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dpatschke/kd_tree_notebook.ipynb

Created April 12, 2018 13:59
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KD_tree example with numba (failing)
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kd_tree_notebook.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# KD-tree test notebook\n",
"import numpy as np\n",
"import numba"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_obs = 100000\n",
"n_cols = 3\n",
"\n",
"x = np.random.random_sample(n_obs * n_cols)\n",
"x = np.reshape(x, (n_obs, n_cols))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data = x\n",
"leaf_size = 30\n",
"\n",
"# validate data\n",
"if data.size == 0:\n",
" raise ValueError(\"X is an empty array\")\n",
"\n",
"if leaf_size < 1:\n",
" raise ValueError(\"leaf_size must be greater than or equal to 1\")\n",
"\n",
"n_samples = data.shape[0]\n",
"n_features = data.shape[1]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# determine number of levels in the tree, and from this\n",
"# the number of splits in the tree. This results in leaf nodes\n",
"# with numbers of points betweeen 0 and leaf_size\n",
"n_levels = np.ceil(np.log2((n_samples / leaf_size)))\n",
"n_splits = int(2 ** n_levels) - 1"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"12.0\n",
"4095\n"
]
}
],
"source": [
"print(n_levels)\n",
"print(n_splits)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# allocate arrays for storage\n",
"\n",
"# Will identify whether split is a leaf node\n",
"split_is_leaf = np.zeros(n_splits, dtype=np.int32)\n",
"\n",
"# If a split is leaf, then we want to store several values:\n",
"# 1. the indices\n",
"# 2. the number of children\n",
"# Will hold the indices of the children in the leaf node\n",
"split_idx_membership = np.zeros(n_samples, dtype=np.int32)\n",
"# Will hold the number of children in each leaf node\n",
"split_n_children = np.zeros(n_splits, dtype=np.int32)\n",
"\n",
"# If a split is not a leaf, then there will be several values\n",
"# needed as well\n",
"# 1. The split dimension (index value)\n",
"# 2. The split value\n",
"# 3. The index of the left child/split \n",
"# 4. The index of the right child/split\n",
"# The last two values will be values that lie between 0 and n_splits\n",
"# Holds index of split dimension\n",
"split_dimension = np.zeros(n_splits, dtype=np.int32)\n",
"# Holds split value for non-leaf nodes\n",
"split_values = np.zeros(n_splits, dtype=np.float64)\n",
"# store the values of the left and right children\n",
"split_left_child = np.zeros(n_splits, dtype=np.int32)\n",
"split_right_child = np.zeros(n_splits, dtype=np.int32)\n",
"\n",
"# For all splits, we want to store the max and min values\n",
"# for each column. This will assist in faster querying\n",
"split_maxes = np.zeros((n_splits, n_features))\n",
"split_mins = np.zeros((n_splits, n_features))\n",
"\n",
"# Set initial values for working arrays\n",
"maxes = np.max(data, axis=0)\n",
"mins = np.min(data, axis=0)\n",
"idx = np.arange(data.shape[0])"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"@numba.jit(nopython=True)\n",
"def determine_split(split_col_array, split_col_idx, maxes, mins):\n",
" # sliding midpoint rule; see Maneewongvatana and Mount 1999\n",
" # for arguments that this is a good idea.\n",
" \n",
" # Switching to splitting on median value in order to\n",
" # construct more balanced trees\n",
" #maxval = maxes[split_col_idx]\n",
" #minval = mins[split_col_idx]\n",
" split = np.median(split_col_array)\n",
" \n",
" less_idx = np.nonzero(split_col_array <= split)[0]\n",
" greater_idx = np.nonzero(split_col_array > split)[0]\n",
" \n",
" if len(less_idx) == 0:\n",
" split = np.min(split_col_array)\n",
" less_idx = np.nonzero(split_col_array <= split)[0]\n",
" greater_idx = np.nonzero(split_col_array > split)[0]\n",
" if len(greater_idx) == 0:\n",
" split = np.max(split_col_array)\n",
" less_idx = np.nonzero(split_col_array < split)[0]\n",
" greater_idx = np.nonzero(split_col_array >= split)[0]\n",
" if len(less_idx) == 0:\n",
" # _still_ zero? all must have the same value\n",
" if not np.all(split_col_array == split_col_array[0]):\n",
" raise ValueError(\"Troublesome data array\")\n",
" split = split_col_array[0]\n",
" less_idx = np.arange(len(split_col_array)-1)\n",
" greater_idx = np.array([len(split_col_array)-1])\n",
" \n",
" lessmaxes = maxes.copy()\n",
" lessmaxes[split_col_idx] = split\n",
" greatermins = mins.copy()\n",
" greatermins[split_col_idx] = split\n",
" \n",
" return split, less_idx, greater_idx, lessmaxes, greatermins"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"@numba.jit(nopython=True)\n",
"def recursive_build(i_split, idx,\n",
" data, maxes, mins,\n",
" split_maxes, split_mins,\n",
" split_is_leaf, split_n_children,\n",
" split_dimension, split_values,\n",
" split_idx_membership, \n",
" split_left_child, split_right_child,\n",
" n_splits, leaf_size):\n",
"\n",
" i_child = 2 * i_split + 1\n",
" \n",
" # Regardless of whether we are in a leaf node or an innernode\n",
" # need to assign the max and min values for this node\n",
