Julia_LinkPrediction_TensorFactorization_Vechgrad.ipynb

{
  "nbformat": 4,
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  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "name": "Julia_LinkPrediction_TensorFactorization_Vechgrad.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "4NTOzLBPZx2d"
      ]
    },
    "kernelspec": {
      "display_name": "Julia",
      "language": "julia",
      "name": "julia"
    },
    "language_info": {
      "file_extension": ".jl",
      "mimetype": "application/julia",
      "name": "julia"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tQ1r1bbb0yBv"
      },
      "source": [
        "# <img src=\"https://github.com/JuliaLang/julia-logo-graphics/raw/master/images/julia-logo-color.png\" height=\"100\" /> _Colab Notebook Template_\n",
        "\n",
        "## Instructions\n",
        "1. Work on a copy of this notebook: _File_ > _Save a copy in Drive_ (you will need a Google account). Alternatively, you can download the notebook using _File_ > _Download .ipynb_, then upload it to [Colab](https://colab.research.google.com/).\n",
        "2. If you need a GPU: _Runtime_ > _Change runtime type_ > _Harware accelerator_ = _GPU_.\n",
        "3. Execute the following cell (click on it and press Ctrl+Enter) to install Julia, IJulia and other packages (if needed, update `JULIA_VERSION` and the other parameters). This takes a couple of minutes.\n",
        "4. Reload this page (press Ctrl+R, or ⌘+R, or the F5 key) and continue to the next section.\n",
        "\n",
        "_Notes_:\n",
        "* If your Colab Runtime gets reset (e.g., due to inactivity), repeat steps 2, 3 and 4.\n",
        "* After installation, if you want to change the Julia version or activate/deactivate the GPU, you will need to reset the Runtime: _Runtime_ > _Factory reset runtime_ and repeat steps 3 and 4."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GIeFXS0F0zww",
        "outputId": "66491ed8-ffe7-4fd1-a979-9b7d874fc0c1"
      },
      "source": [
        "%%shell\n",
        "set -e\n",
        "\n",
        "#---------------------------------------------------#\n",
        "JULIA_VERSION=\"1.5.0\" # any version ≥ 0.7.0\n",
        "JULIA_PACKAGES=\"IJulia BenchmarkTools Plots StatsBase Optim DelimitedFiles\"\n",
        "JULIA_PACKAGES_IF_GPU=\"CuArrays\"\n",
        "JULIA_NUM_THREADS=2\n",
        "#---------------------------------------------------#\n",
        "\n",
        "if [ -n \"$COLAB_GPU\" ] && [ -z `which julia` ]; then\n",
        "  # Install Julia\n",
        "  JULIA_VER=`cut -d '.' -f -2 <<< \"$JULIA_VERSION\"`\n",
        "  echo \"Installing Julia $JULIA_VERSION on the current Colab Runtime...\"\n",
        "  BASE_URL=\"https://julialang-s3.julialang.org/bin/linux/x64\"\n",
        "  URL=\"$BASE_URL/$JULIA_VER/julia-$JULIA_VERSION-linux-x86_64.tar.gz\"\n",
        "  wget -nv $URL -O /tmp/julia.tar.gz # -nv means \"not verbose\"\n",
        "  tar -x -f /tmp/julia.tar.gz -C /usr/local --strip-components 1\n",
        "  rm /tmp/julia.tar.gz\n",
        "\n",
        "  # Install Packages\n",
        "  if [ \"$COLAB_GPU\" = \"1\" ]; then\n",
        "      JULIA_PACKAGES=\"$JULIA_PACKAGES $JULIA_PACKAGES_IF_GPU\"\n",
        "  fi\n",
        "  for PKG in `echo $JULIA_PACKAGES`; do\n",
        "    echo \"Installing Julia package $PKG...\"\n",
        "    julia -e 'using Pkg; pkg\"add '$PKG'; precompile;\"'\n",
        "  done\n",
        "\n",
        "  # Install kernel and rename it to \"julia\"\n",
        "  echo \"Installing IJulia kernel...\"\n",
        "  julia -e 'using IJulia; IJulia.installkernel(\"julia\", env=Dict(\n",
        "      \"JULIA_NUM_THREADS\"=>\"'\"$JULIA_NUM_THREADS\"'\"))'\n",
        "  KERNEL_DIR=`julia -e \"using IJulia; print(IJulia.kerneldir())\"`\n",
        "  KERNEL_NAME=`ls -d \"$KERNEL_DIR\"/julia*`\n",
        "  mv -f $KERNEL_NAME \"$KERNEL_DIR\"/julia  \n",
        "\n",
        "  echo ''\n",
        "  echo \"Success! Please reload this page and jump to the next section.\"\n",
        "fi"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Installing Julia 1.5.0 on the current Colab Runtime...\n",
            "2020-11-22 14:29:00 URL:https://storage.googleapis.com/julialang2/bin/linux/x64/1.5/julia-1.5.0-linux-x86_64.tar.gz [105098627/105098627] -> \"/tmp/julia.tar.gz\" [1]\n",
            "Installing Julia package IJulia...\n",
            "\u001b[32m\u001b[1m Installing\u001b[22m\u001b[39m known registries into `~/.julia`\n",
            "######################################################################## 100.0%\n",
