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348 lines
173 KiB
348 lines
173 KiB
3 years ago
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 19,
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"id": "cc79f1dd",
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"metadata": {},
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"outputs": [],
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"source": [
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"from matplotlib import pyplot as plt\n",
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"import sympy as sp\n",
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"sp.init_printing()\n",
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"plt.style.use('seaborn-deep')\n",
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"plt.rcParams['figure.dpi'] = 140\n",
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"f, mu, delta, l, p_dc, p_opt, f, eta, n = sp.symbols(r'f \\mu \\delta l p_{dc} p_{opt} f \\eta n')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "1ac718e2",
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"metadata": {},
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"outputs": [],
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"source": [
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"approx_values = {\n",
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" r'\\mu': 1,\n",
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" 'f': 1,\n",
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" r'\\delta': 0.2,\n",
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" 'l': 1,\n",
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" r'p_{dc}': 0.02,\n",
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" r'p_{opt}': 0.01,\n",
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" r'\\eta': 0.2\n",
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"}\n",
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"variables = {\n",
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" r'\\mu': mu,\n",
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" 'f': f,\n",
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" r'\\delta': delta,\n",
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" 'l': l,\n",
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" r'p_{dc}': p_dc,\n",
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" r'p_{opt}': p_opt,\n",
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" r'\\eta': eta\n",
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"}"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "b65f4f73",
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"metadata": {},
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"outputs": [],
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"source": [
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"def pop_in_place(d, k):\n",
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" return {key: d[key] for key in d.keys() if key != k}"
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]
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},
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{
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"cell_type": "markdown",
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"id": "01aa0680",
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"metadata": {},
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"source": [
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"**Key generation rate:**\n",
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"\n",
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"$$R=\\dfrac 12 f (\\mu t \\eta + 2p_{dc})$$\n",
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"\n",
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"**Error rate:**\n",
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"\n",
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"$$E=\\dfrac{p_{dc} + p_{opt} n t \\eta}{2 p_{dc} + n t \\eta}$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "e7c63373",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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\n",
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"text/latex": [
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"$\\displaystyle 10^{- \\frac{\\delta l}{10}}$"
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],
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"text/plain": [
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" -\\delta⋅l \n",
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" ──────────\n",
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" 10 \n",
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"10 "
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"t = 10 ** (-l * delta / 10)\n",
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"t"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"id": "9a69c84c",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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\n",
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"text/latex": [
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"$\\displaystyle \\frac{f \\left(2 p_{dc} + 10^{- \\frac{\\delta l}{10}} \\eta \\mu\\right)}{2}$"
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],
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"text/plain": [
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" ⎛ -\\delta⋅l ⎞\n",
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" ⎜ ────────── ⎟\n",
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" ⎜ 10 ⎟\n",
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"f⋅⎝2⋅p_{dc} + 10 ⋅\\eta⋅\\mu⎠\n",
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"────────────────────────────────────\n",
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" 2 "
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]
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},
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"execution_count": 22,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"R = f * (mu*t*eta+2*p_dc) / 2\n",
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"R"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"id": "6637fe0a",
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"metadata": {},
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"outputs": [],
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"source": [
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"E = (p_dc + p_opt * n * t * eta) / (2 * p_dc + n * t * eta)"
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]
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},
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{
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"cell_type": "code",
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|
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"execution_count": 24,
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||
|
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"id": "82a82472",
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"metadata": {},
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"outputs": [],
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"source": [
|
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"def plot_for_key(key, key_range, title='', show=True):\n",
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" subs = pop_in_place(approx_values, key)\n",
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" if subs.get('\\mu') is not None:\n",
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" subs['n'] = subs['\\mu']\n",
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" plot = sp.plotting.plot(R.evalf(subs=subs), E.evalf(subs=subs), (variables[key], *key_range), xlabel=f'${key}$', ylabel='', show=False, title=title or f'$R$ and $E$ vs. ${key}$')\n",
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" plot[1].line_color = 'r'\n",
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" if show:\n",
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" plot.show()\n",
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" return plot"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"id": "bf4db181",
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"metadata": {},
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"outputs": [
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||
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{
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"ename": "ValueError",
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"evalue": "The same variable should be used in all univariate expressions being plotted.",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-25-9cbfa17e5309>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplot_for_key\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mr'\\mu'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-24-2836792b187f>\u001b[0m in \u001b[0;36mplot_for_key\u001b[0;34m(key, key_range, title, show)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msubs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'\\mu'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0msubs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'n'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msubs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'\\mu'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mplot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplotting\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mE\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevalf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msubs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mvariables\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mkey_range\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34mf'${key}$'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mylabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshow\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtitle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtitle\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;34mf'$R$ and $E$ vs. ${key}$'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mline_color\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mshow\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m/usr/lib/python3.9/site-packages/sympy/plotting/plot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(show, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1726\u001b[0m \u001b[0mfree\u001b[0m \u001b[0;34m|=\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfree_symbols\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1727\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfree\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1728\u001b[0;31m raise ValueError(\n\u001b[0m\u001b[1;32m 1729\u001b[0m \u001b[0;34m'The same variable should be used in all '\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1730\u001b[0m 'univariate expressions being plotted.')\n",
|
||
|
|
"\u001b[0;31mValueError\u001b[0m: The same variable should be used in all univariate expressions being plotted."
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plot_for_key(r'\\mu', (0.5, 3))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 9,
|
||
|
|
"id": "a4d125cc",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 840x560 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<sympy.plotting.plot.Plot at 0x7fd53264ddf0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 9,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plot_for_key(r'l', (0.5, 10))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 18,
|
||
|
|
"id": "35cb0bcc",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 840x560 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<sympy.plotting.plot.Plot at 0x7fd53209ceb0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 18,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plot_for_key(r'p_{dc}', (0, 1))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"id": "5cc66fa2",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 840x560 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<sympy.plotting.plot.Plot at 0x7fd5325d3c70>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plot_for_key(r'p_{opt}', (0, 1))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 12,
|
||
|
|
"id": "9c2bd9df",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 840x560 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<sympy.plotting.plot.Plot at 0x7fd5325cac70>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 12,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plot_for_key(r'\\eta', (0, 1))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"id": "b0675f39",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"h = lambda p: - (p * sp.log(p, 2) + (1 - p) * sp.log(1 - p, 2))\n",
|
||
|
|
"R_sec = R * (- h (E))"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"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": "3.9.7"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|