" split_maxes[i_split] = maxes\n",
" split_mins[i_split] = mins\n",
"\n",
" # if we've already reached our split limit, then we need to just\n",
" # create a leaf node even if we have more observations than\n",
" # what leaf_size says we should have\n",
" if i_child >= n_splits:\n",
" split_is_leaf[i_split] = True\n",
" split_idx_membership[idx] = i_split\n",
" split_n_children[i_split] = len(idx)\n",
" if len(idx) > 2 * leaf_size:\n",
" # this shouldn't happen if our memory allocation is correct.\n",
" # We'll proactively prevent memory errors, but raise a\n",
" # warning saying we're doing so.\n",
" #warnings.warn(\"Internal: memory layout is flawed: \"\n",
" # \"not enough nodes allocated\")\n",
" pass\n",
"\n",
" elif len(idx) < 2:\n",
" # again, this shouldn't happen if our memory allocation is correct.\n",
" #warnings.warn(\"Internal: memory layout is flawed: \"\n",
" # \"too many nodes allocated\")\n",
" split_is_leaf[i_split] = True\n",
" split_idx_membership[idx] = i_split\n",
" split_n_children[i_split] = len(idx)\n",
"\n",
" else:\n",
" # split node and recursively construct child nodes.\n",
" if len(idx) <= leaf_size:\n",
" split_is_leaf[i_split] = True\n",
" split_idx_membership[idx] = i_split\n",
" split_n_children[i_split] = len(idx)\n",
" else:\n",
" split_column = np.argmax(maxes - mins)\n",
" maxval = maxes[split_column]\n",
" minval = mins[split_column]\n",
" if maxval == minval:\n",
" split_is_leaf[i_split] = True\n",
" split_idx_membership[idx] = i_split\n",
" split_n_children[i_split] = len(idx)\n",
" else:\n",
" split_is_leaf[i_split] = False\n",
" n_mid, less_idx, greater_idx, lessmaxes, greatermins = \\\n",
" determine_split(data[idx, split_column], split_column, maxes, mins)\n",
" split_dimension[i_split] = split_column\n",
" split_values[i_split] = n_mid\n",
" split_n_children[i_split] = len(idx)\n",
" split_left_child[i_split] = i_child\n",
" split_right_child[i_split] = i_child + 1\n",
" less_idx = idx[less_idx]\n",
" greater_idx = idx[greater_idx]\n",
" recursive_build(i_child, less_idx, \n",
" data, lessmaxes, mins,\n",
" split_maxes, split_mins,\n",
" split_is_leaf, split_n_children,\n",
" split_dimension, split_values,\n",
" split_idx_membership,\n",
" split_left_child, split_right_child,\n",
" n_splits, leaf_size)\n",
" recursive_build(i_child + 1, greater_idx, \n",
" data, maxes, greatermins,\n",
" split_maxes, split_mins,\n",
" split_is_leaf, split_n_children,\n",
" split_dimension, split_values,\n",
" split_idx_membership,\n",
" split_left_child, split_right_child,\n",
" n_splits, leaf_size)\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 37.5 ms, sys: 544 µs, total: 38 ms\n",
"Wall time: 38 ms\n"
]
}
],
"source": [
"# Allocate tree-specific data \n",
"%time recursive_build(0, idx, \\\n",
" data, maxes, mins, \\\n",
" split_maxes, split_mins, \\\n",
" split_is_leaf, split_n_children,\\\n",
" split_dimension, split_values, \\\n",
" split_idx_membership, \\\n",
" split_left_child, split_right_child, \\\n",
" n_splits, leaf_size)"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"@numba.jit(nopython=True)\n",
"def minkowski_dist_numba(x, y, p):\n",
" if p == 1:\n",
" return np.sum(np.abs(y-x), axis=-1)\n",
" else:\n",
" return np.sum(np.abs(y-x)**p, axis=-1)\n",
"\n",
"@numba.jit(nopython=True)\n",
"def min_distance_split_point_numba(maxes, mins, point, p=2):\n",
" maxes_actual = np.maximum(maxes, mins).astype(maxes.dtype)\n",
" mins_actual = np.minimum(maxes, mins).astype(maxes.dtype)\n",
" mins_diff = mins_actual - point\n",
" maxes_diff = point - maxes_actual\n",
" max_diffs = np.maximum(mins_diff, maxes_diff)\n",
" dist = minkowski_dist_numba(0, np.maximum(0, max_diffs), p)\n",
" return dist\n",
"\n",
"@numba.jit(nopython=True)\n",
"def max_distance_split_point_numba(maxes, mins, point, p=2):\n",
" maxes_actual = np.maximum(maxes, mins).astype(maxes.dtype)\n",
" mins_actual = np.minimum(maxes, mins).astype(maxes.dtype)\n",
" dist = minkowski_dist_numba(0, np.maximum(maxes_actual-point, point-mins_actual), p)\n",
" return dist"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"@numba.jit(nopython=True)\n",
"def traverse_tree_numba(data, point, r, p, eps,\n",
" split_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=True):\n",
" \n",
" if not check:\n",
" if split_is_leaf[split_idx]:\n",
" leaf_member_idx = np.where(split_idx_membership == split_idx)[0]\n",
" return leaf_member_idx.astype(np.int32)\n",
" else:\n",
" left_child_idx = split_left_child[split_idx]\n",
" right_child_idx = split_right_child[split_idx]\n",
" left_child_points = \\\n",
" traverse_tree_numba(data, point, r, p, eps,\n",
" left_child_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=False)\n",
" right_child_points = \\\n",
" traverse_tree_numba(data, point, r, p, eps,\n",
" right_child_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=False)\n",
" points = np.concatenate((left_child_points, right_child_points))\n",
" return points.astype(np.int32)\n",
" else:\n",
" min_dist = \\\n",
" min_distance_split_point_numba(split_maxes[split_idx],\n",
" split_mins[split_idx], point, p)\n",
