pms/uczenie-maszynowe
16
17
Fork 2
Code Issues Pull Requests Projects Releases Wiki Activity
c5d82d65af
uczenie-maszynowe/wyk/03_Regresja_liniowa_2.ipynb
Paweł Skórzewski c5d82d65af Wykład 3
2022-10-18 13:52:38 +02:00

1366 lines
246 KiB
Plaintext
Raw Blame History

This file contains invisible Unicode characters

This file contains invisible Unicode characters that are indistinguishable to humans but may be processed differently by a computer. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Uczenie maszynowe\n",
"# 3. Regresja liniowa – część 2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 3.1. Regresja liniowa wielu zmiennych"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Do przewidywania wartości $y$ możemy użyć więcej niż jednej cechy $x$:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Przykład – ceny mieszkań"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" y:price x1:isNew x2:rooms x3:floor x4:location x5:sqrMetres\n",
"1 476118.0 False 3 1 Centrum 78\n",
"2 459531.0 False 3 2 Sołacz 62\n",
"3 411557.0 False 3 0 Sołacz 15\n",
"4 496416.0 False 4 0 Sołacz 14\n",
"5 406032.0 False 3 0 Sołacz 15\n",
"... ... ... ... ... ... ...\n",
"1335 349000.0 False 4 0 Szczepankowo 29\n",
"1336 399000.0 False 5 0 Szczepankowo 68\n",
"1337 234000.0 True 2 7 Wilda 50\n",
"1338 210000.0 True 2 1 Wilda 65\n",
"1339 279000.0 True 2 2 Łazarz 36\n",
"\n",
"[1339 rows x 6 columns]\n"
]
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"data = pd.read_csv(\"data02_train.tsv\", sep=\"\\t\")\n",
"data.rename(columns={col: f\"x{i}:{col}\" if i > 0 else f\"y:{col}\" for i, col in enumerate(data.columns)}, inplace=True)\n",
"data.index = np.arange(1, len(data) + 1)\n",
"print(data)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"$$ x^{(2)} = ({\\rm \"False\"}, 3, 2, {\\rm \"Sołacz\"}, 62), \\quad x_3^{(2)} = 2 $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Hipoteza"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"W naszym przypadku (wybraliśmy 5 cech):\n",
"\n",
"$$ h_\\theta(x) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_3 + \\theta_4 x_4 + \\theta_5 x_5 $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"W ogólności ($n$ cech):\n",
"\n",
"$$ h_\\theta(x) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\ldots + \\theta_n x_n $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Jeżeli zdefiniujemy $x_0 = 1$, będziemy mogli powyższy wzór zapisać w bardziej kompaktowy sposób:\n",
"\n",
"$$\n",
"\\begin{array}{rcl}\n",
"h_\\theta(x)\n",
" & = & \\theta_0 x_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\ldots + \\theta_n x_n \\\\\n",
" & = & \\displaystyle\\sum_{i=0}^{n} \\theta_i x_i \\\\\n",
" & = & \\theta^T \\, x \\\\\n",
" & = & x^T \\, \\theta \\\\\n",
"\\end{array}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Metoda gradientu prostego – notacja macierzowa"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Metoda gradientu prostego przyjmie bardzo elegancką formę, jeżeli do jej zapisu użyjemy wektorów i macierzy."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"$$\n",
"X=\\left[\\begin{array}{cc}\n",
"1 & \\left( \\vec x^{(1)} \\right)^T \\\\\n",
"1 & \\left( \\vec x^{(2)} \\right)^T \\\\\n",
"\\vdots & \\vdots\\\\\n",
"1 & \\left( \\vec x^{(m)} \\right)^T \\\\\n",
"\\end{array}\\right] \n",
"= \\left[\\begin{array}{cccc}\n",
"1 & x_1^{(1)} & \\cdots & x_n^{(1)} \\\\\n",
"1 & x_1^{(2)} & \\cdots & x_n^{(2)} \\\\\n",
"\\vdots & \\vdots & \\ddots & \\vdots\\\\\n",
"1 & x_1^{(m)} & \\cdots & x_n^{(m)} \\\\\n",
"\\end{array}\\right]\n",
"\\quad\n",
"\\vec{y} = \n",
"\\left[\\begin{array}{c}\n",
"y^{(1)}\\\\\n",
"y^{(2)}\\\\\n",
"\\vdots\\\\\n",
"y^{(m)}\\\\\n",
"\\end{array}\\right]\n",
"\\quad\n",
"\\theta = \\left[\\begin{array}{c}\n",
"\\theta_0\\\\\n",
"\\theta_1\\\\\n",
"\\vdots\\\\\n",
"\\theta_n\\\\\n",
"\\end{array}\\right]\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"# Wersje macierzowe funkcji rysowania wykresów punktowych oraz krzywej regresyjnej\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"\n",
"def h(theta, x):\n",
" return x * theta\n",
"\n",
"\n",
"def regdots(x, y, xlabel=\"populacja\", ylabel=\"zysk\"):\n",
" fig = plt.figure(figsize=(16 * 0.6, 9 * 0.6))\n",
" ax = fig.add_subplot(111)\n",
" fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
" ax.scatter([x[:, 1]], [y], c=\"r\", s=50, label=\"Dane\")\n",
"\n",
" ax.set_xlabel(xlabel)\n",
" ax.set_ylabel(ylabel)\n",
" ax.margins(0.05, 0.05)\n",
" plt.ylim(y.min() - 1, y.max() + 1)\n",
" plt.xlim(np.min(x[:, 1]) - 1, np.max(x[:, 1]) + 1)\n",
" return fig\n",
"\n",
"\n",
"def regline(fig, fun, theta, x):\n",
" ax = fig.axes[0]\n",
" x_min = np.min(x[:, 1])\n",
" x_max = np.max(x[:, 1])\n",
" x_range = [x_min, x_max]\n",
" x_matrix = np.matrix([1, x_min, 1, x_max]).reshape(2, 2)\n",
" ax.plot(\n",
" x_range,\n",
" fun(theta, x_matrix),\n",
" linewidth=\"2\",\n",
" label=(\n",
" r\"$y={theta0:.2}{op}{theta1:.2}x$\".format(\n",
" theta0=float(theta[0][0]),\n",
" theta1=(\n",
" float(theta[1][0]) if theta[1][0] >= 0 else float(-theta[1][0])\n",
" ),\n",
" op=\"+\" if theta[1][0] >= 0 else \"-\",\n",
" )\n",
" ),\n",
" )\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x[:5]=matrix([[ 1., 3., 1., 78.],\n",
" [ 1., 3., 2., 62.],\n",
" [ 1., 3., 0., 15.],\n",
" [ 1., 4., 0., 14.],\n",
" [ 1., 3., 0., 15.]])\n",
"x.shape=(1339, 4)\n",
"y[:5]=matrix([[476118.],\n",
" [459531.],\n",
" [411557.],\n",
" [496416.],\n",
" [406032.]])\n",
"y.shape=(1339, 1)\n"
]
}
],
"source": [
"# Wczytwanie danych z pliku – regresja liniowa wielu zmiennych – notacja macierzowa\n",
"\n",
"import pandas as pd\n",
"\n",
"data = pd.read_csv(\n",
" \"data02_train.tsv\", delimiter=\"\\t\", usecols=[\"price\", \"rooms\", \"floor\", \"sqrMetres\"]\n",
")\n",
"m, n_plus_1 = data.values.shape\n",
"n = n_plus_1 - 1\n",
"xn = data.values[:, 1:].reshape(m, n)\n",
"\n",
"# Dodaj kolumnę jedynek do macierzy\n",
"x = np.matrix(np.concatenate((np.ones((m, 1)), xn), axis=1)).reshape(m, n_plus_1)\n",
"y = np.matrix(data.values[:, 0]).reshape(m, 1)\n",
"\n",
"print(f\"{x[:5]=}\")\n",
"print(f\"{x.shape=}\")\n",
"print(f\"{y[:5]=}\")\n",
"print(f\"{y.shape=}\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Funkcja kosztu – notacja macierzowa"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"$$J(\\theta)=\\dfrac{1}{2|\\vec y|}\\left(X\\theta-\\vec{y}\\right)^T\\left(X\\theta-\\vec{y}\\right)$$ \n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\Large J(\\theta) = 85104141370.9717$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.display import display, Math, Latex\n",
"\n",
"\n",
"def J(theta, X, y):\n",
" \"\"\"Wersja macierzowa funkcji kosztu\"\"\"\n",
" m = len(y)\n",
" cost = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n",
" return cost.item()\n",
"\n",
"\n",
"theta = np.matrix([10, 90, -1, 2.5]).reshape(4, 1)\n",
"\n",
"cost = J(theta, x, y)\n",
"display(Math(r\"\\Large J(\\theta) = %.4f\" % cost))\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Gradient – notacja macierzowa"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"$$\\nabla J(\\theta) = \\frac{1}{|\\vec y|} X^T\\left(X\\theta-\\vec y\\right)$$"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Wyświetlanie macierzy w LaTeX-u\n",
"\n",
"\n",
"def latex_matrix(matrix):\n",
" ltx = r\"\\left[\\begin{array}\"\n",
" m, n = matrix.shape\n",
" ltx += \"{\" + (\"r\" * n) + \"}\"\n",
" for i in range(m):\n",
" ltx += r\" & \".join([(\"%.4f\" % j.item()) for j in matrix[i]]) + r\" \\\\ \"\n",
" ltx += r\"\\end{array}\\right]\"\n",
" return ltx\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\large \\theta = \\left[\\begin{array}{r}10.0000 \\\\ 90.0000 \\\\ -1.0000 \\\\ 2.5000 \\\\ \\end{array}\\right]\\quad\\large \\nabla J(\\theta) = \\left[\\begin{array}{r}-373492.7442 \\\\ -1075656.5086 \\\\ -989554.4921 \\\\ -23806475.6561 \\\\ \\end{array}\\right]$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from IPython.display import display, Math, Latex\n",
"\n",
"\n",
"def dJ(theta, X, y):\n",
" \"\"\"Wersja macierzowa gradientu funckji kosztu\"\"\"\n",
" return 1.0 / len(y) * (X.T * (X * theta - y))\n",
"\n",
"\n",
"theta = np.matrix([10, 90, -1, 2.5]).reshape(4, 1)\n",
"\n",
"display(\n",
" Math(\n",
" r\"\\large \\theta = \"\n",
" + latex_matrix(theta)\n",
" + r\"\\quad\"\n",
" + r\"\\large \\nabla J(\\theta) = \"\n",
" + latex_matrix(dJ(theta, x, y))\n",
" )\n",
")\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Algorytm gradientu prostego – notacja macierzowa"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"$$ \\theta := \\theta - \\alpha \\, \\nabla J(\\theta) $$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\large\\textrm{Wynik:}\\quad \\theta = \\left[\\begin{array}{r}17446.2135 \\\\ 86476.7960 \\\\ -1374.8950 \\\\ 2165.0689 \\\\ \\end{array}\\right] \\quad J(\\theta) = 10324864803.1591 \\quad \\textrm{po 374575 iteracjach}$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Implementacja algorytmu gradientu prostego za pomocą numpy i macierzy\n",
"\n",
"\n",
"def gradient_descent(fJ, fdJ, theta, X, y, alpha, eps):\n",
" current_cost = fJ(theta, X, y)\n",
" history = [[current_cost, theta]]\n",
" while True:\n",
" theta = theta - alpha * fdJ(theta, X, y) # implementacja wzoru\n",
" current_cost, prev_cost = fJ(theta, X, y), current_cost\n",
" if abs(prev_cost - current_cost) <= eps:\n",
" break\n",
" if current_cost > prev_cost:\n",
" print(\"Długość kroku (alpha) jest zbyt duża!\")\n",
" break\n",
" history.append([current_cost, theta])\n",
" return theta, history\n",
"\n",
"\n",
"theta_start = np.zeros((n + 1, 1))\n",
"\n",
"# Zmieniamy wartości alpha (rozmiar kroku) oraz eps (kryterium stopu)\n",
"theta_best, history = gradient_descent(J, dJ, theta_start, x, y, alpha=0.0001, eps=0.1)\n",
"\n",
"display(\n",
" Math(\n",
" r\"\\large\\textrm{Wynik:}\\quad \\theta = \"\n",
" + latex_matrix(theta_best)\n",
" + (r\" \\quad J(\\theta) = %.4f\" % history[-1][0])\n",
" + r\" \\quad \\textrm{po %d iteracjach}\" % len(history)\n",
" )\n",
")\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 3.2. Metoda gradientu prostego w praktyce"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Kryterium stopu"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Algorytm gradientu prostego polega na wykonywaniu określonych kroków w pętli. Pytanie brzmi: kiedy należy zatrzymać wykonywanie tej pętli?\n",
"\n",
"W każdej kolejnej iteracji wartość funkcji kosztu maleje o coraz mniejszą wartość.\n",
"Parametr `eps` określa, jaka wartość graniczna tej różnicy jest dla nas wystarczająca:\n",
"\n",
" * Im mniejsza wartość `eps`, tym dokładniejszy wynik, ale dłuższy czas działania algorytmu.\n",
" * Im większa wartość `eps`, tym krótszy czas działania algorytmu, ale mniej dokładny wynik."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Na wykresie zobaczymy porównanie regresji dla różnych wartości `eps`"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"ename": "ValueError",
