mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-12 06:22:00 +00:00
mixed problem solution
This commit is contained in:
Jukka Aho
@@ -188,14 +188,14 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"30-Sep 09:08:39:INFO:root:Testing element MyQuad4\n",
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"30-Sep 09:08:39:INFO:root:number of basis functions in this element: 4\n",
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"30-Sep 09:08:39:INFO:root:Initializing element\n",
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"30-Sep 09:08:40:INFO:root:Element dimension: 2\n",
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"30-Sep 09:08:40:INFO:root:Creating new scalar field JuliaFEM.Field{Array{Int64,1}}(0.0,1,[1,2,3,4])\n",
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"30-Sep 09:08:40:INFO:root:Pushing field to element.\n",
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"30-Sep 09:08:40:INFO:root:Interpolating scalar field at [0.0,0.0]\n",
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"30-Sep 09:08:40:INFO:root:Value: 2.5\n"
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"07-Oct 09:28:37:INFO:root:Testing element MyQuad4\n",
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"07-Oct 09:28:37:INFO:root:number of basis functions in this element: 4\n",
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"07-Oct 09:28:37:INFO:root:Initializing element\n",
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"07-Oct 09:28:37:INFO:root:Element dimension: 2\n",
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"07-Oct 09:28:37:INFO:root:Creating new scalar field JuliaFEM.Field{Array{Int64,1}}(0.0,1,[1,2,3,4])\n",
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"07-Oct 09:28:37:INFO:root:Pushing field to element.\n",
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"07-Oct 09:28:38:INFO:root:Interpolating scalar field at [0.0,0.0]\n",
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"07-Oct 09:28:38:INFO:root:Value: 2.5\n"
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]
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},
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{
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@@ -244,7 +244,7 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"30-Sep 09:08:40:INFO:root:Element MyQuad4 passed tests.\n"
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"07-Oct 09:28:38:INFO:root:Element MyQuad4 passed tests.\n"
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]
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}
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],
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@@ -762,20 +762,22 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"30-Sep 09:08:43:DEBUG:root:Problem (matrix) dimension: 4\n"
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"07-Oct 09:28:41:DEBUG:root:total dofs: 4\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"dofmap: Dict(4=>[3],2=>[1],3=>[2],5=>[4])\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"(\n",
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"4x4 Array{Float64,2}:\n",
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" 4.0 -1.0 -2.0 -1.0\n",
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" -1.0 4.0 -1.0 -2.0\n",
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" -2.0 -1.0 4.0 -1.0\n",
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" -1.0 -2.0 -1.0 4.0,\n",
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"\n",
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"[300.0,300.0,0.0,0.0])"
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"4x1 sparse matrix with 2 Float64 entries:\n",
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"\t[1, 1] = 300.0\n",
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"\t[2, 1] = 300.0"
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]
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},
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"execution_count": 23,
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@@ -784,13 +786,14 @@
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}
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],
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"source": [
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"using JuliaFEM: set_global_dofs!, get_global_dofs, add_element!, get_equations, get_matrix_dimension\n",
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"using JuliaFEM: get_connectivity, set_global_dofs!, get_global_dofs\n",
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"using JuliaFEM: add_element!, get_equations, get_matrix_dimension\n",
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"\n",
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"# create elements and add necessary properties like connectivity and geometry\n",
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"el1 = Quad4([1, 2, 3, 4])\n",
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"el1 = Quad4([2, 3, 4, 5])\n",
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"new_field!(el1, :Geometry, Field(0.0, Vector[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]]))\n",
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"new_field!(el1, \"temperature thermal conductivity\", Field(0.0, 6.0))\n",
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"el2 = Seg2([1, 2])\n",
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"el2 = Seg2([2, 3])\n",
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"new_field!(el2, :Geometry, Field(0.0, Vector[[0.0, 0.0], [0.0, 1.0]]))\n",
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"new_field!(el2, \"temperature flux\", Field(1.0, 600.0))\n",
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"\n",
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@@ -798,25 +801,92 @@
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"add_element!(problem, el1)\n",
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"add_element!(problem, el2)\n",
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"\n",
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"# set global dofs for equations\n",
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"set_global_dofs!(problem)\n",
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"\n",
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"n = get_matrix_dimension(problem)\n",
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"\n",
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"# integrate and assembly\n",
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"t = 1.0\n",
