{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
],
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"<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# https://plot.ly/python/subplots/\n",
"import plotly as py\n",
"import plotly.graph_objs as go\n",
"from plotly.offline import download_plotlyjs\n",
"\n",
"# Когда выгоднее использовать быструю, а когда - медленную в зависимости от длины входных данных\n",
"# Корелляция - все то же самое\n",
"\n",
"py.offline.init_notebook_mode(connected=True)\n",
"\n",
"# import matplotlib\n",
"# import matplotlib.pyplot as plt\n",
"# import matplotlib.gridspec as gridspec\n",
"\n",
"import numpy as np\n",
"from sklearn.metrics import mean_squared_error\n",
"\n",
"colors = ['k','b','r','m','g','Brown','DarkBlue','Tomato','Violet', 'Tan','Salmon','Pink',\n",
" 'SaddleBrown', 'SpringGreen', 'RosyBrown','Silver',]\n",
"\n",
"def print_mse(got, predicted, prefix=''):\n",
" mse = mean_squared_error(got, predicted)\n",
" if isinstance(mse, np.complex):\n",
" print('%s Mean Squared Error: (%.2g, %.2g)' % (prefix, mse.real, mse.imag))\n",
" else:\n",
" print('%s Mean Squared Error: %.2g' % (prefix, mse))\n",
"\n",
"def convolve(s1, s2):\n",
" nOut = len(s1) + len(s2) - 1\n",
"\n",
" s1_padded = np.pad(s1, (0, nOut - len(s1)), 'constant', constant_values=(0,0))\n",
" s2_padded = np.pad(s2, (0, nOut - len(s2)), 'constant', constant_values=(0,0))\n",
"# res = []\n",
"# for n in range(nOut):\n",
"# v = 0;\n",
"# for m in range(nOut):\n",
"# v += s1_padded[m] * s2_padded[n - m]\n",
"# res.append(v)\n",
"# return res# return res\n",
" return [sum(s1_padded[m] * s2_padded[n - m] for m in range(nOut)) for n in range(nOut)] \n",
"\n",
"def fconvolve(s1, s2):\n",
" nOut = len(s1) + len(s2) - 1\n",
"\n",
" s1_padded = np.pad(s1, (0, nOut - len(s1)), 'constant', constant_values=(0,0))\n",
" s2_padded = np.pad(s2, (0, nOut - len(s2)), 'constant', constant_values=(0,0))\n",
" \n",
" fft1 = np.fft.fft(s1_padded)\n",
" fft2 = np.fft.fft(s2_padded)\n",
" return np.fft.ifft(fft1 * fft2)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (2.1e-26, -5e-26)\n",
"conv/npconv Mean Squared Error: 3.5e-27\n",
"fconv/npconv Mean Squared Error: (1.7e-26, -4.9e-26)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"f1 = 20 # Hz\n",
"f2 = 20 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s1 = np.sin(w1 * t / T)\n",
"s2 = np.sin(w2 * t / T)\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 1, cols = 1)\n",
"\n",
"fig['layout'].update(height=450, width=900)\n",
"\n",
"fig.append_trace(tr_conv, 1, 1)\n",
"fig.append_trace(tr_fconv, 1, 1)\n",
"fig.append_trace(tr_npconv, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (3.5e-27, -1.6e-26)\n",
"conv/npconv Mean Squared Error: 9.6e-28\n",
"fconv/npconv Mean Squared Error: (2.6e-27, -1.7e-26)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
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0.6002794441212058, 0.25185721522023957, 0.06512309057141097, 7.913911869004741e-16, -9.610591131521204e-30], \"name\": \"numpy\", \"xaxis\": \"x1\", \"yaxis\": \"y1\"}], {\"xaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"y1\"}, \"yaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"x1\"}, \"height\": 450, \"width\": 900}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"f1 = 20 # Hz\n",
"f2 = 21 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s1 = np.sin(w1 * t / T)\n",
"s2 = np.sin(w2 * t / T)\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 1, cols = 1)\n",
"\n",
"fig['layout'].update(height=450, width=900)\n",
"\n",
"fig.append_trace(tr_conv, 1, 1)\n",
"fig.append_trace(tr_fconv, 1, 1)\n",
"fig.append_trace(tr_npconv, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (2.5e-27, -1.1e-27)\n",
"conv/npconv Mean Squared Error: 2.2e-28\n",
"fconv/npconv Mean Squared Error: (2.4e-27, -1.2e-27)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
"data": [
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"f1 = 20 # Hz\n",
"f2 = 22 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s1 = np.sin(w1 * t / T)\n",
"s2 = np.sin(w2 * t / T)\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 1, cols = 1)\n",
"\n",
"fig['layout'].update(height=450, width=900)\n",
"\n",
"fig.append_trace(tr_conv, 1, 1)\n",
"fig.append_trace(tr_fconv, 1, 1)\n",
"fig.append_trace(tr_npconv, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (7.5e-29, -1.1e-27)\n",
"conv/npconv Mean Squared Error: 9.4e-29\n",
"fconv/npconv Mean Squared Error: (5.6e-29, -1.1e-27)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"f1 = 20 # Hz\n",
"f2 = 23 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s1 = np.sin(w1 * t / T)\n",
"s2 = np.sin(w2 * t / T)\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 1, cols = 1)\n",
"\n",
"fig['layout'].update(height=450, width=900)\n",
"\n",
"fig.append_trace(tr_conv, 1, 1)\n",
"fig.append_trace(tr_fconv, 1, 1)\n",
"fig.append_trace(tr_npconv, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (1.8e-28, -1.1e-28)\n",
"conv/npconv Mean Squared Error: 3.2e-29\n",