            "\u001b[32m\u001b[1m      Added\u001b[22m\u001b[39m registry `General` to `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m SoftGlobalScope ─ v1.1.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m ZMQ ───────────── v1.2.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Conda ─────────── v1.5.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m ZeroMQ_jll ────── v4.3.2+5\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m VersionParsing ── v1.2.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m IJulia ────────── v1.23.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m JSON ──────────── v0.21.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m JLLWrappers ───── v1.1.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Artifacts ─────── v1.3.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m MbedTLS_jll ───── v2.16.8+1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m MbedTLS ───────── v1.0.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Parsers ───────── v1.0.12\n",
            "\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: ZeroMQ\n",
            "######################################################################## 100.0%\n",
            "\u001b[1A\u001b[2K\u001b[?25h\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: MbedTLS\n",
            "######################################################################## 100.0%\n",
            "\u001b[1A\u001b[2K\u001b[?25h\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
            " \u001b[90m [7073ff75] \u001b[39m\u001b[92m+ IJulia v1.23.0\u001b[39m\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Manifest.toml`\n",
            " \u001b[90m [56f22d72] \u001b[39m\u001b[92m+ Artifacts v1.3.0\u001b[39m\n",
            " \u001b[90m [8f4d0f93] \u001b[39m\u001b[92m+ Conda v1.5.0\u001b[39m\n",
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            " \u001b[90m [c8ffd9c3] \u001b[39m\u001b[92m+ MbedTLS_jll v2.16.8+1\u001b[39m\n",
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            " \u001b[90m [8dfed614] \u001b[39m\u001b[92m+ Test\u001b[39m\n",
            " \u001b[90m [cf7118a7] \u001b[39m\u001b[92m+ UUIDs\u001b[39m\n",
            " \u001b[90m [4ec0a83e] \u001b[39m\u001b[92m+ Unicode\u001b[39m\n",
            "\u001b[32m\u001b[1m   Building\u001b[22m\u001b[39m Conda ─→ `~/.julia/packages/Conda/x5ml4/deps/build.log`\n",
            "\u001b[32m\u001b[1m   Building\u001b[22m\u001b[39m IJulia → `~/.julia/packages/IJulia/ljYVo/deps/build.log`\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing Julia package BenchmarkTools...\n",
            "\u001b[32m\u001b[1m   Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m BenchmarkTools ─ v0.5.0\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
            " \u001b[90m [6e4b80f9] \u001b[39m\u001b[92m+ BenchmarkTools v0.5.0\u001b[39m\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Manifest.toml`\n",
            " \u001b[90m [6e4b80f9] \u001b[39m\u001b[92m+ BenchmarkTools v0.5.0\u001b[39m\n",
            " \u001b[90m [37e2e46d] \u001b[39m\u001b[92m+ LinearAlgebra\u001b[39m\n",
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            " \u001b[90m [10745b16] \u001b[39m\u001b[92m+ Statistics\u001b[39m\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing Julia package Plots...\n",
            "\u001b[32m\u001b[1m   Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Libgcrypt_jll ──────────────── v1.8.5+4\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m FreeType2_jll ──────────────── v2.10.1+5\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m JpegTurbo_jll ──────────────── v2.0.1+3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Xorg_libxcb_jll ────────────── v1.13.0+3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Adapt ──────────────────────── v2.3.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m GeometryBasics ─────────────── v0.3.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Latexify ───────────────────── v0.14.5\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Plots ──────────────────────── v1.9.1\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Xorg_libpthread_stubs_jll ──── v0.1.0+3\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m OrderedCollections ─────────── v1.3.2\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m IteratorInterfaceExtensions ── v1.0.0\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Requires ───────────────────── v1.1.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m EarCut_jll ─────────────────── v2.1.5+1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m IniFile ────────────────────── v0.5.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m StaticArrays ───────────────── v0.12.5\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Missings ───────────────────── v0.4.4\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m IterTools ──────────────────── v1.3.0\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Gettext_jll ────────────────── v0.20.1+7\n",
