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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "7c1065dd",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pyerrors as pe"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "20f67709",
"metadata": {},
"outputs": [],
"source": [
"plt.style.use('./base_style.mplstyle')\n",
"plt.rc('text', usetex=True)"
]
},
{
"cell_type": "markdown",
"id": "e5764fd0",
"metadata": {},
"source": [
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"We can load data from a preprocessed file which contains a list of `pyerror` `Obs`:"
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]
},
{
"cell_type": "code",
"execution_count": 3,
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"id": "fbfa65f5",
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"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Data has been written using pyerrors 2.0.0.\n",
"Format version 0.1\n",
"Written by fjosw on 2022-01-06 11:11:19 +0100 on host XPS139305, Linux-5.11.0-44-generic-x86_64-with-glibc2.29\n",
"\n",
"Description: Test data for the correlator example\n"
]
}
],
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"source": [
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"correlator_data = pe.input.json.load_json(\"./data/correlator_test\")"
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]
},
{
"cell_type": "markdown",
"id": "ae93c7c2",
"metadata": {},
"source": [
"With this list a `Corr` object can be initialised"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "33a8fdec",
"metadata": {},
"outputs": [],
"source": [
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"my_correlator = pe.Corr(correlator_data)\n",
"my_correlator.gamma_method()"
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]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5f954607",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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"Corr T=96 N=1\n",
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"x0/a\tCorr(x0/a)\n",
"------------------\n",
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"8\t 548(13)\n",
"9\t 433(11)\n",
"10\t 343.1(8.6)\n",
"11\t 273.2(6.6)\n",
"12\t 217.5(5.6)\n",
"13\t 172.9(4.9)\n",
"14\t 137.6(4.6)\n",
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"\n"
]
}
],
"source": [
"my_correlator.print([8, 14])"
]
},
{
"cell_type": "markdown",
"id": "b00d670b",
"metadata": {},
"source": [
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"The `show` method can display the correlator. The argument <code>auto_gamma</code> tells `show` to calculate the y-errors using the gamma method with the default parameters."
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]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b71529d0",
"metadata": {},
"outputs": [
{
"data": {
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"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"my_correlator.show(auto_gamma=True)"
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]
},
{
"cell_type": "markdown",
"id": "c659557e",
"metadata": {},
"source": [
"## Manipulating correlators"
]
},
{
"cell_type": "markdown",
"id": "416cf39a",
"metadata": {},
"source": [
"`Corr` objects can be shifted"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "e8d65dd5",
"metadata": {},
"outputs": [],
"source": [
"shifted_correlator = my_correlator.roll(20)\n",
"shifted_correlator.tag = r'Correlator shifted by $x_0/a=20$'"
]
},
{
"cell_type": "markdown",
"id": "634dd613",
"metadata": {},
"source": [
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"or symmetrised"
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]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "127a661d",
"metadata": {},
"outputs": [],
"source": [
"symmetrised_correlator = my_correlator.symmetric()\n",
"symmetrised_correlator.tag = 'Symmetrised correlator'"
]
},
{
