Weighted kernel density estimation based on `scipy.stats.gaussian_kde`.

weighted_kde.ipynb

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      "import numpy as np\n",
      "from scipy.spatial.distance import cdist\n",
      "\n",
      "class gaussian_kde(object):\n",
      "    \"\"\"Representation of a kernel-density estimate using Gaussian kernels.\n",
      "\n",
      "    Kernel density estimation is a way to estimate the probability density\n",
      "    function (PDF) of a random variable in a non-parametric way.\n",
      "    `gaussian_kde` works for both uni-variate and multi-variate data.   It\n",
      "    includes automatic bandwidth determination.  The estimation works best for\n",
      "    a unimodal distribution; bimodal or multi-modal distributions tend to be\n",
      "    oversmoothed.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    dataset : array_like\n",
      "        Datapoints to estimate from. In case of univariate data this is a 1-D\n",
      "        array, otherwise a 2-D array with shape (# of dims, # of data).\n",
      "    bw_method : str, scalar or callable, optional\n",
      "        The method used to calculate the estimator bandwidth.  This can be\n",
      "        'scott', 'silverman', a scalar constant or a callable.  If a scalar,\n",
      "        this will be used directly as `kde.factor`.  If a callable, it should\n",
      "        take a `gaussian_kde` instance as only parameter and return a scalar.\n",
      "        If None (default), 'scott' is used.  See Notes for more details.\n",
      "    weights : array_like, shape (n, ), optional, default: None\n",
      "        An array of weights, of the same shape as `x`.  Each value in `x`\n",
      "        only contributes its associated weight towards the bin count\n",
      "        (instead of 1).\n",
      "\n",
      "    Attributes\n",
      "    ----------\n",
      "    dataset : ndarray\n",
      "        The dataset with which `gaussian_kde` was initialized.\n",
      "    d : int\n",
      "        Number of dimensions.\n",
      "    n : int\n",
      "        Number of datapoints.\n",
      "    neff : float\n",
      "        Effective sample size using Kish's approximation.\n",
      "    factor : float\n",
      "        The bandwidth factor, obtained from `kde.covariance_factor`, with which\n",
      "        the covariance matrix is multiplied.\n",
      "    covariance : ndarray\n",
      "        The covariance matrix of `dataset`, scaled by the calculated bandwidth\n",
      "        (`kde.factor`).\n",
      "    inv_cov : ndarray\n",
      "        The inverse of `covariance`.\n",
      "\n",
      "    Methods\n",
      "    -------\n",
      "    kde.evaluate(points) : ndarray\n",
      "        Evaluate the estimated pdf on a provided set of points.\n",
      "    kde(points) : ndarray\n",
      "        Same as kde.evaluate(points)\n",
      "    kde.pdf(points) : ndarray\n",
      "        Alias for ``kde.evaluate(points)``.\n",
      "    kde.set_bandwidth(bw_method='scott') : None\n",
      "        Computes the bandwidth, i.e. the coefficient that multiplies the data\n",
      "        covariance matrix to obtain the kernel covariance matrix.\n",
      "        .. versionadded:: 0.11.0\n",
      "    kde.covariance_factor : float\n",
      "        Computes the coefficient (`kde.factor`) that multiplies the data\n",
      "        covariance matrix to obtain the kernel covariance matrix.\n",
      "        The default is `scotts_factor`.  A subclass can overwrite this method\n",
      "        to provide a different method, or set it through a call to\n",
      "        `kde.set_bandwidth`.\n",
      "\n",
      "    Notes\n",
