├── GP_algorithm.py ├── README.md ├── README_files ├── README_11_0.png ├── README_4_0.png ├── README_6_0.png └── README_8_0.png └── Test_Example_notebook.ipynb /GP_algorithm.py: -------------------------------------------------------------------------------- 1 | 2 | ''' 3 | COPYRIGHT sebastiano.bontorin@unitn.it 4 | ''' 5 | 6 | 7 | 8 | import matplotlib.pyplot as plt 9 | import numpy as np 10 | from scipy import stats 11 | 12 | def td_embedding(data,emb,tau): 13 | ''' 14 | Time delay embedding of timeseries of scalars 15 | Args: 16 | timeseries: array of scalars 17 | emb: (int) embedding dimension 18 | tau = (int) time delay between values in phase space reconstruction 19 | Returns: 20 | array of embedded vectors: 21 | [x[i],x[i+tau],x[i+2*tau],...,x[i + (m-1)*tau]] 22 | ''' 23 | indexes = np.arange(0,emb,1)*tau 24 | return np.array([data[indexes +i] for i in range(len(data)-(emb-1)*tau)]) 25 | 26 | 27 | def logarithmic_r(min_n, max_n, factor): 28 | ''' 29 | Creates array of values distributed such as log(values) is an array of 30 | evenly spaced (space between values = log(factor)) values between log(min_n) and log(max_n) 31 | Args: 32 | arg1: min_n: minimum value 33 | arg2: max_n: maximum value ( > arg1 ) 34 | factor: log(factor) is the space between values 35 | Returns: 36 | min_n, min_n * factor, min_n * factor^2, ... min_n * factor^i < max_n 37 | ''' 38 | 39 | if max_n <= min_n: 40 | raise ValueError("arg1 has to be < arg2") 41 | if factor <= 1: 42 | raise ValueError("factor(arg3) has to be > 1") 43 | max_i = int(np.floor(np.log(1.0 * max_n / min_n) / np.log(factor))) 44 | return np.array([min_n * (factor ** i) for i in range(max_i + 1)]) 45 | 46 | 47 | def grassberg_procaccia(data,emb_dim,time_delay,plot = None): 48 | ''' 49 | Implementation of the Gassberger-Procaccia algorithm to estimate the 50 | correlation dimension of a set of points in an m-dimensional space. 51 | 52 | This code takes in input a timeseries of scalar values and the embedding dimension + time delay 53 | necessary to perform a time-delay embedding in phase space to reconstruct the attractor 54 | 55 | Args: 56 | data: array of scalars - a timeseries 57 | emb_dim: (int) embedding dimension 58 | time_delay = (int) time delay between values in phase space reconstruction 59 | Kwargs: 60 | plot: if set to True: plots the logarithm of the correlation 61 | sums against the logarithm of the set of values of r considered in the algorithm 62 | 63 | r is the scaling factor, it tells the threshold distance between points. if we have a plateau 64 | of local slopes means that we are in a scaling range. 65 | 66 | Returns: 67 | Correlation dimension (scalar) 68 | 69 | ''' 70 | 71 | # Phase space points reconstructed via time-delay embedding 72 | orbit = td_embedding(data, emb_dim, time_delay) 73 | n_points = len(orbit) 74 | 75 | # Timeseries standard deviation 76 | data_std = np.std(data) 77 | 78 | # Generate a series of r distances evenly spaced in log scale, these are 79 | # generated starting from the timeseries of scalars standard deviation. 80 | # The r distance is a scalar used to find the fraction of points in phase space for which 81 | # the euclidean distance between them is smaller than r 82 | r_vals = logarithmic_r(0.1 * data_std, 0.7 * data_std, 1.03) 83 | 84 | distances = np.zeros(shape=(n_points,n_points)) 85 | r_matrix_base = np.zeros(shape=(n_points,n_points)) 86 | 87 | # Euclidean distance of points in phase space 88 | for i in range(n_points): 89 | for j in range(i,n_points): 90 | distances[i][j] = np.linalg.norm(orbit[i]-orbit[j]) 91 | r_matrix_base[i][j] = 1 92 | 93 | # Correlation sum 94 | C_r = [] 95 | for r in r_vals: 96 | r_matrix = r_matrix_base*r 97 | heavi_matrix = np.heaviside( r_matrix - distances, 0) 98 | corr_sum = (2/float(n_points*(n_points-1)))*np.sum(heavi_matrix) 99 | C_r.append(corr_sum) 100 | 101 | #strong assumption: the log-log plot is assumed to be a smooth, monotonic function, 102 | #hence the slope in the scaling region should be the maximum gradient ( in this case 103 | #is taken as the mean of the last five maximum gradients as they are calculated for every point ) 104 | gradients = np.gradient(np.log2(C_r),np.log2(r_vals)) 105 | gradients.sort() 106 | D = np.mean(gradients[-5:]) 107 | 108 | if plot: 109 | # plot the trend of Cr) 110 | plt.plot(np.log2(r_vals),np.log2(C_r)) 111 | plt.xlabel("Distance r") 112 | plt.ylabel("C(r)") 113 | plt.title("Correlation sum in log2-log2 plot. Dimension D is "+str(round(D,2))) 114 | plt.show() 115 | 116 | return D 117 | 118 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # README 2 | 3 | (Open the notebook for a better visualization of plots axes) 4 | 5 | Implementation of the Grassberger-Procaccia algorithm to estimate the correlation dimension of a set. Please refer to: http://www.scholarpedia.org/article/Grassberger-Procaccia_algorithm for more information on the Grassberger-Procaccia algorithm and the correlation dmension 6 | 7 | Correlation dimension is a fractal dimension (such as Box-counting dimension or Hausdorff dimension) and it is characteristic of the set of points. If an attractor in phase space is being studied, once the attractor is completely unfolded in m dimensions, correlation dimension becomes an invariant and further embeddings in more dimensions do not influence its value, thus remaining constant. 8 | 9 | # Test Example 10 | 11 | Test of the `grassberg_procaccia` function (found in `GP_algorithm.py`) that implements the G-P algorithm, to estimate the correlation dimension of a set of points in a m dimensional space. This code takes in input a timeseries of scalar values and the embedding dimension (m) + time delay (tau) necessary to perform a time-delay embedding in phase space to reconstruct the attractor. See: https://en.wikipedia.org/wiki/Takens%27s_theorem for more information regarding the phase space reconstruction. 12 | 13 | Function `grassberg_procaccia` is the main reference for the implementation. Some notes: 14 | 15 | - it assumes the user has only a timeseries of scalar values coming from a dynamical system 16 | - It assumes the time delay is known 17 | 18 | Additonaly, this function can be used: 19 | 20 | - It will be used to find the ideal embedding dimension m in which to unfold the attractor 21 | - While this implementation was successfully tested with Lorentz and Henon attractors, with High dimensional attractors coming from a stochastic-deterministic hybrid dynamics (with additive or even multiplicative noise) the Correlation sum in log-log shows two different scaling regions. Thus results can not be trusted. 22 | 23 | 24 | # Test example of the implementation of Grassberger-Procaccia algorithm 25 | 26 | 27 | ```python 28 | import matplotlib.pyplot as plt 29 | import numpy as np 30 | 31 | import GP_algorithm as gp 32 | 33 | plt.rcParams['figure.figsize'] = [5, 5] 34 | ``` 35 | 36 | ## Generation of a timeseries from Lorenz attractor 37 | 38 | The following code for the timeseries generation from the Lorenz dynamical system was directly copied from https://matplotlib.org/stable/gallery/mplot3d/lorenz_attractor.html. © Copyright 2002 - 2012 John Hunter, Darren Dale, Eric Firing, Michael Droettboom and the Matplotlib development team; 2012 - 2021 