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            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m StatsBase ──────────────────── v0.33.2\n",
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            " \u001b[90m [91a5bcdd] \u001b[39m\u001b[92m+ Plots v1.9.1\u001b[39m\n",
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            " \u001b[90m [1a1011a3] \u001b[39m\u001b[92m+ SharedArrays\u001b[39m\n",
            "\u001b[32m\u001b[1m   Building\u001b[22m\u001b[39m GR → `~/.julia/packages/GR/RlE5Y/deps/build.log`\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing Julia package StatsBase...\n",
            "\u001b[32m\u001b[1m   Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
            " \u001b[90m [2913bbd2] \u001b[39m\u001b[92m+ StatsBase v0.33.2\u001b[39m\n",
            "\u001b[32m\u001b[1mNo Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.5/Manifest.toml`\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing Julia package Optim...\n",
            "\u001b[32m\u001b[1m   Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m PositiveFactorizations ─────── v0.2.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m DiffResults ────────────────── v1.0.2\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m UnPack ─────────────────────── v1.0.2\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m SpecialFunctions ───────────── v0.10.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CommonSubexpressions ───────── v0.3.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m LineSearches ───────────────── v7.1.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m ForwardDiff ────────────────── v0.10.12\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Optim ──────────────────────── v1.2.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CompilerSupportLibraries_jll ─ v0.3.4+0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m DiffRules ──────────────────── v1.0.2\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m OpenSpecFun_jll ────────────── v0.5.3+4\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m FillArrays ─────────────────── v0.9.7\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m NLSolversBase ──────────────── v7.7.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m ArrayInterface ─────────────── v2.13.7\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Parameters ─────────────────── v0.12.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m FiniteDiff ─────────────────── v2.7.1\n",
            "\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: CompilerSupportLibraries\n",
            "######################################################################## 100.0%\n",
            "\u001b[1A\u001b[2K\u001b[?25h\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: OpenSpecFun\n",
            "######################################################################## 100.0%\n",
            "\u001b[1A\u001b[2K\u001b[?25h\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
            " \u001b[90m [429524aa] \u001b[39m\u001b[92m+ Optim v1.2.0\u001b[39m\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Manifest.toml`\n",
            " \u001b[90m [4fba245c] \u001b[39m\u001b[92m+ ArrayInterface v2.13.7\u001b[39m\n",
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            " \u001b[90m [f6369f11] \u001b[39m\u001b[92m+ ForwardDiff v0.10.12\u001b[39m\n",
            " \u001b[90m [d3d80556] \u001b[39m\u001b[92m+ LineSearches v7.1.0\u001b[39m\n",
            " \u001b[90m [d41bc354] \u001b[39m\u001b[92m+ NLSolversBase v7.7.1\u001b[39m\n",
            " \u001b[90m [efe28fd5] \u001b[39m\u001b[92m+ OpenSpecFun_jll v0.5.3+4\u001b[39m\n",
            " \u001b[90m [429524aa] \u001b[39m\u001b[92m+ Optim v1.2.0\u001b[39m\n",
            " \u001b[90m [d96e819e] \u001b[39m\u001b[92m+ Parameters v0.12.1\u001b[39m\n",
            " \u001b[90m [85a6dd25] \u001b[39m\u001b[92m+ PositiveFactorizations v0.2.3\u001b[39m\n",
            " \u001b[90m [276daf66] \u001b[39m\u001b[92m+ SpecialFunctions v0.10.3\u001b[39m\n",
            " \u001b[90m [3a884ed6] \u001b[39m\u001b[92m+ UnPack v1.0.2\u001b[39m\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing Julia package DelimitedFiles...\n",
            "\u001b[32m\u001b[1m   Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
            " \u001b[90m [8bb1440f] \u001b[39m\u001b[92m+ DelimitedFiles\u001b[39m\n",