      "    -----\n",
      "    Bandwidth selection strongly influences the estimate obtained from the KDE\n",
      "    (much more so than the actual shape of the kernel).  Bandwidth selection\n",
      "    can be done by a \"rule of thumb\", by cross-validation, by \"plug-in\n",
      "    methods\" or by other means; see [3]_, [4]_ for reviews.  `gaussian_kde`\n",
      "    uses a rule of thumb, the default is Scott's Rule.\n",
      "\n",
      "    Scott's Rule [1]_, implemented as `scotts_factor`, is::\n",
      "\n",
      "        n**(-1./(d+4)),\n",
      "\n",
      "    with ``n`` the number of data points and ``d`` the number of dimensions.\n",
      "    Silverman's Rule [2]_, implemented as `silverman_factor`, is::\n",
      "\n",
      "        (n * (d + 2) / 4.)**(-1. / (d + 4)).\n",
      "\n",
      "    Good general descriptions of kernel density estimation can be found in [1]_\n",
      "    and [2]_, the mathematics for this multi-dimensional implementation can be\n",
      "    found in [1]_.\n",
      "\n",
      "    References\n",
      "    ----------\n",
      "    .. [1] D.W. Scott, \"Multivariate Density Estimation: Theory, Practice, and\n",
      "           Visualization\", John Wiley & Sons, New York, Chicester, 1992.\n",
      "    .. [2] B.W. Silverman, \"Density Estimation for Statistics and Data\n",
      "           Analysis\", Vol. 26, Monographs on Statistics and Applied Probability,\n",
      "           Chapman and Hall, London, 1986.\n",
      "    .. [3] B.A. Turlach, \"Bandwidth Selection in Kernel Density Estimation: A\n",
      "           Review\", CORE and Institut de Statistique, Vol. 19, pp. 1-33, 1993.\n",
      "    .. [4] D.M. Bashtannyk and R.J. Hyndman, \"Bandwidth selection for kernel\n",
      "           conditional density estimation\", Computational Statistics & Data\n",
      "           Analysis, Vol. 36, pp. 279-298, 2001.\n",
      "\n",
      "    Examples\n",
      "    --------\n",
      "    Generate some random two-dimensional data:\n",
      "\n",
      "    >>> from scipy import stats\n",
      "    >>> def measure(n):\n",
      "    >>>     \"Measurement model, return two coupled measurements.\"\n",
      "    >>>     m1 = np.random.normal(size=n)\n",
      "    >>>     m2 = np.random.normal(scale=0.5, size=n)\n",
      "    >>>     return m1+m2, m1-m2\n",
      "\n",
      "    >>> m1, m2 = measure(2000)\n",
      "    >>> xmin = m1.min()\n",
      "    >>> xmax = m1.max()\n",
      "    >>> ymin = m2.min()\n",
      "    >>> ymax = m2.max()\n",
      "\n",
      "    Perform a kernel density estimate on the data:\n",
      "\n",
      "    >>> X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]\n",
      "    >>> positions = np.vstack([X.ravel(), Y.ravel()])\n",
      "    >>> values = np.vstack([m1, m2])\n",
      "    >>> kernel = stats.gaussian_kde(values)\n",
      "    >>> Z = np.reshape(kernel(positions).T, X.shape)\n",
      "\n",
      "    Plot the results:\n",
      "\n",
      "    >>> import matplotlib.pyplot as plt\n",
      "    >>> fig = plt.figure()\n",
      "    >>> ax = fig.add_subplot(111)\n",
      "    >>> ax.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,\n",
      "    ...           extent=[xmin, xmax, ymin, ymax])\n",
      "    >>> ax.plot(m1, m2, 'k.', markersize=2)\n",
      "    >>> ax.set_xlim([xmin, xmax])\n",
      "    >>> ax.set_ylim([ymin, ymax])\n",
      "    >>> plt.show()\n",
      "\n",
      "    \"\"\"\n",
      "    def __init__(self, dataset, bw_method=None, weights=None):\n",
      "        self.dataset = np.atleast_2d(dataset)\n",
      "        if not self.dataset.size > 1:\n",
      "            raise ValueError(\"`dataset` input should have multiple elements.\")\n",