"evalue": "x and y must be the same size",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[0;32mIn [18], line 3\u001b[0m\n\u001b[1;32m 1\u001b[0m theta_start \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mzeros((\u001b[39m2\u001b[39m, \u001b[39m1\u001b[39m))\n\u001b[0;32m----> 3\u001b[0m fig \u001b[39m=\u001b[39m regdots(x[\u001b[39m1\u001b[39m], y)\n",
"Cell \u001b[0;32mIn [6], line 15\u001b[0m, in \u001b[0;36mregdots\u001b[0;34m(x, y, xlabel, ylabel)\u001b[0m\n\u001b[1;32m 13\u001b[0m ax \u001b[39m=\u001b[39m fig\u001b[39m.\u001b[39madd_subplot(\u001b[39m111\u001b[39m)\n\u001b[1;32m 14\u001b[0m fig\u001b[39m.\u001b[39msubplots_adjust(left\u001b[39m=\u001b[39m\u001b[39m0.1\u001b[39m, right\u001b[39m=\u001b[39m\u001b[39m0.9\u001b[39m, bottom\u001b[39m=\u001b[39m\u001b[39m0.1\u001b[39m, top\u001b[39m=\u001b[39m\u001b[39m0.9\u001b[39m)\n\u001b[0;32m---> 15\u001b[0m ax\u001b[39m.\u001b[39;49mscatter([x[:, \u001b[39m1\u001b[39;49m]], [y], c\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mr\u001b[39;49m\u001b[39m\"\u001b[39;49m, s\u001b[39m=\u001b[39;49m\u001b[39m50\u001b[39;49m, label\u001b[39m=\u001b[39;49m\u001b[39m\"\u001b[39;49m\u001b[39mDane\u001b[39;49m\u001b[39m\"\u001b[39;49m)\n\u001b[1;32m 17\u001b[0m ax\u001b[39m.\u001b[39mset_xlabel(xlabel)\n\u001b[1;32m 18\u001b[0m ax\u001b[39m.\u001b[39mset_ylabel(ylabel)\n",
"File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/__init__.py:1423\u001b[0m, in \u001b[0;36m_preprocess_data.<locals>.inner\u001b[0;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1420\u001b[0m \u001b[39m@functools\u001b[39m\u001b[39m.\u001b[39mwraps(func)\n\u001b[1;32m 1421\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39minner\u001b[39m(ax, \u001b[39m*\u001b[39margs, data\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs):\n\u001b[1;32m 1422\u001b[0m \u001b[39mif\u001b[39;00m data \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m-> 1423\u001b[0m \u001b[39mreturn\u001b[39;00m func(ax, \u001b[39m*\u001b[39;49m\u001b[39mmap\u001b[39;49m(sanitize_sequence, args), \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m 1425\u001b[0m bound \u001b[39m=\u001b[39m new_sig\u001b[39m.\u001b[39mbind(ax, \u001b[39m*\u001b[39margs, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs)\n\u001b[1;32m 1426\u001b[0m auto_label \u001b[39m=\u001b[39m (bound\u001b[39m.\u001b[39marguments\u001b[39m.\u001b[39mget(label_namer)\n\u001b[1;32m 1427\u001b[0m \u001b[39mor\u001b[39;00m bound\u001b[39m.\u001b[39mkwargs\u001b[39m.\u001b[39mget(label_namer))\n",
"File \u001b[0;32m~/.local/lib/python3.10/site-packages/matplotlib/axes/_axes.py:4512\u001b[0m, in \u001b[0;36mAxes.scatter\u001b[0;34m(self, x, y, s, c, marker, cmap, norm, vmin, vmax, alpha, linewidths, edgecolors, plotnonfinite, **kwargs)\u001b[0m\n\u001b[1;32m 4510\u001b[0m y \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mma\u001b[39m.\u001b[39mravel(y)\n\u001b[1;32m 4511\u001b[0m \u001b[39mif\u001b[39;00m x\u001b[39m.\u001b[39msize \u001b[39m!=\u001b[39m y\u001b[39m.\u001b[39msize:\n\u001b[0;32m-> 4512\u001b[0m \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39m\"\u001b[39m\u001b[39mx and y must be the same size\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m 4514\u001b[0m \u001b[39mif\u001b[39;00m s \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[1;32m 4515\u001b[0m s \u001b[39m=\u001b[39m (\u001b[39m20\u001b[39m \u001b[39mif\u001b[39;00m mpl\u001b[39m.\u001b[39mrcParams[\u001b[39m'\u001b[39m\u001b[39m_internal.classic_mode\u001b[39m\u001b[39m'\u001b[39m] \u001b[39melse\u001b[39;00m\n\u001b[1;32m 4516\u001b[0m mpl\u001b[39m.\u001b[39mrcParams[\u001b[39m'\u001b[39m\u001b[39mlines.markersize\u001b[39m\u001b[39m'\u001b[39m] \u001b[39m*\u001b[39m\u001b[39m*\u001b[39m \u001b[39m2.0\u001b[39m)\n",
"\u001b[0;31mValueError\u001b[0m: x and y must be the same size"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"theta_start = np.zeros((2, 1))\n",
"\n",
"fig = regdots(x[1], y)\n",
"# theta_e1, history1 = GDMx(\n",
"# JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.01\n",
"# ) # niebieska linia\n",
"# reglineMx(fig, hMx, theta_e1, XMx)\n",
"# theta_e2, history2 = GDMx(\n",
"# JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.000001\n",
"# ) # pomarańczowa linia\n",
"# reglineMx(fig, hMx, theta_e2, XMx)\n",
"# legend(fig)\n"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\theta_{10^{-2}} = \\left[\\begin{array}{r}0.0531 \\\\ 0.8365 \\\\ \\end{array}\\right]\\quad\\theta_{10^{-6}} = \\left[\\begin{array}{r}-3.4895 \\\\ 1.1786 \\\\ \\end{array}\\right]$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"display(\n",
" Math(\n",
" r\"\\theta_{10^{-2}} = \"\n",
" + latex_matrix(theta_e1)\n",
" + r\"\\quad\\theta_{10^{-6}} = \"\n",
" + latex_matrix(theta_e2)\n",
" )\n",
")\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Długość kroku ($\\alpha$)"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Jak zmienia się koszt w kolejnych krokach w zależności od alfa\n",
"\n",
"\n",
"def costchangeplot(history):\n",
" fig = plt.figure(figsize=(16 * 0.6, 9 * 0.6))\n",
" ax = fig.add_subplot(111)\n",
" fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
" ax.set_xlabel(\"krok\")\n",
" ax.set_ylabel(r\"$J(\\theta)$\")\n",
"\n",
" X = np.arange(0, 500, 1)\n",
" Y = [history[step][0] for step in X]\n",
" ax.plot(X, Y, linewidth=\"2\", label=(r\"$J(\\theta)$\"))\n",
" return fig\n",
"\n",
"\n",
"def slide7(alpha):\n",
" best_theta, history = gradient_descent(\n",
" h, J, [0.0, 0.0], x, y, alpha=alpha, eps=0.0001\n",
" )\n",
" fig = costchangeplot(history)\n",
" legend(fig)\n",
"\n",
"\n",
"sliderAlpha1 = widgets.FloatSlider(\n",
" min=0.01, max=0.03, step=0.001, value=0.02, description=r\"$\\alpha$\", width=300\n",
")\n"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "52b0d91e39104f4facbb7f57819aae0c",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=0.02, description='$\\\\alpha$', max=0.03, min=0.01, step=0.001), Button…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<function __main__.slide7(alpha)>"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"widgets.interact_manual(slide7, alpha=sliderAlpha1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 3.3. Normalizacja danych"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Normalizacja danych to proces, który polega na dostosowaniu danych wejściowych w taki sposób, żeby ułatwić działanie algorytmowi gradientu prostego.\n",
"\n",
"Wyjaśnię to na przykladzie."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Użyjemy danych z „Gratka flats challenge 2017”.\n",
"\n",
"Rozważmy model $h(x) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2$, w którym cena mieszkania prognozowana jest na podstawie liczby pokoi $x_1$ i metrażu $x_2$:"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>price</th>\n",
" <th>rooms</th>\n",
" <th>sqrMetres</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>476118.00</td>\n",
" <td>3</td>\n",
" <td>78</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>459531.00</td>\n",
" <td>3</td>\n",
" <td>62</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>411557.00</td>\n",
" <td>3</td>\n",
" <td>15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>496416.00</td>\n",
" <td>4</td>\n",
" <td>14</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>406032.00</td>\n",
" <td>3</td>\n",
" <td>15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>450026.00</td>\n",
" <td>3</td>\n",
" <td>80</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>571229.15</td>\n",
" <td>2</td>\n",
" <td>39</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>325000.00</td>\n",
" <td>3</td>\n",
" <td>54</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>268229.00</td>\n",
" <td>2</td>\n",
" <td>90</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>604836.00</td>\n",
" <td>4</td>\n",
" <td>40</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" price rooms sqrMetres\n",
"0 476118.00 3 78\n",
"1 459531.00 3 62\n",
"2 411557.00 3 15\n",
"3 496416.00 4 14\n",
"4 406032.00 3 15\n",
"5 450026.00 3 80\n",
"6 571229.15 2 39\n",
"7 325000.00 3 54\n",
"8 268229.00 2 90\n",
"9 604836.00 4 40"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Wczytanie danych przy pomocy biblioteki pandas\n",
"import pandas\n",
"\n",
"alldata = pandas.read_csv(\n",
" \"data_flats.tsv\", header=0, sep=\"\\t\", usecols=[\"price\", \"rooms\", \"sqrMetres\"]\n",
")\n",
"alldata[:10]\n"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Funkcja, która pokazuje wartości minimalne i maksymalne w macierzy X\n",
"\n",
"\n",
"def show_mins_and_maxs(XMx):\n",
" mins = np.amin(XMx, axis=0).tolist()[0] # wartości minimalne\n",
" maxs = np.amax(XMx, axis=0).tolist()[0] # wartości maksymalne\n",
" for i, (xmin, xmax) in enumerate(zip(mins, maxs)):\n",
" display(Math(r\"${:.2F} \\leq x_{} \\leq {:.2F}$\".format(xmin, i, xmax)))\n"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Przygotowanie danych\n",
"\n",
"import numpy as np\n",
"\n",
"%matplotlib inline\n",
"\n",
"data2 = np.matrix(alldata[['rooms', 'sqrMetres', 'price']])\n",
"\n",
"m, n_plus_1 = data2.shape\n",
"n = n_plus_1 - 1\n",
"Xn = data2[:, 0:n]\n",
"\n",
"XMx2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
"yMx2 = np.matrix(data2[:, -1]).reshape(m, 1) / 1000.0"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Cechy w danych treningowych przyjmują wartości z zakresu:"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 1.00 \\leq x_0 \\leq 1.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle 2.00 \\leq x_1 \\leq 7.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle 12.00 \\leq x_2 \\leq 196.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"show_mins_and_maxs(XMx2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Jak widzimy, $x_2$ przyjmuje wartości dużo większe niż $x_1$.\n",
"Powoduje to, że wykres funkcji kosztu jest bardzo „spłaszczony” wzdłuż jednej z osi:"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"def contour_plot(X, y, rescale=10**8):\n",
" theta0_vals = np.linspace(-100000, 100000, 100)\n",
" theta1_vals = np.linspace(-100000, 100000, 100)\n",
"\n",
" J_vals = np.zeros(shape=(theta0_vals.size, theta1_vals.size))\n",
" for t1, element in enumerate(theta0_vals):\n",
" for t2, element2 in enumerate(theta1_vals):\n",
" thetaT = np.matrix([1.0, element, element2]).reshape(3, 1)\n",
" J_vals[t1, t2] = JMx(thetaT, X, y) / rescale\n",
"\n",
" plt.figure()\n",
" plt.contour(theta0_vals, theta1_vals, J_vals.T, np.logspace(-2, 3, 20))\n",
" plt.xlabel(r\"$\\theta_1$\")\n",
