deletions | additions       diff --git a/figures/sample-datasets/FittingData.ipynb b/figures/sample-datasets/FittingData.ipynb  index f6c5319..28c6022 100644  --- a/figures/sample-datasets/FittingData.ipynb  +++ b/figures/sample-datasets/FittingData.ipynb 
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"cell_type": "markdown",  "metadata": {},  "source": [  "##Create a class `sampleDataSets`\n",  "This sets up "We also need to import  a custom `Python`  class to make the fake datasets." datasets. You will need the file `measurements.py` to be in the same directory as this notebook."  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "from numpy measurements  import linspace,zeros\n",  "from numpy.random import standard_normal, random, random_integers\n",  "\n",  "class sampleDataSets:\n",  " \"\"\"\n",  " Sets up a linear relation, y = m*x + b. Datasets can be generated \n",  " from this relation by adding gaussian fluctuations to each y. The std. \n",  " deviation of the fluctuation are chosen from a uniform random distribution \n",  " between 0.3 and 0.7. There are 3 choices for datasets.\n",  " 1. Fits the data much better than would be indicated by the size of its\n",  " quoted uncertainties. The real fluctations have a std. dev. that is \n",  " 1/5 of the quoted one.\n",  " 2. Uncertainties are drawn from a normal distribution with a standard\n",  " deviation matching the size of the errorbars. This should produce\n",  " an ideal chi^2 distribution if many trials are conducted.\n",  " 3. Identical to 2, but 20% of the datapoints are given 5 sigma \n",  " fluctuations.\n",  " \"\"\"\n",  " \n",  " _slope = 3.0\n",  " _intercept = 1.0\n",  " _sig_low = 0.3\n",  " _sig_high = 0.7\n",  "\n",  " def __init__(self):\n",  " \"\"\"\n",  " Sets the relation, the nominal size of the errorbars, and the actual \n",  " size of the errorbars.\n",  " \"\"\"\n",  " a = self._sig_low\n",  " b = self._sig_high\n",  " self._amp = (b-a)*random() + a\n",  " self._fake = 0.2*self._amp\n",  " \n",  " def make_dataset(self,x,use_fake=False,with_outliers=False):\n",  " \"\"\"\n",  " Constructs a dataset from the given relation with errorbars drawn from \n",  " a normal distribution.\n",  " \n",  " Arguments\n",  " ---------\n",  " x := [array-like] the values at which the relation should be \n",  " evaluated\n",  " use_fake := if True, then reduce the standard deviation of the \n",  " fluctuations by a factor of 10. This dataset will \n",  " have an anomalously low chi^2.\n",  " with_outliers:= if True, then 20% of the points will have 10 sigma \n",  " fluctuations.\n",  " \n",  " Returns\n",  " -------\n",  " y := an ndarray of length(x.size) containing the dataset\n",  " \"\"\"\n",  " \n",  " m = self._slope\n",  " b = self._intercept\n",  " if use_fake:\n",  " sig = self._fake\n",  " else:\n",  " sig = self._amp\n",  " y = m*x + b + sig*standard_normal(len(x))\n",  " if with_outliers:\n",  " n = int(0.2*x.size)\n",  " sgn = zeros(n)\n",  " for i in range(n):\n",  " if random() < 0.5:\n",  " sgn[i] = -1.0\n",  " else:\n",  " sgn[i] = 1.0\n",  " indcs = random_integers(0,x.size-1,size=(2))\n",  " y[indcs] = m*x[indcs] + b + sgn*5.0*sig\n",  " return y\n",  " \n",  " def quoted_error(self):\n",  " \"\"\"\n",  " returns the quoted standard deviation\n",  " \"\"\"\n",  " return self._amp\n",  " \n",  " def unrealistic_dataset(self,x):\n",  " \"\"\"\n",  " Returns a dataset with actual uncertainties much less than the quoted \n",  " errorbars.\n",  " \n",  " Arguments\n",  " ---------\n",  " x := [array-like] the values at which the relation should be \n",  " evaluated\n",  " \n",  " Returns\n",  " -------\n",  " y := an ndarray of length(x.size) containing the dataset \n",  " \"\"\"\n",  " \n",  " return self.make_dataset(x,use_fake=True)\n",  "\n",  " def realistic_dataset(self,x):\n",  " \"\"\"\n",  " Returns a dataset with uncertainties that agree with the quoted \n",  " errorbars.\n",  " \n",  " Arguments\n",  " ---------\n",  " x := [array-like] the values at which the relation should be \n",  " evaluated\n",  " \n",  " Returns\n",  " -------\n",  " y := an ndarray of length(x.size) containing the dataset \n",  " \"\"\"\n",  "\n",  " return self.make_dataset(x,use_fake=False)\n",  "\n",  " def dataset_with_outliers(self,x):\n",  " \"\"\"\n",  " Returns a dataset with 80% of the points drawn from the normal \n",  " distribution, and 20% of the points having 10-sigma fluctuations.\n",  "\n",  " Arguments\n",  " ---------\n",  " x := [array-like] the values at which the relation should be \n",  " evaluated\n",  " \n",  " Returns\n",  " -------\n",  " y := an ndarray of length(x.size) containing the dataset \n",  " \"\"\"\n",  "\n",  " return self.make_dataset(x,use_fake=False,with_outliers=True)\n",  " \n",  " def fit(self,x):\n",  " \"\"\"\n",  " Returns the true relation, y = m*x + b\n",  "\n",  " Arguments\n",  " ---------\n",  " x := [array-like] the values at which the relation should be \n",  " evaluated\n",  " \n",  " Returns\n",  " -------\n",  " y := an ndarray of length(x.size) containing the underlying \n",  " relation.\n",  " \"\"\"\n",  " \n",  " m = self._slope\n",  " b = self._intercept\n",  " return m*x + b\n" measurementWithUncertainty"  ],  "language": "python",  "metadata": {},