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"A = zeros(n, n)\n",
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"b = zeros(n)\n",
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"for eq in get_equations(problem)\n",
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" dofs = get_global_dofs(eq)\n",
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" if has_lhs(eq)\n",
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" A[dofs, dofs] += integrate_lhs(eq, t)\n",
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"function JuliaFEM.get_connectivity(pr::Problem)\n",
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" conn = Int[]\n",
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" for eq in get_equations(pr)\n",
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" el = get_element(eq)\n",
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" append!(conn, get_connectivity(el))\n",
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" end\n",
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" if has_rhs(eq)\n",
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" b[dofs] += integrate_rhs(eq, t)\n",
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" conn = unique(conn)\n",
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" return conn\n",
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"end\n",
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"\n",
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"\"\"\"\n",
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"Calculate global dofs for equations, maybe using some bandwidth\n",
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"minimizing or fill reducing algorithm\n",
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"\"\"\"\n",
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"function calculate_global_dofs(pr::Problem)\n",
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" conn = get_connectivity(pr)\n",
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" dim = get_dimension(typeof(pr))\n",
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" ndofs = dim*length(conn)\n",
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" Logging.debug(\"total dofs: $ndofs\")\n",
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"\n",
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" mconn = maximum(conn)\n",
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" gdofs = reshape(collect(1:mconn), dim, mconn)\n",
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" dofmap = Dict{Int64, Array{Int64, 1}}()\n",
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" for (i, c) in enumerate(conn)\n",
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" dofmap[c] = gdofs[:, i]\n",
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" end\n",
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" return dofmap\n",
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"end\n",
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"\n",
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"\"\"\"\n",
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"Assign global dofs for equations.\n",
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"\"\"\"\n",
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"function assign_global_dofs!(pr::Problem, dofmap)\n",
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" for eq in get_equations(pr)\n",
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" el = get_element(eq)\n",
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" c = get_connectivity(el)\n",
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" #gdofs = [dofmap[ci] for ci in c]\n",
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" gdofs = Int64[]\n",
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" for ci in c\n",
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" append!(gdofs, dofmap[ci])\n",
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" end\n",
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" set_global_dofs!(eq, gdofs)\n",
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" end\n",
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"end\n",
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"A, b"
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"\n",
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"dofmap = calculate_global_dofs(problem)\n",
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"println(\"dofmap: $dofmap\")\n",
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"assign_global_dofs!(problem, dofmap)\n",
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"\n",
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"function get_lhs(pr::Problem, t::Float64)\n",
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" I = Int64[]\n",
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" J = Int64[]\n",
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" V = Float64[]\n",
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" dim = get_dimension(typeof(pr))\n",
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" for eq in filter(has_lhs, get_equations(pr))\n",
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" dofs = get_global_dofs(eq)\n",
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" lhs = integrate_lhs(eq, t)\n",
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" for (li, i) in enumerate(dofs)\n",
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" for (lj, j) in enumerate(dofs)\n",
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" push!(I, i)\n",
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" push!(J, j)\n",
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" push!(V, lhs[li, lj])\n",
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" end\n",
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" end\n",
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" end\n",
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" return I, J, V\n",
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"end\n",
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"\n",
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"function get_rhs(pr::Problem, t::Float64)\n",
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" I = Int64[]\n",
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" V = Float64[]\n",
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" dim = get_dimension(typeof(pr))\n",
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" for eq in filter(has_rhs, get_equations(pr))\n",
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" dofs = get_global_dofs(eq)\n",
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" rhs = integrate_rhs(eq, t)\n",