            "\u001b[32m\u001b[1mNo Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.5/Manifest.toml`\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing Julia package CuArrays...\n",
            "\u001b[32m\u001b[1m   Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General`\n",
            "\u001b[32m\u001b[1m  Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CEnum ────────── v0.3.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CodeTracking ─── v1.0.5\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CUDAapi ──────── v4.0.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m GPUCompiler ──── v0.2.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m DataStructures ─ v0.17.20\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m NNlib ────────── v0.7.7\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m LLVM ─────────── v1.7.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CuArrays ─────── v2.2.2\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m AbstractFFTs ─── v0.5.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m AbstractTrees ── v0.3.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Adapt ────────── v1.1.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m Cthulhu ──────── v1.3.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m TimerOutputs ─── v0.5.7\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m BinaryProvider ─ v0.5.10\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CUDAdrv ──────── v6.3.0\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m GPUArrays ────── v3.4.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m ExprTools ────── v0.1.3\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m FoldingTrees ─── v1.0.1\n",
            "\u001b[32m\u001b[1m  Installed\u001b[22m\u001b[39m CUDAnative ───── v3.2.0\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Project.toml`\n",
            " \u001b[90m [3a865a2d] \u001b[39m\u001b[92m+ CuArrays v2.2.2\u001b[39m\n",
            "\u001b[32m\u001b[1mUpdating\u001b[22m\u001b[39m `~/.julia/environments/v1.5/Manifest.toml`\n",
            " \u001b[90m [621f4979] \u001b[39m\u001b[92m+ AbstractFFTs v0.5.0\u001b[39m\n",
            " \u001b[90m [1520ce14] \u001b[39m\u001b[92m+ AbstractTrees v0.3.3\u001b[39m\n",
            " \u001b[90m [79e6a3ab] \u001b[39m\u001b[95m↓ Adapt v2.3.0 ⇒ v1.1.0\u001b[39m\n",
            " \u001b[90m [b99e7846] \u001b[39m\u001b[92m+ BinaryProvider v0.5.10\u001b[39m\n",
            " \u001b[90m [fa961155] \u001b[39m\u001b[92m+ CEnum v0.3.0\u001b[39m\n",
            " \u001b[90m [3895d2a7] \u001b[39m\u001b[92m+ CUDAapi v4.0.0\u001b[39m\n",
            " \u001b[90m [c5f51814] \u001b[39m\u001b[92m+ CUDAdrv v6.3.0\u001b[39m\n",
            " \u001b[90m [be33ccc6] \u001b[39m\u001b[92m+ CUDAnative v3.2.0\u001b[39m\n",
            " \u001b[90m [da1fd8a2] \u001b[39m\u001b[92m+ CodeTracking v1.0.5\u001b[39m\n",
            " \u001b[90m [f68482b8] \u001b[39m\u001b[92m+ Cthulhu v1.3.0\u001b[39m\n",
            " \u001b[90m [3a865a2d] \u001b[39m\u001b[92m+ CuArrays v2.2.2\u001b[39m\n",
            " \u001b[90m [864edb3b] \u001b[39m\u001b[95m↓ DataStructures v0.18.8 ⇒ v0.17.20\u001b[39m\n",
            " \u001b[90m [e2ba6199] \u001b[39m\u001b[92m+ ExprTools v0.1.3\u001b[39m\n",
            " \u001b[90m [1eca21be] \u001b[39m\u001b[92m+ FoldingTrees v1.0.1\u001b[39m\n",
            " \u001b[90m [0c68f7d7] \u001b[39m\u001b[92m+ GPUArrays v3.4.1\u001b[39m\n",
            " \u001b[90m [61eb1bfa] \u001b[39m\u001b[92m+ GPUCompiler v0.2.0\u001b[39m\n",
            " \u001b[90m [929cbde3] \u001b[39m\u001b[92m+ LLVM v1.7.0\u001b[39m\n",
            " \u001b[90m [872c559c] \u001b[39m\u001b[92m+ NNlib v0.7.7\u001b[39m\n",
            " \u001b[90m [a759f4b9] \u001b[39m\u001b[92m+ TimerOutputs v0.5.7\u001b[39m\n",
            "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
            "Installing IJulia kernel...\n",
            "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mInstalling julia kernelspec in /root/.local/share/jupyter/kernels/julia-1.5\n",
            "\n",
            "Success! Please reload this page and jump to the next section.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              ""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-OS3Ac017T1i"
      },
      "source": [
        "# Checking the Installation\n",
        "The `versioninfo()` function should print your Julia version and some other info about the system:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EEzvvzCl1i0F",
        "outputId": "9780d444-60cc-4bc9-faa7-1646b000b348"
      },
      "source": [
        "versioninfo()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Julia Version 1.5.0\n",
