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Add Network Modeling Assignment 1 notes

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David Doebel
2026-03-22 15:58:12 +01:00
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IML Projects/Task 1b /Task 1b.pdf Normal file
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IML Projects/Task 1b /task1b_ql4jfi6af0/results.csv Normal file
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IML Projects/Task 1b /task1b_ql4jfi6af0/sample.csv Normal file
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IML Projects/Task 1b /task1b_ql4jfi6af0/template_solution.ipynb Normal file
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### General guidance\n",
"\n",
"This serves as a template which will guide you through the implementation of this task. It is advised\n",
"to first read the whole template and get a sense of the overall structure of the code before trying to fill in any of the TODO gaps.\n",
"This is the jupyter notebook version of the template. For the python file version, please refer to the file `template_solution.py`.\n",
"\n",
"First, we import necessary libraries:"
]
},
{
"cell_type": "code",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.169924Z",
"start_time": "2026-03-15T18:22:13.165934Z"
}
},
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"# Add any additional imports here (however, the task is solvable without using \n",
"# any additional imports)\n",
"# import ..."
],
"outputs": [],
"execution_count": 30
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" #### Loading data"
]
},
{
"cell_type": "code",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.190312Z",
"start_time": "2026-03-15T18:22:13.181357Z"
}
},
"source": [
"data = pd.read_csv(\"train.csv\")\n",
"y = data[\"y\"].to_numpy()\n",
"data = data.drop(columns=[\"Id\", \"y\"])\n",
"# print a few data samples\n",
"print(data.head())\n",
"X = data.to_numpy()"
],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" x1 x2 x3 x4 x5\n",
"0 0.02 0.05 -0.09 -0.43 -0.08\n",
"1 -0.13 0.11 -0.08 -0.29 -0.03\n",
"2 0.08 0.06 -0.07 -0.41 -0.03\n",
"3 0.02 -0.12 0.01 -0.43 -0.02\n",
"4 -0.14 -0.12 -0.08 -0.02 -0.08\n"
]
}
],
"execution_count": 31
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Transform features"
]
},
{
"cell_type": "code",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.201976Z",
"start_time": "2026-03-15T18:22:13.198370Z"
}
},
"source": [
"\"\"\"\n",
"Transform the 5 input features of matrix X (x_i denoting the i-th component of a given row in X) \n",
"into 21 new features phi(X) in the following manner:\n",
"5 linear features: phi_1(X) = x_1, phi_2(X) = x_2, phi_3(X) = x_3, phi_4(X) = x_4, phi_5(X) = x_5\n",
"5 quadratic features: phi_6(X) = x_1^2, phi_7(X) = x_2^2, phi_8(X) = x_3^2, phi_9(X) = x_4^2, phi_10(X) = x_5^2\n",
"5 exponential features: phi_11(X) = exp(x_1), phi_12(X) = exp(x_2), phi_13(X) = exp(x_3), phi_14(X) = exp(x_4), phi_15(X) = exp(x_5)\n",
"5 cosine features: phi_16(X) = cos(x_1), phi_17(X) = cos(x_2), phi_18(X) = cos(x_3), phi_19(X) = cos(x_4), phi_20(X) = cos(x_5)\n",
"1 constant feature: phi_21(X)=1\n",
"\n",
"Parameters\n",
"----------\n",
"X: matrix of floats, dim = (700,5), inputs with 5 features\n",
"\n",
"Compute\n",
"----------\n",
"X_transformed: matrix of floats: dim = (700,21), transformed input with 21 features\n",
"\"\"\"\n",
"X_transformed = np.zeros((700, 21))\n",
"quadratic_features = np.power(X,2)\n",
"exponential_features = np.exp(X)\n",
"cosine_features = np.cos(X)\n",
"constant_feature = np.ones((X.shape[0],1))\n",
"X_transformed = np.concatenate((X, quadratic_features, exponential_features, cosine_features, constant_feature), axis=1)\n",
"assert X_transformed.shape == (700, 21)"
],
"outputs": [],
"execution_count": 32
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Fit data"
]
},
{
"cell_type": "code",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.625674Z",
"start_time": "2026-03-15T18:22:13.217438Z"
}
},
"source": [
"\"\"\"\n",
"Use the transformed data points X_transformed and fit the logistic regression on this \n",
