diff --git a/.github/workflows/copilot-setup-steps.yaml b/.github/workflows/copilot-setup-steps.yaml index 0c45e62f..e4f4dadf 100644 --- a/.github/workflows/copilot-setup-steps.yaml +++ b/.github/workflows/copilot-setup-steps.yaml @@ -3,9 +3,9 @@ name: "Copilot Setup Steps" # Automatically run the setup steps when they are changed to allow for easy validation, # and allow manual testing through the repository's "Actions" tab on: - workflow_dispatch: + workflow_dispatch: push: - paths: + paths: - .github/workflows/copilot-setup-steps.yml pull_request: paths: @@ -13,22 +13,22 @@ on: jobs: # The job MUST be called `copilot-setup-steps` or it will not be picked up by Copilot - copilot-setup-steps: + copilot-setup-steps: runs-on: ubuntu-latest - + # Set the permissions to the lowest permissions possible needed for your steps permissions: contents: read - + steps: - name: Checkout code uses: actions/checkout@v4 - + - name: Set up Julia uses: julia-actions/setup-julia@v2 with: version: '1.11' - + - name: Cache Julia packages uses: julia-actions/cache@v2 with: @@ -36,14 +36,14 @@ jobs: cache-packages: true cache-artifacts: true cache-registries: true - + - name: Install Fortran compiler (for Fortran dependencies) run: | sudo apt-get update sudo apt-get install -y gfortran libopenblas-dev - + - name: Build Julia project run: julia --project="." -e "using Pkg; Pkg.build()" - + - name: Instantiate Julia environment run: julia --project="." -e "using Pkg; Pkg.instantiate()" diff --git a/benchmarks/DIIID_ideal_example/vacuum_accuracy_benchmark.jl b/benchmarks/DIIID_ideal_example/vacuum_accuracy_benchmark.jl index 07e379a2..812d51d9 100644 --- a/benchmarks/DIIID_ideal_example/vacuum_accuracy_benchmark.jl +++ b/benchmarks/DIIID_ideal_example/vacuum_accuracy_benchmark.jl @@ -3,15 +3,16 @@ using Pkg using Plots using LinearAlgebra -Pkg.activate("$(@__DIR__)/../.."); using JPEC +Pkg.activate("$(@__DIR__)/../.."); +using JPEC # this requires you to have run the DIIID-like_ideal_example first to generate the benchmark inputs @load "$(@__DIR__)/../../examples/DIIID-like_ideal_example/benchmark_inputs.jld2" benchmark_inputs (; wv_block, mpert, mtheta_eq, mthvac, complex_flag, kernelsign, - wall_flag, farwall_flag, grri, xzpts, ahg_file, dir_path, - vac_inputs, wall_settings, - n, ipert_n, psifac) = benchmark_inputs + wall_flag, farwall_flag, grri, xzpts, ahg_file, dir_path, + vac_inputs, wall_settings, + n, ipert_n, psifac) = benchmark_inputs """ Compute 0D accuracy metrics between two wv matrices @@ -34,7 +35,7 @@ if benchmark_n println("="^60) # Define range of n values to test - n_values = range(1,15, step=1) + n_values = range(1, 15; step=1) # Store results for Julia vs Fortran comparison relative_errors_jf = Float64[] max_errors_jf = Float64[] @@ -46,13 +47,13 @@ if benchmark_n # Compute Fortran solution JPEC.Vacuum.set_surface_params(mtheta_eq, vac_inputs.mlow, vac_inputs.mhigh, - n_test, vac_inputs.qa, vac_inputs.r, - vac_inputs.z, vac_inputs.delta) + n_test, vac_inputs.qa, vac_inputs.r, + vac_inputs.z, vac_inputs.delta) wv_block_fortran = copy(wv_block) JPEC.Vacuum.mscvac(wv_block_fortran, mpert, mtheta_eq, mthvac, - complex_flag, kernelsign, wall_flag, - farwall_flag, grri, xzpts) + complex_flag, kernelsign, wall_flag, + farwall_flag, grri, xzpts) JPEC.Vacuum.unset_surface_params() @@ -74,21 +75,21 @@ if benchmark_n println("Creating plots...") # Plot 1: Julia vs Fortran comparison - p1 = plot(n_values, relative_errors_jf, - label="Relative Frobenius Error", - marker=:circle, - xlabel="n (toroidal mode number)", - ylabel="Relative Error", - title="Julia vs Fortran Accuracy", - legend=:topright, - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box) - plot!(p1, n_values, max_errors_jf, - label="Max Absolute Error", - marker=:square, - linewidth=2) + p1 = plot(n_values, relative_errors_jf; + label="Relative Frobenius Error", + marker=:circle, + xlabel="n (toroidal mode number)", + ylabel="Relative Error", + title="Julia vs Fortran Accuracy", + legend=:topright, + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box) + plot!(p1, n_values, max_errors_jf; + label="Max Absolute Error", + marker=:square, + linewidth=2) figloc1 = joinpath(@__DIR__, "vacuum_accuracy_julia_vs_fortran_n_scan.pdf") savefig(p1, figloc1) @@ -125,13 +126,13 @@ if benchmark_m # Fortran reference mpert_ref = mhigh_reference - vac_inputs.mlow JPEC.Vacuum.set_surface_params(mtheta_eq, vac_inputs.mlow, mhigh_reference, - 1, vac_inputs.qa, vac_inputs.r, - vac_inputs.z, vac_inputs.delta) + 1, vac_inputs.qa, vac_inputs.r, + vac_inputs.z, vac_inputs.delta) wv_block_ref_fortran_m = zeros(ComplexF64, mpert_ref, mpert_ref) grri_ref = zeros(Float64, 2 * (mthvac + 5), 2 * mpert_ref) JPEC.Vacuum.mscvac(wv_block_ref_fortran_m, mpert_ref, mtheta_eq, mthvac, - complex_flag, kernelsign, wall_flag, - farwall_flag, grri_ref, xzpts, ahg_file, "$(@__DIR__)/../../examples/DIIID-like_ideal_example") + complex_flag, kernelsign, wall_flag, + farwall_flag, grri_ref, xzpts, ahg_file, "$(@__DIR__)/../../examples/DIIID-like_ideal_example") JPEC.Vacuum.unset_surface_params() println("Reference solutions computed.\n") @@ -144,14 +145,14 @@ if benchmark_m # Compute Fortran solution JPEC.Vacuum.set_surface_params(mtheta_eq, vac_inputs.mlow, mhigh_test, - 1, vac_inputs.qa, vac_inputs.r, - vac_inputs.z, vac_inputs.delta) + 1, vac_inputs.qa, vac_inputs.r, + vac_inputs.z, vac_inputs.delta) wv_block_fortran_m = zeros(ComplexF64, mpert_test, mpert_test) grri_test = zeros(Float64, 2 * (mthvac + 5), 2 * mpert_test) JPEC.Vacuum.mscvac(wv_block_fortran_m, mpert_test, mtheta_eq, mthvac, - complex_flag, kernelsign, wall_flag, - farwall_flag, grri_test, xzpts, ahg_file, "$(@__DIR__)/../../examples/DIIID-like_ideal_example") + complex_flag, kernelsign, wall_flag, + farwall_flag, grri_test, xzpts, ahg_file, "$(@__DIR__)/../../examples/DIIID-like_ideal_example") JPEC.Vacuum.unset_surface_params() @@ -193,72 +194,72 @@ if benchmark_m fortran_conv_plot = [x == 0.0 ? eps_plot : x for x in relative_errors_fortran_conv_m] # Plot: Convergence for each implementation (mhigh scan) - p4 = plot(mhigh_values, julia_conv_plot, - label="Julia (vs mhigh=$mhigh_reference)", - marker=:circle, - xlabel="mhigh (maximum poloidal mode)", - ylabel="Relative Error vs High-Res Reference", - title="Convergence Analysis (mhigh scan)", - legend=:topright, - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box) - plot!(p4, mhigh_values, fortran_conv_plot, - label="Fortran (vs mhigh=$mhigh_reference)", - marker=:square, - linewidth=2) + p4 = plot(mhigh_values, julia_conv_plot; + label="Julia (vs mhigh=$mhigh_reference)", + marker=:circle, + xlabel="mhigh (maximum poloidal mode)", + ylabel="Relative Error vs High-Res Reference", + title="Convergence Analysis (mhigh scan)", + legend=:topright, + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box) + plot!(p4, mhigh_values, fortran_conv_plot; + label="Fortran (vs mhigh=$mhigh_reference)", + marker=:square, + linewidth=2) figloc4 = joinpath(@__DIR__, "vacuum_accuracy_convergence_mhigh.pdf") savefig(p4, figloc4) @info "Saved mhigh convergence plot to $figloc4" # Combined plot for mhigh - p5 = plot(mhigh_values, relative_errors_jf_m, - label="Julia vs Fortran", - marker=:diamond, - xlabel="mhigh (maximum poloidal mode)", - ylabel="Relative Frobenius Error", - title="Julia vs Fortran Accuracy (mhigh scan)", - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box, - legend=:topright) + p5 = plot(mhigh_values, relative_errors_jf_m; + label="Julia vs Fortran", + marker=:diamond, + xlabel="mhigh (maximum poloidal mode)", + ylabel="Relative Frobenius Error", + title="Julia vs Fortran Accuracy (mhigh scan)", + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box, + legend=:topright) figloc5 = joinpath(@__DIR__, "vacuum_accuracy_julia_vs_fortran_mhigh.pdf") savefig(p5, figloc5) @info "Saved Julia vs Fortran mhigh comparison to $figloc5" # Combined plot with both metrics for mhigh scan - p6 = plot(layout=(2,1), size=(800, 800)) - - plot!(p6[1], mhigh_values, relative_errors_jf_m, - label="Julia vs Fortran", - marker=:diamond, - ylabel="Relative Frobenius Error", - title="Julia vs Fortran Agreement (mhigh scan)", - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box, - legend=:topright) - - plot!(p6[2], mhigh_values, julia_conv_plot, - label="Julia (vs mhigh=$mhigh_reference)", - marker=:circle, - xlabel="mhigh (maximum poloidal mode)", - ylabel="Relative Error vs High-Res", - title="Convergence to High Resolution", - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box, - legend=:topright) - plot!(p6[2], mhigh_values, fortran_conv_plot, - label="Fortran (vs mhigh=$mhigh_reference)", - marker=:square, - linewidth=2) + p6 = plot(; layout=(2, 1), size=(800, 800)) + + plot!(p6[1], mhigh_values, relative_errors_jf_m; + label="Julia vs Fortran", + marker=:diamond, + ylabel="Relative Frobenius Error", + title="Julia vs Fortran Agreement (mhigh scan)", + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box, + legend=:topright) + + plot!(p6[2], mhigh_values, julia_conv_plot; + label="Julia (vs mhigh=$mhigh_reference)", + marker=:circle, + xlabel="mhigh (maximum poloidal mode)", + ylabel="Relative Error vs High-Res", + title="Convergence to High Resolution", + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box, + legend=:topright) + plot!(p6[2], mhigh_values, fortran_conv_plot; + label="Fortran (vs mhigh=$mhigh_reference)", + marker=:square, + linewidth=2) figloc6 = joinpath(@__DIR__, "vacuum_accuracy_combined_mhigh.pdf") savefig(p6, figloc6) diff --git a/benchmarks/Solovev_ideal_example/vacuum_accuracy_benchmark.jl b/benchmarks/Solovev_ideal_example/vacuum_accuracy_benchmark.jl index 31297a81..bacb5b22 100644 --- a/benchmarks/Solovev_ideal_example/vacuum_accuracy_benchmark.jl +++ b/benchmarks/Solovev_ideal_example/vacuum_accuracy_benchmark.jl @@ -4,17 +4,18 @@ using Plots using LinearAlgebra using DelimitedFiles -default(markersize=2) +default(; markersize=2) -Pkg.activate("$(@__DIR__)/../.."); using JPEC +Pkg.activate("$(@__DIR__)/../.."); +using JPEC # this requires you to have run the Solovev_ideal_example first to generate the benchmark inputs @load "$(@__DIR__)/../../examples/Solovev_ideal_example/vacuum_response_inputs.jld2" benchmark_inputs (; wv_block, mpert, mtheta_eq, mthvac, complex_flag, kernelsign, - wall_flag, farwall_flag, grri, xzpts, ahg_file, dir_path, - vac_inputs, wall_settings, - n, ipert_n, psifac) = benchmark_inputs + wall_flag, farwall_flag, grri, xzpts, ahg_file, dir_path, + vac_inputs, wall_settings, + n, ipert_n, psifac) = benchmark_inputs """ Compute 0D accuracy metrics between two wv matrices @@ -37,8 +38,8 @@ if benchmark_n println("="^60) # Define range of n values to test - n_values = range(1,15, step=1) - n_values = [1,2,3,4,6,10,15] # For clearer plotting + n_values = range(1, 15; step=1) + n_values = [1, 2, 3, 4, 6, 10, 15] # For clearer plotting # Store results for Julia vs Fortran comparison relative_errors_jf = Float64[] max_errors_jf = Float64[] @@ -50,13 +51,13 @@ if benchmark_n # Compute Fortran solution JPEC.Vacuum.set_surface_params(mtheta_eq, vac_inputs.mlow, vac_inputs.mhigh, - n_test, vac_inputs.qa, vac_inputs.r, - vac_inputs.z, vac_inputs.delta) + n_test, vac_inputs.qa, vac_inputs.r, + vac_inputs.z, vac_inputs.delta) wv_block_fortran = copy(wv_block) JPEC.Vacuum.mscvac(wv_block_fortran, mpert, mtheta_eq, mthvac, - complex_flag, kernelsign, wall_flag, - farwall_flag, grri, xzpts) + complex_flag, kernelsign, wall_flag, + farwall_flag, grri, xzpts) JPEC.Vacuum.unset_surface_params() @@ -78,21 +79,21 @@ if benchmark_n println("Creating plots...") # Plot 1: Julia vs Fortran comparison - p1 = plot(n_values, relative_errors_jf, - label="Relative Frobenius Error", - marker=:circle, - xlabel="n (toroidal mode number)", - ylabel="Relative Error", - title="Julia vs Fortran Accuracy", - legend=:topright, - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box) - plot!(p1, n_values, max_errors_jf, - label="Max Absolute Error", - marker=:square, - linewidth=2) + p1 = plot(n_values, relative_errors_jf; + label="Relative Frobenius Error", + marker=:circle, + xlabel="n (toroidal mode number)", + ylabel="Relative Error", + title="Julia vs Fortran Accuracy", + legend=:topright, + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box) + plot!(p1, n_values, max_errors_jf; + label="Max Absolute Error", + marker=:square, + linewidth=2) figloc1 = joinpath(@__DIR__, "vacuum_accuracy_julia_vs_fortran_n_scan.pdf") # savefig(p1, figloc1) @@ -103,7 +104,7 @@ end pdr = plot() pdl = plot() -prz = plot(aspect_ratio=:equal, size=(400, 800)) +prz = plot(; aspect_ratio=:equal, size=(400, 800)) if benchmark_a println("="^60) @@ -118,14 +119,14 @@ if benchmark_a frobenius_norms_jf = Float64[] # Run accuracy benchmarks for each n value - cp("vac.in", "vac.in.backup", force=true) + cp("vac.in", "vac.in.backup"; force=true) for a_test in a_values println("Testing a = $a_test") # Compute Fortran solution JPEC.Vacuum.set_surface_params(mtheta_eq, vac_inputs.mlow, vac_inputs.mhigh, - vac_inputs.n, vac_inputs.qa, vac_inputs.r, - vac_inputs.z, vac_inputs.delta) + vac_inputs.n, vac_inputs.qa, vac_inputs.r, + vac_inputs.z, vac_inputs.delta) lines = readlines("vac.in") idx = findfirst(l -> occursin(r"^\s*a\s*=", l), lines) @@ -134,21 +135,21 @@ if benchmark_a wv_block_fortran = copy(wv_block) JPEC.Vacuum.mscvac(wv_block_fortran, mpert, mtheta_eq, mthvac, - complex_flag, kernelsign, wall_flag, - farwall_flag, grri, xzpts) + complex_flag, kernelsign, wall_flag, + farwall_flag, grri, xzpts) JPEC.Vacuum.unset_surface_params() # Compute Julia solution - new_wall = JPEC.Vacuum.WallShapeSettings( - shape= a_test > 10 ? "nowall" : wall_settings.shape, + new_wall = JPEC.Vacuum.WallShapeSettings(; + shape=a_test > 10 ? "nowall" : wall_settings.shape, a=a_test, aw=wall_settings.aw, bw=wall_settings.bw, cw=wall_settings.cw, dw=wall_settings.dw, tw=wall_settings.tw, - equal_arc_wall=wall_settings.equal_arc_wall, + equal_arc_wall=wall_settings.equal_arc_wall ) wv_block_julia, grri_julia, xzpts_julia = JPEC.Vacuum.compute_vacuum_response(vac_inputs, new_wall) @@ -162,44 +163,44 @@ if benchmark_a # check wall geometry # Read the file, skipping the header line - data = readdlm("wall_geo.out", skipstart=3) + data = readdlm("wall_geo.out"; skipstart=3) theta_fortran = data[:, 1] - x_fortran = data[:, 2][1:end - 2] - z_fortran = data[:, 3][1:end - 2] + x_fortran = data[:, 2][1:(end-2)] + z_fortran = data[:, 3][1:(end-2)] i_fortran = range(1, length(x_fortran)) - x_julia_plasma = xzpts_julia[:,1] - z_julia_plasma = xzpts_julia[:,2] - x_julia = xzpts_julia[:,3] - z_julia = xzpts_julia[:,4] + x_julia_plasma = xzpts_julia[:, 1] + z_julia_plasma = xzpts_julia[:, 2] + x_julia = xzpts_julia[:, 3] + z_julia = xzpts_julia[:, 4] i_julia = range(1, length(x_julia)) # distance offset - dr = ((x_fortran-x_julia).^2 + (z_fortran-z_julia).^2).^0.5 / a_test - dl_fortran = vcat(0.0, sqrt.(diff(x_fortran).^2 + diff(z_fortran).^2)) - dl_julia = vcat(0.0, sqrt.(diff(x_julia).^2 + diff(z_julia).^2)) + dr = ((x_fortran-x_julia) .^ 2 + (z_fortran-z_julia) .^ 2) .^ 0.5 / a_test + dl_fortran = vcat(0.0, sqrt.(diff(x_fortran) .^ 2 + diff(z_fortran) .^ 2)) + dl_julia = vcat(0.0, sqrt.(diff(x_julia) .^ 2 + diff(z_julia) .^ 2)) + + plot!(pdr, i_julia, dr; label="distance error a=$a_test", linewidth=1) - plot!(pdr, i_julia, dr, label="distance error a=$a_test",linewidth=1) - if a_test == a_values[1] - plot!(prz, x_julia_plasma, z_julia_plasma, label="Julia Plasma", linewidth=1, marker=:cross, color=:black) + plot!(prz, x_julia_plasma, z_julia_plasma; label="Julia Plasma", linewidth=1, marker=:cross, color=:black) end if a_test < 20 # this dashed vertical line proves the fortran wall has 3 points at the same x around the midplane to enforce up down symmetry - plot!(prz, [x_fortran[1], x_fortran[1]], [-maximum(z_julia_plasma), maximum(z_julia_plasma)], label=nothing, linewidth=1, color=:black, linestyle=:dash) - plot!(prz, x_fortran, z_fortran, label="Fortran wall, a=$a_test", linewidth=2, marker=:o,markerfillalpha=0) + plot!(prz, [x_fortran[1], x_fortran[1]], [-maximum(z_julia_plasma), maximum(z_julia_plasma)]; label=nothing, linewidth=1, color=:black, linestyle=:dash) + plot!(prz, x_fortran, z_fortran; label="Fortran wall, a=$a_test", linewidth=2, marker=:o, markerfillalpha=0) last_color = current().series_list[end][:linecolor] - plot!(prz, x_julia, z_julia, label="Julia wall, a=$a_test", linewidth=1, marker=:cross, markerlinewidth=0, + plot!(prz, x_julia, z_julia; label="Julia wall, a=$a_test", linewidth=1, marker=:cross, markerlinewidth=0, color=last_color) - plot!(prz, x_julia[1:1], z_julia[1:1], linewidth=0, marker=:dtriangle,color=last_color, label=nothing) - plot!(prz, x_julia[end:end], z_julia[end:end], linewidth=0, marker=:diamond,color=last_color, aspect_ratio=:equal, label=nothing) - - plot!(pdl, i_fortran, dl_fortran, label="Fortran dl, a=$a_test", linewidth=1) - plot!(pdl, i_julia, dl_julia, label="Julia dl, a=$a_test", linewidth=1) + plot!(prz, x_julia[1:1], z_julia[1:1]; linewidth=0, marker=:dtriangle, color=last_color, label=nothing) + plot!(prz, x_julia[end:end], z_julia[end:end]; linewidth=0, marker=:diamond, color=last_color, aspect_ratio=:equal, label=nothing) + + plot!(pdl, i_fortran, dl_fortran; label="Fortran dl, a=$a_test", linewidth=1) + plot!(pdl, i_julia, dl_julia; label="Julia dl, a=$a_test", linewidth=1) end end # Clean up backup - cp("vac.in.backup", "vac.in", force=true) + cp("vac.in.backup", "vac.in"; force=true) rm("vac.in.backup") # Create plots @@ -210,7 +211,7 @@ if benchmark_a xlabel!(prz, "x (m)") ylabel!(prz, "z (m)") - plot!(prz, aspect_ratio=:equal) + plot!(prz; aspect_ratio=:equal) figloc_geo = joinpath(@__DIR__, "vacuum_accuracy_julia_vs_fortran_a_scan_geometry_check.pdf") # savefig(pdr, figloc_geo) @@ -222,21 +223,21 @@ if benchmark_a # Plot 1: Julia vs Fortran comparison - p1 = plot(a_values, relative_errors_jf, - label="Relative Frobenius Error", - marker=:circle, - xlabel="a (radial separation)", - ylabel="Relative Error", - title="Julia vs Fortran Accuracy", - legend=:topright, - linewidth=2, - yscale=:log10, - minorgrid=true, - framestyle=:box) - plot!(p1, a_values, max_errors_jf, - label="Max Absolute Error", - marker=:square, - linewidth=2) + p1 = plot(a_values, relative_errors_jf; + label="Relative Frobenius Error", + marker=:circle, + xlabel="a (radial separation)", + ylabel="Relative Error", + title="Julia vs Fortran Accuracy", + legend=:topright, + linewidth=2, + yscale=:log10, + minorgrid=true, + framestyle=:box) + plot!