commit 7fd087a23ee8be94a64d3247e6d46246c6bf07fe Author: yuloveyet Date: Fri Nov 4 09:01:06 2022 +0800 first commit diff --git a/LICENSE b/LICENSE new file mode 100755 index 0000000..c409c3a --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2022 LIYu + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100755 index 0000000..186f396 --- /dev/null +++ b/README.md @@ -0,0 +1,122 @@ +# Topology-Optimization-in-Julia + +Julia Codes for Structural Topology Optimization Design + +## Codes + +A personal [Julia](https://epubs.siam.org/doi/10.1137/141000671) code is given mainly based on a compact and efficient Matlab implementation **top99neo** of compliance topology optimization (TO) for 2D continua[^1], which is a v3.0 version of the celebrated **top99** Matlab code developed by Sigmund[^2] and **top88** by its heir[^3]. + +Assemble just one half of the sysmetric stiffness matrix, thus substantial speedups are acheived. + +`top_oc/` and `top_mma/` contain corresponding files related to the TO with OC and MMA algorithms, respectively. + +Running codes could be tried out as: + +```julia +include("./top99neo_mma.jl") +setup = SetUp() # problem setup +mat = Mat() # material property +disfeature = DiscretizationFeature(setup, mat) # model discretization +load = LoadsSupportsBCs(setup, disfeature) # boudary conditions +ini = Initialization(setup, disfeature, mat) # initial conditions +filter = Filter(setup) # filtering +xPhys, opt_hist, vf_hist, anim = Optimization(setup, mat, load, filter, ini, disfeature) # optimization process +gif(anim, "./res/des_hist.gif", fps=20) # design result visulization +``` + +## Results + +A benchmark MBB example is presented. TO design results are saved in `./res/` folder and a evolution history is shown as below. + + + +
+ +👍 💯 +
+ +## Packages + +Run [the Julia REPL](https://docs.julialang.org/en/v1/stdlib/REPL/), enter `]` to bring up Julia's [package manager](https://docs.julialang.org/en/v1/stdlib/Pkg/), +and add the listed packages: + +> julia> ] +> +> (@v1.7) pkg> add #pkg_name# + +- Scientific computing + - LinearAlgebra + - SparseArrays + - Statistics : mean +- Image process + - ImageFiltering: imfilter +- Modelling + - [Gmsh](https://onlinelibrary.wiley.com/doi/10.1002/nme.2579) +- FEM + - [Gridap](https://joss.theoj.org/papers/10.21105/joss.02520) +- AD + - [ForwardDiff](https://arxiv.org/abs/1607.07892) + - [Zygote](https://arxiv.org/abs/1810.07951) +- Optimization + - [NLopt](https://github.com/stevengj/nlopt) +- Visualization + - Plots + +## TODOs + +- [x] [`top99neo.jl`](./top_oc/top99neo.jl) + top99neo.m rewritten in Julia +- [x] [`MMA.jl`](./top_mma/MMA.jl) + MMA algorithm (mmasub.m + subsolve.m) rewritten in Julia +- [x] [`top99neo_mma.jl`](./top_mma/top99neo_mma.jl) + 2D code (top99neo + MMA) written in Julia +- [ ] `top99neo_AD.jl` + Sensitivity Analysis using Automatic Differentiation +- [ ] `top99neo_NLopt.jl` + Optimization solved with NLopt +- [ ] `top3D.jl` + 3D code (top3D125 + MMA) written in Julia +- [ ] `top_flux.jl` + Combine TO with machine learning through [Flux](https://arxiv.org/abs/1811.01457) + +## Acknowledgements + +- [TopOpt Group](https://www.topopt.mek.dtu.dk/) 🇩🇰 +Matlab codes for topology optimization + + - v1.0 [**top99.m**](https://www.topopt.mek.dtu.dk/Apps-and-software/A-99-line-topology-optimization-code-written-in-MATLAB) + Educatianal TO enlightenment for every beginners + - v2.0 [**top88.m**](https://www.topopt.mek.dtu.dk/Apps-and-software/Efficient-topology-optimization-in-MATLAB) + Loop vectorization and memory preallocation + - v3.0 [**top99neo.m**](https://www.topopt.mek.dtu.dk/Apps-and-software/New-99-line-topology-optimization-code-written-in-MATLAB) + Half matrix assembly operation, filter implementation and volume-preserving density projection + +- Prof. [Krister Svanberg](https://people.kth.se/~krille/) 🇸🇪 + - Freely available [Matlab code](http://www.smoptit.se/) for CCSA/MMA[^4] and GCMMA + +## Author ©️ + +📧 Please contact to liyu_npu@outlook.com + +⚠️ Disclaimer: The author reserves all rights but does not guarantee that the code is free from errors. Furthermore, we shall not be liable in any event. + +| Name | Info. | Hobby | Food | +| ----- | :--------: | :-----------: | :-------: | +| Yu Li | 🇨🇳 🎓 1️⃣9️⃣9️⃣0️⃣ ♑ | 🎧 🃏 🎮 🏀 🏊 🏃 🚴‍♂️ | 🍦 🦞 🍣 🌽 🍌 | + +```bibtex +@misc{Yu2022, + author = {Yu Li}, + title = {Topology Optimization in Julia}, + year = {2022}, + publisher = {GitHub}, + journal = {GitHub repository}, + howpublished = {\url{https://github.com/yuloveyet/Topology-Optimization-in-Julia}}, + } +``` + +**References** +[^1]: Ferrari, F., & Sigmund, O. (2020). A new generation 99 line Matlab code for compliance topology optimization and its extension to 3D. Structural and Multidisciplinary Optimization, 62(4), 2211-2228. +[^2]:Sigmund, O. (2001). A 99 line topology optimization code written in Matlab. Structural and multidisciplinary optimization, 21(2), 120-127. +[^3]:Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., & Sigmund, O. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 43(1), 1-16. +[^4]: Svanberg, K. (2002). A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization, 12(2), 555-573. diff --git a/top_mma/MMA.jl b/top_mma/MMA.jl new file mode 100755 index 0000000..123f458 --- /dev/null +++ b/top_mma/MMA.jl @@ -0,0 +1,407 @@ +######################################################################################################## +### MMA-Julia (1.7.1) +######################################################################################################## +### MODIFIED BY YULI 2022/5/4 +######################################################################################################## +export mmasub +# Loading modules +using LinearAlgebra +using SparseArrays + +######################################################################################################## +### MMA FUNCTIONS ### +######################################################################################################## + +# Function for the MMA sub problem +function mmasub(m::Int, n::Int, iter::Int, xval::Array{Float64}, xmin::Array{Float64}, + xmax::Array{Float64}, xold1::Array{Float64}, xold2::Array{Float64}, f0val, + df0dx::Array{Float64}, df0dx2:: Array{Float64}, + fval::Float64, dfdx::Array{Float64}, dfdx2::Array{Float64}, + low::Array{Float64}, upp::Array{Float64}, a0::Float64, + a::Array{Float64}, c::Array{Float64}, d::Array{Float64}) + + # """ + # This function mmasub performs one MMA-iteration, aimed at solving the nonlinear programming problem: + # + # Minimize f_0(x) + a_0*z + sum( c_i*y_i + 0.5*d_i*(y_i)^2 ) + # subject to f_i(x) - a_i*z - y_i < = 0, i = 1, ..., m + # xmin_j < = x_j < = xmax_j, j = 1, ..., n + # z > = 0, y_i > = 0, i = 1, ..., m + # INPUT: + # + # m = The number of general constraints. + # n = The number of variables x_j. + # iter = Current iteration number ( =1 the first time mmasub is called). + # xval = Column vector with the current values of the variables x_j. + # xmin = Column vector with the lower bounds for the variables x_j. + # xmax = Column vector with the upper bounds for the variables x_j. + # xold1 = xval, one iteration ago (provided that iter>1). + # xold2 = xval, two iterations ago (provided that iter>2). + # f0val = The value of the objective function f_0 at xval. + # df0dx = Column vector with the derivatives of the objective function + # f_0 with respect to the variables x_j, calculated at xval. + # fval = Column vector with the values of the constraint functions f_i, calculated at xval. + # dfdx = (m x n)-matrix with the derivatives of the constraint functions + # f_i with respect to the variables x_j, calculated at xval. + # dfdx(i,j) = the derivative of f_i with respect to x_j. + # low = Column vector with the lower asymptotes from the previous + # iteration (provided that iter>1). + # upp = Column vector with the upper asymptotes from the previous + # iteration (provided that iter>1). + # a0 = The constants a_0 in the term a_0*z. + # a = Column vector with the constants a_i in the terms a_i*z. + # c = Column vector with the constants c_i in the terms c_i*y_i. + # d = Column vector with the constants d_i in the terms 0.5*d_i*(y_i)^2. + # + # OUTPUT: + # + # xmma = Column vector with the optimal values of the variables x_j + # in the current MMA subproblem. + # ymma = Column vector with the optimal values of the variables y_i + # in the current MMA subproblem. + # zmma = Scalar with the optimal value of the variable z + # in the current MMA subproblem. + # lam = Lagrange multipliers for the m general MMA constraints. + # xsi = Lagrange multipliers for the n constraints alfa_j - x_j < = 0. + # eta = Lagrange multipliers for the n constraints x_j - beta_j < = 0. + # mu = Lagrange multipliers for the m constraints -y_i < = 0. + # zet = Lagrange multiplier for the single constraint -z < = 0. + # s = Slack variables for the m general MMA constraints. + # low = Column vector with the lower asymptotes, calculated and used + # in the current MMA subproblem. + # upp = Column vector with the upper asymptotes, calculated and used + # in the current MMA subproblem. + # """ + + epsimin = sqrt(m + n) * 10^(-9) + feps = 0.000001 + asyinit = 0.5 + asyincr = 1.05 + asydecr = 0.65 + albefa = 0.1 + een = ones(n, 1) + zeron = zeros(n, 1) + + + if iter <= 2 + low = xval - asyinit .* (xmax - xmin) + upp = xval + asyinit .* (xmax - xmin) + else + zzz = (xval - xold1) .* (xold1 - xold2) + factor = copy(een) + factor[findall(zzz .> 0.0)] .= asyincr + factor[findall(zzz .< 0.0)] .= asydecr + low = xval - factor .* (xold1 - low) + upp = xval + factor .* (upp - xold1) + lowmin = xval - 10.0 .* (xmax - xmin) + lowmax = xval - 0.01 .* (xmax - xmin) + uppmin = xval + 0.01 .* (xmax - xmin) + uppmax = xval + 10.0 .* (xmax - xmin) + low = max.(low, lowmin) + low = min.(low, lowmax) + upp = min.(upp, uppmax) + upp = max.(upp, uppmin) + end + + zzz = low + albefa .* (xval - low) + alfa = max.(zzz, xmin) + + zzz = upp - albefa .* (upp - xval) + beta = min.(zzz, xmax) + + + ux1 = upp - xval + ux2 = ux1 .* ux1 + ux3 = ux2 .* ux1 + xl1 = xval - low + xl2 = xl1 .* xl1 + xl3 = xl2 .* xl1 + ul1 = upp - low + ulinv1 = een ./ ul1 + + uxinv1 = een ./ ux1 + xlinv1 = een ./ xl1 + uxinv3 = een ./ ux3 + xlinv3 = een ./ xl3 + diap = (ux3 .* xl1) ./ (2 * ul1) + diaq = (ux1 .* xl3) ./ (2 * ul1) + + p0 = copy(zeron) + q0 = copy(zeron) + p0[findall(df0dx .> 0.0)] = df0dx[findall(df0dx .> 0.0)] + p0 = p0 + 0.001 .* abs.(df0dx) + feps * ulinv1 + p0 = p0 .* ux2 + # q0 = zeron + q0[findall(df0dx .< 0.0)] = -df0dx[findall(df0dx .< 0.0)] + q0 = q0 + 0.001 * abs.(df0dx) + feps * ulinv1 + q0 = q0 .* xl2 + dg0dx2 = 2 * (p0 ./ ux3 + q0 ./ xl3) + del0 = df0dx2 - dg0dx2 + delpos0 = copy(zeron) + delpos0[findall(del0 .> 0.0)] = del0[findall(del0 .> 0.0)] + p0 = p0 + delpos0 .* diap + q0 = q0 + delpos0 .* diaq + P = spzeros(m, n) + P[findall(dfdx .> 0.0)] = dfdx[findall(dfdx .> 0.0)] + # P = P * diag(ux2); + # P = P * spdiagm(n, n, 0 => ux2) + P = P * sparse(Diagonal(ux2[:])) + Q = spzeros(m, n) + Q[findall(dfdx .< 0.0)] = -dfdx[findall(dfdx .< 0.0)] + # Q = Q * diag(xl2); + # Q = Q * spdiagm(n, n, 0 => xl2) + Q = Q * sparse(Diagonal(xl2[:])) + # dgdx2 = 2.0*(P*diag(uxinv3) + Q*diag(xlinv3)); + # dgdx2 = P * spdiagm(n, n, 0 => uxinv3) + Q * spdiagm(n, n, 0 => xlinv3) + dgdx2 = P * sparse(Diagonal(uxinv3[:])) + Q * sparse(Diagonal(xlinv3[:])) + dgdx2 = 2.0 * dgdx2 + del = dfdx2 - dgdx2 + delpos = zeros(m, n) + delpos[findall(del .> 0.0)] = del[findall(del .> 0.0)] + # P = P + delpos*diag(diap); + # P = P + delpos * spdiagm(n, n, 0 => diap) + P = P + delpos * sparse(Diagonal(diap[:])) + # Q = Q + delpos*diag(diaq); + # Q = Q + delpos * spdiagm(n, n, 0 => diap) + Q = Q + delpos * sparse(Diagonal(diap[:])) + b = P * uxinv1 + Q * xlinv1 .- fval + + + # b = P * uxinv + Q * xlinv - fval + # Solving the subproblem by a primal-dual Newton method + xmma, ymma, zmma, lam, xsi, eta, mu, zet, s = + subsolv(m, n, epsimin, low, upp, alfa, beta, p0, q0, P, Q, a0, a, b, c, d) + # Return values + return xmma, ymma, zmma, lam, xsi, eta, mu, zet, s, low, upp +end + + +# Function for solving the subproblem (can be used for MMA and GCMMA) +function subsolv(m::Int, n::Int, epsimin::Float64, low::Array{Float64}, upp::Array{Float64}, + alfa::Array{Float64}, beta::Array{Float64}, p0::Array{Float64}, q0::Array{Float64}, + P::Array{Float64}, Q::Array{Float64}, a0::Float64, a::Array{Float64}, b::Array{Float64}, + c::Array{Float64}, d::Array{Float64}) + + # """ + # This function subsolv solves the MMA subproblem: + # + # minimize SUM[p0j/(uppj-xj) + q0j/(xj-lowj)] + a0*z + SUM[ci*yi + 0.5*di*(yi)^2], + # + # subject to SUM[pij/(uppj-xj) + qij/(xj-lowj)] - ai*z - yi < = bi, + # alfaj < = xj < = betaj, yi > = 0, z > = 0. + # + # Input : m, n, low, upp, alfa, beta, p0, q0, P, Q, a0, a, b, c, d. + # Output: xmma, ymma, zmma, slack variables and Lagrange multiplers. + # """ + + een = ones(Float64, n) + eem = ones(Float64, m) + epsi = 1.0 + epsvecn = epsi .* een + epsvecm = epsi .* eem + x = 0.5 .* (alfa + beta) + y = copy(eem) + z = 1.0 + lam = copy(eem) + xsi = een ./ (x - alfa) + xsi = max.(xsi, een) + eta = een ./ (beta - x) + eta = max.(eta, een) + mu = max.(eem, 0.5 .* c) + zet = 1.0 + s = copy(eem) + itera = 0 + + while epsi > epsimin # Start while epsi>epsimin + epsvecn = epsi .* een + epsvecm = epsi .* eem + ux1 = upp - x + xl1 = x - low + ux2 = ux1 .* ux1 + xl2 = xl1 .* xl1 + uxinv1 = een ./ ux1 + xlinv1 = een ./ xl1 + + plam = p0 + (P)' * lam + qlam = q0 + (Q)' * lam + gvec = P * uxinv1 + Q * xlinv1 + dpsidx = (plam ./ ux2) - (qlam ./ xl2) + + rex = dpsidx - xsi + eta + rey = c + d .* y - mu - lam + rez = a0 .- zet .- (a)' * lam + relam = gvec - a .* z - y + s - b + rexsi = xsi .* (x - alfa) - epsvecn + reeta = eta .* (beta - x) - epsvecn + remu = mu .* y - epsvecm + rezet = zet * z - epsi + res = lam .* s - epsvecm + + residu1 = [rex' rey' rez]' + residu2 = [relam' rexsi' reeta' remu' rezet res']' + residu = [residu1' residu2']' + residunorm = norm(residu, 2) + residumax = maximum(abs.(residu)) + + ittt = 0 + while (residumax > 0.9 * epsi) && (ittt < 100) # Start while (residumax>0.9*epsi) and (ittt<100) + ittt = ittt + 1 + itera = itera + 1 + + if ittt == 100 + println("max inner iter reached") + end + ux1 = upp - x + xl1 = x - low + ux2 = ux1 .* ux1 + xl2 = xl1 .* xl1 + ux3 = ux1 .* ux2 + xl3 = xl1 .* xl2 + uxinv1 = een ./ ux1 + xlinv1 = een ./ xl1 + uxinv2 = een ./ ux2 + xlinv2 = een ./ xl2 + plam = p0 + (P)' * lam + qlam = q0 + (Q)' * lam + gvec = P * uxinv1 + Q * xlinv1 + # GG = P .* transpose(uxinv2) - Q .* transpose(xlinv2) + # GG = P .* spdiagm(n,n, 0 => uxinv2) - Q .* spdiagm(n, n, 0 => xlinv2) + GG = P * sparse(Diagonal(uxinv2[:])) - Q * sparse(Diagonal(xlinv2[:])) + dpsidx = (plam ./ ux2) - (qlam ./ xl2) + delx = dpsidx - epsvecn ./ (x - alfa) + epsvecn ./ (beta - x) + dely = c + d .* y - lam - epsvecm ./ y + delz = a0 .- transpose(a) * lam .- epsi / z + dellam = gvec - a .* z - y - b + epsvecm ./ lam + diagx = plam ./ ux3 + qlam ./ xl3 + diagx = 2.0 .* diagx + xsi ./ (x - alfa) + eta ./ (beta - x) + diagxinv = een ./ diagx + diagy = d + mu ./ y + diagyinv = eem ./ diagy + diaglam = s ./ lam + diaglamyi = diaglam + diagyinv + + if m < n # Start if m < n + blam = dellam .+ dely ./ diagy .