{
"cells": [
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"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>"
]
},
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"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 numpy as np\n",
"from sklearn.metrics import mean_squared_error\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 correlate(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, (nOut - len(s2), 0), 'constant', constant_values=(0,0))\n",
" return [sum(s1_padded[m] * s2_padded[n + m] for m in range(nOut - n)) for n in range(nOut)]\n",
"\n",
"def fcorrelate(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.fftshift((np.fft.ifft(np.conj(fft1) * fft2)))"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cross/fcross Mean Squared Error: (5.6e-26, 2.8e-26)\n",
"cross/npcross Mean Squared Error: 1.9e-27\n",
"fcross/npcross Mean Squared Error: (5.4e-26, 2.9e-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 = 5 # Hz\n",
"f2 = 5 # Hz\n",
"w1 = 2 * np.pi * f1\n",
"w2 = 2 * np.pi * f2\n",
"\n",
"t = np.linspace(0, T, N)\n",
"t_ext = np.linspace(-T, T, 2 * N - 1)\n",
"s1 = np.cos(w1 * t / T)\n",
"s2 = np.cos(w2 * t / T)\n",
"\n",
"cross = correlate(s1, s2)\n",
"fcross = fcorrelate(s1, s2)\n",
"npcross = np.correlate(s1, s2, mode='full')[::-1]\n",
"\n",
"print_mse(cross, fcross, 'cross/fcross')\n",
"print_mse(cross, npcross, 'cross/npcross')\n",
"print_mse(fcross, npcross, 'fcross/npcross')\n",
"\n",
"tr_cross = go.Scatter(\n",
" x = t_ext,\n",
" y = cross,\n",
" name='cross'\n",
")\n",
"\n",
"tr_fcross = go.Scatter(\n",
" x = t_ext,\n",
" y = fcross.real,\n",
" name='fcross'\n",
")\n",
"\n",
"tr_npcross = go.Scatter(\n",
" x = t_ext,\n",
" y = npcross.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_cross, 1, 1)\n",
"fig.append_trace(tr_fcross, 1, 1)\n",
"fig.append_trace(tr_npcross, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cross/fcross Mean Squared Error: (-1.9e-28, 1e-27)\n",
"cross/npcross Mean Squared Error: 0\n",
"fcross/npcross Mean Squared Error: (-1.9e-28, 1e-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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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(-T, T, 2 * N - 1)\n",
"s1 = [0 if i < 50 or i > 150 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",
"cross = correlate(s1, s2)\n",
"fcross = fcorrelate(s1, s2)\n",
"npcross = np.correlate(s1, s2, mode='full')[::-1]\n",
"\n",
"print_mse(cross, fcross, 'cross/fcross')\n",
"print_mse(cross, npcross, 'cross/npcross')\n",
"print_mse(fcross, npcross, 'fcross/npcross')\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 = cross,\n",
" name='cross'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t_ext,\n",
" y = fcross.real,\n",
" name='fcross'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t_ext,\n",
" y = npcross.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": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cross/fcross Mean Squared Error: (-1.9e-28, 1e-27)\n",
"cross/npcross Mean Squared Error: 0\n",
"fcross/npcross Mean Squared Error: (-1.9e-28, 1e-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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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(-T, T, 2 * N - 1)\n",
"s1 = [0 if i < 50 or i > 150 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",
"cross = correlate(s1, s2)\n",
"fcross = fcorrelate(s1, s2)\n",
"npcross = np.correlate(s1, s2, mode='full')[::-1]\n",
"\n",
"print_mse(cross, fcross, 'cross/fcross')\n",
"print_mse(cross, npcross, 'cross/npcross')\n",
"print_mse(fcross, npcross, 'fcross/npcross')\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 = cross,\n",
" name='cross'\n",
")\n",
"\n",
"tr_fconv = go.Scatter(\n",
" x = t_ext,\n",
" y = fcross.real,\n",
" name='fcross'\n",
")\n",
"\n",
"tr_npconv = go.Scatter(\n",
" x = t_ext,\n",
" y = npcross.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": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"cross/fcross Mean Squared Error: (2.1e-29, 1.8e-29)\n",
"cross/npcross Mean Squared Error: 1.7e-30\n",
"fcross/npcross Mean Squared Error: (1.9e-29, 1.6e-29)\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 = 50\n",
"T = 1.0 # s\n",
"\n",
"t = np.linspace(0, T, N)\n",
"t_ext = np.linspace(-T, T, 2 * N - 1)\n",
"\n",
"s1 = np.random.rand(N)\n",
"s2 = np.random.rand(N)\n",
"\n",
"cross = correlate(s1, s2)\n",
"fcross = fcorrelate(s1, s2)\n",
"npcross = np.correlate(s1, s2, mode='full')[::-1]\n",
"\n",
"print_mse(cross, fcross, 'cross/fcross')\n",
"print_mse(cross, npcross, 'cross/npcross')\n",
"print_mse(fcross, npcross, 'fcross/npcross')\n",
"\n",
"tr_cross = go.Scatter(\n",
" x = t_ext,\n",
" y = cross,\n",
" name='cross'\n",
")\n",
"\n",
"tr_fcross = go.Scatter(\n",
" x = t_ext,\n",
" y = fcross.real,\n",
" name='fcross'\n",
")\n",
"\n",
"tr_npcross = go.Scatter(\n",
" x = t_ext,\n",
" y = npcross.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_cross, 1, 1)\n",
"fig.append_trace(tr_fcross, 1, 1)\n",
"fig.append_trace(tr_npcross, 1, 1)\n",
"\n",
"py.offline.iplot(fig)"
]
}
],
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