"cell_type": "markdown",
"id": "3d733872",
"metadata": {},
"source": [
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"We can compare different `Corr` objects by passing `comp` to the `show` method"
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]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "8e264aed",
"metadata": {},
"outputs": [
{
"data": {
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"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"shifted_correlator.show(comp=symmetrised_correlator, logscale=True, auto_gamma=True)"
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]
},
{
"cell_type": "markdown",
"id": "232e88af",
"metadata": {},
"source": [
"## Effective mass"
]
},
{
"cell_type": "markdown",
"id": "83dc751c",
"metadata": {},
"source": [
"The effective mass of the correlator can be obtained by calling the `m_eff` method"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "c686f7e0",
"metadata": {},
"outputs": [],
"source": [
"m_eff = symmetrised_correlator.m_eff()\n",
"m_eff.tag = 'Effective mass'"
]
},
{
"cell_type": "markdown",
"id": "4a9d13b2",
"metadata": {},
"source": [
"We can also use the priodicity of the lattice in order to obtain the cosh effective mass"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5acde8cf",
"metadata": {},
"outputs": [],
"source": [
"periodic_m_eff = symmetrised_correlator.m_eff('periodic')\n",
"periodic_m_eff.tag = 'Cosh effective mass'"
]
},
{
"cell_type": "markdown",
"id": "c658b000",
"metadata": {},
"source": [
"We can compare the two and see how the standard effective mass deviates form the plateau at the center of the lattice"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "1d6ea22a",
"metadata": {},
"outputs": [
{
"data": {
2022-02-18 09:46:07 +01:00
"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"periodic_m_eff.show([4,47], comp=m_eff, ylabel=r'$am_\\mathrm{eff}$')"
]
},
{
"cell_type": "markdown",
"id": "e3762e68",
"metadata": {},
"source": [
"Arithmetic operations and mathematical functions are also overloaded for the `Corr` class. We can compute the difference between the two variants of the effective mass as follows."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e56d164c",
"metadata": {},
"outputs": [
{
"data": {
2022-02-18 09:46:07 +01:00
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAAGNCAYAAADaX58UAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAq7ElEQVR4nO3df2xd5Z3n8c+TlMQwse/NjzExxIE4tGVMujBOnJaoaFaDzZLRZItGSYgEXQmtSMioq261VdJUdLOIKplEbVdoqjJx/2wy6hBmBAqasGBmFlE1DVAP0oZsmGIDodQZE4d7b9Jgh7W/+8c917m+uT/OOb4/zr33/ZIscs85OfdhzjT58Dzf53ucmQkAAADBzav1AAAAAOoVQQoAACAkghQAAEBIBCkAAICQCFIAAAAhEaQAAABCIkgBAACE9LlaD8AP51xc0nZJMrODtR0NAABAWr3MSPVJWlrrQQAAAGSrixkpM3vWObdEUjzo73XOOUk3SbpY7nEBAICG1irpd1bkNTBVC1Le8txWSVvMrD/P+V2SEt7HeBmX8G6S9Nsy3QsAADSXFZI+KnSyKkHKOdcjaZ3SM0pL8pzfJUlmNuB97nPOHTKzHWX4+ouS9OGHH6qtra0MtwMAAI0ulUqps7NTKrGiVZUgZWZDkoacc5sLXLJH0qqs6wedcy9LKkeQkiS1tbURpAAAQFnVvNjcOdel9FJeIs+5vhD3W+ica8v8KL2+CQAAUHY1D1KSugocT8grLvcCVb+k/iKzWhl7JCWzfqiPAgAAFRHlXXsX5NVTmdmgpEGfv2+/pB9lfW4VYQoAAFRAlIPUNUXpfpjZpKTJzOd09wMAAIDyi8LS3kiB4/Ei5wAAAGqu5kHKzEYkJbyi89xzfpfzAAAAqq7aQarQct1+pV8DI0nyCsoHqjIiAACAkKoSpJxzXV7TzR2SepxzB7J333ldzOPOuc3e8d4yNeMEAACoGFfk9TENwesllUwmkzTkBAAAvqRSKcViMUmKmVmq0HU1r5ECAACoVwQpAACAkAhSAAAAIRGkAAAAQiJIAQAAhESQAgAACIkgBQAAEBJBCgAAICSCFAAAQEgEKQAAgJAIUgAAACERpAAAAEIiSAEAAIREkAIAAAiJIAUAABASQQoAACAkghQAAEBIBCkAAICQCFIAAAAhEaQAAABC+lytBwAAAFALU9Om19+7oLGLE2pvbdH6VUs0f54LdA+CFAAAaDovnhrVE8dOazQ5MXOsI9aivZu6df+aDt/3cWZWifFFhnOuTVIymUyqra2t1sMBAAAV5GeW6cVTo9p5eEi5CShz1dMP92jDyj9QLBaTpJiZpQp9HzNSAACgIfiZZRpNfKrHnzt1TYiSNHPs8edO6W//07/z9Z0UmwMAgEibmjadGB7X8299pBPD45qavjYGZWaZskOUJJ1LTmjn4SG9eGpUkvTkC6d1/tKVot93/tIVHfxfZ3yNjRkpAAAQWX5mmaamTU8cO11wlslJeuLYafV3L9enn035+l6/1zEjBQAAIsnvLNPRN89ec002kzSanNDRN89q67pOX9/9F3+8wtd1BCkAAFB1pZbrSs0ySelZpqlp009fe8/Xd/70tfd03x3L1RFrUaEmB07pGa8//aMbfd2TpT0AAFBVfpbrgswyPXrPKn3nH06V/N5H71ml+fOc9m7q1s7DQ3LSrKCWCVd7N3X77ifFjBQAAKgav8t1QWaZtqxb6WuWacu6lZKk+9d06OmHe7Q81jLruuWxFj39cE+gPlLMSAEAgLIo1cMpSFF4pWeZ7l/Tof7u5XQ2BwAAtVfu5bot61bqqVfe1bnkRN7g5ZSeQcqdZcodw/Ii3crnz3O6e/XSUP++M+OgszkAAJgLP53C71/ToXt/+L81/PHvS95v9R/+gV75b/9+5r5S/lmmfMtw5Xh/niSlUilfnc2pkQIAAAWVc3fdo/es8vWdmevC1DJlZpm+dtfNunv10lAhKgiW9gAAQF61Xq6TylfLVCnMSAEAgGtUYnddpihc0jU77Iq1Hqj2LFMQBCkAADBL1JbrooylPQAAmkypguyX3j7na7nupbfPNeRyXRAEKQAAmoifuqdn3vzQ172eefNDbfxSR6hO4eVoPRAFLO0BANAk/NY9XX/dfF/3y1zXaMt1QdBHCgCABlBquW408ak2/fgXOn/pSsF7LFu0QMe+8VVJ8n1tR/x632OoJ377SNXF0p5zbrOkJZLWSjpqZoM1HhIAAJHhZ7nuyRdOFw1GknT+0hU9+cJp/eThtfr+A2uKNsP8/gNrZoUoqXGW64KI/NKec65HksxsQNJuSUdrOyIAAKLD73Ldp59N+bpf5rpmXq4Loh5mpJZI6pf0rJklnHMXnHM9ZjZU64EBAFBLQV4CvHVdp/75nY9L3nPrus6ZXzfS7rpKKUuQcs7FJW2VtMXM+vOc3yUp4X2Mm9lBv/f2lvGyl/KWEKIAAM2gVM1R0K7iHbGWkm0K7rtj+azjzbhcF8Scg5S39LZOUlzp2aPc87ukmaU5Oef6nHOHzGxHiO86JOnROQ0YAIA64KfuKUhX8W3rbwnVpgDFlW3XnlcQvsfM1uYc/0TSKjNLZB0zM3Per3dJyhd1x7Nnrrz7y8yeDTgudu0BAOpKpu4p92/oTMTJ1Cj9/PUP9J1/OFXyfn/1F2u0bf0tM/cuFdAQkV17zrkupZfyEnnO9ZnZoJ9lPudcn6SEmQ16M2AJMxsp/4gBAKgsP20KHn/uVNHXszz+3CnduSLe9F3Fo6DSxeZdBY4nlF4KLMkLY0e9X0vpYFbwaTvnFkpamHWo1c/3AABQaZVoU9DMXcWjoFbtDy4oTz1VPmY2YmaLs35KReY9kpJZP7+d21ABAJg72hQ0plq1P/AVokLaL+lHWZ9bRZgCANQQbQoaV6WDVKE6pniRc3NiZpOSJjOfveVAAAAqplTd00tvn/PVpuClt8/pvjuW06agjlQ0SJnZiHMu4Zzryi0O5zUvAIBG4Kfu6Zk3P/R1r2fe/FAbv9RBm4I6Us4aqULLdfsl9WU+eG0MBsr4vQAA1ITfuqfrr5vv636Z66h7qh9z7iPl7arbLOlBST2SDkp6I7vfk9crKjMj1Wtmu+f0pcHGRx8pAEBgftoUbPrxL4rusFu2aIGOfeOrkuT72uwXAZcaAyrHbx+psjXkjCqCFAAgKD/LdX95+Nf6x1PnSt7rz9Ys108eXjszeyXlX65jpila/AapWrU/AAAgkmhTgCBq1f4AAIDIoU0BgiJIAQDgoU0BgmJpDwDQNKamTSeGx/X8Wx/pxPC4pqZnR6AgbQrmz3Pau6lb0tU6pwzaFDQPZqQAAE3BTwF52DYFufddnnNfNC527QEAGl6mgDz3b7zcHXNBWhrQpqCxsWsPAACl+z09/typggXkJunx505pNPGpOuLX6/sPrJFT/uU6J+n7D6yZFaKkq3VPX7vrZt29eikhqokQpAAAda1U3dOTL5wuOsMkSecvXdGTL5yWRJsCBEONFACgbvmpewra70miTQH8Y0YKAFCX/DbOzO7jVEzudSzXwQ+CFACg7gSpe8r0eyoUg5zSs1i5/Z4APwhSAIDIKWfdE/2eUEnUSAEAIqUSdU/0e0Kl0EcKABAZfvs9Hf8/o9p5ZKjk/Z5+qEcbv3Q1JNHvCX757SPFjBQAoCpKhZhSdU9Suu7pzhVx3nOHyCBIAQAqzs9yXZC6p588vFZ7N3Vr5+EhOWlWmKLuCdVEsTkAoKL8tikIW/dE40zUEjNSAIDQyrlct3Vdp/75nY9Lfmd2vycaZ6LWCFIAgFD8LNf94KV3fC3X/eCld3Rw853UPaHusLQHAAjM73Ld6j9c5Ot+q/9wEf2eUJcIUgCAWUo1w5yaNj1x7HTR5bonjp3W1LRp+ONLvr4zcx11T6g3LO0BAGb4Wa576e1z18xEZTNJo8kJvfT2OX37vi/q1X/9uOjy3rJFC/Tt+74485m6J9QTZqQAAJL8L9c98+aHvu73zJsfqiN+vb7/wBo55V+uc5K+/8AadcSvn3WOFwajXhCkAACBXgJ8/XXzfd0zcx3LdWh
2021-10-11 18:31:02 +01:00
"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"difference_m_eff = np.abs(periodic_m_eff - m_eff)\n",
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"difference_m_eff.show([0, 47], logscale=True, auto_gamma=True)"
2021-10-11 18:31:02 +01:00
]
},
{
"cell_type": "markdown",
"id": "472ab97b",
"metadata": {},
"source": [
"## Derivatives"
]
},
{
"cell_type": "markdown",
"id": "d99414fe",
"metadata": {},
"source": [
"We can obtain derivatives of correlators in the following way"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "03007f8a",
"metadata": {},
"outputs": [],
"source": [
"first_derivative = symmetrised_correlator.deriv()\n",
"first_derivative.tag = 'First derivative'"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "c0311739",
"metadata": {},
"outputs": [],
"source": [
"second_derivative = symmetrised_correlator.second_deriv()\n",
"second_derivative.tag = 'Second derivative'"
]
},
{
"cell_type": "code",
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"execution_count": 19,
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"id": "165550d9",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"symmetrised_correlator.show([5, 20], comp=[first_derivative, second_derivative], y_range=[-500, 1300], auto_gamma=True)"
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]
},
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{
"cell_type": "markdown",
"id": "18c75d20",
"metadata": {},
"source": [
"## Missing Values \n",