" if min_dist > (r / (1.0 + eps)):\n",
" return np.array([]).astype(np.int32)\n",
" else:\n",
" max_dist = \\\n",
" max_distance_split_point_numba(split_maxes[split_idx], \n",
" split_mins[split_idx], point, p)\n",
" if max_dist < (r * (1.0 + eps)):\n",
" return traverse_tree_numba(data, point, r, p, eps,\n",
" split_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=False)\n",
" elif split_is_leaf[split_idx]:\n",
" leaf_member_idx = np.where(split_idx_membership == split_idx)[0]\n",
" leaf_data = data[leaf_member_idx]\n",
" leaf_member_dists = minkowski_dist_numba(leaf_data, point, p)\n",
" leaf_member_idx = leaf_member_idx[leaf_member_dists <= r]\n",
" return leaf_member_idx.astype(np.int32)\n",
" else:\n",
" left_child_idx = split_left_child[split_idx]\n",
" right_child_idx = split_right_child[split_idx]\n",
" left_child_points = \\\n",
" traverse_tree_numba(data, point, r, p, eps,\n",
" left_child_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=True)\n",
" right_child_points = \\\n",
" traverse_tree_numba(data, point, r, p, eps,\n",
" right_child_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=True)\n",
" points = np.concatenate((left_child_points, right_child_points))\n",
" return points.astype(np.int32)"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"@numba.jit(nopython=True) \n",
"def query_ball_point_numba(data, point, r, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership, \n",
" p=2., eps=0):\n",
"\n",
" split_idx = 0\n",
" return traverse_tree_numba(data, point, r, p, eps,\n",
" split_idx, \n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" check=True)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"point = x[100]\n",
"r = 0.001"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"scrolled": true
},
"outputs": [
{
"ename": "TypingError",
"evalue": "Failed at nopython (nopython frontend)\nFailed at nopython (nopython frontend)\nFailed at nopython (nopython frontend)\nInternal error at <numba.typeinfer.CallConstraint object at 0x10c9bffd0>:\n--%<-----------------------------------------------------------------\nTraceback (most recent call last):\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/errors.py\", line 259, in new_error_context\n yield\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 413, in __call__\n fnty = typevars[self.func].getone()\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 104, in getone\n assert self.type is not None\nAssertionError\n\nDuring handling of the above exception, another exception occurred:\n\nTraceback (most recent call last):\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 137, in propagate\n constraint(typeinfer)\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 415, in __call__\n self.resolve(typeinfer, typevars, fnty)\n File \"//anaconda/envs/py36/lib/python3.6/contextlib.py\", line 99, in __exit__\n self.gen.throw(type, value, traceback)\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/errors.py\", line 265, in new_error_context\n six.reraise(type(newerr), newerr, sys.exc_info()[2])\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/six.py\", line 658, in reraise\n raise value.with_traceback(tb)\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/errors.py\", line 259, in new_error_context\n yield\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 413, in __call__\n fnty = typevars[self.func].getone()\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 104, in getone\n assert self.type is not None\nnumba.errors.InternalError: \n[1] During: typing of call at <ipython-input-86-4ca9f146870d> (34)\n--%<-----------------------------------------------------------------\n\nFile \"<ipython-input-86-4ca9f146870d>\", line 34\n[1] During: resolving callee type: recursive(type(CPUDispatcher(<function traverse_tree_numba at 0x10c8e8ea0>)))\n[2] During: typing of call at <ipython-input-86-4ca9f146870d> (21)\n[3] During: resolving callee type: type(CPUDispatcher(<function traverse_tree_numba at 0x10c8e8ea0>))\n[4] During: typing of call at <ipython-input-87-937d59342dd4> (14)",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mTypingError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<timed eval>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36m_compile_for_args\u001b[0;34m(self, *args, **kws)\u001b[0m\n\u001b[1;32m 328\u001b[0m for i, err in failed_args))\n\u001b[1;32m 329\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpatch_message\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 330\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 331\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 332\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0minspect_llvm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36m_compile_for_args\u001b[0;34m(self, *args, **kws)\u001b[0m\n\u001b[1;32m 305\u001b[0m \u001b[0margtypes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtypeof_pyval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 306\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 307\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margtypes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 