{ "cells": [ { "cell_type": "markdown", "source": [ "# Layouts versus drawings of wiring diagrams\n", "\n", "\n", "In Catlab, layout and drawing (rendering) of wiring diagrams are mostly\n", "decoupled. This notebook shows how to lay out diagrams using Graphviz's\n", "rank-based layout or Catlab's series-parallel layout and then render them\n", "using Compose.jl or TikZ." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "The morphism we will visualize is:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "f⊗(f⋅g)⊗(f⋅g⋅h): X⊗X⊗X → X⊗X⊗X", "text/latex": "$f \\otimes \\left(f \\cdot g\\right) \\otimes \\left(f \\cdot g \\cdot h\\right) : X \\otimes X \\otimes X \\to X \\otimes X \\otimes X$" }, "metadata": {}, "execution_count": 1 } ], "cell_type": "code", "source": [ "using Catlab.Theories\n", "\n", "X = Ob(FreeSymmetricMonoidalCategory, :X)\n", "f, g, h = (Hom(sym, X, X) for sym in (:f, :g, :h))\n", "\n", "expr = otimes(f, compose(f,g), compose(f,g,h))" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Let's convert this expression into a wiring diagram. This yields a purely\n", "combinatorial object, as evidenced by its underlying graph." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Catlab.WiringDiagrams.DirectedWiringDiagrams.WiringDiagramGraphACSet{Int64} with elements V = 1:8, E = 1:9\n┌───┬─────┐\n│ V │ box │\n├───┼─────┤\n│ 1 │ 1 │\n│ 2 │ 2 │\n│ 3 │ 3 │\n│ 4 │ 4 │\n│ 5 │ 5 │\n│ 6 │ 6 │\n│ 7 │ -2 │\n│ 8 │ -1 │\n└───┴─────┘\n┌───┬─────┬─────┬──────┐\n│ E │ src │ tgt │ wire │\n├───┼─────┼─────┼──────┤\n│ 1 │ 2 │ 3 │ 1 │\n│ 2 │ 5 │ 6 │ 2 │\n│ 3 │ 4 │ 5 │ 3 │\n│ 4 │ 7 │ 1 │ 1 │\n│ 5 │ 7 │ 2 │ 2 │\n│ 6 │ 7 │ 4 │ 3 │\n│ 7 │ 1 │ 8 │ 1 │\n│ 8 │ 3 │ 8 │ 2 │\n│ 9 │ 6 │ 8 │ 3 │\n└───┴─────┴─────┴──────┘\n", "text/html": [ "
\n", "Catlab.WiringDiagrams.DirectedWiringDiagrams.WiringDiagramGraphACSet{Int64} with elements V = 1:8, E = 1:9\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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\n" ] }, "metadata": {}, "execution_count": 2 } ], "cell_type": "code", "source": [ "using Catlab.WiringDiagrams, Catlab.Graphics\n", "\n", "diagram = to_wiring_diagram(expr)\n", "WiringDiagrams.graph(diagram)" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "## Graphviz layout" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Calling to_graphviz both lays out and draws the diagram, entirely within\n", "Graphviz." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"dot\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Subgraph(\"\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n0in1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"in1\")), Catlab.Graphics.Graphviz.Node(\"n0in2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"in2\")), Catlab.Graphics.Graphviz.Node(\"n0in3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"in3\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n0in1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n0in2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n0in3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rank => \"source\", :rankdir => \"TB\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\", :shape => \"none\", :label => \"\", :width => \"0\", :height => \"0.333\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\")), Catlab.Graphics.Graphviz.Subgraph(\"\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n0out1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"out1\")), Catlab.Graphics.Graphviz.Node(\"n0out2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"out2\")), Catlab.Graphics.Graphviz.Node(\"n0out3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"out3\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n0out1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n0out2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n0out3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rank => \"sink\", :rankdir => \"TB\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\", :shape => \"none\", :label => \"\", :width => \"0\", :height => \"0.333\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\")), Catlab.Graphics.Graphviz.Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:color => \"black\", :comment => \"f\", :fillcolor => \"white\", :id => \"n1\", :label => Catlab.Graphics.Graphviz.Html(\"\\n\\n\\n\\n\\n\\n