            "Commit 96786e22cc (2020-08-01 23:44 UTC)\n",
            "Platform Info:\n",
            "  OS: Linux (x86_64-pc-linux-gnu)\n",
            "  CPU: Intel(R) Xeon(R) CPU @ 2.20GHz\n",
            "  WORD_SIZE: 64\n",
            "  LIBM: libopenlibm\n",
            "  LLVM: libLLVM-9.0.1 (ORCJIT, broadwell)\n",
            "Environment:\n",
            "  JULIA_NUM_THREADS = 2\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yQlpeR9wNOi8",
        "outputId": "34c8ca4d-3b32-4021-bc74-65b6d11724f3"
      },
      "source": [
        "using BenchmarkTools\n",
        "\n",
        "M = rand(2048, 2048)\n",
        "@benchmark M^2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "BenchmarkTools.Trial: \n",
              "  memory estimate:  32.00 MiB\n",
              "  allocs estimate:  2\n",
              "  --------------\n",
              "  minimum time:     392.793 ms (0.00% GC)\n",
              "  median time:      399.581 ms (0.00% GC)\n",
              "  mean time:        418.871 ms (3.80% GC)\n",
              "  maximum time:     520.873 ms (17.25% GC)\n",
              "  --------------\n",
              "  samples:          12\n",
              "  evals/sample:     1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XciCcMAJOT3_",
        "outputId": "2ad2d5e4-fcaf-4410-b4b8-7509a4135d23"
      },
      "source": [
        "if ENV[\"COLAB_GPU\"] == \"1\"\n",
        "    using CuArrays\n",
        "\n",
        "    M_gpu = cu(M)\n",
        "    @benchmark CuArrays.@sync M_gpu^2\n",
        "else\n",
        "    println(\"No GPU found.\")\n",
        "end"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: CUDA10.1\n",
            "\u001b[?25l"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "######################################################################### 100.0%\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\u001b[1A\u001b[2K\u001b[?25h\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: CUDNN+CUDA10.1\n",
            "\u001b[?25l"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "######################################################################### 100.0%\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\u001b[1A\u001b[2K\u001b[?25h\u001b[32m\u001b[1mDownloading\u001b[22m\u001b[39m artifact: CUTENSOR+CUDA10.1\n",
            "\u001b[?25l"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "######################################################################### 100.0%\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\u001b[1A\u001b[2K\u001b[?25h"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "BenchmarkTools.Trial: \n",
              "  memory estimate:  336 bytes\n",
              "  allocs estimate:  7\n",
              "  --------------\n",
              "  minimum time:     2.510 ms (0.00% GC)\n",
              "  median time:      3.976 ms (0.00% GC)\n",
              "  mean time:        4.006 ms (0.04% GC)\n",
              "  maximum time:     8.110 ms (24.33% GC)\n",
              "  --------------\n",
              "  samples:          1247\n",
              "  evals/sample:     1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8RC1QNNqk6h1"
      },
      "source": [
        "# Need Help?\n",
        "\n",
        "* Learning: https://julialang.org/learning/\n",
        "* Documentation: https://docs.julialang.org/\n",
        "* Questions & Discussions:\n",
        "  * https://discourse.julialang.org/\n",
        "  * http://julialang.slack.com/\n",
        "  * https://stackoverflow.com/questions/tagged/julia\n",
        "\n",
        "If you ever ask for help or file an issue about Julia, you should generally provide the output of `versioninfo()`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2UMidUQB03vJ"
      },
      "source": [
        "Add new code cells by clicking the `+ Code` button (or _Insert_ > _Code cell_).\n",
        "\n",
        "Have fun!\n",
        "\n",
        "<img src=\"https://raw.githubusercontent.com/JuliaLang/julia-logo-graphics/master/images/julia-logo-mask.png\" height=\"100\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X5866tRNXcB8"
      },
      "source": [
        "# Link Prediction with Tensor Factorization (VecHGrad method)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wWX8COPJBSFC"
      },
      "source": [
        "*Last edited: 2020-11-22*\n",
        "\n",
        "### Theoretical tools\n",
        "*Based on work from:*\n",
        "\n",
        "Gao, Sheng, Ludovic Denoyer, and Patrick Gallinari. \"Link pattern prediction with tensor decomposition in multi-relational networks.\" In 2011 IEEE Symposium on Computational Intelligence and Data Mining (CIDM), pp. 333-340. IEEE, 2011.\n",