"transformed data. Finally, compute the weights of the fitted logistic regression. \n",
"\n",
"Parameters\n",
"----------\n",
"X_transformed: array of floats: dim = (700,21), transformed input with 21 features\n",
"y: array of integers \\in {0,1}, dim = (700,), input labels\n",
"\n",
"Compute\n",
"----------\n",
"w: array of floats: dim = (21,), optimal parameters of logistic regression\n",
"\"\"\"\n",
"weights = np.zeros((21,))\n",
"learning_rate = 2 * X.shape[0] / np.linalg.svd(X_transformed, compute_uv=False)[0]**2\n",
"tolerance = 0.001\n",
"sigma = lambda x : 1/(1+np.exp(-x))\n",
"gradient = lambda w, X, y: X.T @ (sigma(X @ w) - y) / X.shape[0]\n",
"update = 1000000\n",
"while np.linalg.norm(update) > tolerance:\n",
" # Select a random batch (SGD)\n",
" selection = np.random.choice(X_transformed.shape[0], 100, replace=False)\n",
" X_random = X_transformed[selection,:]\n",
" update = learning_rate * gradient(weights, X_random, y[selection])\n",
" weights -= update\n",
"\n",
"assert weights.shape == (21,)"
],
"outputs": [],
"execution_count": 33
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.630314Z",
"start_time": "2026-03-15T18:22:13.629075Z"
}
},
"cell_type": "code",
"source": "",
"outputs": [],
"execution_count": null
},
{
"cell_type": "code",
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.636358Z",
"start_time": "2026-03-15T18:22:13.633885Z"
}
},
"source": [
"# Save results in the required format\n",
"np.savetxt(\"./results.csv\", weights, fmt=\"%.12f\")"
],
"outputs": [],
"execution_count": 34
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.643898Z",
"start_time": "2026-03-15T18:22:13.641041Z"
}
},
"cell_type": "code",
"source": [
"matrix = np.array([[1,2],[3,4],[5,6],[7,8],[9,10]])\n",
"np.linalg.svd(X_transformed,compute_uv=False)\n",
"matrix[np.random.choice(matrix.shape[0], 1, replace=False), :]"
],
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 2]])"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"execution_count": 35
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2026-03-15T18:22:13.707327Z",
"start_time": "2026-03-15T18:22:13.706165Z"
}
},
"cell_type": "code",
"source": "",
"outputs": [],
"execution_count": null
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"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": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

69
IML Projects/Task 1b /task1b_ql4jfi6af0/template_solution.py Normal file
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# This serves as a template which will guide you through the implementation of this task. It is advised
# to first read the whole template and get a sense of the overall structure of the code before trying to fill in any of the TODO gaps.
# First, we import necessary libraries:
import numpy as np
import pandas as pd
# Add any additional imports here (however, the task is solvable without using
# any additional imports)
# import ...
def transform_features(X):
"""
This function transforms the 5 input features of matrix X (x_i denoting the i-th component in a given row of X)
into 21 new features phi(X) in the following manner:
5 linear features: phi_1(X) = x_1, phi_2(X) = x_2, phi_3(X) = x_3, phi_4(X) = x_4, phi_5(X) = x_5
5 quadratic features: phi_6(X) = x_1^2, phi_7(X) = x_2^2, phi_8(X) = x_3^2, phi_9(X) = x_4^2, phi_10(X) = x_5^2
5 exponential features: phi_11(X) = exp(x_1), phi_12(X) = exp(x_2), phi_13(X) = exp(x_3), phi_14(X) = exp(x_4), phi_15(X) = exp(x_5)
5 cosine features: phi_16(X) = cos(x_1), phi_17(X) = cos(x_2), phi_18(X) = cos(x_3), phi_19(X) = cos(x_4), phi_20(X) = cos(x_5)
1 constant feature: phi_21(X)=1
Parameters
----------
X: matrix of floats, dim = (700,5), inputs with 5 features
Returns
----------
X_transformed: matrix of floats: dim = (700,21), transformed input with 21 features
"""
X_transformed = np.zeros((700, 21))
# TODO: Enter your code here
assert X_transformed.shape == (700, 21)
return X_transformed
def fit_logistic_regression(X, y):
"""
This function receives training data points, transforms them, and then fits the logistic regression on this
transformed data. Finally, it outputs the weights of the fitted logistic regression.