      "        self.d, self.n = self.dataset.shape\n",
      "            \n",
      "        if weights is not None:\n",
      "            self.weights = weights / np.sum(weights)\n",
      "        else:\n",
      "            self.weights = np.ones(self.n) / self.n\n",
      "            \n",
      "        # Compute the effective sample size \n",
      "        # http://surveyanalysis.org/wiki/Design_Effects_and_Effective_Sample_Size#Kish.27s_approximate_formula_for_computing_effective_sample_size\n",
      "        self.neff = 1.0 / np.sum(self.weights ** 2)\n",
      "\n",
      "        self.set_bandwidth(bw_method=bw_method)\n",
      "\n",
      "    def evaluate(self, points):\n",
      "        \"\"\"Evaluate the estimated pdf on a set of points.\n",
      "\n",
      "        Parameters\n",
      "        ----------\n",
      "        points : (# of dimensions, # of points)-array\n",
      "            Alternatively, a (# of dimensions,) vector can be passed in and\n",
      "            treated as a single point.\n",
      "\n",
      "        Returns\n",
      "        -------\n",
      "        values : (# of points,)-array\n",
      "            The values at each point.\n",
      "\n",
      "        Raises\n",
      "        ------\n",
      "        ValueError : if the dimensionality of the input points is different than\n",
      "                     the dimensionality of the KDE.\n",
      "\n",
      "        \"\"\"\n",
      "        points = np.atleast_2d(points)\n",
      "\n",
      "        d, m = points.shape\n",
      "        if d != self.d:\n",
      "            if d == 1 and m == self.d:\n",
      "                # points was passed in as a row vector\n",
      "                points = np.reshape(points, (self.d, 1))\n",
      "                m = 1\n",
      "            else:\n",
      "                msg = \"points have dimension %s, dataset has dimension %s\" % (d,\n",
      "                    self.d)\n",
      "                raise ValueError(msg)\n",
      "\n",
      "        # compute the normalised residuals\n",
      "        chi2 = cdist(points.T, self.dataset.T, 'mahalanobis', VI=self.inv_cov) ** 2\n",
      "        # compute the pdf\n",
      "        result = np.sum(np.exp(-.5 * chi2) * self.weights, axis=1) / self._norm_factor\n",
      "\n",
      "        return result\n",
      "\n",
      "    __call__ = evaluate\n",
      "\n",
      "    def scotts_factor(self):\n",
      "        return np.power(self.neff, -1./(self.d+4))\n",
      "\n",
      "    def silverman_factor(self):\n",
      "        return np.power(self.neff*(self.d+2.0)/4.0, -1./(self.d+4))\n",
      "\n",
      "    #  Default method to calculate bandwidth, can be overwritten by subclass\n",
      "    covariance_factor = scotts_factor\n",
      "\n",
      "    def set_bandwidth(self, bw_method=None):\n",
      "        \"\"\"Compute the estimator bandwidth with given method.\n",
      "\n",
      "        The new bandwidth calculated after a call to `set_bandwidth` is used\n",
      "        for subsequent evaluations of the estimated density.\n",
      "\n",
      "        Parameters\n",
      "        ----------\n",
      "        bw_method : str, scalar or callable, optional\n",
      "            The method used to calculate the estimator bandwidth.  This can be\n",
      "            'scott', 'silverman', a scalar constant or a callable.  If a\n",
      "            scalar, this will be used directly as `kde.factor`.  If a callable,\n",
      "            it should take a `gaussian_kde` instance as only parameter and\n",
      "            return a scalar.  If None (default), nothing happens; the current\n",
      "            `kde.covariance_factor` method is kept.\n",