- GG * (delx ./ diagx) + bb = [blam' delz]' + # Alam = spdiagm(0 => diaglamyi) + (GG .* transpose(diagxinv)) * transpose(GG) + # Alam = spdiagm(m, m, 0 => diaglamyi) + (GG .* spdiagm(n, n, 0 => diagxinv)) * transpose(GG) + Alam = sparse(Diagonal(diaglamyi[:])) + (GG * sparse(Diagonal(diagxinv[:]))) * (GG)' + AA = [Alam a + a' -zet/z] + solut = AA \ bb + dlam = solut[1:m] + dz = solut[m+1] + dx = -delx ./ diagx - ((GG)' * dlam) ./ diagx + else + diaglamyiinv = eem ./ diaglamyi + dellamyi = dellam + dely ./ diagy + # Axx = spdiagm(0 => diagx) + (transpose(GG) .* transpose(diaglamyiinv)) * GG + # Axx = spdiagm(n,n, 0 => diagx) + (transpose(GG) .* spdiagm(m, m, 0 => diaglamyiinv)) * GG + Axx = sparse(Diagonal(diagx[:])) + ((GG)' .* sparse(Diagonal(diaglamyiinv[:]))) * GG + azz = zet / z + (a)' * (a ./ diaglamyi) + axz = -(GG)' * (a ./ diaglamyi) + bx = delx + (GG)' * (dellamyi ./ diaglamyi) + bz = delz - (a)' * (dellamyi ./ diaglamyi) + # AAr1 = [Axx axz] + # AAr2 = [transpose(axz) azz] + # AA = [AAr1; AAr2] + AA = [Axx axz + axz' azz] + bb = [-bx' -bz]' + solut = AA \ bb + dx = solut[1:n] + dz = solut[n+1] + dlam = (GG * dx) ./ diaglamyi - dz .* (a ./ diaglamyi) + dellamyi ./ diaglamyi + end # End if mresidunorm) and (itto<50) + while (resinew > residunorm) && (itto < 50) + itto = itto + 1 + + x = xold + steg .* dx + y = yold + steg .* dy + z = zold + steg * dz + lam = lamold + steg .* dlam + xsi = xsiold + steg .* dxsi + eta = etaold + steg .* deta + mu = muold + steg .* dmu + zet = zetold + steg * dzet + s = sold + steg .* ds + ux1 = upp - x + xl1 = x - low + ux2 = ux1 .* ux1 + xl2 = xl1 .* xl1 + uxinv1 = een ./ ux1 + xlinv1 = een ./ xl1 + plam = p0 + (P)' * lam + qlam = q0 + (Q)' * lam + gvec = P * uxinv1 + Q * xlinv1 + dpsidx = plam ./ ux2 - qlam ./ xl2 + + rex = dpsidx - xsi + eta + rey = c .+ d .* y - mu - lam + rez = a0 - zet .- (a)' * lam + relam = gvec - a .* z - y + s - b + rexsi = xsi .* (x - alfa) - epsvecn + reeta = eta .* (beta - x) - epsvecn + remu = mu .* y - epsvecm + rezet = zet * z - epsi + res = lam .* s - epsvecm + + residu1 = [rex' rey' rez]' + residu2 = [relam' rexsi' reeta' remu' rezet res']' + residu = [residu1' residu2']' + resinew = norm(residu, 2) + steg = steg / 2.0 + end # End: while (resinew>residunorm) and (itto<50) + residunorm = copy(resinew) + residumax = maximum(abs.(residu)) + steg = 2.0 * steg + end # End: while (residumax>0.9*epsi) and (ittt<200) + epsi = 0.1 * epsi + end # End: while epsi>epsimin + xmma = copy(x) + ymma = copy(y) + zmma = copy(z) + lamma = lam + xsimma = xsi + etamma = eta + mumma = mu + zetmma = zet + smma = s + # Return values + return xmma, ymma, zmma, lamma, xsimma, etamma, mumma, zetmma, smma +end + diff --git a/top_mma/TEST.ipynb b/top_mma/TEST.ipynb new file mode 100755 index 0000000..fb1a693 --- /dev/null +++ b/top_mma/TEST.ipynb @@ -0,0 +1,770 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# module TopOpt99neo\n", + "\n", + "# include(\"FastConv.jl/src/FastConv.jl\")\n", + "# import .FastConv.fastconv\n", + "\n", + "using LinearAlgebra, SparseArrays\n", + "using Plots\n", + "# : heatmap, savefig, @animate\n", + "using ImageFiltering: imfilter\n", + "using Statistics: mean\n", + "\n", + "using BenchmarkTools\n", + "using Zygote\n", + "\n", + "BLAS.set_num_threads(1)\n", + "\n", + "# abstract type top99neo end\n", + "\n", + "include(\"utils.jl\")\n", + "include(\"MMA.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct SetUp\n", + " nelx::Int\n", + " nely::Int\n", + "\n", + " eta::Float64\n", + " beta::Int\n", + " betaCnt::NTuple{4,Int}\n", + "\n", + " move::Float64\n", + " maxit::Int\n", + " maxchang::Float64\n", + "\n", + " pasS::Array{Int}\n", + " pasV::Array{Int}\n", + "\n", + " function SetUp()\n", + " nelx = 30\n", + " nely = 10\n", + " # volfrac = 0.3\n", + " maxit = 300\n", + " move = 0.1\n", + " beta = 2\n", + " eta = 0.5\n", + " maxchang = 1e-6\n", + " # penalCnt = {maxit+1, 3, 25, 0.25}\n", + " betaCnt = (1, 32, 10, 2) # continuation scheme on beta parCont = { istart,maxPar,steps,deltaPar }\n", + " \n", + " # elNrs = reshape(1:nely*nelx, nely, nelx)\n", + " # a1 = elNrs[Int.(nely/4:nely/2), Int.(nelx/4:nelx/2)]\n", + " # pasS, pasV = Array([]), a1[:]\n", + " pasS, pasV = Array([]), Array([])\n", + " \n", + " new(nelx, nely, eta, beta, betaCnt, move, maxit, maxchang, pasS, pasV)\n", + " end\n", + "\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "setup = SetUp()\n", + "# setup.nelx = 20\n", + "# setup.nely = 10\n", + "# setup.maxit = 100\n", + "# typeof(setup.nodeNrs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "mutable struct Mat\n", + " E0::Float64\n", + " Emin::Float64\n", + " ν::Float64\n", + " penal::Float64\n", + " volfrac::Float64\n", + "\n", + " function Mat()\n", + " E0 = 1\n", + " Emin = 1e-9\n", + " ν = 0.3\n", + " penal = 3.0\n", + " volfrac = 0.3\n", + " new(E0, Emin, ν, penal, volfrac)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mat = Mat()\n", + "# mat.volfrac" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct DiscretizationFeature\n", + " nEl::Int\n", + " nodeNrs::Array{Int,2}\n", + " nDof::Int\n", + " act\n", + "\n", + " cMat::Array{Int}\n", + " Iar::Array{Int}\n", + " Ke::Array{Float64,1}\n", + " Ke0::Array{Float64,2}\n", + " \n", + " function DiscretizationFeature(setup::SetUp, mat::Mat)\n", + " nelx = setup.nelx\n", + " nely = setup.nely\n", + " pasS, pasV = setup.pasS, setup.pasV\n", + " ν = mat.ν\n", + " \n", + " nEl = nely * nelx\n", + " nodeNrs = reshape(1:(1+nelx)*(1+nely), nely + 1, nelx + 1)\n", + " nDof = (nely + 1) * (nelx + 1) * 2\n", + " act = setdiff(collect(1:nEl), union(pasS, pasV))\n", + " \n", + " cVec = reshape(2 * nodeNrs[1:end-1, 1:end-1] .+ 1, nEl, 1)\n", + " # cMat = cVec + Int.([0 1 2 * nely .+ [2 3 0 1] -2 -1])\n", + " cMat = Int.(repeat(cVec, 1, 8) + repeat([0 1 2 * nely .+ [2 3 0 1] -2 -1], nelx * nely, 1))\n", + " # nDof = (nely + 1) * (nelx + 1) * 2\n", + " FuckRow = [1 2 3 4 5 6 7 8]\n", + " sI::Array{Int}, sII::Array{Int} = copy(FuckRow), fill(1, 1, 8)\n", + " for j in 2:8\n", + " sI = cat(sI, FuckRow[j:8]'; dims=2)\n", + " # sI = append!(sI, convert(Array{Int},[j:8]))\n", + " # sII = cat(2, sII, repmat(j, 1, 8 - j + 1))\n", + " sII = cat(sII, fill(j, 1, 8 - j + 1); dims=2)\n", + " end\n", + " iK::Array{Int,2}, jK::Array{Int,2} = cMat[:, sI][:, 1, :]', cMat[:, sII][:, 1, :]'\n", + " Iar = sort([iK[:] jK[:]]; dims=2, rev=true) # comma is a newline\n", + " # iK[:], jK[:] .= 0.0, 0.0\n", + " c1 = [12, 3, -6, -3, -6, -3, 0, 3, 12, 3, 0, -3, -6, -3, -6, 12, -3, 0, -3, -6, 3, 12, 3, -6, 3, -6, 12, 3, -6, -3, 12, 3, 0, 12, -3, 12]\n", + " c2 = [-4, 3, -2, 9, 2, -3, 4, -9, -4, -9, 4, -3, 2, 9, -2, -4, -3, 4, 9, 2, 3, -4, -9, -2, 3, 2, -4, 3, -2, 9, -4, -9, 4, -4, -3, -4]\n", + " Ke = 1 / (1 - ν^2) / 24 .* (c1 .+ ν .* c2) # half-KE vector\n", + " # full KE\n", + " # Ke0::Array{Float64} = zeros(8, 8)\n", + " # start_id, end_id = 1, 8\n", + " # for i in 1:8\n", + " # Ke0[i:8, i] = Ke[start_id:end_id]\n", + " # start_id, end_id = end_id + 1, 2 * end_id - start_id\n", + " # end\n", + " \n", + " Ke0::Array{Float64} = zeros(8, 8)\n", + " # Index::Array{Int} = [sI' sII']\n", + " # Ke0[sI, sII] = Ke\n", + " Index = findall(isequal(1), tril(ones(8, 8)))\n", + " Ke0[Index] = Ke'\n", + " # Ke0 = reshape(Ke0, 8, 8)\n", + " Ke0 = Ke0 + Ke0' - diagm(diag(Ke0))\n", + " new(nEl, nodeNrs, nDof, act, cMat, Iar, Ke, Ke0)\n", + " end\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "disfeature = DiscretizationFeature(setup, mat)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct LoadsSupportsBCs\n", + " # setup::SetUp\n", + " lcDof::Array{Int}\n", + " F\n", + " free::Array{Int}\n", + " fixed::Array{Int}\n", + "\n", + " function LoadsSupportsBCs(setup::SetUp, disfeature::DiscretizationFeature)\n", + " nelx = setup.nelx\n", + " nely = setup.nely\n", + " nodeNrs = disfeature.nodeNrs\n", + " nDof = disfeature.nDof\n", + " \n", + " load_position::Symbol = :half_MBB\n", + " if load_position == :half_MBB\n", + " load_nodey, load_nodex = 1, 1\n", + " # fixed = union([1:2:2*(nely+1)], 2 * nodeNrs[nely+1, nelx+1])\n", + " fixed = union(collect(1:2:2*(nely+1)), 2 * nodeNrs[end, end])\n", + " elseif load_position == :cantilever\n", + " load_nodey = nely + 1\n", + " load_nodex = nelx / 2 + 1\n", + " fixed = 1:2*(nely+1)\n", + " end\n", + " \n", + " F = spzeros(nDof)\n", + " \n", + " load_type::Symbol = :pin\n", + " if load_type == :pin # 1 point\n", + " lcDof = collect(2 * nodeNrs[load_nodey, load_nodex])\n", + " F[2, 1] = -1.0\n", + " elseif load_type == :points # 5 points\n", + " lcDof = collect(2 * nodeNrs[load_nodey, load_nodex], nodeNrs[load_nodey, load_nodex-1], nodeNrs[load_nodey, load_nodex-2], nodeNrs[load_nodey, load_nodex+1], nodeNrs[load_nodey, load_nodex+2])\n", + " F[lcDof', ones(length(lcDof'))] .= -1.0\n", + " elseif load_type == :line\n", + " lcDof = [2:2*(nely+1):nDof]\n", + " F = spzeros(nDof, 1)\n", + " # F = sparse(lcDof', ones(length(lcDof')), -1.0)\n", + " end\n", + " all = collect(1:nDof)\n", + " free = setdiff(all, fixed)\n", + " \n", + " new(lcDof, F, free, fixed)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "load = LoadsSupportsBCs(setup, disfeature)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct Initialization \n", + " # setup::SetUp\n", + " x::Array{Float64}\n", + " xPhys::Array{Float64}\n", + " xOld::Array{Float64}\n", + " ch::Float64\n", + " loop::Int\n", + " # U::Array{Float64}\n", + " # dsK::Array{Float64}\n", + " # dV::Array{Float64}\n", + "\n", + " function Initialization(setup::SetUp, disfeature::DiscretizationFeature, mat::Mat)\n", + " pasV = setup.pasV\n", + " pasS = setup.pasS\n", + " act = disfeature.act\n", + " volfrac = mat.volfrac\n", + " nEl = disfeature.nEl\n", + " nDof = disfeature.nDof\n", + " # column vectors\n", + " x = zeros(nEl, 1)\n", + " # dV[act, 1] .= 1.0 / nEl / volfrac\n", + " x[act] .= volfrac\n", + " x[pasS] .= 1.0\n", + " xPhys, xOld, ch, loop = copy(x), ones(nEl, 1), 1.0, 0\n", + " # x̅ x̃\n", + " \n", + " new(x, xPhys, xOld, ch, loop)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ini = Initialization(setup, disfeature, mat)\n", + "# typeof(ini.x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct Filter \n", + " rmin::Float64\n", + " ft::Int\n", + " h::Array{Float64}\n", + " Hs::Array{Float64}\n", + " dHs::Array{Float64}\n", + "\n", + " function Filter(setup::SetUp)\n", + " nelx = setup.nelx\n", + " nely = setup.nely\n", + " # bcF = setup.bcF\n", + " rmin = 6.5\n", + " ft = 3\n", + " dy, dx = meshgrid(-ceil(rmin)+1:ceil(rmin)-1, -ceil(rmin)+1:ceil(rmin)-1)\n", + " h = max.(0, rmin .- sqrt.(dx .^ 2 + dy .^ 2))\n", + " Hs = imfilter(ones(nely, nelx), h, \"symmetric\")\n", + " dHs = Hs\n", + " new(rmin, ft, h, Hs, dHs)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "\n", + "filter = Filter(setup)\n", + "# filter.Hs" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "FiniteElementAnalasys (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function FiniteElementAnalasys(mat::Mat, disfeature::DiscretizationFeature, load::LoadsSupportsBCs, xPhys::Array{Float64})\n", + " nEl, nDof, Iar, Ke = disfeature.nEl, disfeature.nDof, disfeature.Iar, disfeature.Ke\n", + " act = disfeature.act\n", + " Emin, penal, E0 = mat.Emin, mat.penal, mat.E0\n", + " F, free = load.F, load.free\n", + "\n", + " sK = Emin .+ xPhys .^ penal .* (E0 - Emin)\n", + " sK = reshape(Ke[:] * sK', length(Ke) * nEl, 1)\n", + " K = sparse(Iar[:, 1], Iar[:, 2], vec(sK), nDof, nDof)\n", + " U = zeros(nDof)\n", + " #~\n", + " # U[free] = cholesky(Symmetric(K[free, free], :L), check=false) \\ F[free]\n", + " K0 = K + K' - diagm(diag(K))\n", + " U[free] = K0[free, free] \\ F[free]\n", + " #~\n", + " Obj = F' * U\n", + " Vf = mean(xPhys[act])\n", + " return U, Obj, Vf\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1-element Vector{Float64}:\n", + " 4558.123953305818" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "U, C, vf = FiniteElementAnalasys(mat, disfeature, load, xval)\n", + "C" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function SensitivityAnalasys(setup::SetUp, filter::Filter, mat::Mat, disfeature::DiscretizationFeature, \n", + " U::Array{Float64}, xPhys::Array{Float64})\n", + " nelx, nely, act = setup.nelx, setup.nely, disfeature.act\n", + " dHs, h = filter.dHs, filter.h\n", + " E0, Emin, penal = mat.E0, mat.Emin, mat.penal\n", + " nEl, cMat, Ke0 = disfeature.nEl, disfeature.cMat, disfeature.Ke0\n", + " act = disfeature.act\n", + "\n", + " dsK, dV = zeros(nEl, 1), zeros(nEl, 1)\n", + " dV[act, 1] .= 1.0 / length(act)\n", + " dsK[act] = -penal * (E0 - Emin) .* xPhys[act] .^ (penal - 1)\n", + "\n", + " dc = dsK .* sum((U[cMat] * Ke0) .* U[cMat], dims=2)\n", + " dc = imfilter(reshape(dc, nely, nelx) ./ dHs, h, \"symmetric\")\n", + " dV0 = imfilter(reshape(dV, nely, nelx) ./ dHs, h, \"symmetric\")\n", + "\n", + " return reshape(dc, nEl, 1), reshape(dV0, nEl, 1)\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function AutomaticDifferentiation(mat::Mat, disfeature::DiscretizationFeature, load::LoadsSupportsBCs, xPhys::Array{Float64})\n", + " # fea = FiniteElementAnalasys()\n", + " dc_AD = gradient(x -> FiniteElementAnalasys(mat, disfeature, load, x), xPhys)\n", + " # dv_AD = gradient(x)\n", + "\n", + " return dc_AD\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "xval = ini.x\n", + "dc_AD = AutomaticDifferentiation(mat, disfeature, load, xval)\n", + "typeof(dc_AD)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "typeof(dc_AD)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function Visualization(setup::SetUp, x::Array{Float64}, loop::Int)\n", + " nelx, nely = setup.nelx, setup.nely\n", + " # cmap = cgrad(:Blues_9, rev=false)\n", + " plot = heatmap(reshape(x, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400,nely/nelx*400) , legend=:none, display_type=:gui)\n", + " display(plot)\n", + " savefig(plot, \"./top/res_$loop.pdf\")\n", + " # PLOT FINAL DESIGN\n", + " # heatmap(1.0 .- x[end:-1:1, :], yaxis=false, xaxis=false, legend=:none,color=:greys, grid=false, border=nothing, aspect_ratio=:equal)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function Optimization(setup::SetUp, mat::Mat, load::LoadsSupportsBCs,\n", + " filter::Filter, ini::Initialization, disfeature::DiscretizationFeature)\n", + " ch, loop = ini.ch, ini.loop\n", + " x, xPhys, xOld = ini.x, ini.xPhys, ini.xOld\n", + "\n", + " maxit, maxchang = setup.maxit, setup.maxchang\n", + " nely, nelx = setup.nely, setup.nelx\n", + " eta, beta, betaCnt = setup.eta, setup.beta, setup.betaCnt\n", + " volfrac, penal, nEl = mat.volfrac, mat.penal, disfeature.nEl\n", + " act = disfeature.act\n", + "\n", + " Hs, h, ft = filter.Hs, filter.h, filter.ft\n", + "\n", + " opt_hist = []\n", + " vf_hist = []\n", + "\n", + " ### Initiation of MMA ###\n", + " xval = copy(x[act])\n", + " xold1 = copy(xval)\n", + " xold2 = copy(xold1)\n", + "\n", + " low = copy(xval)\n", + " upp = copy(low)\n", + " #########################\n", + "\n", + " anim = @animate while ch > maxchang && loop < maxit || beta < betaCnt[2]\n", + " @time begin\n", + " loop = loop + 1\n", + " # COMPUTE PHYSICAL DENSITY FIELD \n", + " xTilde = imfilter(reshape(x, nely, nelx), h, \"symmetric\") ./ Hs\n", + " xPhys[act] = copy(xTilde[act])\n", + " if ft > 1\n", + " f = (mean(prj(xPhys[act], eta, beta)) .