{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "\n# Data depth computation for multiple distributions \n\nSample usage of depth computation for multiple distributions.\nIt will plot samples based on different depth notions.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "from depth.model.DepthEucl import DepthEucl \nimport numpy as np\nfrom matplotlib import pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "np.random.seed(2801)\nmat1=[[1, 0],[0, 2]]\nX1=np.random.normal([0,0],1,(100,2))\ndist1=np.repeat(0,100)\nX2=np.random.normal([5,5],1,(100,2))\ndist2=np.repeat(1,100)\nX3=np.random.normal([-5,5],1,(100,2))\ndist3=np.repeat(2,100)\nX=np.concatenate((np.concatenate((X1,X2),axis=0),X3),axis=0) \ndists=np.concatenate((np.concatenate((dist1,dist2),axis=0),dist3),axis=0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.figure()\nplt.scatter(X1[:,0],X1[:,1],color=\"blue\",label=\"First distribution\",)\nplt.scatter(X2[:,0],X2[:,1],color=\"red\",label=\"Second distribution\",)\nplt.scatter(X3[:,0],X3[:,1],color=\"green\",label=\"Third distribution\")\nplt.xlabel(\"First component\")\nplt.ylabel(\"Second component\")\nplt.title(\"Multiple distibution samples\")\nplt.legend()\nplt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "modelMult=DepthEucl().load_dataset(X,distribution=dists)\nmodelMult.L2(X)\ncolors=[\"blue\",\"red\",\"green\"]\nplt.figure(figsize=(15,5))\nfor i in range(3):\n    plt.subplot(1,3,1,)\n    plt.scatter(modelMult.L2Depth[0][modelMult.distribution==i],\n                modelMult.L2Depth[1][modelMult.distribution==i],color=colors[i])\n    plt.subplot(1,3,2)\n    plt.scatter(modelMult.L2Depth[0][modelMult.distribution==i],\n                modelMult.L2Depth[2][modelMult.distribution==i],color=colors[i])\n    plt.subplot(1,3,3)\n    plt.scatter(modelMult.L2Depth[1][modelMult.distribution==i],\n                modelMult.L2Depth[2][modelMult.distribution==i],color=colors[i])\n    \nplt.subplot(1,3,1,)\nplt.xlabel(\"Depth w.r.t. distribution 1\")\nplt.ylabel(\"Depth w.r.t. distribution 2\")\nplt.subplot(1,3,2)\nplt.xlabel(\"Depth w.r.t. distribution 1\")\nplt.ylabel(\"Depth w.r.t. distribution 3\")\nplt.subplot(1,3,3)\nplt.xlabel(\"Depth w.r.t. distribution 2\")\nplt.ylabel(\"Depth w.r.t. distribution 3\")\nplt.legend([\"First distribution\",\"Second distribution\",\"Third distribution\"])\n\nplt.suptitle(\"Multiple distribution using L2 depth\")\nplt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "modelMult.halfspace(X)\ncolors=[\"blue\",\"red\",\"green\"]\nplt.figure(figsize=(15,5))\nfor i in range(3):\n    plt.subplot(1,3,1,)\n    plt.scatter(modelMult.halfspaceDepth[0][modelMult.distribution==i],\n                modelMult.halfspaceDepth[1][modelMult.distribution==i],color=colors[i])\n    plt.subplot(1,3,2)\n    plt.scatter(modelMult.halfspaceDepth[0][modelMult.distribution==i],\n                modelMult.halfspaceDepth[2][modelMult.distribution==i],color=colors[i])\n    plt.subplot(1,3,3)\n    plt.scatter(modelMult.halfspaceDepth[1][modelMult.distribution==i],\n                modelMult.halfspaceDepth[2][modelMult.distribution==i],color=colors[i])\n    \nplt.subplot(1,3,1,)\nplt.xlabel(\"Depth w.r.t. distribution 1\")\nplt.ylabel(\"Depth w.r.t. distribution 2\")\nplt.subplot(1,3,2)\nplt.xlabel(\"Depth w.r.t. distribution 1\")\nplt.ylabel(\"Depth w.r.t. distribution 3\")\nplt.subplot(1,3,3)\nplt.xlabel(\"Depth w.r.t. distribution 2\")\nplt.ylabel(\"Depth w.r.t. distribution 3\")\nplt.legend([\"First distribution\",\"Second distribution\",\"Third distribution\"])\n\nplt.suptitle(\"Multiple distribution using halfspace depth\")\nplt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "modelMult.simplicialVolume(X)\ncolors=[\"blue\",\"red\",\"green\"]\nplt.figure(figsize=(15,5))\nfor i in range(3):\n    plt.subplot(1,3,1,)\n    plt.scatter(modelMult.simplicialVolumeDepth[0][modelMult.distribution==i],\n                modelMult.simplicialVolumeDepth[1][modelMult.distribution==i],color=colors[i])\n    plt.subplot(1,3,2)\n    plt.scatter(modelMult.simplicialVolumeDepth[0][modelMult.distribution==i],\n                modelMult.simplicialVolumeDepth[2][modelMult.distribution==i],color=colors[i])\n    plt.subplot(1,3,3)\n    plt.scatter(modelMult.simplicialVolumeDepth[1][modelMult.distribution==i],\n                modelMult.simplicialVolumeDepth[2][modelMult.distribution==i],color=colors[i])\n    \nplt.subplot(1,3,1,)\nplt.xlabel(\"Depth w.r.t. distribution 1\")\nplt.ylabel(\"Depth w.r.t. distribution 2\")\nplt.subplot(1,3,2)\nplt.xlabel(\"Depth w.r.t. distribution 1\")\nplt.ylabel(\"Depth w.r.t. distribution 3\")\nplt.subplot(1,3,3)\nplt.xlabel(\"Depth w.r.t. distribution 2\")\nplt.ylabel(\"Depth w.r.t. distribution 3\")\nplt.legend([\"First distribution\",\"Second distribution\",\"Third distribution\"])\n\nplt.suptitle(\"Multiple distribution using simplicial volume depth\")\nplt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "plt.figure(figsize=(15,5))\nfor i in range(3):\n    plt.subplot(1,3,i+1,)\n    plt.scatter(modelMult.simplicialVolumeDepth[i][modelMult.distribution==i],\n                modelMult.halfspaceDepth[i][modelMult.distribution==i],color=colors[i])\n\n    plt.xlabel(f\"SimplicialVolume depth w.r.t. distribution {i}\")\n    plt.ylabel(f\"Halfspace depth w.r.t. distribution {i}\")\n    plt.title(fr\"Distribution {i} depth$\\times$depth plot\")\nplt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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      "file_extension": ".py",
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      "nbconvert_exporter": "python",
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