" plt.ylabel(r\"$\\theta_2$\")\n"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"457.840312pt\" height=\"314.667469pt\" viewBox=\"0 0 457.840312 314.667469\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n <cc:Work>\n <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n <dc:date>2022-10-14T11:22:55.380282</dc:date>\n <dc:format>image/svg+xml</dc:format>\n <dc:creator>\n <cc:Agent>\n <dc:title>Matplotlib v3.6.1, https://matplotlib.org/</dc:title>\n </cc:Agent>\n </dc:creator>\n </cc:Work>\n </rdf:RDF>\n </metadata>\n <defs>\n <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n <g id=\"patch_1\">\n <path d=\"M 0 314.667469 \nL 457.840312 314.667469 \nL 457.840312 0 \nL 0 0 \nz\n\" style=\"fill: #ffffff\"/>\n </g>\n <g id=\"axes_1\">\n <g id=\"patch_2\">\n <path d=\"M 74.432812 277.111219 \nL 431.552813 277.111219 \nL 431.552813 10.999219 \nL 74.432812 10.999219 \nz\n\" style=\"fill: #ffffff\"/>\n </g>\n <g id=\"matplotlib.axis_1\">\n <g id=\"xtick_1\">\n <g id=\"line2d_1\">\n <defs>\n <path id=\"mf31e2b1581\" d=\"M 0 0 \nL 0 3.5 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </defs>\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"74.432812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_1\">\n <!-- −100000 -->\n <g transform=\"translate(51.155469 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-2212\" d=\"M 678 2272 \nL 4684 2272 \nL 4684 1741 \nL 678 1741 \nL 678 2272 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-31\" d=\"M 794 531 \nL 1825 531 \nL 1825 4091 \nL 703 3866 \nL 703 4441 \nL 1819 4666 \nL 2450 4666 \nL 2450 531 \nL 3481 531 \nL 3481 0 \nL 794 0 \nL 794 531 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \nQ 1547 4250 1301 3770 \nQ 1056 3291 1056 2328 \nQ 1056 1369 1301 889 \nQ 1547 409 2034 409 \nQ 2525 409 2770 889 \nQ 3016 1369 3016 2328 \nQ 3016 3291 2770 3770 \nQ 2525 4250 2034 4250 \nz\nM 2034 4750 \nQ 2819 4750 3233 4129 \nQ 3647 3509 3647 2328 \nQ 3647 1150 3233 529 \nQ 2819 -91 2034 -91 \nQ 1250 -91 836 529 \nQ 422 1150 422 2328 \nQ 422 3509 836 4129 \nQ 1250 4750 2034 4750 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"401.904297\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_2\">\n <g id=\"line2d_2\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"119.072812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_2\">\n <!-- −75000 -->\n <g transform=\"translate(98.976719 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-37\" d=\"M 525 4666 \nL 3525 4666 \nL 3525 4397 \nL 1831 0 \nL 1172 0 \nL 2766 4134 \nL 525 4134 \nL 525 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-35\" d=\"M 691 4666 \nL 3169 4666 \nL 3169 4134 \nL 1269 4134 \nL 1269 2991 \nQ 1406 3038 1543 3061 \nQ 1681 3084 1819 3084 \nQ 2600 3084 3056 2656 \nQ 3513 2228 3513 1497 \nQ 3513 744 3044 326 \nQ 2575 -91 1722 -91 \nQ 1428 -91 1123 -41 \nQ 819 9 494 109 \nL 494 744 \nQ 775 591 1075 516 \nQ 1375 441 1709 441 \nQ 2250 441 2565 725 \nQ 2881 1009 2881 1497 \nQ 2881 1984 2565 2268 \nQ 2250 2553 1709 2553 \nQ 1456 2553 1204 2497 \nQ 953 2441 691 2322 \nL 691 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_3\">\n <g id=\"line2d_3\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"163.712812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_3\">\n <!-- −50000 -->\n <g transform=\"translate(143.616719 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_4\">\n <g id=\"line2d_4\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"208.352812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_4\">\n <!-- −25000 -->\n <g transform=\"translate(188.256719 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-32\" d=\"M 1228 531 \nL 3431 531 \nL 3431 0 \nL 469 0 \nL 469 531 \nQ 828 903 1448 1529 \nQ 2069 2156 2228 2338 \nQ 2531 2678 2651 2914 \nQ 2772 3150 2772 3378 \nQ 2772 3750 2511 3984 \nQ 2250 4219 1831 4219 \nQ 1534 4219 1204 4116 \nQ 875 4013 500 3803 \nL 500 4441 \nQ 881 4594 1212 4672 \nQ 1544 4750 1819 4750 \nQ 2544 4750 2975 4387 \nQ 3406 4025 3406 3419 \nQ 3406 3131 3298 2873 \nQ 3191 2616 2906 2266 \nQ 2828 2175 2409 1742 \nQ 1991 1309 1228 531 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_5\">\n <g id=\"line2d_5\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"252.992813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_5\">\n <!-- 0 -->\n <g transform=\"translate(249.811563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-30\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_6\">\n <g id=\"line2d_6\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"297.632812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_6\">\n <!-- 25000 -->\n <g transform=\"translate(281.726562 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-32\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_7\">\n <g id=\"line2d_7\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"342.272813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_7\">\n <!-- 50000 -->\n <g transform=\"translate(326.366563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-35\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_8\">\n <g id=\"line2d_8\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"386.912813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_8\">\n <!-- 75000 -->\n <g transform=\"translate(371.006563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-37\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_9\">\n <g id=\"line2d_9\">\n <g>\n <use xlink:href=\"#mf31e2b1581\" x=\"431.552813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_9\">\n <!-- 100000 -->\n <g transform=\"translate(412.465313 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-31\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"318.115234\"/>\n </g>\n </g>\n </g>\n <g id=\"text_10\">\n <!-- $\\theta_1$ -->\n <g transform=\"translate(247.542813 305.387781) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-Oblique-3b8\" d=\"M 2913 2219 \nL 925 2219 \nQ 791 1284 928 888 \nQ 1100 400 1566 400 \nQ 2034 400 2391 891 \nQ 2703 1322 2913 2219 \nz\nM 3009 2750 \nQ 3094 3638 2984 3950 \nQ 2813 4444 2353 4444 \nQ 1875 4444 1525 3956 \nQ 1250 3563 1034 2750 \nL 3009 2750 \nz\nM 2444 4913 \nQ 3194 4913 3494 4250 \nQ 3794 3591 3566 2422 \nQ 3341 1256 2781 594 \nQ 2225 -72 1475 -72 \nQ 722 -72 425 594 \nQ 128 1256 353 2422 \nQ 581 3591 1134 4250 \nQ 1691 4913 2444 4913 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-Oblique-3b8\" transform=\"translate(0 0.234375)\"/>\n <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(61.181641 -16.171875) scale(0.7)\"/>\n </g>\n </g>\n </g>\n <g id=\"matplotlib.axis_2\">\n <g id=\"ytick_1\">\n <g id=\"line2d_10\">\n <defs>\n <path id=\"m65cf3f4be8\" d=\"M 0 0 \nL -3.5 0 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </defs>\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_11\">\n <!-- −100000 -->\n <g transform=\"translate(20.878125 280.910437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"401.904297\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_2\">\n <g id=\"line2d_11\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"243.847219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_12\">\n <!-- −75000 -->\n <g transform=\"translate(27.240625 247.646437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_3\">\n <g id=\"line2d_12\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"210.583219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_13\">\n <!-- −50000 -->\n <g transform=\"translate(27.240625 214.382437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_4\">\n <g id=\"line2d_13\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"177.319219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_14\">\n <!-- −25000 -->\n <g transform=\"translate(27.240625 181.118437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_5\">\n <g id=\"line2d_14\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"144.055219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_15\">\n <!-- 0 -->\n <g transform=\"translate(61.070312 147.854437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-30\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_6\">\n <g id=\"line2d_15\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"110.791219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_16\">\n <!-- 25000 -->\n <g transform=\"translate(35.620312 114.590437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-32\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_7\">\n <g id=\"line2d_16\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"77.527219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_17\">\n <!-- 50000 -->\n <g transform=\"translate(35.620312 81.326437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-35\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_8\">\n <g id=\"line2d_17\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"44.263219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_18\">\n <!-- 75000 -->\n <g transform=\"translate(35.620312 48.062437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-37\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_9\">\n <g id=\"line2d_18\">\n <g>\n <use xlink:href=\"#m65cf3f4be8\" x=\"74.432812\" y=\"10.999219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_19\">\n <!-- 100000 -->\n <g transform=\"translate(29.257812 14.798437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-31\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"318.115234\"/>\n </g>\n </g>\n </g>\n <g id=\"text_20\">\n <!-- $\\theta_2$ -->\n <g transform=\"translate(14.798437 149.505219) rotate(-90) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-Oblique-3b8\" transform=\"translate(0 0.234375)\"/>\n <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(61.181641 -16.171875) scale(0.7)\"/>\n </g>\n </g>\n </g>\n <g id=\"PathCollection_1\"/>\n <g id=\"PathCollection_2\"/>\n <g id=\"PathCollection_3\">\n <path d=\"M 283.654631 145.402152 \nL 283.136749 145.399219 \nL 283.654631 145.393819 \nL 287.261903 145.374498 \nL 290.869176 145.371291 \nL 294.476449 145.37997 \nL 298.083722 145.397665 \nL 298.294674 145.399219 \nL 298.083722 145.400895 \nL 294.476449 145.416796 \nL 290.869176 145.420769 \nL 287.261903 145.415278 \nL 283.654631 145.402152 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 211.509176 142.72931 \nL 208.04449 142.711219 \nL 211.509176 142.69431 \nL 215.116449 142.68896 \nL 218.723722 142.693358 \nL 222.330994 142.7056 \nL 223.370375 142.711219 \nL 222.330994 142.721301 \nL 218.723722 142.738055 \nL 215.116449 142.739392 \nL 211.509176 142.72931 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_4\">\n <path d=\"M 276.440085 145.42313 \nL 273.816662 145.399219 \nL 276.440085 145.334081 \nL 280.047358 145.282757 \nL 283.654631 145.258963 \nL 287.261903 145.253941 \nL 290.869176 145.262293 \nL 294.476449 145.280507 \nL 298.083722 145.306205 \nL 301.690994 145.337713 \nL 305.298267 145.373825 \nL 307.5423 145.399219 \nL 305.298267 145.437721 \nL 301.690994 145.47776 \nL 298.083722 145.499607 \nL 294.476449 145.507622 \nL 290.869176 145.504875 \nL 287.261903 145.493591 \nL 283.654631 145.475418 \nL 280.047358 145.45161 \nL 276.440085 