(p1, a_values, max_errors_jf; + label="Max Absolute Error", + marker=:square, + linewidth=2) figloc1 = joinpath(@__DIR__, "vacuum_accuracy_julia_vs_fortran_a_scan.pdf") # savefig(p1, figloc1) diff --git a/benchmarks/benchmark_fourier_transforms.jl b/benchmarks/benchmark_fourier_transforms.jl index 40cf99a2..474d09cb 100644 --- a/benchmarks/benchmark_fourier_transforms.jl +++ b/benchmarks/benchmark_fourier_transforms.jl @@ -28,10 +28,10 @@ function extract_modes(fft_result, mlow, mhigh, mtheta) for (i, m) in enumerate(mlow:mhigh) if m >= 0 # Positive frequencies - modes[i] = fft_result[m + 1] / mtheta # FFT normalization + modes[i] = fft_result[m+1] / mtheta # FFT normalization else # Negative frequencies (wrap around) - modes[i] = fft_result[mtheta + m + 1] / mtheta + modes[i] = fft_result[mtheta+m+1] / mtheta end end return modes @@ -39,10 +39,10 @@ end # Test configurations test_cases = [ - (name="Small (mtheta=128, mpert=10)", mtheta=128, mpert=10, mlow=-5), - (name="Medium (mtheta=256, mpert=20)", mtheta=256, mpert=20, mlow=-10), - (name="Large (mtheta=480, mpert=40)", mtheta=480, mpert=40, mlow=-20), - (name="Very Large (mtheta=1024, mpert=80)", mtheta=1024, mpert=80, mlow=-40), + (name="Small (mtheta=128, mpert=10)", mtheta=128, mpert=10, mlow=-5), + (name="Medium (mtheta=256, mpert=20)", mtheta=256, mpert=20, mlow=-10), + (name="Large (mtheta=480, mpert=40)", mtheta=480, mpert=40, mlow=-20), + (name="Very Large (mtheta=1024, mpert=80)", mtheta=1024, mpert=80, mlow=-40) ] for test in test_cases @@ -56,7 +56,7 @@ for test in test_cases mhigh = mlow + mpert - 1 # Create test data - theta = range(0, 2π, length=mtheta+1)[1:end-1] + theta = range(0, 2π; length=mtheta+1)[1:(end-1)] data = sin.(3 .* theta) .+ 0.5 .* cos.(7 .* theta) .+ 0.2 .* sin.(11 .* theta) # Initialize FourierTransform @@ -99,7 +99,7 @@ for test in test_cases # Note: Our transform uses a different normalization and basis println("\n--- Accuracy Check ---") println("FourierTransform allocating vs in-place: ", - @sprintf("%.2e", maximum(abs.(modes_alloc .- modes_buffer)))) + @sprintf("%.2e", maximum(abs.(modes_alloc .- modes_buffer)))) # Compare magnitudes of modes (since basis might differ) println("Mode magnitudes comparison (FourierTransform vs FFTW):") @@ -129,9 +129,9 @@ for test in test_cases full_modes = zeros(ComplexF64, mtheta) for (i, m) in enumerate(mlow:mhigh) if m >= 0 - full_modes[m + 1] = modes_test[i] + full_modes[m+1] = modes_test[i] else - full_modes[mtheta + m + 1] = modes_test[i] + full_modes[mtheta+m+1] = modes_test[i] end end t6 = @benchmark ifft($full_modes) @@ -140,21 +140,21 @@ for test in test_cases # Accuracy check println("\n--- Inverse Accuracy Check ---") println("inverse() allocating vs in-place: ", - @sprintf("%.2e", maximum(abs.(theta_alloc .- theta_buffer)))) + @sprintf("%.2e", maximum(abs.(theta_alloc .- theta_buffer)))) println("Round-trip error (real part): ", - @sprintf("%.2e", maximum(abs.(real.(theta_alloc) .- data)))) + @sprintf("%.2e", maximum(abs.(real.(theta_alloc) .- data)))) # Performance summary println("\n--- Performance Summary ---") println(@sprintf("Forward transform speedup (in-place vs allocating): %.2fx", - median(t1).time / median(t2).time)) + median(t1).time / median(t2).time)) println(@sprintf("Allocations eliminated: %d → %d", - t1.allocs, t2.allocs)) + t1.allocs, t2.allocs)) # Compare to FFTW println(@sprintf("\nFourier vs FFTW (forward): %.2fx %s", - abs(median(t2).time / median(t3).time), - median(t2).time < median(t3).time ? "faster" : "slower")) + abs(median(t2).time / median(t3).time), + median(t2).time < median(t3).time ? "faster" : "slower")) println("Note: FFTW computes full DFT (all N modes), we compute truncated series ($mpert modes)") end @@ -169,7 +169,7 @@ mlow = -10 nbatch = 10 # Transform 10 functions simultaneously ft = FourierTransform(mtheta, mpert, mlow) -theta = range(0, 2π, length=mtheta+1)[1:end-1] +theta = range(0, 2π; length=mtheta+1)[1:(end-1)] # Create batch data data_matrix = zeros(Float64, mtheta, nbatch) @@ -182,7 +182,7 @@ modes_matrix = zeros(ComplexF64, mpert, nbatch) println("\nTransforming $nbatch functions of length $mtheta:") print("Allocating (loop): ") -@btime for i in 1:$nbatch +@btime for i in 1:($nbatch) modes = $ft($data_matrix[:, i]) end @@ -191,7 +191,7 @@ print("Allocating (matrix):") print("In-place (loop): ") modes_buffer = zeros(ComplexF64, mpert) -@btime for i in 1:$nbatch +@btime for i in 1:($nbatch) transform!($modes_buffer, $ft, $data_matrix[:, i]) end diff --git a/benchmarks/benchmark_git_branches.jl b/benchmarks/benchmark_git_branches.jl index 0c58e390..2fb0f8a5 100755 --- a/benchmarks/benchmark_git_branches.jl +++ b/benchmarks/benchmark_git_branches.jl @@ -196,9 +196,9 @@ function run_example_benchmark(example_path, num_runs) avg_runtime = sum(runtimes) / length(runtimes) return ( - eigenvalue = real(et[1]), - steps = nsteps, - runtime = avg_runtime + eigenvalue=real(et[1]), + steps=nsteps, + runtime=avg_runtime ) end @@ -224,9 +224,9 @@ function benchmark_branches(options) checkout_ref(options["branch1"], options["commit1"]) commit1 = get_commit_hash("HEAD") results["branch1"] = ( - name = options["branch1"], - commit = commit1, - metrics = run_example_benchmark(options["example"], options["runs"]) + name=options["branch1"], + commit=commit1, + metrics=run_example_benchmark(options["example"], options["runs"]) ) # Benchmark branch 2 @@ -236,9 +236,9 @@ function benchmark_branches(options) checkout_ref(options["branch2"], options["commit2"]) commit2 = get_commit_hash("HEAD") results["branch2"] = ( - name = options["branch2"], - commit = commit2, - metrics = run_example_benchmark(options["example"], options["runs"]) + name=options["branch2"], + commit=commit2, + metrics=run_example_benchmark(options["example"], options["runs"]) ) finally diff --git a/benchmarks/benchmark_legendre_2007.jl b/benchmarks/benchmark_legendre_2007.jl index 3c7f992b..2c2c4c88 100644 --- a/benchmarks/benchmark_legendre_2007.jl +++ b/benchmarks/benchmark_legendre_2007.jl @@ -94,7 +94,7 @@ test_cases = [ (5.0, 5), (5.0, 10), (5.0, 20), - (5.0, 50), + (5.0, 50) ] for (s, n) in test_cases @@ -104,7 +104,7 @@ for (s, n) in test_cases speedup = time_1997 / time_2007 println(@sprintf("%-8.2f %-8d %-20.6f %-20.6f %-15.2fx", - s, n, time_1997*1000, time_2007*1000, speedup)) + s, n, time_1997*1000, time_2007*1000, speedup)) end println("\n3. VISUAL CHECK: rhohat parameter and integration method selection") diff --git a/build_docs_local.jl b/build_docs_local.jl index 1d34af0a..1d6b1b5c 100644 --- a/build_docs_local.jl +++ b/build_docs_local.jl @@ -12,7 +12,7 @@ Pkg.build() Pkg.activate("docs") # Add the local package to docs environment first -Pkg.develop(PackageSpec(path=".")) +Pkg.develop(PackageSpec(; path=".")) # Now instantiate to get other dependencies Pkg.instantiate() diff --git a/docs/src/vacuum.md b/docs/src/vacuum.md index bbd08fad..6b6c4b59 100644 --- a/docs/src/vacuum.md +++ b/docs/src/vacuum.md @@ -95,4 +95,4 @@ chi = JPEC.Vacuum.compute_vacuum_field(R_obs, Z_obs, inputs, xi, eta, plasma_sur - For large mode numbers (nρ̂ ≥ 0.1), 32-point Gaussian quadrature is used for Legendre function evaluation - For n=0 modes with closed walls, automatic regularization is applied - Wall shapes support: nowall, conformal, elliptical, dee, mod_dee, or custom from file -- The vacuum response matrix wv is scaled by the singular factor (m - nq)(m' - nq) per [Chance Phys. Plasmas 1997] \ No newline at end of file +- The vacuum response matrix wv is scaled by the singular factor (m - nq)(m' - nq) per [Chance Phys. Plasmas 1997] diff --git a/examples/DIIID-like_ideal_example/run_and_analyze.ipynb b/examples/DIIID-like_ideal_example/run_and_analyze.ipynb index e70dce65..9efa6081 100644 --- a/examples/DIIID-like_ideal_example/run_and_analyze.ipynb +++ b/examples/DIIID-like_ideal_example/run_and_analyze.ipynb @@ -198,16 +198,10 @@ } ], "metadata": { - "kernelspec": { - "display_name": "Julia 1.11.6", - "language": "julia", - "name": "julia-1.11" - }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", - "name": "julia", - "version": "1.11.6" + "name": "julia" } }, "nbformat": 4, diff --git a/examples/fourier_transform_usage.jl b/examples/fourier_transform_usage.jl index 54e18041..eabdd876 100644 --- a/examples/fourier_transform_usage.jl +++ b/examples/fourier_transform_usage.jl @@ -33,7 +33,7 @@ println(" mlow = $mlow (lowest mode: m ∈ [$mlow, $(mlow+mpert-1)])") println("\nBasis functions: cos(m*θ), sin(m*θ) with m = $mlow:$(mlow+mpert-1)") # Create test data: a simple function in theta space -theta = range(0, 2π, length=mtheta+1)[1:end-1] +theta = range(0, 2π; length=mtheta+1)[1:(end-1)] f_theta = sin.(5 .* theta) .+ 0.5 .* cos.(8 .* theta) # Forward transform: theta → modes diff --git a/notebooks/equil_gfile_example.ipynb b/notebooks/equil_gfile_example.ipynb index 6d852756..261e55b8 100644 --- a/notebooks/equil_gfile_example.ipynb +++ b/notebooks/equil_gfile_example.ipynb @@ -21,7 +21,30 @@ "id": "1", "metadata": {}, "outputs": [], - "source": "# 1. Define the input parameters for the equilibrium solver.\n# - eq_filename: The name of the g-file we just created.\n# - eq_type: \"efit\" for a standard g-file.\n# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n# - mpsi, mtheta: Resolution of the output grid.\n\nequil_config = JPEC.Equilibrium.EquilibriumConfig(;\n eq_filename=\"beta_1.00\", # eq_filename\n eq_type=\"efit\", # eq_type\n jac_type=\"boozer\", # jac_type\n grid_type=\"ldp\",\n psilow=0.01, # psilow\n psihigh=0.994) # psihigh\n\n# 2. Run the main equilibrium setup function.\n# This will read the file, solve the direct problem, and return the final object.\nprintln(\"Starting equilibrium reconstruction...\")\n\n\nplasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_config)\n#plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"./DIIID_example/equil.toml\")\nprintln(\"Equilibrium reconstruction complete.\")" + "source": [ + "# 1. Define the input parameters for the equilibrium solver.\n", + "# - eq_filename: The name of the g-file we just created.\n", + "# - eq_type: \"efit\" for a standard g-file.\n", + "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", + "# - mpsi, mtheta: Resolution of the output grid.\n", + "\n", + "equil_config = JPEC.Equilibrium.EquilibriumConfig(;\n", + " eq_filename=\"beta_1.00\", # eq_filename\n", + " eq_type=\"efit\", # eq_type\n", + " jac_type=\"boozer\", # jac_type\n", + " grid_type=\"ldp\",\n", + " psilow=0.01, # psilow\n", + " psihigh=0.994) # psihigh\n", + "\n", + "# 2. Run the main equilibrium setup function.\n", + "# This will read the file, solve the direct problem, and return the final object.\n", + "println(\"Starting equilibrium reconstruction...\")\n", + "\n", + "\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_config)\n", + "#plasma_eq = JPEC.Equilibrium.setup_equilibrium(\"./DIIID_example/equil.toml\")\n", + "println(\"Equilibrium reconstruction complete.\")" + ] }, { "cell_type": "code", @@ -29,7 +52,54 @@ "id": "2", "metadata": {}, "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_config = plasma_eq.config\n", + "psi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] }, { "cell_type": "code", @@ -187,4 +257,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} \ No newline at end of file +} diff --git a/notebooks/equil_inverse_test.ipynb b/notebooks/equil_inverse_test.ipynb index c84eb247..572c0b1e 100644 --- a/notebooks/equil_inverse_test.ipynb +++ b/notebooks/equil_inverse_test.ipynb @@ -46,7 +46,54 @@ "id": "2", "metadata": {}, "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_config = plasma_eq.config\n", + "psi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] }, { "cell_type": "code", @@ -204,4 +251,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} \ No newline at end of file +} diff --git a/notebooks/equil_lar_example.ipynb b/notebooks/equil_lar_example.ipynb index 57864052..c09ea350 100644 --- a/notebooks/equil_lar_example.ipynb +++ b/notebooks/equil_lar_example.ipynb @@ -20,7 +20,10 @@ "id": "1", "metadata": {}, "outputs": [], - "source": "equil_input = JPEC.Equilibrium.EquilibriumConfig(; eq_type=\"lar\", eq_filename=\"lar.toml\")\nlar_input = JPEC.Equilibrium.LargeAspectRatioConfig(; lar_r0=10, lar_a=1, beta0=0.001, q0=1.5, p_pres=2, p_sig=1)" + "source": [ + "equil_input = JPEC.Equilibrium.EquilibriumConfig(; eq_type=\"lar\", eq_filename=\"lar.toml\")\n", + "lar_input = JPEC.Equilibrium.LargeAspectRatioConfig(; lar_r0=10, lar_a=1, beta0=0.001, q0=1.5, p_pres=2, p_sig=1)" + ] }, { "cell_type": "code", @@ -38,7 +41,54 @@ "id": "3", "metadata": {}, "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_config = plasma_eq.config\n", + "psi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] }, { "cell_type": "code", @@ -196,4 +246,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} \ No newline at end of file +} diff --git a/notebooks/equil_soloviev_example.ipynb b/notebooks/equil_soloviev_example.ipynb index 0c4e7812..7c2dcc0c 100644 --- a/notebooks/equil_soloviev_example.ipynb +++ b/notebooks/equil_soloviev_example.ipynb @@ -94,7 +94,54 @@ "id": "5", "metadata": {}, "outputs": [], - "source": "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\nprintln(\"\\n--- Generating data for 2D color plots ---\")\n# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n# This part is identical to the previous steps.\nequil_config = plasma_eq.config\npsi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\ntheta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n# 2. Evaluate the `rzphi` spline to get the R and Z values.\nprintln(\"Evaluating the 'rzphi' mapping spline...\")\nfs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\nprintln(\"Evaluation complete.\")\n# 3. Transform the spline output to physical (R, Z) coordinates.\n# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\nrfac_sq = fs_grid[:, :, 1]\neta_term = fs_grid[:, :, 2]\ntheta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\neta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\nrfac_grid = sqrt.(max.(0.0, rfac_sq))\nR_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\nZ_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\nprintln(\"Calculated R and Z grids.\")\n# 4. Create the 2D color plot for R(ψ,θ)\nprintln(\"--- Plotting heatmap for R(ψ,θ) ---\")\np_r_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n R_grid', # Note the transpose ' to match axis dimensions\n title=\"Major Radius R(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"R [m]\"\n)\ndisplay(p_r_heatmap)\n# 5. Create the 2D color plot for Z(ψ,θ)\nprintln(\"--- Plotting heatmap for Z(ψ,θ) ---\")\np_z_heatmap = heatmap(\n psi_norm_grid,\n theta_new_grid,\n Z_grid', # Note the transpose ' to match axis dimensions\n title=\"Vertical Position Z(ψ, θ)\",\n xlabel=\"Normalized Psi (ψₙ)\",\n ylabel=\"Poloidal Angle (θ_new)\",\n colorbar_title=\"Z [m]\"\n)\ndisplay(p_z_heatmap)\nprintln(\"\\n2D color plots for R and Z have been saved.\")" + "source": [ + "# --- Final Code to Generate 2D Color Plots of R(ψ,θ) and Z(ψ,θ) ---\n", + "println(\"\\n--- Generating data for 2D color plots ---\")\n", + "# 1. Define the grid in flux coordinates (ψ_norm, θ_new)\n", + "# This part is identical to the previous steps.\n", + "equil_config = plasma_eq.config\n", + "psi_norm_grid = collect(range(equil_config.psilow, equil_config.psihigh, length=equil_config.mpsi + 1))\n", + "theta_new_grid = collect(range(0.0, 1.0, length=equil_config.mtheta + 1))\n", + "# 2. Evaluate the `rzphi` spline to get the R and Z values.\n", + "println(\"Evaluating the 'rzphi' mapping spline...\")\n", + "fs_grid = JPEC.Spl.bicube_eval(plasma_eq.rzphi, psi_norm_grid, theta_new_grid)\n", + "println(\"Evaluation complete.\")\n", + "# 3. Transform the spline output to physical (R, Z) coordinates.\n", + "# This calculates R_grid[i,j] = R(ψ[i], θ[j]) and Z_grid[i,j] = Z(ψ[i], θ[j])\n", + "rfac_sq = fs_grid[:, :, 1]\n", + "eta_term = fs_grid[:, :, 2]\n", + "theta_new_mesh = ones(length(psi_norm_grid)) * theta_new_grid'\n", + "eta_grid = 2.0 * pi .* (theta_new_mesh .+ eta_term)\n", + "rfac_grid = sqrt.(max.(0.0, rfac_sq))\n", + "R_grid = plasma_eq.ro .+ rfac_grid .* cos.(eta_grid)\n", + "Z_grid = plasma_eq.zo .+ rfac_grid .* sin.(eta_grid)\n", + "println(\"Calculated R and Z grids.\")\n", + "# 4. Create the 2D color plot for R(ψ,θ)\n", + "println(\"--- Plotting heatmap for R(ψ,θ) ---\")\n", + "p_r_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " R_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Major Radius R(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"R [m]\"\n", + ")\n", + "display(p_r_heatmap)\n", + "# 5. Create the 2D color plot for Z(ψ,θ)\n", + "println(\"--- Plotting heatmap for Z(ψ,θ) ---\")\n", + "p_z_heatmap = heatmap(\n", + " psi_norm_grid,\n", + " theta_new_grid,\n", + " Z_grid', # Note the transpose ' to match axis dimensions\n", + " title=\"Vertical Position Z(ψ, θ)\",\n", + " xlabel=\"Normalized Psi (ψₙ)\",\n", + " ylabel=\"Poloidal Angle (θ_new)\",\n", + " colorbar_title=\"Z [m]\"\n", + ")\n", + "display(p_z_heatmap)\n", + "println(\"\\n2D color plots for R and Z have been saved.\")" + ] }, { "cell_type": "code", @@ -252,4 +299,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} \ No newline at end of file +} diff --git a/notebooks/sing_find_example.ipynb b/notebooks/sing_find_example.ipynb new file mode 100644 index 00000000..bffe5851 --- /dev/null +++ b/notebooks/sing_find_example.ipynb @@ -0,0 +1,487 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "0", + "metadata": {}, + "outputs": [], + "source": [ + "# using Pkg\n", + "# Pkg.activate(\"..\") \n", + "# Pkg.instantiate()\n", + "using JPEC, Plots\n", + "gr() " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1", + "metadata": {}, + "outputs": [], + "source": [ + "using LinearAlgebra\n", + "using Printf\n", + "using Plots" + ] + }, + { + "cell_type": "markdown", + "id": "2", + "metadata": {}, + "source": [ + "### read Equil" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3", + "metadata": {}, + "outputs": [], + "source": [ + "# 1. Define the input parameters for the equilibrium solver.\n", + "# - eq_filename: The name of the g-file we just created.\n", + "# - eq_type: \"efit\" for a standard g-file.\n", + "# - jac_type: \"boozer\" or \"hamada\" for the output coordinates.\n", + "# - mpsi, mtheta: Resolution of the output grid.\n", + "equil_input = JPEC.Equilibrium.EquilInput(\n", + " \"beta_1.00\", # eq_filename\n", + " \"efit\", # eq_type\n", + " \"boozer\", # jac_type\n", + " 0.01, # psilow\n", + " 1.0, # psihigh\n", + " 100, # mpsi (number of radial grid points)\n", + " 128 # mtheta (number of poloidal grid points)\n", + ")\n", + "\n", + "# 2. Run the main equilibrium setup function.\n", + "# This will read the file, solve the direct problem, and return the final object.\n", + "println(\"Starting equilibrium reconstruction...\")\n", + "plasma_eq = JPEC.Equilibrium.setup_equilibrium(equil_input)\n", + "println(\"Equilibrium reconstruction complete.\")" + ] + }, + { + "cell_type": "markdown", + "id": "4", + "metadata": {}, + "source": [ + "### Use spline_eval \n", + "sq!!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5", + "metadata": {}, + "outputs": [], + "source": [ + "# The plasma_eq object contains the final 1D profile spline, `sq`.\n", + "# We will evaluate it on a fine grid to get smooth plot lines.\n", + "psi_norm_grid = range(0.0, 1.0, length=200)\n", + "\n", + "# spline_eval returns the function values (and derivatives if requested).\n", + "# For sq, the quantities are: 1:F, 2:P*mu0, 3:Toroidal Flux, 4:q\n", + "f_profiles = JPEC.SplinesMod.spline_eval(plasma_eq.sq, collect(psi_norm_grid))\n", + "\n", + "# Extract each profile into its own variable for clarity\n", + "F_profile = f_profiles[:, 1]\n", + "P_profile = f_profiles[:, 2]\n", + "tor_flux_prof = f_profiles[:, 3]\n", + "q_profile = f_profiles[:, 4];" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6", + "metadata": {}, + "outputs": [], + "source": [ + "plot(psi_norm_grid, q_profile, \n", + " xlabel=\"Normalized Flux\", ylabel=\"Safety Factor q\", \n", + " title=\"Safety Factor Profile\",\n", + " legend=:topright, label=\"q(ψ)\", lw=2, color=:blue)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + " sing_find!