diff --git a/Project.toml b/Project.toml index 8606cd2..efe54c9 100644 --- a/Project.toml +++ b/Project.toml @@ -9,6 +9,7 @@ ExaModels = "1037b233-b668-4ce9-9b63-f9f681f55dd2" JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819" PowerModels = "c36e90e8-916a-50a6-bd94-075b64ef4655" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +LuksanVleckBenchmark = "dc0393f0-98a3-4386-a65b-465e1307889b" [compat] CUDA = "5.2.0" diff --git a/data/tetra.jl b/data/tetra.jl new file mode 100644 index 0000000..2e05d2c --- /dev/null +++ b/data/tetra.jl @@ -0,0 +1,25 @@ +xe_tetra = [ + 0 0 0 + 1 0 0 + 0 1 0 + 0 0 1 + 5//10 2//10 1//10 +]; + +Tets_tetra = [ + 1 2 3 5 + 5 4 3 1 + 5 4 1 2 + 5 2 3 4 +]; + +Tets_tetra = vec(reshape(Tets_tetra, 16, 1)); +xe_tetra = vec(reshape(xe_tetra, 15, 1)); +Constants_tetra = [1, 2, 3, 4]; + +include("tetra_duct12.jl") +include("tetra_duct15.jl") +include("tetra_duct20.jl") +include("tetra_hook.jl") +include("tetra_foam5.jl") +include("tetra_gear.jl") diff --git a/data/tetra_duct12.jl b/data/tetra_duct12.jl new file mode 100644 index 0000000..d1e3375 --- /dev/null +++ b/data/tetra_duct12.jl @@ -0,0 +1,25329 @@ +xe_duct12 = [ + 1 -3.81000000000000e+01 -3.81000000000000e+01 2.19100000000000e+02 + 2 3.81000000000000e+01 -3.81000000000000e+01 2.19100000000000e+02 + 3 3.81000000000000e+01 3.81000000000000e+01 2.19100000000000e+02 + 4 -3.81000000000000e+01 3.81000000000000e+01 2.19100000000000e+02 + 5 -3.81000000000000e+01 0.00000000000000e+00 2.19100000000000e+02 + 6 -3.81000000000000e+01 -1.27000000000000e+01 2.19100000000000e+02 + 7 -3.81000000000000e+01 -2.54000000000000e+01 2.19100000000000e+02 + 8 -2.54000000000000e+01 -3.81000000000000e+01 2.19100000000000e+02 + 9 -3.81000000000000e+01 -3.81000000000000e+01 2.07035000000000e+02 + 10 -1.27000000000000e+01 -3.81000000000000e+01 2.19100000000000e+02 + 11 0.00000000000000e+00 -3.81000000000000e+01 2.19100000000000e+02 + 12 1.27000000000000e+01 3.81000000000000e+01 2.19100000000000e+02 + 13 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mode 100644 index 0000000..ec2a1e6 --- /dev/null +++ b/data/triangle.jl @@ -0,0 +1,20 @@ +xe = [ + 0 0 + 1 0 + 0 1 + 64//100 25//100 +]; + +Tr = [ + 1 2 4 + 4 2 3 + 4 3 1 +]; + +Tr = vec(reshape(Tr, 9, 1)); +xe = vec(reshape(xe, 8, 1)); +Constants = [1, 2, 3]; + +include("triangle_deer.jl") +include("triangle_pacman.jl") +include("triangle_turtle.jl") diff --git a/data/triangle_deer.jl b/data/triangle_deer.jl new file mode 100644 index 0000000..411dd7f --- /dev/null +++ b/data/triangle_deer.jl @@ -0,0 +1,3391 @@ +xe_deer = [ + 1 2.90000000000000e+00 1.20000000000000e+00 + 2 3.60000000000000e+00 1.20000000000000e+00 + 3 3.35000000000000e+00 1.20000000000000e+00 + 4 3.11610000000000e+00 1.44660000000000e+00 + 5 2.85000000000000e+00 1.47500000000000e+00 + 6 6.30000000000000e+00 1.25000000000000e+00 + 7 3.40300000000000e+00 1.65960000000000e+00 + 8 3.07730000000000e+00 1.69830000000000e+00 + 9 2.80000000000000e+00 1.75000000000000e+00 + 10 6.25360000000000e+00 1.36610000000000e+00 + 11 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-include("bearing.jl") +include("bearing.jl") include("camshape.jl") include("elec.jl") include("steering.jl") include("pinene.jl") include("marine.jl") include("gasoil.jl") +include("pde_models.jl") +include("catmix.jl") +include("chain.jl") +include("channel.jl") +include("glider.jl") +include("minsurf.jl") +include("polygon.jl") +include("tetra.jl") +include("torsion.jl") +include("triangle.jl") +include("methanol.jl") const NAMES = filter(names(ExaModelsExamples; all = true)) do x str = string(x) diff --git a/src/bearing.jl b/src/bearing.jl index 4c48245..97dfe1e 100644 --- a/src/bearing.jl +++ b/src/bearing.jl @@ -5,7 +5,7 @@ # COPS 3.1 - March 2004 -function bearing_model(nx, ny; T = Float64, backend = nothing, kwargs...) +function bearing_model(nx, ny; T = Float64, backend = CUDABackend(), kwargs...) b = 10 # grid is (0,2*pi)x(0,2*b) e = 0.1 # eccentricity @@ -38,7 +38,4 @@ function bearing_model(nx, ny; T = Float64, backend = nothing, kwargs...) ExaModels.constraint(core, v[nx+2, i] - 0.0 for i in 1:nx+2) return ExaModels.ExaModel(core; kwargs...) -end - - - +end \ No newline at end of file diff --git a/src/catmix.jl b/src/catmix.jl new file mode 100644 index 0000000..e0479c1 --- /dev/null +++ b/src/catmix.jl @@ -0,0 +1,74 @@ +# Catalyst Mixing Problem +# Collocation formulation +# COPS 3.0 - November 2002 +# COPS 3.1 - March 2004 + +function catmix_model(nh; T = Float64, backend = nothing, kwargs...) + ne = 2 + nc = 3 + + tf = 1 + h = tf / nh # Final time + + rho = [ + 0.11270166537926, + 0.50000000000000, + 0.88729833462074, + ] + bc = [1.0, 0.0] # Boundary conditions for x + alpha = 0.0 # Smoothing parameter + rho_index = [(i, rho[i]) for i in 1:nc] + + c = ExaModels.ExaCore(T; backend = backend) + u = ExaModels.variable(c, nh, nc; lvar = zeros(nh, nc), uvar = ones(nh, nc), start = zeros(nh, nc)) + v = ExaModels.variable(c, nh, ne; start = [mod(j, ne) for i in 1:nh, j in 1:ne]) + w = ExaModels.variable(c, nh, nc, ne; start = zeros(nh, nc, ne)) + pp = ExaModels.variable(c, nh, nc, ne; start = [mod(k, ne) for i in 1:nh, j in 1:nc, k in 1:ne]) + Dpp = ExaModels.variable(c, nh, nc, ne; start = zeros(nh, nc, ne)) + ppf = ExaModels.variable(c, ne; start = [mod(i,ne) for i in 1:ne]) + + ExaModels.objective(c, -1.0 + ppf[1] + ppf[2]) + ExaModels.objective(c, alpha/h*(u[i+1, j] - u[i, j])^2 for i in 1:nh-1, j in 1:nc) + + ExaModels.constraint( + c, + pp[i, k, s] - v[i, s] - h*sum(w[i, j, s]*(rho^j/factorial(j)) for j in 1:nc) for i=1:nh, (k, rho) in rho_index, s=1:ne + ) + + ExaModels.constraint( + c, + Dpp[i, k, s] - sum(w[i, j, s]*(rho^(j-1)/factorial(j-1)) for j in 1:nc) for i=1:nh, (k, rho) in rho_index, s=1:ne + ) + + ExaModels.constraint( + c, + ppf[s] - v[nh, s] - h * sum(w[nh, j, s] / factorial(j) for j in 1:nc) for s in 1:ne + ) + + ExaModels.constraint( + c, + v[i, s] + sum(w[i, j, s] * h / factorial(j) for j in 1:nc) - v[i+1, s] for i in 1:nh-1, s in 1:ne + ) + + + + ExaModels.constraint( + c, + Dpp[i,j,1] - u[i,j] * (10.0*pp[i,j,2] - pp[i,j,1]) for i=1:nh, j=1:nc + ) + + ExaModels.constraint( + c, + Dpp[i,j,2] - u[i,j] * (pp[i,j,1] - 10.0*pp[i,j,2]) + (1 - u[i,j])*pp[i,j,2] for i=1:nh, j=1:nc + ) + + + ExaModels.constraint( + c, + v[1, s] - bc for (s, bc) in [(i, bc[i]) for i in 1:ne] + ) + + return ExaModels.ExaModel(c; kwargs...) +end + + diff --git a/src/chain.jl b/src/chain.jl new file mode 100644 index 0000000..7a04b68 --- /dev/null +++ b/src/chain.jl @@ -0,0 +1,72 @@ +# Hanging Chain + +# Find the chain (of uniform density) of length L suspended between two points with minimal +# potential energy. + +# This is problem 4 in the COPS (Version 3) collection of +# E. Dolan and J. More' +# see "Benchmarking Optimization Software with COPS" +# Argonne National Labs Technical Report ANL/MCS-246 (2004) + +function chain_model(n; T = Float64, backend = nothing, kwargs...) + nh = max(2, div(n - 4, 4)) + + L = 4 + a = 1 + b = 3 + tmin = b > a ? 