Parameters
----------
X: matrix of floats, dim = (700,5), inputs with 5 features
y: array of integers \in {0,1}, dim = (700,), input labels
Returns
----------
weights: array of floats: dim = (21,), optimal parameters of logistic regression
"""
weights = np.zeros((21,))
X_transformed = transform_features(X)
# TODO: Enter your code here
assert weights.shape == (21,)
return weights
# Main function. You don't have to change this
if __name__ == "__main__":
# Data loading
data = pd.read_csv("train.csv")
y = data["y"].to_numpy()
data = data.drop(columns=["Id", "y"])
# print a few data samples
print(data.head())
X = data.to_numpy()
# The function retrieving optimal LR parameters
w = fit_logistic_regression(X, y)
# Save results in the required format
np.savetxt("./results.csv", w, fmt="%.12f")

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IML Projects/Task 1b /task1b_ql4jfi6af0/train.csv Normal file
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Id,y,x1,x2,x3,x4,x5
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1,0,-0.13000000000000006,0.10999999999999999,-0.08000000000000007,-0.29000000000000004,-0.030000000000000027
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18,1,-0.06000000000000005,-0.22000000000000003,-0.010000000000000009,-0.3500000000000001,-0.07000000000000006
19,0,0.04999999999999993,0.039999999999999925,-0.010000000000000009,-0.3500000000000001,-0.06000000000000005
20,1,-0.11000000000000004,-0.16000000000000003,-0.06000000000000005,-0.4,-0.06000000000000005
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22,0,0.16999999999999993,0.06999999999999995,-0.14000000000000007,-0.26000000000000006,-0.07000000000000006
23,0,-0.13000000000000006,-0.030000000000000027,-0.040000000000000036,-0.43000000000000005,-0.010000000000000009
24,0,-0.10000000000000003,-0.030000000000000027,-0.040000000000000036,-0.41000000000000003,0.019999999999999907
25,0,-0.050000000000000044,-0.050000000000000044,-0.040000000000000036,-0.050000000000000044,-0.020000000000000018
26,0,0.029999999999999916,-0.11000000000000004,-0.030000000000000027,-0.37000000000000005,0.029999999999999916
27,1,0.009999999999999898,-0.09000000000000008,0.039999999999999925,-0.38000000000000006,-0.050000000000000044
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29,0,0.24,0.31999999999999995,-0.20000000000000007,-0.17000000000000004,0.0
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32,0,-0.18000000000000005,0.04999999999999993,0.04999999999999993,-0.44000000000000006,-0.030000000000000027
33,0,-0.23000000000000004,-0.010000000000000009,-0.050000000000000044,-0.13000000000000006,-0.050000000000000044
34,0,0.21999999999999997,0.17999999999999994,-0.14000000000000007,-0.30000000000000004,-0.13000000000000006
35,1,0.17999999999999994,0.10999999999999999,-0.09000000000000008,-0.22000000000000003,-0.14000000000000007
36,0,0.15999999999999992,0.04999999999999993,-0.11000000000000004,-0.26000000000000006,-0.020000000000000018
37,0,-0.16000000000000003,-0.11000000000000004,0.009999999999999898,-0.38000000000000006,0.0
38,0,0.029999999999999916,-0.030000000000000027,-0.13000000000000006,-0.12000000000000005,-0.06000000000000005
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68,1,-0.09000000000000008,-0.17000000000000004,0.029999999999999916,-0.41000000000000003,0.009999999999999898