- volfrac) * (ft == 3)\n", + " while abs(f) > maxchang\n", + " eta = eta - f / mean(deta(xPhys[:], eta, beta))\n", + " f = mean(prj(xPhys[act], eta, beta)) - volfrac\n", + " end\n", + " filter.dHs = Hs ./ reshape(dprj(xTilde, eta, beta), nely, nelx)\n", + " xPhys = prj(xPhys, eta, beta)\n", + " end\n", + " ch = norm(xPhys - xOld) ./ sqrt(nEl)\n", + " xOld = copy(xPhys)\n", + " #~ SETUP AND SOLVE EQUILIBRIUM EQUATIONS\n", + " U, C, Vf = FiniteElementAnalasys(mat, disfeature, load, xPhys)\n", + " push!(opt_hist, C)\n", + " push!(vf_hist, Vf)\n", + " #~ COMPUTE SENSITIVITIES\n", + " dc, dV0 = SensitivityAnalasys(setup, filter, mat, disfeature, U, xPhys)\n", + " #~ MMA iteration\n", + " xmma, low, upp = MMAupdate(xval, low, upp, xold1, xold2, C, Vf, dc, dV0, loop, Mat().volfrac)\n", + " # Some vectors are updated:\n", + " xold2 = copy(xold1)\n", + " xold1 = copy(xval)\n", + " xval = copy(xmma)\n", + "\n", + " x[act] = xval\n", + "\n", + " #~ CONTINUATION\n", + " beta = cnt(beta, betaCnt, loop, ch, maxchang)\n", + "\n", + " heatmap(reshape(xPhys, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400, nely / nelx * 400), legend=:none)\n", + "\n", + " end\n", + " if mod(loop, 10) == 0\n", + " println(\"It.: $loop C.: $C Vf.: $Vf ch.: $ch, p.: $penal beta.:$beta eta.: $eta \")\n", + " Visualization(setup, xPhys, loop)\n", + " end\n", + " end\n", + " gif(anim, \"./top/top_hist.gif\", fps=8)\n", + " return xPhys, opt_hist, vf_hist, anim\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# @time xPhys, opt_hist, vf_hist, loop = Optimization(setup, mat, load, filter, ini, disfeature)\n", + "Optimization(setup, mat, load, filter, ini, disfeature)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function MMAupdate(xval::Array{Float64}, low::Array{Float64}, upp::Array{Float64}, \n", + " xold1::Array{Float64}, xold2::Array{Float64},\n", + " Obj::Float64, Vf::Float64, dc::Array{Float64}, dV0::Array{Float64}, loop::Int, volfrac::Float64)\n", + " move = 0.1\n", + " ### Initiation of MMA ###\n", + " m = 1\n", + " # active design variable\n", + " n = length(act)\n", + " onen = ones(n, 1)\n", + " onem = ones(m, 1)\n", + " zeron = zeros(n, 1)\n", + " zerom = zeros(m, 1)\n", + " a_mma = zerom\n", + " c_mma = 1.0e3 * onem\n", + " d_mma = zerom\n", + " a0 = 1.0\n", + " # column vector\n", + " # xval = xval\n", + " xmin = max.(xval .- move, zeron)\n", + " xmax = min.(xval .+ move, onen)\n", + "\n", + " # low = low\n", + " # upp = upp\n", + " # objective function \n", + " f0val = Obj\n", + " df0dx = dc[act]\n", + " df0dx2 = 0.0 * df0dx\n", + " # constraint function\n", + " fval = Vf / volfrac - 1.0 # column vector\n", + " dfdx = reshape(dV0[act], 1, length(act)) ./ volfrac # (m * n)\n", + " dfdx2 = 0.0 * dfdx\n", + "\n", + " # The MMA subproblem is solved at the point xval:\n", + " xmma, ymma, zmma, lam, xsi, eta, mu, zet, s, low, upp =\n", + " mmasub(m, n, loop, xval, xmin, xmax, xold1, xold2,\n", + " f0val, df0dx, df0dx2, fval, dfdx, dfdx2, low, upp, a0, a_mma, c_mma, d_mma)\n", + " \n", + " return xmma, low, upp\n", + " # xmma =\n", + " # mmasub(m, n, loop, xval, xmin, xmax, xold1, xold2,\n", + " # f0val, df0dx, df0dx2, fval, dfdx, dfdx2, low, upp, a0, a_mma, c_mma, d_mma)\n", + " # return xmma\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "include(\"MMA.jl\")\n", + "### Initiation of MMA ###\n", + "x = ones(disfeature.nEl, 1) * 0.5\n", + "act = disfeature.act\n", + "xval = copy(x[act])\n", + "xold1 = copy(xval)\n", + "xold2 = copy(xold1)\n", + "\n", + "low = copy(xval)\n", + "upp = copy(low)\n", + "\n", + "xval, low, upp = MMAupdate(xval, low, upp, xold1, xold2, 1.0, 0.3, x[act],\n", + " reshape(x[act], 1, length(act)) , 1, Mat().volfrac)\n", + "# ux2 = MMAupdate(xval, low, upp, xold1, xold2, 1.0, 0.3, x[act],\n", + "# reshape(x[act], 1, length(act)) , 1, Mat().volfrac)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "size(xval)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using NLopt\n", + "\n", + "function myfunc(x::Vector, grad::Vector)\n", + " if length(grad) > 0\n", + " grad[1] = 0\n", + " grad[2] = 0.5/sqrt(x[2])\n", + " end\n", + " return sqrt(x[2])\n", + "end\n", + "\n", + "function myconstraint(x::Vector, grad::Vector, a, b)\n", + " if length(grad) > 0\n", + " grad[1] = 3a * (a*x[1] + b)^2\n", + " grad[2] = -1\n", + " end\n", + " (a*x[1] + b)^3 - x[2]\n", + "end\n", + "\n", + "opt = Opt(:LD_MMA, 2)\n", + "opt.lower_bounds = [-Inf, 0.]\n", + "opt.xtol_rel = 1e-4\n", + "\n", + "opt.min_objective = myfunc\n", + "inequality_constraint!(opt, (x,g) -> myconstraint(x,g,2,0), 1e-8)\n", + "inequality_constraint!(opt, (x,g) -> myconstraint(x,g,-1,1), 1e-8)\n", + "\n", + "(minf,minx,ret) = optimize(opt, [1.234, 5.678])\n", + "numevals = opt.numevals # the number of function evaluations\n", + "println(\"got $minf at $minx after $numevals iterations (returned $ret)\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using NLopt\n", + "function update_NLopt(act, xval, low, upp, C, Vf, dc, dV0)\n", + " alg = \":LD_MMA\"\n", + " n = length(act)\n", + " opt = Opt(alg, n)\n", + " opt.lower_bounds = low\n", + " opt.upper_bounds = upp\n", + "\n", + " opt.min_objective = ObjectiveFunction\n", + "\n", + " inequality_constraint!(opt, (x, g) -> VolumeConstraint(x, g;), 1e-8)\n", + "\n", + " return\n", + "end\n", + "\n", + "function ObjectiveFunction(x, grad; act, obj, dobj)\n", + " if length(grad) > 0\n", + " grad[:] = dobj[act]\n", + " end\n", + " return obj\n", + "end\n", + "\n", + "function VolumeConstraint(x, g; )\n", + " if length(grad) > 0\n", + " grad[:] = dV0\n", + " end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "f(x::Matrix, y) = sum(sin, x) + prod(tan, x) * sum(sqrt, x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using Zygote\n", + "grad = gradient(y -> f(y), rand(3))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "typeof(grad)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.7.2", + "language": "julia", + "name": "julia-1.7" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/top_mma/main_test.ipynb b/top_mma/main_test.ipynb new file mode 100755 index 0000000..557c146 --- /dev/null +++ b/top_mma/main_test.ipynb @@ -0,0 +1,682 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Filter(6.5, 3, [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], [288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766; 288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766; … ; 288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766; 288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766], [288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766; 288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766; … ; 288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766; 288.13372312595766 288.13372312595766 … 288.13372312595766 288.13372312595766])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# module test\n", + "# export main\n", + "# push!(LOAD_PATH, \"C:/Users/Yu/Desktop/test/top_mma\")\n", + "push!(LOAD_PATH, \"/Users/yu/TopCodes/Julia/test/top_mma\")\n", + "include(\"top99neo_mma.jl\")\n", + "# include(joinpath(@__DIR__, \"top99neo.jl\"))\n", + "# using .TopOpt99neo_MMA\n", + "# function main()\n", + "setup = SetUp()\n", + "setup.nely = 40\n", + "setup.nelx = setup.nely * 3\n", + "mat = Mat()\n", + "mat.penal = 1.0\n", + "disfeature = DiscretizationFeature(setup, mat)\n", + "load = LoadsSupportsBCs(setup, disfeature)\n", + "ini = Initialization(setup, disfeature, mat)\n", + "filter = Filter(setup)\n", + " \n", + " # return xPhys, opt_hist, vf_hist, anim\n", + "# end\n", + "\n", + "# end" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 23.633891 seconds (32.13 M allocations: 1.795 GiB, 4.36% gc time, 89.25% compilation time)\n", + " 7.542493 seconds (5.40 M allocations: 417.024 MiB, 1.99% gc time, 66.27% compilation time)\n", + " 7.043414 seconds (4.24 M allocations: 351.043 MiB, 1.29% gc time, 64.35% compilation time)\n", + " 7.015602 seconds (4.24 M allocations: 342.473 MiB, 1.36% gc time, 64.18% compilation time)\n", + " 2.483729 seconds (35.93 k allocations: 166.313 MiB, 0.92% gc time)\n", + " 2.491934 seconds (36.24 k allocations: 167.530 MiB, 0.97% gc time)\n", + " 2.474496 seconds (33.89 k allocations: 158.970 MiB, 0.89% gc time)\n", + " 2.509636 seconds (33.89 k allocations: 158.970 MiB, 0.92% gc time)\n", + " 2.474636 seconds (33.90 k allocations: 158.971 MiB, 0.94% gc time)\n", + " 2.468103 seconds (32.68 k allocations: 154.140 MiB, 0.95% gc time)\n", + " 2.469903 seconds (32.99 k allocations: 155.356 MiB, 0.96% gc time)\n", + " 2.477608 seconds (31.51 k allocations: 149.860 MiB, 0.99% gc time)\n", + " 2.512768 seconds (36.50 k allocations: 168.197 MiB, 0.91% gc time)\n", + " 2.476235 seconds (33.86 k allocations: 158.420 MiB, 0.93% gc time)\n", + " 2.483626 seconds (35.03 k allocations: 162.700 MiB, 0.90% gc time)\n", + " 2.481973 seconds (35.03 k allocations: 162.700 MiB, 0.95% gc time)\n", + " 2.482441 seconds (36.20 k allocations: 166.980 MiB, 0.95% gc time)\n", + " 2.484969 seconds (36.50 k allocations: 168.197 MiB, 0.95% gc time)\n", + " 2.509633 seconds (39.46 k allocations: 179.191 MiB, 1.57% gc time)\n", + " 2.507952 seconds (39.46 k allocations: 179.191 MiB, 0.98% gc time)\n", + "It.: 20 C.: 252.06388217784087 Vf.: 0.3000000486842581 ch.: 0.005533489179191518, p.: 1.2 beta.:2.0 eta.: 0.335377776945556 \n", + " 2.495551 seconds (37.11 k allocations: 170.630 MiB, 1.24% gc time)\n", + " 2.508090 seconds (42.10 k allocations: 188.968 MiB, 0.98% gc time)\n", + " 2.554228 seconds (49.83 k allocations: 218.256 MiB, 0.90% gc time)\n", + " 2.542736 seconds (48.05 k allocations: 211.543 MiB, 1.48% gc time)\n", + " 2.549749 seconds (51.00 k allocations: 222.536 MiB, 1.49% gc time)\n", + " 2.532716 seconds (51.00 k allocations: 222.536 MiB, 0.89% gc time)\n", + " 2.538830 seconds (51.31 k allocations: 223.753 MiB, 0.87% gc time)\n", + " 2.552852 seconds (51.92 k allocations: 226.187 MiB, 1.45% gc time)\n", + " 2.565990 seconds (55.78 k allocations: 240.831 MiB, 1.50% gc time)\n", + " 2.560013 seconds (54.00 k allocations: 234.117 MiB, 1.48% gc time)\n", + " 2.582743 seconds (52.22 k allocations: 227.404 MiB, 1.45% gc time)\n", + " 2.566921 seconds (55.78 k allocations: 240.831 MiB, 0.92% gc time)\n", + " 2.542359 seconds (50.74 k allocations: 221.907 MiB, 0.94% gc time)\n", + " 2.699591 seconds (50.44 k allocations: 220.690 MiB, 1.65% gc time)\n", + " 2.599058 seconds (50.44 k allocations: 220.690 MiB, 0.92% gc time)\n", + " 2.507772 seconds (50.44 k allocations: 220.690 MiB, 1.55% gc time)\n", + " 2.487814 seconds (50.44 k allocations: 220.690 MiB, 1.51% gc time)\n", + " 2.451477 seconds (49.83 k allocations: 218.256 MiB, 0.89% gc time)\n", + " 2.613078 seconds (49.53 k allocations: 217.039 MiB, 2.27% gc time)\n", + " 2.613632 seconds (49.53 k allocations: 217.039 MiB, 1.03% gc time)\n", + "It.: 40 C.: 282.4183621732244 Vf.: 0.3000000015869856 ch.: 0.0018822135118330065, p.: 1.4 beta.:2.0 eta.: 0.32753725626501584 \n", + " 2.744842 seconds (49.83 k allocations: 218.256 MiB, 1.71% gc time)\n", + " 2.984513 seconds (53.09 k allocations: 230.470 MiB, 0.85% gc time)\n", + " 2.722451 seconds (57.60 k allocations: 248.132 MiB, 1.53% gc time)\n", + " 2.613040 seconds (51.92 k allocations: 226.187 MiB, 1.60% gc time)\n", + " 2.539466 seconds (51.92 k allocations: 226.187 MiB, 1.05% gc time)\n", + " 2.654197 seconds (49.27 k allocations: 216.410 MiB, 1.66% gc time)\n", + " 2.655350 seconds (50.44 k allocations: 220.690 MiB, 1.00% gc time)\n", + " 2.555461 seconds (50.44 k allocations: 220.690 MiB, 1.59% gc time)\n", + " 2.560210 seconds (50.44 k allocations: 220.690 MiB, 1.03% gc time)\n", + " 2.550502 seconds (49.83 k allocations: 218.256 MiB, 1.60% gc time)\n", + " 2.535319 seconds (49.83 k allocations: 218.256 MiB, 1.02% gc time)\n", + " 2.541149 seconds (48.66 k allocations: 213.976 MiB, 1.57% gc time)\n", + " 2.545415 seconds (49.83 k allocations: 218.256 MiB, 1.02% gc time)\n", + " 2.572688 seconds (49.83 k allocations: 218.256 MiB, 1.02% gc time)\n", + " 2.528090 seconds (49.83 k allocations: 218.256 MiB, 0.99% gc time)\n", + " 2.557792 seconds (52.18 k allocations: 226.817 MiB, 1.61% gc time)\n", + " 2.539763 seconds (52.18 k allocations: 226.817 MiB, 0.99% gc time)\n", + " 2.563995 seconds (53.35 k allocations: 231.097 MiB, 1.67% gc time)\n", + " 2.569799 seconds (53.35 k allocations: 231.097 MiB, 1.06% gc time)\n", + " 2.563906 seconds (53.35 k allocations: 231.097 MiB, 1.69% gc time)\n", + "It.: 60 C.: 321.96174126605825 Vf.: 0.30000000042517155 ch.: 0.0010504298988921721, p.: 1.5999999999999999 beta.:2.0 eta.: 0.32468471888413036 \n", + " 2.578507 seconds (59.56 k allocations: 254.301 MiB, 1.12% gc time)\n", + " 2.569300 seconds (60.47 k allocations: 257.952 MiB, 1.04% gc time)\n", + " 2.642531 seconds (70.89 k allocations: 297.604 MiB, 2.24% gc time)\n", + " 2.629846 seconds (71.76 k allocations: 300.668 MiB, 1.61% gc time)\n", + " 2.749413 seconds (71.45 k allocations: 299.451 MiB, 1.65% gc time)\n", + " 2.871839 seconds (71.45 k allocations: 299.451 MiB, 1.76% gc time)\n", + " 2.687989 seconds (69.67 k allocations: 292.737 MiB, 1.69% gc time)\n", + " 2.887680 seconds (67.59 k allocations: 284.807 MiB, 1.91% gc time)\n", + " 2.868877 seconds (65.50 k allocations: 276.876 MiB, 1.71% gc time)\n", + " 2.789235 seconds (63.12 k allocations: 267.729 MiB, 1.82% gc time)\n", + " 2.526885 seconds (61.34 k allocations: 261.015 MiB, 1.71% gc time)\n", + " 2.502833 seconds (61.34 k allocations: 261.015 MiB, 1.81% gc time)\n", + " 2.544037 seconds (61.34 k allocations: 261.015 MiB, 1.05% gc time)\n", + " 2.580909 seconds (61.34 k allocations: 261.015 MiB, 1.90% gc time)\n", + " 2.594493 seconds (61.34 k allocations: 261.015 MiB, 1.84% gc time)\n", + " 2.524158 seconds (61.03 k allocations: 259.798 MiB, 1.09% gc time)\n", + " 2.506165 seconds (62.20 k allocations: 264.078 MiB, 1.83% gc time)\n", + " 2.443902 seconds (59.56 k allocations: 254.301 MiB, 1.17% gc time)\n", + " 2.458091 seconds (59.56 k allocations: 254.301 MiB, 1.80% gc time)\n", + " 2.453842 seconds (59.56 k allocations: 254.301 MiB, 1.84% gc time)\n", + "It.: 80 C.: 367.10092322947565 Vf.: 0.3000000001615869 ch.: 0.0009730860406811991, p.: 1.7999999999999998 beta.:2.0 eta.: 0.32247505983507935 \n", + " 2.454556 seconds (59.86 k allocations: 255.518 MiB, 1.23% gc time)\n", + " 2.489507 seconds (61.64 k allocations: 262.232 MiB, 1.99% gc time)\n", + " 2.510904 seconds (75.06 k allocations: 313.465 MiB, 1.80% gc time)\n", + " 2.495871 seconds (76.53 k allocations: 318.962 MiB, 1.79% gc time)\n", + " 2.483227 seconds (76.53 k allocations: 318.962 MiB, 1.78% gc time)\n", + " 2.486615 seconds (76.53 k allocations: 318.962 MiB, 1.86% gc time)\n", + " 2.713940 seconds (77.70 k allocations: 323.243 MiB, 1.94% gc time)\n", + " 2.608192 seconds (77.40 k allocations: 322.026 MiB, 1.93% gc time)\n", + " 2.810418 seconds (77.40 k allocations: 322.026 MiB, 1.89% gc time)\n", + " 2.698368 seconds (75.62 k allocations: 315.312 MiB, 1.75% gc time)\n", + " 2.632153 seconds (75.62 k allocations: 315.312 MiB, 1.97% gc time)\n", + " 2.618081 seconds (77.40 k allocations: 322.026 MiB, 1.86% gc time)\n", + " 2.544162 seconds (77.40 k allocations: 322.026 MiB, 1.85% gc time)\n", + " 2.530027 seconds (77.40 k allocations: 322.026 MiB, 1.88% gc time)\n", + " 2.682546 seconds (78.88 k allocations: 327.523 MiB, 1.78% gc time)\n", + " 2.677404 seconds (77.40 