"\n",
"Apart from the build-in functions, there is another reason, why one should use a **Corr** instead of a list of **Obs**. \n",
"Missing values are handled for you. \n",
"We will create a second correlator with missing values. "
]
},
{
"cell_type": "code",
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"execution_count": 17,
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"id": "1db86a4c",
"metadata": {},
"outputs": [
{
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"name": "stdout",
"output_type": "stream",
"text": [
"Corr T=96 N=1\n",
"x0/a\tCorr(x0/a)\n",
"------------------\n",
"0\t 62865(41)\n",
"1\t 23756(32)\n",
"2\t 6434(25)\n",
"3\t 2886(20)\n",
"4\t 1735(21)\n",
"5\t 1213(21)\n",
"6\n",
"7\t 699(17)\n",
"8\n",
"9\n",
"10\t 343.1(8.6)\n",
"11\t 273.2(6.6)\n",
"12\n",
"13\t 172.9(4.9)\n",
"14\n",
"15\n",
"16\t 88.0(3.9)\n",
"17\t 70.6(3.2)\n",
"18\t 56.6(2.6)\n",
"19\t 45.3(2.1)\n",
"20\n",
"21\t 29.2(1.4)\n",
"22\t 23.4(1.2)\n",
"\n"
]
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}
],
"source": [
"new_content=[(my_correlator.content[i] if i not in [6,8,9,12,14,15,20] else None ) for i in range(my_correlator.T) ] # We reuse the old example and replace a few values with None\n",
"correlator_incomplete=pe.Corr(new_content)\n",
"\n",
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"correlator_incomplete.print([0, 22]) # Print the correlator in the range 0 - 22"
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]
},
{
"cell_type": "markdown",
"id": "602d81fa",
"metadata": {},
"source": [
"We see that this is still a valid correlator. It is just missing some values. \n",
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"When we perform operations, which generate new correlators, the missing values are handled automatically."
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]
},
{
"cell_type": "markdown",
"id": "6479a999",
"metadata": {},
"source": [
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"Some functions might also return correlators with missing values. We already looked at the derivative. \n",
"The symmertic derivative is not defined for the first and last timeslice. \n",
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"\n",
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"The important thing is that, whatever you do, correlators keep their length **T**. So there will never be confusion about how you count timeslices. You can also take a plateau or perform a fit, even though some values might be missing."
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]
},
{
"cell_type": "code",
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"execution_count": 18,
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"id": "f3c4609c",
"metadata": {},
"outputs": [],
"source": [
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"assert first_derivative.T == my_correlator.T == len(first_derivative.content) == len(my_correlator.content)\n",
"assert first_derivative.content[0] is None\n",
"assert first_derivative.content[-1] is None"
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]
},
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{
"cell_type": "markdown",
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"id": "7fcbcac4",
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"metadata": {},
"source": [
"There is a range of addtional methods of the `Corr` class which can be found in the documentation."
]
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}
],
"metadata": {
"kernelspec": {
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"display_name": "Python 3",
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"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",
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"version": "3.8.8"
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}
},
"nbformat": 4,
"nbformat_minor": 5
}