308\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTypingError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 309\u001b[0m \u001b[0;31m# Intercept typing error that may be due to an argument\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sig)\u001b[0m\n\u001b[1;32m 577\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 578\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache_misses\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 579\u001b[0;31m \u001b[0mcres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compiler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 580\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 581\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, args, return_type)\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[0mimpl\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 80\u001b[0;31m flags=flags, locals=self.locals)\n\u001b[0m\u001b[1;32m 81\u001b[0m \u001b[0;31m# Check typing error if object mode is used\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 82\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtyping_error\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mflags\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menable_pyobject\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[0;34m(typingctx, targetctx, func, args, return_type, flags, locals, library)\u001b[0m\n\u001b[1;32m 777\u001b[0m pipeline = Pipeline(typingctx, targetctx, library,\n\u001b[1;32m 778\u001b[0m args, return_type, flags, locals)\n\u001b[0;32m--> 779\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mpipeline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile_extra\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 780\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 781\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[0;34m(self, func)\u001b[0m\n\u001b[1;32m 360\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlifted\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 361\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlifted_from\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 362\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile_bytecode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 363\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 364\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mcompile_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunc_ir\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlifted\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlifted_from\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_bytecode\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 736\u001b[0m \"\"\"\n\u001b[1;32m 737\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc_ir\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 738\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 739\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 740\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_compile_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 723\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 724\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfinalize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 725\u001b[0;31m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 726\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 727\u001b[0m \u001b[0;31m# Early pipeline completion\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m 246\u001b[0m \u001b[0;31m# No more fallback pipelines?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 247\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mis_final_pipeline\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 248\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mpatched_exception\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 249\u001b[0m \u001b[0;31m# Go to next fallback pipeline\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 250\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m 238\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 239\u001b[0m \u001b[0mevent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstage_name\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 240\u001b[0;31m \u001b[0mstage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 241\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0m_EarlyPipelineCompletion\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 242\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mstage_nopython_frontend\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 452\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 453\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 454\u001b[0;31m self.locals)\n\u001b[0m\u001b[1;32m 455\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 456\u001b[0m with self.fallback_context('Function \"%s\" has invalid return type'\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mtype_inference_stage\u001b[0;34m(typingctx, interp, args, return_type, locals)\u001b[0m\n\u001b[1;32m 879\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 