69,0,0.25,0.2899999999999999,-0.09000000000000008,-0.19000000000000006,0.0
70,0,-0.08000000000000007,-0.14000000000000007,-0.040000000000000036,-0.32000000000000006,0.0
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78,1,0.06999999999999995,0.009999999999999898,0.029999999999999916,-0.16000000000000003,-0.18000000000000005
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699,0,-0.09000000000000008,-0.09000000000000008,-0.06000000000000005,-0.41000000000000003,-0.06000000000000005
1 Id y x1 x2 x3 x4 x5
2 0 0 0.019999999999999907 0.04999999999999993 -0.09000000000000008 -0.43000000000000005 -0.08000000000000007
3 1 0 -0.13000000000000006 0.10999999999999999 -0.08000000000000007 -0.29000000000000004 -0.030000000000000027
4 2 0 0.07999999999999996 0.05999999999999994 -0.07000000000000006 -0.41000000000000003 -0.030000000000000027
5 3 0 0.019999999999999907 -0.12000000000000005 0.009999999999999898 -0.43000000000000005 -0.020000000000000018
6 4 1 -0.14000000000000007 -0.12000000000000005 -0.08000000000000007 -0.020000000000000018 -0.08000000000000007
7 5 1 -0.050000000000000044 -0.16000000000000003 0.0 -0.39 -0.07000000000000006
8 6 0 -0.06000000000000005 -0.020000000000000018 -0.08000000000000007 0.08999999999999997 -0.030000000000000027
9 7 0 -0.08000000000000007 -0.11000000000000004 0.029999999999999916 -0.36000000000000004 0.019999999999999907
10 8 1 -0.010000000000000009 -0.06000000000000005 0.09999999999999998 -0.20000000000000007 -0.07000000000000006
11 9 0 -0.16000000000000003 -0.17000000000000004 0.039999999999999925 -0.41000000000000003 0.019999999999999907
12 10 1 -0.13000000000000006 -0.17000000000000004 -0.020000000000000018 -0.3500000000000001 -0.030000000000000027
13 11 1 -0.14000000000000007 -0.19000000000000006 0.029999999999999916 -0.36000000000000004 -0.040000000000000036
14 12 1 -0.16000000000000003 -0.14000000000000007 0.009999999999999898 -0.21000000000000008 -0.030000000000000027
15 13 1 0.039999999999999925 -0.16000000000000003 -0.040000000000000036 -0.10000000000000003 -0.030000000000000027
16 14 0 0.09999999999999998 -0.010000000000000009 -0.11000000000000004 -0.37000000000000005 -0.10000000000000003
17 15 1 -0.10000000000000003 -0.12000000000000005 -0.040000000000000036 -0.45000000000000007 -0.06000000000000005
18 16 1 -0.09000000000000008 -0.17000000000000004 -0.06000000000000005 -0.45000000000000007 -0.07000000000000006
19 17 0 0.019999999999999907 -0.09000000000000008 -0.020000000000000018 -0.45000000000000007 -0.050000000000000044
20 18 1 -0.06000000000000005 -0.22000000000000003 -0.010000000000000009 -0.3500000000000001 -0.07000000000000006
21 19 0 0.04999999999999993 0.039999999999999925 -0.010000000000000009 -0.3500000000000001 -0.06000000000000005
22 20 1 -0.11000000000000004 -0.16000000000000003 -0.06000000000000005 -0.4 -0.06000000000000005
23 21 0 -0.13000000000000006 -0.12000000000000005 -0.08000000000000007 -0.3400000000000001 -0.050000000000000044
24 22 0 0.16999999999999993 0.06999999999999995 -0.14000000000000007 -0.26000000000000006 -0.07000000000000006
25 23 0 -0.13000000000000006 -0.030000000000000027 -0.040000000000000036 -0.43000000000000005 -0.010000000000000009
