(S, evaluate(rank_constraints[3], [2], [indep_val]))
x_vals = PolynomialRoots.roots(x_constraint.coeffs)
t₂_vals = PolynomialRoots.roots(t₂_constraint.coeffs)
=#