k allocations: 322.026 MiB, 1.81% gc time)\n", + " 2.550289 seconds (73.23 k allocations: 306.165 MiB, 1.27% gc time)\n", + " 2.594195 seconds (75.01 k allocations: 312.878 MiB, 1.98% gc time)\n", + " 2.640601 seconds (75.01 k allocations: 312.878 MiB, 2.02% gc time)\n", + " 2.543590 seconds (73.23 k allocations: 306.165 MiB, 1.21% gc time)\n", + "It.: 100 C.: 416.1971100563556 Vf.: 0.3000000001854986 ch.: 0.0014653446652638112, p.: 1.9999999999999998 beta.:2.0 eta.: 0.3200760499923675 \n", + " 2.887247 seconds (69.98 k allocations: 293.954 MiB, 10.03% gc time)\n", + " 2.812550 seconds (78.62 k allocations: 326.893 MiB, 7.84% gc time)\n", + " 2.717321 seconds (100.37 k allocations: 409.849 MiB, 2.11% gc time)\n", + " 2.612134 seconds (100.37 k allocations: 409.849 MiB, 2.21% gc time)\n", + " 2.671393 seconds (100.37 k allocations: 409.849 MiB, 2.24% gc time)\n", + " 2.762367 seconds (99.20 k allocations: 405.569 MiB, 2.35% gc time)\n", + " 2.813349 seconds (102.45 k allocations: 417.780 MiB, 2.21% gc time)\n", + " 2.807382 seconds (102.45 k allocations: 417.780 MiB, 2.27% gc time)\n", + " 2.735045 seconds (102.45 k allocations: 417.780 MiB, 2.47% gc time)\n", + " 2.710863 seconds (100.98 k allocations: 412.283 MiB, 2.02% gc time)\n", + " 2.717637 seconds (100.98 k allocations: 412.283 MiB, 2.31% gc time)\n", + " 2.730000 seconds (100.98 k allocations: 412.283 MiB, 2.40% gc time)\n", + " 2.579725 seconds (100.98 k allocations: 412.283 MiB, 2.13% gc time)\n", + " 2.608467 seconds (99.20 k allocations: 405.569 MiB, 2.63% gc time)\n", + " 2.556019 seconds (99.20 k allocations: 405.569 MiB, 2.25% gc time)\n", + " 2.633828 seconds (102.15 k allocations: 416.563 MiB, 2.38% gc time)\n", + " 2.753143 seconds (99.20 k allocations: 405.569 MiB, 2.20% gc time)\n", + " 2.595887 seconds (102.15 k allocations: 416.563 MiB, 2.32% gc time)\n", + " 2.587585 seconds (102.15 k allocations: 416.563 MiB, 2.35% gc time)\n", + " 2.713205 seconds (103.32 k allocations: 420.843 MiB, 1.92% gc time)\n", + "It.: 120 C.: 465.3388211209528 Vf.: 0.30000000041901226 ch.: 0.002540014752051178, p.: 2.1999999999999997 beta.:2.0 eta.: 0.3171960041698332 \n", + " 2.766800 seconds (97.11 k allocations: 397.638 MiB, 2.65% gc time)\n", + " 2.647607 seconds (98.94 k allocations: 404.939 MiB, 2.10% gc time)\n", + " 2.860128 seconds (119.21 k allocations: 482.398 MiB, 2.58% gc time)\n", + " 2.860843 seconds (123.99 k allocations: 500.693 MiB, 2.97% gc time)\n", + " 3.022834 seconds (126.38 k allocations: 509.840 MiB, 3.23% gc time)\n", + " 2.901080 seconds (132.58 k allocations: 533.045 MiB, 2.77% gc time)\n", + " 2.895750 seconds (125.46 k allocations: 506.190 MiB, 3.34% gc time)\n", + " 2.856286 seconds (120.38 k allocations: 486.678 MiB, 2.97% gc time)\n", + " 3.010390 seconds (118.00 k allocations: 477.531 MiB, 2.26% gc time)\n", + " 2.799958 seconds (112.92 k allocations: 458.020 MiB, 2.98% gc time)\n", + " 2.746013 seconds (112.92 k allocations: 458.020 MiB, 2.23% gc time)\n", + " 2.671821 seconds (110.22 k allocations: 447.655 MiB, 2.26% gc time)\n", + " 2.700583 seconds (109.01 k allocations: 442.788 MiB, 2.44% gc time)\n", + " 2.662198 seconds (109.01 k allocations: 442.788 MiB, 2.50% gc time)\n", + " 2.725580 seconds (106.32 k allocations: 432.424 MiB, 2.70% gc time)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 2.891894 seconds (103.93 k allocations: 423.277 MiB, 2.73% gc time)\n", + " 2.780316 seconds (103.93 k allocations: 423.277 MiB, 2.66% gc time)\n", + " 2.817546 seconds (102.15 k allocations: 416.563 MiB, 2.64% gc time)\n", + " 2.954268 seconds (103.93 k allocations: 423.277 MiB, 2.75% gc time)\n", + " 2.865322 seconds (102.15 k allocations: 416.563 MiB, 1.99% gc time)\n", + "It.: 140 C.: 485.4863462826721 Vf.: 0.29999999678142314 ch.: 0.002157310008095807, p.: 2.4 beta.:2.0 eta.: 0.3129772980314933 \n", + " 2.777329 seconds (98.02 k allocations: 401.289 MiB, 2.81% gc time)\n", + " 2.761179 seconds (98.37 k allocations: 403.056 MiB, 2.10% gc time)\n", + " 2.928009 seconds (134.71 k allocations: 541.563 MiB, 3.34% gc time)\n", + " 2.921204 seconds (134.71 k allocations: 541.563 MiB, 3.48% gc time)\n", + " 3.021942 seconds (157.42 k allocations: 628.756 MiB, 3.37% gc time)\n", + " 2.975619 seconds (152.64 k allocations: 610.461 MiB, 3.42% gc time)\n", + " 2.969731 seconds (150.26 k allocations: 601.314 MiB, 3.47% gc time)\n", + " 2.988683 seconds (151.17 k allocations: 604.965 MiB, 3.49% gc time)\n", + " 3.006252 seconds (148.17 k allocations: 593.384 MiB, 3.68% gc time)\n", + " 3.039890 seconds (146.09 k allocations: 585.453 MiB, 9.10% gc time)\n", + " 2.884480 seconds (148.78 k allocations: 595.817 MiB, 3.37% gc time)\n", + " 2.856648 seconds (144.00 k allocations: 577.522 MiB, 2.74% gc time)\n", + " 2.884919 seconds (147.87 k allocations: 592.167 MiB, 3.22% gc time)\n", + " 2.845730 seconds (140.40 k allocations: 563.508 MiB, 3.05% gc time)\n", + " 2.923810 seconds (150.82 k allocations: 603.161 MiB, 3.76% gc time)\n", + " 2.894663 seconds (147.26 k allocations: 589.733 MiB, 3.08% gc time)\n", + " 2.873834 seconds (144.87 k allocations: 580.586 MiB, 3.18% gc time)\n", + " 2.905532 seconds (151.12 k allocations: 604.377 MiB, 3.22% gc time)\n", + " 2.906499 seconds (151.43 k allocations: 605.594 MiB, 3.25% gc time)\n", + " 2.909038 seconds (151.43 k allocations: 605.594 MiB, 3.30% gc time)\n", + "It.: 160 C.: 506.484108735154 Vf.: 0.29999999764667856 ch.: 0.0012929730417375583, p.: 2.6 beta.:2.0 eta.: 0.3123593961872853 \n", + " 2.835279 seconds (129.37 k allocations: 521.421 MiB, 2.68% gc time)\n", + " 2.940898 seconds (155.68 k allocations: 622.592 MiB, 3.48% gc time)\n", + " 3.046937 seconds (181.03 k allocations: 719.516 MiB, 3.85% gc time)\n", + " 3.011518 seconds (175.09 k allocations: 696.988 MiB, 3.46% gc time)\n", + " 3.009457 seconds (170.92 k allocations: 681.127 MiB, 3.59% gc time)\n", + " 3.031882 seconds (168.23 k allocations: 670.763 MiB, 3.65% gc time)\n", + " 2.998234 seconds (168.23 k allocations: 670.763 MiB, 3.77% gc time)\n", + " 3.007260 seconds (167.88 k allocations: 668.996 MiB, 3.82% gc time)\n", + " 2.985724 seconds (163.11 k allocations: 650.701 MiB, 3.36% gc time)\n", + " 2.974466 seconds (155.64 k allocations: 622.043 MiB, 3.40% gc time)\n", + " 2.942412 seconds (153.25 k allocations: 612.895 MiB, 3.02% gc time)\n", + " 2.932406 seconds (146.70 k allocations: 587.905 MiB, 3.63% gc time)\n", + " 2.933973 seconds (146.39 k allocations: 586.396 MiB, 3.17% gc time)\n", + " 2.895362 seconds (141.92 k allocations: 569.562 MiB, 3.21% gc time)\n", + " 2.918303 seconds (141.92 k allocations: 569.573 MiB, 3.29% gc time)\n", + " 2.902668 seconds (136.23 k allocations: 547.646 MiB, 2.81% gc time)\n", + " 2.868826 seconds (133.84 k allocations: 538.499 MiB, 2.93% gc time)\n", + " 2.831245 seconds (121.60 k allocations: 491.546 MiB, 2.94% gc time)\n", + " 2.817204 seconds (116.52 k allocations: 472.034 MiB, 3.02% gc time)\n", + " 2.758677 seconds (106.36 k allocations: 433.011 MiB, 2.36% gc time)\n", + "It.: 180 C.: 531.7174853082188 Vf.: 0.2999998676883111 ch.: 0.0008734051328254364, p.: 2.8000000000000003 beta.:2.0 eta.: 0.38681581566094736 \n", + " 2.743737 seconds (106.36 k allocations: 433.165 MiB, 2.47% gc time)\n", + " 2.840415 seconds (126.42 k allocations: 510.529 MiB, 2.95% gc time)\n", + " 2.884370 seconds (138.05 k allocations: 555.063 MiB, 2.89% gc time)\n", + " 2.876649 seconds (138.35 k allocations: 556.343 MiB, 2.93% gc time)\n", + " 2.871201 seconds (135.66 k allocations: 545.973 MiB, 3.01% gc time)\n", + " 2.866094 seconds (135.32 k allocations: 544.147 MiB, 3.04% gc time)\n", + " 2.855630 seconds (122.16 k allocations: 493.553 MiB, 2.43% gc time)\n", + " 2.855827 seconds (122.16 k allocations: 493.460 MiB, 3.16% gc time)\n", + " 2.803037 seconds (119.78 k allocations: 483.962 MiB, 2.58% gc time)\n", + " 2.818501 seconds (119.17 k allocations: 481.963 MiB, 2.68% gc time)\n", + " 2.812715 seconds (119.47 k allocations: 483.109 MiB, 2.58% gc time)\n", + " 2.819715 seconds (114.70 k allocations: 464.451 MiB, 2.66% gc time)\n", + " 2.796620 seconds (114.70 k allocations: 464.806 MiB, 2.77% gc time)\n", + " 2.797383 seconds (114.70 k allocations: 464.847 MiB, 2.05% gc time)\n", + " 2.827795 seconds (114.70 k allocations: 464.882 MiB, 2.87% gc time)\n", + " 2.826913 seconds (115.56 k allocations: 468.111 MiB, 2.93% gc time)\n", + " 2.814646 seconds (111.40 k allocations: 452.227 MiB, 2.24% gc time)\n", + " 3.091060 seconds (105.45 k allocations: 429.273 MiB, 13.66% gc time)\n", + " 2.685124 seconds (103.06 k allocations: 420.409 MiB, 2.10% gc time)\n", + " 2.700202 seconds (115.92 k allocations: 421.298 MiB, 2.13% gc time, 0.44% compilation time)\n", + "It.: 200 C.: 558.4819501817269 Vf.: 0.30000006191116096 ch.: 0.0006629482699576825, p.: 3.0000000000000004 beta.:2.0 eta.: 0.4956558115373888 \n", + " 2.716640 seconds (105.10 k allocations: 427.652 MiB, 2.45% gc time)\n", + " 2.710414 seconds (105.75 k allocations: 430.867 MiB, 2.25% gc time)\n", + " 2.724300 seconds (110.83 k allocations: 450.171 MiB, 2.34% gc time)\n", + " 2.719633 seconds (105.75 k allocations: 431.028 MiB, 2.35% gc time)\n", + " 2.714736 seconds (105.71 k allocations: 430.096 MiB, 2.41% gc time)\n", + " 2.875826 seconds (105.10 k allocations: 427.877 MiB, 2.56% gc time)\n", + " 2.761255 seconds (103.36 k allocations: 421.509 MiB, 2.22% gc time)\n", + " 2.750557 seconds (99.84 k allocations: 408.580 MiB, 2.29% gc time)\n", + " 2.766420 seconds (100.71 k allocations: 411.640 MiB, 2.27% gc time)\n", + " 2.764967 seconds (100.71 k allocations: 411.903 MiB, 2.36% gc time)\n", + " 2.756127 seconds (100.71 k allocations: 411.854 MiB, 2.39% gc time)\n", + " 2.755379 seconds (101.88 k allocations: 416.175 MiB, 2.42% gc time)\n", + " 2.752523 seconds (100.71 k allocations: 411.851 MiB, 2.03% gc time)\n", + " 2.778746 seconds (100.71 k allocations: 411.838 MiB, 2.55% gc time)\n", + " 2.768649 seconds (100.71 k allocations: 411.916 MiB, 2.61% gc time)\n", + " 2.763283 seconds (101.88 k allocations: 416.067 MiB, 2.62% gc time)\n", + " 2.771204 seconds (100.71 k allocations: 412.141 MiB, 2.00% gc time)\n", + " 2.753624 seconds (100.71 k allocations: 411.927 MiB, 2.66% gc time)\n", + " 2.733184 seconds (100.71 k allocations: 411.947 MiB, 2.09% gc time)\n", + " 2.732905 seconds (99.24 k allocations: 406.554 MiB, 2.23% gc time)\n", + "It.: 220 C.: 484.2853128321875 Vf.: 0.2999999996524318 ch.: 0.05545768358497312, p.: 3.0000000000000004 beta.:4.0 eta.: 0.5530403414702602 \n", + " 2.768047 seconds (101.28 k allocations: 414.564 MiB, 2.84% gc time)\n", + " 2.784755 seconds (111.14 k allocations: 451.500 MiB, 2.30% gc time)\n", + " 2.814559 seconds (115.00 k allocations: 466.305 MiB, 2.84% gc time)\n", + " 2.797690 seconds (111.14 k allocations: 451.274 MiB, 2.89% gc time)\n", + " 2.777880 seconds (105.75 k allocations: 430.680 MiB, 2.35% gc time)\n", + " 2.768970 seconds (103.37 k allocations: 421.404 MiB, 2.43% gc time)\n", + " 2.767990 seconds (103.37 k allocations: 422.107 MiB, 2.54% gc time)\n", + " 2.774871 seconds (103.67 k allocations: 422.960 MiB, 2.56% gc time)\n", + " 2.772815 seconds (103.67 k allocations: 422.744 MiB, 2.50% gc time)\n", + " 2.808310 seconds (100.41 k allocations: 410.984 MiB, 2.59% gc time)\n", + " 2.787294 seconds (100.41 k allocations: 410.612 MiB, 2.57% gc time)\n", + " 2.777564 seconds (103.37 k allocations: 421.606 MiB, 2.63% gc time)\n", + " 2.764378 seconds (103.67 k allocations: 423.028 MiB, 2.02% gc time)\n", + " 2.781587 seconds (101.59 k allocations: 414.829 MiB, 2.67% gc time)\n", + " 2.807668 seconds (101.59 k allocations: 414.883 MiB, 2.73% gc time)\n", + " 2.772745 seconds (99.50 k allocations: 406.969 MiB, 2.04% gc time)\n", + " 2.782651 seconds (100.67 k allocations: 411.409 MiB, 2.87% gc time)\n", + " 2.762864 seconds (99.20 k allocations: 405.727 MiB, 2.10% gc time)\n", + " 3.021428 seconds (96.25 k allocations: 394.740 MiB, 2.71% gc time)\n", + " 2.960838 seconds (99.46 k allocations: 406.908 MiB, 2.45% gc time)\n", + "It.: 240 C.: 415.08074138149163 Vf.: 0.2999996542927569 ch.: 0.044421757368782, p.: 3.0000000000000004 beta.:6.0 eta.: 0.5514174098451565 \n", + " 2.856999 seconds (109.31 k allocations: 443.841 MiB, 2.90% gc time)\n", + " 2.853918 seconds (117.35 k allocations: 474.344 MiB, 2.86% gc time)\n", + " 2.852463 seconds (122.12 k allocations: 492.539 MiB, 2.13% gc time)\n", + " 2.849461 seconds (119.73 k allocations: 483.568 MiB, 2.27% gc time)\n", + " 3.233889 seconds (112.87 k allocations: 457.380 MiB, 14.54% gc time)\n", + " 2.750043 seconds (111.40 k allocations: 451.876 MiB, 2.52% gc time)\n", + " 2.720483 seconds (107.23 k allocations: 436.902 MiB, 2.18% gc time)\n", + " 2.725903 seconds (105.15 k allocations: 427.947 MiB, 2.61% gc time)\n", + " 2.717881 seconds (105.15 k allocations: 428.939 MiB, 2.30% gc time)\n", + " 2.732698 seconds (105.15 k allocations: 428.087 MiB, 2.34% gc time)\n", + " 2.714888 seconds (104.54 k allocations: 425.657 MiB, 1.98% gc time)\n", + " 2.722403 seconds (100.67 k allocations: 411.472 MiB, 2.44% gc time)\n", + " 2.744401 seconds (107.79 k allocations: 437.874 MiB, 2.50% gc time)\n", + " 2.725835 seconds (108.40 k allocations: 440.273 MiB, 2.13% gc time)\n", + " 2.752625 seconds (109.88 k allocations: 445.834 MiB, 2.64% gc time)\n", + " 2.741217 seconds (106.32 k allocations: 432.527 MiB, 2.29% gc time)\n", + " 2.787592 seconds (110.53 k allocations: 449.221 MiB, 2.67% gc time)\n", + " 2.756697 seconds (110.53 k allocations: 449.008 MiB, 2.35% gc time)\n", + " 2.787903 seconds (115.31 k allocations: 467.221 MiB, 2.84% gc time)\n", + " 2.811796 seconds (119.47 k allocations: 483.434 MiB, 2.88% gc time)\n", + "It.: 260 C.: 378.5089343314532 Vf.: 0.29999999991624204 ch.: 0.03132870878007018, p.: 3.0000000000000004 beta.:8.0 eta.: 0.5546214369887977 \n", + " 2.862694 seconds (130.81 k allocations: 526.329 MiB, 2.89% gc time)\n", + " 2.943738 seconds (149.61 k allocations: 598.292 MiB, 3.35% gc time)\n", + " 2.919757 seconds (149.61 k allocations: 598.292 MiB, 2.89% gc time)\n", + " 2.949663 seconds (147.22 k allocations: 589.077 MiB, 3.42% gc time)\n", + " 2.937967 seconds (143.35 k allocations: 574.500 MiB, 3.00% gc time)\n", + " 2.884123 seconds (135.63 k allocations: 545.211 MiB, 3.13% gc time)\n", + " 2.843292 seconds (127.55 k allocations: 514.118 MiB, 2.67% gc time)\n", + " 2.877420 seconds (127.51 k allocations: 513.531 MiB, 3.25% gc time)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 2.811137 seconds (119.13 k allocations: 481.223 MiB, 2.74% gc time)\n", + " 2.848024 seconds (119.13 k allocations: 481.222 MiB, 2.87% gc time)\n", + " 2.816933 seconds (120.91 k allocations: 487.936 MiB, 2.27% gc time)\n", + " 2.822074 seconds (120.91 k allocations: 487.936 MiB, 2.88% gc time)\n", + " 2.828007 seconds (119.43 k allocations: 482.439 MiB, 2.95% gc time)\n", + " 2.850612 seconds (122.69 k allocations: 494.650 MiB, 2.98% gc time)\n", + " 2.853051 seconds (125.64 k allocations: 505.644 MiB, 3.02% gc time)\n", + " 2.828906 seconds (125.64 k allocations: 505.644 MiB, 2.44% gc time)\n", + " 2.890272 seconds (131.93 k allocations: 529.874 MiB, 3.03% gc time)\n", + " 2.896557 seconds (130.46 k allocations: 524.526 MiB, 3.15% gc time)\n", + " 2.878258 seconds (130.20 k allocations: 523.896 MiB, 3.21% gc time)\n", + " 