examples update

iitis · Jul 10, 2019 · 1aae7aa · 1aae7aa
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diff --git a/examples/ex01_path_propagation.ipynb b/examples/ex01_path_propagation.ipynb
@@ -22,7 +22,8 @@
    "source": [
     "using QSWalk\n",
     "using PyPlot # for plot\n",
-    "using LightGraphs # for PathGraph"
+    "using LightGraphs # for PathGraph\n",
+    "using LinearAlgebra # for diag method"
    ]
   },
   {
@@ -48,10 +49,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "dim = 251 # odd for unique middle point\n",
+    "dim = 151 # odd for unique middle point\n",
     "midpoint = ceil(Int, dim/2)\n",
     "w = 0.5\n",
-    "timepoint = 100.\n",
+    "timepoint = 50.\n",
     "adjacency = adjacency_matrix(PathGraph(dim));"
    ]
   },
@@ -109,7 +110,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "positions = (collect(1:dim) - midpoint)\n",
+    "positions = (collect(1:dim) .- midpoint)\n",
     "plot(positions, real.(diag(rho_local)), \"k\")\n",
     "plot(positions, real.(diag(rho_global)), \"b\")\n",
     "xlabel(\"position\")\n",
@@ -140,10 +141,10 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "dim = 251 #odd for unique middle point\n",
+    "dim = 151 #odd for unique middle point\n",
     "midpoint = ceil(Int, dim/2)\n",
     "w = 0.5\n",
-    "timepoints = collect(0:5:100)\n",
+    "timepoints = collect(0:2.5:50)\n",
     "adjacency = adjacency_matrix(PathGraph(dim));"
    ]
   },
@@ -199,7 +200,7 @@
    "source": [
     "secmoment_global = Float64[]\n",
     "secmoment_local = Float64[]\n",
-    "positions = (collect(1:dim) - midpoint)\n",
+    "positions = (collect(1:dim) .- midpoint)\n",
     "\n",
     "for (rho_global, rho_local) = zip(global_states, local_states)\n",
     "  push!(secmoment_global, sum(positions.^2 .* diag(rho_global)))\n",
@@ -231,16 +232,20 @@
   }
  ],
  "metadata": {
+  "@webio": {
+   "lastCommId": null,
+   "lastKernelId": null
+  },
   "kernelspec": {
-   "display_name": "Julia 0.6.0",
+   "display_name": "Julia 1.0.1",
    "language": "julia",
-   "name": "julia-0.6"
+   "name": "julia-1.0"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "0.6.0"
+   "version": "1.0.1"
   }
  },
  "nbformat": 4,

diff --git a/examples/ex01_path_propagation.jl b/examples/ex01_path_propagation.jl
@@ -1,4 +1,4 @@
-
+#!/usr/bin/env python
 # coding: utf-8
 
 # # Propagation on the path graph
@@ -8,17 +8,18 @@
 using QSWalk
 using PyPlot # for plot
 using LightGraphs # for PathGraph
+using LinearAlgebra # for diag method
 
 
 # ## Evolution on path graph for fixed time, global vs local interaction
 
 # Basic parameters. Note that *dim* should be an odd number. Otherwise the middle point *midpoint* is not unique. Matrix
 # *adjacency* can be alternatively generated as *adjacency = spdiagm((ones(dim-1), ones(dim-1)), (-1, 1))*.
 
-dim = 251 # odd for unique middle point
+dim = 151 # odd for unique middle point
 midpoint = ceil(Int, dim/2)
 w = 0.5
-timepoint = 100.
+timepoint = 50.
 adjacency = adjacency_matrix(PathGraph(dim));
 
 
@@ -37,7 +38,7 @@ rho_local = evolve(op_local, proj(midpoint, dim), timepoint);
 
 # To plot the result of the cannonical measurement, we take a diagonal of the states. Note that both *rhoglobal* and *rholocal* are complex matrices, hence we need to take the real part only. Argument *positions* is generated assuming that *midpoint* (the initial position) is at 0. Note that we have very heavy tails in the global interaction case, which confirms fast propagation in this model.
 
-positions = (collect(1:dim) - midpoint)
+positions = (collect(1:dim) .- midpoint)
 plot(positions, real.(diag(rho_local)), "k")
 plot(positions, real.(diag(rho_global)), "b")
 xlabel("position")
@@ -50,10 +51,10 @@ show()
 # Basic parameters. Note that *dim* should be an odd number. Otherwise the middle point *midpoint* is not unique. Matrix
 # *adjacency* can be alternatively generated as *adjacency = spdiagm((ones(dim-1), ones(dim-1)), (-1, 1))*.
 
