Exercise_06_Similarity.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Temporal and Spatial DataMining\n",
    "\n",
    "## Exercise_06_Similarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from utils.TimeSeries import TS_1, TS_2\n",
    "from scipy.linalg import norm\n",
    "from matplotlib import cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1: DTW"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a)** Understanding DTW\n",
    "\n",
    "Explain the procedure of the DTW algorithm \n",
    "\n",
    ">**Tip:** Take a look at the lecture notes, in \"Information Retrieval for Music and Motion\" by Müller (Chapter 4, as an e-book in the library), in the \"Everything you know about Dynamic Time Warping is Wrong\" by Ratanamahatana and Keogh, in \"Exact Indexing of Dynamic Time Warping\" by Keogh.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q1.** What is a \"local cost function\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q2.** What is a \"DTW matrix\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q3.** What is a warping path?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q4.** What is indexing and what are \"lower bounds\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q5.(UPDATE)** In which cases is it possible to obtain more than one warping path when calculating the similarity of two Time Series? What is the difference between the obtained paths?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q6.** Is DTW robust against outliers? (that is, do outliers change the DTW value?)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q7.** What is the difference between norm and metric?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q8.** Is Euclidean Distance a Metric? What must be fulfilled to call a function  $d(\\mathbf{x},\\mathbf{y})$ a metric?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q9.** Is DTW a metric?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " **---  Your Text Here ----** \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b)** Implement the calculation of the accumulated cost matrix in the function **dtw**. Then execute the function with the given **x** and **y** values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dtw(x, y, dist, warp=1):\n",
    "    \"\"\"\n",
    "    Computes Dynamic Time Warping (DTW) of two sequences.\n",
    "    :param array x: N1*M array\n",
    "    :param array y: N2*M array\n",
    "    :param func dist: distance used as cost measure\n",
    "    :param int warp: how many shifts are computed.\n",
    "    Returns the minimum distance, the cost matrix, the accumulated cost matrix, and the wrap path.\n",
    "    \"\"\"\n",
    "    assert len(x)\n",
    "    assert len(y)\n",
    "    r, c = len(x), len(y)\n",
    "    D0 = np.zeros((r + 1, c + 1))\n",
    "    D0[0, 1:] = np.inf\n",
    "    D0[1:, 0] = np.inf\n",
    "    D1 = D0[1:, 1:]  # view\n",
    "    for i in range(r):\n",
    "        for j in range(c):\n",
    "            D1[i, j] = dist(x[i], y[j])\n",
    "    C = D1.copy()\n",
    "    ####################\n",
    "    for i in range(r):\n",
    "        for j in range(c):\n",
    "            if i == 0 and j == 0:\n",
    "                D1[i, j] = C[i, j]\n",
    "            elif i == 0:\n",
    "                D1[i, j] = C[i, j] + D1[i, j-1]\n",
    "            elif j == 0:\n",
    "                D1[i, j] = C[i, j] + D1[i-1, j]\n",
    "            else:\n",
    "                D1[i, j] = C[i, j] + min(D1[i-1, j], D1[i, j-1], D1[i-1, j-1])\n",
    "    ####################\n",
    "    if len(x)==1:\n",
    "        path = np.zeros(len(y)), range(len(y))\n",
    "    elif len(y) == 1:\n",
    "        path = range(len(x)), np.zeros(len(x))\n",
    "    else:\n",
    "        path = _traceback(D0)\n",
    "        \n",
    "    return D1[-1, -1] / sum(D1.shape), C, D1, path\n",