1 / 4 : 3 / 4 + tf = 1.0 + h = tf / nh + + c = ExaModels.ExaCore(T; backend = backend) + u = ExaModels.variable(c, nh + 1; start = [4 * abs(b - a) * (k / nh - tmin) for k in 1:nh+1]) + x1 = ExaModels.variable(c, nh + 1; start = [4 * abs(b - a) * k / nh * (1 / 2 * k / nh - tmin) + a for k in 1:nh+1]) + x2 = ExaModels.variable(c, nh + 1; start = [(4 * abs(b - a) * k / nh * (1 / 2 * k / nh - tmin) + a) * + (4 * abs(b - a) * (k / nh - tmin)) for k in 1:nh+1]) + x3 = ExaModels.variable(c, nh + 1; start = [4 * abs(b - a) * (k / nh - tmin) for k in 1:nh+1]) + + ExaModels.objective(c, x2[nh + 1]) + + ExaModels.constraint( + c, + x1[j + 1] - x1[j] - 1 / 2 * h * (u[j] + u[j + 1]) for j in 1:nh + ) + + ExaModels.constraint( + c, + x1[1] - a + ) + + ExaModels.constraint( + c, + x1[nh + 1] - b + ) + + ExaModels.constraint( + c, + x2[1] + ) + + ExaModels.constraint( + c, + x3[1] + ) + + ExaModels.constraint( + c, + x3[nh+1] - L + ) + + ExaModels.constraint( + c, + x2[j + 1] - x2[j] - 1 / 2 * h * (x1[j] * sqrt(1 + u[j]^2) + x1[j + 1] * sqrt(1 + u[j + 1]^2)) for j in 1:nh + ) + + ExaModels.constraint( + c, + x3[j + 1] - x3[j] - 1 / 2 * h * (sqrt(1 + u[j]^2) + sqrt(1 + u[j + 1]^2)) for j in 1:nh + ) + + return ExaModels.ExaModel(c; kwargs...) +end + diff --git a/src/channel.jl b/src/channel.jl index a05bdac..8d2020a 100644 --- a/src/channel.jl +++ b/src/channel.jl @@ -15,7 +15,14 @@ function channel_model(nh; T = Float64, backend = nothing, kwargs...) bc = [0.0 1.0; 0.0 0.0] rho = [0.06943184420297, 0.33000947820757, 0.66999052179243, 0.93056815579703] t = [(i-1)*h for i in 1:nh+1] - + tuples = Vector{Tuple{Int, Int, Int}}() + for s in 1:nd + for j in s:nd + push!(tuples, (s, j, factorial(j-s))) + end + end + array = [(i,j, factorial(j+nd-i)) for i in 1:nd, j in 1:nc] + rho_j = [(j, rho[j]) for j in 1:nc] # Initial value v0 = zeros(nh, nd) for i in 1:nh @@ -27,55 +34,71 @@ function channel_model(nh; T = Float64, backend = nothing, kwargs...) core = ExaModels.ExaCore(T; backend= backend) - v = ExaModels.variable(model, 1:nh, 1:nd) - w = ExaModels.variable(model, 1:nh, 1:nc; start=0.0) + v = ExaModels.variable(core, nh, nd;) + w = ExaModels.variable(core, nh, nc; start=0.0) - uc = ExaModels.variable(model, 1:nh, 1:nc, 1:nd; start=[v0[i, s] for i=1:nh, j=1:nc, s=1:nd]) - Duv = ExaModels.variable(model, 1:nh, 1:nc, 1:nd; start=0.0) + uc = ExaModels.variable(core, nh, nc, nd; start=[v0[i, s] for i=1:nh, j=1:nc, s=1:nd]) + Duc = ExaModels.variable(core, nh, nc, nd; start=0.0) + y = ExaModels.variable(core, 1; lvar =1, uvar =1, start = 1) # Constant objective - ExaModels.objective(model, Min, 1.0) + ExaModels.objective(core, y[1]) # Collocation model ExaModels.constraint( - model, - [i=1:nh, j=1:nc, s=1:nd], - uc[i, j, s] == v[i,s] + h*sum(w[i,k]*(rho[j]^k/factorial(k)) for k in 1:nc), + core, + uc[i, j, s] - v[i,s] - h*sum(w[i,k]*(rho^k/factorial(k)) for k in 1:nc) for i in 1:nh, (j,rho) in rho_j, s in 1:nd ) - ExaModels.constraint( - model, - [i=1:nh, j=1:nc, s=1:nd], - Duc[i, j, s] == sum(v[i,k]*((rho[j]*h)^(k-s)/factorial(k-s)) for k in s:nd) + - h^(nd-s+1) * sum(w[i, k]*(rho[j]^(k+nd-s)/factorial(k+nd-s)) for k in 1:nc) + c1 = ExaModels.constraint( + core, + Duc[i, j, s] for i in 1:nh, j in 1:nc, s in 1:nd + ) + + ExaModels.constraint!( + core, + c1, + (s-1)*nc*nh + (j-1)*nh + i=> - v[i,k]*((rho*h)^(k-s))/fac_k for i in 1:nh, (j,rho) in rho_j, (s, k, fac_k) in tuples + ) + + ExaModels.constraint!( + core, + c1, + (s-1)*nc*nh + (j-1)*nh + i => - h^(nd-s+1) * w[i, k]*(rho^(k+nd-s)/fac_nd) for i in 1:nh, (j,rho) in rho_j, (s, k, fac_nd) in array ) + # Boundary - ExaModels.constraint(model, bc_1, v[1, 1] == bc[1, 1]) - ExaModels.constraint(model, bc_2, v[1, 2] == bc[2, 1]) + ExaModels.constraint(core, v[1, 1] - bc[1, 1]) + ExaModels.constraint(core, v[1, 2] - bc[2, 1]) ExaModels.constraint( - model, - bc_3, + core, sum(v[nh, k]*(h^(k-1)/factorial(k-1)) for k in 1:nd) + - h^nd * sum(w[nh, k]/factorial(k+nd-1) for k in 1:nc) == bc[1, 2] + h^nd * sum(w[nh, k]/factorial(k+nd-1) for k in 1:nc) - bc[1, 2] ) ExaModels.constraint( - model, - bc_4, + core, sum(v[nh, k]*(h^(k-2)/factorial(k-2)) for k in 2:nd) + - h^(nd-1) * sum(w[nh, k]/factorial(k+nd-2) for k in 1:nc) == bc[2, 2] + h^(nd-1) * sum(w[nh, k]/factorial(k+nd-2) for k in 1:nc) - bc[2, 2] ) - ExaModels.constraint( - model, - continuity[i=1:nh-1, s=1:nd], - sum(v[i, k]*(h^(k-s)/factorial(k-s)) for k in s:nd) - + h^(nd-s+1)* sum(w[i, k]/factorial(k+nd-s) for k in 1:nc) == v[i+1, s] + c2 = ExaModels.constraint( + core, + - v[i+1, s] for i in 1:nh-1, s in 1:nd + ) + ExaModels.constraint!( + core, + c2, + (s-1)*(nh-1) + i => v[i, k]*(h^(k-s)/fac_k) for i in 1:nh-1, (s, k, fac_k) in tuples + ) + ExaModels.constraint!