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We\n", "can then render this layout using Compose.jl. 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Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}((1.0w + -1.0mm, 1.0h + -1.0mm), 1.0mm, 0.0, 1.5707963267948966, false)], Symbol(\"\")), Compose.Form{Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}((1.0mm, 1.0h + -1.0mm), 1.0mm, 1.5707963267948966, 3.141592653589793, false)], Symbol(\"\")), Compose.Form{Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.AbsoluteLength}((1.0w + -1.0mm, 1.0mm), 1.0mm, 4.71238898038469, 0.0, false)], Symbol(\"\")), Compose.Form{Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}, Measures.AbsoluteLength}((1.0mm, 1.0mm), 1.0mm, 3.141592653589793, 4.71238898038469, false)], Symbol(\"\")), Compose.Form{Compose.LinePrimitive}(Compose.LinePrimitive[Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(1.0mm, 0.0h), (1.0w + -1.0mm, 0.0h)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(0.0w, 1.0mm), (0.0w, 1.0h + -1.0mm)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(1.0mm, 1.0h), (1.0w + -1.0mm, 1.0h)]), Compose.LinePrimitive{Tuple{Measures.Measure, Measures.Measure}}(Tuple{Measures.Measure, Measures.Measure}[(1.0w, 1.0mm), (1.0w, 1.0h + -1.0mm)])], Symbol(\"\"))]), List([]), 2, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\")), Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([]), List([Compose.Form{Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}((1.0w + -1.0mm, 1.0h + -1.0mm), 1.0mm, 0.0, 1.5707963267948966, true)], Symbol(\"\")), Compose.Form{Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}}, Measures.AbsoluteLength}((1.0mm, 1.0h + -1.0mm), 1.0mm, 1.5707963267948966, 3.141592653589793, true)], Symbol(\"\")), Compose.Form{Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.AbsoluteLength}((1.0w + -1.0mm, 1.0mm), 1.0mm, 4.71238898038469, 0.0, true)], Symbol(\"\")), Compose.Form{Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}, Measures.AbsoluteLength}}(Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}, Measures.AbsoluteLength}[Compose.ArcPrimitive{Tuple{Measures.AbsoluteLength, Measures.AbsoluteLength}, Measures.AbsoluteLength}((1.0mm, 1.0mm), 1.0mm, 3.141592653589793, 4.71238898038469, true)], Symbol(\"\")), Compose.Form{Compose.RectanglePrimitive{Tuple{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Length{:w, Float64}, Measures.Add{Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}}}(Compose.RectanglePrimitive{Tuple{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Length{:w, Float64}, Measures.Add{Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}}[Compose.RectanglePrimitive{Tuple{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.Length{:w, Float64}, Measures.Add{Measures.Add{Measures.Length{:h, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}}((0.0w, 0.7354497354497354mm), 1.0w, 1.0h + -2.0mm + 0.5291005291005292mm)], Symbol(\"\")), Compose.Form{Compose.RectanglePrimitive{Tuple{Measures.AbsoluteLength, Measures.Length{:h, Float64}}, Measures.Add{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.Length{:h, Float64}}}(Compose.RectanglePrimitive{Tuple{Measures.AbsoluteLength, Measures.Length{:h, Float64}}, Measures.Add{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.Length{:h, Float64}}[Compose.RectanglePrimitive{Tuple{Measures.AbsoluteLength, Measures.Length{:h, Float64}}, Measures.Add{Measures.Add{Measures.Length{:w, Float64}, Measures.AbsoluteLength}, Measures.AbsoluteLength}, Measures.Length{:h, Float64}}((0.7354497354497354mm, 0.0h), 1.0w + -2.0mm + 0.5291005291005292mm, 1.0h)], Symbol(\"\"))]), List([Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))])]), 1, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([Compose.Property{Compose.FillPrimitive}(Compose.FillPrimitive[Compose.FillPrimitive(RGBA{Float64}(0.0,0.0,0.0,0.0))]), Compose.Property{Compose.StrokePrimitive}(Compose.StrokePrimitive[Compose.StrokePrimitive(RGBA{Float64}(0.0,0.0,0.0,1.0))])]), 1, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, Symbol(\"\"))]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, :box)]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, :boxes)]), List([]), List([]), 0, false, false, false, false, nothing, nothing, 0.0, :diagram), 71.2611111111111mm, 38.80555555555555mm)", "text/html": [ "\n", "\n" ], "image/svg+xml": [ "\n", "\n" ] }, "metadata": {}, "execution_count": 4 } ], "cell_type": "code", "source": [ "import Compose\n", "\n", "layout = graphviz_layout(diagram, orientation=LeftToRight)\n", "layout_to_composejl(layout, base_unit=Compose.pt)" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "The same layout can be rendered in TikZ:" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Catlab.Graphics.TikZ.Document(Catlab.Graphics.TikZ.Picture(Catlab.Graphics.TikZ.Statement[Catlab.Graphics.TikZ.Node(\"root\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"outer