      "\n",
      "        Notes\n",
      "        -----\n",
      "        .. versionadded:: 0.11\n",
      "\n",
      "        Examples\n",
      "        --------\n",
      "        >>> x1 = np.array([-7, -5, 1, 4, 5.])\n",
      "        >>> kde = stats.gaussian_kde(x1)\n",
      "        >>> xs = np.linspace(-10, 10, num=50)\n",
      "        >>> y1 = kde(xs)\n",
      "        >>> kde.set_bandwidth(bw_method='silverman')\n",
      "        >>> y2 = kde(xs)\n",
      "        >>> kde.set_bandwidth(bw_method=kde.factor / 3.)\n",
      "        >>> y3 = kde(xs)\n",
      "\n",
      "        >>> fig = plt.figure()\n",
      "        >>> ax = fig.add_subplot(111)\n",
      "        >>> ax.plot(x1, np.ones(x1.shape) / (4. * x1.size), 'bo',\n",
      "        ...         label='Data points (rescaled)')\n",
      "        >>> ax.plot(xs, y1, label='Scott (default)')\n",
      "        >>> ax.plot(xs, y2, label='Silverman')\n",
      "        >>> ax.plot(xs, y3, label='Const (1/3 * Silverman)')\n",
      "        >>> ax.legend()\n",
      "        >>> plt.show()\n",
      "\n",
      "        \"\"\"\n",
      "        if bw_method is None:\n",
      "            pass\n",
      "        elif bw_method == 'scott':\n",
      "            self.covariance_factor = self.scotts_factor\n",
      "        elif bw_method == 'silverman':\n",
      "            self.covariance_factor = self.silverman_factor\n",
      "        elif np.isscalar(bw_method) and not isinstance(bw_method, string_types):\n",
      "            self._bw_method = 'use constant'\n",
      "            self.covariance_factor = lambda: bw_method\n",
      "        elif callable(bw_method):\n",
      "            self._bw_method = bw_method\n",
      "            self.covariance_factor = lambda: self._bw_method(self)\n",
      "        else:\n",
      "            msg = \"`bw_method` should be 'scott', 'silverman', a scalar \" \\\n",
      "                  \"or a callable.\"\n",
      "            raise ValueError(msg)\n",
      "\n",
      "        self._compute_covariance()\n",
      "\n",
      "    def _compute_covariance(self):\n",
      "        \"\"\"Computes the covariance matrix for each Gaussian kernel using\n",
      "        covariance_factor().\n",
      "        \"\"\"\n",
      "        self.factor = self.covariance_factor()\n",
      "        # Cache covariance and inverse covariance of the data\n",
      "        if not hasattr(self, '_data_inv_cov'):\n",
      "            # Compute the mean and residuals\n",
      "            _mean = np.sum(self.weights * self.dataset, axis=1)\n",
      "            _residual = (self.dataset - _mean[:, None])\n",
      "            # Compute the biased covariance\n",
      "            self._data_covariance = np.atleast_2d(np.dot(_residual * self.weights, _residual.T))\n",
      "            # Correct for bias (http://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_covariance)\n",
      "            self._data_covariance /= (1 - np.sum(self.weights ** 2))\n",
      "            self._data_inv_cov = np.linalg.inv(self._data_covariance)\n",
      "\n",
      "        self.covariance = self._data_covariance * self.factor**2\n",
      "        self.inv_cov = self._data_inv_cov / self.factor**2\n",
      "        self._norm_factor = np.sqrt(np.linalg.det(2*np.pi*self.covariance)) #* self.n"
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      "Unweighted test"
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     "input": [
      "%pylab inline\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy import stats\n",
      "\n",
      "#Define parameters\n",
      "num_samples = 1000\n",
      "xmax = 5\n",
      "bins=21\n",
      "\n",