( + core, + c2, + (s-1)*(nh-1) + i => h^(nd-s+1)* w[i, k]/fac_nd for i in 1:nh-1, (s, k, fac_nd) in array + ) ExaModels.constraint( - model, - collocation[i=1:nh, j=1:nc], - sum(w[i, k] * (rho[j]^(k-1)/factorial(k-1)) for k in 1:nc) == - R * (Duc[i, j, 2] * Duc[i, j, 3] - Duc[i, j, 1] * Duc[i, j, 4]) + core, + sum(w[i, k] * (rho^(k-1)/factorial(k-1)) for k in 1:nc) - + R * (Duc[i, j, 2] * Duc[i, j, 3] - Duc[i, j, 1] * Duc[i, j, 4]) for i in 1:nh, (j,rho) in rho_j ) return ExaModels.ExaModel(core; kwargs...) end - diff --git a/src/glider.jl b/src/glider.jl new file mode 100644 index 0000000..b81a78f --- /dev/null +++ b/src/glider.jl @@ -0,0 +1,107 @@ +# Hang Glider Problem +# Trapezoidal formulation +# David Bortz - Summer 1998 +# COPS 2.0 - September 2000 +# COPS 3.0 - November 2002 +# COPS 3.1 - March 2004 + +function glider_model(nh; T = Float64, backend = nothing, kwargs...) + # Design parameters + x_0 = 0.0 + y_0 = 1000.0 + y_f = 900.0 + vx_0 = 13.23 + vx_f = 13.23 + vy_0 = -1.288 + vy_f = -1.288 + u_c = 2.5 + r_0 = 100.0 + m = 100.0 + g = 9.81 + c0 = 0.034 + c1 = 0.069662 + S = 14.0 + rho = 1.13 + cL_min = 0.0 + cL_max = 1.4 + + c = ExaModels.ExaCore(T; backend = backend) + t_f = ExaModels.variable(c, 1; lvar = 0, start = 1) + x = ExaModels.variable(c, nh+1; lvar = zeros(nh+1), start = [x_0 + vx_0*(k/nh) for k in 0:nh]) + y = ExaModels.variable(c, nh+1; start = [y_0 + (k/nh)*(y_f - y_0) for k in 0:nh]) + vx = ExaModels.variable(c, nh+1; lvar = zeros(nh+1), start = fill(vx_0, nh+1)) + vy = ExaModels.variable(c, nh+1; start = fill(vy_0, nh+1)) + cL = ExaModels.variable(c, nh+1; lvar = fill(cL_min,nh+1), uvar = fill(cL_max, nh+1), start = fill(cL_max/2, nh+1)) + + ExaModels.objective(c, -x[nh+1]) + + ExaModels.constraint( + c, + x[j] - (x[j-1] + 0.5/nh * (vx[j] + vx[j-1]) * t_f[1]) for j in 2:nh+1 + ) + + ExaModels.constraint( + c, + y[j] - (y[j-1] + 0.5 * t_f[1]/nh * (vy[j] + vy[j-1])) for j in 2:nh+1 + ) + + ExaModels.constraint( + c, + vx[i] - (vx[i-1] + + 0.5 * t_f[1]/nh * ((-(0.5*cL[i]*rho*S*(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))^2)*((vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))/( sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))) - (0.5*(c0+c1*cL[i]^2)*rho*S*(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))^2)*(vx[i]/(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))))/m + + (-(0.5*cL[i-1]*rho*S*(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))^2)*((vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))/( sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))) - (0.5*(c0+c1*cL[i-1]^2)*rho*S*(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))^2)*(vx[i-1]/(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))))/m)) for i in 2:nh+1 + ) + #The following two lengthy expressions represent vx_dot and vy_dot respectively. This is due to ExaModels does not support @expression. + # @variables(model, begin + # 0 <= t_f, (start=1.0) + # 0.0 <= x[k=0:nh], (start=x_0 + vx_0*(k/nh)) + # y[k=0:nh], (start=y_0 + (k/nh)*(y_f - y_0)) + # 0.0 <= vx[k=0:nh], (start=vx_0) + # vy[k=0:nh], (start=vy_0) + # cL_min <= cL[k=0:nh] <= cL_max, (start=cL_max/2.0) + # end) + + ExaModels.constraint( + c, + vy[i] - (vy[i-1] + + 0.5 * t_f[1]/nh * (((0.5*cL[i]*rho*S*(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))^2)*(vx[i]/(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))) - (0.5*(c0+c1*cL[i]^2)*rho*S*(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))^2)*((vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))/(sqrt(vx[i]^2 + (vy[i] - u_c*(1 - (x[i]/r_0 - 2.5)^2)*exp(-(x[i]/r_0 - 2.5)^2))^2))))/m - g + + ((0.5*cL[i-1]*rho*S*(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))^2)*(vx[i-1]/(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))) - (0.5*(c0+c1*cL[i-1]^2)*rho*S*(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))^2)*((vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))/(sqrt(vx[i-1]^2 + (vy[i-1] - u_c*(1 - (x[i-1]/r_0 - 2.5)^2)*exp(-(x[i-1]/r_0 - 2.5)^2))^2))))/m - g)) for i in 2:nh+1 + ) + + ExaModels.constraint( + c, + x[1] - x_0 + ) + + ExaModels.constraint( + c, + y[1] - y_0 + ) + + ExaModels.constraint( + c, + y[nh+1] - y_f + ) + + ExaModels.constraint( + c, + vx[1] - vx_0 + ) + + ExaModels.constraint( + c, + vx[nh+1] - vx_f + ) + + ExaModels.constraint( + c, + vy[1] - vy_0 + ) + + ExaModels.constraint( + c, + vy[nh+1] - vy_f + ) + + ExaModels.ExaModel(c,; kwargs...) +end \ No newline at end of file diff --git a/src/methanol.jl b/src/methanol.jl new file mode 100644 index 0000000..90e73d9 --- /dev/null +++ b/src/methanol.jl @@ -0,0 +1,127 @@ +# Methanol-to-Hydrocarbons Problem +# Collocation formulation +# Michael Merritt - Summer 2000 +# COPS 2.0 - September 2000 +# COPS 3.0 - November 2002 +# COPS 3.1 - March 2004 + +function methanol_model(nh; T = Float64, backend = nothing, kwargs...) + ne = 3 + np = 5 + nc = 3 + nm = 17 + + rho = [0.11270166537926, 0.5, 0.88729833462074] + # times at which observations made + tau = [ + 0, + 0.050, + 0.065, + 0.080, + 0.123, + 0.233, + 0.273, + 0.354, + 0.397, + 0.418, + 0.502, + 0.553, + 0.681, + 0.750, + 0.916, + 0.937, + 1.122, + ] + tf = tau[nm] # ODEs defined in [0,tf] + h = tf / nh # uniform interval length + t = [(i-1)*h for i in 1:nh+1] # partition + + # itau[i] is the largest integer k with t[k] <= tau[i] + itau = Int[min(nh, floor(tau[i]/h)+1) for i in 1:nm] + + # Concentrations + z = [ + 1.0000 0 0; + 0.7085 0.1621 0.0811; + 0.5971 0.1855 0.0965; + 0.5537 0.1989 0.1198; + 0.3684 0.2845 0.1535; + 0.1712 0.3491 0.2097; + 0.1198 0.3098 0.2628; + 0.0747 0.3576 0.2467; + 0.0529 0.3347 0.2884; + 0.0415 0.3388 0.2757; + 0.0261 0.3557 0.3167; + 0.0208 0.3483 0.2954; + 0.0085 0.3836 0.2950; + 0.0053 0.3611 0.2937; + 0.0019 0.3609 0.2831; + 0.0018 0.3485 0.2846; + 0.0006 0.3698 0.2899; + ] + con1_matrix = [(j, s, itau[j], tau[j], z[j,s], t[itau[j]]) for j in 1:nm, s in 1:ne] + bc = [1.0, 0.0, 0.0] + + # Starting-value + v0 = zeros(nh, ne) + for i in 1:itau[1], s in 1:ne + v0[i, s] = bc[s] + end + for j in 2:nm, i in itau[j-1]+1:itau[j], s in 1:ne + v0[i, s] = z[j, s] + end + for i in itau[nm]+1:nh, s in 1:ne + v0[i, s] = z[nm, s] + end + v0 .