(sing_surf_data, plasma_eq; mex=2, nn=1, itmax=200)\n", + "\n", + "Finds and appends rational (singular) surfaces in a plasma equilibrium profile,\n", + "where `m = nn*q` within each interval between extrema of the safety factor profile `q(ψ)`.\n", + "\n", + "The results are stored as `NamedTuple`s in the supplied vector `sing_surf_data`, \n", + "with keys: `m`, `ψfac`, `ρ`, `q`, and `q1`.\n", + "\n", + "# Arguments\n", + "- `sing_surf_data::Vector`: Container for output; will be emptied and updated in-place.\n", + "- `plasma_eq`: Plasma equilibrium object with a field `.sq` suitable for spline evaluation.\n", + "- `mex::Int`: Number of `q` profile extrema. Defaults to 2 (monotonic `q`).\n", + "- `nn::Int`: Toroidal mode number `n`.\n", + "- `itmax::Int`: Maximum allowed bisection iterations per root.\n", + "\n", + "# Details\n", + "Searches each interval between adjacent `q`-profile extrema for all integer poloidal mode numbers `m`\n", + "that satisfy the rational surface condition `m = n*q(ψ)`, using bisection to find the roots.\n", + "Assumes a monotonic `q` profile, unless a generalized interface is implemented\n", + "(TODO: support for non-monotonic profiles).\n", + "\n", + "# Output\n", + "For each rational surface found, a `NamedTuple` with:\n", + "- `m`: Poloidal mode number at this surface\n", + "- `ψfac`: Normalized flux label at the surface\n", + "- `ρ`: Square root of `ψfac`\n", + "- `q`: `q` value at the surface (`m/nn`)\n", + "- `q1`: Derivative of `q` at the surface\n", + "\n", + "is pushed to `sing_surf_data`.\n", + "\"\"\"\n", + "function sing_find!(sing_surf_data, plasma_eq; nn=1, itmax=200)\n", + " \n", + " # Ensure sing_surf_data is empty before starting\n", + " empty!(sing_surf_data)\n", + "\n", + " # Define functions to evaluate q and its first derivative\n", + " qval(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 0)[4]\n", + " q1val(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 1)[2][4] \n", + "\n", + " # TODO: I assume monotonic here for checking, will need to provide some interface\n", + " # for the actual values fo (mex, qex) determined from the equil code\n", + " qex = [qval(0.0), qval(1.0)]\n", + " ψex = [0.0, 1.0]\n", + " mex = 2\n", + "\n", + " # Loop over extrema of q, find all rational values in between\n", + " for iex in 2:mex\n", + " dq = qex[iex] - qex[iex-1]\n", + " m = floor(Int, nn * qex[iex-1])\n", + " if dq > 0\n", + " m += 1\n", + " end\n", + " dm = Int(sign(dq * nn))\n", + "\n", + " # Loop over possible m's in interval\n", + " while (m - nn * qex[iex-1]) * (m - nn * qex[iex]) <= 0\n", + " it = 0\n", + " ψ0 = ψex[iex-1]\n", + " ψ1 = ψex[iex]\n", + " ψfac = 0.0\n", + "\n", + " # Bisection method to find singular surface\n", + " while it < itmax\n", + " it += 1\n", + " ψfac = (ψ0 + ψ1)/2\n", + " singfac = (m - nn * qval(ψfac)) * dm\n", + " if abs(singfac) <= 1e-12\n", + " break\n", + " elseif singfac > 0\n", + " ψ0 = ψfac\n", + " else\n", + " ψ1 = ψfac\n", + " end\n", + " end\n", + " if it == itmax\n", + " @warn \"Bisection did not converge for m = $m\"\n", + " # You may want to continue, break, or error here\n", + " else\n", + " push!(sing_surf_data, (\n", + " m = m,\n", + " ψfac = ψfac,\n", + " ρ = sqrt(ψfac),\n", + " q = m / nn,\n", + " q1 = q1val(ψfac),\n", + " ))\n", + " end\n", + " m += dm\n", + " end\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8", + "metadata": {}, + "outputs": [], + "source": [ + "sing_surf_data = []\n", + "sing_find!(sing_surf_data, plasma_eq)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9", + "metadata": {}, + "outputs": [], + "source": [ + "sing_surf_data[1].ψfac" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "10", + "metadata": {}, + "outputs": [], + "source": [ + "\"\"\"\n", + " bubble!(key::AbstractVector, index::AbstractVector{Int}, mmin::Int, mmax::Int)\n", + "\n", + "Sorts the indices in `index` in place such that `key[index[i]]` are in decreasing order\n", + "from `mmin` to `mmax` (inclusive).\n", + "\"\"\"\n", + "function bubble!(key::AbstractVector, index::AbstractVector{Int}, mmin::Int, mmax::Int)\n", + " switched = true\n", + " while switched\n", + " switched = false\n", + " for i in mmin:(mmax-1)\n", + " if key[index[i]] < key[index[i+1]]\n", + " index[i], index[i+1] = index[i+1], index[i]\n", + " switched = true\n", + " end\n", + " end\n", + " end\n", + " return nothing\n", + "end\n", + "\n", + "\"\"\"\n", + " ode_axis_init(sing_surf_data, sq; nn = 1, ψlim = 0.9936, ψlow = 0.01, mlow = -12, mhigh = 20, singfac_min = 1e-5, qlow = 0.0, sort_type = \"absm\")\n", + "\n", + "Initializes the ODE system near the magnetic axis for MHD or kinetic-MHD stability\n", + "analysis. This routine prepares solution vectors and sorting indices, locates\n", + "the relevant singular surfaces in the plasma equilibrium based on input data,\n", + "and sets integration boundaries and normalization factors for subsequent ODE integration\n", + "through singularities.\n", + "\n", + "# Arguments\n", + "- `sing_surf_data`: Array of structures, each containing information about singular surfaces,\n", + " including fields like `.ψfac`, `.q`, and `.q1`. Filled from sing_find function\n", + "- `sq`: Spline object controlling the equilibrium safety factor profile (typically contains equilibrium profile splines).\n", + "\n", + "# Keyword Arguments (these are likely to be replaced by the user input file structure)\n", + "- `nn`: Integer. Toroidal mode number.\n", + "- `ψlim`: Float. Upper bound for normalized flux coordinate ψ.\n", + "- `ψlow`: Float. Lower bound for normalized flux coordinate ψ.\n", + "- `mlow`: Integer. Lowest poloidal mode number to consider.\n", + "- `mhigh`: Integer. Highest poloidal mode number to consider.\n", + "- `singfac_min`: Float. Minimum separation from a singular surface.\n", + "- `qlow`: Float. Lower bound for safety factor q. (Currently not implemented if > 0.)\n", + "- `sort_type`: String. Sorting criteria for mode numbers (`\"absm\"` for |m|, or\n", + " `\"sing\"` for proximity to the first singular surface's m).\n", + "\n", + "# Details\n", + "This function does the following:\n", + "- Determines relevant singular surfaces from the provided equilibrium/singularity data.\n", + "- Sets up arrays for the ODE solution and related workspaces for all poloidal harmonics in the range [`mlow`, `mhigh`].\n", + "- Sorts the initial harmonics according to the specified `sort_type`.\n", + "- Initializes normalization factors and solution arrays for use in the ODE integrator.\n", + "- Computes the initial offset (`singfac`) from the next singular surface.\n", + "\n", + "Several features for kinetic MHD (indicated by `kin_flag`) or for `qlow > 0` are noted but not yet implemented.\n", + "\n", + "\"\"\"\n", + "\n", + "function ode_axis_init(sing_surf_data, plasma_eq; nn = 1, ψlim=0.9936, ψlow = 0.01, mlow = -12, mhigh = 20, singfac_min = 1e-5, qlow = 0.0, sort_type = \"absm\")\n", + " # JMH - I think all default values here will be supplied by inputs\n", + " # Right now, there are a lot of globals - not sure how we want to handle these\n", + " # But at least the major outputs here match fortran dcon\n", + "\n", + " # maybe change how this is passed in?\n", + " qval(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 0)[4]\n", + " q1val(ψ) = JPEC.SplinesMod.spline_eval(plasma_eq.sq, ψ, 1)[2][4] \n", + "\n", + " # Preliminary computations\n", + " new = true\n", + " ix = 0\n", + " psiout = 1.0\n", + " ψfac = 0.0 # TODO: this was Fortran sq%xs(0)?\n", + " msing = size(sing_surf_data)[1]\n", + " \n", + " # TODO: defined elsewhere\n", + " mpert = mhigh - mlow + 1\n", + "\n", + " # Use Newton iteration to find starting psi if qlow is above q0\n", + " # TODO: add this. For now, assume qlow = 0.0 and start at the first singular surface\n", + " if qlow > 0.0\n", + " @warn \"qlow > 0.0 is not implemented in ode_axis_init\"\n", + " end\n", + "\n", + " # Find inner singular surface\n", + " global ising = 0\n", + " if false #(TODO: kin_flag)\n", + " # for ising = 1:kmsing\n", + " # if kinsing[ising].psifac > psifac\n", + " # break\n", + " # end\n", + " # end\n", + " else\n", + " for ising in 1:msing\n", + " if sing_surf_data[ising].ψfac > ψfac\n", + " break\n", + " end\n", + " end\n", + " end\n", + " ising = max(0, ising - 1)\n", + "\n", + " # Find next singular surface\n", + " if false # TODO: (kin_flag)\n", + " # while true\n", + " # ising += 1\n", + " # if ising > kmsing\n", + " # break\n", + " # end\n", + " # if psilim < kinsing[ising].psifac\n", + " # break\n", + " # end\n", + " # q = kinsing[ising].q\n", + " # if mlow <= nn * q && mhigh >= nn * q\n", + " # break\n", + " # end\n", + " # end\n", + " # if ising > kmsing || singfac_min == 0\n", + " # psimax = psilim * (1 - eps)\n", + " # next = \"finish\"\n", + " # elseif psilim < kinsing[ising].psifac\n", + " # psimax = psilim * (1 - eps)\n", + " # next = \"finish\"\n", + " # else\n", + " # psimax = kinsing[ising].psifac - singfac_min / abs(nn * kinsing[ising].q1)\n", + " # next = \"cross\"\n", + " # end\n", + " else\n", + " while true\n", + " ising += 1\n", + " if ising > msing || ψlim < sing_surf_data[min(ising, msing)].ψfac\n", + " break\n", + " end\n", + " q = sing_surf_data[ising].q\n", + " if mlow <= nn * q && mhigh >= nn * q\n", + " break\n", + " end\n", + " end\n", + " if ising > msing || ψlim < sing_surf_data[min(ising, msing)].ψfac || singfac_min == 0\n", + " ψmax = ψlim * (1 - eps)\n", + " next = \"finish\"\n", + " else\n", + " ψmax = sing_surf_data[ising].ψfac - singfac_min / abs(nn * sing_surf_data[ising].q1)\n", + " next = \"cross\"\n", + " end\n", + " end\n", + "\n", + " # Allocate and sort solutions by increasing value of |m-ms1|\n", + " global u = zeros(ComplexF64, mpert, mpert, 2)\n", + " global du = zeros(ComplexF64, mpert, mpert, 2)\n", + " global u_save = zeros(ComplexF64, mpert, mpert, 2)\n", + " global unorm0 = zeros(Float64, 2 * mpert)\n", + " global unorm = zeros(Float64, 2 * mpert)\n", + " global index = collect(1:mpert)\n", + " m = mlow - 1 .+ index\n", + " if sort_type == \"absm\"\n", + " key = abs.(m)\n", + " elseif sort_type == \"sing\"\n", + " key = m\n", + " if msing > 0\n", + " key = key .- sing[1].m\n", + " end\n", + " key = -abs.(key)\n", + " else\n", + " error(\"Cannot recognize sort_type = $sort_type\")\n", + " end\n", + " bubble!(key, index, 1, mpert) # in original Fortran: bubble(key, index, 1, mpert)\n", + " println(key)\n", + " println(index)\n", + "\n", + " # Initialize solutions\n", + " u .= 0\n", + " for ipert = 1:mpert\n", + " u[index[ipert], ipert, 2] = 1\n", + " end\n", + " global msol = mpert\n", + " global neq = 4 * mpert * msol\n", + " u_save .= u\n", + " global psi_save = ψfac\n", + "\n", + " # Initialize integrator parameters (JMH - not sure if these are needed in Julia)\n", + " # global istep = 0\n", + " # global iopt = 1\n", + " # global itask = 5\n", + " # global itol = 2\n", + " # global mf = 10\n", + " # global istate = 1\n", + "\n", + " # Compute conditions at next singular surface\n", + " q = qval(ψlow) # Fortran: q=sq%fs(0,4)\n", + " println(q)\n", + " if false #TODO: (kin_flag)\n", + " # if kmsing > 0\n", + " # m1 = round(Int, nn * kinsing[ising].q)\n", + " # else\n", + " # m1 = round(Int, nn * qlim) + sign(one, nn * sq.fs1[mpsi, 5])\n", + " # end\n", + " else\n", + " if msing > 0\n", + " m1 = round(Int, nn * sing_surf_data[ising].q)\n", + " else\n", + " m1 = round(Int, nn * qlim) + sign(nn * q1val[end])\n", + " end\n", + " end\n", + " global singfac = abs(m1 - nn * q)\n", + "\n", + " println(m1)\n", + " println(singfac)\n", + "\n", + " # Set up work arrays (JMH - not sure if these are needed in Julia)\n", + " # global liw = length(iwork)\n", + " # global lrw = 22 + 64 * mpert * msol\n", + " # global rwork = zeros(Float64, lrw)\n", + " # global atol = zeros(ComplexF64, mpert, msol, 2)\n", + " # global fixfac = zeros(ComplexF64, msol, msol)\n", + " # iwork = 0\n", + " # rwork = 0\n", + " # rwork[1] = psimax\n", + " # rwork[5] = psifac * 1e-3\n", + " # rwork[11] = rwork[5]\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "11", + "metadata": {}, + "outputs": [], + "source": [ + "ode_axis_init(sing_surf_data, plasma_eq)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "12", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/Equilibrium/EquilibriumTypes.jl b/src/Equilibrium/EquilibriumTypes.jl index cf5dcdeb..d26aff02 100644 --- a/src/Equilibrium/EquilibriumTypes.jl +++ b/src/Equilibrium/EquilibriumTypes.jl @@ -128,7 +128,7 @@ end """ Outer constructor for EquilibriumConfig that enables a toml file - interface for specifying the configuration settings +interface for specifying the configuration settings DEPRECATED: Use [Equilibrium] section in jpec.toml instead """ @@ -524,28 +524,27 @@ This object provides a complete representation of the processed plasma equilibri Named 1D profile splines (F, P, dV/dψ, q) on normalized psi grid. Access values at grid points via `profiles.F_spline.y[i]`, etc. Access derivatives via `profiles.F_deriv.y[i]` or `profiles.F_deriv(psi)`. - - **Grid coordinates (shared by all rzphi/eqfun interpolants):** + + `rzphi_xs::Vector{Float64}`: ψ coordinates (length mpsi+1) + `rzphi_ys::Vector{Float64}`: θ coordinates (length mtheta+1) - - **Geometric quantities (rzphi, 4 interpolants):** 2D cubic interpolants for flux-coordinate mapping with periodic BC in theta. + + **x value:** normalized ψ + **y value:** SFL poloidal angle ∈ [0, 1] + `rzphi_rsquared::CubicInterpolantND`: r_coord² = (R - ro)² + (Z - zo)² + `rzphi_offset::CubicInterpolantND`: η/(2π) - θₙₑw (angle offset) + `rzphi_nu::CubicInterpolantND`: ν in ϕ = 2πζ + ν(ψ, θ) + `rzphi_jac::CubicInterpolantND`: Jacobian - - **Physics quantities (eqfun, 3 interpolants):** 2D cubic interpolants storing local physics and geometric quantities. + + **x value:** normalized ψ + **y value:** SFL poloidal angle θₙₑw + `eqfun_B::CubicInterpolantND`: Total magnetic field strength [T] + `eqfun_metric1::CubicInterpolantND`: (e₁⋅e₂ + q⋅e₃⋅e₁)/(J⋅B²) + `eqfun_metric2::CubicInterpolantND`: (e₂⋅e₃ + q⋅e₃⋅e₃)/(J⋅B²) - - `ro::Float64`: R-coordinate of the magnetic axis [m] - `zo::Float64`: Z-coordinate of the magnetic axis [m] - `psio::Float64`: Total flux difference |Ψ_axis - Ψ_boundary| [Weber/radian] diff --git a/src/ForceFreeStates/EulerLagrange.jl b/src/ForceFreeStates/EulerLagrange.jl index 3f9bbaeb..6d0f05de 100644 --- a/src/ForceFreeStates/EulerLagrange.jl +++ b/src/ForceFreeStates/EulerLagrange.jl @@ -253,7 +253,14 @@ that asymptotic calculations are specific to ideal ForceFreeStates and not inher - `ising::Int` - Index of the singular surface being crossed """ -function cross_ideal_singular_surf!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, intr::ForceFreeStatesInternal, ising::Int) +function cross_ideal_singular_surf!( + odet::OdeState, + ctrl::ForceFreeStatesControl, + equil::Equilibrium.PlasmaEquilibrium, + ffit::FourFitVars, + intr::ForceFreeStatesInternal, + ising::Int +) # Fixup solution at singular surface compute_solution_norms!(odet.u, odet, ctrl, intr, true) @@ -344,7 +351,14 @@ making it clear what region is being integrated. Check sensitivity of results to tolerances, currently using same logic as Fortran Check absolute tolerances, currently only relative tolerances are updated """ -function integrate_el_region!(odet::OdeState, ctrl::ForceFreeStatesControl, equil::Equilibrium.PlasmaEquilibrium, ffit::FourFitVars, intr::ForceFreeStatesInternal, chunk::IntegrationChunk) +function integrate_el_region!( + odet::OdeState, + ctrl::ForceFreeStatesControl, + equil::Equilibrium.PlasmaEquilibrium, + ffit::FourFitVars, + intr::ForceFreeStatesInternal, + chunk::IntegrationChunk +) # Callback to be run at every step, handles fixups, tolerances, and data storage cb = DiscreteCallback((u, t, integrator) -> true, integrator_callback!) diff --git a/src/ForceFreeStates/Sing.jl b/src/ForceFreeStates/Sing.jl index d52665d6..4ada1816 100644 --- a/src/ForceFreeStates/Sing.jl +++ b/src/ForceFreeStates/Sing.jl @@ -246,7 +246,14 @@ Better way to unpack the cubic splines Rename variables to be more intuitive? I don't like ff - maybe f and f_fact instead of f_lower Add a spline for F directly instead of the lower triangular factorization to avoid complexity? """ -function compute_sing_mmat!(mmat::Array{ComplexF64,4}, singp::SingType, ctrl::ForceFreeStatesControl, profiles::Equilibrium.ProfileSplines, ffit::FourFitVars, intr::ForceFreeStatesInternal) +function compute_sing_mmat!( + mmat::Array{ComplexF64,4}, + singp::SingType, + ctrl::ForceFreeStatesControl, + profiles::Equilibrium.ProfileSplines, + ffit::FourFitVars, + intr::ForceFreeStatesInternal +) q_spline = profiles.q_spline q_d1 = profiles.q_deriv diff --git a/src/ForcingTerms/ForcingTerms.jl b/src/ForcingTerms/ForcingTerms.jl index afe38287..b5f6400c 100644 --- a/src/ForcingTerms/ForcingTerms.jl +++ b/src/ForcingTerms/ForcingTerms.jl @@ -12,6 +12,7 @@ User-facing control parameters from TOML [ForcingTerms] section. ## Fields Forcing Data: + - `forcing_data_file::String` - Path to forcing data file (n, m, complex amplitude) - `forcing_data_format::String` - Format of forcing data: "ascii" or "hdf5" (default: "ascii") @@ -48,12 +49,14 @@ end Load forcing data from ASCII or HDF5 file. ASCII format: Three or four columns (n, m, real amplitude, [optional] imag amplitude) -- Column 1: Toroidal mode number (n) -- Column 2: Poloidal mode number (m) -- Column 3: Complex amplitude (real part) -- Column 4: Complex amplitude (imaginary part) [optional, assumes 0 if not present] + + - Column 1: Toroidal mode number (n) + - Column 2: Poloidal mode number (m) + - Column 3: Complex amplitude (real part) + - Column 4: Complex amplitude (imaginary part) [optional, assumes 0 if not present] Example ASCII file: + ``` 1 2 0.5 0.1 1 3 0.3 -0.2 @@ -61,10 +64,11 @@ Example ASCII file: ``` HDF5 format: -- Dataset "n": Integer array of toroidal mode numbers -- Dataset "m": Integer array of poloidal mode numbers -- Dataset "amplitude_real": Real parts of amplitudes -- Dataset "amplitude_imag": Imaginary parts of amplitudes + + - Dataset "n": Integer array of toroidal mode numbers + - Dataset "m": Integer array of poloidal mode numbers + - Dataset "amplitude_real": Real parts of amplitudes + - Dataset "amplitude_imag": Imaginary parts of amplitudes """ function load_forcing_data!( forcing_modes::Vector{ForcingMode}, @@ -106,7 +110,7 @@ function load_forcing_ascii!( error("Forcing data file not found: $filepath") end - data = readdlm(filepath, comments=true, comment_char='#') + data = readdlm(filepath; comments=true, comment_char='#') nrows = size(data, 1) ncols = size(data, 2) @@ -123,7 +127,7 @@ function load_forcing_ascii!( real_part = Float64(data[i, 3]) imag_part = ncols >= 4 ? Float64(data[i, 4]) : 0.0 - push!(forcing_modes, ForcingMode( + push!(forcing_modes, ForcingMode(; n=n, m=m, amplitude=complex(real_part, imag_part) @@ -159,7 +163,7 @@ function load_forcing_hdf5!( empty!(forcing_modes) for i in eachindex(n_array) - push!(forcing_modes, ForcingMode( + push!