145.42313 \nz\n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 200.687358 142.732092 \nL 198.87782 142.711219 \nL 200.687358 142.678791 \nL 204.294631 142.635972 \nL 207.901903 142.612056 \nL 211.509176 142.602462 \nL 215.116449 142.603978 \nL 218.723722 142.614286 \nL 222.330994 142.631671 \nL 225.938267 142.654836 \nL 229.54554 142.682784 \nL 232.735744 142.711219 \nL 229.54554 142.786435 \nL 225.938267 142.833212 \nL 222.330994 142.853967 \nL 218.723722 142.856857 \nL 215.116449 142.846955 \nL 211.509176 142.827575 \nL 207.901903 142.800981 \nL 204.294631 142.768768 \nL 200.687358 142.732092 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_5\">\n <path d=\"M 265.618267 145.418062 \nL 264.171984 145.399219 \nL 265.618267 145.286518 \nL 269.22554 145.123524 \nL 272.832812 145.044397 \nL 276.440085 145.010011 \nL 280.047358 145.0023 \nL 283.654631 145.011774 \nL 287.261903 145.032964 \nL 290.869176 145.062501 \nL 294.476449 145.098195 \nL 298.083722 145.138559 \nL 301.690994 145.18255 \nL 305.298267 145.229415 \nL 308.90554 145.278594 \nL 312.512812 145.329664 \nL 316.120085 145.382302 \nL 317.208394 145.399219 \nL 316.120085 145.444463 \nL 312.512812 145.551242 \nL 308.90554 145.61775 \nL 305.298267 145.65668 \nL 301.690994 145.6759 \nL 298.083722 145.680544 \nL 294.476449 145.674104 \nL 290.869176 145.659041 \nL 287.261903 145.637137 \nL 283.654631 145.609714 \nL 280.047358 145.577775 \nL 276.440085 145.542092 \nL 272.832812 145.503274 \nL 269.22554 145.461801 \nL 265.618267 145.418062 \nz\n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 189.86554 142.721518 \nL 189.209246 142.711219 \nL 189.86554 142.682848 \nL 193.472812 142.569437 \nL 197.080085 142.498549 \nL 200.687358 142.456581 \nL 204.294631 142.435174 \nL 207.901903 142.428906 \nL 211.509176 142.434108 \nL 215.116449 142.448209 \nL 218.723722 142.469351 \nL 222.330994 142.49616 \nL 225.938267 142.527599 \nL 229.54554 142.562869 \nL 233.152813 142.601343 \nL 236.760085 142.642527 \nL 240.367358 142.686021 \nL 242.323187 142.711219 \nL 240.367358 142.85507 \nL 236.760085 143.002518 \nL 233.152813 143.073777 \nL 229.54554 143.103639 \nL 225.938267 143.108511 \nL 222.330994 143.097141 \nL 218.723722 143.07462 \nL 215.116449 143.044115 \nL 211.509176 143.007694 \nL 207.901903 142.966771 \nL 204.294631 142.92234 \nL 200.687358 142.875123 \nL 197.080085 142.825658 \nL 193.472812 142.774351 \nL 189.86554 142.721518 \nz\n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_6\">\n <path d=\"M 254.796449 145.438561 \nL 252.328948 145.399219 \nL 251.189176 144.648912 \nL 247.581903 144.182719 \nL 243.974631 144.029004 \nL 240.367358 143.92515 \nL 236.760085 143.838424 \nL 233.152813 143.7596 \nL 229.54554 143.685068 \nL 225.938267 143.613129 \nL 222.330994 143.542874 \nL 218.723722 143.473776 \nL 215.116449 143.405506 \nL 211.509176 143.337849 \nL 207.901903 143.270659 \nL 204.294631 143.203833 \nL 200.687358 143.137296 \nL 197.080085 143.070992 \nL 193.472812 143.004879 \nL 189.86554 142.938925 \nL 186.258267 142.873103 \nL 182.650994 142.807394 \nL 179.043722 142.741781 \nL 177.403911 142.711219 \nL 179.043722 142.525124 \nL 182.650994 142.281328 \nL 186.258267 142.152263 \nL 189.86554 142.083963 \nL 193.472812 142.051722 \nL 197.080085 142.042628 \nL 200.687358 142.049276 \nL 204.294631 142.067115 \nL 207.901903 142.093195 \nL 211.509176 142.125519 \nL 215.116449 142.162686 \nL 218.723722 142.203686 \nL 222.330994 142.247771 \nL 225.938267 142.294376 \nL 229.54554 142.343066 \nL 233.152813 142.393501 \nL 236.760085 142.44541 \nL 240.367358 142.498576 \nL 243.974631 142.552824 \nL 247.581903 142.608008 \nL 251.189176 142.664008 \nL 254.170591 142.711219 \nL 254.796449 143.249532 \nL 258.403722 143.897274 \nL 262.010994 144.065242 \nL 265.618267 144.173016 \nL 269.22554 144.261354 \nL 272.832812 144.340995 \nL 276.440085 144.415995 \nL 280.047358 144.488229 \nL 283.654631 144.55868 \nL 287.261903 144.627917 \nL 290.869176 144.696287 \nL 294.476449 144.76402 \nL 298.083722 144.831267 \nL 301.690994 144.898139 \nL 305.298267 144.964712 \nL 308.90554 145.031046 \nL 312.512812 145.097183 \nL 316.120085 145.163158 \nL 319.727358 145.228997 \nL 323.334631 145.294721 \nL 326.941903 145.360347 \nL 329.039572 145.399219 \nL 326.941903 145.625008 \nL 323.334631 145.848697 \nL 319.727358 145.967839 \nL 316.120085 146.030557 \nL 312.512812 146.05937 \nL 308.90554 146.066219 \nL 305.298267 146.058029 \nL 301.690994 146.039088 \nL 298.083722 146.012197 \nL 294.476449 145.979262 \nL 290.869176 145.941624 \nL 287.261903 145.900254 \nL 283.654631 145.855875 \nL 280.047358 145.809032 \nL 276.440085 145.760149 \nL 272.832812 145.709554 \nL 269.22554 145.657512 \nL 265.618267 145.604234 \nL 262.010994 145.549893 \nL 258.403722 145.494629 \nL 254.796449 145.438561 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_7\">\n <path d=\"M 334.156449 148.120846 \nL 331.566867 148.087219 \nL 330.549176 147.953533 \nL 326.941903 147.615602 \nL 319.727358 147.236852 \nL 305.298267 146.793692 \nL 272.832812 146.087662 \nL 236.760085 145.370624 \nL 229.54554 144.750817 \nL 218.723722 144.20542 \nL 200.687358 143.617854 \nL 168.221903 142.842453 \nL 162.1058 142.711219 \nL 161.007358 142.354368 \nL 157.400085 141.716174 \nL 150.18554 141.184252 \nL 139.363722 140.782412 \nL 114.112812 140.176189 \nL 106.736683 140.023219 \nL 106.898267 140.015369 \nL 114.112812 139.783378 \nL 124.934631 139.655316 \nL 142.970994 139.689854 \nL 174.991275 140.023219 \nL 175.436449 140.084228 \nL 179.043722 140.452506 \nL 186.258267 140.850404 \nL 200.687358 141.302693 \nL 233.152813 142.012529 \nL 269.469021 142.711219 \nL 276.440085 143.327176 \nL 287.261903 143.885473 \nL 305.298267 144.479519 \nL 337.763722 145.257938 \nL 344.351522 145.399219 \nL 344.978267 145.619929 \nL 348.58554 146.341813 \nL 352.192813 146.686308 \nL 359.407358 147.069128 \nL 373.836449 147.514128 \nL 399.636667 148.087219 \nL 399.087358 148.113055 \nL 391.872813 148.334199 \nL 381.050994 148.454973 \nL 363.014631 148.415829 \nL 334.156449 148.120846 \nL 334.156449 148.120846 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_8\">\n <path d=\"M 431.552813 150.824008 \nL 427.94554 150.805442 \nL 424.338267 150.783095 \nL 423.262496 150.775219 \nL 420.730994 150.46636 \nL 417.123722 150.277576 \nL 413.516449 150.1604 \nL 409.909176 150.06672 \nL 406.301903 149.983638 \nL 402.694631 149.906236 \nL 399.087358 149.832231 \nL 395.480085 149.760419 \nL 391.872813 149.690106 \nL 388.26554 149.620861 \nL 384.658267 149.552405 \nL 381.050994 149.484549 \nL 377.443722 149.417158 \nL 373.836449 149.350136 \nL 370.229176 149.283412 \nL 366.621903 149.21693 \nL 363.014631 149.150651 \nL 359.407358 149.08454 \nL 355.800085 149.018572 \nL 352.192813 148.952726 \nL 348.58554 148.886984 \nL 344.978267 148.821334 \nL 341.370994 148.755762 \nL 337.763722 148.69026 \nL 334.156449 148.624819 \nL 330.549176 148.559433 \nL 326.941903 148.494095 \nL 323.334631 148.4288 \nL 319.727358 148.363545 \nL 316.120085 148.298324 \nL 312.512812 148.233135 \nL 308.90554 148.167975 \nL 305.298267 148.102841 \nL 304.45198 148.087219 \nL 301.690994 147.925048 \nL 298.083722 147.734407 \nL 294.476449 147.563886 \nL 290.869176 147.409018 \nL 287.261903 147.26657 \nL 283.654631 147.134139 \nL 280.047358 147.009908 \nL 276.440085 146.89247 \nL 272.832812 146.780727 \nL 269.22554 146.673801 \nL 265.618267 146.57099 \nL 262.010994 146.471719 \nL 258.403722 146.375517 \nL 254.796449 146.281992 \nL 251.189176 146.190817 \nL 247.581903 146.101715 \nL 243.974631 146.014452 \nL 240.367358 145.928827 \nL 236.760085 145.844668 \nL 233.152813 145.761827 \nL 229.54554 145.680172 \nL 225.938267 145.599593 \nL 222.330994 145.519988 \nL 218.723722 145.441272 \nL 216.802887 145.399219 \nL 215.116449 145.282136 \nL 211.509176 145.052276 \nL 207.901903 144.848691 \nL 204.294631 144.665574 \nL 200.687358 144.498709 \nL 197.080085 144.344964 \nL 193.472812 144.201965 \nL 189.86554 144.067877 \nL 186.258267 143.941259 \nL 182.650994 143.820968 \nL 179.043722 143.706079 \nL 175.436449 143.595842 \nL 171.829176 143.489639 \nL 168.221903 143.386955 \nL 164.614631 143.287362 \nL 161.007358 143.190496 \nL 157.400085 143.096049 \nL 153.792812 143.00376 \nL 150.18554 142.9134 \nL 146.578267 142.824774 \nL 142.970994 142.737712 \nL 141.879813 142.711219 \nL 139.363722 142.466206 \nL 135.756449 142.169082 \nL 132.149176 141.920266 \nL 128.541903 141.706112 \nL 124.934631 141.517674 \nL 121.327358 141.34884 \nL 117.720085 141.195292 \nL 114.112812 141.053893 \nL 110.50554 140.922311 \nL 106.898267 140.798774 \nL 103.290994 140.681913 \nL 99.683722 140.570651 \nL 96.076449 140.464133 \nL 92.469176 140.361668 \nL 88.861903 140.262695 \nL 85.254631 140.16675 \nL 81.647358 140.073448 \nL 79.692873 140.023219 \nL 78.040085 138.534934 \nL 74.432812 138.038552 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 137.282353 \nL 78.040085 137.300466 \nL 81.647358 137.322419 \nL 83.433169 137.335219 \nL 85.254631 137.57423 \nL 88.861903 137.796948 \nL 92.469176 137.924655 \nL 96.076449 138.023241 \nL 99.683722 138.10911 \nL 103.290994 138.188292 \nL 106.898267 138.263527 \nL 110.50554 138.336237 \nL 114.112812 138.407233 \nL 117.720085 138.477014 \nL 121.327358 138.545902 \nL 124.934631 138.614113 \nL 128.541903 138.681801 \nL 132.149176 138.749075 \nL 135.756449 138.816015 \nL 139.363722 138.882684 \nL 142.970994 138.949128 \nL 146.578267 139.015384 \nL 150.18554 139.081481 \nL 153.792812 139.147443 \nL 157.400085 139.213289 \nL 161.007358 139.279034 \nL 164.614631 139.344691 \nL 168.221903 139.410271 \nL 171.829176 139.475783 \nL 175.436449 139.541236 \nL 179.043722 139.606634 \nL 182.650994 139.671985 \nL 186.258267 139.737294 \nL 189.86554 139.802563 \nL 193.472812 139.867797 \nL 197.080085 139.933 \nL 200.687358 139.998174 \nL 202.048962 140.023219 \nL 204.294631 140.155859 \nL 207.901903 140.349916 \nL 211.509176 140.523075 \nL 215.116449 140.680023 \nL 218.723722 140.824142 \nL 222.330994 140.957936 \nL 225.938267 141.083294 \nL 229.54554 141.201674 \nL 233.152813 141.314215 \nL 236.760085 141.42182 \nL 240.367358 141.525217 \nL 243.974631 141.624995 \nL 247.581903 141.72164 \nL 251.189176 141.815554 \nL 254.796449 141.907074 \nL 258.403722 141.996481 \nL 262.010994 142.084016 \nL 265.618267 142.169885 \nL 269.22554 142.254264 \nL 272.832812 142.337304 \nL 276.440085 142.419139 \nL 280.047358 142.499882 \nL 283.654631 142.579636 \nL 287.261903 142.658489 \nL 289.676056 142.711219 \nL 290.869176 142.794612 \nL 294.476449 143.028714 \nL 298.083722 143.235564 \nL 301.690994 143.421248 \nL 305.298267 143.590168 \nL 308.90554 143.745581 \nL 312.512812 143.889956 \nL 316.120085 144.02519 \nL 319.727358 144.152773 \nL 323.334631 144.273886 \nL 326.941903 144.389478 \nL 330.549176 144.500323 \nL 334.156449 144.607055 \nL 337.763722 144.710201 \nL 341.370994 144.810202 \nL 344.978267 