"fconv/npconv Mean Squared Error: (1.6e-28, -1.1e-28)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"f1 = 20 # Hz\n",
"f2 = 25 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"t = np.linspace(0, T, N)\n",
"s1 = np.sin(w1 * t / T)\n",
"s2 = np.sin(w2 * t / T)\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 1, cols = 1)\n",
"\n",
"fig['layout'].update(height=450, width=900)\n",
"\n",
"fig.append_trace(tr_conv, 1, 1)\n",
"fig.append_trace(tr_fconv, 1, 1)\n",
"fig.append_trace(tr_npconv, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (7.3e-29, 4.1e-29)\n",
"conv/npconv Mean Squared Error: 1.8e-30\n",
"fconv/npconv Mean Squared Error: (6.7e-29, 3.9e-29)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"f1 = 20 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"\n",
"t = np.linspace(0, T, N)\n",
"t_ext = np.linspace(0, 2 * T - T / N, 2 * N - 1)\n",
"s1 = np.sin(w1 * t / T)\n",
"s2 = [0 if i < 200 or i > 300 else 1 for i in range(N)]\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t_ext,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t_ext,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t_ext,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 1, cols = 1)\n",
"\n",
"fig['layout'].update(height=450, width=900)\n",
"\n",
"fig.append_trace(tr_conv, 1, 1)\n",
"fig.append_trace(tr_fconv, 1, 1)\n",
"fig.append_trace(tr_npconv, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"conv/fconv Mean Squared Error: (-1.3e-27, -6.8e-27)\n",
"conv/npconv Mean Squared Error: 0\n",
"fconv/npconv Mean Squared Error: (-1.3e-27, -6.8e-27)\n",
"This is the format of your plot grid:\n",
"[ (1,1) x1,y1 ]\n",
"[ (2,1) x2,y2 ]\n",
"\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], \"name\": \"numpy\", \"xaxis\": \"x2\", \"yaxis\": \"y2\"}], {\"xaxis1\": {\"domain\": [0.0, 1.0], \"anchor\": \"y1\"}, \"yaxis1\": {\"domain\": [0.575, 1.0], \"anchor\": \"x1\"}, \"xaxis2\": {\"domain\": [0.0, 1.0], \"anchor\": \"y2\"}, \"yaxis2\": {\"domain\": [0.0, 0.425], \"anchor\": \"x2\"}, \"height\": 900, \"width\": 900}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 500\n",
"T = 1.0 # s\n",
"\n",
"t = np.linspace(0, T, N)\n",
"t_ext = np.linspace(0, 2 * T - T / N, 2 * N - 1)\n",
"s1 = [0 if i < 200 or i > 300 else 1 for i in range(N)]\n",
"s2 = [0 if i < 200 or i > 300 else 1 for i in range(N)]\n",
"\n",
"conv = convolve(s1, s2)\n",
"fconv = fconvolve(s1, s2)\n",
"npconv = np.convolve(s1, s2)\n",
"\n",
"print_mse(conv, fconv, 'conv/fconv')\n",
"print_mse(conv, npconv, 'conv/npconv')\n",
"print_mse(fconv, npconv, 'fconv/npconv')\n",
"\n",
"tr_signal1 = go.Scatter(\n",
" x = t,\n",
" y = s1,\n",
" name='s1'\n",
")\n",
"\n",
"tr_signal2 = go.Scatter(\n",
" x = t,\n",
" y = s2,\n",
" name='s2'\n",
")\n",
"\n",
"tr_conv = go.Scatter(\n",
" x = t_ext,\n",
" y = conv,\n",
" name='conv'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t_ext,\n",
" y = fconv.real,\n",
" name='fconv'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t_ext,\n",
" y = npconv.real,\n",
" name='numpy'\n",
")\n",
"\n",
"fig = py.tools.make_subplots(rows = 2, cols = 1)\n",
"\n",
"fig['layout'].update(height=900, width=900)\n",
"\n",
"fig.append_trace(tr_signal1, 1, 1)\n",
"fig.append_trace(tr_signal2, 1, 1)\n",
"fig.append_trace(tr_conv, 2, 1)\n",
"fig.append_trace(tr_fconv, 2, 1)\n",
"fig.append_trace(tr_npconv, 2, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"N = 50\n",
"5.15 ms ± 536 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
"154 µs ± 13.9 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n",
"9.31 µs ± 499 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
"\n",
"N = 100\n",
"17.2 ms ± 64.3 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
"314 µs ± 17.9 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
"15.4 µs ± 137 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n",
"\n",
"N = 500\n",
"334 ms ± 4.56 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
"317 µs ± 3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
"100 µs ± 2.71 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n",
"\n",
"N = 1000\n",
"1.5 s ± 149 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
"17.8 ms ± 1.59 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
"272 µs ± 3.69 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
"\n",
"N = 2000\n",
"5.94 s ± 500 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
"1.36 ms ± 171 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
"860 µs ± 6.24 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n",
"\n"
]
}
],
"source": [
"for N in [50, 100, 500, 1000, 2000]:\n",
" T = N / 50 # s\n",
" \n",
" f = 20 # Hz\n",
" w = 2 * np.pi * f\n",
"\n",
" t = np.linspace(0, T, N)\n",
" s1 = np.sin(w * t / T)\n",
" s2 = [0 if i < 200 or i > 300 else t[i] for i in range(N)]\n",
"\n",
" print('N = {}'.format(N)) \n",
" %timeit convolve(s1, s2)\n",
" %timeit fconvolve(s1, s2)\n",
" %timeit np.convolve(s1, s2)\n",
" print('')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}