26 24 0 -0.10000000000000003 -0.030000000000000027 -0.040000000000000036 -0.41000000000000003 0.019999999999999907
27 25 0 -0.050000000000000044 -0.050000000000000044 -0.040000000000000036 -0.050000000000000044 -0.020000000000000018
28 26 0 0.029999999999999916 -0.11000000000000004 -0.030000000000000027 -0.37000000000000005 0.029999999999999916
29 27 1 0.009999999999999898 -0.09000000000000008 0.039999999999999925 -0.38000000000000006 -0.050000000000000044
30 28 0 0.06999999999999995 0.10999999999999999 0.009999999999999898 -0.32000000000000006 -0.07000000000000006
31 29 0 0.24 0.31999999999999995 -0.20000000000000007 -0.17000000000000004 0.0
32 30 0 -0.030000000000000027 -0.020000000000000018 -0.13000000000000006 -0.4600000000000001 0.009999999999999898
33 31 0 -0.050000000000000044 -0.050000000000000044 -0.13000000000000006 0.30999999999999994 -0.040000000000000036
34 32 0 -0.18000000000000005 0.04999999999999993 0.04999999999999993 -0.44000000000000006 -0.030000000000000027
35 33 0 -0.23000000000000004 -0.010000000000000009 -0.050000000000000044 -0.13000000000000006 -0.050000000000000044
36 34 0 0.21999999999999997 0.17999999999999994 -0.14000000000000007 -0.30000000000000004 -0.13000000000000006
37 35 1 0.17999999999999994 0.10999999999999999 -0.09000000000000008 -0.22000000000000003 -0.14000000000000007
38 36 0 0.15999999999999992 0.04999999999999993 -0.11000000000000004 -0.26000000000000006 -0.020000000000000018
39 37 0 -0.16000000000000003 -0.11000000000000004 0.009999999999999898 -0.38000000000000006 0.0
40 38 0 0.029999999999999916 -0.030000000000000027 -0.13000000000000006 -0.12000000000000005 -0.06000000000000005
41 39 0 0.009999999999999898 -0.030000000000000027 -0.030000000000000027 -0.22000000000000003 -0.030000000000000027
42 40 0 0.29999999999999993 0.12 -0.17000000000000004 -0.32000000000000006 -0.020000000000000018
43 41 0 0.29999999999999993 0.17999999999999994 -0.050000000000000044 -0.16000000000000003 -0.010000000000000009
44 42 0 0.22999999999999998 0.009999999999999898 -0.15000000000000008 -0.28 0.029999999999999916
45 43 0 -0.15000000000000008 -0.020000000000000018 -0.17000000000000004 -0.36000000000000004 -0.050000000000000044
46 44 1 -0.19000000000000006 -0.20000000000000007 0.0 -0.38000000000000006 -0.08000000000000007
47 45 1 -0.030000000000000027 -0.25000000000000006 0.019999999999999907 -0.17000000000000004 -0.09000000000000008
48 46 1 0.17999999999999994 0.18999999999999995 0.019999999999999907 -0.09000000000000008 -0.16000000000000003
49 47 1 -0.07000000000000006 -0.17000000000000004 -0.040000000000000036 -0.2700000000000001 -0.08000000000000007
50 48 0 0.17999999999999994 0.009999999999999898 -0.050000000000000044 -0.28 0.019999999999999907
51 49 1 -0.14000000000000007 -0.32000000000000006 -0.22000000000000003 -0.4 -0.06000000000000005
52 50 1 -0.08000000000000007 -0.17000000000000004 -0.050000000000000044 -0.3500000000000001 -0.040000000000000036
53 51 0 -0.15000000000000008 -0.030000000000000027 -0.11000000000000004 -0.42000000000000004 -0.040000000000000036
54 52 0 -0.11000000000000004 -0.10000000000000003 -0.010000000000000009 -0.13000000000000006 -0.010000000000000009
55 53 1 0.0 -0.08000000000000007 0.019999999999999907 -0.29000000000000004 -0.050000000000000044
56 54 1 0.07999999999999996 0.029999999999999916 0.0 -0.33000000000000007 -0.10000000000000003