144.907428 \nL 348.58554 145.002194 \nL 352.192813 145.09477 \nL 355.800085 145.185386 \nL 359.407358 145.274242 \nL 363.014631 145.361513 \nL 364.570573 145.399219 \nL 366.621903 145.601382 \nL 370.229176 145.906406 \nL 373.836449 146.160747 \nL 377.443722 146.37891 \nL 381.050994 146.570348 \nL 384.658267 146.741483 \nL 388.26554 146.896832 \nL 391.872813 147.039667 \nL 395.480085 147.172411 \nL 399.087358 147.296901 \nL 402.694631 147.414554 \nL 406.301903 147.526479 \nL 409.909176 147.633558 \nL 413.516449 147.736502 \nL 417.123722 147.835887 \nL 420.730994 147.932188 \nL 424.338267 148.0258 \nL 426.732876 148.087219 \nL 427.94554 149.452505 \nL 431.552813 150.062826 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_9\">\n <path d=\"M 431.552813 151.873586 \nL 427.94554 151.81019 \nL 424.338267 151.746687 \nL 420.730994 151.683087 \nL 417.123722 151.619402 \nL 413.516449 151.555642 \nL 409.909176 151.491814 \nL 406.301903 151.427926 \nL 402.694631 151.363982 \nL 399.087358 151.299989 \nL 395.480085 151.235951 \nL 391.872813 151.171872 \nL 388.26554 151.107756 \nL 384.658267 151.043606 \nL 381.050994 150.979424 \nL 377.443722 150.915213 \nL 373.836449 150.850976 \nL 370.229176 150.786714 \nL 369.597281 150.775219 \nL 366.621903 150.64565 \nL 363.014631 150.497566 \nL 359.407358 150.358511 \nL 355.800085 150.227094 \nL 352.192813 150.102194 \nL 348.58554 149.982902 \nL 344.978267 149.868468 \nL 341.370994 149.758271 \nL 337.763722 149.651792 \nL 334.156449 149.548592 \nL 330.549176 149.448301 \nL 326.941903 149.350599 \nL 323.334631 149.255215 \nL 319.727358 149.161912 \nL 316.120085 149.070485 \nL 312.512812 148.980756 \nL 308.90554 148.892567 \nL 305.298267 148.805781 \nL 301.690994 148.720275 \nL 298.083722 148.635941 \nL 294.476449 148.552683 \nL 290.869176 148.470415 \nL 287.261903 148.389059 \nL 283.654631 148.308546 \nL 280.047358 148.228813 \nL 276.440085 148.149805 \nL 273.571982 148.087219 \nL 272.832812 148.0511 \nL 269.22554 147.879086 \nL 265.618267 147.71753 \nL 262.010994 147.564974 \nL 258.403722 147.42022 \nL 254.796449 147.282273 \nL 251.189176 147.150298 \nL 247.581903 147.023595 \nL 243.974631 146.901567 \nL 240.367358 146.783704 \nL 236.760085 146.669568 \nL 233.152813 146.55878 \nL 229.54554 146.451011 \nL 225.938267 146.345973 \nL 222.330994 146.243416 \nL 218.723722 146.143116 \nL 215.116449 146.044877 \nL 211.509176 145.948526 \nL 207.901903 145.853907 \nL 204.294631 145.760882 \nL 200.687358 145.669327 \nL 197.080085 145.579129 \nL 193.472812 145.49019 \nL 189.86554 145.402417 \nL 189.73549 145.399219 \nL 186.258267 145.208056 \nL 182.650994 145.023032 \nL 179.043722 144.849704 \nL 175.436449 144.686447 \nL 171.829176 144.531922 \nL 168.221903 144.385016 \nL 164.614631 144.244801 \nL 161.007358 144.110491 \nL 157.400085 143.981419 \nL 153.792812 143.857015 \nL 150.18554 143.736789 \nL 146.578267 143.620317 \nL 142.970994 143.507231 \nL 139.363722 143.397209 \nL 135.756449 143.289969 \nL 132.149176 143.185262 \nL 128.541903 143.082868 \nL 124.934631 142.982593 \nL 121.327358 142.884262 \nL 117.720085 142.78772 \nL 114.826847 142.711219 \nL 114.112812 142.662708 \nL 110.50554 142.428142 \nL 106.898267 142.214011 \nL 103.290994 142.016838 \nL 99.683722 141.833891 \nL 96.076449 141.662993 \nL 92.469176 141.502393 \nL 88.861903 141.350662 \nL 85.254631 141.206623 \nL 81.647358 141.0693 \nL 78.040085 140.937874 \nL 74.432812 140.811655 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 136.226216 \nL 78.040085 136.289709 \nL 81.647358 136.353302 \nL 85.254631 136.416985 \nL 88.861903 136.480747 \nL 92.469176 136.544579 \nL 96.076449 136.608474 \nL 99.683722 136.672426 \nL 103.290994 136.736428 \nL 106.898267 136.800477 \nL 110.50554 136.864567 \nL 114.112812 136.928695 \nL 117.720085 136.992858 \nL 121.327358 137.057052 \nL 124.934631 137.121276 \nL 128.541903 137.185526 \nL 132.149176 137.249801 \nL 135.756449 137.314098 \nL 136.92106 137.335219 \nL 139.363722 137.441783 \nL 142.970994 137.591392 \nL 146.578267 137.731736 \nL 150.18554 137.864255 \nL 153.792812 137.990103 \nL 157.400085 138.110217 \nL 161.007358 138.22537 \nL 164.614631 138.336199 \nL 168.221903 138.443237 \nL 171.829176 138.546933 \nL 175.436449 138.647668 \nL 179.043722 138.745767 \nL 182.650994 138.84151 \nL 186.258267 138.935137 \nL 189.86554 139.026858 \nL 193.472812 139.116854 \nL 197.080085 139.205288 \nL 200.687358 139.292298 \nL 204.294631 139.378009 \nL 207.901903 139.462532 \nL 211.509176 139.545965 \nL 215.116449 139.628395 \nL 218.723722 139.709902 \nL 222.330994 139.790554 \nL 225.938267 139.870417 \nL 229.54554 139.949546 \nL 232.928195 140.023219 \nL 233.152813 140.034219 \nL 236.760085 140.207878 \nL 240.367358 140.370846 \nL 243.974631 140.524622 \nL 247.581903 140.670439 \nL 251.189176 140.809318 \nL 254.796449 140.942113 \nL 258.403722 141.069544 \nL 262.010994 141.19222 \nL 265.618267 141.310662 \nL 269.22554 141.425319 \nL 272.832812 141.536575 \nL 276.440085 141.644769 \nL 280.047358 141.750191 \nL 283.654631 141.853099 \nL 287.261903 141.953719 \nL 290.869176 142.052251 \nL 294.476449 142.148871 \nL 298.083722 142.243737 \nL 301.690994 142.336991 \nL 305.298267 142.428758 \nL 308.90554 142.519151 \nL 312.512812 142.608272 \nL 316.120085 142.696214 \nL 316.731099 142.711219 \nL 319.727358 142.876409 \nL 323.334631 143.06321 \nL 326.941903 143.238061 \nL 330.549176 143.402634 \nL 334.156449 143.558304 \nL 337.763722 143.70621 \nL 341.370994 143.847307 \nL 344.978267 143.982397 \nL 348.58554 144.112162 \nL 352.192813 144.237184 \nL 355.800085 144.357965 \nL 359.407358 144.474936 \nL 363.014631 144.588473 \nL 366.621903 144.698904 \nL 370.229176 144.806516 \nL 373.836449 144.911561 \nL 377.443722 145.014265 \nL 381.050994 145.114824 \nL 384.658267 145.213417 \nL 388.26554 145.310199 \nL 391.635933 145.399219 \nL 391.872813 145.415389 \nL 395.480085 145.653042 \nL 399.087358 145.869712 \nL 402.694631 146.068999 \nL 406.301903 146.253725 \nL 409.909176 146.426132 \nL 413.516449 146.588024 \nL 417.123722 146.74087 \nL 420.730994 146.885876 \nL 424.338267 147.024045 \nL 427.94554 147.156213 \nL 431.552813 147.283088 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_10\">\n <path d=\"M 431.552813 153.624797 \nL 427.94554 153.556481 \nL 424.338267 153.488314 \nL 423.024692 153.463219 \nL 420.730994 153.379829 \nL 417.123722 153.251905 \nL 413.516449 153.128592 \nL 409.909176 153.009404 \nL 406.301903 152.893919 \nL 402.694631 152.781772 \nL 399.087358 152.672645 \nL 395.480085 152.566257 \nL 391.872813 152.462364 \nL 388.26554 152.360748 \nL 384.658267 152.261215 \nL 381.050994 152.163594 \nL 377.443722 152.067732 \nL 373.836449 151.973491 \nL 370.229176 151.880748 \nL 366.621903 151.789392 \nL 363.014631 151.699322 \nL 359.407358 151.610448 \nL 355.800085 151.522686 \nL 352.192813 151.435962 \nL 348.58554 151.350207 \nL 344.978267 151.265358 \nL 341.370994 151.181358 \nL 337.763722 151.098155 \nL 334.156449 151.015699 \nL 330.549176 150.933947 \nL 326.941903 150.852858 \nL 323.463668 150.775219 \nL 323.334631 150.770016 \nL 319.727358 150.625303 \nL 316.120085 150.485841 \nL 312.512812 150.35113 \nL 308.90554 150.220731 \nL 305.298267 150.094257 \nL 301.690994 149.971366 \nL 298.083722 149.851755 \nL 294.476449 149.735155 \nL 290.869176 149.621325 \nL 287.261903 149.510048 \nL 283.654631 149.40113 \nL 280.047358 149.294397 \nL 276.440085 149.18969 \nL 272.832812 149.086866 \nL 269.22554 148.985796 \nL 265.618267 148.88636 \nL 262.010994 148.788452 \nL 258.403722 148.691972 \nL 254.796449 148.59683 \nL 251.189176 148.502943 \nL 247.581903 148.410236 \nL 243.974631 148.318638 \nL 240.367358 148.228084 \nL 236.760085 148.138515 \nL 234.689156 148.087219 \nL 233.152813 148.019579 \nL 229.54554 147.863942 \nL 225.938267 147.714074 \nL 222.330994 147.569444 \nL 218.723722 147.429581 \nL 215.116449 147.294073 \nL 211.509176 147.16255 \nL 207.901903 147.034686 \nL 204.294631 146.910188 \nL 200.687358 146.788794 \nL 197.080085 146.670268 \nL 193.472812 146.554398 \nL 189.86554 146.440992 \nL 186.258267 146.329876 \nL 182.650994 146.220893 \nL 179.043722 146.113897 \nL 175.436449 146.00876 \nL 171.829176 145.90536 \nL 168.221903 145.803588 \nL 164.614631 145.703343 \nL 161.007358 145.604533 \nL 157.400085 145.507073 \nL 153.792812 145.410883 \nL 153.357267 145.399219 \nL 150.18554 145.246046 \nL 146.578267 145.078534 \nL 142.970994 144.917746 \nL 139.363722 144.763045 \nL 135.756449 144.613869 \nL 132.149176 144.469724 \nL 128.541903 144.330174 \nL 124.934631 144.194832 \nL 121.327358 144.063352 \nL 117.720085 143.935426 \nL 114.112812 143.810778 \nL 110.50554 143.689158 \nL 106.898267 143.570343 \nL 103.290994 143.454131 \nL 99.683722 143.340338 \nL 96.076449 143.228798 \nL 92.469176 143.119358 \nL 88.861903 143.011881 \nL 85.254631 142.906241 \nL 81.647358 142.80232 \nL 78.442538 142.711219 \nL 78.040085 142.689116 \nL 74.432812 142.494548 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 134.475242 \nL 78.040085 134.543615 \nL 81.647358 134.611836 \nL 83.503649 134.647219 \nL 85.254631 134.710898 \nL 88.861903 134.839595 \nL 92.469176 134.963601 \nL 96.076449 135.083413 \nL 99.683722 135.199462 \nL 103.290994 135.312119 \nL 106.898267 135.421711 \nL 110.50554 135.528523 \nL 114.112812 135.632804 \nL 117.720085 135.734777 \nL 121.327358 135.834638 \nL 124.934631 135.932562 \nL 128.541903 136.028703 \nL 132.149176 136.123203 \nL 135.756449 136.216187 \nL 139.363722 136.307767 \nL 142.970994 136.398045 \nL 146.578267 136.487115 \nL 150.18554 136.575059 \nL 153.792812 136.661954 \nL 157.400085 136.74787 \nL 161.007358 136.832869 \nL 164.614631 136.917011 \nL 168.221903 137.000348 \nL 171.829176 137.082929 \nL 175.436449 137.1648 \nL 179.043722 137.246002 \nL 182.650994 137.326573 \nL 183.034397 137.335219 \nL 186.258267 137.464799 \nL 189.86554 137.605005 \nL 193.472812 137.740391 \nL 197.080085 137.871405 \nL 200.687358 137.99844 \nL 204.294631 138.121845 \nL 207.901903 138.241928 \nL 211.509176 138.358962 \nL 215.116449 138.473193 \nL 218.723722 138.584841 \nL 222.330994 138.694103 \nL 225.938267 138.801155 \nL 229.54554 138.906158 \nL 233.152813 139.009259 \nL 236.760085 139.110587 \nL 240.367358 139.210264 \nL 243.974631 139.308398 \nL 247.581903 139.40509 \nL 251.189176 139.500431 \nL 254.796449 139.594505 \nL 258.403722 139.687388 \nL 262.010994 139.779153 \nL 265.618267 139.869863 \nL 269.22554 139.959581 \nL 271.797348 140.023219 \nL 272.832812 140.068855 \nL 276.440085 140.225363 \nL 280.047358 140.376021 \nL 283.654631 140.52137 \nL 287.261903 140.661888 \nL 290.869176 140.797997 \nL 294.476449 140.93007 \nL 298.083722 141.05844 \nL 301.690994 141.183405 \nL 305.298267 141.30523 \nL 308.90554 141.424155 \nL 312.512812 141.540395 \nL 316.120085 141.654145 \nL 319.727358 141.765581 \nL 323.334631 141.874863 \nL 326.941903 141.982137 \nL 330.549176 142.087536 \nL 334.156449 