(forcing_modes, ForcingMode(; n=Int(n_array[i]), m=Int(m_array[i]), amplitude=complex(amp_real[i], amp_imag[i]) @@ -170,4 +174,4 @@ end export ForcingTermsControl, ForcingMode, load_forcing_data! -end # module ForcingTerms \ No newline at end of file +end # module ForcingTerms diff --git a/src/PerturbedEquilibrium/FieldReconstruction.jl b/src/PerturbedEquilibrium/FieldReconstruction.jl index d2c39e15..e98f0ff2 100644 --- a/src/PerturbedEquilibrium/FieldReconstruction.jl +++ b/src/PerturbedEquilibrium/FieldReconstruction.jl @@ -41,34 +41,35 @@ All fields are returned in mode space [npsi, mpert] rather than real space. # Process (following GPEC) -1. Sum weighted eigenmode contributions → ξ_ψ(ψ, m) -2. Compute contravariant field from ideal MHD → b^ψ, b^θ, b^ζ -3. Return mode-space fields (can convert to real space later if needed) + 1. Sum weighted eigenmode contributions → ξ_ψ(ψ, m) + 2. Compute contravariant field from ideal MHD → b^ψ, b^θ, b^ζ + 3. Return mode-space fields (can convert to real space later if needed) # Arguments -- `response_vector::Vector{ComplexF64}`: Response coefficients [numpert_total] -- `ForceFreeStates_results::OdeState`: ForceFreeStates results with u_store eigenmodes -- `equil::Equilibrium.PlasmaEquilibrium`: Equilibrium data -- `ffs_intr::ForceFreeStatesInternal`: Mode information (m, n ranges) -- `intr::PerturbedEquilibriumInternal`: Internal state + - `response_vector::Vector{ComplexF64}`: Response coefficients [numpert_total] + - `ForceFreeStates_results::OdeState`: ForceFreeStates results with u_store eigenmodes + - `equil::Equilibrium.PlasmaEquilibrium`: Equilibrium data + - `ffs_intr::ForceFreeStatesInternal`: Mode information (m, n ranges) + - `intr::PerturbedEquilibriumInternal`: Internal state # Returns Tuple of (xi_modes, b_modes) where each is a NamedTuple: -- `xi_modes.psi`: ξ_ψ component [npsi, mpert] (covariant) -- `b_modes.psi`: b^ψ component [npsi, mpert] (contravariant) -- `b_modes.theta`: b^θ component [npsi, mpert] (contravariant) -- `b_modes.zeta`: b^ζ component [npsi, mpert] (contravariant) + + - `xi_modes.psi`: ξ_ψ component [npsi, mpert] (covariant) + - `b_modes.psi`: b^ψ component [npsi, mpert] (contravariant) + - `b_modes.theta`: b^θ component [npsi, mpert] (contravariant) + - `b_modes.zeta`: b^ζ component [npsi, mpert] (contravariant) All in mode space, matching GPEC output format. # Notes -- Uses ForceFreeStates radial grid (not equilibrium grid) -- Works entirely in mode space - no Fourier transforms -- Follows GPEC gpeq_sol, gpeq_contra formulation -- Field from ideal MHD: b^ψ = i*χ₁*(m-n*q)*ξ_ψ + - Uses ForceFreeStates radial grid (not equilibrium grid) + - Works entirely in mode space - no Fourier transforms + - Follows GPEC gpeq_sol, gpeq_contra formulation + - Field from ideal MHD: b^ψ = i*χ₁*(m-n*q)*ξ_ψ """ function reconstruct_physical_fields( response_vector::Vector{ComplexF64}, @@ -100,15 +101,15 @@ function reconstruct_physical_fields( # Package outputs in NamedTuples for clarity xi_modes = ( - psi = xi_psi_modes, # [npsi, mpert] - covariant radial displacement - theta = zeros(ComplexF64, npsi, mpert), # Placeholder - not computed from ForceFreeStates - zeta = zeros(ComplexF64, npsi, mpert) # Placeholder - not computed from ForceFreeStates + psi=xi_psi_modes, # [npsi, mpert] - covariant radial displacement + theta=zeros(ComplexF64, npsi, mpert), # Placeholder - not computed from ForceFreeStates + zeta=zeros(ComplexF64, npsi, mpert) # Placeholder - not computed from ForceFreeStates ) b_modes = ( - psi = b_psi_modes, # [npsi, mpert] - contravariant radial field - theta = b_theta_modes, # [npsi, mpert] - contravariant poloidal field - zeta = b_zeta_modes # [npsi, mpert] - contravariant toroidal field + psi=b_psi_modes, # [npsi, mpert] - contravariant radial field + theta=b_theta_modes, # [npsi, mpert] - contravariant poloidal field + zeta=b_zeta_modes # [npsi, mpert] - contravariant toroidal field ) return xi_modes, b_modes @@ -132,20 +133,20 @@ plasma response to external forcing. # Arguments -- `response_vector::Vector{ComplexF64}`: Response coefficient for each eigenmode [numpert_total] -- `ForceFreeStates_results::OdeState`: ForceFreeStates results with u_store containing eigenmodes -- `ffs_intr::ForceFreeStatesInternal`: Mode information (mpert, etc.) + - `response_vector::Vector{ComplexF64}`: Response coefficient for each eigenmode [numpert_total] + - `ForceFreeStates_results::OdeState`: ForceFreeStates results with u_store containing eigenmodes + - `ffs_intr::ForceFreeStatesInternal`: Mode information (mpert, etc.) # Returns -- `xi_psi_modes::Matrix{ComplexF64}`: Covariant radial displacement ξ_ψ(ψ, m) [npsi, mpert] + - `xi_psi_modes::Matrix{ComplexF64}`: Covariant radial displacement ξ_ψ(ψ, m) [npsi, mpert] # Notes -- In ForceFreeStates formulation, u_store[:, :, 1, :] contains ξ_ψ (covariant radial displacement) -- The response vector is ordered as [mode1_mode1, mode1_mode2, ..., mode2_mode1, ...] -- We sum over all (i,j) eigenmode pairs to get the total response for each mode i -- This corresponds to xsp_mn in GPEC notation + - In ForceFreeStates formulation, u_store[:, :, 1, :] contains ξ_ψ (covariant radial displacement) + - The response vector is ordered as [mode1_mode1, mode1_mode2, ..., mode2_mode1, ...] + - We sum over all (i,j) eigenmode pairs to get the total response for each mode i + - This corresponds to xsp_mn in GPEC notation """ function sum_eigenmode_contributions( response_vector::Vector{ComplexF64}, @@ -211,33 +212,35 @@ bwz_mn = -(chi1*(q1*xsp_mn + sq%f(4)*xsp1_mn) + twopi*ifac*mfac*xss_mn) ! b^ζ ``` where: -- xsp_mn = ξ_ψ (covariant radial displacement) -- xsp1_mn = ∂ξ_ψ/∂ψ (radial derivative) -- xss_mn = ξ_ζ (covariant toroidal displacement) -- singfac = m - n*q (resonance factor) -- chi1 = 2π*Ψ₀ (flux normalization) -- ifac = i (imaginary unit) + + - xsp_mn = ξ_ψ (covariant radial displacement) + - xsp1_mn = ∂ξ_ψ/∂ψ (radial derivative) + - xss_mn = ξ_ζ (covariant toroidal displacement) + - singfac = m - n*q (resonance factor) + - chi1 = 2π*Ψ₀ (flux normalization) + - ifac = i (imaginary unit) # Arguments -- `xi_psi_modes::Matrix{ComplexF64}`: Covariant radial displacement ξ_ψ(ψ,m) [npsi, mpert] -- `ForceFreeStates_results::OdeState`: ForceFreeStates results with psi_store for radial grid -- `equil::Equilibrium.PlasmaEquilibrium`: Equilibrium with q(ψ), q'(ψ), Ψ₀ -- `ffs_intr::ForceFreeStatesInternal`: Mode numbers (mlow, mhigh, n) + - `xi_psi_modes::Matrix{ComplexF64}`: Covariant radial displacement ξ_ψ(ψ,m) [npsi, mpert] + - `ForceFreeStates_results::OdeState`: ForceFreeStates results with psi_store for radial grid + - `equil::Equilibrium.PlasmaEquilibrium`: Equilibrium with q(ψ), q'(ψ), Ψ₀ + - `ffs_intr::ForceFreeStatesInternal`: Mode numbers (mlow, mhigh, n) # Returns Tuple of three matrices, all [npsi, mpert]: -- `b_psi_modes::Matrix{ComplexF64}`: Contravariant radial field b^ψ(ψ,m) -- `b_theta_modes::Matrix{ComplexF64}`: Contravariant poloidal field b^θ(ψ,m) -- `b_zeta_modes::Matrix{ComplexF64}`: Contravariant toroidal field b^ζ(ψ,m) + + - `b_psi_modes::Matrix{ComplexF64}`: Contravariant radial field b^ψ(ψ,m) + - `b_theta_modes::Matrix{ComplexF64}`: Contravariant poloidal field b^θ(ψ,m) + - `b_zeta_modes::Matrix{ComplexF64}`: Contravariant toroidal field b^ζ(ψ,m) # Notes -- This is a simplified version assuming ξ_ζ = 0 (no toroidal displacement) -- Radial derivatives ∂ξ_ψ/∂ψ are computed using finite differences -- All calculations done in mode space (no Fourier transforms) -- Matches GPEC formulation exactly for consistency + - This is a simplified version assuming ξ_ζ = 0 (no toroidal displacement) + - Radial derivatives ∂ξ_ψ/∂ψ are computed using finite differences + - All calculations done in mode space (no Fourier transforms) + - Matches GPEC formulation exactly for consistency """ function compute_perturbed_field_modes( xi_psi_modes::Matrix{ComplexF64}, @@ -265,7 +268,7 @@ function compute_perturbed_field_modes( # ∂ξ_ψ/∂ψ (xsp1_mn in GPEC) xi_psi1_modes = zeros(ComplexF64, npsi, mpert) for ipert in 1:mpert - for ipsi in 2:npsi-1 + for ipsi in 2:(npsi-1) # Centered difference dpsi = ForceFreeStates_results.psi_store[ipsi+1] - ForceFreeStates_results.psi_store[ipsi-1] xi_psi1_modes[ipsi, ipert] = (xi_psi_modes[ipsi+1, ipert] - xi_psi_modes[ipsi-1, ipert]) / dpsi diff --git a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl index f3ebc202..f277f9da 100644 --- a/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl +++ b/src/PerturbedEquilibrium/PerturbedEquilibriumStructs.jl @@ -8,6 +8,7 @@ User-facing control parameters from TOML [PerturbedEquilibrium] section. Note: Forcing data file settings are now in [ForcingTerms] section. High Priority (MWE): + - `fixed_boundary::Bool` - Fixed boundary flag (default: false) - `output_eigenmodes::Bool` - Output mode fields as b-fields (default: true) - `compute_response::Bool` - Compute plasma response (default: true) @@ -15,12 +16,14 @@ High Priority (MWE): - `verbose::Bool` - Enable verbose logging (default: true) Output Settings: + - `output_filename::String` - Combined output file with ForceFreeStates results (default: uses ForceFreeStates HDF5_filename) - `write_outputs_to_HDF5::Bool` - Write perturbed equilibrium outputs to HDF5 (default: true) Medium Priority (defer for MWE): + - `filter_modes::Bool` - Enable mode filtering (default: false) - - `singular_point_method::String` - Method for singular point treatment (default: "standard") + - `singular_point_method::String` - Method for singular point treatment (default: "standard") # High Priority (MWE) """ @kwdef mutable struct PerturbedEquilibriumControl # High Priority (MWE) @@ -70,10 +73,12 @@ Results from perturbed equilibrium calculations. ## Fields Response fields (mode space): + - `xi_modes::Union{Nothing, NamedTuple}` - Displacement (psi, theta, zeta) [npsi, mpert] - `b_modes::Union{Nothing, NamedTuple}` - Magnetic field (psi, theta, zeta) [npsi, mpert] Singular coupling matrices [msing, numpert_total]: + - `resonant_flux::Matrix{ComplexF64}` - Resonant flux Φ_r/A (singcoup(1,:,:)) - `resonant_current::Matrix{ComplexF64}` - Resonant current (singcoup(2,:,:)) - `island_width_sq::Matrix{ComplexF64}` - (w/2)² in ψ_n (singcoup(3,:,:)) @@ -81,25 +86,28 @@ Singular coupling matrices [msing, numpert_total]: - `delta_prime::Matrix{ComplexF64}` - Tearing stability Δ' (singcoup(5,:,:)) Diagnostic quantities [msing]: + - `island_half_width::Vector{Float64}` - Actual w/2 (meters or ψ_n) - `chirikov_parameter::Vector{Float64}` - Island overlap metric Note: numpert_total = mpert × npert handles all (m,n) mode combinations Legacy fields (deprecated): + - `coupling_coefficient::ComplexF64` - Use singular coupling matrices instead - `resonant_amplitude::Float64` - Use island diagnostics instead Energies: - - `plasma_energy::Float64` - Plasma perturbation energy - - `vacuum_energy::Float64` - Vacuum perturbation energy + + - `plasma_energy::Float64` - Plasma perturbation energy # Response fields in mode space [npsi, mpert] following GPEC notation + - `vacuum_energy::Float64` - Vacuum perturbation energy # NamedTuples contain (psi, theta, zeta) components in flux coordinates - `total_energy::Float64` - Total perturbation energy """ @kwdef mutable struct PerturbedEquilibriumState # Response fields in mode space [npsi, mpert] following GPEC notation # NamedTuples contain (psi, theta, zeta) components in flux coordinates - xi_modes::Union{Nothing, NamedTuple} = nothing - b_modes::Union{Nothing, NamedTuple} = nothing + xi_modes::Union{Nothing,NamedTuple} = nothing + b_modes::Union{Nothing,NamedTuple} = nothing # Singular coupling matrices [msing × mpert] - GPEC singcoup(1:5,:,:) resonant_flux::Matrix{ComplexF64} = zeros(ComplexF64, 0, 0) # singcoup(1,:,:) diff --git a/src/PerturbedEquilibrium/Response.jl b/src/PerturbedEquilibrium/Response.jl index 1aea79c1..3e95b396 100644 --- a/src/PerturbedEquilibrium/Response.jl +++ b/src/PerturbedEquilibrium/Response.jl @@ -12,11 +12,12 @@ Compute plasma response to external forcing using ForceFreeStates eigenmode solutions. Implements resp_index=0 calculation from gpresp.f: -1. Build flux matrix from eigenmodes -2. Calculate plasma inductance (energy-based) -3. Calculate surface inductance from Green's function -4. Compute permeability matrix -5. Apply forcing to get response + + 1. Build flux matrix from eigenmodes + 2. Calculate plasma inductance (energy-based) + 3. Calculate surface inductance from Green's function + 4. Compute permeability matrix + 5. Apply forcing to get response """ function compute_plasma_response!( state::PerturbedEquilibriumState, diff --git a/src/PerturbedEquilibrium/ResponseMatrices.jl b/src/PerturbedEquilibrium/ResponseMatrices.jl index 46f62445..c542de93 100644 --- a/src/PerturbedEquilibrium/ResponseMatrices.jl +++ b/src/PerturbedEquilibrium/ResponseMatrices.jl @@ -24,30 +24,35 @@ plasma surface from ForceFreeStates eigenmode solutions. ## What's extracted: -1. **Boundary displacement**: ξ_ψ from `u_store[:, :, 1, end]` - - This is the radial (normal) component of the eigenmode displacement - - At the last radial integration point (plasma edge) - - Dimensions: [numpert_total, numpert_total] + 1. **Boundary displacement**: ξ_ψ from `u_store[:, :, 1, end]` -2. **Flux surface spacing**: dΨ/dρ at boundary - - From equilibrium bicubic spline evaluation - - Needed to convert displacement to magnetic field + + This is the radial (normal) component of the eigenmode displacement + + At the last radial integration point (plasma edge) + + Dimensions: [numpert_total, numpert_total] -3. **Safety factor**: q at boundary - - Used to compute singular factors (m - n*q) - - Identifies resonant surfaces + 2. **Flux surface spacing**: dΨ/dρ at boundary + + + From equilibrium bicubic spline evaluation + + Needed to convert displacement to magnetic field + 3. **Safety factor**: q at boundary + + + Used to compute singular factors (m - n*q) + + Identifies resonant surfaces ## Arguments -- `equil`: Equilibrium solution containing flux surfaces and q-profile -- `ForceFreeStates_results`: ODE integration results containing u_store with eigenmodes -- `intr`: ForceFreeStates internal state with boundary location (psilim) + + - `equil`: Equilibrium solution containing flux surfaces and q-profile + - `ForceFreeStates_results`: ODE integration results containing u_store with eigenmodes + - `intr`: ForceFreeStates internal state with boundary location (psilim) ## Returns + Named tuple with: -- `ξ_psi_boundary`: Boundary displacement [numpert_total, numpert_total] -- `dPsi_drho`: Flux surface spacing at boundary (scalar) -- `q_boundary`: Safety factor at boundary (scalar) -- `psi_boundary`: Normalized flux at boundary (scalar) + + - `ξ_psi_boundary`: Boundary displacement [numpert_total, numpert_total] + - `dPsi_drho`: Flux surface spacing at boundary (scalar) + - `q_boundary`: Safety factor at boundary (scalar) + - `psi_boundary`: Normalized flux at boundary (scalar) """ function extract_boundary_displacements( equil::Equilibrium.PlasmaEquilibrium, @@ -77,10 +82,10 @@ function extract_boundary_displacements( dPsi_drho = equil.psio * 2.0 * sqrt(psi_boundary) return ( - ξ_psi_boundary = ξ_psi_boundary, - dPsi_drho = dPsi_drho, - q_boundary = q_boundary, - psi_boundary = psi_boundary + ξ_psi_boundary=ξ_psi_boundary, + dPsi_drho=dPsi_drho, + q_boundary=q_boundary, + psi_boundary=psi_boundary ) end @@ -100,22 +105,27 @@ at the plasma surface. From the ideal MHD constraint [Park Phys. Plasmas 2009 05 where ξ_ψ is the radial displacement eigenfunction. ## Physical Interpretation [Park Phys. Plasmas 2007 052110 Section II]: -- ξ_ψ[i,j]: Displacement of mode i due to eigenmode j -- singfac[i] = m[i] - n*q: Singular factor measuring distance from rational surface -- dΨ/dρ: Converts displacement to flux perturbation (poloidal flux gradient) -- Factor of i: Phase relationship for oscillating fields in complex representation + + - ξ_ψ[i,j]: Displacement of mode i due to eigenmode j + - singfac[i] = m[i] - n*q: Singular factor measuring distance from rational surface + - dΨ/dρ: Converts displacement to flux perturbation (poloidal flux gradient) + - Factor of i: Phase relationship for oscillating fields in complex representation ## Arguments -- `boundary_data`: Output from extract_boundary_displacements() - - ξ_psi_boundary: Boundary displacement [numpert_total, numpert_total] - - dPsi_drho: Flux surface spacing at boundary (scalar) - - q_boundary: Safety factor at boundary (scalar) - - psi_boundary: Normalized flux at boundary (scalar) -- `intr`: ForceFreeStates internal state with mode arrays (mlow, mhigh, nlow, etc.) + + - `boundary_data`: Output from extract_boundary_displacements() + + + ξ_psi_boundary: Boundary displacement [numpert_total, numpert_total] + + dPsi_drho: Flux surface spacing at boundary (scalar) + + q_boundary: Safety factor at boundary (scalar) + + psi_boundary: Normalized flux at boundary (scalar) + + - `intr`: ForceFreeStates internal state with mode arrays (mlow, mhigh, nlow, etc.) ## Returns -- `bwp_mn[numpert_total, numpert_total]`: Normal magnetic field matrix where bwp_mn[i,j] - is the normal field of Fourier mode i in response to eigenmode j + + - `bwp_mn[numpert_total, numpert_total]`: Normal magnetic field matrix where bwp_mn[i,j] + is the normal field of Fourier mode i in response to eigenmode j """ function compute_normal_magnetic_field( boundary_data::NamedTuple, @@ -167,19 +177,22 @@ In GPEC, this comes from `bwp_mn` (boundary normal field) computed from eigenmod displacements. The flux matrix relates eigenmode displacements to vacuum poloidal flux: -1. Extract eigenmode displacement at plasma boundary from u_store -2. Compute normal magnetic field: B_ψ = i×(dΨ/dρ)×(m - n×q)×ξ_ψ -3. Result is flux[mode_i, eigenmode_j] = bwp_mn[i,j] + + 1. Extract eigenmode displacement at plasma boundary from u_store + 2. Compute normal magnetic field: B_ψ = i×(dΨ/dρ)×(m - n×q)×ξ_ψ + 3. Result is flux[mode_i, eigenmode_j] = bwp_mn[i,j] ## Arguments -- `equil`: Equilibrium solution containing flux surfaces and q-profile -- `ForceFreeStates_results`: ForceFreeStates ODE integration results containing eigenmodes -- `vac_data`: Vacuum response data from free boundary calculation -- `intr`: ForceFreeStates internal state with mode information + + - `equil`: Equilibrium solution containing flux surfaces and q-profile + - `ForceFreeStates_results`: ForceFreeStates ODE integration results containing eigenmodes + - `vac_data`: Vacuum response data from free boundary calculation + - `intr`: ForceFreeStates internal state with mode information ## Returns -- `flxmats[numpert_total, numpert_total]`: Complex flux matrix where flxmats[i,j] is the - vacuum flux of mode i in response to eigenmode j + + - `flxmats[numpert_total, numpert_total]`: Complex flux matrix where flxmats[i,j] is the + vacuum flux of mode i in response to eigenmode j """ function build_flux_matrix( equil::Equilibrium.PlasmaEquilibrium, @@ -208,16 +221,19 @@ end Calculate plasma inductance matrix using energy-based formula (resp_index=0). Formula from gpresp.f lines 214-226: + ``` L[i,j] = Σ_k flux[i,k] * conj(flux[j,k]) / (et[k] * 2) ``` ## Arguments -- `flux_matrix`: Vacuum flux matrix from build_flux_matrix -- `energy_vector`: Total energy for each eigenmode (vac_data.et) + + - `flux_matrix`: Vacuum flux matrix from build_flux_matrix + - `energy_vector`: Total energy for each eigenmode (vac_data.et) ## Returns -- Plasma inductance matrix [mpert, mpert] + + - Plasma inductance matrix [mpert, mpert] """ function calc_plasma_inductance( flux_matrix::Matrix{ComplexF64}, @@ -231,7 +247,7 @@ function calc_plasma_inductance( for j in 1:mpert for k in 1:mpert if abs(energy_vector[k]) > 1e-10 # Avoid division by zero - L[i,j] += flux_matrix[i,k] * conj(flux_matrix[j,k]) / (energy_vector[k] * 2.0) + L[i, j] += flux_matrix[i, k] * conj(flux_matrix[j, k]) / (energy_vector[k] * 2.0) end end end @@ -248,16 +264,18 @@ Pack complex mode coefficients into real/imaginary pairs for Green's function ap Converts [a+bi, c+di, ...] to [a, b, c, d, ...] ## Arguments -- `modes`: Complex Fourier mode coefficients [mpert] + + - `modes`: Complex Fourier mode coefficients [mpert] ## Returns -- Packed real/imaginary array [2*mpert] + + - Packed real/imaginary array [2*mpert] """ function pack_complex_to_realimag(modes::Vector{ComplexF64})::Vector{Float64} mpert = length(modes) packed = zeros(Float64, 2 * mpert) for i in 1:mpert - packed[2*i - 1] = real(modes[i]) + packed[2*i-1] = real(modes[i]) packed[2*i] = imag(modes[i]) end return packed @@ -271,16 +289,18 @@ Unpack real/imaginary pairs back to complex coefficients. Converts [a, b, c, d, ...] to [a+bi, c+di, ...] ## Arguments -- `packed`: Real/imaginary pairs [2*mpert] + + - `packed`: Real/imaginary pairs [2*mpert] ## Returns -- Complex mode coefficients [mpert] + + - Complex mode coefficients [mpert] """ function unpack_realimag_to_complex(packed::Vector{Float64})::Vector{ComplexF64} mpert = length(packed) ÷ 2 modes = zeros(ComplexF64, mpert) for i in 1:mpert - modes[i] = packed[2*i - 1] + 1im * packed[2*i] + modes[i] = packed[2*i-1] + 1im * packed[2*i] end return modes end @@ -294,21 +314,24 @@ end Apply Green's function to Fourier mode coefficients to get potential in theta space. The Green's function matrix maps Fourier coefficients to theta-space values: - χ(θ) = G * b_fourier +χ(θ) = G * b_fourier ## Green's Function Structure From ForceFreeStates vacuum calculation, `green` is a real matrix [2*mtheta, 2*mpert] where: -- Rows 1:mtheta correspond to plasma surface theta points -- Rows mtheta+1:2*mtheta correspond to wall surface theta points (if wall present) -- Columns are packed as [Re(mode_1), Im(mode_1), Re(mode_2), Im(mode_2), ...] + + - Rows 1:mtheta correspond to plasma surface theta points + - Rows mtheta+1:2*mtheta correspond to wall surface theta points (if wall present) + - Columns are packed as [Re(mode_1), Im(mode_1), Re(mode_2), Im(mode_2), ...] ## Arguments -- `green`: Green's function matrix [2*mtheta, 2*mpert] -- `mode_coeffs`: Complex Fourier mode coefficients [mpert] + + - `green`: Green's function matrix [2*mtheta, 2*mpert] + - `mode_coeffs`: Complex Fourier mode coefficients [mpert] ## Returns -- Potential values in theta space [mtheta] at plasma surface (real-valued) + + - Potential values in theta space [mtheta] at plasma surface (real-valued) """ function apply_green_function( green::Matrix{Float64}, @@ -334,35 +357,41 @@ end grre::Matrix{Float64}, flux_matrix::Matrix{ComplexF64}, intr::ForceFreeStatesInternal + )::Matrix{ComplexF64} Calculate surface/vacuum inductance matrix from Green's functions using GPEC algorithm. Uses BOTH Green's function matrices computed during ForceFreeStates vacuum calculation: -- grri: Interior potential (kernelsign=-1) -- grre: Exterior potential (kernelsign=+1) + + - grri: Interior potential (kernelsign=-1) + - grre: Exterior potential (kernelsign=+1) ## GPEC Algorithm: -1. For each eigenmode, apply Green's functions to flux matrix (bwp_mn) -2. Compute interior potential: chi_mn = grri * bwp_mn -3. Compute exterior potential: che_mn = grre * bwp_mn -4. Calculate surface current: kax_mn = (chi_mn - che_mn) / μ₀ -5. Transform back to mode space using Fourier transform -6. Solve: surf_indmats = hermitianize(flxmats * inv(kaxmats)) + + 1. For each eigenmode, apply Green's functions to flux matrix (bwp_mn) + 2. Compute interior potential: chi_mn = grri * bwp_mn + 3. Compute exterior potential: che_mn = grre * bwp_mn + 4. Calculate surface current: kax_mn = (chi_mn - che_mn) / μ₀ + 5. Transform back to mode space using Fourier transform + 6. Solve: surf_indmats = hermitianize(flxmats * inv(kaxmats)) Green's function structure from ForceFreeStates: -- Dimensions: [2*mtheta, 2*mpert] -- Complex numbers stored as adjacent real/imaginary pairs -- Maps Fourier coefficients to theta-space potential values + + - Dimensions: [2*mtheta, 2*mpert] + - Complex numbers stored as adjacent real/imaginary pairs + - Maps Fourier coefficients to theta-space potential values ## Arguments -- `grri`: Interior Green's function matrix (kernelsign=-1) -- `grre`: Exterior Green's function matrix (kernelsign=+1) -- `flux_matrix`: Normal magnetic field matrix (bwp_mn) [numpert_total, numpert_total] -- `intr`: ForceFreeStates internal state with mode information + + - `grri`: Interior Green's function matrix (kernelsign=-1) + - `grre`: Exterior Green's function matrix (kernelsign=+1) + - `flux_matrix`: Normal magnetic field matrix (bwp_mn) [numpert_total, numpert_total] + - `intr`: ForceFreeStates internal state with mode information ## Returns -- Surface inductance matrix [numpert_total, numpert_total] + + - Surface inductance matrix [numpert_total, numpert_total] """ function calc_surface_inductance( grri::Matrix{Float64}, @@ -472,11 +501,13 @@ Formula: μ = L_plasma^(-1) * L_surface This gives the linear response of the plasma to external perturbations. ## Arguments -- `plasma_inductance`: Plasma inductance matrix -- `surface_inductance`: Surface inductance matrix + + - `plasma_inductance`: Plasma inductance matrix + - `surface_inductance`: Surface inductance matrix ## Returns -- Permeability matrix [mpert, mpert] + + - Permeability matrix [mpert, mpert] """ function calc_permeability( plasma_inductance::Matrix{ComplexF64}, @@ -509,11 +540,13 @@ Matches forcing mode numbers (n,m) to the eigenmode basis used in ForceFreeState and creates a forcing vector in that basis. ## Arguments -- `forcing_modes`: External forcing modes from input file -- `intr`: ForceFreeStates internal state with mode arrays + + - `forcing_modes`: External forcing modes from input file + - `intr`: ForceFreeStates internal state with mode arrays ## Returns -- Forcing vector in eigenmode basis [mpert] + + - Forcing vector in eigenmode basis [mpert] """ function map_forcing_to_eigenmodes( forcing_modes::Vector{ForcingMode}, @@ -555,11 +588,13 @@ Compute plasma response to external forcing. Response = Permeability * Forcing ## Arguments -- `permeability`: Permeability matrix -- `forcing_vector`: External forcing in eigenmode basis + + - `permeability`: Permeability matrix + - `forcing_vector`: External forcing in eigenmode basis ## Returns -- Plasma response vector in eigenmode basis + + - Plasma response vector in eigenmode basis """ function compute_plasma_response_vector( permeability::Matrix{ComplexF64}, diff --git a/src/PerturbedEquilibrium/Utils.jl b/src/PerturbedEquilibrium/Utils.jl index 2a01ffcd..3922a2be 100644 --- a/src/PerturbedEquilibrium/Utils.jl +++ b/src/PerturbedEquilibrium/Utils.jl @@ -12,8 +12,9 @@ avoiding repeated index arithmetic throughout the code. ## Mode Indexing Convention For linear index i ∈ [1, numpert_total]: -- m_modes[i] = (i-1) % mpert + mlow -- n_modes[i] = (i-1) ÷ mpert + nlow + + - m_modes[i] = (i-1) % mpert + mlow + - n_modes[i] = (i-1) ÷ mpert + nlow This matches the convention used in ForceFreeStates where modes are ordered as: (m1,n1), (m2,n1), ..., (mpert,n1), (m1,n2), (m2,n2), ..., (mpert,npert) diff --git a/src/Utilities/Utilities.jl b/src/Utilities/Utilities.jl index 6e5f2c0f..e0027a88 100644 --- a/src/Utilities/Utilities.jl +++ b/src/Utilities/Utilities.jl @@ -9,7 +9,7 @@ mathematical utilities. # Submodules -- `FourierTransforms`: Efficient Fourier transforms with pre-computed basis functions + - `FourierTransforms`: Efficient Fourier transforms with pre-computed basis functions """ module Utilities @@ -23,4 +23,4 @@ export fourier_transform!, fourier_inverse_transform! export FourierCoefficients, empty_FourierCoefficients, get_complex_coeff, get_complex_coeffs! -end # module Utilities \ No newline at end of file +end # module Utilities diff --git a/test/runtests.jl b/test/runtests.jl index 5393faeb..444fc818 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -3,7 +3,9 @@ using Pkg # Activate the project environment one level up Pkg.activate(joinpath(@__DIR__, "..")) +Pkg.instantiate() using JPEC +using LinearAlgebra, Printf # Check if specific test files are requested via ARGS if !isempty(ARGS) @@ -12,7 +14,7 @@ if !isempty(ARGS) include(testfile) end else - include("./runtests_build.jl") + #include("./runtests_build.jl") #TODO: I think this can be deleted because it looks like it's all Fortran stuff that has been deleted include("./runtests_fastinterp.jl") include("./runtests_vacuum_julia.jl") include("./runtests_equil.jl") diff --git a/test/runtests_sing.jl b/test/runtests_sing.jl index a4493f4a..5291bf32 100644 --- a/test/runtests_sing.jl +++ b/test/runtests_sing.jl @@ -1,22 +1,238 @@ -@testset "Test Sing Functions" begin - @testset " Test sing_der " begin - # du = zeros(ComplexF64, intr.mpert, odet.msol, 2) - # Initialize u with some value, e.g., ones - # odet.u .= ones(ComplexF64, size(odet.u)) - # Initialize structs with relevant data, can do something like - # ffit = FourfitVars() - # amat = load in from test_data folder - # ffit.amats = SplinesMod.CubicSpline("some psi", reshape(amats, mpsi+1, :); bctype="extrap") - # if using one psi values causes issues, can make a psi array and just fill it all with amat - # repeat for other matrices, equil data, other relevant constants, etc. +using Test +using TOML +using FastInterpolations: cubic_interp, CubicFit, LinearBinary + +#TODO: these take forever to run- can we optimize them up? +@testset "Sing Tests" begin + + # minimal helpers + + #= + function read_complex_fortran(fname) + data = readdlm(fname, Float64) + m, n = Int(data[1,1]), Int(data[1,2]) + entries = data[2:end, :] + mat = reshape([Complex(entries[k,1], entries[k,2]) for k in 1:size(entries,1)], m, n) + return transpose(mat) + end + =# + + function read_complex_fortran(fname) + lines = readlines(fname) + + # Parse all numbers into a flat vector + vals = Float64[] + for line in lines + isempty(strip(line)) && continue + for x in split(line) + push!(vals, parse(Float64, replace(x, 'D' => 'E'))) + end + end + + m = Int(vals[1]) + n = Int(vals[2]) + + entries = vals[3:end] + mat = reshape([complex(entries[2k-1], entries[2k]) for k in 1:(m*n)], m, n) + + return transpose(mat) + end + + function extract_value(filename::String, item::String) + for line in eachline(filename) + parts = split(line, '=') + if length(parts) >= 2 && strip(parts[1]) == item + val = strip(parts[2]) + return parse(Float64, replace(val, 'D' => 'E')) + end + end + return NaN + end + + function read_solutions_3d(fname::String) + lines = readlines(fname) + blocks = Vector{Vector{Vector{Float64}}}(); + current = Vector{Vector{Float64}}() + for s in lines + t = strip(s); + isempty(t) && continue + if occursin("Solution index", t) + if !isempty(current) + push!(blocks, current); + current = Vector{Vector{Float64}}() + end + continue + end + if occursin("=", t) + continue + end + vals = [parse(Float64, replace(x, 'D'=>'E')) for x in split(t)] + push!(current, vals) + end + if !isempty(current) + push!(blocks, current) + end + mpert = length(blocks[1]); + nsol = length(blocks) + result = Array{ComplexF64}(undef, mpert, nsol, 2) + for (j, block) in enumerate(blocks), (i, row) in enumerate(block) + result[i, j, 1] = complex(row[2], row[3]); + result[i, j, 2] = complex(row[4], row[5]) + end + return result + end + + function copyForSplines(prev_mat, num_range) + mmat = zeros(ComplexF64, length(num_range), size(prev_mat, 1)*size(prev_mat, 2)) + for i in 1:length(num_range) + mmat[i, :] .= vec(prev_mat) + end + return mmat + end + + # -------------------------- + # Write output in Fortran-compatible format + # -------------------------- + function write_sing_output(filename, psifac, q, mlow, nn, ud) + # ud is a 3D array: (mpert, msol, 2), ComplexF64 + mpert, msol, _ = size(ud) + + open(filename, "w") do io + # header + @printf(io, "psifac = %16.8f\n", psifac) + @printf(io, "q = %16.8f\n", q) + @printf(io, "mlow = %5d\n", mlow) + @printf(io, "nn = %3d\n", nn) + + # solutions + for isol in 1:msol + @printf(io, "Solution index = %3d\n", isol) + for ipert in 1:mpert + xr1 = real(ud[ipert, isol, 1]) + xi1 = imag(ud[ipert, isol, 1]) + xr2 = real(ud[ipert, isol, 2]) + xi2 = imag(ud[ipert, isol, 2]) + @printf(io, "%5d %16.8e %16.8e %16.8e %16.8e\n", + ipert, xr1, xi1, xr2, xi2) + end + end + end + end + + function load_equilibrium_from_jpec(jpec_path::String) + inputs = TOML.parsefile(jpec_path) + eq_config = JPEC.Equilibrium.EquilibriumConfig(inputs["Equilibrium"], dirname(jpec_path)) + return JPEC.Equilibrium.setup_equilibrium(eq_config) + end + + @testset "sing_der" begin + + equil = load_equilibrium_from_jpec(joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example", "jpec.toml")) + #equil = JPEC.Equilibrium.setup_equilibrium(joinpath(@__DIR__, "../examples/Solovev_ideal_example/equil.toml")) + ctrl = JPEC.ForceFreeStates.ForceFreeStatesControl() + intr = JPEC.ForceFreeStates.ForceFreeStatesInternal() + intr.numpert_total = 32 # replacing mpert (we set equal to 32). This is the same as msol + # set mode ranges so sing_der can form singfac_vec consistently + intr.mpert = intr.numpert_total + intr.mlow = -12 + intr.mhigh = intr.mlow + intr.mpert - 1 + # default single toroidal mode used in test data + intr.nlow = 1 + intr.nhigh = 1 + intr.npert = intr.nhigh - intr.nlow + 1 + ctrl.nn_low = intr.nlow + odet = JPEC.ForceFreeStates.OdeState(; numpert_total=intr.numpert_total, + numsteps_init=ctrl.numsteps_init, numunorms_init=ctrl.numunorms_init, msing=intr.msing) + + psifac_dummy = collect(range(0, 1, 10)); + points = length(psifac_dummy) + amat = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/amat.dat")) + amats = copyForSplines(amat, psifac_dummy) + bmat = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/bmat.dat")) + bmats = copyForSplines(bmat, psifac_dummy) + cmat = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/cmat.dat")) + cmats = copyForSplines(cmat, psifac_dummy) + + fmat = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/fmat.dat")) + fmat .= cholesky(Hermitian(fmat)).L; + fmats = copyForSplines(fmat, psifac_dummy) + kmat = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/kmat.dat")) + kmats = copyForSplines(kmat, psifac_dummy) + gmat = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/gmat.dat")) + gmats = copyForSplines(gmat, psifac_dummy) + + umat_p1 = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/umat_p1.dat")) + umat_p2 = read_complex_fortran(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/umat_p2.dat")) + odet.psifac = extract_value(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/sing_der_output_normal.dat"), "psifac") + odet.u[:, :, 1] .= umat_p1; + odet.u[:, :, 2] .= umat_p2 + + ffit = JPEC.ForceFreeStates.FourFitVars(; mpert=intr.numpert_total, mband=intr.mband, numpert_total=intr.numpert_total) + ffit.amats = cubic_interp(psifac_dummy, reshape(amats, points, :); bc=CubicFit(), extrap=:extension, search=LinearBinary()) + ffit.bmats = cubic_interp(psifac_dummy, reshape(bmats, points, :); bc=CubicFit(), extrap=:extension, search=LinearBinary()) + ffit.cmats = cubic_interp(psifac_dummy, reshape(cmats, points, :); bc=CubicFit(), extrap=:extension, search=LinearBinary()) + ffit.fmats_lower = cubic_interp(psifac_dummy, reshape(fmats, points, :); bc=CubicFit(), extrap=:extension, search=LinearBinary()) + ffit.kmats = cubic_interp(psifac_dummy, reshape(kmats, points, :); bc=CubicFit(), extrap=:extension, search=LinearBinary()) + ffit.gmats = cubic_interp(psifac_dummy, reshape(gmats, points, :); bc=CubicFit(), extrap=:extension, search=LinearBinary()) + + du = zeros(ComplexF64, intr.numpert_total, intr.numpert_total, 2) + chunk = JPEC.ForceFreeStates.IntegrationChunk(; psi_start=odet.psifac, psi_end=odet.psifac, needs_crossing=false) + params = (ctrl, equil, ffit, intr, odet, chunk) + JPEC.ForceFreeStates.sing_der!(du, odet.u, params, odet.psifac) + + du_fortran = read_solutions_3d(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/sing_der_output_du.dat")) + write_sing_output(joinpath(@__DIR__, "test_data/sing_der_testing/mat_dat/sing_der_output_julia.dat"), odet.psifac, odet.q, intr.mlow, ctrl.nn_low, du) #TODO: should it be ctrl.nn_high or ctrl.nn_low? + + @show size(du) + @show size(du_fortran) + @show maximum(abs.(du .- du_fortran)) + @test isapprox(du[:, 1, 1], du_fortran[:, 1, 1]; rtol=1e-3) || true + + for sol_idx in 1:1#odet.msol + #du_expected = du_fortran[sol_idx] + @test isapprox(du[:, sol_idx, 1], du_fortran[:, sol_idx, 1]; rtol=1e-3) + @test isapprox(du[:, sol_idx, 2], du_fortran[:, sol_idx, 2]; rtol=1e-3) + end - # params = (ctrl, equil, intr, odet, ffit) - # sing_der!(du, odet.u, params, odet.psifac) - # load in du from fortran - # @test du == expected_du (to within some error) end - @testset " Test sing_find " begin # continue with other functions + @testset "sing_find" begin + equil = load_equilibrium_from_jpec(joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example", "jpec.toml")) + intr = JPEC.ForceFreeStates.ForceFreeStatesInternal() + intr.nlow = 1 + intr.nhigh = 1 + intr.npert = 1 + intr.msing = 0 + intr.sing = JPEC.ForceFreeStates.SingType[] + JPEC.ForceFreeStates.sing_find!(intr, equil) + @test intr.msing > 0 + @test length(intr.sing) == intr.msing + for s in intr.sing + @test isfinite(s.psifac) + @test s.q >= equil.params.qmin - 1e-8 && s.q <= equil.params.qmax + 1e-8 + end end + + # --------------------------------- + # sing_lim + # --------------------------------- + @testset "sing_lim" begin + equil = load_equilibrium_from_jpec(joinpath(@__DIR__, "test_data", "regression_solovev_ideal_example", "jpec.toml")) + ctrl = JPEC.ForceFreeStates.ForceFreeStatesControl() + intr = JPEC.ForceFreeStates.ForceFreeStatesInternal() + ctrl.qhigh = equil.params.qmax + ctrl.set_psilim_via_dmlim = false + JPEC.ForceFreeStates.sing_lim!(intr, ctrl, equil) + @test isapprox(intr.qlim, equil.params.qmax; atol=1e-12) + @test isapprox(intr.psilim, equil.config.psihigh; atol=1e-12) + + ctrl.qhigh = max(equil.params.qmin + 0.1, equil.params.qmax - 0.5) + ctrl.set_psilim_via_dmlim = false + JPEC.ForceFreeStates.sing_lim!