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" for (li, i) in enumerate(dofs)\n",
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" push!(I, i)\n",
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" push!(V, rhs[li])\n",
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" end\n",
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" end\n",
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" return I, V\n",
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"end\n",
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"\n",
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"t = 1.0\n",
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"A = sparse(get_lhs(problem, t)...)\n",
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"b = sparsevec(get_rhs(problem, t)..., size(A, 1))"
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]
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},
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{
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@@ -829,9 +899,9 @@
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{
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"data": {
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"text/plain": [
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"2-element Array{Float64,1}:\n",
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" 100.0\n",
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" 100.0"
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"2x1 sparse matrix with 2 Float64 entries:\n",
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"\t[1, 1] = 100.0\n",
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"\t[2, 1] = 100.0"
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]
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},
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"execution_count": 24,
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@@ -864,7 +934,7 @@
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{
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"data": {
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"text/plain": [
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"InterfaceProblem"
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"DirichletProblem"
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]
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},
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"execution_count": 25,
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@@ -873,15 +943,17 @@
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}
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],
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"source": [
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"type InterfaceProblem <: Problem\n",
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"abstract BoundaryProblem <: Problem\n",
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"\n",
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"type DirichletProblem <: BoundaryProblem\n",
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" equations :: Array{Equation, 1}\n",
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"end\n",
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"InterfaceProblem() = InterfaceProblem([])"
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"DirichletProblem() = DirichletProblem([])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"execution_count": 26,
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"metadata": {
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"collapsed": false
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},
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@@ -892,7 +964,7 @@
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"get_equation (generic function with 4 methods)"
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]
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},
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"execution_count": 48,
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"execution_count": 26,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -910,110 +982,62 @@
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" global_dofs :: Array{Int64, 1}\n",
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" fieldval :: Function\n",
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"end\n",
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"#function DBC2D2(el::Seg2, args...)\n",
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"function DBC2D2(el::Seg2)\n",
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" integration_points = [\n",
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" IntegrationPoint([-sqrt(1/3)], 1.0),\n",
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" IntegrationPoint([+sqrt(1/3)], 1.0)]\n",
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" new_field!(el, \"reaction force\")\n",
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" fieldval(X, t) = 0.0\n",
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"# if length(args) != 0\n",
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"# for (k, v) in args\n",
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"# if k == :fieldval\n",
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"# fieldval = v\n",
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"# end\n",
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"# end\n",
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"# end\n",
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" DBC2D2(el, integration_points, [], fieldval)\n",
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"end\n",
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"\n",
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"function JuliaFEM.get_lhs(eq::DBC2D2, ip, t)\n",
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" el = get_element(eq)\n",
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" h = get_basis(el)(ip.xi)\n",
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" println(\"basis h: $h\")\n",
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" out = h*h'\n",
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" return out\n",
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" return h*h'\n",
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"end\n",
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"\n",
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"function JuliaFEM.get_rhs(eq::DBC2D2, ip, t)\n",
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" el = get_element(eq)\n",