-dim = 251 #odd for unique middle point
+dim = 151 #odd for unique middle point
 midpoint = ceil(Int, dim/2)
 w = 0.5
-timepoints = collect(0:5:100)
+timepoints = collect(0:2.5:50)
 adjacency = adjacency_matrix(PathGraph(dim));
 
 
@@ -74,7 +75,7 @@ local_states = evolve(op_local, proj(midpoint, dim), timepoints);
 
 secmoment_global = Float64[]
 secmoment_local = Float64[]
-positions = (collect(1:dim) - midpoint)
+positions = (collect(1:dim) .- midpoint)
 
 for (rho_global, rho_local) = zip(global_states, local_states)
   push!(secmoment_global, sum(positions.^2 .* diag(rho_global)))

diff --git a/examples/ex02_convergence.ipynb b/examples/ex02_convergence.ipynb
@@ -22,7 +22,8 @@
    "source": [
     "using QSWalk\n",
     "using LightGraphs # for graph functions \n",
-    "using GraphPlot # for ploting graphs "
+    "using GraphPlot # for ploting graphs \n",
+    "using LinearAlgebra # for linear algebra utilities"
    ]
   },
   {
@@ -52,8 +53,8 @@
     "digraph = erdos_renyi(dim, prob, is_directed=true)\n",
     "graph = Graph(digraph)\n",
     "\n",
-    "adj_digraph = full(adjacency_matrix(digraph, dir=:in))\n",
-    "adj_graph = full(adjacency_matrix(graph))\n",
+    "adj_digraph = Matrix(adjacency_matrix(digraph, dir=:in))\n",
+    "adj_graph = Matrix(adjacency_matrix(graph))\n",
     "time = 100.\n",
     "\n",
     "println(\"The graph is strongly connected: $(is_strongly_connected(digraph))\")\n",
@@ -107,13 +108,13 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "eigendecomposition = eigfact(evo_gen)\n",
-    "zeroindex = find(x -> abs(x)<=1.e-5, eigendecomposition[:values])\n",
-    "stationary_state = unres(vec(eigendecomposition[:vectors][:, zeroindex]))\n",
+    "eigendecomposition = eigen(evo_gen)\n",
+    "zeroindex = findfirst(x -> abs(x)<=1.e-5, eigendecomposition.values)\n",
+    "stationary_state = unres(vec(eigendecomposition.vectors[:, zeroindex]))\n",
     "\n",
-    "println(\"Trace of stationary state: $(trace(stationary_state))\")\n",
-    "stationary_state /= trace(stationary_state)\n",
-    "println(\"Trace of stationary state after the normalization: $(trace(stationary_state))\")"
+    "println(\"Trace of stationary state: $(sum(diag(stationary_state)))\")\n",
+    "stationary_state /= sum(diag(stationary_state))\n",
+    "println(\"Trace of stationary state after the normalization: $(sum(diag(stationary_state)))\")"
    ]
   },
   {
@@ -138,7 +139,7 @@
    "source": [
     "rhoinit1 = proj(1, dim)\n",
     "rhoinit2 = proj(3, dim)\n",
-    "rhoinit3 = eye(dim)/dim;"
+    "rhoinit3 = Diagonal(I,dim)/dim"
    ]
   },
   {
@@ -180,16 +181,20 @@
   }
  ],
  "metadata": {
+  "@webio": {
+   "lastCommId": null,
+   "lastKernelId": null
+  },
   "kernelspec": {
-   "display_name": "Julia 0.6.0",
+   "display_name": "Julia 1.0.1",
    "language": "julia",
-   "name": "julia-0.6"
+   "name": "julia-1.0"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "0.6.0"
+   "version": "1.0.1"
   }
  },
  "nbformat": 4,

diff --git a/examples/ex02_convergence.jl b/examples/ex02_convergence.jl
@@ -1,4 +1,4 @@
-
+#!/usr/bin/env python
 # coding: utf-8
 
 # # Convergence on local interaction model
@@ -9,6 +9,7 @@
 using QSWalk
 using LightGraphs # for graph functions 
 using GraphPlot # for ploting graphs 
+using LinearAlgebra # for linear algebra utilities
 
 
 # ## Numerical proof of unique stationary state
@@ -22,8 +23,8 @@ prob = 0.5
 digraph = erdos_renyi(dim, prob, is_directed=true)
 graph = Graph(digraph)
 
-adj_digraph = full(adjacency_matrix(digraph, dir=:in))
-adj_graph = full(adjacency_matrix(graph))
+adj_digraph = Matrix(adjacency_matrix(digraph, dir=:in))
+adj_graph = Matrix(adjacency_matrix(graph))
 time = 100.
 
 println("The graph is strongly connected: $(is_strongly_connected(digraph))")
@@ -44,13 +45,13 @@ println("Dimensionality of null-space of the evolution operator: $null_dim")
 
 # This allows efficient stationary state generation. Note that the trace may differ from one, as the eigenstate is normalized according to different norm.
 