        "\n",
        "*Improvements in tensor decomposition from:*\n",
        "\n",
        "VecHGrad: https://arxiv.org/abs/1905.12413\n",
        "\n",
        "VecHGrad Code: https://github.com/dagrate/vechgrad\n",
        "\n",
        "### Data\n",
        "\n",
        "* bowling-green.american-assembly from https://github.com/pol-is/openData\n",
        "  * Filled in with 0 for missing data\n",
        "  * Split in two matrices, one with positive observations (1) and one with negative observations (-1).\n",
        "\n",
        "### How to use\n",
        "\n",
        "* Matrices with pos-neg layer data need to be uploaded to Google Colab\n",
        "* Vector *a* (line 6 below) needs to be updated with dimensions of input data\n",
        "  * Can also be extracted by the csv files themselves\n",
        "* Run helper function cells and main program\n",
        "* Resulting latent feature matrices A, B and C are the ones that minimize the weighted least squares error for the missing data.\n",
        "\n",
        "### ToDo / Improvements\n",
        "\n",
        "* Convert notebook to Python...\n",
        "* ... or go further into Julia territory, utilizing https://github.com/Jutho/TensorOperations.jl"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4NTOzLBPZx2d"
      },
      "source": [
        "## Helper functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4lpTBrB71v3A"
      },
      "source": [
        "### TNSRUTILS.JI FUNCTIONS\n",
        "\n",
        "function buildCP3(A, B, C)\n",
        "    I = size(A)[1] ;\n",
        "    J = size(B)[1] ;\n",
        "    K = size(C)[1] ;\n",
        "    Xh = zeros(I,J,K) ;\n",
        "#\n",
        "# manage the case where R == 1\n",
        "    if length( size( A ) ) == 1\n",
        "        tmp = kron( C, kron( A, B' ) ) ;\n",
        "        irow = 1 ;\n",
        "        for lk = 1:K\n",
        "            Xh[:,:,lk] += tmp[irow:irow+I-1, :] ;\n",
        "            irow += I ;\n",
        "        end\n",
        "    else\n",
        "        R = size(A)[2] ;\n",
        "        for li = 1:I\n",
        "        \tfor lj = 1:J\n",
        "        \t\tfor lk = 1:K\n",
        "        \t\t\tfor lr = 1:R\n",
        "        \t\t\t\tXh[li,lj,lk] += A[li, lr] * B[lj, lr] * C[lk, lr] ;\n",
        "        \t\t\tend\n",
        "        \t\tend\n",
        "        \tend\n",
        "        end\n",
        "        #kron is highly inefficient for medium to large tensors\n",
        "        #for lr = 1:R\n",
        "        #    tmp = kron( C[:,lr], kron( A[:,lr], B[:,lr]' ) ) ;\n",
        "        #    irow = 1 ;\n",
        "        #    for lk = 1:K\n",
        "        #        Xh[:,:,lk] += tmp[irow:irow+I-1, :] ;\n",
        "        #        irow += I ;\n",
        "        #    end\n",
        "        #end\n",
        "    end\n",
        "    return Xh ;\n",
        "#\n",
        "# Last card of function buildCP3.\n",
        "#\n",
        "end\n",
        "\n",
        "#function objfun(X, Xh)\n",
        "#    Z = errorfun(X,Xh) ;\n",
        "#    return sqrt( sum(Z) ) ;\n",
        "\n",
        "# Weighted least squares error\n",
        "function objfunweighted(X, Xh, W)\n",
        "    Z = errorfun(X,Xh) ;\n",
        "    for l=1:size(Z)[3]\n",
        "      Z[:,:,l] = Z[:,:,l] .* W ;\n",
        "    end\n",
        "    return sqrt( sum(Z) ) ;\n",
        "#\n",
        "# Last card of function objfun\n",
        "#\n",
        "end\n",
        "\n",
        "function krao(matC,matD)\n",
        "    (I,F) = size(matC) ;\n",
        "    (J,F1) = size(matD) ;\n",
        "#\n",
        "    kraomat = zeros(I*J, F) ;\n",
        "    for f = 1:F\n",
        "        kraom = matD[:,f] * matC[:,f]' ;\n",
        "        kraomat[:,f] = kraom[:];\n",
        "    end\n",
        "    return kraomat ;\n",
        "#\n",
        "# Last card of function krao\n",
        "#\n",
        "end\n",
        "\n",
        "function tnsrunfold(X, mode)\n",
        "    dim = collect(size(X)) ;\n",
        "    ncol = Int(cumprod(dim)[end]/dim[mode]) ;\n",
        "    if mode == 1\n",
        "        Z = reshape(permutedims(X, [1,2,3]), dim[mode], ncol) ;\n",
        "    elseif mode == 2\n",
        "        Z = reshape(permutedims(X, [2,1,3]), dim[mode], ncol) ;\n",
        "    elseif mode == 3\n",
        "        Z = reshape(permutedims(X, [3,1,2]), dim[mode], ncol) ;\n",
        "    end\n",
        "    return Z ;\n",
        "#\n",
        "# Last card of function tnsrunfold.\n",
        "#\n",
        "end\n",
        "\n",
        "function cp3init(a, latfact)\n",
        "    R = latfact ;\n",