      "#Generate equal-weighted samples\n",
      "samples = np.random.normal(size=num_samples)\n",
      "weights = np.ones(num_samples) / num_samples\n",
      "\n",
      "#Plot a histogram\n",
      "plt.hist(samples, bins, (-xmax, xmax), histtype='stepfilled', \n",
      "         alpha=.2, normed=True, color='k', label='histogram')\n",
      "\n",
      "#Construct a KDE and plot it\n",
      "pdf = gaussian_kde(samples)\n",
      "x = np.linspace(-xmax, xmax, 200)\n",
      "y = pdf(x)\n",
      "plt.plot(x, y, label='kde')\n",
      "\n",
      "#Plot the samples\n",
      "plt.scatter(samples, np.zeros_like(samples), marker='x', \n",
      "            color='k', alpha=.1, label='samples')\n",
      "\n",
      "#Plot the true pdf\n",
      "y = stats.norm().pdf(x)\n",
      "plt.plot(x,y, label='true PDF')\n",
      "\n",
      "#Boiler plate\n",
      "plt.xlabel('Variable')\n",
      "plt.ylabel('Density')\n",
      "plt.legend(loc='best', frameon=False)\n",
      "plt.tight_layout()\n",
      "plt.show()"
     ],
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Z0JOvt39tdEhCHEeSlBBVkJFhYffuAFp1TmVb7jZ6NulpdEhnzWqFIUNKn/u6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\npmqapOnA/cCvIuJ9XT85SZwKnCPpbGAGMFvSLyP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       "text": [
        "<matplotlib.figure.Figure at 0x10bbbc210>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Weighted test"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import stats\n",
      "\n",
      "#Define a Gaussian mixture to draw samples from\n",
      "num_samples = 10000\n",
      "xmin, xmax = -10, 8\n",
      "#Weight attributed to each component of the mixture\n",
      "gaussian_weights = np.array([2, 1], dtype=np.float)\n",
      "gaussian_weights /= np.sum(gaussian_weights)\n",
      "#Mean and std of each mixture\n",
      "gaussian_means = np.array([-1, 1])\n",
      "gaussian_std = np.array([2, 1])\n",
      "#Observation probability of each mixture\n",
      "gaussian_observation = np.array([1, .5])\n",
      "\n",
      "#How many samples belong to each mixture?\n",
      "gaussian_samples = np.random.multinomial(num_samples, gaussian_weights)\n",
      "samples = []\n",
      "weights = []\n",
      "#Generate samples and observed samples for each mixture component\n",
      "for n, m, s, o in zip(gaussian_samples, gaussian_means, gaussian_std, gaussian_observation):\n",
      "    _samples = np.random.normal(m, s, n)\n",
      "    _samples = _samples[o > np.random.uniform(size=n)]\n",
      "    samples.extend(_samples)\n",
      "    weights.extend(np.ones_like(_samples) / o)\n",
      "\n",
      "#Renormalise the sample weights\n",
      "weights = np.array(weights, np.float)\n",
      "weights /= np.sum(weights)\n",
      "samples = np.array(samples)\n",
      "\n",
      "#Compute the true pdf\n",
      "x = np.linspace(xmin, xmax, 200)\n",
      "true_pdf = 0\n",
      "for w, m, s in zip(gaussian_weights, gaussian_means, gaussian_std):\n",
      "    true_pdf = true_pdf + w * stats.norm(m, s).pdf(x)\n",
      "    \n",
      "#Plot a histogram\n",
      "plt.hist(samples, bins, (xmin, xmax), histtype='stepfilled', \n",
      "         alpha=.2, normed=True, color='k', label='histogram', weights=weights)\n",
      "\n",
      "#Construct a KDE and plot it\n",
      "pdf = gaussian_kde(samples, weights=weights)\n",
      "y = pdf(x)\n",
      "plt.plot(x, y, label='weighted kde')\n",
      "\n",
      "#Compare with a naive kde\n",
      "pdf = stats.gaussian_kde(samples)\n",
      "y = pdf(x)\n",
      "plt.plot(x, y, label='unweighted kde')\n",
      "\n",
      "#Plot the samples\n",
      "plt.scatter(samples, np.zeros_like(samples), marker='x', \n",