-eigendecomposition = eigfact(evo_gen)
-zeroindex = find(x -> abs(x)<=1.e-5, eigendecomposition[:values])
-stationary_state = unres(vec(eigendecomposition[:vectors][:, zeroindex]))
+eigendecomposition = eigen(evo_gen)
+zeroindex = findfirst(x -> abs(x)<=1.e-5, eigendecomposition.values)
+stationary_state = unres(vec(eigendecomposition.vectors[:, zeroindex]))
 
-println("Trace of stationary state: $(trace(stationary_state))")
-stationary_state /= trace(stationary_state)
-println("Trace of stationary state after the normalization: $(trace(stationary_state))")
+println("Trace of stationary state: $(sum(diag(stationary_state)))")
+stationary_state /= sum(diag(stationary_state))
+println("Trace of stationary state after the normalization: $(sum(diag(stationary_state)))")
 
 
 # ## Convergence
@@ -59,7 +60,7 @@ println("Trace of stationary state after the normalization: $(trace(stationary_s
 
 rhoinit1 = proj(1, dim)
 rhoinit2 = proj(3, dim)
-rhoinit3 = eye(dim)/dim;
+rhoinit3 = Diagonal(I,dim)/dim
 
 
 # Since we apply the same evolution for all of the initial states, it is more efficient to calulate exponent once.

diff --git a/examples/ex03_moralization_simple.ipynb b/examples/ex03_moralization_simple.ipynb
@@ -21,8 +21,9 @@
    "outputs": [],
    "source": [
     "using QSWalk\n",
-    "using TikzGraphs # For plotting graph\n",
-    "using LightGraphs "
+    "using GraphPlot # For plotting graph\n",
+    "using LightGraphs \n",
+    "using LinearAlgebra"
    ]
   },
   {
@@ -49,7 +50,7 @@
     "add_edge!(digraph, 1, 3)\n",
     "add_edge!(digraph, 2, 3)\n",
     "\n",
-    "TikzGraphs.plot(digraph)"
+    "gplot(digraph)"
    ]
   },
   {
@@ -67,7 +68,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "adjacency = full(transpose(adjacency_matrix(digraph)))\n",
+    "adjacency = Matrix(transpose(adjacency_matrix(digraph)))\n",
     "timepoint = 100.\n",
     "\n",
     "opmoral = evolve_generator(zero(adjacency), [adjacency])\n",
@@ -172,16 +173,20 @@
   }
  ],
  "metadata": {
+  "@webio": {
+   "lastCommId": null,
+   "lastKernelId": null
+  },
   "kernelspec": {
-   "display_name": "Julia 0.6.0",
+   "display_name": "Julia 1.0.1",
    "language": "julia",
-   "name": "julia-0.6"
+   "name": "julia-1.0"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "0.6.0"
+   "version": "1.0.1"
   }
  },
  "nbformat": 4,

diff --git a/examples/ex03_moralization_simple.jl b/examples/ex03_moralization_simple.jl
@@ -1,13 +1,14 @@
-
+#!/usr/bin/env python
 # coding: utf-8
 
 # # Spontaneous moralization on simple graph
 
 # ## Loading modules
 
 using QSWalk
-using TikzGraphs # For plotting graph
+using GraphPlot # For plotting graph
 using LightGraphs 
+using LinearAlgebra
 
 
 # ## Moralizing evolution
@@ -18,14 +19,14 @@ digraph = DiGraph(3)
 add_edge!(digraph, 1, 3)
 add_edge!(digraph, 2, 3)
 
-TikzGraphs.plot(digraph)
+gplot(digraph)
 
 
 # Here we generate some basic operators. Note in the case of directed graphs we need to transpose adjacency matrix, as *QSWalk.jl* multiplies the state on the right side of evolution operator. Note we choose zero matrix as Hamiltonian of the system. 
 # 
 # As we deal with the graph of very small size, we choose full-matrix evolution algorithm. In order to do such, we need to provide in opmoral at least one full matrix.
 
-adjacency = full(transpose(adjacency_matrix(digraph)))
+adjacency = Matrix(transpose(adjacency_matrix(digraph)))
 timepoint = 100.
 
 opmoral = evolve_generator(zero(adjacency), [adjacency])