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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"a = np.array([[1,2,3],[4,5,6]])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 2, 3],\n",
" [4, 5, 6]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"b = np.array([[2,3,4],[5,6,9]])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[2, 3, 4],\n",
" [5, 6, 9]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"b"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 2, 3],\n",
" [4, 5, 6]])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-1, -1, -1],\n",
" [-1, -1, -3]])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a - b"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.7320508075688772"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.argmin([np.linalg.norm(a[i] - b[i]) for i in range(len(a))])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"np.min?"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"\n",
"\"\"\"\n",
"This is a module for IDW Spatial Interpolation\n",
"\"\"\"\n",
"import numpy as np\n",
"import pandas as pd\n",
"from copy import deepcopy\n",
"class idw():\n",
" \"\"\" A class that is declared for performing IDW Interpolation.\n",
" For more information on how this method works, kindly refer to\n",
" https://en.wikipedia.org/wiki/Inverse_distance_weighting\n",
"\n",
" Parameters\n",
" ----------\n",
" exponent : positive float, optional\n",
" The rate of fall of values from source data points.\n",
" Higher the exponent, lower is the value when we move\n",
" across space. Default value is 2.\n",
" resolution: str, optional\n",
" Decides the smoothness of the interpolation. Note that\n",
" interpolation is done over a grid. Higher the resolution\n",
" means more grid cells and more time for interpolation.\n",
" Default value is 'standard'\n",
" coordinate_type: str, optional\n",
" Decides the distance metric to be used, while performing\n",
" interpolation. Euclidean by default. \n",
" \"\"\"\n",
" def __init__(self, exponent = 2, resolution = 'standard', coordinate_type='Euclidean'):\n",
" \n",
" self.exponent = exponent\n",
" self.resolution = resolution\n",
" self.coordinate_type = coordinate_type\n",
" self.interpolated_values = None\n",
" self.x_grid = None\n",
" self.y_grid = None\n",
"\n",
" def make_grid(self, x, y, res, offset=0.2):\n",
"\n",
" \"\"\" This function returns the grid to perform interpolation on.\n",
" This function is used inside the fit() attribute of the idw class.\n",
" \n",
" Parameters\n",
" ----------\n",
" x: array-like, shape(n_samples,)\n",
" The first coordinate values of all points where\n",
" ground truth is available\n",
" y: array-like, shape(n_samples,)\n",
" The second coordinate values of all points where\n",
" ground truth is available\n",
" res: int\n",
" The resolution value\n",
" offset: float, optional\n",
" A value between 0 and 0.5 that specifies the extra interpolation to be done\n",
" Default is 0.2\n",
" \n",
" Returns\n",
" -------\n",
" xx : {array-like, 2D}, shape (n_samples, n_samples)\n",
" yy : {array-like, 2D}, shape (n_samples, n_samples)\n",
" \"\"\"\n",
" y_min = y.min() - offset\n",
" y_max = y.max()+ offset\n",
" x_min = x.min()-offset\n",
" x_max = x.max()+offset\n",
" x_arr = np.linspace(x_min,x_max,res)\n",
" y_arr = np.linspace(y_min,y_max,res)\n",
" xx,yy = np.meshgrid(x_arr,y_arr) \n",
" return xx,yy\n",
"\n",
" \n",
" def fit(self, X, y):\n",
" \"\"\" The function call to fit the model on the given data. \n",
" Parameters\n",
" ----------\n",
" X: {array-like, 2D matrix}, shape(n_samples, 2)\n",
" The set of all coordinates, where we have ground truth\n",
" values\n",
" y: array-like, shape(n_samples,)\n",
" The set of all the ground truth values using which\n",
" we perform interpolation\n",
"\n",
" Returns\n",
" -------\n",
" self : object\n",
" Returns self\n",
" \"\"\"\n",
"\n",
"# if self.coordinate_type == 'latlong_small':\n",
"# \t \t\"\"\"\n",