    "\n",
    "def _traceback(D):\n",
    "    i, j = np.array(D.shape) - 2\n",
    "    p, q = [i], [j]\n",
    "    while (i > 0) or (j > 0):\n",
    "        tb = np.argmin((D[i, j], D[i, j+1], D[i+1, j]))\n",
    "        if tb == 0:\n",
    "            i -= 1\n",
    "            j -= 1\n",
    "        elif tb == 1:\n",
    "            i -= 1\n",
    "        else:  # (tb == 2):\n",
    "            j -= 1\n",
    "        p.insert(0, i)\n",
    "        q.insert(0, j)\n",
    "    return np.array(p), np.array(q)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0. inf inf inf inf inf]\n",
      " [inf  0.  0.  0.  0.  0.]\n",
      " [inf  0.  0.  0.  0.  0.]\n",
      " [inf  0.  0.  0.  0.  0.]\n",
      " [inf  0.  0.  0.  0.  0.]\n",
      " [inf  0.  0.  0.  0.  0.]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### test code zum Verständnis ###\n",
    "D0 = np.zeros((6, 6))\n",
    "D0[0, 1:] = np.inf\n",
    "D0[1:, 0] = np.inf\n",
    "print(D0)\n",
    "\n",
    "D1 = D0[1:, 1:]\n",
    "D1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1,c = TS_1(x1=5, samples=50)\n",
    "t2,d = TS_2(x1=5, samples=40)\n",
    "\n",
    "x=c.reshape(-1,1)\n",
    "y=d.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe010390e80>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t1,c)\n",
    "plt.plot(t2,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_distance(X1, X2, p):\n",
    "    return np.sum(np.abs(X1-X2)**p)**(1/p)\n",
    "\n",
    "# plot the accumulated cost martix and the wrap path\n",
    "dist, cost, acc, path = dtw(x, y, dist=lambda x, y: simple_distance(x, y, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.imshow(cost, origin='lower')\n",
    "plt.plot(path[1], path[0], color='r')\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2: LCSS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a)** Implement the function **lcss** and output the longest subsequence of the two given sequences.\n",
    "\n",
    "**Hint**:\n",
    "[The lcss function defined](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem):\n",
    "\n",
    "1. $lcss(x_i, y_i)=\\varnothing$, if $i = 0$ or $j = 0$\n",
    "2. $lcss(x_i, y_i)=lcss(x_{i-1}, y_{j-1})^{\\wedge}x_i$, if $i,j > 0$ and $x_i=y_j$\n",
    "3. $lcss(x_i, y_i)=max\\{lcss(x_i, y_{j-1}), lcss(x_{i-1}, y_j)\\}$, if $i,j > 0$ and $x_i\\neq y_j$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lcss(x, y):\n",
    "    '''\n",
    "    x: a string with length of N\n",
    "    y: a string with length of M\n",
    "    Output: the longest subsequences.\n",
    "    '''\n",
    "    matrix = [''] * (len(x) + 1)\n",
    "    for index_x in range(len(matrix)):\n",
    "        matrix[index_x] = [''] * (len(y) + 1)\n",
    "    \n",
    "    ####################\n",
    "    for i in range(len(x)+1):\n",
    "        for j in range(len(y)+1):\n",
    "            if i == 0 or j == 0:\n",
    "                matrix[i][j] = ''\n",
    "            elif x[i-1] == y[j-1]:\n",
    "                matrix[i][j] = matrix[i-1][j-1] + x[i-1]\n",
    "            else:\n",
    "                matrix[i][j] = max(matrix[i-1][j], matrix[i][j-1], key=len)\n",
    "    ####################\n",
    "    print(np.array(matrix))\n",
    "    return matrix[len(x)][len(y)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[['' '' '' '' '' '' '' '' '' '']\n",
      " ['' 'a' 'a' 'a' 'a' 'a' 'a' 'a' 'a' 'a']\n",
      " ['' 'a' 'a' 'a' 'ab' 'ab' 'ab' 'ab' 'ab' 'ab']\n",
      " ['' 'a' 'a' 'a' 'ab' 'abc' 'abc' 'abc' 'abc' 'abc']\n",
      " ['' 'a' 'ad' 'ad' 'ab' 'abc' 'abc' 'abc' 'abcd' 'abcd']\n",
      " ['' 'a' 'ad' 'ad' 'ab' 'abc' 'abce' 'abce' 'abcd' 'abcd']\n",
      " ['' 'a' 'ad' 'ad' 'ab' 'abc' 'abce' 'abce' 'abcd' 'abcdf']]\n",
      "The longest subsequences is: abcdf\n"
     ]
    }
   ],
   "source": [
    "x = \"abcdef\"\n",
    "y = \"adabceqdf\"\n",