880\u001b[0m \u001b[0minfer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_constraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 881\u001b[0;31m \u001b[0minfer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpropagate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 882\u001b[0m \u001b[0mtypemap\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrestype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcalltypes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minfer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 883\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sig)\u001b[0m\n\u001b[1;32m 577\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 578\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache_misses\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 579\u001b[0;31m \u001b[0mcres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compiler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 580\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 581\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, args, return_type)\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[0mimpl\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 80\u001b[0;31m flags=flags, locals=self.locals)\n\u001b[0m\u001b[1;32m 81\u001b[0m \u001b[0;31m# Check typing error if object mode is used\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 82\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtyping_error\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mflags\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menable_pyobject\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[0;34m(typingctx, targetctx, func, args, return_type, flags, locals, library)\u001b[0m\n\u001b[1;32m 777\u001b[0m pipeline = Pipeline(typingctx, targetctx, library,\n\u001b[1;32m 778\u001b[0m args, return_type, flags, locals)\n\u001b[0;32m--> 779\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mpipeline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile_extra\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 780\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 781\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_bytecode\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 736\u001b[0m \"\"\"\n\u001b[1;32m 737\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc_ir\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 738\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 739\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 740\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_compile_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 723\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 724\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfinalize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 725\u001b[0;31m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 726\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 727\u001b[0m \u001b[0;31m# Early pipeline completion\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m 246\u001b[0m \u001b[0;31m# No more fallback pipelines?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 247\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mis_final_pipeline\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 248\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mpatched_exception\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 249\u001b[0m \u001b[0;31m# Go to next fallback pipeline\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 250\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m 238\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 239\u001b[0m \u001b[0mevent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstage_name\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 240\u001b[0;31m \u001b[0mstage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 241\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0m_EarlyPipelineCompletion\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 242\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mstage_nopython_frontend\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 452\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 453\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 454\u001b[0;31m self.locals)\n\u001b[0m\u001b[1;32m 455\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 456\u001b[0m with self.fallback_context('Function \"%s\" has invalid return type'\n",