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" h = get_basis(el)\n",
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" #f = eq.fieldval\n",
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" #X = interpolate(el, :Geometry, ip.xi, t)\n",
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" #return h(ip.xi, t)*f(X, t)\n",
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" return [0.0, 0.0]\n",
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" f = eq.fieldval\n",
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" X = interpolate(el, :Geometry, ip.xi, t)\n",
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" return h(ip.xi)*f(X, t)\n",
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"end\n",
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"JuliaFEM.has_lhs(eq::DBC2D2) = true\n",
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"JuliaFEM.has_rhs(eq::DBC2D2) = true\n",
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"JuliaFEM.get_dimension(pr::Type{InterfaceProblem}) = 1\n",
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"JuliaFEM.get_equation(pr::Type{InterfaceProblem}, el::Type{Seg2}) = DBC2D2"
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"JuliaFEM.get_dimension(pr::Type{DirichletProblem}) = 1\n",
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"JuliaFEM.get_equation(pr::Type{DirichletProblem}, el::Type{Seg2}) = DBC2D2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"execution_count": 27,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"30-Sep 09:15:17:DEBUG:root:Problem (matrix) dimension: 2\n"
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]
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"lhs\n"
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]
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},
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{
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"ename": "LoadError",
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"evalue": "LoadError: MethodError: `call` has no method matching call(::JuliaFEM.Basis, ::Array{Float64,1}, ::Float64)\nClosest candidates are:\n BoundsError(!Matched::Any...)\n TypeVar(!Matched::Any...)\n TypeConstructor(!Matched::Any...)\n ...\nwhile loading In[49], in expression starting on line 17",
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"output_type": "error",
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"traceback": [
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"LoadError: MethodError: `call` has no method matching call(::JuliaFEM.Basis, ::Array{Float64,1}, ::Float64)\nClosest candidates are:\n BoundsError(!Matched::Any...)\n TypeVar(!Matched::Any...)\n TypeConstructor(!Matched::Any...)\n ...\nwhile loading In[49], in expression starting on line 17",
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"",
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" in get_lhs at In[48]:32",
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" in integrate at /home/jukka/.julia/v0.4/JuliaFEM/src/equations.jl:69",
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" in integrate_lhs at /home/jukka/.julia/v0.4/JuliaFEM/src/equations.jl:36",
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" [inlined code] from In[49]:21",
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" in anonymous at no file:0"
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]
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"data": {
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"text/plain": [
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"1-element Array{JuliaFEM.Equation,1}:\n",
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" DBC2D2(JuliaFEM.Seg2([4,5],JuliaFEM.Basis(basis,j),Dict(:Geometry=>JuliaFEM.Field[JuliaFEM.Field{Array{Array{T,1},1}}(0.0,1,Array{T,1}[[0.0,0.0],[0.0,1.0]])],symbol(\"reaction force\")=>JuliaFEM.Field[])),[JuliaFEM.IntegrationPoint([-0.5773502691896257],1.0,Dict{Any,Any}()),JuliaFEM.IntegrationPoint([0.5773502691896257],1.0,Dict{Any,Any}())],Int64[],fieldval)"
|
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]
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},
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"execution_count": 27,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# create elements and add necessary properties like connectivity and geometry\n",
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"el3 = Seg2([1, 2])\n",
|
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"new_field!(el2, :Geometry, Field(0.0, Vector[[0.0, 0.0], [0.0, 1.0]]))\n",
|
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"el3 = Seg2([4, 5])\n",
|
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"new_field!(el3, :Geometry, Field(0.0, Vector[[0.0, 0.0], [0.0, 1.0]]))\n",
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"\n",
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"bc1 = InterfaceProblem()\n",
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"add_element!(bc1, el3)\n",
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"\n",
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"# set global dofs for equations\n",
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"set_global_dofs!(bc1)\n",
|
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"\n",
|
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"n = get_matrix_dimension(bc1)\n",
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"\n",
|
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"# integrate and assembly\n",
|
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"t = 1.0\n",
|
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"A = zeros(n, n)\n",
|
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"b = zeros(n)\n",
|
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"for eq in get_equations(bc1)\n",
|
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" dofs = get_global_dofs(eq)\n",
|
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" println(\"lhs\")\n",
|
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" if has_lhs(eq)\n",
|
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" A[dofs, dofs] += integrate_lhs(eq, t)\n",
|
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" end\n",
|
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" println(\"rhs\")\n",
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" if has_rhs(eq)\n",
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" b[dofs] += integrate_rhs(eq, t)\n",
|
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" end\n",
|
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"end\n",
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"A2, b2"