    "print('The longest subsequences is:', lcss(x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">LCSS Matrix:\n",
    "\n",
    "```\n",
    "[['', '', '', '', '', '', '', '', '', ''],\n",
    " ['', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a'],\n",
    " ['', 'a', 'a', 'a', 'ab', 'ab', 'ab', 'ab', 'ab', 'ab'],\n",
    " ['', 'a', 'a', 'a', 'ab', 'abc', 'abc', 'abc', 'abc', 'abc'],\n",
    " ['', 'a', 'ad', 'ad', 'ab', 'abc', 'abc', 'abc', 'abcd', 'abcd'],\n",
    " ['', 'a', 'ad', 'ad', 'ab', 'abc', 'abce', 'abce', 'abcd', 'abcd'],\n",
    " ['', 'a', 'ad', 'ad', 'ab', 'abc', 'abce', 'abce', 'abcd', 'abcdf']]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3: ED\n",
    "\n",
    "**a)** Implement the function to calculate edit distance based on the following formulas:\n",
    "\n",
    "\n",
    "1. $dist1 = ED(i-1, j-1)$, if $x_i=y_i$\n",
    "2. $dist2 = ED(i-1, j-1) + 1$, (replace)\n",
    "3. $dist3 = ED(i, j-1) + 1$, (insert)\n",
    "4. $dist4 = ED(i-1, j) + 1$, (delete)\n",
    "\n",
    "$ED(i,j) = min\\{dist1, dist2, dist3, dist4\\}$, with $ED(0,0)=0$, $ED(i,0)=i$ and $ED(0,j)=j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def edit_distance(str_a,str_b):\n",
    "    \"\"\"\n",
    "    :param str_a:\n",
    "    :param str_b:\n",
    "    :return: Edit distance\n",
    "    \"\"\"\n",
    "    str_a = str_a.lower()\n",
    "    str_b = str_b.lower()\n",
    "    matrix_ed = np.zeros((len(str_a)+1, len(str_b)+1), dtype=int)\n",
    "    matrix_ed[0] = np.arange(len(str_b)+1)\n",
    "    matrix_ed[:,0] = np.arange(len(str_a)+1)\n",
    "    \n",
    "    for i in range(1, len(str_a)+1):\n",
    "        for j in range(1, len(str_b)+1):\n",
    "            d1 = matrix_ed[i-1][j-1]\n",
    "            if str_a[i-1] != str_b[j-1]:\n",
    "                d1 += 1\n",
    "            d2 = matrix_ed[i][j-1] + 1\n",
    "            d3 = matrix_ed[i-1][j] + 1\n",
    "            matrix_ed[i][j] = min(d1, d2, d3)\n",
    "            \n",
    "    print(matrix_ed)        \n",
    "    return matrix_ed[-1,-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b)** Calculate the edit distance between x1 and x2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2 3 4 5]\n",
      " [1 0 1 2 3 4]\n",
      " [2 1 0 1 2 3]\n",
      " [3 2 1 1 2 3]\n",
      " [4 3 2 2 2 2]]\n",
      "The edit distance between x1 and x2 is: 2\n"
     ]
    }
   ],
   "source": [
    "x1 = 'love'\n",
    "x2 = 'lolpe'\n",
    "\n",
    "print('The edit distance between x1 and x2 is:', edit_distance(x1, x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">ED Matrix:\n",
    "\n",
    "```\n",
    "array([[0, 1, 2, 3, 4, 5],\n",
    "       [1, 0, 1, 2, 3, 4],\n",
    "       [2, 1, 0, 1, 2, 3],\n",
    "       [3, 2, 1, 1, 2, 3],\n",
    "       [4, 3, 2, 2, 2, 2]])\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 4: TWED (Bonus)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a)** Read the paper entitled \"Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching\" http://ieeexplore.ieee.org/Xplore/home.jsp of Pierre-François Marteau \n",
    "> Sections: **3, 3.1, and 4.1 - 4.4**\n",
    "\n",
    "> Furthermore: Wikipedia [article](https://de.wikipedia.org/wiki/Time_Warp_Edit_Distance) on TWED. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b)** What is \"Stiffness Adjustment\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The stiffness $\\nu$ expresses the cost/penalty of changing the time alignment.\n",
    "- Lower $\\nu$ allows more flexibility. \n",
    "- Higher $\\nu$ penalizes time warping\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c)** Is TWED a metric? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, because for $\\nu \\geq 0$ it fulfills the characteristics of a metric:\n",
    "- $\\delta_{\\lambda, \\nu}(A, B) \\geq 0$\n",