box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"202\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"110\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"0\", \"0\"), \"\"), Catlab.Graphics.TikZ.Node(\"n1\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"16\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"25\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"54\", \"42.5\"), \"\\$f\\$\"), Catlab.Graphics.TikZ.Node(\"n2\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"16\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"25\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"-56\", \"0.5\"), \"\\$f\\$\"), Catlab.Graphics.TikZ.Node(\"n3\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"20\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"25\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"-2\", \"0.5\"), \"\\$g\\$\"), Catlab.Graphics.TikZ.Node(\"n4\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"16\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"25\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"-56\", \"-42.5\"), \"\\$f\\$\"), Catlab.Graphics.TikZ.Node(\"n5\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"20\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"25\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"-2\", \"-42.5\"), \"\\$g\\$\"), Catlab.Graphics.TikZ.Node(\"n6\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"box\", nothing), Catlab.Graphics.TikZ.Property(\"minimum width\", \"20\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"minimum height\", \"25\\\\tikzunit\")], Catlab.Graphics.TikZ.Coordinate(\"54\", \"-42.5\"), \"\\$h\\$\"), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"\\$(root.west)+(-0.0,41.5)\\$\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"-180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"n1.west\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"\\$(root.west)+(-0.0,-0.5)\\$\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"-180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"n2.west\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"\\$(root.west)+(-0.0,-42.5)\\$\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"-180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"n4.west\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"n2.east\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"-180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"n3.west\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"n4.east\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"-180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"n5.west\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"n5.east\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"-180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"n6.west\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"n1.east\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"\\$(root.east)+(0.0,41.5)\\$\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"n3.east\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"\\$(root.east)+(0.0,-0.5)\\$\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)]), Catlab.Graphics.TikZ.Edge(Catlab.Graphics.TikZ.PathExpression[Catlab.Graphics.TikZ.NodeCoordinate(\"n6.east\"), Catlab.Graphics.TikZ.PathOperation(\"to\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"out\", \"0\"), Catlab.Graphics.TikZ.Property(\"in\", \"180\")]), Catlab.Graphics.TikZ.NodeCoordinate(\"\\$(root.east)+(0.0,-42.5)\\$\")], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"wire\", nothing)])], Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"unit length/.code\", \"{{\\\\newdimen\\\\tikzunit}\\\\setlength{\\\\tikzunit}{#1}}\"), Catlab.Graphics.TikZ.Property(\"unit length\", \"1pt\"), Catlab.Graphics.TikZ.Property(\"x\", \"\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"y\", \"\\\\tikzunit\"), Catlab.Graphics.TikZ.Property(\"semithick\", nothing), Catlab.Graphics.TikZ.Property(\"box/.style\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"rectangle\", nothing), Catlab.Graphics.TikZ.Property(\"draw\", nothing), Catlab.Graphics.TikZ.Property(\"solid\", nothing), Catlab.Graphics.TikZ.Property(\"rounded corners\", nothing)]), Catlab.Graphics.TikZ.Property(\"outer box/.style\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"draw\", \"none\")]), Catlab.Graphics.TikZ.Property(\"wire/.style\", Catlab.Graphics.TikZ.Property[Catlab.Graphics.TikZ.Property(\"draw\", nothing)])]), [\"calc\", \"shapes.geometric\"], [\"amssymb\"])", "image/svg+xml": [ "\n", "\n", "\n" ] }, "metadata": {}, "execution_count": 5 } ], "cell_type": "code", "source": [ "import TikzPictures\n", "\n", "layout_to_tikz(layout, base_unit=\"1pt\")" ], "metadata": {}, "execution_count": 5 }, { "cell_type": "markdown", "source": [ "## Series-parallel layout" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "Catlab has its own layout system based on series-parallel decomposition. In\n", "this case, the layout exactly recovers the structure of the morphism\n", "expression created at the beginning." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "ComposePicture(Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), Compose.UnitBox{Float64, Float64, Float64, Float64}(-7.0, -5.0, 14.0, 10.0, 0.0mm, 0.0mm, 0.0mm, 0.0mm), nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), (1.0w, 1.0h)), nothing, nothing, nothing, nothing, List([Compose.Context(Measures.BoundingBox{Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}, Tuple{Measures.Length{:w, Float64}, Measures.Length{:h, Float64}}}((0.0w, 0.0h), 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