The Matplotlib development team. 39 | 40 | 41 | ```python 42 | def lorenz(x, y, z, s=10, r=28, b=2.667): 43 | '''Given: 44 | x, y, z: a point of interest in three dimensional space 45 | s, r, b: parameters defining the lorenz attractor 46 | Returns: 47 | x_dot, y_dot, z_dot: values of the lorenz attractor's partial derivatives at the point x, y, z''' 48 | x_dot = s*(y - x) 49 | y_dot = r*x - y - x*z 50 | z_dot = x*y - b*z 51 | return x_dot, y_dot, z_dot 52 | 53 | dt = 0.01 54 | num_steps = 10000 55 | 56 | # Need one more for the initial values 57 | xs = np.empty(num_steps + 1) 58 | ys = np.empty(num_steps + 1) 59 | zs = np.empty(num_steps + 1) 60 | 61 | # Set initial values 62 | xs[0], ys[0], zs[0] = (0., 1., 1.05) 63 | 64 | # Step through "time", calculating the partial derivatives at the current point and using them to estimate the next point 65 | for i in range(num_steps): 66 | x_dot, y_dot, z_dot = lorenz(xs[i], ys[i], zs[i]) 67 | xs[i + 1] = xs[i] + (x_dot * dt) 68 | ys[i + 1] = ys[i] + (y_dot * dt) 69 | zs[i + 1] = zs[i] + (z_dot * dt) 70 | 71 | # Plot the attractor 72 | ax = plt.figure().add_subplot(projection='3d') 73 | ax.plot(xs, ys, zs, lw=0.5) 74 | ax.set_title("Lorenz Attractor") 75 | plt.show() 76 | ``` 77 | 78 | 79 | 80 | ![png](README_files/README_4_0.png) 81 | 82 | 83 | 84 | # X dimension timeseries 85 | 86 | To test the GP algorithm we will use the previously generated timeseries coming from the X dimension to reconstruct back the phase space (in the assumption we have data of which we don't know the original deterministic model, and we have only a timeseries of scalars) and then estimate the Correlation dimension 87 | 88 | 89 | ```python 90 | # plot only X dimension, the first 1500 steps 91 | 92 | plt.plot(range(num_steps)[:1500], xs[:1500]) 93 | plt.title("Lorenz Attractor - X dimension timeseries") 94 | plt.xlabel("Step in time") 95 | plt.ylabel("X") 96 | plt.show() 97 | ``` 98 | 99 | 100 | 101 | ![png](README_files/README_6_0.png) 102 | 103 | 104 | 105 | # Correlation Dimension of X timeseries 106 | 107 | Following Takens theorem, the necessary embedding dimension for the reconstruction is 2*dim (2 times the original dimension from which ). 108 | Correlation sum C(r) scales as r^{D}. Thus the correlation dimension can be reconstructed in a log log plot 109 | 110 | 111 | ```python 112 | # Test the function for a single value 113 | emb_dim = 3 114 | # Arbitrary time delay 115 | time_delay = 20 116 | timeseries = xs[:1500] 117 | 118 | # Algortuhm execution to get the dimension 119 | D = gp.grassberg_procaccia(timeseries,emb_dim,time_delay,plot = True) 120 | ``` 121 | 122 | 123 | 124 | ![png](README_files/README_8_0.png) 125 | 126 | 127 | 128 | ## Finding the best embedding dimension for the Lorenz attractor using the correlation dimension 129 | 130 | We compute the correlation dimension for different candidate embedding dimensions for the timeseries X of scalar values coming from the original lorentz system. We find that D reaches a plateau at embedding_dim equal to 3, as the original one (Also note that the dimension given by Takens’s theorem is only an upper limit. A lower embedding dimension may suffice) 131 | 132 | 133 | ```python 134 | # Compute the correlation dimension for a set of different embedding dimensions of the timeseries 135 | Ds = [] 136 | 137 | for emb_dim in range(1,8): 138 | 139 | time_delay = 20 140 | timeseries = xs[:1500] 141 | 142 | D = gp.grassberg_procaccia(timeseries,emb_dim,time_delay,plot = False) 143 | Ds.append(D) 144 | 145 | ``` 146 | 147 | 148 | ```python 149 | # Plot 150 | 151 | plt.plot(range(1,8),Ds,'o-') 152 | plt.xlabel("Embedding dimension") 153 | plt.ylabel("D") 154 | plt.title("Correlation dimension D versus embedding dimension") 155 | plt.show() 156 | ``` 157 | 158 | 159 | 160 | ![png](README_files/README_11_0.png) 161 | 162 | 163 | -------------------------------------------------------------------------------- /README_files/README_11_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/notsebastiano/GP_algorithm/4950e284b611a74db2d2482acaa52ed1422b2b94/README_files/README_11_0.png -------------------------------------------------------------------------------- /README_files/README_4_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/notsebastiano/GP_algorithm/4950e284b611a74db2d2482acaa52ed1422b2b94/README_files/README_4_0.png -------------------------------------------------------------------------------- /README_files/README_6_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/notsebastiano/GP_algorithm/4950e284b611a74db2d2482acaa52ed1422b2b94/README_files/README_6_0.png -------------------------------------------------------------------------------- /README_files/README_8_0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/notsebastiano/GP_algorithm/4950e284b611a74db2d2482acaa52ed1422b2b94/README_files/README_8_0.png -------------------------------------------------------------------------------- /Test_Example_notebook.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# README\n", 8 | "\n", 9 | "Implementation of the Grassberger-Procaccia algorithm to estimate the correlation dimension of a set. Please refer to: http://www.scholarpedia.org/article/Grassberger-Procaccia_algorithm for more information on the Grassberger-Procaccia algorithm and the correlation dmension\n", 10 | "\n", 11 | "Correlation dimension is a fractal dimension (such as Box-counting dimension or Hausdorff dimension) and it is characteristic of the set of points. If an attractor in phase space is being studied, once the attractor is completely unfolded in m dimensions, correlation dimension becomes an invariant and further embeddings in more dimensions do not influence its value, thus remaining constant.\n", 12 | "\n", 13 | "# Notebook implementation\n", 14 | "\n", 15 | "Test of the `grassberg_procaccia` function that implements the G-P algorithm, to estimate the correlation dimension of a set of points in a m dimensional space. This code takes in input a timeseries of scalar values and the embedding dimension (m) + time delay (tau) necessary to perform a time-delay embedding in phase space to reconstruct the attractor. See: https://en.wikipedia.org/wiki/Takens%27s_theorem for more information regarding the phase space reconstruction.\n", 16 | "\n", 17 | "Function `grassberg_procaccia` is the main reference for the implementation. Some notes:\n", 18 | "\n", 19 | "- it assumes the user has only a timeseries of scalar values coming from a dynamical system\n", 20 | "- It assumes the time delay is known\n", 21 | "\n", 22 | "Additonaly, this function can be used:\n", 23 | "\n", 24 | "- It will be used to find the ideal embedding dimension m in which to unfold the attractor \n", 25 | "- While this implementation was successfully tested with Lorentz and Henon attractors, with High dimensional attractors coming from a stochastic-deterministic hybrid dynamics (with additive or even multiplicative noise) the Correlation sum in log-log shows two different scaling regions. Thus results can not be trusted.