    "- $\\delta_{\\lambda, \\nu}(A, B) = 0 \\iff A = B$\n",
    "- $\\delta_{\\lambda, \\nu}(A, B) \\leq \\delta_{\\lambda, \\nu}(A, C) + \\delta_{\\lambda, \\nu}(C, B)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**d)** Implement the TWED function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# not needed, redundant\n",
    "def init_matrix(data):\n",
    "    for i in range(len(data)):\n",
    "        data[i][0] = float('inf')\n",
    "    for i in range(len(data[0])):\n",
    "        data[0][i] = float('inf')\n",
    "    data[0][0] = 0\n",
    "    return data\n",
    "\n",
    "\n",
    "def lp_dist(time_pt_1, time_pt_2, p=2):\n",
    "    \"\"\" Computes the LP distance between two points \"\"\"\n",
    "    return np.sum(np.abs(time_pt_1-time_pt_2)**p) ** (1/p)\n",
    "\n",
    "\n",
    "def TWED(t1, t2, lam, nu):\n",
    "    \"\"\"\"\n",
    "    Requires: \n",
    "    t1: multivariate time series in numpy matrix format. \n",
    "    t2: multivariate time series in numpy matrix format. \n",
    "    lam: penalty lambda parameter, \n",
    "    nu: stiffness coefficient\n",
    "    \n",
    "    Returns the TWED distance between the two time series. \n",
    "    \"\"\"\n",
    "    t1_time, t1_data = t1\n",
    "    t2_time, t2_data = t2\n",
    "\n",
    "    t1_data = t1_data.reshape(-1,1)\n",
    "    t2_data = t2_data.reshape(-1,1)\n",
    "\n",
    "    # insert zero at the beginning\n",
    "    t1_time = np.insert(t1_time, 0, 0, axis=0)\n",
    "    t1_data = np.insert(t1_data, 0, 0, axis=0)\n",
    "    t2_time = np.insert(t2_time, 0, 0, axis=0)\n",
    "    t2_data = np.insert(t2_data, 0, 0, axis=0)\n",
    "\n",
    "    N, M = len(t1_time), len(t2_time)\n",
    "    result = np.zeros((N, M))\n",
    "    result[0, 1:] = np.inf\n",
    "    result[1:, 0] = np.inf\n",
    "\n",
    "    for i in range(1, N):\n",
    "        for j in range(1, M):\n",
    "            # delete_A\n",
    "            c1 = (\n",
    "                result[i-1, j] \n",
    "                + lp_dist(t1_data[i-1], t1_data[i]) \n",
    "                + nu * (t1_time[i] - t1_time[i-1]) \n",
    "                + lam\n",
    "            )\n",
    "\n",
    "            # detete_B\n",
    "            c2 = (\n",
    "                result[i, j-1] \n",
    "                + lp_dist(t2_data[j-1], t2_data[j])\n",
    "                + nu * (t2_time[j] - t2_time[j-1]) \n",
    "                + lam\n",
    "            )\n",
    "\n",
    "            # match\n",
    "            c3 = (\n",
    "                result[i-1, j-1] \n",
    "                + lp_dist(t1_data[i], t2_data[j]) \n",
    "                + lp_dist(t1_data[i-1], t2_data[j-1]) \n",
    "                + nu * (np.abs(t1_time[i] - t2_time[j]) + np.abs(t1_time[i-1] - t2_time[j-1]))\n",
    "            )\n",
    "\n",
    "            result[i, j] = min(c1, c2, c3)\n",
    "\n",
    "    return result[N-1, M-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.758128896677505"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_1 = TS_1(x1=5, samples=50)\n",
    "ts_2 = TS_2(x1=5, samples=50)\n",
    "\n",
    "# calculate the distance between time series ts_1 and ts_2\n",
    "TWED(ts_1, ts_2, lam=0.1, nu=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# try different values for lam and nu\n",
    "lambdas = [0, 0.25, 0.5, 0.75, 1]\n",
    "nus = [10e-5, 10e-4, 10e-3, 10e-2, 10e-1, 1]\n",
    "\n",
    "distances = np.array([[TWED(ts_1, ts_2, lam, nu) for lam in lambdas] for nu in nus])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(distances, origin='lower')\n",
    "plt.xlabel('$\\lambda$')\n",
    "plt.ylabel('$\\\\nu$')\n",
    "plt.xticks(ticks=range(len(lambdas)), labels=lambdas)\n",
    "plt.yticks(ticks=range(len(nus)), labels=nus)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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