= 0.001 + + c = ExaModels.ExaCore(T; backend = backend) + theta = ExaModels.variable(c, np; lvar = 0, start = fill(1, np)) + v = ExaModels.variable(c, nh, ne; start = v0) + w = ExaModels.variable(c, nh, nc, ne; start = 0) + uc = ExaModels.variable(c, nh, nc, ne; start = [v0[i,s] for i=1:nh, j=1:nc, s=1:ne]) + Duc = ExaModels.variable(c, nh, nc, ne; start = 0) + + ExaModels.objective(c, (v[itau,s] + sum(w[itau,k,s]*(tau-t)^k/(factorial(k)*h^(k-1)) for k in 1:nc) - z)^2 for (j,s,itau,tau,z,t) in con1_matrix) + + ExaModels.constraint( + c, + uc[i, j, s] - v[i,s] - h*sum(w[i,k,s]*(rho^k/factorial(k)) for k in 1:nc) for i=1:nh, (j,rho) in [(j, rho[j]) for j in 1:nc], s=1:ne + ) + + ExaModels.constraint( + c, + Duc[i, j, s] - sum(w[i,k,s]*(rho^(k-1)/factorial(k-1)) for k in 1:nc) for i=1:nh, (j,rho) in [(j, rho[j]) for j in 1:nc], s=1:ne + ) + + ExaModels.constraint( + c, + v[1, s] - bc for (s, bc) in [(s, bc[s]) for s in 1:ne] + + ) + + ExaModels.constraint( + c, + v[i, s] + sum(w[i, j, s]*h/factorial(j) for j in 1:nc) - v[i+1, s] for i=1:nh-1, s=1:ne + ) + + ExaModels.constraint( + c, + Duc[i,j,1] + ((2*theta[2] - (theta[1]*uc[i,j,2])/((theta[2]+theta[5])*uc[i,j,1]+uc[i,j,2]) + + theta[3] + theta[4])*uc[i,j,1]) for i=1:nh, j=1:nc + ) + + ExaModels.constraint( + c, + Duc[i,j,2] - ((theta[1]*uc[i,j,1]*(theta[2]*uc[i,j,1]-uc[i,j,2]))/ ((theta[2]+theta[5])*uc[i,j,1]+uc[i,j,2]) + + theta[3]*uc[i,j,1]) for i=1:nh, j=1:nc + ) + + ExaModels.constraint( + c, + Duc[i,j,3] - ((theta[1]*uc[i,j,1]*(uc[i,j,2]+theta[5]*uc[i,j,1]))/ ((theta[2]+theta[5])*uc[i,j,1]+uc[i,j,2]) + + theta[4]*uc[i,j,1]) for i=1:nh, j=1:nc + ) + + return ExaModels.ExaModel(c; kwargs...) +end diff --git a/src/minsurf.jl b/src/minsurf.jl new file mode 100644 index 0000000..09a93e7 --- /dev/null +++ b/src/minsurf.jl @@ -0,0 +1,68 @@ +# Minimal surface with obstacle problem + +# Find the surface with minimal area, given boundary conditions, +# and above an obstacle. + +# This is problem 17=the COPS (Version 3) collection of +# E. Dolan and J. More' +# see "Benchmarking Optimization Software with COPS" +# Argonne National Labs Technical Report ANL/MCS-246 (2004) +# classification OBR2-AN-V-V + +function minsurf_model(nx::Int, ny::Int;T = Float64, backend = nothing, kwargs...) + x_mesh = LinRange(0, 1, nx + 2) # coordinates of the mesh points x + + v0 = zeros(nx + 2, ny + 2) # Surface matrix initialization + for i = 1:(nx + 2), j = 1:(ny + 2) + v0[i, j] = 1 - (2 * x_mesh[i] - 1)^2 + end + + hx = 1 / (nx + 1) + hy = 1 / (ny + 1) + area = 1 // 2 * hx * hy + + c = ExaModels.ExaCore(T; backend = backend) + v = ExaModels.variable(c, nx+2, ny+2; start = v0) + + ExaModels.objective(c, area * (1 + ((v[i + 1, j] - v[i, j]) / hx)^2 + ((v[i, j + 1] - v[i, j]) / hy)^2)^(1 / 2) for + i = 1:(nx + 1), j = 1:(ny + 1)) + ExaModels.objective(c, area * (1 + ((v[i - 1, j] - v[i, j]) / hx)^2 + ((v[i, j - 1] - v[i, j]) / hy)^2)^(1 / 2) for + i = 2:(nx + 2), j = 2:(ny + 2)) + + ExaModels.constraint( + c, + v[1, j + 1] for j in 0:ny+1 + ) + + ExaModels.constraint( + c, + v[nx + 2, j + 1] for j in 0:ny+1 + ) + + ExaModels.constraint( + c, + v[i + 1, 1] - 1 + (2 * i * hx - 1)^2 for i in 0:nx+1 + ) + + ExaModels.constraint( + c, + v[i + 1, 1] - 1 + (2 * i * hx - 1)^2 for i in 0:nx+1 + ) + + ExaModels.constraint( + c, + v[i + 1, j + 1] for j in 0:ny+1, i in 0:nx+1; + lcon = 0, + ucon = Inf + ) + + ExaModels.constraint( + c, + v[i + 1, j + 1] for i in Int(floor(0.25 / hx)):Int(ceil(0.75 / hx)), j in Int(floor(0.25 / hy)):Int(ceil(0.75 / hy)); + lcon = 1, + ucon = Inf + ) + + return ExaModels.ExaModel(c; kwargs...) +end + diff --git a/src/opf.jl b/src/opf.jl index 4136370..f47edf7 100644 --- a/src/opf.jl +++ b/src/opf.jl @@ -222,3 +222,127 @@ function ac_power_model( return ExaModels.ExaModel(w; kwargs...) end + + +function ac_rectangle_power_model( + filename = "pglib_opf_case3_lmbd.m"; + backend = nothing, + T = Float64, + kwargs..., +) + + data = parse_ac_power_data(filename, backend) + + w = ExaModels.ExaCore(T; backend = backend) + + # real parts of voltage + vr = ExaModels.variable(w, length(data.bus); start = fill(1, length(data.bus))) + + # imaginary parts of voltage + vi = ExaModels.variable(w, length(data.bus);) + + # active power generation + pg = ExaModels.variable(w, length(data.gen); lvar = data.pmin, uvar = data.pmax) + + # reactive power generation + qg = ExaModels.variable(w, length(data.gen); lvar = data.qmin, uvar = data.qmax) + + # active power in arc + p = ExaModels.variable(w, length(data.arc); lvar = -data.rate_a, uvar = data.rate_a) + + # reactive power in arc + q = ExaModels.variable(w, length(data.arc); lvar = -data.rate_a, uvar = data.rate_a) + + ExaModels.objective( + w, + g.cost1 * pg[g.i]^2 + g.cost2 * pg[g.i] + g.cost3 for g in data.gen + ) + + # reference bus + ExaModels.constraint( + w, + vi[i] for i in data.ref_buses + ) + + # vmin <= v[i] <= vmax + ExaModels.constraint( + w, + vr[i]^2 + vi[i]^2 for i in 1:length(data.bus); + lcon = data.vmin .^2, + ucon = data.vmax .^2 + ) + + # power balance + p_bal = ExaModels.constraint(w, b.pd + b.gs * (vi[b.i]^2 + vr[b.i]^2) for b in data.bus) + + q_bal = ExaModels.constraint(w, b.qd - b.bs * (vi[b.i]^2 + vr[b.i]^2) for b in data.bus) + + ExaModels.constraint!(w, p_bal, a.bus => p[a.i] for a in data.arc) + + ExaModels.constraint!(w, q_bal, a.bus => q[a.i] for a in data.arc) + + ExaModels.constraint!(w, p_bal, g.bus => -pg[g.i] for g in data.gen) + + ExaModels.constraint!(w, q_bal, g.bus => -qg[g.i] for g in data.gen) + + # ohms_yt_form + ExaModels.constraint( + w, + p[b.f_idx] - b.c5 * (vi[b.f_bus]^2 + vr[b.f_bus]^2) - + b.c3 * (vi[b.f_bus] * vi[b.t_bus] + vr[b.f_bus] * vr[b.t_bus]) - + b.c4 * (vi[b.f_bus] * vr[b.t_bus] - vr[b.f_bus] * vi[b.t_bus]) for + b in data.branch + ) + + ExaModels.constraint( + w, + q[b.f_idx] + b.c6 * (vi[b.f_bus]^2 + vr[b.f_bus]^2) + + b.c4 * (vi[b.f_bus] * vi[b.t_bus] + vr[b.f_bus] * vr[b.t_bus]) - + b.c3 * (vi[b.f_bus] * vr[b.t_bus] - vr[b.f_bus] * vi[b.t_bus]) for + b in data.branch + ) + + # ohms_yt_to + ExaModels.constraint( + w, + p[b.t_idx] - b.c7 * (vi[b.t_bus]^2 + vr[b.t_bus]^2) - + b.c1 * (vi[b.f_bus] * vi[b.t_bus] + vr[b.f_bus] * vr[b.t_bus]) - + b.c2 * (-(vi[b.f_bus] * vr[b.t_bus] - vr[b.f_bus] * vi[b.t_bus])) for + b in data.branch + ) + + ExaModels.constraint( + w, + q[b.t_idx] + b.c8 * (vi[b.t_bus]^2 + vr[b.t_bus]^2) + + b.c2 * (vi[b.f_bus] * vi[b.t_bus] + vr[b.f_bus] * vr[b.t_bus]) - + b.c1 * (-(vi[b.f_bus] * vr[b.t_bus] - vr[b.f_bus] * vi[b.t_bus])) for + b in data.branch + ) + + ExaModels.constraint( + w, + (vi[b.f_bus] * vr[b.t_bus] - vr[b.f_bus] * vi[b.t_bus]) - angmin * (vr[b.f_bus] * vr[b.t_bus] + vi[b.f_bus] * vi[b.t_bus]) for (b, angmin) in [data.branch[i], data.angmin[i] for i in 1:length(data.angmin)]; + lcon = 0, + ucon = Inf + ) + + ExaModels.constraint( + w, + (vi[b.f_bus] * vr[b.t_bus] - vr[b.f_bus] * vi[b.t_bus]) - angmax * (vr[b.f_bus] * vr[b.t_bus] + vi[b.f_bus] * vi[b.t_bus]) for (b, angmax) in [data.branch[i], data.angmin[i] for i in 1:length(data.angmax)]; + lcon = -Inf, + ucon = 0 + ) + + ExaModels.constraint( + w, + p[b.f_idx]^2 + q[b.f_idx]^2 - b.rate_a_sq for b in data.branch; + lcon = fill!