\n" 26 | ] 27 | }, 28 | { 29 | "cell_type": "markdown", 30 | "metadata": {}, 31 | "source": [ 32 | "# Test example of the implementation of Grassberger-Procaccia algorithm" 33 | ] 34 | }, 35 | { 36 | "cell_type": "code", 37 | "execution_count": 1, 38 | "metadata": {}, 39 | "outputs": [], 40 | "source": [ 41 | "import matplotlib.pyplot as plt\n", 42 | "import numpy as np\n", 43 | "\n", 44 | "import GP_algorithm as gp\n", 45 | "\n", 46 | "plt.rcParams['figure.figsize'] = [5, 5]" 47 | ] 48 | }, 49 | { 50 | "cell_type": "markdown", 51 | "metadata": {}, 52 | "source": [ 53 | "## Generation of a timeseries from Lorenz attractor\n", 54 | "\n", 55 | "The following code for the timeseries generation from the Lorenz dynamical system was directly copied from https://matplotlib.org/stable/gallery/mplot3d/lorenz_attractor.html. © Copyright 2002 - 2012 John Hunter, Darren Dale, Eric Firing, Michael Droettboom and the Matplotlib development team; 2012 - 2021 The Matplotlib development team." 56 | ] 57 | }, 58 | { 59 | "cell_type": "code", 60 | "execution_count": 2, 61 | "metadata": {}, 62 | "outputs": [ 63 | { 64 | "data": { 65 | "image/png": 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\n", 66 | "text/plain": [ 67 | "
" 68 | ] 69 | }, 70 | "metadata": { 71 | "needs_background": "light" 72 | }, 73 | "output_type": "display_data" 74 | } 75 | ], 76 | "source": [ 77 | "def lorenz(x, y, z, s=10, r=28, b=2.667):\n", 78 | " '''Given:\n", 79 | " x, y, z: a point of interest in three dimensional space\n", 80 | " s, r, b: parameters defining the lorenz attractor\n", 81 | " Returns:\n", 82 | " x_dot, y_dot, z_dot: values of the lorenz attractor's partial derivatives at the point x, y, z'''\n", 83 | " x_dot = s*(y - x)\n", 84 | " y_dot = r*x - y - x*z\n", 85 | " z_dot = x*y - b*z\n", 86 | " return x_dot, y_dot, z_dot\n", 87 | "\n", 88 | "dt = 0.01\n", 89 | "num_steps = 10000\n", 90 | "\n", 91 | "# Need one more for the initial values\n", 92 | "xs = np.empty(num_steps + 1)\n", 93 | "ys = np.empty(num_steps + 1)\n", 94 | "zs = np.empty(num_steps + 1)\n", 95 | "\n", 96 | "# Set initial values\n", 97 | "xs[0], ys[0], zs[0] = (0., 1., 1.05)\n", 98 | "\n", 99 | "# Step through \"time\", calculating the partial derivatives at the current point and using them to estimate the next point\n", 100 | "for i in range(num_steps):\n", 101 | " x_dot, y_dot, z_dot = lorenz(xs[i], ys[i], zs[i])\n", 102 | " xs[i + 1] = xs[i] + (x_dot * dt)\n", 103 | " ys[i + 1] = ys[i] + (y_dot * dt)\n", 104 | " zs[i + 1] = zs[i] + (z_dot * dt)\n", 105 | "\n", 106 | "# Plot the attractor\n", 107 | "ax = plt.figure().add_subplot(projection='3d')\n", 108 | "ax.plot(xs, ys, zs, lw=0.5)\n", 109 | "ax.set_title(\"Lorenz Attractor\")\n", 110 | "plt.show()" 111 | ] 112 | }, 113 | { 114 | "cell_type": "markdown", 115 | "metadata": {}, 116 | "source": [ 117 | "# X dimension timeseries\n", 118 | "\n", 119 | "To test the GP algorithm we will use the previously generated timeseries coming from the X dimension to reconstruct back the phase space (in the assumption we have data of which we don't know the original deterministic model, and we have only a timeseries of scalars) and then estimate the Correlation dimension" 120 | ] 121 | }, 122 | { 123 | "cell_type": "code", 124 | "execution_count": 3, 125 | "metadata": {}, 126 | "outputs": [ 127 | { 128 | "data": { 129 | "image/png": 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\n", 130 | "text/plain": [ 131 | "