2.849862 seconds (123.64 k allocations: 499.059 MiB, 2.56% gc time)\n", + "It.: 280 C.: 357.2256484209688 Vf.: 0.299999999824066 ch.: 0.022588191628482784, p.: 3.0000000000000004 beta.:10.0 eta.: 0.5578136018010208 \n", + " 2.990229 seconds (144.83 k allocations: 580.157 MiB, 3.20% gc time)\n", + " 3.000765 seconds (154.69 k allocations: 617.951 MiB, 3.87% gc time)\n", + " 2.982562 seconds (153.51 k allocations: 613.523 MiB, 3.24% gc time)\n", + " 2.975805 seconds (148.74 k allocations: 595.229 MiB, 3.25% gc time)\n", + " 2.981175 seconds (146.65 k allocations: 587.297 MiB, 3.31% gc time)\n", + " 2.950235 seconds (142.79 k allocations: 573.008 MiB, 3.32% gc time)\n", + " 2.973505 seconds (146.91 k allocations: 588.069 MiB, 3.33% gc time)\n", + " 2.970157 seconds (146.61 k allocations: 586.710 MiB, 2.68% gc time)\n", + " 2.967808 seconds (146.91 k allocations: 587.927 MiB, 2.80% gc time)\n", + " 2.977080 seconds (146.91 k allocations: 588.595 MiB, 3.56% gc time)\n", + " 2.988707 seconds (146.91 k allocations: 587.927 MiB, 3.54% gc time)\n", + " 2.985652 seconds (144.53 k allocations: 578.780 MiB, 3.74% gc time)\n", + " 3.252498 seconds (146.00 k allocations: 584.425 MiB, 14.27% gc time)\n", + " 2.884485 seconds (140.92 k allocations: 564.913 MiB, 2.66% gc time)\n", + " 2.833859 seconds (135.23 k allocations: 542.969 MiB, 2.83% gc time)\n", + " 2.839562 seconds (137.62 k allocations: 551.968 MiB, 2.87% gc time)\n", + " 2.895343 seconds (148.39 k allocations: 593.424 MiB, 2.94% gc time)\n", + " 2.897684 seconds (146.00 k allocations: 584.277 MiB, 3.02% gc time)\n", + " 2.888651 seconds (148.39 k allocations: 593.444 MiB, 3.07% gc time)\n", + " 2.893580 seconds (146.34 k allocations: 586.595 MiB, 3.13% gc time)\n", + "It.: 300 C.: 343.68547199745956 Vf.: 0.29999999990459136 ch.: 0.016997420934861212, p.: 3.0000000000000004 beta.:12.0 eta.: 0.5603002811326168 \n", + " 2.956780 seconds (151.69 k allocations: 606.383 MiB, 3.39% gc time)\n", + " 2.943691 seconds (160.98 k allocations: 642.343 MiB, 3.25% gc time)\n", + " 2.945438 seconds (158.59 k allocations: 633.181 MiB, 3.32% gc time)\n", + " 2.938848 seconds (158.59 k allocations: 633.286 MiB, 2.98% gc time)\n", + " 2.936004 seconds (156.51 k allocations: 625.356 MiB, 3.14% gc time)\n", + " 2.946696 seconds (149.35 k allocations: 597.823 MiB, 3.21% gc time)\n", + " 2.933589 seconds (149.35 k allocations: 597.912 MiB, 3.29% gc time)\n", + " 2.940946 seconds (147.26 k allocations: 589.959 MiB, 3.36% gc time)\n", + " 2.925719 seconds (146.96 k allocations: 588.743 MiB, 3.43% gc time)\n", + " 2.918412 seconds (146.96 k allocations: 588.720 MiB, 2.99% gc time)\n", + " 2.958671 seconds (146.96 k allocations: 588.950 MiB, 3.69% gc time)\n", + " 2.944889 seconds (146.96 k allocations: 588.676 MiB, 3.23% gc time)\n", + " 2.956998 seconds (151.13 k allocations: 604.627 MiB, 3.18% gc time)\n", + " 2.930835 seconds (146.96 k allocations: 588.676 MiB, 3.23% gc time)\n", + " 2.948490 seconds (146.96 k allocations: 588.676 MiB, 3.28% gc time)\n", + " 2.995130 seconds (151.13 k allocations: 604.536 MiB, 3.20% gc time)\n", + " 2.974932 seconds (156.21 k allocations: 624.048 MiB, 3.31% gc time)\n", + " 2.973642 seconds (151.13 k allocations: 605.224 MiB, 3.37% gc time)\n", + " 2.958699 seconds (151.13 k allocations: 604.431 MiB, 3.42% gc time)\n", + " 2.972236 seconds (151.16 k allocations: 605.718 MiB, 3.46% gc time)\n", + "It.: 320 C.: 334.40408460098314 Vf.: 0.2999999999662704 ch.: 0.013495841885321179, p.: 3.0000000000000004 beta.:14.0 eta.: 0.5621363365527481 \n", + " 3.039928 seconds (163.07 k allocations: 650.410 MiB, 4.06% gc time)\n", + " 3.147202 seconds (185.17 k allocations: 735.188 MiB, 4.02% gc time)\n", + " 3.137165 seconds (190.25 k allocations: 754.753 MiB, 4.07% gc time)\n", + " 3.144591 seconds (190.25 k allocations: 754.608 MiB, 4.08% gc time)\n", + " 3.136797 seconds (188.16 k allocations: 746.699 MiB, 4.15% gc time)\n", + " 3.127759 seconds (180.69 k allocations: 718.182 MiB, 3.58% gc time)\n", + " 3.089528 seconds (178.31 k allocations: 708.771 MiB, 3.63% gc time)\n", + " 3.121633 seconds (178.31 k allocations: 708.963 MiB, 4.32% gc time)\n", + " 3.096037 seconds (178.00 k allocations: 707.924 MiB, 3.69% gc time)\n", + " 3.134197 seconds (173.23 k allocations: 689.456 MiB, 3.73% gc time)\n", + " 3.068973 seconds (168.15 k allocations: 669.935 MiB, 3.85% gc time)\n", + " 3.078937 seconds (165.45 k allocations: 659.599 MiB, 3.32% gc time)\n", + " 3.054454 seconds (163.07 k allocations: 650.416 MiB, 3.98% gc time)\n", + " 3.041331 seconds (162.76 k allocations: 649.157 MiB, 3.33% gc time)\n", + " 3.024806 seconds (158.59 k allocations: 633.472 MiB, 3.42% gc time)\n", + " 3.013809 seconds (153.21 k allocations: 612.613 MiB, 3.43% gc time)\n", + " 3.031681 seconds (153.21 k allocations: 612.554 MiB, 3.58% gc time)\n", + " 3.012214 seconds (153.21 k allocations: 612.715 MiB, 3.51% gc time)\n", + " 3.014559 seconds (153.21 k allocations: 612.564 MiB, 3.54% gc time)\n", + " 3.031961 seconds (153.25 k allocations: 613.174 MiB, 3.78% gc time)\n", + "It.: 340 C.: 327.5280971107868 Vf.: 0.29999999998975985 ch.: 0.011214545146629855, p.: 3.0000000000000004 beta.:16.0 eta.: 0.563461511048329 \n", + " 3.405735 seconds (173.49 k allocations: 690.264 MiB, 14.44% gc time)\n", + " 3.094647 seconds (203.92 k allocations: 807.077 MiB, 3.65% gc time)\n", + " 3.120909 seconds (207.83 k allocations: 822.027 MiB, 4.09% gc time)\n", + " 3.145450 seconds (213.17 k allocations: 842.185 MiB, 4.18% gc time)\n", + " 3.162598 seconds (213.17 k allocations: 842.240 MiB, 3.92% gc time)\n", + " 3.148805 seconds (208.70 k allocations: 825.107 MiB, 4.06% gc time)\n", + " 3.154534 seconds (206.31 k allocations: 815.813 MiB, 4.17% gc time)\n", + " 3.143632 seconds (205.09 k allocations: 811.377 MiB, 4.32% gc time)\n", + " 3.136390 seconds (205.09 k allocations: 811.138 MiB, 3.94% gc time)\n", + " 3.142005 seconds (203.01 k allocations: 802.986 MiB, 4.13% gc time)\n", + " 3.121860 seconds (197.93 k allocations: 783.451 MiB, 4.17% gc time)\n", + " 3.116755 seconds (197.93 k allocations: 783.469 MiB, 3.82% gc time)\n", + " 3.134295 seconds (197.63 k allocations: 782.433 MiB, 3.89% gc time)\n", + " 3.107208 seconds (190.77 k allocations: 756.093 MiB, 4.05% gc time)\n", + " 3.110194 seconds (188.38 k allocations: 747.207 MiB, 4.09% gc time)\n", + " 3.112493 seconds (188.07 k allocations: 745.928 MiB, 3.84% gc time)\n", + " 3.136546 seconds (185.69 k allocations: 736.629 MiB, 4.22% gc time)\n", + " 3.084509 seconds (183.30 k allocations: 727.555 MiB, 3.83% gc time)\n", + " 3.089995 seconds (183.30 k allocations: 727.616 MiB, 3.94% gc time)\n", + " 3.105482 seconds (185.42 k allocations: 733.091 MiB, 3.48% gc time)\n", + "It.: 360 C.: 322.2361566263041 Vf.: 0.29999999999737204 ch.: 0.009432440649259376, p.: 3.0000000000000004 beta.:18.0 eta.: 0.5644105152488157 \n", + " 3.166705 seconds (200.62 k allocations: 791.035 MiB, 4.65% gc time)\n", + " 3.207829 seconds (215.25 k allocations: 846.865 MiB, 4.52% gc time)\n", + " 3.208013 seconds (217.64 k allocations: 856.175 MiB, 4.10% gc time)\n", + " 3.283984 seconds (220.03 k allocations: 865.237 MiB, 4.64% gc time)\n", + " 3.248593 seconds (218.86 k allocations: 861.202 MiB, 4.73% gc time)\n", + " 3.229041 seconds (216.47 k allocations: 852.136 MiB, 4.19% gc time)\n", + " 3.229439 seconds (216.47 k allocations: 852.098 MiB, 4.32% gc time)\n", + " 3.256648 seconds (217.64 k allocations: 856.334 MiB, 4.85% gc time)\n", + " 3.251724 seconds (217.64 k allocations: 856.405 MiB, 4.43% gc time)\n", + " 3.251480 seconds (217.64 k allocations: 856.704 MiB, 4.47% gc time)\n", + " 3.253525 seconds (217.64 k allocations: 856.414 MiB, 4.55% gc time)\n", + " 3.227747 seconds (215.25 k allocations: 847.223 MiB, 4.02% gc time)\n", + " 3.256640 seconds (215.25 k allocations: 847.180 MiB, 4.70% gc time)\n", + " 3.269801 seconds (215.25 k allocations: 847.204 MiB, 4.68% gc time)\n", + " 3.250006 seconds (215.25 k allocations: 847.183 MiB, 4.18% gc time)\n", + " 3.266634 seconds (210.78 k allocations: 830.096 MiB, 4.23% gc time)\n", + " 3.238350 seconds (210.74 k allocations: 829.751 MiB, 4.34% gc time)\n", + " 3.235989 seconds (210.74 k allocations: 829.727 MiB, 4.33% gc time)\n", + " 3.269812 seconds (210.74 k allocations: 829.573 MiB, 4.44% gc time)\n", + " 3.238799 seconds (210.78 k allocations: 830.098 MiB, 4.55% gc time)\n", + "It.: 380 C.: 318.1182992677304 Vf.: 0.2999994564015827 ch.: 0.007942650883332809, p.: 3.0000000000000004 beta.:20.0 eta.: 0.5650911207226489 \n", + " 3.274143 seconds (217.03 k allocations: 853.992 MiB, 4.62% gc time)\n", + " 3.400100 seconds (245.17 k allocations: 962.198 MiB, 5.15% gc time)\n", + " 3.574873 seconds (275.95 k allocations: 1.055 GiB, 5.55% gc time)\n", + " 3.624406 seconds (291.24 k allocations: 1.113 GiB, 5.50% gc time)\n", + " 3.609306 seconds (290.63 k allocations: 1.111 GiB, 5.55% gc time)\n", + " 3.546408 seconds (276.56 k allocations: 1.058 GiB, 5.12% gc time)\n", + " 3.508500 seconds (266.10 k allocations: 1.018 GiB, 5.22% gc time)\n", + " 3.482009 seconds (258.32 k allocations: 1012.766 MiB, 5.32% gc time)\n", + " 3.427681 seconds (247.25 k allocations: 970.221 MiB, 4.72% gc time)\n", + " 3.396692 seconds (244.56 k allocations: 959.664 MiB, 4.84% gc time)\n", + " 3.349867 seconds (224.50 k allocations: 882.241 MiB, 4.96% gc time)\n", + " 3.505269 seconds (224.50 k allocations: 882.368 MiB, 10.53% gc time)\n", + " 3.122810 seconds (224.50 k allocations: 882.217 MiB, 4.28% gc time)\n", + " 3.107517 seconds (219.72 k allocations: 863.790 MiB, 4.15% gc time)\n", + " 3.102803 seconds (219.69 k allocations: 863.560 MiB, 3.83% gc time)\n", + " 3.096997 seconds (219.69 k allocations: 863.564 MiB, 3.90% gc time)\n", + " 3.128069 seconds (219.69 k allocations: 863.565 MiB, 4.06% gc time)\n", + " 3.119673 seconds (217.60 k allocations: 855.690 MiB, 4.14% gc time)\n", + " 3.118781 seconds (215.52 k allocations: 847.645 MiB, 4.22% gc time)\n", + " 3.144952 seconds (217.64 k allocations: 856.190 MiB, 4.44% gc time)\n", + "It.: 400 C.: 314.8596621689841 Vf.: 0.2999997850258232 ch.: 0.006737333944051288, p.: 3.0000000000000004 beta.:22.0 eta.: 0.5655673549772373 \n", + " 3.191571 seconds (224.50 k allocations: 882.225 MiB, 4.48% gc time)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 3.404268 seconds (287.94 k allocations: 1.100 GiB, 4.95% gc time)\n", + " 3.620685 seconds (343.60 k allocations: 1.310 GiB, 5.84% gc time)\n", + " 3.744015 seconds (352.29 k allocations: 1.343 GiB, 6.00% gc time)\n", + " 3.684597 seconds (346.60 k allocations: 1.321 GiB, 6.19% gc time)\n", + " 3.618192 seconds (330.44 k allocations: 1.260 GiB, 5.60% gc time)\n", + " 3.614902 seconds (325.06 k allocations: 1.240 GiB, 6.12% gc time)\n", + " 3.565542 seconds (318.16 k allocations: 1.214 GiB, 5.41% gc time)\n", + " 3.591322 seconds (314.86 k allocations: 1.201 GiB, 5.88% gc time)\n", + " 3.603408 seconds (314.86 k allocations: 1.201 GiB, 5.66% gc time)\n", + " 3.557944 seconds (312.77 k allocations: 1.194 GiB, 5.28% gc time)\n", + " 3.581016 seconds (314.86 k allocations: 1.201 GiB, 5.35% gc time)\n", + " 3.597784 seconds (309.78 k allocations: 1.183 GiB, 6.01% gc time)\n", + " 3.514336 seconds (296.01 k allocations: 1.131 GiB, 5.22% gc time)\n", + " 3.493817 seconds (287.33 k allocations: 1.098 GiB, 5.38% gc time)\n", + " 3.482553 seconds (281.08 k allocations: 1.074 GiB, 5.43% gc time)\n", + " 3.408968 seconds (258.93 k allocations: 1014.873 MiB, 5.21% gc time)\n", + " 3.391438 seconds (256.24 k allocations: 1004.507 MiB, 4.87% gc time)\n", + " 3.260961 seconds (231.10 k allocations: 907.581 MiB, 4.38% gc time)\n", + " 3.321518 seconds (238.26 k allocations: 935.002 MiB, 4.93% gc time)\n", + "It.: 420 C.: 312.213568814291 Vf.: 0.29999992195488506 ch.: 0.005838325119809017, p.: 3.0000000000000004 beta.:24.0 eta.: 0.5658779376925755 \n", + " 3.434441 seconds (267.62 k allocations: 1.024 GiB, 4.82% gc time)\n", + " 3.851392 seconds (360.36 k allocations: 1.373 GiB, 6.26% gc time)\n", + " 3.960401 seconds (378.90 k allocations: 1.443 GiB, 6.21% gc time)\n", + " 3.932204 seconds (378.90 k allocations: 1.443 GiB, 6.27% gc time)\n", + " 3.933374 seconds (370.52 k allocations: 1.411 GiB, 6.50% gc time)\n", + " 3.907447 seconds (365.14 k allocations: 1.391 GiB, 6.05% gc time)\n", + " 3.837415 seconds (351.68 k allocations: 1.340 GiB, 6.23% gc time)\n", + " 3.801876 seconds (342.99 k allocations: 1.307 GiB, 5.83% gc time)\n", + " 3.782927 seconds (332.83 k allocations: 1.269 GiB, 5.98% gc time)\n", + " 3.716500 seconds (323.54 k allocations: 1.234 GiB, 5.56% gc time)\n", + " 3.663843 seconds (309.78 k allocations: 1.182 GiB, 5.66% gc time)\n", + " 3.607287 seconds (289.72 k allocations: 1.107 GiB, 5.34% gc time)\n", + " 3.497286 seconds (264.88 k allocations: 1.013 GiB, 5.00% gc time)\n", + " 3.335920 seconds (231.97 k allocations: 910.818 MiB, 4.57% gc time)\n", + " 3.347859 seconds (231.97 k allocations: 910.817 MiB, 4.65% gc time)\n", + " 3.336467 seconds (224.50 k allocations: 882.159 MiB, 4.75% gc time)\n", + " 3.300821 seconds (224.50 k allocations: 882.147 MiB, 4.19% gc time)\n", + " 3.326798 seconds (224.50 k allocations: 882.146 MiB, 4.89% gc time)\n", + " 3.702558 seconds (224.50 k allocations: 882.173 MiB, 15.07% gc time)\n", + " 3.126800 seconds (223.63 k allocations: 879.260 MiB, 4.23% gc time)\n", + "It.: 440 C.: 310.0156229023772 Vf.: 0.2999999797254422 ch.: 0.005116573678712227, p.: 3.0000000000000004 beta.:26.0 eta.: 0.5660585950328253 \n", + " 3.233456 seconds (251.42 k allocations: 986.469 MiB, 4.54% gc time)\n", + " 3.618405 seconds (351.98 k allocations: 1.342 GiB, 6.00% gc time)\n", + " 3.727749 seconds (378.29 k allocations: 1.440 GiB, 5.99% gc time)\n", + " 3.738851 seconds (380.68 k allocations: 1.449 GiB, 6.05% gc time)\n", + " 3.790438 seconds (380.68 k allocations: 1.450 GiB, 6.16% gc time)\n", + " 3.706503 seconds (367.22 k allocations: 1.399 GiB, 5.70% gc time)\n", + " 3.704693 seconds (361.84 k allocations: 1.379 GiB, 6.16% gc time)\n", + " 3.671323 seconds (356.45 k allocations: 1.358 GiB, 5.71% gc time)\n", + " 3.635570 seconds (341.78 k allocations: 1.303 GiB, 5.90% gc time)\n", + " 3.636467 seconds (336.66 k allocations: 1.283 GiB, 5.68% gc time)\n", + " 3.641096 seconds (331.27 k allocations: 1.263 GiB, 5.95% gc time)\n", + " 3.587355 seconds (322.29 k allocations: 1.229 GiB, 5.56% gc time)\n", + " 3.542006 seconds (303.14 k allocations: 1.157 GiB, 5.29% gc time)\n", + " 3.432158 seconds (280.99 k allocations: 1.074 GiB, 5.14% gc time)\n", + " 3.534994 seconds (278.61 k allocations: 1.065 GiB, 5.40% gc time)\n", + " 3.627488 seconds (283.69 k allocations: 1.084 GiB, 5.37% gc time)\n", + " 3.602926 seconds (280.99 k allocations: 1.074 GiB, 5.26% gc time)\n", + " 3.452102 seconds (262.15 k allocations: 1.003 GiB, 5.27% gc time)\n", + " 3.685309 seconds (263.67 k allocations: 1.009 GiB, 5.23% gc time)\n", + " 3.632310 seconds (273.87 k allocations: 1.047 GiB, 5.26% gc time)\n", + "It.: 460 C.: 308.255457632036 Vf.: 0.29999999469596245 ch.: 0.004462094127377467, p.: 3.0000000000000004 beta.:28.0 eta.: 0.5661941739787812 \n", + " 3.626899 seconds (296.93 k allocations: 1.135 GiB, 5.24% gc time)\n", + " 3.940196 seconds (369.61 k allocations: 1.407 GiB, 6.35% gc time)\n", + " 3.972303 seconds (394.14 k allocations: 1.500 GiB, 6.70% gc time)\n", + " 3.962256 seconds (394.10 k allocations: 1.499 GiB, 6.34% gc time)\n", + " 3.960124 seconds (388.11 k allocations: 1.477 GiB, 6.45% gc time)\n", + " 3.929533 seconds (370.79 k allocations: 1.412 GiB, 6.60% gc time)\n", + " 3.909596 seconds (369.57 k allocations: 1.407 GiB, 6.30% gc time)\n", + " 3.879363 seconds (366.57 k allocations: 1.396 GiB, 6.38% gc time)\n", + " 3.851237 seconds (354.59 k allocations: 1.350 GiB, 6.01% gc time)\n", + " 3.758345 seconds (335.14 k allocations: 1.277 GiB, 6.14% gc time)\n", + " 3.680884 seconds (321.11 k allocations: 1.225 GiB, 5.31% gc time)\n", + " 3.632713 seconds (301.36 k allocations: 1.150 GiB, 5.50% gc time)\n", + " 3.618993 seconds (298.67 k allocations: 1.140 GiB, 5.61% gc time)\n", + " 3.633018 seconds (295.97 k allocations: 1.130 GiB, 5.68% gc time)\n", + " 3.578093 seconds (288.77 k allocations: 1.103 GiB, 5.29% gc time)\n", + " 3.563222 seconds (285.21 k allocations: 1.090 GiB, 5.33% gc time)\n", + " 3.556202 seconds (282.21 k allocations: 1.078 GiB, 5.47% gc time)\n", + " 3.550007 seconds (279.82 k allocations: 1.069 GiB, 5.44% gc time)\n", + " 3.531790 seconds (274.13 k allocations: 1.048 GiB, 5.55% gc time)\n", + " 3.512562 seconds (273.87 k allocations: 1.047 GiB, 5.07% gc time)\n", + "It.: 480 C.: 306.8149335750237 Vf.: 0.2999999993143613 ch.: 0.003940290008221013, p.: 3.0000000000000004 beta.:30.0 eta.: 0.566290748820883 \n", + " 3.619640 seconds (294.23 k allocations: 1.124 GiB, 5.59% gc time)\n", + " 4.157837 seconds (372.00 k allocations: 1.416 GiB, 6.21% gc time)\n", + " 4.149579 seconds (394.14 k allocations: 1.500 GiB, 6.80% gc time)\n", + " 4.101276 seconds (394.10 k allocations: 1.499 GiB, 6.33% gc time)\n", + " 4.387298 seconds (386.94 k allocations: 1.472 GiB, 6.43% gc time)\n", + " 4.038902 seconds (374.95 k allocations: 1.427 GiB, 6.54% gc time)\n", + " 4.204323 seconds (369.27 k allocations: 1.406 GiB, 14.41% gc time)\n", + " 3.591830 seconds (353.42 k allocations: 1.346 GiB, 6.07% gc time)\n", + " 4.055418 seconds (353.11 k allocations: 1.345 GiB, 6.13% gc time)\n", + " 4.078036 seconds (339.35 k allocations: 1.293 GiB, 5.84% gc time)\n", + " 3.888227 seconds (318.07 k allocations: 1.213 GiB, 5.81% gc time)\n", + " 3.848059 seconds (310.00 k allocations: 1.183 GiB, 5.28% gc time)\n", + " 3.727023 seconds (304.92 k allocations: 1.164 GiB, 5.33% gc time)\n", + " 3.624231 seconds (302.83 k allocations: 1.156 GiB, 5.42% gc time)\n", + " 4.029414 seconds (302.23 k allocations: 1.154 GiB, 5.46% gc time)\n", + " 3.552889 seconds (291.15 k allocations: 1.112 GiB, 5.06% gc time)\n", + " 3.595443 seconds (286.38 k allocations: 1.094 GiB, 5.27% gc time)\n", + " 3.408583 seconds (275.00 k allocations: 1.051 GiB, 4.72% gc time)\n", + " 3.292193 seconds (257.94 k allocations: 1010.501 MiB, 4.47% gc time)\n", + " 3.333985 seconds (253.20 k allocations: 992.605 MiB, 4.76% gc time)\n", + "It.: 500 C.: 305.6008536187392 Vf.: 0.30000000039826014 ch.: 0.0035126680265421995, p.: 3.0000000000000004 beta.:32.0 eta.: 0.5663445093375037 \n" + ] + }, + { + "data": { + "text/plain": [ + "([0.9999999582493425, 0.9999996831692387, 0.9999757512312559, 0.9888300585909416, 0.06622862001967607, 5.2257460965756266e-5, 4.858260316269315e-8, 7.497230614112974e-11, 3.3828495560358443e-13, 7.382983113763821e-15 … 1.1686321133030153e-8, 6.076134416171764e-6, 0.0013072843016925702, 0.12258094846493357, 0.9094694510800831, 0.9972310443138285, 0.9996161778436916, 0.9998150426361447, 0.9999071368500351, 0.9999489034721819], Any[427.85127712828137, 378.9120256638644, 346.70258747789364, 323.59058745705596, 306.94467702244646, 294.9482389155855, 286.06894837990626, 279.3620395350813, 274.20529088242677, 270.15459626415907 … 306.78151798753646, 306.7791819336303, 306.7768888376776, 306.77461434588406, 306.7723507415415, 306.7700962347439, 306.76785020442344, 306.76561420991356, 306.76338908821106, 305.6008536187392], 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b/top_mma/res/res_90.pdf new file mode 100755 index 0000000..4646159 Binary files /dev/null and b/top_mma/res/res_90.pdf differ diff --git a/top_mma/res/top_hist.gif b/top_mma/res/top_hist.gif new file mode 100755 index 0000000..d7322b3 Binary files /dev/null and b/top_mma/res/top_hist.gif differ diff --git a/top_mma/top99neo_mma.jl b/top_mma/top99neo_mma.jl new file mode 100755 index 0000000..9327a8d --- /dev/null +++ b/top_mma/top99neo_mma.jl @@ -0,0 +1,402 @@ +# __precompile__() +# module TopOpt99neo_MMA + +using LinearAlgebra, SparseArrays +using Plots + # : heatmap, savefig, @animate +using ImageFiltering: imfilter +using Statistics: mean + +using BenchmarkTools + +BLAS.set_num_threads(1) + +# abstract type top99neo end + +include("utils.jl") +include("MMA.jl") + +export SetUp, Mat, DiscretizationFeature, LoadsSupportsBCs, Initialization, Filter +export Optimization, Visualization + +mutable struct SetUp + nelx:: Int + nely:: Int + + eta:: Float64 + beta:: Int + penalCnt:: Array + betaCnt:: Array + + move:: Float64 + maxit:: Int + maxchang:: Float64 + + pasS:: Array{Int} + pasV:: Array{Int} + + function SetUp() + nelx = 120 + nely = 40 + # volfrac = 0.3 + maxit = 500 + move = 0.1 + beta = 2 + eta = 0.5 + maxchang = 1e-6 + penalCnt = [1, 3, 20, 0.2] + betaCnt = [1, 32, 10, 2] + # continuation scheme on beta parCont = { istart,maxPar,steps,deltaPar } + + # elNrs = reshape(1:nely*nelx, nely, nelx) + # a1 = elNrs[Int.(nely/4:nely/2), Int.(nelx/4:nelx/2)] + # pasS, pasV = Array([]), a1[:] + pasS, pasV = Array([]), Array([]) + + new(nelx, nely, eta, beta, penalCnt, betaCnt, move, maxit, maxchang, pasS, pasV) + end + +end + +mutable struct Mat + E0:: Float64 + Emin:: Float64 + ν:: Float64 + penal:: Float64 + volfrac:: Float64 + + function Mat() + E0 = 1.0 + Emin = 1e-9 * E0 + ν = 0.3 + penal = 3.0 + volfrac = 0.3 + new(E0, Emin, ν, penal, volfrac) + end +end + +struct DiscretizationFeature + nEl:: Int + nodeNrs:: Array{Int,2} + nDof:: Int + act + + cMat:: Array{Int} + Iar:: Array{Int} + Ke:: Array{Float64,1} + Ke0:: Array{Float64,2} + + function DiscretizationFeature(setup::SetUp, mat::Mat) + nelx = setup.nelx + nely = setup.nely + pasS, pasV = setup.pasS, setup.pasV + ν = mat.ν + + nEl = nely * nelx + nodeNrs = reshape(1:(1+nelx)*(1+nely), nely + 1, nelx + 1) + nDof = (nely + 1) * (nelx + 1) * 2 + act = setdiff(collect(1:nEl), union(pasS, pasV)) + + cVec = reshape(2 * nodeNrs[1:end-1, 1:end-1] .+ 1, nEl, 1) + cMat = Int.(repeat(cVec, 1, 8) + repeat([0 1 2 * nely .+ [2 3 0 1] -2 -1], nelx * nely, 1)) + + FuckRow = [1 2 3 4 5 6 7 8] + sI::Array{Int}, sII::Array{Int} = copy(FuckRow), fill(1, 1, 8) + @inbounds for j in 2: 8 + sI = cat(sI, FuckRow[j:8]'; dims=2) + # sII = cat(2, sII, repmat(j, 1, 8 - j + 1)) + sII = cat(sII, fill(j, 1, 8 - j + 1); dims=2) + end + iK::Array{Int,2}, jK::Array{Int,2} = cMat[:, sI][:, 1, :]', cMat[:, sII][:, 1, :]' + Iar = sort([iK[:] jK[:]]; dims=2, rev=true) # comma is a newline + # iK[:], jK[:] .= 0.0, 0.0 + c1 = [12, 3, -6, -3, -6, -3, 0, 3, 12, 3, 0, -3, -6, -3, -6, 12, -3, 0, -3, -6, 3, 12, 3, -6, 3, -6, 12, 3, -6, -3, 12, 3, 0, 12, -3, 12] + c2 = [-4, 3, -2, 9, 2, -3, 4, -9, -4, -9, 4, -3, 2, 9, -2, -4, -3, 4, 9, 2, 3, -4, -9, -2, 3, 2, -4, 3, -2, 9, -4, -9, 4, -4, -3, -4] + Ke = 1 / (1 - ν^2) / 24 .* (c1 .+ ν .* c2) # half-KE vector + # full KE + # Ke0::Array{Float64} = zeros(8, 8) + # start_id, end_id = 1, 8 + # for i in 1: 8 + # Ke0[i:8, i] = Ke[start_id:end_id] + # start_id, end_id = end_id + 1, 2 * end_id - start_id + # end + + Ke0::Array{Float64} = zeros(8, 8) + # Index::Array{Int} = [sI' sII'] + # Ke0[sI, sII] = Ke + Index = findall(isequal(1), tril(ones(8, 8))) + Ke0[Index] = Ke' + # Ke0 = reshape(Ke0, 8, 8) + Ke0 = Ke0 + Ke0' - diagm(diag(Ke0)) + # diag return the diag of a matrix + # diagm build a matirx with a diag + new(nEl, nodeNrs, nDof, act, cMat, Iar, Ke, Ke0) + end +end + +mutable struct LoadsSupportsBCs + lcDof:: Array{Int} + F + free:: Array{Int} + fixed:: Array{Int} + + function LoadsSupportsBCs(setup::SetUp, disfeature::DiscretizationFeature) + nelx = setup.nelx + nely = setup.nely + nodeNrs = disfeature.nodeNrs + nDof = disfeature.nDof + + load_position::Symbol = :half_MBB + if load_position == :half_MBB + load_nodey , load_nodex = 1, 1 + # fixed = union([1:2:2*(nely+1)], 2 * nodeNrs[nely+1, nelx+1]) + fixed = union(collect(1:2:2*(nely+1)), 2 * nodeNrs[end, end]) + elseif load_position == :cantilever + load_nodey = nely + 1 + load_nodex = nelx / 2 + 1 + fixed = 1:2*(nely+1) + end + + F = spzeros(nDof) + + load_type::Symbol = :pin + if load_type == :pin # 1 point + lcDof = collect(2 * nodeNrs[load_nodey, load_nodex]) + F[2] = -1.0 + elseif load_type == :points # 5 points + # lcDof = collect(2 * nodeNrs[load_nodey, load_nodex], nodeNrs[load_nodey, load_nodex-1], nodeNrs[load_nodey, load_nodex-2], nodeNrs[load_nodey, load_nodex+1], nodeNrs[load_nodey, load_nodex+2]) + F[lcDof'] .= -1.0 + elseif load_type == :line + lcDof = [2:2*(nely+1):nDof] + F = spzeros(nDof, 1) + F[lcDof'] .= -1.0 + # F = sparse(lcDof', ones(length(lcDof')), -1.0) + end + all = collect(1:nDof) + free = setdiff(all, fixed) + + new(lcDof, F, free, fixed) + end +end + +struct Initialization + x:: Array{Float64} + xPhys:: Array{Float64} + xOld:: Array{Float64} + ch:: Float64 + loop:: Int + + function Initialization(setup::SetUp, disfeature::DiscretizationFeature, mat::Mat) + pasV = setup.pasV + pasS = setup.pasS + act = disfeature.act + volfrac = mat.volfrac + nEl = disfeature.nEl + # nDof = disfeature.nDof + # column vectors + x = zeros(nEl, 1) + x[act] .= volfrac + x[pasS] .= 1.0 + xPhys, xOld, ch, loop = copy(x), ones(nEl, 1), 1.0, 0 + # x̅ x̃ + + new(x, xPhys, xOld, ch, loop) + end +end + +mutable struct Filter + rmin:: Float64 + ft:: Int + h:: Array{Float64} + Hs:: Array{Float64} + dHs:: Array{Float64} + + function Filter(setup::SetUp) + nelx = setup.nelx + nely = setup.nely + # volfrac = mat.volfrac + # bcF = setup.bcF + rmin = 6.5 + ft = 3 # 1 density 2 projection 3 volume preserving + dy, dx = meshgrid(-ceil(rmin)+1:ceil(rmin)-1, -ceil(rmin)+1:ceil(rmin)-1) + h = max.(0, rmin .- sqrt.(dx .^ 2 + dy .^ 2)) + Hs = imfilter(ones(nely, nelx), h, "symmetric") + dHs = Hs + + new(rmin, ft, h, Hs, dHs) + end +end + + +function FiniteElementAnalasys(mat::Mat, disfeature::DiscretizationFeature, load::LoadsSupportsBCs, xPhys::Array{Float64}) + nEl , nDof, Iar, Ke = disfeature.nEl, disfeature.nDof, disfeature.Iar, disfeature.Ke + act = disfeature.act + Emin, penal, E0 = mat.Emin, mat.penal, mat.E0 + F , free = load.F, load.free + # Interplotation model + sK = Emin .+ xPhys .^ penal .* (E0 - Emin) + sK = reshape(Ke[:] * sK', length(Ke) * nEl, 1) + K = sparse(Iar[:, 1], Iar[:, 2], vec(sK), nDof, nDof) + U = zeros(nDof) + # U[free] = cholesky(Symmetric(K[free, free], :L), check=false) \ F[free + U[free] = cholesky(Symmetric(K, :L)[free, free], check=false) \ F[free] + Obj = F' * U + Vf = sum(xPhys[act])/length(act) + return U, Obj, Vf +end + +function SensitivityAnalasys(setup::SetUp, filter::Filter, mat::Mat, disfeature::DiscretizationFeature, U::Array{Float64}, xPhys::Array{Float64}) + nelx, nely, act = setup.nelx, setup.nely, disfeature.act + dHs , h = filter.dHs, filter.h + E0 , Emin, penal = mat.E0, mat.Emin, mat.penal + nEl , cMat, Ke0 = disfeature.nEl, disfeature.cMat, disfeature.Ke0 + act = disfeature.act + + dsK, dV = zeros(nEl), zeros(nEl) + dV[act] .= 1.0/length(act) + dsK[act] = -penal * (E0 - Emin) .* xPhys[act] .^ (penal - 1) + + dc = dsK .* sum((U[cMat] * Ke0) .* U[cMat], dims=2) + dc = imfilter(reshape(dc, nely, nelx) ./ dHs, h, "symmetric") + dV0 = imfilter(reshape(dV, nely, nelx) ./ dHs, h, "symmetric") + + return reshape(dc, nEl, 1), reshape(dV0, nEl, 1) +end + +function MMAupdate(act, xval::Array{Float64}, low::Array{Float64}, upp::Array{Float64}, + xold1:: Array{Float64}, xold2:: Array{Float64}, + Obj, Vf:: Float64, + dc:: Array{Float64}, dV0:: Array{Float64}, loop:: Int, volfrac:: Float64) + move = 0.1 + ### Initiation of MMA ### + m = 1 + # active design variable + n = length(act) + onen = ones(n, 1) + onem = ones(m, 1) + zeron = zeros(n, 1) + zerom = zeros(m, 1) + a_mma = zerom + c_mma = 1.0e3 * onem + d_mma = zerom + a0 = 1.0 + # column vector + # xval = xval + xmin = max.(xval .- move, zeron) + xmax = min.(xval .+ move, onen) + + # low = low + # upp = upp + # objective function + f0val = Obj + df0dx = dc[act] + df0dx2 = 0.0 * df0dx + # constraint function + fval = Vf / volfrac - 1.0 # column vector + dfdx = reshape(dV0[act], 1, length(act)) ./ volfrac # (m * n) + dfdx2 = 0.0 * dfdx + + # The MMA subproblem is solved at the point xval: + xmma, ymma, zmma, lam, xsi, eta, mu, zet, s, low, upp = + mmasub(m, n, loop, xval, xmin, xmax, xold1, xold2, + f0val, df0dx, df0dx2, fval, dfdx, dfdx2, low, upp, a0, a_mma, c_mma, d_mma) + return xmma, low, upp +end + +function Visualization(setup::SetUp, x::Array{Float64}, loop::Int) + nelx, nely = setup.nelx, setup.nely + # cmap = cgrad(:Blues_9, rev=false) + plot = heatmap(reshape(x, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400, nely / nelx * 400), legend=:none, display_type=:gui) + # display(plot) + # if mod(loop, 10) = = 0 + # savefig(plot, "./res/res_$loop.pdf") + savefig(plot, "./res/design_$loop.png") + # end + + # PLOT FINAL DESIGN + # heatmap(1.0 .- x[end:-1:1, :], yaxis=false, xaxis=false, legend=:none,color=:greys, grid=false, border=nothing, aspect_ratio=:equal) + nothing +end + + +function Optimization(setup::SetUp, mat::Mat, load::LoadsSupportsBCs, filter::Filter, ini::Initialization, disfeature::DiscretizationFeature) + ch, loop = ini.ch, ini.loop + x , xPhys, xOld = ini.x, ini.xPhys, ini.xOld + + maxit, maxchang = setup.maxit, setup.maxchang + nely, nelx = setup.nely, setup.nelx + eta, beta, penalCnt, betaCnt = setup.eta, setup.beta, setup.penalCnt, setup.betaCnt + volfrac, penal, nEl = mat.volfrac, mat.penal, disfeature.nEl + act = disfeature.act + + Hs, h, ft = filter.Hs, filter.h, filter.ft + + opt_hist = [] + vf_hist = [] + + ### Initiation of MMA ### + xval = copy(x[act]) + xold1 = copy(xval) + xold2 = copy(xold1) + + low = copy(xval) + upp = copy(low) + ######################### + loop_beta = 0 + anim = @animate while ch > maxchang && loop < maxit || beta < betaCnt[2] + @time begin + loop = loop + 1 + # COMPUTE PHYSICAL DENSITY FIELD + xTilde = imfilter(reshape(x, nely, nelx), h, "symmetric") ./ Hs + xPhys[act] = copy(xTilde[act]) + if ft > 1 + f = (mean(prj(xPhys[act], eta, beta)) .- volfrac) * (ft == 3) + while abs(f) > maxchang + eta = eta - f / mean(deta(xPhys[:], eta, beta)) + f = mean(prj(xPhys[act], eta, beta)) - volfrac + end + filter.dHs = Hs ./ reshape(dprj(xTilde, eta, beta), nely, nelx) + xPhys = prj(xPhys, eta, beta) + end + ch = norm(xPhys - xOld) ./ sqrt(nEl) + xOld = copy(xPhys) + #~ SETUP AND SOLVE EQUILIBRIUM EQUATIONS + U, C, Vf = FiniteElementAnalasys(mat, disfeature, load, xPhys) + push!(opt_hist, C) + push!