(similar(data.branch, Float64, length(data.branch)), -Inf), + ) + ExaModels.constraint( + w, + p[b.t_idx]^2 + q[b.t_idx]^2 - b.rate_a_sq for b in data.branch; + lcon = fill!(similar(data.branch, Float64, length(data.branch)), -Inf), + ) + + return ExaModels.ExaModel(w; kwargs...) +end diff --git a/src/pde_models.jl b/src/pde_models.jl new file mode 100644 index 0000000..89a197c --- /dev/null +++ b/src/pde_models.jl @@ -0,0 +1,265 @@ + +include("shapes/circle.jl") +include("shapes/circle_rec.jl") +include("shapes/rectangle.jl") + +struct PDEProblem + a::Float64 + b::Vector{Float64} + c::Vector{Float64} + d::Vector{Float64} + p::Vector{Float64} +end + +struct PDEDiscretizationDomain + NODES::Int + ELEM::Int + DIMEN::Int + BREAK::Int + AREA::Vector{Float64} + TRIANG::Matrix{Int} + COORDS::Matrix{Float64} + BNDRY::Vector{Int} + EDGE::Array{Float64, 3} + US::Vector{Float64} + UE::Vector{Float64} +end + +function PDEDiscretizationDomain(nh, domain::Dict) + NODES = domain[:NODES] + ELEM = domain[:ELEMS] + COORDS = domain[:COORDS] + BNDRY = domain[:BNDRY] + DIMEN = 2 + BREAK = nh + + + # Description of triangular elements + TRIANG = domain[:TRIANG] + # Edge lengths + EDGE = [ + COORDS[TRIANG[e, mod(d1, DIMEN+1)+1], d2] - COORDS[TRIANG[e, d1], d2] + for e in 1:ELEM, d1 in 1:DIMEN+1, d2 in 1:DIMEN + ] + # Area of element + AREA = [(EDGE[e, 1, 1]*EDGE[e, 2, 2] - EDGE[e, 1, 2]*EDGE[e, 2, 1]) / 2.0 for e in 1:ELEM] + US = domain[:US] # starting point + UE = domain[:UE] # ending point + + return PDEDiscretizationDomain( + NODES, ELEM, DIMEN, BREAK, + AREA, TRIANG, COORDS, BNDRY, EDGE, US, UE, + ) +end + +function _update_values!(integral, energy, u, problem::PDEProblem, dom::PDEDiscretizationDomain) + # Unpack values + a, b, c, d, p = problem.a, problem.b, problem.c, problem.d, problem.p + TRIANG, EDGE = dom.TRIANG, dom.EDGE + + for b1 in 1:dom.BREAK+2, e1 in 1:dom.ELEM + integral[b1, e1] = + dom.AREA[e1]*( + 1 / (dom.DIMEN+1) * + (sum((b[TRIANG[e1,c1]]*u[b1,TRIANG[e1,c1]]^2/2- + c[TRIANG[e1,c1]]*u[b1,TRIANG[e1,c1]]^(p[TRIANG[e1,c1]]+1)/(p[TRIANG[e1,c1]]+1)+ + d[TRIANG[e1,c1]]*u[b1,TRIANG[e1,c1]]) for c1 in 1:dom.DIMEN+1)) + + a / (8*dom.AREA[e1]^2)*( + u[b1,TRIANG[e1,1]]^2*(EDGE[e1,2,1]^2 + EDGE[e1,2,2]^2) + + u[b1,TRIANG[e1,2]]^2*(EDGE[e1,3,1]^2 + EDGE[e1,3,2]^2) + + u[b1,TRIANG[e1,3]]^2*(EDGE[e1,1,1]^2 + EDGE[e1,1,2]^2) + + 2*u[b1,TRIANG[e1,1]]*u[b1,TRIANG[e1,2]]*(EDGE[e1,2,1]*EDGE[e1,3,1] + EDGE[e1,2,2]*EDGE[e1,3,2]) + + 2*u[b1,TRIANG[e1,1]]*u[b1,TRIANG[e1,3]]*(EDGE[e1,2,1]*EDGE[e1,1,1] + EDGE[e1,2,2]*EDGE[e1,1,2]) + + 2*u[b1,TRIANG[e1,2]]*u[b1,TRIANG[e1,3]]*(EDGE[e1,1,1]*EDGE[e1,3,1] + EDGE[e1,1,2]*EDGE[e1,3,2]) + ) + ) + end + for b1 in 1:dom.BREAK+2 + energy[b1] = sum(integral[b1, e1] for e1 in 1:dom.ELEM) + end +end + +function _initial_position!(problem::PDEProblem, d::PDEDiscretizationDomain, niter) + ubar = zeros(d.NODES) + u0 = zeros(d.BREAK+2, d.NODES) + energy0 = zeros(d.BREAK+2) + integral0 = zeros(d.BREAK+2, d.ELEM) + + # Calculate an ending point on the other side of the barrier + for i in 1:niter + for b1 in 1:d.BREAK+2, n in 1:d.NODES + u0[b1, n] = (1 - (b1-1)/(d.BREAK+1))*d.US[n] + ((b1-1)/(d.BREAK+1))*d.UE[n] + end + _update_values!(integral0, energy0, u0, problem, d) + if energy0[end] < 0 + break + end + d.UE .*= 2.0 + end + + # Backtrack to the barrier to get a better representation + ubar .= d.US + for i in 1:niter + for b1 in 1:d.BREAK+2, n in 1:d.NODES + u0[b1, n] = (1 - (b1-1)/(d.BREAK+1))*ubar[n] + ((b1-1)/(d.BREAK+1))*d.UE[n] + end + _update_values!(integral0, energy0, u0, problem, d) + ebar = maximum(energy0[b1] for b1 in 1:d.BREAK+2 if energy0[b1] < 0.0) + bbar = minimum(b1 for b1 in 1:d.BREAK+2 if energy0[b1] == ebar) + ubar .= u0[bbar-1, :] + d.UE .= u0[bbar, :] + end + + for b1 in 1:d.BREAK+2, n in 1:d.NODES + u0[b1, n] = (1 - (b1-1)/(d.BREAK+1))*d.US[n] + ((b1-1)/(d.BREAK+1))*d.UE[n] + end + _update_values!(integral0, energy0, u0, problem, d) + z0 = maximum(energy0[b1] for b1 in 1:d.BREAK+2) + return ( + u=u0, energy=energy0, integral=integral0, z=z0, + ) +end + +function _transition_state_model(problem, dom::PDEDiscretizationDomain; T = Float64, backend = nothing, kwargs...) + a, b, c, d, p = problem.a, problem.b, problem.c, problem.d, problem.p + x0 = _initial_position!(problem, dom, 10) + array1 = [ + ( + e1, + dom.TRIANG[e1, 1], + dom.TRIANG[e1, 2], + dom.TRIANG[e1, 3], + dom.AREA[e1], + dom.EDGE[e1, 1, 1], + dom.EDGE[e1, 1, 2], + dom.EDGE[e1, 2, 1], + dom.EDGE[e1, 2, 2], + dom.EDGE[e1, 3, 1], + dom.EDGE[e1, 3, 2] + ) for e1 in 1:dom.ELEM + ] + array2 = [ + ( + e1 = e1, + AREA = dom.AREA[e1], + b = b[dom.TRIANG[e1, c1]], + c = c[dom.TRIANG[e1, c1]], + d = d[dom.TRIANG[e1, c1]], + p = p[dom.TRIANG[e1, c1]], + TRIANG = dom.TRIANG[e1, c1] + ) + for e1 in 1:dom.ELEM for c1 in 1:(dom.DIMEN + 1) + ] + #_proto_model() + + ALPHA = 2.0 + H = ALPHA / (dom.BREAK+1) * sqrt(sum((dom.US[n] - dom.UE[n])^2 for n in 1:dom.NODES)) + + # Build optimization problem + core = ExaModels.ExaCore(T; backend = backend) + + u = ExaModels.variable(core, 1:dom.BREAK+2, 1:dom.NODES; start=x0.u) + z = ExaModels.variable(core, 1; start=x0.z) + + ExaModels.objective(core, z[1]) + + c1 = ExaModels.constraint( + core, + - z[1] for b1 in 1:dom.BREAK + 2; + lcon = -Inf, + ucon = 0.0, + ) + + ExaModels.constraint!( + core, + c1, + b1 => AREA*( + a / (8*AREA^2)*( + u[b1,TRIANG1]^2*(EDGE_21^2 + EDGE_22^2) + + u[b1,TRIANG2]^2*(EDGE_31^2 + EDGE_32^2) + + u[b1,TRIANG3]^2*(EDGE_11^2 + EDGE_12^2) + + 2*u[b1,TRIANG1]*u[b1,TRIANG2]*(EDGE_21*EDGE_31 + EDGE_22*EDGE_32) + + 2*u[b1,TRIANG1]*u[b1,TRIANG3]*(EDGE_21*EDGE_11 + EDGE_22*EDGE_12) + + 2*u[b1,TRIANG2]*u[b1,TRIANG3]*(EDGE_11*EDGE_31 + EDGE_12*EDGE_32) + ) + ) + for b1 in 1:dom.BREAK+2, (e1, TRIANG1, TRIANG2, TRIANG3, AREA, EDGE_11, EDGE_12, EDGE_21, EDGE_22, EDGE_31, EDGE_32) in array1 + ) + + ExaModels.constraint!