"# \t \t\tUse the conversions and projections for small changes in LatLong\n",
"# \t\t\"\"\"\n",
"# \t \t print (\"To be done later\")\n",
"# return self\n",
"\n",
"# if self.coordinate_type == 'latlong_large':\n",
"# \"\"\"\n",
"# Code to be written after understanding all the projections.\n",
"# \"\"\"\n",
"# print (\"To be done later\")\n",
"# return self\n",
"\n",
" if self.coordinate_type==\"Euclidean\":\n",
" \n",
" X = deepcopy(np.c_[X,y])\n",
"\n",
" if self.resolution=='high':\n",
" xx,yy = self.make_grid(X,y,1000)\n",
" \n",
" if self.resolution=='low':\n",
" xx,yy = self.make_grid(X,y,10)\n",
" \n",
" if self.resolution=='standard':\n",
" xx,yy = self.make_grid(X,y,100)\n",
"\n",
" new = []\n",
" new_arr = deepcopy(X)\n",
" for points in new_arr:\n",
" min_dist = np.inf\n",
" val = 0\n",
" for j in range(len(yy)):\n",
" temp = yy[j][0]\n",
" for i in range(len(xx[0])):\n",
" dist = np.linalg.norm(np.array([xx[0][i],temp]) - points[:2])\n",
" if dist<min_dist:\n",
" min_dist = dist\n",
" val = (i,j)\n",
" new.append((points,val))\n",
" new_grid = np.zeros((len(xx),len(yy)))\n",
" for i in range(len(new)):\n",
" x = new[i][1][0]\n",
" y = new[i][1][1]\n",
" new_grid[x][y] = new[i][0][2]\n",
" x_nz,y_nz = np.nonzero(new_grid)\n",
" list_nz = []\n",
" for i in range(len(x_nz)):\n",
" list_nz.append((x_nz[i],y_nz[i]))\n",
" final = np.copy(new_grid)\n",
" for i in range(len(xx[0])):\n",
" for j in range(len(yy)):\n",
" normalise = 0\n",
" if (i,j) in list_nz:\n",
" continue\n",
" else:\n",
" for elem in range(len(x_nz)):\n",
" source = np.array([x_nz[elem],y_nz[elem]])\n",
" target = np.array([xx[0][i],yy[j][0]])\n",
" dist = (np.abs(xx[0][source[0]] - target[0])**self.exponent + np.abs(yy[source[1]][0] - target[1])**self.exponent)**(1/self.exponent)\n",
" final[i][j]+=new_grid[x_nz[elem],y_nz[elem]]/dist\n",
" normalise+=1/(dist)\n",
" final[i][j]/=normalise\n",
" self.interpolated_values = final\n",
" self.x_grid = xx\n",
" self.y_grid = yy\n",
" \n",
" return self\n",
"\n",
"# def predict(self, X):\n",
"# \"\"\" The function call to predict using the interpolated data\n",
"# Parameters\n",
"# ----------\n",
"# X: {array-like, 2D matrix}, shape(n_samples, 2)\n",
"# The set of all coordinates, where we have ground truth\n",
"# values\n",
" \n",
"\n",
"# Returns\n",
"# -------\n",
"# y: array-like, shape(n_samples,)\n",
"# The set of all the ground truth values using which\n",
"# we perform interpolation \n",
"# \"\"\"\n",
"# if self.coordinate_type == 'Euclidean':\n",
"# for i in range(self.x_grid[0]):\n",
"# for j in range()\n",
" \n",
"# else:\n",
"# print(\"Will be done later\")\n",
"# return \n",
" \n",
" \n",
"# self.x_grid\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<__main__.idw at 0x7f36db6f9c88>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = idw()\n",
"import pandas as pd\n",
"df = pd.read_csv('../../testdata/30-03-18.csv')\n",
"data = np.array(df[['longitude','latitude','value']])\n",
"a.fit(data[:,:2],data[:,2])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[171.89189189, 171.89597641, 171.90813547, ..., 173.89050472,\n",
" 173.89261459, 173.89466512],\n",
" [171.77142857, 171.77625338, 171.79060316, ..., 173.89585441,\n",
" 173.89787202, 173.89983245],\n",
" [171.63636364, 171.64211895, 171.65921778, ..., 173.9012935 ,\n",
" 173.90321551, 173.90508269],\n",
" ...,\n",
" [174.49681529, 174.49676176, 174.49660126, ..., 174.24671184,\n",
" 174.24416446, 174.24164382],\n",
" [174.49056604, 174.49051451, 174.49035999, ..., 174.24671343,\n",
" 174.24419773, 174.2417078 ],\n",
" [174.48447205, 174.48442242, 174.48427358, ..., 174.2466762 ,\n",
" 174.24419219, 174.24173298]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.interpolated_values"
]
}
],
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"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"language_info": {
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"file_extension": ".py",
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