57 55 1 0.07999999999999996 0.0 0.0 -0.3400000000000001 -0.11000000000000004
58 56 0 0.09999999999999998 0.05999999999999994 -0.07000000000000006 -0.4600000000000001 -0.07000000000000006
59 57 0 -0.030000000000000027 -0.12000000000000005 -0.050000000000000044 -0.23000000000000004 -0.010000000000000009
60 58 0 -0.18000000000000005 -0.07000000000000006 -0.030000000000000027 -0.37000000000000005 -0.06000000000000005
61 59 0 -0.11000000000000004 0.019999999999999907 -0.08000000000000007 0.10999999999999999 -0.040000000000000036
62 60 1 -0.13000000000000006 -0.21000000000000008 -0.040000000000000036 -0.040000000000000036 -0.020000000000000018
63 61 1 -0.19000000000000006 -0.24000000000000005 -0.09000000000000008 -0.38000000000000006 -0.11000000000000004
64 62 1 -0.08000000000000007 -0.13000000000000006 -0.050000000000000044 -0.24000000000000005 -0.040000000000000036
65 63 0 -0.15000000000000008 -0.10000000000000003 0.029999999999999916 -0.37000000000000005 0.019999999999999907
66 64 0 -0.020000000000000018 -0.08000000000000007 -0.12000000000000005 -0.48000000000000004 -0.040000000000000036
67 65 0 0.039999999999999925 -0.09000000000000008 -0.11000000000000004 -0.3400000000000001 -0.050000000000000044
68 66 0 -0.22000000000000003 -0.10000000000000003 0.009999999999999898 -0.4700000000000001 -0.010000000000000009
69 67 0 -0.08000000000000007 -0.020000000000000018 -0.010000000000000009 -0.44000000000000006 -0.050000000000000044
70 68 1 -0.09000000000000008 -0.17000000000000004 0.029999999999999916 -0.41000000000000003 0.009999999999999898
71 69 0 0.25 0.2899999999999999 -0.09000000000000008 -0.19000000000000006 0.0
72 70 0 -0.08000000000000007 -0.14000000000000007 -0.040000000000000036 -0.32000000000000006 0.0
73 71 0 0.019999999999999907 -0.050000000000000044 -0.07000000000000006 -0.29000000000000004 0.009999999999999898
74 72 0 0.039999999999999925 -0.06000000000000005 -0.12000000000000005 0.04999999999999993 -0.09000000000000008
75 73 0 -0.11000000000000004 -0.010000000000000009 -0.020000000000000018 0.09999999999999998 -0.09000000000000008
76 74 1 -0.10000000000000003 -0.07000000000000006 0.019999999999999907 -0.33000000000000007 -0.12000000000000005
77 75 1 -0.07000000000000006 -0.14000000000000007 0.0 -0.010000000000000009 -0.14000000000000007
78 76 0 0.06999999999999995 -0.030000000000000027 -0.020000000000000018 -0.16000000000000003 -0.06000000000000005
79 77 0 -0.06000000000000005 -0.020000000000000018 -0.030000000000000027 -0.020000000000000018 -0.050000000000000044
80 78 1 0.06999999999999995 0.009999999999999898 0.029999999999999916 -0.16000000000000003 -0.18000000000000005
81 79 0 -0.13000000000000006 0.009999999999999898 -0.050000000000000044 -0.07000000000000006 -0.08000000000000007
82 80 0 -0.08000000000000007 -0.11000000000000004 -0.010000000000000009 -0.06000000000000005 -0.030000000000000027
83 81 0 -0.06000000000000005 0.019999999999999907 -0.10000000000000003 -0.10000000000000003 -0.10000000000000003
84 82 0 -0.050000000000000044 -0.020000000000000018 0.039999999999999925 0.009999999999999898 0.019999999999999907
85 83 1 -0.020000000000000018 -0.040000000000000036 0.06999999999999995 -0.19000000000000006 -0.10000000000000003