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"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mget_call_template\u001b[0;34m(self, args, kws)\u001b[0m\n\u001b[1;32m 267\u001b[0m \u001b[0;31m# Ensure an overload is available\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 268\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_can_compile\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 269\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 270\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 271\u001b[0m \u001b[0;31m# Create function type for typing\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, sig)\u001b[0m\n\u001b[1;32m 577\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 578\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache_misses\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 579\u001b[0;31m \u001b[0mcres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compiler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 580\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 581\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cache\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave_overload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[0;34m(self, args, return_type)\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[0mimpl\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 80\u001b[0;31m flags=flags, locals=self.locals)\n\u001b[0m\u001b[1;32m 81\u001b[0m \u001b[0;31m# Check typing error if object mode is used\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 82\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtyping_error\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mflags\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0menable_pyobject\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[0;34m(typingctx, targetctx, func, args, return_type, flags, locals, library)\u001b[0m\n\u001b[1;32m 777\u001b[0m pipeline = Pipeline(typingctx, targetctx, library,\n\u001b[1;32m 778\u001b[0m args, return_type, flags, locals)\n\u001b[0;32m--> 779\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mpipeline\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile_extra\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 780\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 781\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_bytecode\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 736\u001b[0m \"\"\"\n\u001b[1;32m 737\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc_ir\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 738\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 739\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 740\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_compile_ir\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 723\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 724\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfinalize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 725\u001b[0;31m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 726\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mres\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 727\u001b[0m \u001b[0;31m# Early pipeline completion\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m 246\u001b[0m \u001b[0;31m# No more fallback pipelines?\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 247\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mis_final_pipeline\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 248\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mpatched_exception\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 249\u001b[0m \u001b[0;31m# Go to next fallback pipeline\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 250\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, status)\u001b[0m\n\u001b[1;32m 238\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 239\u001b[0m \u001b[0mevent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstage_name\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 240\u001b[0;31m \u001b[0mstage\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 241\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0m_EarlyPipelineCompletion\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 242\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mstage_nopython_frontend\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 452\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 453\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreturn_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 454\u001b[0;31m self.locals)\n\u001b[0m\u001b[1;32m 455\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 456\u001b[0m with self.fallback_context('Function \"%s\" has invalid return type'\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/compiler.py\u001b[0m in \u001b[0;36mtype_inference_stage\u001b[0;34m(typingctx, interp, args, return_type, locals)\u001b[0m\n\u001b[1;32m 879\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 880\u001b[0m \u001b[0minfer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuild_constraint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 881\u001b[0;31m \u001b[0minfer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpropagate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 882\u001b[0m \u001b[0mtypemap\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrestype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcalltypes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minfer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 883\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\u001b[0m in \u001b[0;36mpropagate\u001b[0;34m(self, raise_errors)\u001b[0m\n\u001b[1;32m 