( + core, + c1, + b1 => AREA* 1 / (dom.DIMEN+1) * (b*u[b1,TRIANG]^2/2- c*u[b1,TRIANG]^(p+1)/(p+1)+ d*u[b1, TRIANG]) + for b1 in 1:dom.BREAK+2, (e1, AREA, b, c, d, p, TRIANG) in array2 + ) + + c2 = ExaModels.constraint( + core, + dom.BREAK+1; + lcon=-Inf, + ucon=H^2, + ) + + ExaModels.constraint!( + core, + c2, + b1 => (u[b1+1, n] - u[b1, n])^2 for b1 in 1:dom.BREAK+1, n in 1:dom.NODES + ) + + # Boundary + boundary_nodes = findall(isequal(1), dom.BNDRY) + ExaModels.constraint( + core, + u[b1+1, n] for b1 in 1:dom.BREAK, n in boundary_nodes + ) + ExaModels.constraint( + core, + u[1, n] for n in 1:dom.NODES; + lcon=dom.US, + ucon=dom.US, + ) + ExaModels.constraint( + core, + u[dom.BREAK+2, n] for n in 1:dom.NODES; + lcon=dom.UE, + ucon=dom.UE, + ) + return ExaModels.ExaModel(core; kwargs...) +end + +function dirichlet_model(nh; T = Float64, backend = nothing) + dom = PDEDiscretizationDomain(nh, CIRCLE_DOMAIN) + println(dom.ELEM) + pb = PDEProblem( + 0.01, + fill(1.0, dom.NODES), + fill(1.0, dom.NODES), + fill(0.0, dom.NODES), + fill(3.0, dom.NODES), + ) + return _transition_state_model(pb, dom; T = T, backend = backend) +end + +function henon_model(nh; T = Float64, backend = nothing) + dom = PDEDiscretizationDomain(nh, CIRCLE_REC_DOMAIN) + pb = PDEProblem( + 1.0, + fill(0.0, dom.NODES), + sqrt.(dom.COORDS[:, 1].^2 .+ dom.COORDS[:, 2].^2), + fill(0.0, dom.NODES), + fill(3.0, dom.NODES), + ) + return _transition_state_model(pb, dom; T = T, backend = backend) +end + +function lane_emden_model(nh; T = Float64, backend = nothing) + dom = PDEDiscretizationDomain(nh, RECTANGLE_DOMAIN) + pb = PDEProblem( + 1.0, + fill(0.0, dom.NODES), + fill(1.0, dom.NODES), + fill(0.0, dom.NODES), + fill(3.0, dom.NODES), + ) + return _transition_state_model(pb, dom; T = T, backend = backend) +end diff --git a/src/polygon.jl b/src/polygon.jl new file mode 100644 index 0000000..2497349 --- /dev/null +++ b/src/polygon.jl @@ -0,0 +1,50 @@ +# Find the polygon of maximal area, among polygons with nv sides and +# diameter d <= 1 + +# This is problem 1 in the COPS (Version 3) collection of +# E. Dolan and J. More' +# see "Benchmarking Optimization Software with COPS" +# Argonne National Labs Technical Report ANL/MCS-246 (2004) + +function polygon_model(n; T = Float64, backend = nothing, kwargs...) + N = div(n, 2) + + c = ExaModels.ExaCore(T; backend = backend) + r = ExaModels.variable(c, N; lvar = 0, uvar = 1, start = fill(1,N)) + θ = ExaModels.variable(c, N; lvar = 0, uvar = π, start = [i * π / (N - 1) - π / (N - 1) for i in 1:N]) + tuples = Vector{Tuple{Int, Int}}() + for i in 1:N-1 + for j in i+1:N + push!(tuples, (i, j)) + end + end + + ExaModels.constraint( + c, + θ[N] - π + ) + + ExaModels.constraint( + c, + r[N] - 0 + ) + + ExaModels.constraint( + c, + θ[i + 1] - θ[i] for i in 1:N-1; + lcon = 0, + ucon = Inf + ) + + ExaModels.constraint( + c, + r[i]^2 + r[j]^2 - 2 * r[i] * r[j] * cos(θ[i] - θ[j]) - 1 for (i,j) in tuples; + lcon = -Inf, + ucon = 0 + ) + + ExaModels.objective(c, (r[i] * r[i + 1] * sin(θ[i + 1] - θ[i]) /(-2) for i = 1:Int(N - 1))) + + return ExaModels.ExaModel(c; kwargs...) +end + diff --git a/src/scopf.jl b/src/scopf.jl index 90b881a..efacbcb 100644 --- a/src/scopf.jl +++ b/src/scopf.jl @@ -158,7 +158,7 @@ function ac_scopf_model( # Difference of angles c6 = ExaModels.constraint( core, - va[b.f_bus, k] - va[b.t_bus, k] for (b, k) in data.idx_branch + va[b.f_bus, k] - va[b.t_bus, k] for (b, k) in data.idx_branch; lcon = repeat(data.angmin, data.K), ucon = repeat(data.angmax, data.K), ) diff --git a/src/shapes/circle.jl b/src/shapes/circle.jl new file mode 100644 index 0000000..fd8bbea --- /dev/null +++ b/src/shapes/circle.jl @@ -0,0 +1,3116 @@ +const CIRCLE_DOMAIN = Dict( + :NODES => 531, + :ELEMS => 978, + :COORDS => Float64[ + 1.000000000e+00 0.000000000e+00; + 9.921147013e-01 1.253332336e-01; + 9.685831611e-01 2.486898872e-01; + 9.297764859e-01 3.681245527e-01; + 8.763066800e-01 4.817536741e-01; + 8.090169944e-01 5.877852523e-01; + 7.289686274e-01 6.845471059e-01; + 6.374239897e-01 7.705132428e-01; + 5.358267950e-01 8.443279255e-01; + 4.257792916e-01 9.048270525e-01; + 3.090169944e-01 9.510565163e-01; + 1.873813146e-01 9.822872507e-01; + 6.279051953e-02 9.980267284e-01; + -6.279051953e-02 9.980267284e-01; + -1.873813146e-01 9.822872507e-01; + -3.090169944e-01 9.510565163e-01; + -4.257792916e-01 9.048270525e-01; + -5.358267950e-01 8.443279255e-01; + -6.374239897e-01 7.705132428e-01; + -7.289686274e-01 6.845471059e-01; + -8.090169944e-01 5.877852523e-01; + -8.763066800e-01 4.817536741e-01; + -9.297764859e-01 3.681245527e-01; + -9.685831611e-01 2.486898872e-01; + -9.921147013e-01 1.253332336e-01; + -1.000000000e+00 0.000000000e+00; + -9.921147013e-01 -1.253332336e-01; + -9.685831611e-01 -2.486898872e-01; + -9.297764859e-01 -3.681245527e-01; + -8.763066800e-01 -4.817536741e-01; + -8.090169944e-01 -5.877852523e-01; + -7.289686274e-01 -6.845471059e-01; + -6.374239897e-01 -7.705132428e-01; + -5.358267950e-01 -8.443279255e-01; + -4.257792916e-01 -9.048270525e-01; + -3.090169944e-01 -9.510565163e-01; + -1.873813146e-01 -9.822872507e-01; + -6.279051953e-02 -9.980267284e-01; + 6.279051953e-02 -9.980267284e-01; + 1.873813146e-01 -9.822872507e-01; + 3.090169944e-01 -9.510565163e-01; + 4.257792916e-01 -9.048270525e-01; + 5.358267950e-01 -8.443279255e-01; + 6.374239897e-01 -7.705132428e-01; + 7.289686274e-01 -6.845471059e-01; + 8.090169944e-01 -5.877852523e-01; + 8.763066800e-01 -4.817536741e-01; + 9.297764859e-01 -3.681245527e-01; 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+ 7.446012057e-02; + 1.335352466e-01; + 6.509382694e-01; + 6.740258591e-01; + 7.925614823e-02; + 1.712464600e-01; + ], +) diff --git a/src/shapes/circle_rec.jl b/src/shapes/circle_rec.jl new file mode 100644 index 0000000..445eef7 --- /dev/null +++ b/src/shapes/circle_rec.jl @@ -0,0 +1,2274 @@ +const CIRCLE_REC_DOMAIN = Dict( + :NODES => 398, + :ELEMS => 668, + :COORDS => [ + 1.000000000e+00 0.000000000e+00; + 9.921147013e-01 1.253332336e-01; + 9.685831611e-01 2.486898872e-01; + 9.297764859e-01 