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"bc1 = DirichletProblem()\n",
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"#get_equation(typeof(bc1), typeof(el3))\n",
|
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"#DBC2D2(el3)\n",
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"add_element!(bc1, el3)"
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]
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},
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{
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@@ -1026,7 +1050,9 @@
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{
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"data": {
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"text/plain": [
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"DBC2D2"
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"4x1 sparse matrix with 2 Float64 entries:\n",
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"\t[3, 1] = 0.0\n",
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"\t[4, 1] = 0.0"
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]
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},
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"execution_count": 28,
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@@ -1035,7 +1061,21 @@
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}
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],
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"source": [
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"JuliaFEM.get_equation(typeof(bc1), typeof(el3))"
|
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"assign_global_dofs!(bc1, dofmap)\n",
|
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"\n",
|
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"# integrate and assembly\n",
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"t = 1.0\n",
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"A2 = sparse(get_lhs(bc1, t)...)\n",
|
||||
"b2 = sparsevec(get_rhs(bc1, t)...)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"source": [
|
||||
"Now we have two problems defined, "
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -1048,7 +1088,11 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"DBC2D2(JuliaFEM.Seg2([1,2],JuliaFEM.Basis(basis,j),Dict(symbol(\"reaction force\")=>JuliaFEM.Field[])),[JuliaFEM.IntegrationPoint([-0.5773502691896257],1.0,Dict{Any,Any}()),JuliaFEM.IntegrationPoint([0.5773502691896257],1.0,Dict{Any,Any}())],Int64[],fieldval)"
|
||||
"4x4 Array{Float64,2}:\n",
|
||||
" 4.0 -1.0 -2.0 -1.0\n",
|
||||
" -1.0 4.0 -1.0 -2.0\n",
|
||||
" -2.0 -1.0 4.0 -1.0\n",
|
||||
" -1.0 -2.0 -1.0 4.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 29,
|
||||
@@ -1057,7 +1101,7 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"DBC2D2(el3)"
|
||||
"full(A)"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -1070,7 +1114,11 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"JuliaFEM.Seg2([1,2],JuliaFEM.Basis(basis,j),Dict(symbol(\"reaction force\")=>JuliaFEM.Field[]))"
|
||||
"4x1 Array{Float64,2}:\n",
|
||||
" 300.0\n",
|
||||
" 300.0\n",
|
||||
" 0.0\n",
|
||||
" 0.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 30,
|
||||
@@ -1079,8 +1127,219 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"el3"
|
||||
"full(b)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"4x4 Array{Float64,2}:\n",
|
||||
" 0.0 0.0 0.0 0.0 \n",
|
||||
" 0.0 0.0 0.0 0.0 \n",
|
||||
" 0.0 0.0 0.333333 0.166667\n",
|
||||
" 0.0 0.0 0.166667 0.333333"
|
||||
]
|
||||
},
|
||||
"execution_count": 31,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"full(A2)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"4x1 Array{Float64,2}:\n",
|
||||
" 0.0\n",
|
||||
" 0.0\n",
|
||||
" 0.0\n",
|
||||
" 0.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 32,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"full(b2)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"8x8 sparse matrix with 24 Float64 entries:\n",
|
||||
"\t[1, 1] = 4.0\n",
|
||||
"\t[2, 1] = -1.0\n",
|
||||
"\t[3, 1] = -2.0\n",
|
||||
"\t[4, 1] = -1.0\n",
|
||||
"\t[1, 2] = -1.0\n",
|
||||
"\t[2, 2] = 4.0\n",
|
||||
"\t[3, 2] = -1.0\n",
|
||||
"\t[4, 2] = -2.0\n",
|
||||
"\t[1, 3] = -2.0\n",
|
||||
"\t[2, 3] = -1.0\n",
|
||||
"\t⋮\n",
|
||||
"\t[8, 3] = 0.166667\n",
|
||||
"\t[1, 4] = -1.0\n",
|
||||
"\t[2, 4] = -2.0\n",
|
||||
"\t[3, 4] = -1.0\n",
|
||||
"\t[4, 4] = 4.0\n",
|
||||
"\t[7, 4] = 0.166667\n",
|
||||
"\t[8, 4] = 0.333333\n",
|
||||
"\t[3, 7] = 0.333333\n",
|
||||
"\t[4, 7] = 0.166667\n",
|
||||
"\t[3, 8] = 0.166667\n",
|
||||
"\t[4, 8] = 0.333333"
|
||||
]
|
||||
},
|
||||
"execution_count": 33,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"Atot = [A A2; A2 zeros(A2)]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"8x1 sparse matrix with 4 Float64 entries:\n",
|
||||
"\t[1, 1] = 300.0\n",
|
||||
"\t[2, 1] = 300.0\n",
|
||||
"\t[7, 1] = 0.0\n",
|
||||
"\t[8, 1] = 0.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 34,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"btot = [b; b2]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Problem is that now are total matrix Atot has zero rows which needs to be removed."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 36,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"8x8 Array{Float64,2}:\n",
|
||||
" 4.0 -1.0 -2.0 -1.0 0.0 0.0 0.0 0.0 \n",
|
||||
" -1.0 4.0 -1.0 -2.0 0.0 0.0 0.0 0.0 \n",
|
||||
" -2.0 -1.0 4.0 -1.0 0.0 0.0 0.333333 0.166667\n",
|
||||
" -1.0 -2.0 -1.0 4.0 0.0 0.0 0.166667 0.333333\n",
|
||||
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n",
|
||||
" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 \n",
|
||||
" 0.0 0.0 0.333333 0.166667 0.0 0.0 0.0 0.0 \n",
|
||||
" 0.0 0.0 0.166667 0.333333 0.0 0.0 0.0 0.0 "
|
||||
]
|
||||
},
|
||||
"execution_count": 36,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"full(Atot)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Unique rows: [1,2,3,4,7,8]\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"8x1 Array{Float64,2}:\n",
|
||||
" 100.0\n",
|
||||
" 100.0\n",
|
||||
" 0.0\n",
|
||||
" 0.0\n",
|
||||
" 0.0\n",
|
||||
" 0.0\n",
|
||||
" 600.0\n",
|
||||
" 600.0"
|
||||
]
|
||||
},
|
||||
"execution_count": 37,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"r = unique(rowvals(Atot))\n",
|
||||
"println(\"Unique rows: $r\")\n",
|
||||
"xtot = zeros(btot)\n",
|
||||
"F = lufact(Atot[r,r])\n",
|
||||
"s = full(btot[r])\n",
|
||||
"xtot[r] = F \\ s\n",
|
||||
"full(xtot)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
||||
Reference in New Issue
Block a user