142.19118 \nL 337.763722 142.293181 \nL 341.370994 142.393642 \nL 344.978267 142.492654 \nL 348.58554 142.590305 \nL 352.192813 142.686675 \nL 353.109956 142.711219 \nL 355.800085 142.841318 \nL 359.407358 143.009823 \nL 363.014631 143.171506 \nL 366.621903 143.32702 \nL 370.229176 143.476934 \nL 373.836449 143.621751 \nL 377.443722 143.761916 \nL 381.050994 143.897822 \nL 384.658267 144.029821 \nL 388.26554 144.158224 \nL 391.872813 144.283313 \nL 395.480085 144.405341 \nL 399.087358 144.524533 \nL 402.694631 144.641096 \nL 406.301903 144.755216 \nL 409.909176 144.867061 \nL 413.516449 144.976784 \nL 417.123722 145.084526 \nL 420.730994 145.190415 \nL 424.338267 145.294569 \nL 427.94554 145.397094 \nL 428.019943 145.399219 \nL 431.552813 145.591003 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_11\">\n <path d=\"M 431.552813 155.329613 \nL 427.94554 155.225301 \nL 424.338267 155.122626 \nL 420.730994 155.021488 \nL 417.123722 154.921797 \nL 413.516449 154.823468 \nL 409.909176 154.726423 \nL 406.301903 154.630588 \nL 402.694631 154.535899 \nL 399.087358 154.442292 \nL 395.480085 154.349711 \nL 391.872813 154.2581 \nL 388.26554 154.167411 \nL 384.658267 154.077597 \nL 381.050994 153.988615 \nL 377.443722 153.900423 \nL 373.836449 153.812984 \nL 370.229176 153.726262 \nL 366.621903 153.640224 \nL 363.014631 153.554838 \nL 359.407358 153.470075 \nL 359.11754 153.463219 \nL 355.800085 153.343259 \nL 352.192813 153.215542 \nL 348.58554 153.0906 \nL 344.978267 152.968253 \nL 341.370994 152.848337 \nL 337.763722 152.730701 \nL 334.156449 152.615207 \nL 330.549176 152.501727 \nL 326.941903 152.390144 \nL 323.334631 152.280348 \nL 319.727358 152.172241 \nL 316.120085 152.065728 \nL 312.512812 151.960724 \nL 308.90554 151.857148 \nL 305.298267 151.754925 \nL 301.690994 151.653987 \nL 298.083722 151.554267 \nL 294.476449 151.455706 \nL 290.869176 151.358247 \nL 287.261903 151.261838 \nL 283.654631 151.166427 \nL 280.047358 151.07197 \nL 276.440085 150.978422 \nL 272.832812 150.885741 \nL 269.22554 150.793891 \nL 268.494463 150.775219 \nL 265.618267 150.663848 \nL 262.010994 150.526844 \nL 258.403722 150.392951 \nL 254.796449 150.261973 \nL 251.189176 150.133729 \nL 247.581903 150.008053 \nL 243.974631 149.884793 \nL 240.367358 149.763808 \nL 236.760085 149.644967 \nL 233.152813 149.528151 \nL 229.54554 149.413249 \nL 225.938267 149.300155 \nL 222.330994 149.188775 \nL 218.723722 149.079019 \nL 215.116449 148.970803 \nL 211.509176 148.86405 \nL 207.901903 148.758688 \nL 204.294631 148.654648 \nL 200.687358 148.551866 \nL 197.080085 148.450284 \nL 193.472812 148.349846 \nL 189.86554 148.250499 \nL 186.258267 148.152194 \nL 183.861615 148.087219 \nL 182.650994 148.037091 \nL 179.043722 147.889298 \nL 175.436449 147.745155 \nL 171.829176 147.604427 \nL 168.221903 147.466898 \nL 164.614631 147.332371 \nL 161.007358 147.200663 \nL 157.400085 147.071607 \nL 153.792812 146.945048 \nL 150.18554 146.820845 \nL 146.578267 146.698864 \nL 142.970994 146.578984 \nL 139.363722 146.461091 \nL 135.756449 146.34508 \nL 132.149176 146.230852 \nL 128.541903 146.118316 \nL 124.934631 146.007387 \nL 121.327358 145.897984 \nL 117.720085 145.790035 \nL 114.112812 145.683468 \nL 110.50554 145.578219 \nL 106.898267 145.474227 \nL 104.277043 145.399219 \nL 103.290994 145.355426 \nL 99.683722 145.19697 \nL 96.076449 145.042816 \nL 92.469176 144.892676 \nL 88.861903 144.746284 \nL 85.254631 144.6034 \nL 81.647358 144.463803 \nL 78.040085 144.327288 \nL 74.432812 144.19367 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440256; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 132.765291 \nL 78.040085 132.869876 \nL 81.647358 132.972807 \nL 85.254631 133.074186 \nL 88.861903 133.174104 \nL 92.469176 133.272649 \nL 96.076449 133.369898 \nL 99.683722 133.465925 \nL 103.290994 133.560797 \nL 106.898267 133.654577 \nL 110.50554 133.747323 \nL 114.112812 133.83909 \nL 117.720085 133.929928 \nL 121.327358 134.019884 \nL 124.934631 134.109001 \nL 128.541903 134.197322 \nL 132.149176 134.284884 \nL 135.756449 134.371724 \nL 139.363722 134.457875 \nL 142.970994 134.543369 \nL 146.578267 134.628235 \nL 147.381524 134.647219 \nL 150.18554 134.74863 \nL 153.792812 134.876778 \nL 157.400085 135.002125 \nL 161.007358 135.124851 \nL 164.614631 135.245123 \nL 168.221903 135.363093 \nL 171.829176 135.478903 \nL 175.436449 135.59268 \nL 179.043722 135.704543 \nL 182.650994 135.814603 \nL 186.258267 135.92296 \nL 189.86554 136.02971 \nL 193.472812 136.134939 \nL 197.080085 136.238728 \nL 200.687358 136.341153 \nL 204.294631 136.442284 \nL 207.901903 136.542187 \nL 211.509176 136.640922 \nL 215.116449 136.738547 \nL 218.723722 136.835115 \nL 222.330994 136.930676 \nL 225.938267 137.025278 \nL 229.54554 137.118965 \nL 233.152813 137.211777 \nL 236.760085 137.303754 \nL 237.992916 137.335219 \nL 240.367358 137.427194 \nL 243.974631 137.564667 \nL 247.581903 137.699 \nL 251.189176 137.830391 \nL 254.796449 137.959022 \nL 258.403722 138.085062 \nL 262.010994 138.208666 \nL 265.618267 138.329975 \nL 269.22554 138.449121 \nL 272.832812 138.566226 \nL 276.440085 138.681402 \nL 280.047358 138.794755 \nL 283.654631 138.90638 \nL 287.261903 139.016369 \nL 290.869176 139.124807 \nL 294.476449 139.23177 \nL 298.083722 139.337333 \nL 301.690994 139.441564 \nL 305.298267 139.544527 \nL 308.90554 139.646282 \nL 312.512812 139.746886 \nL 316.120085 139.846391 \nL 319.727358 139.944848 \nL 322.619731 140.023219 \nL 323.334631 140.052837 \nL 326.941903 140.201168 \nL 330.549176 140.345814 \nL 334.156449 140.487013 \nL 337.763722 140.624984 \nL 341.370994 140.759926 \nL 344.978267 140.892025 \nL 348.58554 141.021448 \nL 352.192813 141.148353 \nL 355.800085 141.272884 \nL 359.407358 141.395173 \nL 363.014631 141.515346 \nL 366.621903 141.633515 \nL 370.229176 141.749789 \nL 373.836449 141.864265 \nL 377.443722 141.977037 \nL 381.050994 142.088191 \nL 384.658267 142.197807 \nL 388.26554 142.305959 \nL 391.872813 142.412719 \nL 395.480085 142.518153 \nL 399.087358 142.622322 \nL 402.195266 142.711219 \nL 402.694631 142.733414 \nL 406.301903 142.892493 \nL 409.909176 143.047228 \nL 413.516449 143.197911 \nL 417.123722 143.344809 \nL 420.730994 143.488167 \nL 424.338267 143.62821 \nL 427.94554 143.765142 \nL 431.552813 143.899153 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #440256; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_12\">\n <path d=\"M 431.552813 157.669983 \nL 427.94554 157.567882 \nL 424.338267 157.466815 \nL 420.730994 157.366739 \nL 417.123722 157.267615 \nL 413.516449 157.169404 \nL 409.909176 157.072072 \nL 406.301903 156.975582 \nL 402.694631 156.879905 \nL 399.087358 156.785007 \nL 395.480085 156.690862 \nL 391.872813 156.59744 \nL 388.26554 156.504715 \nL 384.658267 156.412663 \nL 381.050994 156.321259 \nL 377.443722 156.230481 \nL 374.277462 156.151219 \nL 373.836449 156.136116 \nL 370.229176 156.012729 \nL 366.621903 155.891165 \nL 363.014631 155.77134 \nL 359.407358 155.653176 \nL 355.800085 155.536598 \nL 352.192813 155.421538 \nL 348.58554 155.307929 \nL 344.978267 155.19571 \nL 341.370994 155.084822 \nL 337.763722 154.97521 \nL 334.156449 154.866822 \nL 330.549176 154.759608 \nL 326.941903 154.653522 \nL 323.334631 154.54852 \nL 319.727358 154.444559 \nL 316.120085 154.341599 \nL 312.512812 154.239603 \nL 308.90554 154.138535 \nL 305.298267 154.03836 \nL 301.690994 153.939046 \nL 298.083722 153.840562 \nL 294.476449 153.742879 \nL 290.869176 153.645967 \nL 287.261903 153.549802 \nL 283.993109 153.463219 \nL 283.654631 153.451009 \nL 280.047358 153.321083 \nL 276.440085 153.193152 \nL 272.832812 153.067124 \nL 269.22554 152.942914 \nL 265.618267 152.820444 \nL 262.010994 152.699638 \nL 258.403722 152.580425 \nL 254.796449 152.462737 \nL 251.189176 152.346513 \nL 247.581903 152.231692 \nL 243.974631 152.118217 \nL 240.367358 152.006036 \nL 236.760085 151.895096 \nL 233.152813 151.785351 \nL 229.54554 151.676754 \nL 225.938267 151.569262 \nL 222.330994 151.462833 \nL 218.723722 151.35743 \nL 215.116449 151.253013 \nL 211.509176 151.149549 \nL 207.901903 151.047002 \nL 204.294631 150.945341 \nL 200.687358 150.844535 \nL 198.19529 150.775219 \nL 197.080085 150.732984 \nL 193.472812 150.597136 \nL 189.86554 150.46346 \nL 186.258267 150.33186 \nL 182.650994 150.202242 \nL 179.043722 150.07452 \nL 175.436449 149.948612 \nL 171.829176 149.824441 \nL 168.221903 149.701933 \nL 164.614631 149.58102 \nL 161.007358 149.461637 \nL 157.400085 149.343722 \nL 153.792812 149.227217 \nL 150.18554 149.112066 \nL 146.578267 148.998218 \nL 142.970994 148.885621 \nL 139.363722 148.774229 \nL 135.756449 148.663998 \nL 132.149176 148.554884 \nL 128.541903 148.446846 \nL 124.934631 148.339846 \nL 121.327358 148.233847 \nL 117.720085 148.128815 \nL 116.288763 148.087219 \nL 114.112812 148.000772 \nL 110.50554 147.85904 \nL 106.898267 147.719695 \nL 103.290994 147.582628 \nL 99.683722 147.447737 \nL 96.076449 147.314924 \nL 92.469176 147.184098 \nL 88.861903 147.055175 \nL 85.254631 146.928072 \nL 81.647358 146.802714 \nL 78.040085 146.679028 \nL 74.432812 146.556946 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #450457; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 130.425579 \nL 78.040085 130.527848 \nL 81.647358 130.629075 \nL 85.254631 130.729305 \nL 88.861903 130.828578 \nL 92.469176 130.926931 \nL 96.076449 131.024401 \nL 99.683722 131.121022 \nL 103.290994 131.216827 \nL 106.898267 131.311847 \nL 110.50554 131.406111 \nL 114.112812 131.499647 \nL 117.720085 131.592482 \nL 121.327358 131.68464 \nL 124.934631 131.776147 \nL 128.541903 131.867025 \nL 132.149176 131.957295 \nL 132.225668 131.959219 \nL 135.756449 132.080223 \nL 139.363722 132.202055 \nL 142.970994 132.322136 \nL 146.578267 132.440545 \nL 150.18554 132.557357 \nL 153.792812 132.672641 \nL 157.400085 132.786465 \nL 161.007358 132.89889 \nL 164.614631 133.009975 \nL 168.221903 133.119777 \nL 171.829176 133.228347 \nL 175.436449 133.335736 \nL 179.043722 133.44199 \nL 182.650994 133.547155 \nL 186.258267 133.651272 \nL 189.86554 133.754381 \nL 193.472812 133.856522 \nL 197.080085 133.95773 \nL 200.687358 134.058039 \nL 204.294631 134.157482 \nL 207.901903 134.256091 \nL 211.509176 134.353896 \nL 215.116449 134.450924 \nL 218.723722 134.547202 \nL 222.330994 134.642757 \nL 222.498817 134.647219 \nL 225.938267 134.771294 \nL 229.54554 134.899511 \nL 233.152813 135.025813 \nL 236.760085 135.150284 \nL 240.367358 135.273004 \nL 243.974631 135.39405 \nL 247.581903 135.513493 \nL 251.189176 135.631401 \nL 254.796449 135.747836 \nL 258.403722 135.86286 \nL 262.010994 135.97653 \nL 265.618267 136.088899 \nL 269.22554 136.200019 \nL 272.832812 136.309938 \nL 276.440085 136.418702 \nL 280.047358 136.526354 \nL 283.654631 136.632938 \nL 287.261903 136.738491 \nL 290.869176 136.843051 \nL 294.476449 136.946655 \nL 298.083722 137.049336 \nL 301.690994 137.151126 \nL 305.298267 137.252057 \nL 308.289217 137.335219 \nL 308.90554 137.358565 \nL 312.512812 137.494733 \nL 316.120085 137.628714 \nL 319.727358 137.760607 \nL 323.334631 137.890504 \nL 326.941903 138.018493 \nL 330.549176 138.144657 \nL 334.156449 138.269074 \nL 337.763722 138.391817 \nL 341.370994 138.512955 \nL 344.978267 138.632555 \nL 348.58554 138.750678 \nL 352.192813 138.867383 \nL 355.800085 138.982726 \nL 359.407358 139.09676 \nL 363.014631 139.209534 \nL 366.621903 139.321097 \nL 370.229176 139.431494 \nL 373.836449 139.540767 \nL 377.443722 139.648958 \nL 381.050994 139.756106 \nL 384.658267 139.862247 \nL 388.26554 139.967418 \nL 390.186219 140.023219 \nL 391.872813 140.090245 \nL 395.480085 140.232323 \nL 399.087358 140.371998 \nL 402.694631 140.509381 \nL 406.301903 140.644574 \nL 409.909176 140.777675 \nL 413.516449 140.908776 \nL 417.123722 141.037963 \nL 420.730994 141.165319 \nL 424.338267 141.290919 \nL 427.94554 141.414837 \nL 431.552813 141.537142 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #450457; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_13\">\n <path d=\"M 431.552813 160.784349 \nL 427.94554 160.675222 \nL 424.338267 160.567017 \nL 420.730994 160.459707 \nL 417.123722 160.353263 \nL 413.516449 160.24766 \nL 409.909176 160.142873 \nL 406.301903 160.038877 \nL 402.694631 159.935649 \nL 399.087358 159.833168 \nL 395.480085 159.73141 \nL 391.872813 159.630356 \nL 388.26554 159.529986 \nL 384.658267 159.430281 \nL 381.050994 159.331222 \nL 377.443722 159.232792 \nL 373.836449 159.134973 \nL 370.229176 159.037749 \nL 366.621903 158.941104 \nL 363.014631 158.845023 \nL 362.797266 158.839219 \nL 359.407358 158.725697 \nL 355.800085 158.606045 \nL 352.192813 158.487583 \nL 348.58554 158.370272 \nL 344.978267 158.254078 \nL 341.370994 158.138963 \nL 337.763722 158.024894 \nL 334.156449 157.91184 \nL 330.549176 157.79977 \nL 326.941903 157.688652 \nL 323.334631 157.57846 \nL 319.727358 157.469166 \nL 316.120085 157.360743 \nL 312.512812 157.253166 \nL 308.90554 157.14641 \nL 305.298267 157.040453 \nL 301.690994 156.935272 \nL 298.083722 156.830845 \nL 294.476449 156.727151 \nL 290.869176 156.62417 \nL 287.261903 156.521882 \nL 283.654631 156.42027 \nL 280.047358 156.319315 \nL 276.440085 156.218999 \nL 273.994442 156.151219 \nL 272.832812 156.110849 \nL 269.22554 155.985882 \nL 265.618267 155.86222 \nL 262.010994 155.73982 \nL 258.403722 155.618643 \nL 254.796449 155.49865 \nL 251.189176 155.379805 \nL 247.581903 155.262071 \nL 243.974631 155.145415 \nL 240.367358 155.029804 \nL 236.760085 154.915207 \nL 233.152813 154.801595 \nL 229.54554 154.688938 \nL 225.938267 154.577208 \nL 222.330994 154.46638 \nL 218.723722 154.356426 \nL 215.116449 154.247323 \nL 211.509176 154.139047 \nL 207.901903 154.031575 \nL 204.294631 153.924884 \nL 200.687358 153.818954 \nL 197.080085 153.713765 \nL 193.472812 153.609295 \nL 189.86554 153.505527 \nL 188.392707 153.463219 \nL 186.258267 153.386343 \nL 182.650994 153.257268 \nL 179.043722 153.129585 \nL 175.436449 153.003251 \nL 171.829176 152.878221 \nL 168.221903 152.754456 \nL 164.614631 152.631915 \nL 161.007358 152.510562 \nL 157.400085 152.390359 \nL 153.792812 152.271273 \nL 150.18554 152.153269 \nL 146.578267 152.036316 \nL 142.970994 151.920384 \nL 139.363722 151.805441 \nL 135.756449 151.691461 \nL 132.149176 151.578415 \nL 128.541903 151.466277 \nL 124.934631 151.355023 \nL 121.327358 151.244627 \nL 117.720085 151.135065 \nL 114.112812 151.026316 \nL 110.50554 150.918357 \nL 106.898267 150.811168 \nL 105.687084 150.775219 \nL 103.290994 150.685858 \nL 99.683722 150.552372 \nL 96.076449 150.420389 \nL 92.469176 150.289861 \nL 88.861903 150.160742 \nL 85.254631 150.032985 \nL 81.647358 149.906549 \nL 78.040085 149.781393 \nL 74.432812 149.657477 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #450559; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 127.310392 \nL 78.040085 127.419663 \nL 81.647358 127.528008 \nL 85.254631 127.635453 \nL 88.861903 127.742028 \nL 92.469176 127.847759 \nL 96.076449 127.95267 \nL 99.683722 128.056786 \nL 103.290994 128.160131 \nL 106.898267 128.262727 \nL 110.50554 128.364595 \nL 114.112812 128.465756 \nL 117.720085 128.566231 \nL 121.327358 128.666038 \nL 124.934631 128.765195 \nL 128.541903 128.863722 \nL 132.149176 128.961635 \nL 135.756449 129.05895 \nL 139.363722 129.155684 \nL 142.970994 129.251852 \nL 143.696507 129.271219 \nL 146.578267 129.36772 \nL 150.18554 129.487553 \nL 153.792812 129.60619 \nL 157.400085 129.72367 \nL 161.007358 129.840029 \nL 164.614631 129.955303 \nL 168.221903 130.069526 \nL 171.829176 130.18273 \nL 175.436449 130.294946 \nL 179.043722 130.406204 \nL 182.650994 130.516533 \nL 186.258267 130.625961 \nL 189.86554 130.734513 \nL 193.472812 130.842216 \nL 197.080085 130.949093 \nL 200.687358 131.055169 \nL 204.294631 131.160466 \nL 207.901903 131.265005 \nL 211.509176 131.368808 \nL 215.116449 131.471896 \nL 218.723722 131.574287 \nL 222.330994 131.676 \nL 225.938267 131.777053 \nL 229.54554 131.877465 \nL 232.496236 131.959219 \nL 233.152813 131.982037 \nL 236.760085 132.107199 \nL 240.367358 132.231049 \nL 243.974631 132.353631 \nL 247.581903 132.474985 \nL 251.189176 132.595149 \nL 254.796449 132.714161 \nL 258.403722 132.832056 \nL 262.010994 132.948868 \nL 265.618267 133.06463 \nL 269.22554 133.179374 \nL 272.832812 133.293129 \nL 276.440085 133.405925 \nL 280.047358 133.51779 \nL 283.654631 133.62875 \nL 287.261903 133.738831 \nL 290.869176 133.848058 \nL 294.476449 133.956454 \nL 298.083722 134.064044 \nL 301.690994 134.170849 \nL 305.298267 134.27689 \nL 308.90554 134.382188 \nL 312.512812 134.486763 \nL 316.120085 134.590633 \nL 318.090403 134.647219 \nL 319.727358 134.706181 \nL 323.334631 134.835461 \nL 326.941903 134.963342 \nL 330.549176 135.089868 \nL 334.156449 135.215084 \nL 337.763722 135.339029 \nL 341.370994 135.461744 \nL 344.978267 135.583267 \nL 348.58554 135.703634 \nL 352.192813 135.82288 \nL 355.800085 135.941038 \nL 359.407358 136.058141 \nL 363.014631 136.17422 \nL 366.621903 136.289304 \nL 370.229176 136.403422 \nL 373.836449 136.516601 \nL 377.443722 136.628869 \nL 381.050994 136.74025 \nL 384.658267 136.85077 \nL 388.26554 136.960451 \nL 391.872813 137.069316 \nL 395.480085 137.177389 \nL 399.087358 137.284689 \nL 400.790116 137.335219 \nL 402.694631 137.406255 \nL 406.301903 137.53996 \nL 409.909176 137.672154 \nL 413.516449 137.802886 \nL 417.123722 137.932203 \nL 420.730994 138.060151 \nL 424.338267 138.186773 \nL 427.94554 138.312109 \nL 431.552813 138.4362 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #450559; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_14\">\n <path d=\"M 431.552813 164.911597 \nL 427.94554 164.81015 \nL 424.338267 164.709212 \nL 420.730994 164.608774 \nL 417.123722 164.508824 \nL 413.516449 164.409354 \nL 409.909176 164.310352 \nL 406.427507 164.215219 \nL 406.301903 164.211158 \nL 402.694631 164.094458 \nL 399.087358 163.978575 \nL 395.480085 163.863491 \nL 391.872813 163.749186 \nL 388.26554 163.635643 \nL 384.658267 163.522844 \nL 381.050994 163.410773 \nL 377.443722 163.299412 \nL 373.836449 163.188746 \nL 370.229176 163.07876 \nL 366.621903 162.969439 \nL 363.014631 162.860768 \nL 359.407358 162.752732 \nL 355.800085 162.645319 \nL 352.192813 162.538516 \nL 348.58554 162.432308 \nL 344.978267 162.326683 \nL 341.370994 162.22163 \nL 337.763722 162.117136 \nL 334.156449 162.01319 \nL 330.549176 161.909781 \nL 326.941903 161.806897 \nL 323.334631 161.704529 \nL 319.727358 161.602665 \nL 317.047187 161.527219 \nL 316.120085 161.496378 \nL 312.512812 161.376547 \nL 308.90554 161.257575 \nL 305.298267 161.139442 \nL 301.690994 161.02213 \nL 298.083722 160.905619 \nL 294.476449 160.789891 \nL 290.869176 160.674929 \nL 287.261903 160.560715 \nL 283.654631 160.447233 \nL 280.047358 160.334467 \nL 276.440085 160.222401 \nL 272.832812 160.111019 \nL 269.22554 160.000308 \nL 265.618267 159.890253 \nL 262.010994 159.780839 \nL 258.403722 159.672054 \nL 254.796449 159.563884 \nL 251.189176 159.456316 \nL 247.581903 159.349339 \nL 243.974631 159.242939 \nL 240.367358 159.137105 \nL 236.760085 159.031826 \nL 233.152813 158.92709 \nL 230.114099 158.839219 \nL 229.54554 158.819791 \nL 225.938267 158.696631 \nL 222.330994 158.574381 \nL 218.723722 158.453022 \nL 215.116449 158.332532 \nL 211.509176 158.212891 \nL 207.901903 158.094081 \nL 204.294631 157.976082 \nL 200.687358 157.858877 \nL 197.080085 157.742447 \nL 193.472812 157.626776 \nL 189.86554 157.511847 \nL 186.258267 157.397644 \nL 182.650994 157.284151 \nL 179.043722 157.171354 \nL 175.436449 157.059237 \nL 171.829176 156.947786 \nL 168.221903 156.836987 \nL 164.614631 156.726827 \nL 161.007358 156.617292 \nL 157.400085 156.50837 \nL 153.792812 156.400048 \nL 150.18554 156.292314 \nL 146.578267 156.185156 \nL 145.43499 156.151219 \nL 142.970994 156.064793 \nL 139.363722 155.938923 \nL 135.756449 155.814005 \nL 132.149176 155.690018 \nL 128.541903 155.566941 \nL 124.934631 155.444751 \nL 121.327358 155.323431 \nL 117.720085 155.202959 \nL 114.112812 155.083316 \nL 110.50554 154.964486 \nL 106.898267 154.846449 \nL 103.290994 154.729188 \nL 99.683722 154.612686 \nL 96.076449 154.496928 \nL 92.469176 154.381897 \nL 88.861903 154.267578 \nL 85.254631 154.153955 \nL 81.647358 154.041015 \nL 78.040085 153.928743 \nL 74.432812 153.817125 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #460a5d; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 123.184393 \nL 78.040085 123.285919 \nL 81.647358 123.386935 \nL 85.254631 123.487449 \nL 88.861903 123.587474 \nL 92.469176 123.687018 \nL 96.076449 123.786092 \nL 99.683722 123.884704 \nL 100.067813 123.895219 \nL 103.290994 123.999515 \nL 106.898267 124.115518 \nL 110.50554 124.230721 \nL 114.112812 124.345142 \nL 117.720085 124.458798 \nL 121.327358 124.571708 \nL 124.934631 124.683887 \nL 128.541903 124.795354 \nL 132.149176 124.906123 \nL 135.756449 125.01621 \nL 139.363722 125.125631 \nL 142.970994 125.234399 \nL 146.578267 125.342529 \nL 150.18554 125.450035 \nL 153.792813 125.55693 \nL 157.400085 125.663227 \nL 161.007358 125.768939 \nL 164.614631 125.874077 \nL 168.221903 125.978655 \nL 171.829176 126.082683 \nL 175.436449 126.186173 \nL 179.043722 126.289135 \nL 182.650994 126.391582 \nL 186.258267 126.493522 \nL 189.445359 126.583219 \nL 189.86554 126.597196 \nL 193.472812 126.717156 \nL 197.080085 126.836253 \nL 200.687358 126.954508 \nL 204.294631 127.071941 \nL 207.901903 127.188569 \nL 211.509176 127.304412 \nL 215.116449 127.419486 \nL 218.723722 127.53381 \nL 222.330994 127.647399 \nL 225.938267 127.76027 \nL 229.54554 127.872439 \nL 233.152813 127.983921 \nL 236.760085 128.094731 \nL 240.367358 128.204883 \nL 243.974631 128.314391 \nL 247.581903 128.423269 \nL 251.189176 128.531529 \nL 254.796449 128.639186 \nL 258.403722 128.746251 \nL 262.010994 128.852736 \nL 265.618267 128.958653 \nL 269.22554 