86 84 0 0.10999999999999999 0.05999999999999994 -0.16000000000000003 -0.13000000000000006 -0.06000000000000005
87 85 0 -0.28 0.019999999999999907 -0.3500000000000001 -0.43000000000000005 -0.050000000000000044
88 86 0 -0.17000000000000004 -0.12000000000000005 -0.21000000000000008 -0.4 -0.010000000000000009
89 87 0 0.24 0.06999999999999995 -0.11000000000000004 -0.2700000000000001 -0.050000000000000044
90 88 1 -0.06000000000000005 -0.040000000000000036 0.029999999999999916 -0.26000000000000006 -0.050000000000000044
91 89 0 -0.14000000000000007 -0.09000000000000008 -0.040000000000000036 -0.15000000000000008 -0.030000000000000027
92 90 1 -0.20000000000000007 -0.10000000000000003 0.05999999999999994 -0.10000000000000003 -0.050000000000000044
93 91 1 -0.10000000000000003 -0.18000000000000005 -0.09000000000000008 -0.3400000000000001 -0.040000000000000036
94 92 1 -0.16000000000000003 -0.11000000000000004 0.0 -0.36000000000000004 -0.11000000000000004
95 93 1 -0.23000000000000004 -0.13000000000000006 0.07999999999999996 -0.4 -0.040000000000000036
96 94 0 -0.07000000000000006 0.04999999999999993 -0.07000000000000006 -0.31000000000000005 -0.06000000000000005
97 95 1 -0.18000000000000005 -0.06000000000000005 -0.19000000000000006 -0.30000000000000004 -0.13000000000000006
98 96 0 0.1299999999999999 0.1399999999999999 -0.040000000000000036 -0.20000000000000007 -0.10000000000000003
99 97 0 0.04999999999999993 0.15999999999999992 -0.17000000000000004 -0.23000000000000004 0.019999999999999907
100 98 0 0.21999999999999997 0.18999999999999995 -0.16000000000000003 -0.28 -0.030000000000000027
101 99 1 0.07999999999999996 0.009999999999999898 0.009999999999999898 -0.29000000000000004 -0.19000000000000006
102 100 0 -0.20000000000000007 0.019999999999999907 -0.21000000000000008 -0.32000000000000006 -0.12000000000000005
103 101 0 -0.20000000000000007 -0.13000000000000006 -0.17000000000000004 -0.44000000000000006 -0.07000000000000006
104 102 1 -0.09000000000000008 -0.040000000000000036 -0.06000000000000005 -0.16000000000000003 -0.15000000000000008
105 103 1 -0.08000000000000007 -0.33000000000000007 0.009999999999999898 -0.29000000000000004 -0.08000000000000007
106 104 1 -0.09000000000000008 -0.17000000000000004 -0.010000000000000009 -0.32000000000000006 -0.09000000000000008
107 105 0 -0.12000000000000005 0.029999999999999916 -0.20000000000000007 -0.4 -0.040000000000000036
108 106 1 -0.14000000000000007 -0.21000000000000008 -0.020000000000000018 -0.38000000000000006 0.0
109 107 0 -0.26000000000000006 0.0 -0.010000000000000009 -0.38000000000000006 -0.06000000000000005
110 108 0 0.08999999999999997 0.08999999999999997 -0.040000000000000036 -0.4 0.039999999999999925
111 109 0 -0.29000000000000004 0.039999999999999925 -0.08000000000000007 -0.33000000000000007 -0.010000000000000009
112 110 1 -0.11000000000000004 -0.15000000000000008 -0.06000000000000005 -0.10000000000000003 -0.06000000000000005
113 111 0 -0.12000000000000005 -0.040000000000000036 -0.15000000000000008 -0.33000000000000007 -0.050000000000000044
114 112 1 -0.26000000000000006 -0.24000000000000005 0.009999999999999898 -0.37000000000000005 -0.08000000000000007
115 113 1 -0.16000000000000003 -0.12000000000000005 -0.07000000000000006 -0.09000000000000008 -0.07000000000000006
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