3.681245527e-01; + 8.763066800e-01 4.817536741e-01; + 8.090169944e-01 5.877852523e-01; + 7.289686274e-01 6.845471059e-01; + 6.374239897e-01 7.705132428e-01; + 5.358267950e-01 8.443279255e-01; + 4.257792916e-01 9.048270525e-01; + 3.090169944e-01 9.510565163e-01; + 1.873813146e-01 9.822872507e-01; + 6.279051953e-02 9.980267284e-01; + -6.279051953e-02 9.980267284e-01; + -1.873813146e-01 9.822872507e-01; + -3.090169944e-01 9.510565163e-01; + -4.257792916e-01 9.048270525e-01; + -5.358267950e-01 8.443279255e-01; 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+ 117 394 277; + 164 395 72; + 118 277 395; + 148 330 396; + 149 396 330; + 156 158 397; + 157 397 158; + 338 66 398; + ] +) diff --git a/src/shapes/rectangle.jl b/src/shapes/rectangle.jl new file mode 100644 index 0000000..bc8ac1a --- /dev/null +++ b/src/shapes/rectangle.jl @@ -0,0 +1,3219 @@ +const RECTANGLE_DOMAIN = Dict( + :NODES => 545, + :ELEMS => 1024, + :COORDS => [ + -1.000000000e+00 -1.000000000e+00; + 1.000000000e+00 -1.000000000e+00; + 1.000000000e+00 1.000000000e+00; + -1.000000000e+00 1.000000000e+00; + 0.000000000e+00 0.000000000e+00; + -1.000000000e+00 0.000000000e+00; + 0.000000000e+00 -1.000000000e+00; + 1.000000000e+00 0.000000000e+00; + 0.000000000e+00 1.000000000e+00; + -5.000000000e-01 -5.000000000e-01; + -5.000000000e-01 5.000000000e-01; + 5.000000000e-01 -5.000000000e-01; + 5.000000000e-01 5.000000000e-01; + -5.000000000e-01 0.000000000e+00; + -1.000000000e+00 -5.000000000e-01; + -5.000000000e-01 -1.000000000e+00; + 0.000000000e+00 -5.000000000e-01; + -1.000000000e+00 5.000000000e-01; 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Dolan and J. More +# see "Benchmarking Optimization Software with COPS" +# Argonne National Labs Technical Report ANL/MCS-246 (2004) + +include(joinpath("..", "data", "tetra.jl")) + +function tetra_model(x0 = xe_tetra, TETS::Vector{Int64} = Tets_tetra, Const::Vector{Int64} = Constants_tetra,;T = Float64, backend = nothing, kwargs...) + τ = 0.0 + n = length(x0) + N = round(Int, n / 3) + E = round(Int, length(TETS) / 4) + + lvar = fill(-Inf, n) + lvar[Const] .= x0[Const] + lvar[Const .+ N] .= x0[Const .+ N] + lvar[Const .+ 2 * N] .= x0[Const .+ 2 * N] + + uvar = fill(Inf, n) + uvar[Const] .= x0[Const] + uvar[Const .+ N] .= x0[Const .+ N] + uvar[Const .+ 2 * N] .= x0[Const .+ 2 * N] + obj_array = [(TETS[e], TETS[e + E], TETS[e + 2*E], TETS[e + 3*E], TETS[e]+N, TETS[e]+2*N, TETS[e + E]+N, TETS[e + E]+2*N, TETS[e + 2*E]+N, TETS[e + 2*E]+2*N, TETS[e + 3*E]+N, TETS[e + 3*E]+2*N) for e in 1:E] + c1_array = [(e, TETS[e], TETS[e] + N * i, TETS[e] + N * mod(i + 1, 3), TETS[e] + N * mod(i - 1, 3), + TETS[e + E] + N * i, + TETS[e + 2E] + N * mod(i + 1, 3), TETS[e + 2E] + N * mod(i - 1, 3), + TETS[e + 3E] + N * mod(i + 1, 3), TETS[e + 3E] + N * mod(i - 1, 3)) for i in 0:2 for e in 1:E] + + c = ExaModels.ExaCore(T; backend = backend) + + x = ExaModels.variable(c, n; lvar = lvar, uvar = uvar, start = x0) + + ExaModels.objective( + c, + ( + (1 * x[TETS_E] - x[TETS])^2 + ((2 * x[TETS_2E] - x[TETS_E] - x[TETS])^2) / 3 + + ((3 * x[TETS_3E] - x[TETS_2E] -x[TETS_E] - x[TETS])^2) / 6 + + (1 * x[TETS_E_N] - x[TETS_N])^2 + ((2 * x[TETS_2E_N] - x[TETS_E_N] - x[TETS_N])^2) / 3 + + ((3 * x[TETS_3E_N] - x[TETS_2E_N] - x[TETS_E_N] - x[TETS_N])^2) / 6 + + (1 * x[TETS_E_2N] - x[TETS_2N])^2 + ((2 * x[TETS_2E_2N] - x[TETS_E_2N] - x[TETS_2N])^2) / 3 + + ((3 * x[TETS_3E_2N] - x[TETS_2E_2N] - x[TETS_E_2N] - x[TETS_2N])^2) / 6 + ) / ( + 3 * + (( + (x[TETS_E] - x[TETS]) * + ( + (x[TETS_2E_N] - x[TETS_N]) * + (x[TETS_3E_2N] - x[TETS_2N]) - + (x[TETS_2E_2N] - x[TETS_2N]) * + (x[TETS_3E_N] - x[TETS_N]) + ) + + (x[TETS_E_N] - x[TETS_N]) * + ( + (x[TETS_2E_2N] - x[TETS_2N]) * + (x[TETS_3E] - x[TETS]) - + (x[TETS_2E] - x[TETS]) * + (x[TETS_3E_2N] - x[TETS_2N]) + ) + + (x[TETS_E_2N] - x[TETS_2N]) * + ( + (x[TETS_2E] - x[TETS]) * + (x[TETS_3E_N] - x[TETS_N]) - + (x[TETS_2E_N] - x[TETS_N]) * + (x[TETS_3E] - x[TETS]) + )) * + sqrt(2) + )^(2 / 3) + ) for (TETS, TETS_E, TETS_2E, TETS_3E, TETS_N, TETS_2N, TETS_E_N, TETS_E_2N, TETS_2E_N, TETS_2E_2N, TETS_3E_N, TETS_3E_2N) in obj_array + ) + + c1 = ExaModels.constraint( + c, + E; + lcon = τ, + ucon = Inf + ) + + ExaModels.constraint!( + c, + c1, + e => (x[TETS_E_N] - x[TETS_N]) * + ( + (x[TETS_2E_plus] - x[TESTS_N_plus]) * + (x[TETS_3E_minus] - x[TETS_N_minus]) - + (x[TETS_2E_minus] - x[TETS_N_minus]) * + (x[TETS_3E_plus] - x[TESTS_N_plus]) + ) * + sqrt(2) + for (e, TETS, TETS_N, TESTS_N_plus, TETS_N_minus, TETS_E_N, TETS_2E_plus, TETS_2E_minus, TETS_3E_plus, TETS_3E_minus) in c1_array + ) + + return ExaModels.ExaModel(c; kwargs...) +end + +tetra_duct12_model(; T = Float64, backend = nothing) = tetra_model(xe_duct12, TETS_duct12, Const_duct12; T = T, backend = backend) +tetra_duct15_model(; T = Float64, backend = nothing) = tetra_model(xe_duct15, TETS_duct15, Const_duct15; T = T, backend = backend) +tetra_duct20_model(; T = Float64, backend = nothing) = tetra_model(xe_duct20, TETS_duct20, Const_duct20; T = T, backend = backend) +tetra_hook_model(; T = Float64, backend = nothing) = tetra_model(xe_hook, TETS_hook, Const_hook; T = T, backend = backend) +tetra_foam5_model(; T = Float64, backend = nothing) = tetra_model(xe_foam5, TETS_foam5, Const_foam5; T = T, backend = backend) +tetra_gear_model(; T = Float64, backend = nothing) = tetra_model(xe_gear, TETS_gear, Const_gear; T = T, backend = backend) + diff --git a/src/torsion.jl b/src/torsion.jl new file mode 100644 index 0000000..a9e8e8d --- /dev/null +++ b/src/torsion.jl @@ -0,0 +1,47 @@ +# Torsion problem +# Liz Dolan - Summer 2000 +# Version 2.0 - October 2000 +# COPS 3.1 - March 2004 + +function torsion_model(nx, ny; T = Float64, backend = nothing, kwargs...) + c1 = 5.0 + hx = 1.0 / (nx + 1.0) # grid spacing + hy = 1.0 / (ny + 1.0) # grid spacing + area = 0.5 * hx * hy # area of triangle + + # Distance to the boundary. + D = [min(min(i,nx-i+1)*hx, min(j, ny-j+1)*hy) for i in 0:nx+1, j in 0:ny+1] + + c = ExaModels.ExaCore(T; backend = backend) + v = ExaModels.variable(c, nx+2, ny+2; start = D) + + ExaModels.constraint( + c, + v[i,j] for i in 1:nx+2, j in 1:ny+2; + lcon = -D, + ucon = D + ) + + ExaModels.objective( + c, + area * (((v[i+1,j] - v[i,j])/hx)^2 + ((v[i,j+1] - v[i,j])/hy)^2) / 2 for i in 1:nx+1, j in 1:ny +1 + ) + + ExaModels.objective( + c, + area * (((v[i,j] - v[i-1,j])/hx)^2 + ((v[i,j] - v[i,j-1])/hy)^2) / 2 for i in 2:nx+2, j in 2:ny+2 + ) + + ExaModels.objective( + c, + - area * c1* (v[i+1, j] + v[i, j] + v[i, j+1]) /3 for i in 1:nx+1, j in 1:ny+1 + ) + + ExaModels.objective( + c, + - area * c1 * (v[i, j] + v[i-1, j] + v[i, j-1]) / 3 for i in 2:nx+2, j in 2:ny+2 + ) + + return ExaModels.ExaModel(c; kwargs...) +end + diff --git a/src/triangle.jl b/src/triangle.jl new file mode 100644 index 0000000..8719158 --- /dev/null +++ b/src/triangle.jl @@ -0,0 +1,78 @@ +# Minimize the time taken for a robot arm to travel between two points. + +# This is problem 18 in the COPS (Version 3) collection of +# E. Dolan and J. More +# see "Benchmarking Optimization Software with COPS" +# Argonne National Labs Technical Report ANL/MCS-246 (2004) + +include(joinpath("..", "data", "triangle.jl")) + +function triangle_model(x0 = xe, TRIS::Vector{Int64} = Tr, Const::Vector{Int64} = Constants; T = Float64, backend = nothing, kwargs...) + τ = 0.0 + n = length(x0) + N = Int(div(n, 2)) + E = Int(div(length(TRIS), 3)) + + lvar = -Inf * ones(n) + lvar[Const] = x0[Const] + lvar[Const .+ N] = x0[Const .+ N] + + uvar = Inf * ones(n) + uvar[Const] = x0[Const] + uvar[Const .+ N] = x0[Const .+ N] + + c = ExaModels.ExaCore(T; backend = backend) + + x = ExaModels.variable(c, n; lvar = lvar, uvar = uvar, start = x0) + + ExaModels.objective( + c, + + ( + (1 * x[TRIS_E] - x[TRIS])^2 + + (2 * x[TRIS_2E] - x[TRIS_E] - x[TRIS])^2 / 3 + ) + / ( + 2 * ( + 2 * ( + (x[TRIS_E] - x[TRIS]) * (x[TRIS_2E_N] - x[TRIS_N]) - + (x[TRIS_2E] - x[TRIS]) * (x[TRIS_E_N] - x[TRIS_N]) + ) / sqrt(3) + ) + ) for (TRIS, TRIS_E, TRIS_2E, TRIS_N, TRIS_E_N, TRIS_2E_N) in [(TRIS[e], TRIS[e + E], TRIS[e + 2*E], TRIS[e]+N, TRIS[e + E]+N, TRIS[e + 2*E]+N) for e in 1:E] + ) + + ExaModels.objective( + c, + + ( + (1 * x[TRIS_E_N] - x[TRIS_N])^2 + + (2 * x[TRIS_2E_N] - x[TRIS_E_N] - x[TRIS_N])^2 / 3 + ) + / ( + 2 * ( + 2 * ( + (x[TRIS_E] - x[TRIS]) * (x[TRIS_2E_N] - x[TRIS_N]) - + (x[TRIS_2E] - x[TRIS]) * (x[TRIS_E_N] - x[TRIS_N]) + ) / sqrt(3) + ) + ) for (TRIS, TRIS_E, TRIS_2E, TRIS_N, TRIS_E_N, TRIS_2E_N) in [(TRIS[e], TRIS[e + E], TRIS[e + 2*E], TRIS[e]+N, TRIS[e + E]+N, TRIS[e + 2*E]+N) for e in 1:E] + ) + + ExaModels.constraint( + c, + 2 * ( + (x[TRIS_E] - x[TRIS]) * (x[TRIS_2E_N] - x[TRIS_N]) - + (x[TRIS_2E] - x[TRIS]) * (x[TRIS_E_N] - x[TRIS_N]) + ) / sqrt(3) + for (TRIS, TRIS_E, TRIS_2E, TRIS_N, TRIS_E_N, TRIS_2E_N) in [(TRIS[e], TRIS[e + E], TRIS[e + 2*E], TRIS[e]+N, TRIS[e + E]+N, TRIS[e + 2*E]+N) for e in 1:E]; + lcon = τ, + ucon = Inf + ) + + return ExaModels.ExaModel(c; kwargs...) +end + +triangle_deer_model(; T = Float64, backend = nothing) = triangle_model(xe_deer, TRIS_deer, Const_deer; T = T, backend = backend) +triangle_pacman_model(; T = Float64, backend = nothing) = triangle_model(xe_pacman, TRIS_pacman, Const_pacman; T = T, backend = backend) +triangle_turtle_model(; T = Float64, backend = nothing) = triangle_model(xe_turtle, TRIS_turtle, Const_turtle; T = T, backend = backend) diff --git a/test/runtests.jl b/test/runtests.jl index e9b8ca5..3e301f3 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,21 +1,56 @@ -using Test, ExaModelsExamples, MadNLP, MadNLPGPU, KernelAbstractions, CUDA - +using Test, MadNLP, MadNLPGPU, KernelAbstractions, CUDA, MadNLPHSL +import ExaModelsExamples const CONFIGS = [ - (Float32, nothing), - (Float64, nothing), - (Float32, CPU()), - (Float64, CPU()), + (Float64, nothing), + # (Float64, CPU()), (Float64, CUDABackend()), ] +# Note: The results may vary depending on the solver used. +# Additionally, by using MadNLP default solver, if the tolerance (tol) is set to less than 1e-4, +# the solver may diverge. Adjust the tolerance accordingly + +ExaModels_INSTANCES = [ + (ExaModelsExamples.bearing_model, (50, 50), -1.5482e-1), + (ExaModelsExamples.chain_model, (400,), 5.0698), + (ExaModelsExamples.camshape_model, (1000,), 4.27907), + (ExaModelsExamples.catmix_model, (100,), -4.80556e-2), + (ExaModelsExamples.channel_model, (200,), 1.0), + (ExaModelsExamples.elec_model, (50,), 1.0552e3), + (ExaModelsExamples.gasoil_model, (100,), 5.2366e-3), + (ExaModelsExamples.glider_model, (100,), 1.25505e3), + (ExaModelsExamples.goddard_model, (400,), -1.01283), + (ExaModelsExamples.marine_model, (100,), 1.97462e7), + (ExaModelsExamples.methanol_model, (100,), 9.02229e-3), + (ExaModelsExamples.minsurf_model, (50, 50), 2.51488), + (ExaModelsExamples.minsurf_model, (50, 75), 2.50568), + (ExaModelsExamples.minsurf_model, (50, 100), 2.50694), + (ExaModelsExamples.pinene_model, (100,), 1.98721e1), + (ExaModelsExamples.polygon_model, (100,), -0.674981), # N.B: objective depends on the optimizer used. + (ExaModelsExamples.robot_model, (200,), 9.14138), + (ExaModelsExamples.steering_model, (200,), 5.54577e-1), + (ExaModelsExamples.tetra_duct20_model, (), 4.82685e3), + (ExaModelsExamples.tetra_duct15_model, (), 1.04951e4), + (ExaModelsExamples.tetra_foam5_model, (), 6.42560e3), + (ExaModelsExamples.tetra_gear_model, (), 4.15163e3), + (ExaModelsExamples.tetra_hook_model, (), 6.05735e3), + (ExaModelsExamples.torsion_model, (50, 50), -4.18087e-1), + (ExaModelsExamples.dirichlet_model, (20,), 1.71464e-2), + (ExaModelsExamples.henon_model, (20,), 6.667736), # N.B: objective depends on the optimizer used. + (ExaModelsExamples.lane_emden_model, (20,), 9.11000), + (ExaModelsExamples.triangle_deer_model, (), 2.01174e3), + (ExaModelsExamples.triangle_pacman_model, (), 1.25045e3), + (ExaModelsExamples.triangle_turtle_model, (), 4.21523e3), +] + function runtests() @testset "ExaModelsExamples test" begin - for name in ExaModelsExamples.NAMES + for (instance, params, result) in ExaModels_INSTANCES for (T, backend) in CONFIGS - m = eval(name)(; T = T, backend = backend) - result = madnlp(m; print_level = MadNLP.ERROR) + m = eval(instance)(params...; T = T, backend = backend) + result = madnlp(m;) - @testset "$name" begin + @testset "$instance" begin @test result.status == MadNLP.SOLVE_SUCCEEDED end end