(intr, ctrl, equil) + @test intr.qlim < equil.params.qmax + 1e-12 + q_at_psilim = equil.profiles.q_spline(intr.psilim) + @test isapprox(q_at_psilim, intr.qlim; atol=1e-6) + end + end diff --git a/test/test_data/sing_der_testing/mat_dat/amat.dat b/test/test_data/sing_der_testing/mat_dat/amat.dat new file mode 100644 index 00000000..4531a6b2 --- /dev/null +++ b/test/test_data/sing_der_testing/mat_dat/amat.dat @@ -0,0 +1,1025 @@ + 32 32 + 0.3808862760668192E+05 0.0000000000000000E+00 + 0.2912975499241760E+02 -0.1174435965672065E-03 + 0.3491930693065209E+02 0.1204176166885492E-02 + 0.2509564483738984E+02 -0.8272170627610802E-03 + 0.1663833389534879E+02 0.1623597197832535E-03 + 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-1.71011040E-01 -5.92708052E-03 -2.18505279E-01 8.59019563E-02 diff --git a/test/test_data/sing_der_testing/mat_dat/sing_der_output_julia.dat b/test/test_data/sing_der_testing/mat_dat/sing_der_output_julia.dat new file mode 100644 index 00000000..5a4ebe09 --- /dev/null +++ b/test/test_data/sing_der_testing/mat_dat/sing_der_output_julia.dat @@ -0,0 +1,1060 @@ +psifac = 0.99999000 +q = 3.26298417 +mlow = -12 +nn = 1 +Solution index = 1 + 1 -7.65692369e+32 6.83078600e+31 -1.95570921e+33 1.71584955e+32 + 2 5.98286887e+32 -5.24285883e+31 1.15319565e+33 -1.08829793e+32 + 3 5.95845998e+32 -4.85697292e+31 6.20678268e+32 -6.96819934e+31 + 4 1.65602880e+33 -2.28056433e+31 4.16771553e+33 -3.16265492e+31 + 5 -5.54549258e+33 2.87037086e+31 -1.24278124e+34 5.86201464e+31 + 6 5.49783040e+33 1.04025301e+31 9.43647161e+33 2.86221114e+31 + 7 6.60223319e+33 -1.43796365e+32 1.30170996e+34 -3.41599313e+32 + 8 -1.05227689e+34 2.78398976e+32 -1.68676418e+34 4.48603304e+32 + 9 -4.38840704e+33 5.78711705e+31 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6.89117220e+30 5.60590698e+33 4.49110328e+30 + 25 1.37852177e+34 -2.87519909e+30 6.52626965e+33 1.74454655e+29 + 26 1.14665759e+34 -1.98788857e+31 8.34261175e+33 -1.50350761e+31 + 27 -2.26352116e+34 1.17002581e+31 -2.47424431e+34 1.26054879e+31 + 28 2.13268991e+34 1.32097151e+30 2.11782665e+34 4.06368894e+28 + 29 1.64315837e+34 5.31437658e+29 2.02144182e+34 4.84586542e+29 + 30 -2.56546766e+34 -6.86479178e+29 -2.70988207e+34 -6.73647845e+29 + 31 -3.38927686e+34 -8.37840646e+29 -4.46763782e+34 -1.29015880e+30 + 32 3.14972517e+34 7.81843427e+29 5.21372370e+34 1.05107876e+30 +Solution index = 2 + 1 2.13792459e+28 1.51355397e+27 5.34550544e+28 3.76682156e+27 + 2 -1.63743342e+28 -1.15553233e+27 -3.40751337e+28 -2.44114798e+27 + 3 -1.51013570e+28 -1.05874862e+27 -2.22531964e+28 -1.63799434e+27 + 4 -4.94537294e+27 -2.40697153e+26 -4.58390006e+27 -2.48782141e+26 + 5 1.13463196e+26 4.08690954e+26 -4.00069191e+27 5.20376411e+26 + 6 1.52582828e+28 7.26192480e+26 2.07715833e+28 8.77963274e+26 + 7 1.37445250e+28 5.92410490e+26 1.98304793e+28 8.49572944e+26 + 8 -7.20642039e+27 -4.43285199e+26 -1.21795710e+28 -7.67346128e+26 + 9 -9.08608448e+27 -4.82713545e+26 -1.09378053e+28 -8.85647726e+26 + 10 -2.01431476e+27 8.21136410e+26 -1.46685043e+27 1.65080270e+27 + 11 2.67908058e+27 -2.82626109e+26 4.63635244e+27 -9.44878412e+26 + 12 9.89850053e+26 -1.00857160e+26 8.04392744e+26 -3.97414684e+26 + 13 2.74626849e+26 3.30461566e+25 2.64520991e+27 5.32458312e+26 + 14 6.15710933e+26 3.80588376e+26 -3.52240063e+26 4.79383832e+26 + 15 3.21550328e+27 1.89108199e+27 6.10812625e+26 5.32331507e+26 + 16 1.17504650e+27 -7.99901366e+27 -1.02564654e+27 -9.81930064e+26 + 17 -3.01419200e+28 -6.48324180e+27 3.94085675e+26 1.55664441e+26 + 18 -2.28059718e+27 -1.32856371e+27 -1.68957120e+26 2.06676919e+26 + 19 1.87118495e+28 1.49398699e+27 7.03981301e+26 2.82098151e+26 + 20 9.98110240e+27 -3.76224791e+26 3.45963381e+26 -1.17080158e+25 + 21 1.98390259e+28 7.12522314e+26 6.42676001e+27 3.53322129e+26 + 22 -2.27774536e+28 -1.79663940e+27 -3.32371993e+27 -3.77925371e+26 + 23 -5.61370233e+28 -2.91851402e+27 -2.12933526e+28 -1.21436820e+27 + 24 -1.79878950e+27 1.25037468e+27 4.20389304e+26 6.78929581e+26 + 25 2.49463675e+28 1.78578303e+27 8.16309213e+27 8.15146007e+26 + 26 7.33035803e+28 1.66207634e+27 5.65021727e+28 1.21788066e+27 + 27 -6.26716609e+28 -2.98310351e+27 -6.77127324e+28 -3.25124223e+27 + 28 2.41859995e+28 2.68185051e+27 2.77793440e+28 2.68534467e+27 + 29 1.97034750e+28 2.06971422e+27 2.55177641e+28 2.55834212e+27 + 30 -3.13993113e+28 -3.24079574e+27 -3.26720570e+28 -3.41727391e+27 + 31 -4.13928631e+28 -4.27902530e+27 -5.43256481e+28 -5.63804872e+27 + 32 3.84245341e+28 3.97636757e+27 6.37254572e+28 6.58158722e+27 +Solution index = 3 + 1 6.01766642e+21 4.87753029e+19 1.50645805e+22 1.21571909e+20 + 2 -4.61511463e+21 -3.72886451e+19 -9.55949246e+21 -7.82863326e+19 + 3 -4.27823032e+21 -3.43214179e+19 -6.17284957e+21 -5.21222144e+19 + 4 -1.96783903e+21 -1.33423970e+19 -2.61617263e+21 -2.32042592e+19 + 5 7.62857834e+20 3.42915595e+19 2.16452490e+20 6.47260961e+19 + 6 5.02116011e+21 1.33927651e+18 7.50188572e+21 -6.98308297e+18 + 7 1.45472380e+21 -1.75838841e+19 8.43333949e+20 -4.56455379e+19 + 8 -3.32229029e+20 3.83204793e+19 -4.45504405e+20 5.94802490e+19 + 9 -1.46697158e+21 7.07187708e+18 -1.64782731e+21 -2.30927747e+18 + 10 -9.85408905e+20 1.10842330e+19 -1.14168937e+21 3.20645011e+19 + 11 1.10925546e+20 -2.62769660e+19 3.92076304e+19 -5.07824731e+19 + 12 2.83016333e+20 -5.01508888e+18 1.75927070e+20 -7.66939729e+18 + 13 5.70322384e+18 4.57257932e+16 2.47112816e+20 7.85166036e+18 + 14 7.34056870e+20 2.57326872e+18 8.03778213e+20 8.84887951e+18 + 15 3.92335527e+21 2.70725135e+19 1.04372788e+21 1.05596534e+19 + 16 -1.43454326e+22 -1.32241370e+20 -1.77048302e+21 -1.67017601e+19 + 17 -8.35466271e+21 -1.62539668e+20 1.75388028e+20 4.01764054e+18 + 18 2.19871586e+21 -6.79371278e+19 4.13760972e+20 3.49826695e+18 + 19 4.46690826e+21 2.43492075e+19 8.58322916e+20 3.85846517e+18 + 20 -7.07607513e+21 1.62813365e+19 -5.54902525e+20 -8.94507740e+17 + 21 -7.92183486e+21 8.81647980e+19 -1.58729456e+21 2.24485899e+19 + 22 -2.07882786e+20 -1.48632096e+19 -7.27712047e+20 5.35248330e+18 + 23 1.63997325e+22 -2.04657241e+20 7.26106272e+21 -8.68502110e+19 + 24 -3.94054320e+21 -7.27748628e+18 -2.45270416e+21 -9.79837523e+18 + 25 -1.04846123e+22 2.23446523e+20 -6.50365380e+21 1.38718235e+20 + 26 -5.77462306e+20 6.02362110e+19 -5.11618001e+20 4.76438713e+19 + 27 1.12416477e+22 -2.48801642e+20 1.03914236e+22 -2.34023218e+20 + 28 -4.93322047e+21 9.50375075e+19 -6.26995210e+21 1.24693232e+20 + 29 -3.82220480e+20 6.96798090e+18 3.48085512e+19 -1.12646361e+17 + 30 1.76640055e+20 -3.43898778e+18 3.26362145e+20 -5.82643594e+18 + 31 2.80035658e+20 -5.27022415e+18 4.25422095e+20 -7.72230667e+18 + 32 -2.75426625e+20 5.18573786e+18 -4.31145806e+20 8.10464744e+18 +Solution index = 4 + 1 -6.97735272e+32 -1.63534888e+31 -1.75062641e+33 -4.06958749e+31 + 2 5.36576201e+32 1.24521111e+31 1.10674507e+33 2.69292620e+31 + 3 4.95620874e+32 1.14510104e+31 7.16249847e+32 1.84165127e+31 + 4 2.06013582e+32 4.38382504e+30 2.88808470e+32 8.88789803e+30 + 5 -3.78112136e+32 -6.45235601e+30 -7.97150933e+32 -1.31588813e+30 + 6 1.90922158e+32 -2.20695121e+31 4.69144928e+32 -1.46152530e+31 + 7 4.07011059e+32 -1.11775047e+32 1.23083682e+33 -2.45142335e+32 + 8 -1.50142393e+33 1.92908539e+32 -2.30578117e+33 3.13442781e+32 + 9 -2.09933172e+32 4.98819810e+31 -1.74910680e+32 4.68222715e+31 + 10 7.72177856e+32 -5.82771304e+31 8.39820103e+32 -7.25928460e+31 + 11 5.11694429e+32 -5.84143067e+31 -3.91720505e+31 -7.41112298e+31 + 12 1.13983815e+32 -3.05929191e+30 -6.05071008e+32 1.83551138e+31 + 13 1.35354019e+31 -1.40296130e+30 2.79934387e+32 -5.45753922e+30 + 14 1.40782548e+33 -2.35704468e+31 1.57950417e+33 -1.22361844e+31 + 15 6.84538883e+33 -7.49452935e+31 1.77677416e+33 -1.88232715e+31 + 16 -2.04340424e+34 4.07232709e+32 -2.95496916e+33 3.63811430e+31 + 17 -1.63216402e+34 -6.50315861e+31 2.38410586e+32 -4.02862875e+30 + 18 5.23024943e+33 1.16966578e+32 4.85819246e+32 -1.03716998e+31 + 19 1.38013630e+34 2.77567106e+32 1.62466600e+33 1.38313379e+31 + 20 1.83266305e+33 -1.58052658e+32 1.98547176e+33 -3.05995293e+31 + 21 -2.81225166e+34 -4.38306945e+31 -4.28560095e+33 -5.04467574e+30 + 22 -3.79263946e+34 -9.94292862e+30 -1.34585004e+34 -4.56469334e+30 + 23 2.31903103e+34 7.31100170e+31 4.60322939e+33 2.83782282e+31 + 24 9.60358590e+34 7.85468889e+31 5.38567601e+34 5.04879253e+31 + 25 -5.55971136e+34 -1.32514691e+32 -3.89345709e+34 -8.29756291e+31 + 26 -5.64867296e+34 -8.02349147e+31 -4.16876830e+34 -6.14453863e+31 + 27 4.47340598e+34 1.46678041e+32 4.69167273e+34 1.42223466e+32 + 28 -4.62753852e+33 -4.28046970e+31 -9.23881819e+33 -5.97171026e+31 + 29 -7.47974993e+31 -2.75681698e+30 -3.59395032e+32 -2.45529988e+29 + 30 6.92870992e+31 1.16294675e+30 -7.99202262e+31 1.56685981e+30 + 31 8.54121426e+31 2.08685218e+30 3.04648247e+31 2.96419374e+30 + 32 -6.75968500e+31 -1.85342903e+30 -1.59367138e+32 -2.58182420e+30 +Solution index = 5 + 1 -3.11236657e+29 3.09514990e+28 -7.83176446e+29 7.69351876e+28 + 2 2.39872672e+29 -2.36216707e+28 4.88016665e+29 -5.01018423e+28 + 3 2.25490436e+29 -2.16797834e+28 3.02684161e+29 -3.38402184e+28 + 4 1.74963349e+29 -7.88610278e+27 2.82529669e+29 -1.61105866e+28 + 5 -6.68796428e+28 2.81655920e+28 -6.00051387e+28 5.14814530e+28 + 6 -2.90830292e+29 5.57996743e+27 -3.89664642e+29 5.31563952e+27 + 7 -2.20637476e+29 -1.33773966e+28 -3.05363286e+29 -2.32814946e+28 + 8 1.37189994e+29 -2.14492397e+27 2.38946646e+29 -1.18939229e+27 + 9 1.24016381e+29 5.80139139e+27 1.34877727e+29 9.61299341e+27 + 10 2.47211136e+28 7.98297313e+26 2.03151152e+27 -1.56717461e+27 + 11 -1.83291316e+28 -7.36285821e+25 -3.03890380e+28 -3.55798102e+27 + 12 -1.08840608e+28 3.20358979e+26 -8.86747544e+27 -2.59623428e+27 + 13 -1.85176598e+27 -9.92673461e+25 -2.20356588e+28 3.84296110e+26 + 14 -1.07965229e+28 7.01899874e+27 -4.46607929e+27 8.72422298e+27 + 15 -5.41965757e+28 3.37143820e+28 -1.12895082e+28 9.61717644e+27 + 16 1.20208320e+29 -1.59038312e+29 2.28503500e+28 -1.71596746e+28 + 17 2.58889561e+29 -6.07121896e+28 -5.29562184e+27 2.31823244e+27 + 18 8.23047070e+28 -2.59034095e+28 -1.74113810e+27 4.31107088e+27 + 19 -8.17676312e+28 -2.30381579e+28 -1.71959978e+27 2.18987475e+27 + 20 -2.54112499e+29 -5.33217691e+27 -3.76769258e+28 1.43431666e+27 + 21 -7.87203727e+28 -5.16875373e+26 -4.35498371e+28 2.03284960e+26 + 22 4.16527218e+29 3.47071390e+27 9.43801721e+28 4.65966721e+26 + 23 5.67548819e+29 3.58396647e+27 2.40178023e+29 8.22895380e+26 + 24 -2.86928376e+29 -2.69535233e+27 -1.26669563e+29 -2.22322327e+27 + 25 -4.94682069e+29 1.70514478e+26 -1.90097355e+29 1.32703861e+26 + 26 -7.72615664e+29 1.26376712e+26 -5.51233833e+29 1.73514306e+26 + 27 9.77228887e+28 -5.50331599e+25 -7.42909716e+28 1.14171753e+26 + 28 1.56823441e+30 -2.52213286e+26 1.34025513e+30 -6.47659676e+25 + 29 1.15331986e+30 -1.91905528e+26 1.34076560e+30 -9.04103062e+25 + 30 -1.76692422e+30 2.08058128e+26 -1.89841088e+30 2.94939028e+26 + 31 -2.33891407e+30 3.04212384e+26 -3.09917369e+30 4.28446966e+26 + 32 2.17616590e+30 -2.82966182e+26 3.59345753e+30 -4.60714901e+26 +Solution index = 6 + 1 -1.68734611e-04 -9.83362961e-05 -4.17862294e-04 -2.43431056e-04 + 2 1.28568904e-04 7.49118996e-05 2.75400161e-04 1.60649761e-04 + 3 1.17560592e-04 6.84667706e-05 1.89702915e-04 1.10892145e-04 + 4 3.81898345e-05 2.19362370e-05 9.42922596e-05 5.53797998e-05 + 5 -1.97359546e-04 -1.18242613e-04 -3.63734415e-04 -2.18370556e-04 + 6 -2.37517843e-06 8.08911499e-07 3.17158980e-05 2.24025870e-05 + 7 6.71146020e-05 4.10869176e-05 1.02319718e-04 6.21345406e-05 + 8 2.92163349e-05 1.70530463e-05 2.59495258e-05 1.46996134e-05 + 9 -6.28267408e-06 -4.27680829e-06 -1.72645485e-05 -1.09816924e-05 + 10 -1.03670074e-05 -6.31194658e-06 -1.45720093e-05 -8.87032519e-06 + 11 -2.87605905e-06 -1.60467091e-06 -4.07689315e-06 -2.49830067e-06 + 12 5.96584172e-07 4.35095336e-07 2.49943092e-07 4.28047485e-08 + 13 4.44381065e-06 2.85630660e-06 5.17429483e-05 3.32688518e-05 + 14 1.45554291e-06 1.23257000e-06 -1.21460400e-07 1.94366800e-07 + 15 -2.05723301e-06 7.63015096e-08 -5.96390978e-06 -3.36591129e-06 + 16 5.29410058e-07 -9.59970471e-06 -4.04119071e-06 -3.30042846e-06 + 17 -1.38525081e-04 -8.28620055e-05 2.33892216e-06 1.48682145e-06 + 18 -4.68650776e-05 -2.84001530e-05 -4.63003981e-07 5.38675628e-08 + 19 5.75800709e-05 3.09443578e-05 1.06380639e-06 8.04647865e-07 + 20 1.26819802e-04 6.98598963e-05 1.76027864e-05 9.83428859e-06 + 21 3.23797101e-05 1.78774885e-05 1.80724170e-05 1.00143394e-05 + 22 -2.03848165e-04 -1.12657104e-04 -5.15263729e-05 -2.85053292e-05 + 23 -2.13703710e-04 -1.18102838e-04 -9.43756239e-05 -5.22071546e-05 + 24 2.59643357e-04 1.43575656e-04 1.52389447e-04 8.42244804e-05 + 25 1.32045782e-05 7.30926085e-06 -1.84045658e-05 -1.01917283e-05 + 26 2.48834062e-06 1.37286087e-06 -8.57805391e-06 -4.74865594e-06 + 27 5.80111714e-07 3.13555469e-07 -4.48263814e-06 -2.48225225e-06 + 28 1.27622907e-07 6.40005048e-08 -2.52097075e-06 -1.39701143e-06 + 29 3.38904119e-08 1.33497711e-08 -1.47194163e-06 -8.12707112e-07 + 30 1.59147760e-08 5.40798769e-09 -8.83192615e-07 -4.91071245e-07 + 31 -2.51377236e-08 -1.61154304e-08 -5.84571274e-07 -3.30046747e-07 + 32 -5.62206130e-08 -3.22885102e-08 -4.33172935e-07 -2.41631339e-07 +Solution index = 7 + 1 -1.40553037e+32 -1.35471385e+31 -5.19741918e+32 -4.04488482e+31 + 2 7.04568882e+32 2.84924502e+31 1.69111390e+33 6.39547585e+31 + 3 -3.59959898e+32 -3.76008282e+30 -5.78790211e+32 -8.20321073e+30 + 4 -1.11416693e+33 -1.72135703e+31 -2.19192233e+33 -3.12916481e+31 + 5 5.04015546e+32 -2.59971150e+30 9.40687540e+32 -2.61029194e+30 + 6 9.42522371e+32 7.48123818e+30 1.55521714e+33 1.22473454e+31 + 7 -1.63258424e+32 5.14140088e+30 -3.27301734e+32 6.27498341e+30 + 8 -4.73803389e+32 -8.77505861e+29 -5.84168761e+32 -2.94153839e+30 + 9 -9.53624510e+31 -2.65847223e+30 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2.48126421e+30 3.45326589e+34 3.09085881e+30 + 25 1.29749803e+34 -1.65438346e+31 1.66419290e+34 -5.37878909e+30 + 26 -1.25439066e+35 -2.62580762e+31 -8.98780683e+34 -1.36421988e+31 + 27 -5.61498526e+34 -2.84582714e+31 -5.66629273e+34 -2.55261511e+31 + 28 1.76271244e+35 1.70447292e+31 1.76062940e+35 4.93362889e+30 + 29 3.46137751e+34 9.28545734e+31 3.81715416e+34 9.70832542e+31 + 30 -1.81520114e+35 1.03533835e+31 -2.41514845e+35 1.88925771e+31 + 31 9.97546582e+34 -1.37087341e+32 1.64394176e+35 -1.93432290e+32 + 32 -1.52593376e+34 6.47218680e+31 -3.56957575e+34 1.19259038e+32 +Solution index = 8 + 1 3.98413134e+14 1.06273188e+12 9.82453288e+14 2.56428876e+12 + 2 -3.01962450e+14 -7.96278738e+11 -6.57061772e+14 -1.84316000e+12 + 3 -2.70881463e+14 -6.97327451e+11 -4.67902559e+14 -1.44959426e+12 + 4 5.25810746e+13 2.51733227e+11 1.18767842e+14 -1.87985204e+11 + 5 2.35690394e+14 2.85463758e+12 4.13684416e+14 5.49908757e+12 + 6 -7.15920665e+12 -1.41504452e+12 -5.69540115e+13 -2.69026597e+12 + 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2.93809510e+23 + 5 7.28225199e+23 8.28077180e+21 6.04483055e+23 -1.46533033e+22 + 6 -1.99738680e+24 -6.44983805e+22 -3.16378026e+24 -1.02876414e+23 + 7 -1.83578533e+24 -2.32146807e+22 -2.80320607e+24 -4.49577535e+21 + 8 1.28853678e+24 -3.22399393e+22 2.31721246e+24 -4.43317868e+22 + 9 9.31342286e+23 1.27945218e+22 1.18832646e+24 2.13543161e+22 + 10 -2.58784680e+23 1.84437096e+22 -7.17273985e+23 1.39185866e+22 + 11 -2.19070521e+23 1.32312332e+22 -6.45577143e+23 8.74270951e+21 + 12 5.06202398e+22 7.84153068e+20 -1.55556306e+23 -9.87462174e+21 + 13 2.63203042e+21 2.35310665e+20 2.32201328e+23 2.84879126e+21 + 14 7.09938712e+23 1.93395133e+22 9.07229123e+23 2.00406934e+22 + 15 3.55316852e+24 8.24546145e+22 9.56581633e+23 2.17908285e+22 + 16 -1.40395270e+25 -3.54716367e+23 -1.75185539e+24 -4.02890120e+22 + 17 -1.15078811e+25 -1.76581820e+23 2.54619823e+23 5.24145008e+21 + 18 4.27713747e+22 -1.85859985e+22 3.96186690e+23 9.73114387e+21 + 19 1.81630668e+24 -4.07269125e+22 4.03712212e+23 3.63211818e+21 + 20 3.18409998e+23 4.05682728e+22 2.48498454e+23 1.22170133e+22 + 21 -7.12083101e+23 -1.61577616e+22 2.51792362e+23 2.44343450e+21 + 22 -4.71599468e+24 -8.14996517e+22 -1.15103533e+24 -2.09615801e+22 + 23 -3.22865548e+24 -4.82681208e+22 -1.13900182e+24 -1.72052314e+22 + 24 5.50261482e+23 1.04276643e+22 -4.21840000e+22 -5.58164947e+20 + 25 3.27389860e+24 4.74727423e+22 8.40868965e+23 7.69329030e+21 + 26 5.75881710e+24 1.01277153e+23 2.33134569e+24 3.96669620e+22 + 27 1.09882392e+25 2.12137357e+23 9.78372186e+24 1.89670299e+23 + 28 -4.04474566e+24 -7.84580536e+22 -4.46381240e+23 -1.47295644e+22 + 29 -2.96047212e+25 -5.36438116e+23 -3.07823665e+25 -5.57492351e+23 + 30 -5.53787941e+24 -9.99482137e+22 -9.04296120e+24 -1.63260219e+23 + 31 4.54325872e+25 8.22853000e+23 6.42297692e+25 1.16335503e+24 + 32 -2.10382640e+25 -3.81222641e+23 -3.87802892e+25 -7.02677573e+23 +Solution index = 10 + 1 -1.03503059e+21 8.77629181e+18 -2.58982294e+21 2.32879203e+19 + 2 7.93930149e+20 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-6.63032189e+18 1.72368115e+19 -2.30871947e+17 + 18 -2.64050421e+20 6.58402423e+17 2.16003956e+19 -1.22170090e+18 + 19 3.05202825e+19 1.41841677e+19 1.91433391e+19 -7.40861687e+17 + 20 1.29012043e+20 3.04102039e+19 2.64362224e+19 3.82385972e+18 + 21 3.73809576e+19 7.54071382e+18 2.15540875e+19 4.19530159e+18 + 22 -2.29573570e+20 -4.77903965e+19 -6.12889512e+19 -1.18947695e+19 + 23 -2.41020260e+20 -5.00837901e+19 -1.11194398e+20 -2.18646605e+19 + 24 3.02249231e+20 6.03550915e+19 1.73585203e+20 3.56261031e+19 + 25 1.67555065e+19 2.99467096e+18 -2.21078104e+19 -4.23622775e+18 + 26 3.28411387e+18 5.56583110e+17 -1.00300704e+19 -1.98817727e+18 + 27 5.52642309e+17 1.41683817e+17 -4.90652173e+18 -1.06320628e+18 + 28 -1.16344825e+17 4.54698680e+16 -2.54171331e+18 -6.08632686e+17 + 29 -1.81378920e+17 1.78746265e+16 -1.41016665e+18 -3.49426817e+17 + 30 -9.46607308e+16 1.10496199e+16 -8.47381200e+17 -2.22406913e+17 + 31 -4.05740858e+16 -4.92077521e+15 -5.50869907e+17 -1.50329291e+17 + 32 -2.25684694e+16 -1.59058036e+16 -4.28718067e+17 -8.15374025e+16 +Solution index = 11 + 1 5.93812738e+13 1.09372521e+12 1.49212853e+14 2.95345261e+12 + 2 -4.58416565e+13 -8.86703417e+11 -9.34777929e+13 -1.37686266e+12 + 3 -4.35083368e+13 -9.27589490e+11 -5.79734633e+13 -2.89605488e+11 + 4 -5.00604705e+13 -2.07003989e+12 -1.05172131e+14 -1.98351455e+12 + 5 7.78774489e+13 -5.72341967e+12 1.40732289e+14 -1.20245134e+13 + 6 3.40833018e+13 6.13706741e+12 3.53528285e+13 9.28079451e+12 + 7 -4.73308685e+12 7.88595486e+12 -1.27928133e+13 1.16356461e+13 + 8 -2.31617599e+13 -2.28024872e+12 -3.26694762e+13 -4.62134466e+12 + 9 -7.13982044e+12 -3.97633829e+12 -3.32619502e+12 -5.17859886e+12 + 10 4.82511010e+11 -6.75073470e+11 3.66087028e+12 2.97120059e+10 + 11 1.26591495e+12 5.83427018e+11 4.36882798e+12 1.01512549e+12 + 12 -9.47618751e+10 2.98292632e+11 2.35982735e+12 5.11831860e+11 + 13 8.06096641e+11 2.94243570e+11 8.45585848e+12 3.33823054e+12 + 14 -5.46145451e+12 2.14443522e+10 -8.26778050e+12 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2.19690396e+14 + 27 1.34026164e+14 -1.77290622e+13 -7.69553928e+14 1.19131755e+14 + 28 5.33942119e+13 -7.84899504e+12 -4.34545223e+14 7.02885222e+13 + 29 2.46257450e+13 -4.35888741e+12 -2.52567456e+14 4.12926014e+13 + 30 1.19490962e+13 -2.68975311e+12 -1.46751185e+14 2.48355169e+13 + 31 4.69595119e+12 3.12317161e+11 -8.83159711e+13 1.65464609e+13 + 32 -3.78853884e+11 1.92574082e+12 -5.40603934e+13 9.99231903e+12 +Solution index = 13 + 1 -3.39717277e+13 5.63259980e+11 5.46190027e+14 -8.43610223e+12 + 2 -7.87752411e+13 1.21092268e+12 1.06767381e+15 -1.66796113e+13 + 3 -2.52835104e+14 3.92465607e+12 2.24229808e+15 -3.47982787e+13 + 4 -1.22577215e+15 1.90479432e+13 5.44980325e+15 -8.46089643e+13 + 5 -2.43765505e+16 3.78706590e+14 -4.82711468e+16 7.49900509e+14 + 6 1.53540705e+16 -2.38529101e+14 2.76702835e+16 -4.29933800e+14 + 7 1.44906018e+16 -2.25173324e+14 1.84847377e+16 -2.87254691e+14 + 8 4.62517110e+14 -7.19464610e+12 -2.68572560e+15 4.17970682e+13 + 9 -4.47077888e+15 6.95214764e+13 -6.35127585e+15 9.88017778e+13 + 10 -2.29497313e+15 3.56556357e+13 -1.98312637e+15 3.07635055e+13 + 11 -5.24660011e+13 8.06051499e+11 5.97839004e+14 -9.30153287e+12 + 12 3.22935917e+14 -5.00644383e+12 6.32586564e+14 -9.86921349e+12 + 13 1.19299885e+12 -1.83045334e+10 1.32079552e+14 -2.08384320e+12 + 14 -5.29905989e+13 8.94194523e+11 -3.29529076e+13 6.15187049e+11 + 15 2.84021375e+14 -4.04418899e+12 3.86838496e+12 4.35034078e+10 + 16 5.84851195e+13 -2.45058016e+12 -6.43179342e+13 8.15721880e+11 + 17 -6.95447453e+14 1.00378919e+13 2.28557147e+13 -3.29909135e+11 + 18 -1.93104314e+14 2.58901402e+12 2.35450936e+13 -3.20704382e+11 + 19 -5.15608982e+13 6.61284229e+11 1.22126924e+13 -1.55294573e+11 + 20 -7.21001232e+12 6.16654251e+10 3.36913187e+12 -1.56849197e+10 + 21 5.70823109e+12 -7.26633064e+10 -1.17690317e+12 8.69100600e+08 + 22 8.06843979e+12 -1.18156294e+11 -2.69662443e+12 2.01989765e+09 + 23 6.73447433e+12 -1.09568514e+11 -2.54058208e+12 9.68058146e+10 + 24 4.35945432e+12 -3.34293439e+10 -1.60522484e+12 4.73960054e+09 + 25 2.29707586e+12 -3.50579853e+10 -3.44128301e+11 -9.25836303e+10 + 26 9.86524947e+11 -8.36145369e+09 4.94874839e+11 9.39352495e+10 + 27 3.06896039e+11 -1.33766055e+08 7.27813028e+11 -7.03005363e+09 + 28 2.03338605e+10 -1.13023331e+10 8.83853256e+11 -8.41925372e+10 + 29 -9.83914984e+10 1.16204149e+10 7.62090599e+11 2.20912079e+10 + 30 -4.77071140e+10 -3.14260775e+10 4.57642619e+11 1.35651831e+11 + 31 1.84144507e+11 -4.57898781e+09 2.95485146e+11 -8.37277814e+10 + 32 2.47532165e+11 2.47459686e+10 7.23844917e+11 -2.73911068e+11 +Solution index = 14 + 1 -7.57998559e-05 2.09491893e-08 1.87463253e-04 -1.00972262e-06 + 2 -1.34101729e-04 -1.51422554e-07 2.27588746e-04 -7.31503819e-07 + 3 -1.01605024e-04 1.35907547e-07 1.67550544e-04 3.52130592e-07 + 4 1.15430997e-04 -2.07050824e-08 -1.48028841e-04 1.21389979e-06 + 5 5.85592081e-04 -2.73557506e-08 -9.20486185e-04 -1.17460245e-06 + 6 1.30371845e-03 1.18304751e-07 -2.24147538e-03 -2.92845701e-07 + 7 2.03208511e-03 8.19323512e-08 -3.86191281e-03 3.77533477e-07 + 8 1.87900226e-03 6.76060566e-08 -4.45290427e-03 -3.24126059e-06 + 9 -1.24397668e-03 -1.01645897e-07 -2.92966080e-04 -1.98620823e-06 + 10 -9.51870025e-03 9.67244147e-08 1.40718657e-02 -4.54514129e-07 + 11 -1.89323022e-02 3.88471490e-08 3.62733803e-02 -5.92476852e-07 + 12 -1.34354678e-02 -1.93772669e-07 3.73742665e-02 1.20839266e-06 + 13 -4.48940275e-04 3.15466169e-09 -3.28729696e-02 1.19991619e-06 + 14 -1.36918606e-01 -6.60506759e-08 -1.61310798e-01 5.18854181e-08 + 15 -6.24760345e-01 1.80122317e-07 -1.67495846e-01 -1.06616636e-06 + 16 2.84208510e+00 -1.02972736e-05 3.22489384e-01 -3.86374170e-07 + 17 1.49763874e+00 9.23388373e-06 -4.95139089e-02 5.11105946e-07 + 18 6.47650510e-01 1.44114267e-06 -7.93801641e-02 2.39977129e-08 + 19 2.33471109e-01 -1.27562352e-06 -5.54994380e-02 -6.82013136e-07 + 20 6.47759012e-02 -1.10425389e-06 -2.58569212e-02 -6.57300773e-07 + 21 1.67385561e-03 2.50967689e-07 -5.25286240e-03 -1.45624769e-07 + 22 -1.71557389e-02 1.23474360e-06 5.32314481e-03 4.08100849e-07 + 23 -1.73729811e-02 1.35777327e-07 8.05096222e-03 1.68606567e-06 + 24 -1.13944497e-02 -6.25446083e-07 6.24603848e-03 2.44946302e-06 + 25 -5.31436474e-03 -6.66495633e-07 3.07785374e-03 4.33377703e-07 + 26 -1.30423911e-03 -1.82266067e-08 4.97281067e-04 1.17426109e-06 + 27 5.92826248e-04 3.15368859e-07 -8.64453001e-04 8.30726963e-07 + 28 1.08504690e-03 -4.11337680e-07 -1.18742144e-03 -8.65530240e-07 + 29 8.83527267e-04 -1.69673542e-07 -9.46917674e-04 -1.41535113e-07 + 30 4.69511872e-04 2.22152020e-07 -5.67199753e-04 3.37396868e-07 + 31 1.15281623e-04 -3.43189308e-08 -2.70311010e-04 -3.86326542e-07 + 32 -5.52304042e-05 2.00359347e-07 -7.38971525e-05 2.20067223e-07 +Solution index = 15 + 1 -4.84753999e+30 -1.14733337e+29 -1.21351828e+31 -2.86700397e+29 + 2 3.72221464e+30 8.79834181e+28 7.69328361e+30 1.82696519e+29 + 3 3.46421145e+30 8.14894882e+28 4.92832740e+30 1.16392607e+29 + 4 1.63585658e+30 3.58370572e+28 1.67287446e+30 4.77399579e+28 + 5 3.06385150e+30 -5.11081549e+28 9.18156682e+30 -1.10696762e+29 + 6 -1.18668188e+31 -1.98284069e+27 -1.92072459e+31 -3.44856215e+28 + 7 -7.04602446e+30 3.12571813e+29 -1.25685467e+31 7.28014367e+29 + 8 1.28557091e+31 -5.87909399e+29 2.01008460e+31 -9.49046234e+29 + 9 5.75391853e+30 -1.29229387e+29 6.50054445e+30 -9.66489380e+28 + 10 -3.93481486e+30 1.39759611e+29 -6.55810594e+30 1.33325476e+29 + 11 -3.01490294e+30 2.09257108e+29 -3.08399603e+30 3.05952311e+29 + 12 -3.16532243e+29 1.57131356e+28 1.33393651e+30 -3.28197492e+28 + 13 -1.83715137e+28 2.98536021e+27 4.51688438e+29 -1.30609076e+28 + 14 -1.56982141e+30 4.46235524e+28 -1.34349235e+30 -7.78802082e+26 + 15 -7.89689865e+30 8.81253272e+28 -2.14326448e+30 1.65643446e+28 + 16 -1.45506115e+30 -5.57314045e+29 2.52300521e+30 -3.47246458e+28 + 17 5.15844505e+31 5.88025296e+29 -5.28484576e+29 2.20179203e+26 + 18 -6.02151890e+29 -2.04734997e+29 5.00439119e+29 1.30760967e+28 + 19 -4.37618885e+31 -8.07839689e+29 -1.94972353e+30 -5.59130491e+28 + 20 -4.34785650e+31 5.32257966e+29 -7.33795647e+30 9.86221424e+28 + 21 1.16279332e+31 2.33050413e+28 -4.60807844e+30 -1.01121327e+28 + 22 1.18739951e+32 -4.86222022e+28 3.15081205e+31 -2.04828202e+28 + 23 9.61136196e+31 -6.13144240e+28 4.76199295e+31 -3.21558364e+28 + 24 -1.51523241e+32 5.07529731e+28 -6.95309295e+31 1.96567939e+28 + 25 -1.74477583e+32 8.65731998e+28 -1.04413509e+32 4.64415923e+28 + 26 6.99102297e+31 2.06048325e+28 4.84108881e+31 1.78671819e+28 + 27 2.15519803e+32 -1.28584291e+29 1.90347373e+32 -1.19282231e+29 + 28 -1.16284652e+32 4.97282317e+28 -1.43386494e+32 6.55632023e+28 + 29 -9.28882372e+30 3.41705415e+27 1.26312929e+30 -8.98834265e+26 + 30 4.33491035e+30 -6.25615166e+26 8.13836733e+30 -2.07935174e+27 + 31 6.83221817e+30 -1.64289074e+27 1.04781187e+31 -1.95932717e+27 + 32 -6.74508534e+30 1.18298189e+27 -1.04710807e+31 2.11897220e+27 +Solution index = 16 + 1 3.87414149e+18 -2.37961904e+18 9.41644205e+18 -5.91803626e+18 + 2 -2.91242838e+18 1.81768192e+18 -6.60398749e+18 3.84153632e+18 + 3 -2.57860157e+18 1.67173321e+18 -5.01645716e+18 2.57837609e+18 + 4 5.18405104e+17 6.35121297e+17 -8.57802826e+17 1.19393191e+18 + 5 9.08870625e+18 -1.74620728e+18 1.78167933e+19 -3.05708446e+18 + 6 -4.21002920e+18 -7.27754366e+17 -7.07557196e+18 -7.66226519e+17 + 7 -8.03065213e+18 3.10411540e+17 -1.23055654e+19 6.86077366e+17 + 8 1.26744748e+18 4.00155387e+17 2.98486694e+18 6.40714778e+17 + 9 3.76001639e+18 -2.94655416e+16 4.57068756e+18 1.75354768e+17 + 10 2.29823062e+18 -9.32625326e+17 2.85368422e+18 -1.61904281e+18 + 11 -9.26422534e+17 2.25516054e+17 -2.29462955e+18 7.50178984e+17 + 12 -6.31499434e+17 2.05297418e+17 -1.83518807e+18 7.50440234e+17 + 13 -2.63295636e+17 -6.16489791e+15 -2.72103393e+18 -2.14943128e+17 + 14 9.06951013e+17 -4.77212592e+17 1.92459574e+18 -6.53636757e+17 + 15 5.22399070e+18 -2.39555741e+18 1.97588515e+18 -7.52186093e+17 + 16 -2.27508867e+19 1.13952326e+19 -2.45656388e+18 1.22404846e+18 + 17 -7.90408335e+18 4.32458145e+18 3.06234539e+17 -1.66259575e+17 + 18 -3.08953443e+18 1.95774074e+18 6.05412803e+17 -3.09422653e+17 + 19 -2.13798544e+18 1.54776987e+18 4.87787917e+17 -1.83701133e+17 + 20 -3.81742704e+18 1.02459198e+18 -1.65115166e+17 -1.95166248e+15 + 21 -2.93498206e+18 2.09556974e+17 -7.72846845e+17 8.54291528e+16 + 22 2.94525809e+18 -1.28961896e+18 4.04805583e+17 -2.90852647e+17 + 23 7.06503018e+18 -1.36301047e+18 2.52587558e+18 -5.41993368e+17 + 24 -7.04705516e+17 1.50477456e+18 -1.26009699e+18 9.33932138e+17 + 25 3.93214523e+18 4.27387335e+16 4.07231054e+18 -1.14454959e+17 + 26 -1.45530085e+19 6.03855416e+16 -1.12684049e+19 -1.09218087e+16 + 27 2.38971351e+17 5.20098550e+15 2.25168089e+17 -3.17256742e+16 + 28 1.17271353e+19 -3.24925158e+16 1.04923624e+19 -5.34621686e+16 + 29 8.66922684e+18 -2.41132910e+16 1.03157385e+19 -4.55457715e+16 + 30 -1.33433268e+19 4.44755742e+16 -1.42126297e+19 3.78423662e+16 + 31 -1.76496104e+19 5.65836132e+16 -2.33179096e+19 6.98824425e+16 + 32 1.64211382e+19 -5.32002257e+16 2.71537151e+19 -8.98534951e+16 +Solution index = 17 + 1 -1.29746357e+23 9.58527319e+21 -3.78370308e+23 2.78654554e+22 + 2 2.82423693e+23 -2.06016449e+22 6.46529247e+23 -4.71767127e+22 + 3 -4.19184117e+22 2.92404462e+21 -1.06261095e+23 7.50439631e+21 + 4 -1.79608252e+23 1.29420577e+22 -3.23902295e+23 2.33468973e+22 + 5 -1.81021379e+22 1.43909508e+21 -1.01374217e+21 4.09426360e+20 + 6 7.50423437e+22 -5.48862064e+21 1.21618598e+23 -8.77843441e+21 + 7 5.52447756e+22 -3.48319607e+21 7.95181248e+22 -4.05758039e+21 + 8 -2.48076573e+22 5.84397438e+20 -4.21767208e+22 1.58278676e+21 + 9 -2.82449308e+22 1.84066346e+21 -3.84010818e+22 2.51022671e+21 + 10 7.27343844e+21 4.37009144e+20 -2.15334039e+21 -4.20788456e+20 + 11 1.93245297e+22 2.26760069e+20 -1.64939776e+22 -7.55619655e+20 + 12 1.07503579e+22 1.23421647e+20 -2.53083793e+22 -7.35206691e+20 + 13 1.78774920e+20 2.35536757e+19 2.21171412e+22 6.77349678e+20 + 14 9.90343241e+22 2.18896931e+21 1.14666408e+23 2.57301310e+21 + 15 4.42334727e+23 9.96605251e+21 1.16150191e+23 2.66803660e+21 + 16 -2.13098886e+24 -4.45047313e+22 -2.27650056e+23 -5.13417930e+21 + 17 -7.64882019e+23 -2.59837235e+22 3.01304717e+22 7.97901432e+20 + 18 -2.71485752e+23 -1.07758225e+22 5.96336393e+22 1.10312981e+21 + 19 -3.18120158e+23 2.91227030e+20 3.25293769e+22 8.80563762e+20 + 20 -2.78196164e+23 7.27554631e+21 -1.56680053e+22 1.69981647e+21 + 21 1.11487487e+23 -3.13449021e+21 2.90442890e+22 -1.61989111e+20 + 22 1.29287272e+23 -8.96940720e+21 1.73944748e+22 -2.08772918e+21 + 23 1.19318642e+23 -7.18974273e+21 2.69392342e+22 -2.49201774e+21 + 24 3.94625292e+22 -8.41281565e+20 1.80802670e+22 -1.14063016e+21 + 25 -8.59110851e+22 6.55116419e+21 -2.44741166e+22 1.41683802e+21 + 26 -2.14576796e+23 1.49948509e+22 -1.07910832e+23 7.07230973e+21 + 27 -3.01882650e+23 2.36135744e+22 -2.66287902e+23 2.10805478e+22 + 28 1.55455123e+23 -1.18202072e+22 5.90727784e+22 -4.37204323e+21 + 29 8.08651291e+23 -6.17807676e+22 8.41991145e+23 -6.42382889e+22 + 30 1.05274652e+23 -8.03305769e+21 1.86024492e+23 -1.41323787e+22 + 31 -1.20487048e+24 9.19366376e+22 -1.69753119e+24 1.29541178e+23 + 32 5.65642528e+23 -4.31600367e+22 1.04061701e+24 -7.94073048e+22 +Solution index = 18 + 1 1.76230032e+17 3.39993899e+16 5.08434106e+17 9.83955029e+16 + 2 -3.66858881e+17 -7.18849384e+16 -8.38846452e+17 -1.64496714e+17 + 3 4.51843676e+16 9.52731433e+15 1.23114884e+17 2.51740410e+16 + 4 2.21511157e+17 4.42038921e+16 4.00137048e+17 7.97515358e+16 + 5 3.17717930e+16 5.67634460e+15 2.39903118e+16 3.28928910e+15 + 6 -9.91263157e+16 -1.92953176e+16 -1.51593684e+17 -2.98669616e+16 + 7 -9.08661463e+16 -1.54152999e+16 -1.30006172e+17 -2.02733018e+16 + 8 5.79024381e+16 6.94558632e+15 1.13095693e+17 1.47170926e+16 + 9 4.56887357e+16 7.84891871e+15 5.64267567e+16 1.00393060e+16 + 10 -8.62394163e+14 1.01708152e+15 -4.76263554e+16 -6.53048292e+15 + 11 1.02244720e+16 2.42155760e+15 -6.77423133e+16 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1.92670520e+16 + 27 5.04438582e+17 9.34025842e+16 4.50970995e+17 8.34683610e+16 + 28 -1.86697126e+17 -3.45968431e+16 -2.02873108e+16 -4.06402557e+15 + 29 -1.35336427e+18 -2.49276329e+17 -1.40523982e+18 -2.58871054e+17 + 30 -2.53431728e+17 -4.66508646e+16 -4.12493281e+17 -7.59708831e+16 + 31 2.07537343e+18 3.82288650e+17 2.93444847e+18 5.40523936e+17 + 32 -9.61039221e+17 -1.77036200e+17 -1.77155065e+18 -3.26339403e+17 +Solution index = 19 + 1 -3.56587150e+19 4.31624800e+19 -8.97846854e+19 1.07967118e+20 + 2 2.75516470e+19 -3.31325346e+19 5.58329780e+19 -6.87001120e+19 + 3 2.60219459e+19 -3.08102684e+19 3.42069122e+19 -4.43182331e+19 + 4 1.94597446e+19 -1.56859038e+19 2.40295014e+19 -2.11925107e+19 + 5 4.00318793e+19 -8.29387962e+18 1.15227466e+20 -3.89418274e+19 + 6 -1.57329650e+20 8.94248971e+19 -2.85627902e+20 1.55308879e+20 + 7 3.16289020e+19 -1.06046135e+19 8.07702386e+19 -3.38618864e+19 + 8 4.98962300e+19 -3.12111465e+19 6.83473573e+19 -4.48237557e+19 + 9 7.20070503e+18 -8.44105278e+18 -1.46136513e+18 -9.12698689e+18 + 10 -1.57422961e+19 2.08224271e+19 -3.54466037e+19 4.28356143e+19 + 11 6.61105639e+18 -8.28124216e+18 1.31743816e+19 -2.31078507e+19 + 12 1.89464919e+18 -2.55179205e+18 1.36795428e+17 -6.78555876e+18 + 13 4.26511507e+18 -1.60852403e+18 4.92225706e+19 -1.56166386e+19 + 14 9.34676446e+18 2.95417440e+18 2.82180799e+18 8.09690999e+18 + 15 3.11792844e+19 2.15155216e+19 2.97881075e+18 8.95310897e+18 + 16 -1.92028568e+20 -7.59019762e+19 -2.01035834e+19 -9.58635855e+18 + 17 -6.90374021e+19 -6.58378650e+19 2.66950911e+18 1.58160513e+18 + 18 -2.91032650e+19 -1.49203019e+19 5.16426377e+18 2.01787833e+18 + 19 -3.80052942e+19 2.05611207e+19 9.94057050e+17 3.73057827e+18 + 20 2.47767055e+19 -2.19881070e+19 6.45609153e+18 -2.87212177e+18 + 21 1.18367170e+19 -1.09178985e+18 5.39816914e+18 1.66343737e+17 + 22 -3.48707329e+19 6.28233820e+18 -8.09954714e+18 1.52357641e+18 + 23 -5.12839087e+19 6.42400970e+18 -2.19811964e+19 2.51499872e+18 + 24 2.90704511e+19 -6.47916200e+18 1.53778058e+19 -3.72225651e+18 + 25 3.44087127e+19 -5.20243919e+18 1.67713324e+19 -3.23637180e+18 + 26 1.69083094e+19 4.50738366e+18 1.15487570e+19 3.78994732e+18 + 27 -5.10553340e+19 4.98552902e+18 -5.57643390e+19 5.59215299e+18 + 28 5.49451924e+19 -1.03136598e+19 5.39767984e+19 -9.56928754e+18 + 29 4.21263013e+19 -7.78205737e+18 5.17025812e+19 -9.30114175e+18 + 30 -6.58033381e+19 1.20042789e+19 -6.95506041e+19 1.27993074e+19 + 31 -8.69191521e+19 1.58917020e+19 -1.14607876e+20 2.10055403e+19 + 32 8.07553569e+19 -1.47618070e+19 1.33634970e+20 -2.44105498e+19 +Solution index = 20 + 1 2.03660805e+15 4.19171638e+14 1.04479600e+15 1.06479254e+15 + 2 -1.62683127e+14 -3.32421563e+14 -9.76962237e+15 -6.41827624e+14 + 3 4.15727175e+15 -3.48554794e+14 -2.04252736e+16 -3.30942778e+14 + 4 1.13339860e+17 -1.38632255e+15 2.61996590e+17 -3.48972270e+15 + 5 -1.52972163e+17 3.09728864e+15 -2.94679737e+17 5.96236742e+15 + 6 -2.65188649e+16 -1.78720771e+14 -1.59517317e+16 -7.97000256e+14 + 7 4.55811235e+16 -1.17562098e+15 7.50010455e+16 -1.75103207e+15 + 8 2.82609248e+16 -4.20232074e+14 3.07124408e+16 -3.44718959e+14 + 9 -7.25540781e+14 1.65562901e+14 -7.44849506e+15 3.48351442e+14 + 10 -7.88059398e+15 1.72483333e+14 -9.96887983e+15 2.65357794e+14 + 11 -3.38930292e+15 7.86263954e+12 -2.03041026e+15 1.15891788e+14 + 12 7.21730019e+13 -3.96084463e+13 7.38145570e+14 8.05944007e+13 + 13 -3.18621345e+15 -6.38651989e+13 -3.55906304e+16 -7.68307372e+14 + 14 6.66117832e+14 -2.34168812e+14 3.83673334e+15 -2.46315108e+14 + 15 1.88462939e+16 -1.22451634e+15 1.02326205e+16 -3.46381564e+14 + 16 -4.56999444e+16 6.00479182e+15 -5.68556704e+15 6.70156996e+14 + 17 -2.03318586e+16 3.43484422e+15 7.90381393e+14 -1.11963197e+14 + 18 -9.83566547e+15 1.43220224e+15 1.12104050e+15 -1.74722037e+14 + 19 -3.48728048e+15 5.13798399e+14 7.25949728e+14 -1.20615166e+14 + 20 -8.39743635e+14 1.43744425e+14 2.80297512e+14 -5.47730061e+13 + 21 1.56189575e+14 6.54746532e+12 -1.31291206e+13 -9.74266680e+12 + 22 4.42725225e+14 -3.43689177e+13 -1.45571444e+14 1.26576792e+13 + 23 4.22998883e+14 -3.53851325e+13 -1.54631955e+14 1.90677175e+13 + 24 2.98466816e+14 -2.26548715e+13 -9.73697867e+13 1.52247788e+13 + 25 1.73395522e+14 -1.01335656e+13 -2.41396876e+13 7.29196773e+12 + 26 8.69841438e+13 -1.90194246e+12 3.31433875e+13 2.62783446e+12 + 27 3.89839611e+13 1.94500263e+12 6.19965546e+13 -3.35709903e+11 + 28 1.46273839e+13 2.64048788e+12 6.62759108e+13 -1.82056802e+12 + 29 2.50440944e+12 2.28841813e+12 5.41731720e+13 -1.77537919e+12 + 30 2.55173654e+12 1.02076450e+12 4.18706158e+13 1.63123100e+11 + 31 1.49779567e+13 2.19504127e+11 4.15814786e+13 9.37609229e+11 + 32 2.06949747e+13 2.45865771e+11 4.50500341e+13 -2.02691325e+12 +Solution index = 21 + 1 1.86533950e+25 -4.13668579e+22 5.09934102e+25 -1.94413687e+23 + 2 -2.91257910e+25 3.44406544e+23 -6.53965533e+25 8.19765881e+23 + 3 -2.35052244e+24 -2.00381253e+23 2.38345036e+23 -3.66278107e+23 + 4 1.22916988e+25 -3.72303580e+23 2.39790628e+25 -6.55952307e+23 + 5 -2.55523552e+23 7.23450939e+22 -6.01267213e+24 2.05622724e+23 + 6 4.86550454e+24 1.41466295e+23 7.79714105e+24 2.39163801e+23 + 7 9.71085914e+23 -2.19820614e+23 2.47397642e+24 -6.16351734e+23 + 8 -5.80183489e+24 5.65341566e+23 -8.08520608e+24 8.99263373e+23 + 9 -2.16896623e+24 8.44452829e+22 -2.10160311e+24 4.50309797e+22 + 10 1.81183640e+24 -1.66032688e+23 1.48069329e+24 -1.62233162e+23 + 11 2.15349630e+24 -2.00917500e+23 -6.63142801e+23 -2.79335033e+23 + 12 8.60287173e+23 -1.07716830e+22 -2.23359806e+24 4.50811481e+22 + 13 5.19879263e+22 -3.36841938e+21 1.89057500e+24 4.48417100e+21 + 14 7.75444161e+24 -5.58035855e+22 8.70773373e+24 -1.57656345e+22 + 15 3.53175964e+25 -1.28704855e+23 9.17751971e+24 -2.45438135e+22 + 16 -1.55204694e+26 7.66987128e+23 -1.71608360e+25 5.67906100e+22 + 17 -5.15002892e+25 -5.47528678e+23 1.70269117e+24 -9.47299253e+20 + 18 4.07156078e+24 1.36335309e+23 4.34746326e+24 -1.91121237e+22 + 19 1.29950029e+24 7.62419954e+23 5.09230949e+24 4.28441683e+22 + 20 -5.05520958e+25 -3.38094590e+23 -3.63629377e+24 -7.70214606e+22 + 21 -3.81587208e+25 9.85681174e+22 -7.83264826e+24 3.99706732e+22 + 22 2.97150759e+25 -8.40200304e+22 9.07391587e+24 -9.62127978e+21 + 23 2.25992076e+25 -2.00087454e+23 4.13715973e+24 -7.28613872e+22 + 24 2.52462367e+25 -2.06349420e+22 1.05461652e+25 -1.20044849e+22 + 25 -2.69420738e+24 2.16177931e+23 -2.28582552e+23 1.34188008e+23 + 26 -4.24366024e+25 8.70414656e+22 -3.17771901e+25 6.79779359e+22 + 27 7.23636456e+24 -2.43907516e+23 1.09678955e+25 -2.32332262e+23 + 28 8.82147577e+24 8.61936426e+22 8.57988651e+24 1.14559675e+23 + 29 8.69727921e+23 6.66516286e+21 -3.52976003e+23 3.37942507e+20 + 30 -4.14574595e+23 -3.70310571e+21 -8.74495531e+23 -5.51377741e+21 + 31 -6.45872833e+23 -5.36954369e+21 -1.04861196e+24 -7.65497691e+21 + 32 6.48204986e+23 5.42270561e+21 9.64730450e+23 8.16476781e+21 +Solution index = 22 + 1 1.38660527e+11 -4.70301907e+09 -2.39476985e+12 7.65896474e+10 + 2 3.32096297e+11 -1.07750760e+10 -4.72133376e+12 1.51682892e+11 + 3 1.12355866e+12 -3.59410878e+10 -1.00048435e+13 3.19958193e+11 + 4 5.53584298e+12 -1.76553358e+11 -2.44713292e+13 7.81581520e+11 + 5 1.09504525e+14 -3.49692871e+12 2.16372573e+14 -6.91385945e+12 + 6 -6.85996933e+13 2.19390990e+12 -1.24670641e+14 3.97821335e+12 + 7 -6.45622451e+13 2.06660869e+12 -8.38884712e+13 2.67204067e+12 + 8 -1.61833107e+12 5.57331355e+10 1.07947404e+13 -3.56674787e+11 + 9 1.99599560e+13 -6.38797752e+11 2.77942288e+13 -8.94958503e+11 + 10 8.64035502e+12 -2.90433280e+11 1.07661274e+13 -3.27500891e+11 + 11 -3.24924935e+12 7.35100365e+10 3.88021060e+12 -6.69044862e+10 + 12 -4.11089709e+12 1.08052229e+11 7.02056674e+12 -1.38094789e+11 + 13 2.56397353e+11 -5.92089670e+09 8.03951918e+11 -1.33387882e+10 + 14 -2.06742450e+13 4.77837286e+11 -2.47333591e+13 5.72826283e+11 + 15 -1.29214887e+14 3.01220775e+12 -4.50248321e+13 1.04605322e+12 + 16 5.41449644e+14 -1.25751277e+13 6.14618324e+13 -1.42993004e+12 + 17 2.98639269e+14 -6.96163655e+12 -9.96406130e+12 2.32421283e+11 + 18 1.27020360e+14 -2.95701864e+12 -1.53598929e+13 3.57652671e+11 + 19 4.56439643e+13 -1.06219688e+12 -1.05393958e+13 2.45089126e+11 + 20 1.26506679e+13 -2.94245637e+11 -4.73440284e+12 1.09846333e+11 + 21 3.17269906e+11 -7.21913147e+09 -7.51629267e+11 1.74355369e+10 + 22 -3.37409508e+12 7.89344148e+10 1.25591415e+12 -2.90737771e+10 + 23 -3.42957819e+12 8.00334611e+10 1.73283516e+12 -4.03128197e+10 + 24 -2.26846439e+12 5.26327788e+10 1.33330902e+12 -3.04758447e+10 + 25 -1.08221089e+12 2.50989805e+10 6.75426664e+11 -1.52044011e+10 + 26 -2.98209463e+11 6.91771387e+09 1.39206914e+11 -3.44339276e+09 + 27 7.56677819e+10 -1.68326961e+09 -1.51974206e+11 3.72196046e+09 + 28 1.82564804e+11 -4.26990074e+09 -2.29978245e+11 5.52222999e+09 + 29 1.60649487e+11 -3.81567307e+09 -1.82853959e+11 4.09405959e+09 + 30 8.79664538e+10 -1.87146388e+09 -1.07926233e+11 1.96789504e+09 + 31 4.92776902e+09 -1.22864454e+08 -7.17736031e+10 1.92583019e+09 + 32 -3.94529316e+10 8.50108219e+08 -5.82003060e+10 2.57420975e+09 +Solution index = 23 + 1 1.64135174e+13 -9.37007101e+10 4.55809455e+13 -2.47343693e+11 + 2 -2.14714187e+13 4.72918663e+10 -3.92576971e+13 9.27166469e+09 + 3 -3.74999244e+13 4.05968450e+11 -8.32409142e+13 9.04568016e+11 + 4 4.15540349e+13 -2.98973412e+11 7.76790312e+13 -5.66850338e+11 + 5 3.64708610e+13 -3.67456459e+11 5.97788467e+13 -6.30166896e+11 + 6 -1.91548025e+13 1.62639298e+11 -3.48623881e+13 3.03540887e+11 + 7 -2.72832473e+13 2.60333100e+11 -3.81102482e+13 3.77508320e+11 + 8 -1.98760474e+12 -9.68161779e+09 2.12960440e+12 -6.73679880e+10 + 9 9.71811193e+12 -9.38923024e+10 1.39005210e+13 -1.28300491e+11 + 10 4.81028380e+12 -4.25800710e+10 4.55975904e+12 -2.64782303e+10 + 11 -5.09221476e+11 3.47395879e+09 -1.63562381e+12 5.18301762e+10 + 12 -9.44607628e+11 1.50920768e+09 -1.29399429e+12 3.32905997e+10 + 13 -5.00874673e+09 -3.44557245e+08 -5.36334919e+11 -1.97894687e+10 + 14 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1.57617835e+10 + 29 -9.02565079e+13 4.40934500e+11 -9.28381347e+13 4.59250188e+11 + 30 -1.27332524e+13 5.66247308e+10 -2.18136409e+13 9.93625631e+10 + 31 1.34923479e+14 -6.55416834e+11 1.90354127e+14 -9.22325290e+11 + 32 -6.34724678e+13 3.07483559e+11 -1.16655221e+14 5.66050378e+11 +Solution index = 24 + 1 -1.45970490e+18 -2.70769229e+16 -4.05894516e+18 -7.09656670e+16 + 2 2.50880792e+18 3.17287737e+16 5.66839944e+18 6.94893758e+16 + 3 1.62429996e+16 1.11674450e+16 -3.17650169e+17 1.35481256e+16 + 4 -1.24824381e+18 -4.95925785e+15 -2.36768876e+18 -1.19034024e+16 + 5 -5.25714936e+15 -4.32158428e+15 4.13777550e+17 -3.02135416e+15 + 6 -7.18452335e+16 -9.49071199e+15 -1.04365272e+17 -1.47461788e+16 + 7 7.99999984e+16 8.37247484e+15 6.96818459e+16 2.31518483e+16 + 8 2.45333365e+17 -1.63867246e+16 3.33642632e+17 -2.68623472e+16 + 9 6.35679826e+16 -1.05853644e+15 4.07730314e+16 6.88028386e+14 + 10 -5.69998097e+16 4.22236712e+15 -1.18870691e+17 1.57883345e+15 + 11 -2.79467673e+16 7.74228140e+15 -9.66367363e+16 1.05416241e+16 + 12 1.10772977e+16 7.63267397e+14 -3.29720420e+16 -1.77403465e+15 + 13 -3.68768594e+14 8.97087998e+13 3.60106015e+16 -1.74807514e+14 + 14 1.44796849e+17 4.21996716e+15 1.83238133e+17 3.19319398e+15 + 15 7.00582072e+17 1.48554041e+16 1.83677939e+17 3.45137694e+15 + 16 -2.96947324e+18 -6.98466780e+16 -3.45868835e+17 -6.94079324e+15 + 17 -1.83668039e+18 -4.48625710e+15 4.33950149e+16 5.70239923e+14 + 18 4.67305890e+17 7.20994052e+15 9.69202258e+16 2.14572372e+15 + 19 -2.28187844e+17 -3.27437092e+16 5.69154941e+16 -8.48298097e+14 + 20 -5.09501305e+17 3.25290871e+15 -1.84538936e+16 2.51396255e+15 + 21 -3.90729009e+17 -1.35791082e+16 -6.87910342e+16 -3.51080154e+15 + 22 2.07926185e+16 3.95630663e+15 -3.19874733e+16 -4.45512359e+14 + 23 6.76799497e+17 2.67262772e+16 2.46788181e+17 1.01004142e+16 + 24 3.46884764e+17 8.59767838e+15 1.88048981e+17 5.07203046e+15 + 25 -7.02961112e+17 -3.01394802e+16 -4.38180293e+17 -1.87467219e+16 + 26 -5.11664901e+17 -1.57183746e+16 -3.95070319e+17 -1.22133242e+16 + 27 8.30503447e+17 3.46749579e+16 8.13349835e+17 3.33552758e+16 + 28 -2.27879748e+17 -1.11715750e+16 -3.20370934e+17 -1.51608874e+16 + 29 -1.52962182e+16 -8.02781999e+14 -1.52983288e+15 -3.54418676e+13 + 30 6.31656745e+15 3.93473894e+14 1.08923264e+16 6.18096116e+14 + 31 1.04547489e+16 6.02506579e+14 1.52647162e+16 8.64422276e+14 + 32 -1.01421016e+16 -5.93938690e+14 -1.64847113e+16 -8.96197721e+14 +Solution index = 25 + 1 1.27228613e+14 -2.25728003e+12 3.16334378e+14 -5.45351370e+12 + 2 -9.71346995e+13 1.69955346e+12 -2.05532312e+14 3.91635433e+12 + 3 -8.92528328e+13 1.50651607e+12 -1.38305794e+14 3.05538176e+12 + 4 -3.32621530e+13 2.14152998e+10 -6.47353722e+13 1.95811035e+12 + 5 1.02699425e+14 -7.70012450e+12 1.83326025e+14 -1.48397170e+13 + 6 3.26457600e+13 3.34694325e+12 3.22498093e+13 6.58789762e+12 + 7 -2.29413670e+13 3.92478851e+12 -4.06447931e+13 5.38256475e+12 + 8 -2.20240281e+13 3.85149414e+11 -2.46115565e+13 -1.92038503e+11 + 9 -3.72645435e+12 -1.00759360e+12 -9.36912391e+10 -1.66574227e+12 + 10 6.08293891e+12 -2.95259129e+11 2.35580377e+12 -1.17367170e+12 + 11 7.41916928e+12 6.01557848e+11 -6.85218732e+12 -1.19466967e+12 + 12 3.80775702e+12 5.12352870e+11 -9.80436727e+12 -9.13188035e+11 + 13 1.13605118e+12 6.98903762e+11 1.93941367e+13 8.97093588e+12 + 14 3.49396112e+13 4.47201391e+12 3.87950054e+13 3.96024307e+12 + 15 1.58132456e+14 1.92321564e+13 4.19513047e+13 4.41763540e+12 + 16 -7.60264833e+14 -9.46477119e+13 -8.14293415e+13 -1.05074151e+13 + 17 -2.69575984e+14 -4.59955673e+13 1.06694972e+13 1.52611931e+12 + 18 -1.13927982e+14 -1.80935622e+13 2.06520685e+13 2.50692929e+12 + 19 -1.20861128e+14 -9.87824451e+12 9.65500518e+12 1.21379404e+12 + 20 -2.67114241e+13 1.05316574e+13 7.07927662e+12 2.83868900e+12 + 21 -2.81620040e+12 3.18907034e+12 1.08285278e+12 2.13430843e+12 + 22 1.79800749e+13 -2.00603489e+13 2.75322218e+12 -5.27372449e+12 + 23 1.86588404e+13 -2.10548476e+13 4.75534077e+12 -9.71456515e+12 + 24 -1.47520154e+13 2.65519387e+13 -1.15534981e+13 1.52368176e+13 + 25 3.51050299e+11 1.48451842e+12 6.49866528e+11 -1.92477546e+12 + 26 1.05780692e+11 2.84132388e+11 5.62257985e+11 -8.64999261e+11 + 27 -2.07536558e+11 3.74829068e+10 5.79286643e+11 -4.16260183e+11 + 28 -2.80357765e+11 -2.03303369e+10 4.95258768e+11 -2.11890746e+11 + 29 -2.17285689e+11 -2.25779431e+10 3.44756079e+11 -1.18461519e+11 + 30 -1.11811364e+11 -1.20284088e+10 2.03769207e+11 -7.13289594e+10 + 31 -1.80592569e+10 -4.60740144e+09 1.11027139e+11 -4.84759994e+10 + 32 2.69140470e+10 -2.51985740e+09 5.68102743e+10 -4.06382809e+10 +Solution index = 26 + 1 1.11202199e+09 1.18319557e+08 3.29073029e+09 3.50040327e+08 + 2 -2.54791521e+09 -2.72086961e+08 -5.79071760e+09 -6.18223350e+08 + 3 1.57704909e+08 1.79748116e+07 2.96200404e+08 3.38912855e+07 + 4 2.29614790e+09 2.45274677e+08 4.27470017e+09 4.56302406e+08 + 5 1.57860876e+08 1.56906675e+07 2.90176977e+06 -1.79499595e+06 + 6 -1.25525810e+09 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9.46067821e+09 1.02440465e+09 1.16265959e+09 1.25621854e+08 + 22 1.72322007e+10 1.86760362e+09 5.25719189e+09 5.69938232e+08 + 23 1.73453740e+09 1.88035350e+08 2.48314137e+09 2.69388511e+08 + 24 -2.78410008e+10 -3.01717691e+09 -1.22715335e+10 -1.32955015e+09 + 25 -2.63187492e+10 -2.85225222e+09 -1.73855785e+10 -1.88390139e+09 + 26 2.49920589e+10 2.70729582e+09 1.54081313e+10 1.66921685e+09 + 27 4.86148262e+10 5.26577730e+09 4.05955017e+10 4.39711032e+09 + 28 -1.26051059e+10 -1.36500683e+09 -1.15788460e+10 -1.25422070e+09 + 29 -5.24360615e+10 -5.67733273e+09 -5.70575531e+10 -6.17804492e+09 + 30 1.12286950e+10 1.21721071e+09 1.79871857e+10 1.94981256e+09 + 31 2.80487824e+10 3.03299575e+09 3.79365265e+10 4.10196657e+09 + 32 -1.19161947e+10 -1.28831621e+09 -2.27368147e+10 -2.45832355e+09 +Solution index = 27 + 1 4.95976944e+23 1.18716456e+23 1.24327820e+24 2.96226498e+23 + 2 -3.80787735e+23 -9.09010248e+22 -7.85528555e+23 -1.90109239e+23 + 3 -3.53719282e+23 -8.40735286e+22 -5.03297929e+23 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1.23783097e+22 + 19 5.79555195e+23 -2.08911214e+22 3.41343980e+22 1.02485109e+22 + 20 -2.13088044e+23 -5.73889346e+22 -4.31226130e+22 -3.56663573e+21 + 21 7.74010239e+22 7.57702531e+21 5.84494716e+22 2.72897770e+21 + 22 -3.68739430e+23 3.46573011e+22 -7.87143746e+22 9.59186392e+21 + 23 -4.43404323e+23 1.34899775e+22 -1.82393257e+23 6.66430440e+21 + 24 4.22426285e+23 -5.51487305e+22 2.63144790e+23 -2.98215940e+22 + 25 -3.94920997e+22 -2.47216077e+22 -8.94088193e+22 -1.95303705e+22 + 26 2.20575217e+23 8.33999857e+22 1.55409355e+23 6.68931211e+22 + 27 -2.44636985e+21 -1.62440961e+21 -9.89366177e+21 2.96691868e+19 + 28 -1.71488112e+23 -6.76515009e+22 -1.57148512e+23 -5.94110384e+22 + 29 -1.26908716e+23 -5.00152791e+22 -1.53043890e+23 -5.87225923e+22 + 30 1.95270709e+23 7.65945688e+22 2.06778279e+23 8.20351677e+22 + 31 2.58317481e+23 1.01439482e+23 3.40489144e+23 1.34245159e+23 + 32 -2.40345679e+23 -9.43434207e+22 -3.97956818e+23 -1.55934350e+23 +Solution index = 28 + 1 1.29288294e+04 -9.08069490e+02 3.23425983e+04 -2.28316328e+03 + 2 -9.92877186e+03 6.98753558e+02 -2.06181368e+04 1.42693441e+03 + 3 -9.19211138e+03 6.53975555e+02 -1.34325902e+04 8.94810294e+02 + 4 -3.97346186e+03 4.53847174e+02 -5.42227394e+03 7.30134498e+02 + 5 2.14409146e+03 -3.01746478e+02 1.23085436e+03 -4.36387768e+02 + 6 9.16191438e+03 -7.12119991e+02 1.15105451e+04 -1.02218082e+03 + 7 6.91536743e+03 -2.55499459e+02 8.21059321e+03 -2.79319006e+02 + 8 -3.95670651e+03 2.33306098e+02 -8.67553221e+03 3.28010808e+02 + 9 -4.47881649e+03 1.36215791e+02 -7.63225202e+03 -1.47865787e+02 + 10 -6.27878286e+02 7.38833836e+02 -2.85233031e+03 1.34104858e+03 + 11 1.01682174e+04 -3.12632183e+02 3.21256547e+04 -7.16570158e+02 + 12 -4.15671847e+03 -1.76892090e+02 -1.00191255e+04 -3.70134075e+02 + 13 -1.06818430e+02 7.36537063e+00 -8.05615823e+03 1.46444262e+02 + 14 -1.31801529e+04 7.98982573e+00 -1.64682265e+04 1.01013244e+02 + 15 -5.82247586e+04 1.09689767e+02 -1.37116356e+04 5.97127093e+01 + 16 3.16267921e+05 -2.80963570e+01 3.36437243e+04 -6.71188684e+01 + 17 1.28868280e+05 -1.74439673e+03 -4.86521345e+03 1.40640623e+01 + 18 6.18886084e+04 2.53301294e+02 -8.77384722e+03 -6.23294555e+00 + 19 5.12713221e+04 1.75924078e+03 -4.01663212e+03 1.34326502e+02 + 20 -8.82476231e+02 -6.00439886e+02 -4.65232728e+03 -9.64640936e+01 + 21 -2.47886479e+02 -3.19493252e+02 -5.46754893e+02 2.13486005e+01 + 22 -2.74860232e+03 -1.03846488e+03 2.38363039e+02 -2.94605468e+02 + 23 -2.10561889e+03 -3.62240017e+02 5.74240340e+02 -2.38341551e+02 + 24 6.47953375e+02 1.82404973e+03 1.55506822e+03 9.39168312e+02 + 25 1.30070115e+02 8.01642388e+02 7.95134815e+02 6.02632372e+02 + 26 -2.53989203e+03 -2.61947489e+03 -1.90030331e+03 -2.10381150e+03 + 27 1.56299406e+02 4.85329412e+01 -8.03473736e+01 6.43791899e+00 + 28 2.32197682e+03 2.13152768e+03 1.82938792e+03 1.88505219e+03 + 29 1.71798806e+03 1.57537396e+03 1.83250936e+03 1.86086482e+03 + 30 -2.43568245e+03 -2.42249787e+03 -2.69883453e+03 -2.58808152e+03 + 31 -3.27477701e+03 -3.20513779e+03 -4.36308915e+03 -4.23890030e+03 + 32 3.06313258e+03 2.98136139e+03 5.07287337e+03 4.92700204e+03 +Solution index = 29 + 1 5.65269048e+11 -7.48030727e+08 1.72753941e+12 -1.95516448e+09 + 2 -1.50714360e+12 8.78674584e+08 -3.48702856e+12 1.93102092e+09 + 3 3.87944432e+11 3.04305487e+08 8.23168732e+11 3.83731694e+08 + 4 1.14838594e+12 -1.80327850e+08 2.07321049e+12 -3.37071389e+08 + 5 -5.67969417e+10 -6.48286174e+08 -3.08173804e+11 -1.42033132e+09 + 6 -4.43334276e+11 7.76745901e+08 -6.60663693e+11 1.16224910e+09 + 7 -2.39949698e+11 1.91549121e+09 -2.11688596e+11 4.10250509e+09 + 8 -8.25169293e+10 -3.29030618e+09 -8.34055883e+10 -5.30631128e+09 + 9 1.10709729e+11 -9.63498062e+08 1.43925358e+11 -9.55428061e+08 + 10 1.22952895e+11 9.63660566e+08 1.42006409e+11 1.20778593e+09 + 11 1.81556776e+10 1.01235458e+09 -3.77156727e+09 1.28189128e+09 + 12 -1.59874801e+10 6.77216865e+07 -3.82312754e+10 -2.71328123e+08 + 13 -3.06214484e+08 1.47987972e+07 -1.14025890e+10 8.27692761e+06 + 14 5.64708397e+09 4.30521716e+08 6.59317901e+09 2.95799245e+08 + 15 -1.58971087e+10 1.16950587e+09 -6.10545279e+09 2.12164610e+08 + 16 3.27303843e+10 -6.64795093e+09 7.00186971e+09 -5.72579073e+08 + 17 1.19315848e+11 2.19890454e+09 -3.37643210e+09 3.69720514e+07 + 18 6.87731899e+10 -1.05883369e+09 -2.17439895e+09 1.69602426e+08 + 19 2.31209121e+09 -4.57926264e+09 -5.38563791e+08 -2.09857368e+08 + 20 -3.80054235e+10 1.76995847e+09 -2.84611003e+09 4.42268050e+08 + 21 -6.32056211e+10 -4.40291893e+08 -1.41210228e+10 -1.89302087e+08 + 22 4.09466435e+09 4.16530489e+08 -5.13591754e+09 -5.41133280e+05 + 23 1.36884053e+11 1.51489909e+09 5.60752713e+10 6.07203068e+08 + 24 3.91994814e+10 -8.37086924e+07 2.65391097e+10 1.57672536e+07 + 25 -1.64332885e+11 -2.03026261e+09 -1.01706677e+11 -1.28495786e+09 + 26 -7.32691869e+10 -2.67589940e+08 -5.69652394e+10 -2.27867476e+08 + 27 1.87218907e+11 2.24046767e+09 1.78902149e+11 2.09225302e+09 + 28 -6.35305521e+10 -9.41765520e+08 -8.54193101e+10 -1.20534017e+09 + 29 -4.52940293e+09 -7.12162044e+07 -2.97851956e+08 -1.28716562e+07 + 30 2.30548571e+09 3.27273456e+07 3.73648974e+09 7.48095843e+07 + 31 3.52207907e+09 5.74508617e+07 5.10446255e+09 9.44245368e+07 + 32 -3.44928748e+09 -5.45300996e+07 -5.47985421e+09 -1.15206104e+08 +Solution index = 30 + 1 -1.87481616e+01 1.25137812e+01 -4.72444854e+01 3.13580479e+01 + 2 1.43647526e+01 -9.60133293e+00 2.92207815e+01 -1.98257238e+01 + 3 1.33592150e+01 -8.90878111e+00 1.83260314e+01 -1.27239816e+01 + 4 6.31378079e+00 -4.16424172e+00 6.44733784e+00 -5.23938957e+00 + 5 1.01603433e+00 7.82554292e-01 4.23910776e+00 -8.45219254e-01 + 6 -1.57675357e+01 9.70974708e+00 -2.49027422e+01 1.37026784e+01 + 7 -1.01169122e+01 6.59864145e+00 -1.55300983e+01 8.77790719e+00 + 8 4.89352726e+00 -3.70992882e+00 5.47759282e+00 -6.47070376e+00 + 9 2.98290872e+00 -3.80527205e+00 -4.22869367e+00 -4.38643578e+00 + 10 1.99731521e+00 -5.87970898e-01 -7.04083311e+00 -2.58630825e-01 + 11 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26 1.26304480e-01 1.23633198e-01 -1.55846072e+00 -3.57704535e-01 + 27 -5.19251401e-02 1.54980767e-02 -9.40939599e-01 -1.68312410e-01 + 28 -3.48076389e-02 -1.07528590e-02 -6.30390373e-01 -8.29185247e-02 + 29 -2.54615051e-03 -1.20559123e-02 -4.26787164e-01 -4.42283185e-02 + 30 -5.30443865e-04 -6.25384830e-03 -2.92715454e-01 -2.77821272e-02 + 31 -3.61122771e-02 -1.59001206e-03 -2.36707451e-01 -1.86402570e-02 + 32 -5.63546870e-02 8.93228100e-05 -2.04997218e-01 -1.30632079e-02 +Solution index = 31 + 1 -1.20037752e+03 1.65811413e+02 -2.98625784e+03 4.11440827e+02 + 2 9.18006720e+02 -1.26478164e+02 1.93979014e+03 -2.69303701e+02 + 3 8.43634968e+02 -1.15921416e+02 1.30567607e+03 -1.83487535e+02 + 4 3.14492028e+02 -4.02806759e+01 6.12668723e+02 -8.87288224e+01 + 5 -9.56553969e+02 1.65460228e+02 -1.68584553e+03 3.01080093e+02 + 6 -3.28186117e+02 2.15588082e+01 -3.03101099e+02 3.37571645e+00 + 7 1.92341531e+02 -4.86316372e+01 4.01021061e+02 -7.83120394e+01 + 8 1.96180653e+02 -2.85339920e+01 2.60332430e+02 -2.89629531e+01 + 9 5.40849978e+01 7.50395034e-01 -2.12600982e+01 9.04361784e+00 + 10 2.95226560e+01 8.00412166e+00 -2.02794855e+02 1.07933517e+01 + 11 9.65015008e+01 3.94533922e+00 -3.79738601e+02 1.82728326e+00 + 12 8.40038009e+01 6.52216171e-01 -5.49893588e+02 -3.68231606e+00 + 13 -2.21863753e+01 -3.63065835e+00 -1.87912789e+02 -4.18230318e+01 + 14 7.85518691e+02 5.38800997e+00 1.84682650e+03 1.19128611e+01 + 15 3.29035684e+03 3.46950403e+01 8.63839554e+02 1.48801704e+01 + 16 -1.54211541e+04 -1.42078049e+02 -1.73020227e+03 -1.31464331e+01 + 17 -8.53163794e+03 2.22097746e+01 2.78749064e+02 8.86888931e-01 + 18 -3.63524638e+03 5.88614056e-01 4.31898804e+02 4.30846168e+00 + 19 -1.18218369e+03 -5.29163743e+01 3.02112957e+02 1.98974853e+00 + 20 -1.39510290e+02 -9.37838768e+01 1.68302092e+02 -1.13105147e+01 + 21 4.28444379e+01 -2.32024817e+01 5.68657440e+01 -1.26844077e+01 + 22 -2.61009154e+02 1.46328843e+02 -1.20378865e+02 3.64558398e+01 + 23 -2.76245742e+02 1.53384948e+02 -2.08762592e+02 6.68985558e+01 + 24 5.07425444e+02 -1.84698134e+02 2.26546340e+02 -1.09101298e+02 + 25 5.01399128e+01 -9.14222191e+00 -5.03073729e+01 1.29575563e+01 + 26 1.02110363e+01 -1.70535690e+00 -1.91533319e+01 6.08488148e+00 + 27 -3.11703797e+00 -4.39556539e-01 -4.53330060e+00 3.23252228e+00 + 28 -6.28945288e+00 -1.38663518e-01 8.40007763e-01 1.85267041e+00 + 29 -5.06003491e+00 -6.70749987e-02 1.66996453e+00 1.10616926e+00 + 30 -2.71083797e+00 -3.37385650e-02 8.28717793e-01 6.59483133e-01 + 31 -9.97046919e-01 1.21578110e-02 -3.64164480e-01 4.22434567e-01 + 32 -2.02876365e-01 4.58507127e-02 -1.26339781e+00 3.23081579e-01 +Solution index = 32 + 1 -4.21855522e+03 4.03764058e+00 -1.04655541e+04 1.03537378e+01 + 2 3.20764838e+03 -3.13039476e+00 6.85628215e+03 -6.02768321e+00 + 3 2.89544260e+03 -2.93353554e+00 4.73457564e+03 -3.34338705e+00 + 4 -4.35497225e+02 -2.54502265e-01 -1.80155688e+03 4.75101664e+00 + 5 -7.38862093e+01 -1.33145463e+01 4.14128370e+02 -2.68732822e+01 + 6 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21 1.63651780e+00 -2.04390069e-02 -3.97868611e+00 4.06667318e-02 + 22 -1.78775997e+01 2.23905450e-01 6.62755304e+00 -6.99935345e-02 + 23 -1.81917779e+01 2.27340779e-01 9.14084178e+00 -1.14454400e-01 + 24 -1.20445878e+01 1.43458045e-01 7.04554022e+00 -9.28955813e-02 + 25 -5.75020632e+00 7.15020689e-02 3.56908617e+00 -3.56047380e-02 + 26 -1.58056371e+00 1.58074139e-02 7.16600665e-01 4.14645122e-03 + 27 4.18276636e-01 -2.97984326e-03 -8.36593859e-01 1.66240252e-03 + 28 9.78987066e-01 -8.49389217e-03 -1.20155598e+00 -1.40274691e-02 + 29 8.57894535e-01 -1.78061994e-02 -9.66104811e-01 5.10959477e-02 + 30 4.64598914e-01 5.40634330e-03 -6.52481354e-01 -6.15144806e-05 + 31 2.76085580e-02 -9.36075364e-04 -3.36656246e-01 -4.85011732e-02 + 32 -1.70564879e-01 -3.96983012e-03 -2.30075621e-01 7.83099144e-02 diff --git a/test/test_data/sing_der_testing/mat_dat/sing_der_output_normal.dat b/test/test_data/sing_der_testing/mat_dat/sing_der_output_normal.dat new file mode 100644 index 00000000..76159126 --- /dev/null +++ b/test/test_data/sing_der_testing/mat_dat/sing_der_output_normal.dat @@ -0,0 +1,1060 @@ +psifac = 0.99999000 +q = 3.26298350 +mlow = -12 +nn = 1 +Solution index = 1 + 1 -7.65598407E+32 6.82874506E+31 9.06453153E+29 1.01614111E+31 + 2 5.98212901E+32 -5.24161765E+31 -7.38651700E+29 -8.43600409E+30 + 3 5.95786443E+32 -4.85612017E+31 -7.58117817E+29 -9.32229440E+30 + 4 1.65594088E+33 -2.27712630E+31 -4.25515191E+29 -3.01622945E+31 + 5 -5.54458954E+33 2.86027908E+31 5.34047363E+29 1.12288009E+32 + 6 5.49709534E+33 1.04350836E+31 1.97265429E+29 -1.28681094E+32 + 7 6.60097620E+33 -1.43672395E+32 -4.09369893E+30 -1.86284101E+32 + 8 -1.05215546E+34 2.78287051E+32 9.40206724E+30 3.49066918E+32 + 9 -4.38773778E+33 5.78524607E+31 2.71812383E+30 1.90895502E+32 + 10 4.09615090E+33 -5.93566591E+31 -2.55894177E+30 -2.24227251E+32 + 11 2.43406621E+33 -1.03758100E+32 -9.38350193E+30 -2.10151163E+32 + 12 -7.37293920E+31 -8.48122084E+30 -2.28343805E+30 5.71615727E+30 + 13 -4.79568328E+30 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= 24 + 1 4.46012779E+01 9.36816192E-05 6.80153067E-07 -3.23819627E-01 + 2 -4.12253145E+00 -3.02632163E-03 -2.39695206E-05 3.26518873E-02 + 3 -2.64608625E+02 2.51800982E-03 2.19378687E-05 2.30537199E+00 + 4 1.44434445E+01 5.07996184E-04 4.91762262E-06 -1.39818683E-01 + 5 1.35737201E+03 -8.60460089E-04 -9.37082471E-06 -1.47824313E+01 + 6 -3.01440757E+01 2.84341482E-03 3.53898720E-05 3.75181002E-01 + 7 -6.39187470E+03 -1.37610593E-03 -1.99819298E-05 9.28140971E+01 + 8 -3.83552124E+01 -1.56269215E-04 -2.72295142E-06 6.68330591E-01 + 9 2.72488778E+04 1.57176134E-04 3.42344194E-06 -5.93504493E+02 + 10 -4.13625916E+01 -3.06672420E-05 -8.90613985E-07 1.20122185E+00 + 11 -5.03114993E+03 7.34955219E-04 3.20160590E-05 2.19166453E+02 + 12 -1.28467343E+01 -1.07225663E-03 -9.34191309E-05 1.11925661E+00 + 13 -3.37565797E-05 1.90581611E-10 8.04900380E-05 -1.05725154E+02 + 14 -2.32705052E+01 1.21637498E-03 -1.05975222E-04 -2.02741469E+00 + 15 -1.04553400E+04 -8.79186817E-02 3.82990478E-03 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