" 132 | ] 133 | }, 134 | "metadata": { 135 | "needs_background": "light" 136 | }, 137 | "output_type": "display_data" 138 | } 139 | ], 140 | "source": [ 141 | "# plot only X dimension, the first 1500 steps\n", 142 | "\n", 143 | "plt.plot(range(num_steps)[:1500], xs[:1500])\n", 144 | "plt.title(\"Lorenz Attractor - X dimension timeseries\")\n", 145 | "plt.xlabel(\"Step in time\")\n", 146 | "plt.ylabel(\"X\")\n", 147 | "plt.show()" 148 | ] 149 | }, 150 | { 151 | "cell_type": "markdown", 152 | "metadata": {}, 153 | "source": [ 154 | "# Correlation Dimension of X timeseries\n", 155 | "\n", 156 | "Following Takens theorem, the necessary embedding dimension for the reconstruction is 2*dim (2 times the original dimension from which ).\n", 157 | "Correlation sum C(r) scales as r^{D}. Thus the correlation dimension can be reconstructed in a log log plot" 158 | ] 159 | }, 160 | { 161 | "cell_type": "code", 162 | "execution_count": 4, 163 | "metadata": { 164 | "scrolled": true 165 | }, 166 | "outputs": [ 167 | { 168 | "data": { 169 | "image/png": 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\n", 170 | "text/plain": [ 171 | "
" 172 | ] 173 | }, 174 | "metadata": { 175 | "needs_background": "light" 176 | }, 177 | "output_type": "display_data" 178 | } 179 | ], 180 | "source": [ 181 | "# Test the function for a single value\n", 182 | "emb_dim = 3\n", 183 | "# Arbitrary time delay\n", 184 | "time_delay = 20\n", 185 | "timeseries = xs[:1500]\n", 186 | "\n", 187 | "# Algortuhm execution to get the dimension\n", 188 | "D = gp.grassberg_procaccia(timeseries,emb_dim,time_delay,plot = True)" 189 | ] 190 | }, 191 | { 192 | "cell_type": "markdown", 193 | "metadata": {}, 194 | "source": [ 195 | "## Finding the best embedding dimension for the Lorenz attractor using the correlation dimension\n", 196 | "\n", 197 | "We compute the correlation dimension for different candidate embedding dimensions for the timeseries X of scalar values coming from the original lorentz system. We find that D reaches a plateau at embedding_dim equal to 3, as the original one (Also note that the dimension given by Takens’s theorem is only an upper limit. A lower embedding dimension may suffice)" 198 | ] 199 | }, 200 | { 201 | "cell_type": "code", 202 | "execution_count": 5, 203 | "metadata": {}, 204 | "outputs": [], 205 | "source": [ 206 | "# Compute the correlation dimension for a set of different embedding dimensions of the timeseries\n", 207 | "Ds = []\n", 208 | "\n", 209 | "for emb_dim in range(1,8):\n", 210 | " \n", 211 | " time_delay = 20\n", 212 | " timeseries = xs[:1500]\n", 213 | " \n", 214 | " D = gp.grassberg_procaccia(timeseries,emb_dim,time_delay,plot = False)\n", 215 | " Ds.append(D)\n" 216 | ] 217 | }, 218 | { 219 | "cell_type": "code", 220 | "execution_count": 6, 221 | "metadata": {}, 222 | "outputs": [ 223 | { 224 | "data": { 225 | "image/png": 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\n", 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" 228 | ] 229 | }, 230 | "metadata": { 231 | "needs_background": "light" 232 | }, 233 | "output_type": "display_data" 234 | } 235 | ], 236 | "source": [ 237 | "# Plot\n", 238 | "\n", 239 | "plt.plot(range(1,8),Ds,'o-')\n", 240 | "plt.xlabel(\"Embedding dimension\")\n", 241 | "plt.ylabel(\"D\")\n", 242 | "plt.title(\"Correlation dimension D versus embedding dimension\")\n", 243 | "plt.show()" 244 | ] 245 | } 246 | ], 247 | "metadata": { 248 | "kernelspec": { 249 | "display_name": "Python 3 (ipykernel)", 250 | "language": "python", 251 | "name": "python3" 252 | }, 253 | "language_info": { 254 | "codemirror_mode": { 255 | "name": "ipython", 256 | "version": 3 257 | }, 258 | "file_extension": ".py", 259 | "mimetype": "text/x-python", 260 | "name": "python", 261 | "nbconvert_exporter": "python", 262 | "pygments_lexer": "ipython3", 263 | "version": "3.9.9" 264 | } 265 | }, 266 | "nbformat": 4, 267 | "nbformat_minor": 2 268 | } 269 | --------------------------------------------------------------------------------