      "            color='k', alpha=.02, label='samples')\n",
      "\n",
      "#Plot the true pdf\n",
      "plt.plot(x,true_pdf, label='true PDF')\n",
      "\n",
      "#Boiler plate\n",
      "plt.xlabel('Variable')\n",
      "plt.ylabel('Density')\n",
      "plt.legend(loc='best', frameon=False)\n",
      "plt.tight_layout()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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16lVOnDjBqlWrjIYAz58/z+LFizl69Ch37txh586deHt7079/f2bMmMHIkSNJ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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x110e5f210>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "2D weighted test"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import stats\n",
      "\n",
      "#Define a Gaussian mixture to draw samples from\n",
      "num_samples = 10000\n",
      "xmin, xmax = -10, 8\n",
      "#Weight attributed to each component of the mixture\n",
      "gaussian_weights = np.array([2, 1], dtype=np.float)\n",
      "gaussian_weights /= np.sum(gaussian_weights)\n",
      "#Mean and std of each mixture\n",
      "gaussian_means = np.array([-1, 1])\n",
      "gaussian_std = np.array([2, 1])\n",
      "#Observation probability of each mixture\n",
      "gaussian_observation = np.array([1, .5])\n",
      "\n",
      "#How many samples belong to each mixture?\n",
      "gaussian_samples = np.random.multinomial(num_samples, gaussian_weights)\n",
      "samples = []\n",
      "weights = []\n",
      "#Generate samples and observed samples for each mixture component\n",
      "for n, m, s, o in zip(gaussian_samples, gaussian_means, gaussian_std, gaussian_observation):\n",
      "    _samples = np.random.normal(m, s, (n, 2))\n",
      "    _samples = _samples[o > np.random.uniform(size=n)]\n",
      "    samples.extend(_samples)\n",
      "    weights.extend(np.ones(len(_samples)) / o)\n",
      "\n",
      "#Renormalise the sample weights\n",
      "weights = np.array(weights, np.float)\n",
      "weights /= np.sum(weights)\n",
      "samples = np.transpose(samples)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Evaluate the true pdf on a grid\n",
      "x = np.linspace(xmin, xmax, 100)\n",
      "xx, yy = np.meshgrid(x, x)\n",
      "true_pdf = 0\n",
      "for w, m, s in zip(gaussian_weights, gaussian_means, gaussian_std):\n",
      "    true_pdf = true_pdf + w * stats.norm(m, s).pdf(xx) * stats.norm(m, s).pdf(yy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Evaluate the kde on a grid\n",
      "pdf = gaussian_kde(samples, weights=weights)\n",
      "zz = pdf((np.ravel(xx), np.ravel(yy)))\n",
      "zz = np.reshape(zz, xx.shape)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kwargs = dict(extent=(xmin, xmax, xmin, xmax), cmap='hot', origin='lower')\n",
      "#Plot the true pdf\n",
      "plt.subplot(221)\n",
      "plt.imshow(true_pdf.T, **kwargs)\n",
      "plt.title('true PDF')\n",
      "\n",
      "#Plot the kde\n",
      "plt.subplot(222)\n",
      "plt.imshow(zz.T, **kwargs)\n",
      "plt.title('kde')\n",
      "plt.tight_layout()\n",
      "\n",
      "#Plot a histogram\n",
      "ax = plt.subplot(223)\n",
      "plt.hist2d(samples[0], samples[1], bins, ((xmin, xmax), (xmin, xmax)), \n",
      "           True, weights, cmap='hot')\n",
      "ax.set_aspect(1)\n",
      "plt.title('histogram')\n",
      "plt.tight_layout()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sdabK8nDQnNl317p4ZRq37PVQL6ctuiL3lrRyLTe7uPWSo5K0E2/YyTVs6Mm+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\naF5kXsdA9zjBlH6AqrSpOv6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       "text": [
        "<matplotlib.figure.Figure at 0x103b13a90>"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}