(vf_hist, Vf) + #~ COMPUTE SENSITIVITIES + dc, dV0 = SensitivityAnalasys(setup, filter, mat, disfeature, U, xPhys) + #~ MMA iteration + xmma, low, upp = MMAupdate(act, xval, low, upp, xold1, xold2, C, Vf, dc, dV0, loop, Mat().volfrac) + # Some vectors are updated: + xold2 = copy(xold1) + xold1 = copy(xval) + xval = copy(xmma) + + x[act] = xval + + #~ CONTINUATION + # if mat.penal == 1.0 + mat.penal = cnt(mat.penal, penalCnt,loop, ch, maxchang) + # end + if mat.penal < 3.0 + beta = 2.0 + else + loop_beta = loop_beta + 1 + beta = cnt(beta, betaCnt, loop_beta, ch, maxchang) + # restart mma + end + + heatmap(reshape(xPhys, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400, nely / nelx * 400), legend=:none) + + end + if mod(loop, 20) == 0 + println("It.: $loop C.: $C Vf.: $Vf ch.: $ch, p.: $(mat.penal) beta.:$beta eta.: $eta ") + Visualization(setup, xPhys, loop) + end + end + # gif(anim, "./top/cantilever.gif", fps=8) + return xPhys, opt_hist, vf_hist, anim +end + +# end diff --git a/top_mma/utils.jl b/top_mma/utils.jl new file mode 100755 index 0000000..ca4371c --- /dev/null +++ b/top_mma/utils.jl @@ -0,0 +1,57 @@ +# export loads!, bcs!, passive_domain! +export prj, deta, dprj, cnt +export meshgrid +export Visualization + +function prj(v::Array{Float64}, eta::Float64, beta) + return (tanh(beta * eta) .+ tanh.(beta * (v[:] .- eta))) ./ (tanh(beta * eta) + tanh(beta * (1 - eta))) +end + +function deta(v::Array{Float64}, eta::Float64, beta) + return -beta * csch(beta) .* sech.(beta * (v[:] .- eta)) .^ 2 .* sinh.(v[:] * beta) .* sinh.((1 .- v[:]) * beta) +end + +function dprj(v::Array{Float64}, eta::Float64, beta) + return beta * (1 .- tanh.(beta * (v .- eta)) .^ 2) ./ (tanh(beta * eta) + tanh(beta * (1 - eta))) +end + +function cnt(v, vCnt::Array, l::Int, ch::Float64, maxchang::Float64) + return v + (l >= vCnt[1]) * (v < vCnt[2]) * (mod(l, vCnt[3]) == 0 || ch <= maxchang) * vCnt[4] +end + + +""" +meshgrid(vx) +Computes an (x,y)-grid from the vectors (vx,vx). +For more information, see the MATLAB documentation. +""" +meshgrid(v::AbstractVector) = meshgrid(v, v) + +""" +meshgrid(vx,vy) +Computes an (x,y)-grid from the vectors (vx,vy). +For more information, see the MATLAB documentation. +""" +function meshgrid(vx::AbstractVector{T}, vy::AbstractVector{T}) where {T} + m, n = length(vy), length(vx) + vx = reshape(vx, 1, n) + vy = reshape(vy, m, 1) + (repeat(vx, m, 1), repeat(vy, 1, n)) +end + +""" +meshgrid(vx,vy,vz) +Computes an (x,y,z)-grid from the vectors (vx,vy,vz). +For more information, see the MATLAB documentation. +""" +function meshgrid(vx::AbstractVector{T}, vy::AbstractVector{T}, + vz::AbstractVector{T}) where {T} + m, n, o = length(vy), length(vx), length(vz) + vx = reshape(vx, 1, n, 1) + vy = reshape(vy, m, 1, 1) + vz = reshape(vz, 1, 1, o) + om = ones(Int, m) + on = ones(Int, n) + oo = ones(Int, o) + (vx[om, :, oo], vy[:, on, oo], vz[om, on, :]) +end diff --git a/top_oc/TEST.ipynb b/top_oc/TEST.ipynb new file mode 100755 index 0000000..eeeabf7 --- /dev/null +++ b/top_oc/TEST.ipynb @@ -0,0 +1,689 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# module TopOpt99neo\n", + "\n", + "# include(\"FastConv.jl/src/FastConv.jl\")\n", + "# import .FastConv.fastconv\n", + "\n", + "using LinearAlgebra, SparseArrays\n", + "using Plots: heatmap, savefig\n", + "# using PlotUtils:cgrad\n", + "using ImageFiltering: imfilter\n", + "using Statistics: mean\n", + "\n", + "using ForwardDiff\n", + "\n", + "BLAS.set_num_threads(1)\n", + "\n", + "# abstract type top99neo end\n", + "# abstract type top_result end\n", + "\n", + "# abstract type Filter end\n", + "\n", + "include(\"utils.jl\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct SetUp\n", + "# mutable struct SetUp <: top99neo\n", + " nelx::Int\n", + " nely::Int\n", + " # volfrac::Float64\n", + " # rmin::Float64\n", + "\n", + " # ftBC::Symbol\n", + " eta::Float64\n", + " beta::Int\n", + " betaCnt::NTuple{4,Int}\n", + "\n", + " move::Float64\n", + " maxit::Int\n", + " maxchang::Float64\n", + "\n", + " pasS::Array{Int}\n", + " pasV::Array{Int}\n", + " # act\n", + "\n", + " function SetUp()\n", + " nelx = 100\n", + " nely = 50\n", + " # volfrac = 0.3\n", + " maxit = 300\n", + " move = 0.1\n", + " beta = 2\n", + " eta = 0.5\n", + " maxchang = 1e-6\n", + " # penalCnt = {maxit+1, 3, 25, 0.25}\n", + " betaCnt = (1, 50, 10, 2) # continuation scheme on beta parCont = { istart,maxPar,steps,deltaPar }\n", + " \n", + " pasS, pasV = Array([]), Array([])\n", + " # act = setdiff([1:nEl]', union(pasS, pasV))\n", + " \n", + " new(nelx, nely, eta, beta, betaCnt, move, maxit, maxchang, pasS, pasV)\n", + " end\n", + "\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "setup = SetUp()\n", + "# setup.nelx = 20\n", + "# setup.nely = 10\n", + "# setup.maxit = 100\n", + "# typeof(setup.nodeNrs)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "mutable struct Mat\n", + " E0::Float64\n", + " Emin::Float64\n", + " ν::Float64\n", + " penal::Float64\n", + " volfrac::Float64\n", + "\n", + " function Mat()\n", + " # E0 = 1\n", + " # Emin = 1e-9\n", + " # nu = 0.3\n", + " E0 = 1\n", + " Emin = 1e-9\n", + " ν = 0.3\n", + " penal = 3.0\n", + " volfrac = 0.3\n", + " new(E0, Emin, ν, penal, volfrac)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mat = Mat()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct DiscretizationFeature\n", + " nEl::Int\n", + " nodeNrs::Array{Int,2}\n", + " nDof::Int\n", + " act\n", + "\n", + " cMat::Array{Int}\n", + " Iar::Array{Int}\n", + " Ke::Array{Float64,1}\n", + " Ke0::Array{Float64,2}\n", + " \n", + " function DiscretizationFeature(setup::SetUp, mat::Mat)\n", + " nelx = setup.nelx\n", + " nely = setup.nely\n", + " pasS, pasV = setup.pasS, setup.pasV\n", + " ν = mat.ν\n", + " \n", + " nEl = nely * nelx\n", + " nodeNrs = reshape(1:(1+nelx)*(1+nely), nely + 1, nelx + 1)\n", + " nDof = (nely + 1) * (nelx + 1) * 2\n", + " act = setdiff(collect(1:nEl), union(pasS, pasV))\n", + " \n", + " cVec = reshape(2 * nodeNrs[1:end-1, 1:end-1] .+ 1, nEl, 1)\n", + " # cMat = cVec + Int.([0 1 2 * nely .+ [2 3 0 1] -2 -1])\n", + " cMat = Int.(repeat(cVec, 1, 8) + repeat([0 1 2 * nely .+ [2 3 0 1] -2 -1], nelx * nely, 1))\n", + " # nDof = (nely + 1) * (nelx + 1) * 2\n", + " FuckRow = [1 2 3 4 5 6 7 8]\n", + " sI::Array{Int}, sII::Array{Int} = copy(FuckRow), fill(1, 1, 8)\n", + " for j in 2:8\n", + " sI = cat(sI, FuckRow[j:8]'; dims=2)\n", + " # sI = append!(sI, convert(Array{Int},[j:8]))\n", + " # sII = cat(2, sII, repmat(j, 1, 8 - j + 1))\n", + " sII = cat(sII, fill(j, 1, 8 - j + 1); dims=2)\n", + " end\n", + " iK::Array{Int,2}, jK::Array{Int,2} = cMat[:, sI][:, 1, :]', cMat[:, sII][:, 1, :]'\n", + " Iar = sort([iK[:] jK[:]]; dims=2, rev=true) # comma is a newline\n", + " # iK, jK .= 0 , 0\n", + " c1 = [12, 3, -6, -3, -6, -3, 0, 3, 12, 3, 0, -3, -6, -3, -6, 12, -3, 0, -3, -6, 3, 12, 3, -6, 3, -6, 12, 3, -6, -3, 12, 3, 0, 12, -3, 12]\n", + " c2 = [-4, 3, -2, 9, 2, -3, 4, -9, -4, -9, 4, -3, 2, 9, -2, -4, -3, 4, 9, 2, 3, -4, -9, -2, 3, 2, -4, 3, -2, 9, -4, -9, 4, -4, -3, -4]\n", + " Ke = 1 / (1 - ν^2) / 24 .* (c1 .+ ν .* c2) # half-KE vector\n", + " # full KE\n", + " # Ke0::Array{Float64} = zeros(8, 8)\n", + " # start_id, end_id = 1, 8\n", + " # for i in 1:8\n", + " # Ke0[i:8, i] = Ke[start_id:end_id]\n", + " # start_id, end_id = end_id + 1, 2 * end_id - start_id\n", + " # end\n", + " \n", + " Ke0::Array{Float64} = zeros(8, 8)\n", + " # Index::Array{Int} = [sI' sII']\n", + " # Ke0[sI, sII] = Ke\n", + " Index = findall(isequal(1), tril(ones(8, 8)))\n", + " Ke0[Index] = Ke'\n", + " # Ke0 = reshape(Ke0, 8, 8)\n", + " Ke0 = Ke0 + Ke0' - diagm(diag(Ke0))\n", + " new(nEl, nodeNrs, nDof, act, cMat, Iar, Ke, Ke0)\n", + " end\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "disfeature = DiscretizationFeature(setup, mat)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct LoadsSupportsBCs\n", + " # setup::SetUp\n", + " lcDof::Array{Int}\n", + " F::SparseMatrixCSC{Float64}\n", + " free::Array{Int}\n", + " fixed::Array{Int}\n", + "\n", + " function LoadsSupportsBCs(setup::SetUp, disfeature::DiscretizationFeature)\n", + " nelx = setup.nelx\n", + " nely = setup.nely\n", + " nodeNrs = disfeature.nodeNrs\n", + " nDof = disfeature.nDof\n", + " \n", + " load_position::Symbol = :half_MBB\n", + " if load_position == :half_MBB\n", + " load_nodey, load_nodex = 1, 1\n", + " # fixed = union([1:2:2*(nely+1)], 2 * nodeNrs[nely+1, nelx+1])\n", + " fixed = union(collect(1:2:2*(nely+1)), 2 * nodeNrs[end, end])\n", + " elseif load_position == :cantilever\n", + " load_nodey = nely + 1\n", + " load_nodex = nelx / 2 + 1\n", + " fixed = 1:2*(nely+1)\n", + " end\n", + " \n", + " F = spzeros(nDof, 1)\n", + " \n", + " load_type::Symbol = :pin\n", + " if load_type == :pin # 1 point\n", + " lcDof = collect(2 * nodeNrs[load_nodey, load_nodex])\n", + " F[2, 1] = -1.0\n", + " elseif load_type == :points # 5 points\n", + " lcDof = collect(2 * nodeNrs[load_nodey, load_nodex], nodeNrs[load_nodey, load_nodex-1], nodeNrs[load_nodey, load_nodex-2], nodeNrs[load_nodey, load_nodex+1], nodeNrs[load_nodey, load_nodex+2])\n", + " F[lcDof', ones(length(lcDof'))] .= -1.0\n", + " elseif load_type == :line\n", + " lcDof = [2:2*(nely+1):nDof]\n", + " F = spzeros(nDof, 1)\n", + " # F = sparse(lcDof', ones(length(lcDof')), -1.0)\n", + " end\n", + " all = collect(1:nDof)\n", + " free = setdiff(all, fixed)\n", + " \n", + " new(lcDof, F, free, fixed)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "load = LoadsSupportsBCs(setup, disfeature)" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct Initialization \n", + " # setup::SetUp\n", + " x::Array{Float64}\n", + " xPhys::Array{Float64}\n", + " xOld::Array{Float64}\n", + " ch::Float64\n", + " loop::Int\n", + " # U::Array{Float64}\n", + " # dsK::Array{Float64}\n", + " # dV::Array{Float64}\n", + "\n", + " function Initialization(setup::SetUp, disfeature::DiscretizationFeature, mat::Mat)\n", + " pasV = setup.pasV\n", + " pasS = setup.pasS\n", + " act = disfeature.act\n", + " volfrac = mat.volfrac\n", + " nEl = disfeature.nEl\n", + " nDof = disfeature.nDof\n", + " # column vectors\n", + " x = zeros(nEl, 1)\n", + " # dV[act, 1] .= 1.0 / nEl / volfrac\n", + " x[act] .= (volfrac * (nEl - length(pasV)) - length(pasS)) / length(act)\n", + " x[pasS] .= 1.0\n", + " xPhys, xOld, ch, loop = copy(x), ones(nEl, 1), 1.0, 0\n", + " # x̅ x̃\n", + " \n", + " new(x, xPhys, xOld, ch, loop)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ini = Initialization(setup, disfeature, mat)\n", + "# typeof(ini.x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mutable struct Filter \n", + " rmin::Float64\n", + " ft::Int\n", + " h::Array{Float64}\n", + " Hs::Array{Float64}\n", + " dHs::Array{Float64}\n", + "\n", + " function Filter(setup::SetUp)\n", + " nelx = setup.nelx\n", + " nely = setup.nely\n", + " # bcF = setup.bcF\n", + " rmin = 2.5\n", + " ft = 1\n", + " dy, dx = meshgrid(-ceil(rmin)+1:ceil(rmin)-1, -ceil(rmin)+1:ceil(rmin)-1)\n", + " h = max.(0, rmin .- sqrt.(dx .^ 2 + dy .^ 2))\n", + " Hs = imfilter(ones(nely, nelx), h, \"symmetric\")\n", + " dHs = Hs\n", + " new(rmin, ft, h, Hs, dHs)\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "\n", + "filter = Filter(setup)\n", + "# filter.Hs" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function FiniteElementAnalasys(mat::Mat, disfeature::DiscretizationFeature, load::LoadsSupportsBCs, xPhys::Array{Float64})\n", + " nEl, nDof, Iar, Ke = disfeature.nEl, disfeature.nDof, disfeature.Iar, disfeature.Ke\n", + " Emin, penal, E0 = mat.Emin, mat.penal, mat.E0\n", + " F, free = load.F, load.free\n", + "\n", + " sK = Emin .+ xPhys .^ penal .* (E0 - Emin)\n", + " sK = reshape(Ke[:] * sK', length(Ke) * nEl, 1)\n", + " K::SparseMatrixCSC = sparse(Iar[:, 1], Iar[:, 2], vec(sK), nDof, nDof)\n", + " U = zeros(nDof, 1)\n", + " #~\n", + " U[free] = cholesky(Symmetric(K[free, free], :L), check=false) \\ F[free]\n", + " #~\n", + " Obj = F' * U\n", + " Vf = mean(xPhys)\n", + " return U, Obj, Vf\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# U, Obj, Vf = FiniteElementAnalasys(mat::Mat, disfeature::DiscretizationFeature, load::LoadsSupportsBCs, xPhys::Array{Float64})\n", + "# size(Obj)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function SensitivityAnalasys(setup::SetUp, filter::Filter, mat::Mat, disfeature::DiscretizationFeature, U::Array{Float64}, xPhys::Array{Float64})\n", + " nelx, nely, act = setup.nelx, setup.nely, disfeature.act\n", + " dHs, h = filter.dHs, filter.h\n", + " E0, Emin, volfrac, penal = mat.E0, mat.Emin, mat.volfrac, mat.penal\n", + " nEl, cMat, Ke0 = disfeature.nEl, disfeature.cMat, disfeature.Ke0\n", + "\n", + " dsK, dV = zeros(nEl, 1), zeros(nEl, 1)\n", + " dV[act, 1] .= 1.0 / nEl / volfrac\n", + " dsK[act] = -penal * (E0 - Emin) .* xPhys[act] .^ (penal - 1)\n", + "\n", + " dc = dsK .* sum((U[cMat] * Ke0) .* U[cMat], dims=2)\n", + " dc = imfilter(reshape(dc, nely, nelx) ./ dHs, h, \"symmetric\")\n", + " dV0 = imfilter(reshape(dV, nely, nelx) ./ dHs, h, \"symmetric\")\n", + "\n", + " return dc, dV0\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# UPDATE DESIGN VARIABLES AND APPLY CONTINUATION\n", + "function OCupdate!(x::Array{Float64}, setup::SetUp, mat::Mat, disfeature::DiscretizationFeature, dc::Array{Float64}, dV0::Array{Float64})\n", + " act, move, volfrac = disfeature.act, setup.move, mat.volfrac\n", + "\n", + " xT = x[act]\n", + " xU, xL = xT .+ move, xT .- move\n", + " ocP = xT .* real.(sqrt.(-dc[act] ./ dV0[act]))\n", + " l = [0 mean(ocP) / volfrac]\n", + " while (l[2] - l[1]) / (l[2] + l[1]) > 1e-4\n", + " lmid = 0.5 * (l[1] + l[2])\n", + " x[act] = max.(max.(min.(min.(ocP ./ lmid, xU), 1.0), xL), 0.0)\n", + " if mean(x) > volfrac\n", + " l[1] = lmid\n", + " else\n", + " l[2] = lmid\n", + " end\n", + " end\n", + " return x\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "function Visualization(setup::SetUp, x::Array{Float64}, loop::Int)\n", + " nelx, nely = setup.nelx, setup.nely\n", + " # cmap = cgrad(:Blues_9, rev=false)\n", + " plot = heatmap(reshape(x, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400,nely/nelx*400) , legend=:none, display_type=:gui)\n", + " display(plot)\n", + " savefig(plot, \"./top/res_$loop.pdf\")\n", + " # PLOT FINAL DESIGN\n", + " # heatmap(1.0 .- x[end:-1:1, :], yaxis=false, xaxis=false, legend=:none,color=:greys, grid=false, border=nothing, aspect_ratio=:equal)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Optimization (generic function with 1 method)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "function Optimization(setup::SetUp, mat::Mat, load::LoadsSupportsBCs, filter::Filter, ini::Initialization, disfeature::DiscretizationFeature)\n", + " ch, loop, = ini.ch, ini.loop\n", + " x, xPhys, xOld = ini.x, ini.xPhys, ini.xOld\n", + " # U = ini.U\n", + "\n", + " maxit, maxchang = setup.maxit, setup.maxchang\n", + " nely, nelx = setup.nely, setup.nelx\n", + " eta, beta, betaCnt = setup.eta, setup.beta, setup.betaCnt\n", + " volfrac, penal, nEl = mat.volfrac, mat.penal, disfeature.nEl\n", + " act, move = disfeature.act, setup.move\n", + "\n", + " Hs, h, ft = filter.Hs, filter.h, filter.ft\n", + "\n", + " # Emin, E0, penal = mat.Emin, mat.E0, mat.penal\n", + "\n", + " # free = load.free\n", + "\n", + " opt_hist = []\n", + " vf_hist = []\n", + "\n", + " while ch > maxchang && loop < maxit\n", + " loop = loop + 1\n", + " # COMPUTE PHYSICAL DENSITY FIELD \n", + " xTilde = imfilter(reshape(x, nely, nelx), h, \"symmetric\") ./ Hs\n", + " xPhys[act] = xTilde[act]\n", + " if ft > 1\n", + " f = (mean(prj!(xPhys, eta, beta)) .- volfrac) * (ft == 3)\n", + " while abs(f) > maxchang\n", + " eta = eta - f / mean(deta!(xPhys[:], eta, beta))\n", + " f = mean(prj!