844\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 845\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mraise_errors\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 846\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 847\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 848\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mTypingError\u001b[0m: Failed at nopython (nopython frontend)\nFailed at nopython (nopython frontend)\nFailed at nopython (nopython frontend)\nInternal error at <numba.typeinfer.CallConstraint object at 0x10c9bffd0>:\n--%<-----------------------------------------------------------------\nTraceback (most recent call last):\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/errors.py\", line 259, in new_error_context\n yield\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 413, in __call__\n fnty = typevars[self.func].getone()\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 104, in getone\n assert self.type is not None\nAssertionError\n\nDuring handling of the above exception, another exception occurred:\n\nTraceback (most recent call last):\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 137, in propagate\n constraint(typeinfer)\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 415, in __call__\n self.resolve(typeinfer, typevars, fnty)\n File \"//anaconda/envs/py36/lib/python3.6/contextlib.py\", line 99, in __exit__\n self.gen.throw(type, value, traceback)\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/errors.py\", line 265, in new_error_context\n six.reraise(type(newerr), newerr, sys.exc_info()[2])\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/six.py\", line 658, in reraise\n raise value.with_traceback(tb)\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/errors.py\", line 259, in new_error_context\n yield\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 413, in __call__\n fnty = typevars[self.func].getone()\n File \"//anaconda/envs/py36/lib/python3.6/site-packages/numba/typeinfer.py\", line 104, in getone\n assert self.type is not None\nnumba.errors.InternalError: \n[1] During: typing of call at <ipython-input-86-4ca9f146870d> (34)\n--%<-----------------------------------------------------------------\n\nFile \"<ipython-input-86-4ca9f146870d>\", line 34\n[1] During: resolving callee type: recursive(type(CPUDispatcher(<function traverse_tree_numba at 0x10c8e8ea0>)))\n[2] During: typing of call at <ipython-input-86-4ca9f146870d> (21)\n[3] During: resolving callee type: type(CPUDispatcher(<function traverse_tree_numba at 0x10c8e8ea0>))\n[4] During: typing of call at <ipython-input-87-937d59342dd4> (14)"
]
}
],
"source": [
"%time query_ball_point_numba(x, point, r, \\\n",
" split_is_leaf, split_maxes, split_mins, \\\n",
" split_left_child, split_right_child, \\\n",
" split_idx_membership, \\\n",
" p=2., eps=0)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"def search_all_points(x, r, \n",
" split_is_leaf, split_maxes, split_mins, \n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" p=2., eps=0):\n",
"\n",
" for i in range(x.shape[0]):\n",
" point = x[i]\n",
" foo = query_ball_point_numba(x, point, r,\n",
" split_is_leaf, split_maxes, split_mins,\n",
" split_left_child, split_right_child,\n",
" split_idx_membership,\n",
" p=2., eps=0)\n",
" return foo"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1min 6s, sys: 74.9 ms, total: 1min 6s\n",
"Wall time: 1min 6s\n"
]
},
{
"data": {
"text/plain": [
"array([54658, 33464, 99999, 98216], dtype=int32)"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%time search_all_points(x, r, \\\n",
" split_is_leaf, split_maxes, split_mins, \\\n",
" split_left_child, split_right_child, \\\n",
" split_idx_membership, \\\n",
" p=2., eps=0)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Testing out the implementation with scikit-learn\n",
"from sklearn.neighbors import NearestNeighbors"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_obs = 100000\n",
"n_cols = 3\n",
"\n",
"z = np.random.random_sample(n_obs * n_cols)\n",
"z = np.reshape(z, (n_obs, n_cols))\n",
"\n",
"radius = 0.1"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 86.6 ms, sys: 1.35 ms, total: 88 ms\n",
"Wall time: 87.8 ms\n"
]
},
{
"data": {
"text/plain": [
"NearestNeighbors(algorithm='kd_tree', leaf_size=30, metric='minkowski',\n",
" metric_params=None, n_jobs=1, n_neighbors=5, p=2, radius=1.0)"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nn = NearestNeighbors()\n",
"nn.set_params(algorithm='kd_tree')\n",
"%time nn.fit(z)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 4.61 s, sys: 183 ms, total: 4.8 s\n",
"Wall time: 4.8 s\n"
]
}
],
"source": [
"%time ind = nn.radius_neighbors(radius=radius, return_distance=False)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"m_all = np.array([i.size for i in ind])"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([370, 410, 422, ..., 436, 310, 383])"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m_all"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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