        "    A = rand(a[1], R) ;\n",
        "    B = rand(a[2], R) ;\n",
        "    C = rand(a[3], R) ;\n",
        "    return A, B, C ;\n",
        "#\n",
        "# Last card of function cp3init.\n",
        "#\n",
        "end\n",
        "\n",
        "function errorfun(X, Xh)\n",
        "    return (X-Xh) .* (X-Xh) ;\n",
        "#\n",
        "# Last card of function errorfunct.\n",
        "#\n",
        "end"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zlq53yY42ico"
      },
      "source": [
        "### CPUTILS.JI FUNCTIONS\n",
        "\n",
        "function mat2vectcp3( A,B,C )\n",
        "    I = size(A)[1] ;\n",
        "    J = size(B)[1] ;\n",
        "    K = size(C)[1] ;\n",
        "    R = size(A)[2] ;\n",
        "#\n",
        "    x = zeros( I*R + J*R + K*R ) ;\n",
        "    cnt = 1 ;\n",
        "    for n = 1:3\n",
        "        if n == 1\n",
        "            elts = I*R ;\n",
        "            x[cnt:elts] = vcat(A...) ;\n",
        "        elseif n == 2\n",
        "            elts = cnt + J*R - 1 ;\n",
        "            x[cnt:elts] = vcat(B...) ;\n",
        "        elseif n == 3\n",
        "            elts = cnt + K*R - 1 ;\n",
        "            x[cnt:elts] = vcat(C...) ;\n",
        "        end\n",
        "        cnt = elts + 1 ;\n",
        "    end\n",
        "    return x ;\n",
        "#\n",
        "#     Last card of function mat2veccp3.\n",
        "#\n",
        "end"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3UF8gUzt1arh"
      },
      "source": [
        "### ALSCP.JI FUNCTION\n",
        "\n",
        "function nncpals(X, rankR, A, B, C, Weights, maxiter=1000, epsobjfun=1.0E-3)\n",
        "    filepath = \"\" ;\n",
        "\n",
        "    Xsize = collect(size(X)) ;\n",
        "    allmode = collect(1:length(Xsize)) ;\n",
        "    if length(Xsize) > 3\n",
        "        return println(\"Only third order parafac implemented\") ;\n",
        "    end\n",
        "#\n",
        "# we store the evolution of the calculation\n",
        "    fk = zeros( maxiter + 1 ) ;\n",
        "    tmstamp = zeros( maxiter + 1 ) ;\n",
        "#\n",
        "# random initialization\n",
        "    # A = rand(Xsize[1], rankR) ;\n",
        "    # B = rand(Xsize[2], rankR) ;\n",
        "    # C = rand(Xsize[3], rankR) ;\n",
        "    Xh = buildCP3(A,B,C) ;\n",
        "    curvo = objfunweighted(X,Xh,Weights) ;\n",
        "    print(\"   >> initialization    Obj Fun:\") ;\n",
        "    println(round(curvo, digits=3)) ;\n",
        "#\n",
        "    fk[1] = curvo ;\n",
        "    tmstamp[1] = time() ;\n",
        "#\n",
        "# non-negative CP ALS iterative process\n",
        "    i = 1 ;\n",
        "    while i <= maxiter\n",
        "        for mode = 1:length(Xsize)\n",
        "#\n",
        "# Hadamard product on all mode != n\n",
        "            V = ones(rankR, rankR) ;\n",
        "            for n = 1:length(Xsize)\n",
        "                if n != mode\n",
        "                    if n == 1\n",
        "                        tmpV = A ;\n",
        "                    elseif n == 2\n",
        "                        tmpV = B ;\n",
        "                    elseif n == 3\n",
        "                        tmpV = C ;\n",
        "                    end\n",
        "                    V = V .* (tmpV' * tmpV) ;\n",
        "                end\n",
        "            end\n",
        "#\n",
        "# Khatri-Rao product on all mode != n\n",
        "            if mode == 1\n",
        "                W = krao(C, B) ;\n",
        "            elseif mode == 2\n",
        "                W = krao(C, A) ;\n",
        "            elseif mode == 3\n",
        "                W = krao(B, A) ;\n",
        "            end\n",
        "#\n",
        "# non negative update\n",
        "            num = (tnsrunfold(X, mode) * W) .+ 1.0E-9 ;\n",
        "            if mode == 1\n",
        "                denum = (A * (W' * W)) .+ 1.0E-9 ;\n",
        "                A = A .* (num ./ denum) ;\n",
        "            elseif mode == 2\n",
        "                denum = (B * (W' * W)) .+ 1.0E-9 ;\n",
        "                B = B .* (num ./ denum) ;\n",
        "            elseif mode == 3\n",
        "                denum = (C * (W' * W)) .+ 1.0E-9 ;\n",
        "                C = C .* (num ./ denum) ;\n",
        "            end\n",
        "        end\n",
        "#\n",
        "# calculation evolution\n",
        "        Xh = buildCP3(A,B,C) ;\n",
        "        curvo = objfunweighted(X,Xh,Weights) ;\n",
        "        fk[i+1] = curvo ;\n",
        "        tmstamp[i+1] = time() ;\n",