(xPhys, eta, beta)) - volfrac\n", + " end\n", + " dHs = Hs ./ reshape(dprj(xTilde, eta, beta), nely, nelx)\n", + " xPhys = prj!(xPhys, eta, beta)\n", + " end\n", + " ch = norm(xPhys - xOld) ./ sqrt(nEl)\n", + " xOld = xPhys\n", + " # SETUP AND SOLVE EQUILIBRIUM EQUATIONS\n", + " # cMat, Iar, Ke, Ke0 = DiscretizationFeature(setup, mat)\n", + " # sK = Emin .+ xPhys .^ penal .* (E0 - Emin)\n", + " # dsK[act] = -penal * (E0 - Emin) .* xPhys[act] .^ (penal - 1)\n", + " # sK = reshape(Ke[:] * sK', length(Ke) * nEl, 1)\n", + " # K::SparseMatrixCSC = sparse(Iar[:, 1], Iar[:, 2], sK, nDof, nDof)\n", + " # U[free] = cholesky(Symmetric(K[free, free]), check=false) \\ F[free]\n", + " # C = F' * U\n", + " # Vf = mean(xPhys)\n", + " U, C, Vf = FiniteElementAnalasys(mat, disfeature, load, xPhys)\n", + " push!(opt_hist, C)\n", + " push!(vf_hist, Vf)\n", + " # COMPUTE SENSITIVITIES\n", + " # dc = dsK .* sum((U[cMat] * Ke0) .* U[cMat], dims=2)\n", + " # dc = imfilter(reshape(dc, nely, nelx) ./ dHs, h, \"symmetric\")\n", + " # dV0 = imfilter(reshape(dV, nely, nelx) ./ dHs, h, \"symmetric\")\n", + " dc, dV0 = SensitivityAnalasys(setup, filter, mat, disfeature, U, xPhys)\n", + " # OC iteration\n", + " x = OCupdate!(x, setup, mat, dc, dV0)\n", + " # CONTINUATION\n", + " beta = cnt!(beta, betaCnt, loop, ch, maxchang)\n", + "\n", + " @time println(\"It.: $loop C.: $C Vf.: $Vf ch.: $ch, p.: $penal beta.:$beta eta.: $eta \")\n", + "\n", + " Visualization(setup, xPhys, loop)\n", + " end\n", + " return xPhys, opt_hist, vf_hist, loop\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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"julia-1.7" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.7.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/top_oc/main_test.ipynb b/top_oc/main_test.ipynb new file mode 100755 index 0000000..ef6b358 --- /dev/null +++ b/top_oc/main_test.ipynb @@ -0,0 +1,66 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "module test\n", + "export main\n", + "include(\"/Users/yu/TopCodes/Julia/test/top99neo.jl\")\n", + "# include(joinpath(@__DIR__, \"top99neo.jl\"))\n", + "using .TopOpt99neo\n", + "function main()\n", + " setup = SetUp()\n", + " mat = Mat()\n", + " disfeature = DiscretizationFeature(setup, mat)\n", + " load = LoadsSupportsBCs(setup, disfeature)\n", + " ini = Initialization(setup, disfeature, mat)\n", + " filter = Filter(setup)\n", + " xPhys, opt_hist, vf_hist, anim = Optimization(setup, mat, load, filter, ini, disfeature)\n", + " return xPhys, opt_hist, vf_hist, anim\n", + "end\n", + "\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using .test\n", + "\n", + "main()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "using Plots\n", + "gif(anim, \"./top/top_hist.gif\", fps=8)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.7.0", + "language": "julia", + "name": "julia-1.7" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.7.0" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/top_oc/res/output.pdf b/top_oc/res/output.pdf new file mode 100755 index 0000000..7ecc0aa Binary files /dev/null and b/top_oc/res/output.pdf differ diff --git a/top_oc/res/output.svg.pdf b/top_oc/res/output.svg.pdf new file mode 100755 index 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volfrac = 0.3 + maxit = 300 + move = 0.1 + beta = 2 + eta = 0.5 + maxchang = 1e-6 + # penalCnt = {maxit+1, 3, 25, 0.25} + betaCnt = (2, 32, 10, 2) # continuation scheme on beta parCont = { istart,maxPar,steps,deltaPar } + + pasS, pasV = Array([]), Array([]) + + new(nelx, nely, eta, beta, betaCnt, move, maxit, maxchang, pasS, pasV) + end + +end + +mutable struct Mat <: top99neo + E0::Float64 + Emin::Float64 + ν::Float64 + penal::Float64 + volfrac::Float64 + + function Mat() + E0 = 1 + Emin = 1e-9 + ν = 0.3 + penal = 3.0 + volfrac = 0.3 + new(E0, Emin, ν, penal, volfrac) + end +end + +struct DiscretizationFeature <: top99neo + nEl::Int + nodeNrs::Array{Int,2} + nDof::Int + act + + cMat::Array{Int} + Iar::Array{Int} + Ke::Array{Float64,1} + Ke0::Array{Float64,2} + + function DiscretizationFeature(setup::SetUp, mat::Mat) + nelx = setup.nelx + nely = setup.nely + pasS, pasV = setup.pasS, setup.pasV + ν = mat.ν + + nEl = nely * nelx + nodeNrs = reshape(1:(1+nelx)*(1+nely), nely + 1, nelx + 1) + nDof = (nely + 1) * (nelx + 1) * 2 + act = setdiff(collect(1:nEl), union(pasS, pasV)) + + cVec = reshape(2 * nodeNrs[1:end-1, 1:end-1] .+ 1, nEl, 1) + cMat = Int.(repeat(cVec, 1, 8) + repeat([0 1 2 * nely .+ [2 3 0 1] -2 -1], nelx * nely, 1)) + + FuckRow = [1 2 3 4 5 6 7 8] + sI::Array{Int}, sII::Array{Int} = copy(FuckRow), fill(1, 1, 8) + @inbounds for j in 2:8 + sI = cat(sI, FuckRow[j:8]'; dims=2) + # sII = cat(2, sII, repmat(j, 1, 8 - j + 1)) + sII = cat(sII, fill(j, 1, 8 - j + 1); dims=2) + end + iK::Array{Int,2}, jK::Array{Int,2} = cMat[:, sI][:, 1, :]', cMat[:, sII][:, 1, :]' + Iar = sort([iK[:] jK[:]]; dims=2, rev=true) # comma is a newline + # iK, jK .= 0 , 0 + c1 = [12, 3, -6, -3, -6, -3, 0, 3, 12, 3, 0, -3, -6, -3, -6, 12, -3, 0, -3, -6, 3, 12, 3, -6, 3, -6, 12, 3, -6, -3, 12, 3, 0, 12, -3, 12] + c2 = [-4, 3, -2, 9, 2, -3, 4, -9, -4, -9, 4, -3, 2, 9, -2, -4, -3, 4, 9, 2, 3, -4, -9, -2, 3, 2, -4, 3, -2, 9, -4, -9, 4, -4, -3, -4] + Ke = 1 / (1 - ν^2) / 24 .* (c1 .+ ν .* c2) # half-KE vector + # full KE + # Ke0::Array{Float64} = zeros(8, 8) + # start_id, end_id = 1, 8 + # for i in 1:8 + # Ke0[i:8, i] = Ke[start_id:end_id] + # start_id, end_id = end_id + 1, 2 * end_id - start_id + # end + + Ke0::Array{Float64} = zeros(8, 8) + # Index::Array{Int} = [sI' sII'] + # Ke0[sI, sII] = Ke + Index = findall(isequal(1), tril(ones(8, 8))) + Ke0[Index] = Ke' + # Ke0 = reshape(Ke0, 8, 8) + Ke0 = Ke0 + Ke0' - diagm(diag(Ke0)) + new(nEl, nodeNrs, nDof, act, cMat, Iar, Ke, Ke0) + end +end + +mutable struct LoadsSupportsBCs <: top99neo + lcDof::Array{Int} + F + free::Array{Int} + fixed::Array{Int} + + function LoadsSupportsBCs(setup::SetUp, disfeature::DiscretizationFeature) + nelx = setup.nelx + nely = setup.nely + nodeNrs = disfeature.nodeNrs + nDof = disfeature.nDof + + load_position::Symbol = :half_MBB + if load_position == :half_MBB + load_nodey, load_nodex = 1, 1 + # fixed = union([1:2:2*(nely+1)], 2 * nodeNrs[nely+1, nelx+1]) + fixed = union(collect(1:2:2*(nely+1)), 2 * nodeNrs[end, end]) + elseif load_position == :cantilever + load_nodey = nely + 1 + load_nodex = nelx / 2 + 1 + fixed = 1:2*(nely+1) + end + + F = spzeros(nDof) + + load_type::Symbol = :pin + if load_type == :pin # 1 point + lcDof = collect(2 * nodeNrs[load_nodey, load_nodex]) + F[2] = -1.0 + elseif load_type == :points # 5 points + # lcDof = collect(2 * nodeNrs[load_nodey, load_nodex], nodeNrs[load_nodey, load_nodex-1], nodeNrs[load_nodey, load_nodex-2], nodeNrs[load_nodey, load_nodex+1], nodeNrs[load_nodey, load_nodex+2]) + F[lcDof'] .= -1.0 + elseif load_type == :line + lcDof = [2:2*(nely+1):nDof] + F = spzeros(nDof, 1) + F[lcDof'] .= -1.0 + # F = sparse(lcDof', ones(length(lcDof')), -1.0) + end + all = collect(1:nDof) + free = setdiff(all, fixed) + + new(lcDof, F, free, fixed) + end +end + +struct Initialization <: top99neo + x::Array{Float64} + xPhys::Array{Float64} + xOld::Array{Float64} + ch::Float64 + loop::Int + + function Initialization(setup::SetUp, disfeature::DiscretizationFeature, mat::Mat) + pasV = setup.pasV + pasS = setup.pasS + act = disfeature.act + volfrac = mat.volfrac + nEl = disfeature.nEl + # nDof = disfeature.nDof + # column vectors + x = zeros(nEl, 1) + # x[act] .= (volfrac * (nEl - length(pasV)) - length(pasS)) / length(act) + x[act] .= volfrac + x[pasS] .= 1.0 + xPhys, xOld, ch, loop = copy(x), ones(nEl, 1), 1.0, 0 + # x̅ x̃ + + new(x, xPhys, xOld, ch, loop) + end +end + +mutable struct Filter <: top99neo + rmin::Float64 + ft::Int + h::Array{Float64} + Hs::Array{Float64} + dHs::Array{Float64} + + function Filter(setup::SetUp) + nelx = setup.nelx + nely = setup.nely + # volfrac = mat.volfrac + # bcF = setup.bcF + rmin = nely / 20 + ft = 3 # 1 density 2 projection 3 volume preserving + dy, dx = meshgrid(-ceil(rmin)+1:ceil(rmin)-1, -ceil(rmin)+1:ceil(rmin)-1) + h = max.(0, rmin .- sqrt.(dx .^ 2 + dy .^ 2)) + Hs = imfilter(ones(nely, nelx), h, "symmetric") + dHs = Hs + + new(rmin, ft, h, Hs, dHs) + end +end + + +function FiniteElementAnalasys(mat::Mat, disfeature::DiscretizationFeature, load::LoadsSupportsBCs, xPhys::Array{Float64}) + nEl, nDof, Iar, Ke = disfeature.nEl, disfeature.nDof, disfeature.Iar, disfeature.Ke + Emin, penal, E0 = mat.Emin, mat.penal, mat.E0 + F, free = load.F, load.free + + sK = Emin .+ xPhys .^ penal .* (E0 - Emin) + sK = reshape(Ke[:] * sK', length(Ke) * nEl, 1) + K::SparseMatrixCSC = sparse(Iar[:, 1], Iar[:, 2], vec(sK), nDof, nDof) + U = zeros(nDof) + # U[free] = cholesky(Symmetric(K[free, free], :L), check=false) \ F[free + U[free] = cholesky(Symmetric(K, :L)[free, free], check=false) \ F[free] + Obj = F' * U + Vf = mean(xPhys) + return U, Obj, Vf +end + +function SensitivityAnalasys(setup::SetUp, filter::Filter, mat::Mat, disfeature::DiscretizationFeature, U::Array{Float64}, xPhys::Array{Float64}) + nelx, nely, act = setup.nelx, setup.nely, disfeature.act + dHs, h = filter.dHs, filter.h + E0, Emin, volfrac, penal = mat.E0, mat.Emin, mat.volfrac, mat.penal + nEl, cMat, Ke0 = disfeature.nEl, disfeature.cMat, disfeature.Ke0 + + dsK, dV = zeros(nEl, 1), zeros(nEl, 1) + #! active volume fraction in the design domain + # fval = sum(xPhys[act])./length( act )./volfrac.-1.0 + dV[act] .= 1.0 / length(act) / volfrac + dsK[act] = -penal * (E0 - Emin) .* xPhys[act] .^ (penal - 1) + + dc = dsK .* sum((U[cMat] * Ke0) .* U[cMat], dims=2) + dc = imfilter(reshape(dc, nely, nelx) ./ dHs, h, "symmetric") + dV0 = imfilter(reshape(dV, nely, nelx) ./ dHs, h, "symmetric") + + return dc, dV0 +end + +# UPDATE DESIGN VARIABLES AND APPLY CONTINUATION +function OCupdate(x::Array{Float64}, setup::SetUp, mat::Mat, disfeature::DiscretizationFeature, dc::Array{Float64}, dV0::Array{Float64}) + act, move, volfrac = disfeature.act, setup.move, mat.volfrac + xT = zeros(length(act), 1) + xT = x[act] + xU, xL = xT .+ move, xT .- move + ocP = xT .* real.(sqrt.(-dc[act] ./ dV0[act])) + l = [0 mean(ocP) / volfrac] + while (l[2] - l[1]) / (l[2] + l[1]) > 1e-4 + lmid = 0.5 * (l[1] + l[2]) + x[act] = max.(max.(min.(min.(ocP ./ lmid, xU), 1.0), xL), 0.0) + if mean(x) > volfrac + l[1] = lmid + else + l[2] = lmid + end + end + return x +end + +function Visualization(setup::SetUp, x::Array{Float64}, loop::Int) + nelx, nely = setup.nelx, setup.nely + # cmap = cgrad(:Blues_9, rev=false) + plot = heatmap(reshape(x, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400, nely / nelx * 400), legend=:none, display_type=:gui) + # display(plot) + # if mod(loop, 10) == 0 + savefig(plot, "./top/res_$loop.pdf") + # end + + # PLOT FINAL DESIGN + # heatmap(1.0 .- x[end:-1:1, :], yaxis=false, xaxis=false, legend=:none,color=:greys, grid=false, border=nothing, aspect_ratio=:equal) + nothing +end +function Optimization(setup::SetUp, mat::Mat, load::LoadsSupportsBCs, filter::Filter, ini::Initialization, disfeature::DiscretizationFeature) + ch, loop = ini.ch, ini.loop + x, xPhys, xOld = ini.x, ini.xPhys, ini.xOld + + maxit, maxchang = setup.maxit, setup.maxchang + nely, nelx = setup.nely, setup.nelx + eta, beta, betaCnt = setup.eta, setup.beta, setup.betaCnt + volfrac, penal, nEl = mat.volfrac, mat.penal, disfeature.nEl + act = disfeature.act + + Hs, h, ft = filter.Hs, filter.h, filter.ft + + opt_hist = [] + vf_hist = [] + + anim = @animate while ch > maxchang && loop < maxit || beta < betaCnt[2] + @time begin + loop = loop + 1 + # COMPUTE PHYSICAL DENSITY FIELD + xTilde = imfilter(reshape(x, nely, nelx), h, "symmetric") ./ Hs + xPhys[act] = copy(xTilde[act]) + if ft > 1 + f = (mean(prj(xPhys, eta, beta)) .- volfrac) * (ft == 3) + while abs(f) > maxchang + eta = eta - f / mean(deta(xPhys[:], eta, beta)) + f = mean(prj(xPhys, eta, beta)) - volfrac + end + filter.dHs = Hs ./ reshape(dprj(xTilde, eta, beta), nely, nelx) + xPhys = prj(xPhys, eta, beta) + end + ch = norm(xPhys - xOld) ./ sqrt(nEl) + xOld = copy(xPhys) + # SETUP AND SOLVE EQUILIBRIUM EQUATIONS + U, C, Vf = FiniteElementAnalasys(mat, disfeature, load, xPhys) + push!(opt_hist, C) + push!(vf_hist, Vf) + # COMPUTE SENSITIVITIES + dc, dV0 = SensitivityAnalasys(setup, filter, mat, disfeature, U, xPhys) + # OC iteration + x = OCupdate(x, setup, mat, disfeature, dc, dV0) + # CONTINUATION + beta = cnt(beta, betaCnt, loop, ch, maxchang) + + heatmap(reshape(xPhys, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400, nely / nelx * 400), legend=:none) + + end + if mod(loop, 10) == 0 + println("It.: $loop C.: $C Vf.: $Vf ch.: $ch, p.: $penal beta.:$beta eta.: $eta ") + Visualization(setup, xPhys, loop) + end + end + return xPhys, opt_hist, vf_hist, anim +end + +end diff --git a/top_oc/utils.jl b/top_oc/utils.jl new file mode 100755 index 0000000..b38c487 --- /dev/null +++ b/top_oc/utils.jl @@ -0,0 +1,71 @@ +# export loads!, bcs!, passive_domain! +export prj, deta, dprj, cnt +export meshgrid +export Visualization + +function prj(v::Array{Float64}, eta::Float64, beta::Int) + return (tanh(beta * eta) .+ tanh.(beta * (v[:] .- eta))) ./ (tanh(beta * eta) + tanh(beta * (1 - eta))) +end + +function deta(v::Array{Float64}, eta::Float64, beta::Int) + return -beta * csch(beta) .* sech.(beta * (v[:] .- eta)) .^ 2 .* sinh.(v[:] * beta) .* sinh.((1 .- v[:]) * beta) +end + +function dprj(v::Array{Float64}, eta::Float64, beta::Int) + return beta * (1 .- tanh.(beta * (v .- eta)) .^ 2) ./ (tanh(beta * eta) + tanh(beta * (1 - eta))) +end + +function cnt(v::Int, vCnt::NTuple{4,Int}, l::Int, ch::Float64, maxchang::Float64) + return v + (l >= vCnt[1]) * (v < vCnt[2]) * (mod(l, vCnt[3]) == 0 || ch <= maxchang) * vCnt[4] +end + + +""" +meshgrid(vx) +Computes an (x,y)-grid from the vectors (vx,vx). +For more information, see the MATLAB documentation. +""" +meshgrid(v::AbstractVector) = meshgrid(v, v) + +""" +meshgrid(vx,vy) +Computes an (x,y)-grid from the vectors (vx,vy). +For more information, see the MATLAB documentation. +""" +function meshgrid(vx::AbstractVector{T}, vy::AbstractVector{T}) where {T} + m, n = length(vy), length(vx) + vx = reshape(vx, 1, n) + vy = reshape(vy, m, 1) + (repeat(vx, m, 1), repeat(vy, 1, n)) +end + +""" +meshgrid(vx,vy,vz) +Computes an (x,y,z)-grid from the vectors (vx,vy,vz). +For more information, see the MATLAB documentation. +""" +function meshgrid(vx::AbstractVector{T}, vy::AbstractVector{T}, + vz::AbstractVector{T}) where {T} + m, n, o = length(vy), length(vx), length(vz) + vx = reshape(vx, 1, n, 1) + vy = reshape(vy, m, 1, 1) + vz = reshape(vz, 1, 1, o) + om = ones(Int, m) + on = ones(Int, n) + oo = ones(Int, o) + (vx[om, :, oo], vy[:, on, oo], vz[om, on, :]) +end + +function Visualization(setup::SetUp, x::Array{Float64}, loop::Int) + nelx, nely = setup.nelx, setup.nely + # cmap = cgrad(:Blues_9, rev=false) + plot = heatmap(reshape(x, nely, nelx), c=:Blues_9, aspect_ratio=:equal, yflip=true, grid=false, axis=:off, tick=false, colorbar=false, border=nothing, dpi=300, size=(400, nely / nelx * 400), legend=:none, display_type=:gui) + # display(plot) + # if mod(loop, 10) == 0 + savefig(plot, "./top_mma/res_$loop.pdf") + # end + + # PLOT FINAL DESIGN + # heatmap(1.0 .- x[end:-1:1, :], yaxis=false, xaxis=false, legend=:none,color=:greys, grid=false, border=nothing, aspect_ratio=:equal) + nothing +end \ No newline at end of file