include("Engine.jl") using SparseArrays # this problem is from a sangaku by Irisawa Shintarō Hiroatsu. the article below # includes a nice translation of the problem statement, which was recorded in # Uchida Itsumi's book _Kokon sankan_ (_Mathematics, Past and Present_) # # "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki # https://www.nippon.com/en/japan-topics/c12801/ # # initialize the partial gram matrix J = Int64[] K = Int64[] values = BigFloat[] for s in 1:9 # each sphere is represented by a spacelike vector push!(J, s) push!(K, s) push!(values, 1) # the circumscribing sphere is internally tangent to all of the other spheres if s > 1 append!(J, [1, s]) append!(K, [s, 1]) append!(values, [1, 1]) end if s > 3 # each chain sphere is externally tangent to the two nucleus spheres for n in 2:3 append!(J, [s, n]) append!(K, [n, s]) append!(values, [-1, -1]) end # each chain sphere is externally tangent to the next sphere in the chain s_next = 4 + mod(s-3, 6) append!(J, [s, s_next]) append!(K, [s_next, s]) append!(values, [-1, -1]) end end gram = sparse(J, K, values) # make an initial guess guess = hcat( Engine.sphere(BigFloat[0, 0, 0], BigFloat(15)), Engine.sphere(BigFloat[0, 0, -9], BigFloat(5)), Engine.sphere(BigFloat[0, 0, 11], BigFloat(3)), ( Engine.sphere(9*BigFloat[cos(k*π/3), sin(k*π/3), 0], BigFloat(2.5)) for k in 1:6 )... ) frozen = [CartesianIndex(4, k) for k in 1:4] # complete the gram matrix using Newton's method with backtracking L, success, history = Engine.realize_gram(gram, guess, frozen) completed_gram = L'*Engine.Q*L println("Completed Gram matrix:\n") display(completed_gram) if success println("\nTarget accuracy achieved!") else println("\nFailed to reach target accuracy") end println("Steps: ", size(history.scaled_loss, 1)) println("Loss: ", history.scaled_loss[end], "\n") if success println("Chain diameters:") println(" ", 1 / L[4,4], " sun (given)") for k in 5:9 println(" ", 1 / L[4,k], " sun") end end