        "#\n",
        "        if i%(maxiter/10) == 0 || i == maxiter\n",
        "            print(\"   >> \", i / maxiter * 100, \"%\") ;\n",
        "            print(\"     Obj. fun: \", round(curvo, digits=3)) ;\n",
        "            println(\"\") ;\n",
        "            xk = mat2vectcp3(A, B, C) ;\n",
        "            writedlm(string(filepath, string(i), \"xk.txt\"), xk, \",\") ;\n",
        "            writedlm(string(filepath, string(i),\"fk.txt\"), fk, \",\") ;\n",
        "            writedlm(string(filepath, string(i),\"tmstamp.txt\"), tmstamp, \",\") ;\n",
        "        end\n",
        "#\n",
        "        if curvo > epsobjfun\n",
        "            i += 1 ;\n",
        "        else\n",
        "            i = maxiter + 1 ;\n",
        "        end\n",
        "    end\n",
        "    print(\"Number of iterations: \") ;\n",
        "    println(i - 1) ;\n",
        "    Xh = buildCP3(A, B, C) ;\n",
        "    print(\"Overall difference: \") ;\n",
        "    println(round(objfunweighted(X, Xh, Weights), digits=3)) ;\n",
        "#\n",
        "# we save the final results of the calculation\n",
        "    xk = mat2vectcp3(A, B, C) ;\n",
        "    writedlm(string(filepath, string(i), \"xk.txt\"), xk, \",\") ;\n",
        "    writedlm(string(filepath, string(i),\"fk.txt\"), fk, \",\") ;\n",
        "    writedlm(string(filepath, string(i),\"tmstamp.txt\"), tmstamp, \",\") ;\n",
        "#\n",
        "    return A, B, C ;\n",
        "#\n",
        "# Last card of function nncpals.\n",
        "#\n",
        "end"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I4sAjh_XaG36"
      },
      "source": [
        "## Main program"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mFODV1UKucNS",
        "outputId": "4a76673a-817f-40c1-ac54-cfa2baec9a25"
      },
      "source": [
        "using StatsBase\n",
        "using Optim\n",
        "using DelimitedFiles\n",
        "using Random\n",
        "\n",
        "a = (2031, 896, 2) ;  # Participant-votes data, 2 layers (pos,neg)\n",
        "maxitrtn = 1000 ;     # Nr of iterations\n",
        "flpath = \"/content/\"\n",
        "\n",
        "#sim = \"cifar10\" ;\n",
        "#rsltn = 4 ;\n",
        "#desc_bef = [\"fk\", \"xk\", \"tmstamp\"] ;\n",
        "#desc_aft = [\"fk_\", \"xk_\", \"tm_\"] ;\n",
        "#rs = [\"_ros\", \"_par\", \"_ded\", \"_cp\"] ;\n",
        "\n",
        "# we initialize the tensor X and a\n",
        "#a = (32, 32, 16) ;\n",
        "#X = readdlm( string(flpath, \"cifar10_.csv\") ) ;\n",
        "#X = reshape(X, a[1], a[2], a[3]) ;\n",
        "\n",
        "# Assembling the participant-votes tensor\n",
        "X = zeros(a[1], a[2], a[3]) ;\n",
        "Weights = bitrand(a[1], a[2]) ;   # 1 for observations, 0 for missing links (to be predicted)\n",
        "X[:,:,1] = readdlm( string(flpath, \"participant-votes-dataonly-positive.csv\"), ',', Int, '\\n' ) ;\n",
        "X[:,:,2] = readdlm( string(flpath, \"participant-votes-dataonly-negative.csv\"), ',', Int, '\\n' ) ;\n",
        "\n",
        "# resolution of CP\n",
        "latfact = 2 ;\n",
        "A, B, C = cp3init(a, latfact) ;\n",
        "A, B, C = nncpals(X, latfact, A, B, C, Weights, maxitrtn) ;\n",
        "\n",
        "\n",
        "#for n = 1:3\n",
        "#    path1 = \"\" ;\n",
        "#    nm1 = string(path1, string(maxitrtn), desc_bef[n], \".txt\") ;\n",
        "#    nm2 = string(path1, sim, rs[rsltn], \"_als_\", desc_aft[n], string(maxitrtn), \".txt\") ;\n",
        "#    mv(nm1, nm2) ;\n",
        "#end"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "   >> initialization    Obj Fun:556.08\n",
            "   >> 10.0%     Obj. fun: 224.933\n",
            "   >> "
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YdBV9dqTscrR",
        "outputId": "e1937eb4-7c50-4cf5-adbc-282c08f3e2ee"
      },
      "source": [
        "# Naive check on how many participant-votes observations are predicted both positive and negative (obv a mistake)\n",
        "Xh = buildCP3(A, B, C) ;\n",
        "counter = 0\n",
        "for i = 1:size(Xh)[1]\n",
        "  for j = 1:size(Xh)[2]\n",
        "    if Xh[i,j,1] > 0.5 && Xh[i,j,2] < -0.5\n",
        "      counter += 1 ;\n",
        "    end\n",
        "  end\n",
        "end\n",
        "print(\"Mistakes: \")\n",
        "print(counter) ;\n",
        "print(\" out of \")\n",
        "print(size(Xh)[1] * size(Xh)[2]) ;\n",
        "println(\" (\", 100 * counter / (size(Xh)[1] * size(Xh)[2]), \"%)\") ;"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mistakes: 1485 out of 1819776 (0.08160345009495674%)\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}