129.064014 \nL 272.832812 129.16883 \nL 276.374161 129.271219 \nL 276.440085 129.273471 \nL 280.047358 129.396766 \nL 283.654631 129.519147 \nL 287.261903 129.640635 \nL 290.869176 129.76125 \nL 294.476449 129.881014 \nL 298.083722 129.999944 \nL 301.690994 130.11806 \nL 305.298267 130.235381 \nL 308.90554 130.351923 \nL 312.512812 130.467704 \nL 316.120085 130.582741 \nL 319.727358 130.697049 \nL 323.334631 130.810645 \nL 326.941903 130.923543 \nL 330.549176 131.035759 \nL 334.156449 131.147306 \nL 337.763722 131.2582 \nL 341.370994 131.368453 \nL 344.978267 131.478078 \nL 348.58554 131.58709 \nL 352.192813 131.695499 \nL 355.800085 131.803319 \nL 359.407358 131.91056 \nL 361.046781 131.959219 \nL 363.014631 132.028243 \nL 366.621903 132.154253 \nL 370.229176 132.279307 \nL 373.836449 132.403427 \nL 377.443722 132.526634 \nL 381.050994 132.648951 \nL 384.658267 132.770396 \nL 388.26554 132.890989 \nL 391.872813 133.01075 \nL 395.480085 133.129697 \nL 399.087358 133.247848 \nL 402.694631 133.36522 \nL 406.301903 133.48183 \nL 409.909176 133.597695 \nL 413.516449 133.71283 \nL 417.123722 133.827252 \nL 420.730994 133.940974 \nL 424.338267 134.054012 \nL 427.94554 134.16638 \nL 431.552813 134.278092 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #460a5d; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_15\">\n <path d=\"M 431.552813 170.446814 \nL 427.94554 170.341827 \nL 424.338267 170.237259 \nL 420.730994 170.133104 \nL 417.123722 170.029355 \nL 413.516449 169.926007 \nL 409.909176 169.823052 \nL 406.301903 169.720486 \nL 402.694631 169.618301 \nL 401.738578 169.591219 \nL 399.087358 169.506274 \nL 395.480085 169.3911 \nL 391.872813 169.276497 \nL 388.26554 169.162453 \nL 384.658267 169.04896 \nL 381.050994 168.936009 \nL 377.443722 168.823591 \nL 373.836449 168.711696 \nL 370.229176 168.600317 \nL 366.621903 168.489444 \nL 363.014631 168.37907 \nL 359.407358 168.269187 \nL 355.800085 168.159787 \nL 352.192813 168.050861 \nL 348.58554 167.942403 \nL 344.978267 167.834406 \nL 341.370994 167.726861 \nL 337.763722 167.619762 \nL 334.156449 167.513102 \nL 330.549176 167.406874 \nL 326.941903 167.301071 \nL 323.334631 167.195688 \nL 319.727358 167.090717 \nL 316.120085 166.986153 \nL 313.250984 166.903219 \nL 312.512812 166.879086 \nL 308.90554 166.761225 \nL 305.298267 166.643964 \nL 301.690994 166.527292 \nL 298.083722 166.411201 \nL 294.476449 166.29568 \nL 290.869176 166.18072 \nL 287.261903 166.066311 \nL 283.654631 165.952445 \nL 280.047358 165.839113 \nL 276.440085 165.726306 \nL 272.832812 165.614015 \nL 269.22554 165.502233 \nL 265.618267 165.390951 \nL 262.010994 165.280162 \nL 258.403722 165.169856 \nL 254.796449 165.060028 \nL 251.189176 164.95067 \nL 247.581903 164.841773 \nL 243.974631 164.733332 \nL 240.367358 164.625338 \nL 236.760085 164.517786 \nL 233.152813 164.410669 \nL 229.54554 164.303979 \nL 226.535082 164.215219 \nL 225.938267 164.195318 \nL 222.330994 164.075092 \nL 218.723722 163.955492 \nL 215.116449 163.836509 \nL 211.509176 163.718131 \nL 207.901903 163.600348 \nL 204.294631 163.483151 \nL 200.687358 163.36653 \nL 197.080085 163.250476 \nL 193.472812 163.134979 \nL 189.86554 163.020031 \nL 186.258267 162.905621 \nL 182.650994 162.791743 \nL 179.043722 162.678387 \nL 175.436449 162.565545 \nL 171.829176 162.45321 \nL 168.221903 162.341372 \nL 164.614631 162.230024 \nL 161.007358 162.11916 \nL 157.400085 162.00877 \nL 153.792812 161.898848 \nL 150.18554 161.789387 \nL 146.578267 161.68038 \nL 142.970994 161.57182 \nL 141.487349 161.527219 \nL 139.363722 161.45502 \nL 135.756449 161.332751 \nL 132.149176 161.211132 \nL 128.541903 161.090151 \nL 124.934631 160.969797 \nL 121.327358 160.850061 \nL 117.720085 160.730932 \nL 114.112812 160.6124 \nL 110.50554 160.494456 \nL 106.898267 160.377089 \nL 103.290994 160.26029 \nL 99.683722 160.14405 \nL 96.076449 160.028361 \nL 92.469176 159.913213 \nL 88.861903 159.798599 \nL 85.254631 159.684508 \nL 81.647358 159.570934 \nL 78.040085 159.457868 \nL 74.432812 159.345303 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #471365; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 117.648762 \nL 78.040085 117.753814 \nL 81.647358 117.858445 \nL 85.254631 117.962662 \nL 88.861903 118.066473 \nL 92.469176 118.169882 \nL 96.076449 118.272896 \nL 99.683722 118.375521 \nL 103.290994 118.477763 \nL 104.754652 118.519219 \nL 106.898267 118.587896 \nL 110.50554 118.703156 \nL 114.112812 118.817844 \nL 117.720085 118.93197 \nL 121.327358 119.045545 \nL 124.934631 119.158576 \nL 128.541903 119.271074 \nL 132.149176 119.383046 \nL 135.756449 119.494502 \nL 139.363722 119.60545 \nL 142.970994 119.715898 \nL 146.578267 119.825854 \nL 150.18554 119.935326 \nL 153.792812 120.044322 \nL 157.400085 120.15285 \nL 161.007358 120.260916 \nL 164.614631 120.368528 \nL 168.221903 120.475694 \nL 171.829176 120.582419 \nL 175.436449 120.688711 \nL 179.043722 120.794577 \nL 182.650994 120.900023 \nL 186.258267 121.005056 \nL 189.86554 121.109681 \nL 193.240299 121.207219 \nL 193.472813 121.21482 \nL 197.080085 121.33277 \nL 200.687358 121.45012 \nL 204.294631 121.566877 \nL 207.901903 121.683054 \nL 211.509176 121.798658 \nL 215.116449 121.913701 \nL 218.723722 122.02819 \nL 222.330994 122.142136 \nL 225.938267 122.255547 \nL 229.54554 122.368431 \nL 233.152813 122.480798 \nL 236.760085 122.592655 \nL 240.367358 122.70401 \nL 243.974631 122.814872 \nL 247.581903 122.925249 \nL 251.189176 123.035147 \nL 254.796449 123.144575 \nL 258.403722 123.25354 \nL 262.010994 123.362048 \nL 265.618267 123.470107 \nL 269.22554 123.577725 \nL 272.832812 123.684907 \nL 276.440085 123.791659 \nL 279.952882 123.895219 \nL 280.047358 123.898369 \nL 283.654631 124.018687 \nL 287.261903 124.138378 \nL 290.869176 124.257451 \nL 294.476449 124.375917 \nL 298.083722 124.493786 \nL 301.690994 124.611068 \nL 305.298267 124.727773 \nL 308.90554 124.843909 \nL 312.512812 124.959487 \nL 316.120085 125.074516 \nL 319.727358 125.189003 \nL 323.334631 125.302959 \nL 326.941903 125.416391 \nL 330.549176 125.529308 \nL 334.156449 125.641717 \nL 337.763722 125.753628 \nL 341.370994 125.865047 \nL 344.978267 125.975982 \nL 348.58554 126.086441 \nL 352.192813 126.196431 \nL 355.800085 126.305959 \nL 359.407358 126.415033 \nL 363.014631 126.523659 \nL 364.996091 126.583219 \nL 366.621903 126.638493 \nL 370.229176 126.760856 \nL 373.836449 126.882569 \nL 377.443722 127.003642 \nL 381.050994 127.124086 \nL 384.658267 127.243911 \nL 388.26554 127.363128 \nL 391.872813 127.481746 \nL 395.480085 127.599775 \nL 399.087358 127.717225 \nL 402.694631 127.834106 \nL 406.301903 127.950426 \nL 409.909176 128.066195 \nL 413.516449 128.181421 \nL 417.123722 128.296113 \nL 420.730994 128.410279 \nL 424.338267 128.523928 \nL 427.94554 128.637067 \nL 431.552813 128.749705 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #471365; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_16\">\n <path d=\"M 431.552813 177.931354 \nL 427.94554 177.826588 \nL 424.338267 177.722125 \nL 422.024375 177.655219 \nL 420.730994 177.614259 \nL 417.123722 177.500127 \nL 413.516449 177.386402 \nL 409.909176 177.273079 \nL 406.301903 177.160153 \nL 402.694631 177.047619 \nL 399.087358 176.935472 \nL 395.480085 176.823707 \nL 391.872813 176.712321 \nL 388.26554 176.601308 \nL 384.658267 176.490663 \nL 381.050994 176.380384 \nL 377.443722 176.270464 \nL 373.836449 176.160901 \nL 370.229176 176.051689 \nL 366.621903 175.942825 \nL 363.014631 175.834305 \nL 359.407358 175.726124 \nL 355.800085 175.618279 \nL 352.192813 175.510765 \nL 348.58554 175.40358 \nL 344.978267 175.296719 \nL 341.370994 175.190178 \nL 337.763722 175.083955 \nL 334.156449 174.978044 \nL 333.787908 174.967219 \nL 330.549176 174.863064 \nL 326.941903 174.747432 \nL 323.334631 174.632216 \nL 319.727358 174.517413 \nL 316.120085 174.403017 \nL 312.512812 174.289023 \nL 308.90554 174.175426 \nL 305.298267 174.062222 \nL 301.690994 173.949406 \nL 298.083722 173.836973 \nL 294.476449 173.724919 \nL 290.869176 173.613239 \nL 287.261903 173.501929 \nL 283.654631 173.390984 \nL 280.047358 173.2804 \nL 276.440085 173.170173 \nL 272.832812 173.060299 \nL 269.22554 172.950774 \nL 265.618267 172.841593 \nL 262.010994 172.732753 \nL 258.403722 172.62425 \nL 254.796449 172.51608 \nL 251.189176 172.408238 \nL 247.581903 172.300723 \nL 246.860431 172.279219 \nL 243.974631 172.185051 \nL 240.367358 172.067679 \nL 236.760085 171.950739 \nL 233.152813 171.834225 \nL 229.54554 171.718133 \nL 225.938267 171.602456 \nL 222.330994 171.487189 \nL 218.723722 171.372329 \nL 215.116449 171.25787 \nL 211.509176 171.143807 \nL 207.901903 171.030136 \nL 204.294631 170.916851 \nL 200.687358 170.803949 \nL 197.080085 170.691425 \nL 193.472812 170.579274 \nL 189.86554 170.467492 \nL 186.258267 170.356075 \nL 182.650994 170.245018 \nL 179.043722 170.134317 \nL 175.436449 170.023969 \nL 171.829176 169.91397 \nL 168.221903 169.804314 \nL 164.614631 169.694999 \nL 161.18006 169.591219 \nL 161.007358 169.585504 \nL 157.400085 169.466113 \nL 153.792812 169.347172 \nL 150.18554 169.228675 \nL 146.578267 169.110617 \nL 142.970994 168.992992 \nL 139.363722 168.875796 \nL 135.756449 168.759023 \nL 132.149176 168.642667 \nL 128.541903 168.526725 \nL 124.934631 168.41119 \nL 121.327358 168.296059 \nL 117.720085 168.181325 \nL 114.112812 168.066986 \nL 110.50554 167.953036 \nL 106.898267 167.83947 \nL 103.290994 167.726284 \nL 99.683722 167.613473 \nL 96.076449 167.501034 \nL 92.469176 167.388961 \nL 88.861903 167.277252 \nL 85.254631 167.165901 \nL 81.647358 167.054904 \nL 78.040085 166.944258 \nL 76.701118 166.903219 \nL 74.432812 166.82708 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #482071; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 110.164321 \nL 78.040085 110.269134 \nL 81.647358 110.373642 \nL 84.468897 110.455219 \nL 85.254631 110.480101 \nL 88.861903 110.594294 \nL 92.469176 110.708079 \nL 96.076449 110.821461 \nL 99.683722 110.934447 \nL 103.290994 111.047039 \nL 106.898267 111.159244 \nL 110.50554 111.271065 \nL 114.112812 111.382508 \nL 117.720085 111.493576 \nL 121.327358 111.604275 \nL 124.934631 111.714609 \nL 128.541903 111.824582 \nL 132.149176 111.934199 \nL 135.756449 112.043463 \nL 139.363722 112.152378 \nL 142.970994 112.26095 \nL 146.578267 112.369181 \nL 150.18554 112.477076 \nL 153.792812 112.584639 \nL 157.400085 112.691874 \nL 161.007358 112.798783 \nL 164.614631 112.905371 \nL 168.221903 113.011642 \nL 171.829176 113.1176 \nL 172.701434 113.143219 \nL 175.436449 113.231171 \nL 179.043722 113.346866 \nL 182.650994 113.462143 \nL 186.258267 113.577007 \nL 189.86554 113.691463 \nL 193.472812 113.805516 \nL 197.080085 113.919171 \nL 200.687358 114.032433 \nL 204.294631 114.145306 \nL 207.901903 114.257796 \nL 211.509176 114.369906 \nL 215.116449 114.481641 \nL 218.723722 114.593006 \nL 222.330994 114.704004 \nL 225.938267 114.814641 \nL 229.54554 114.924921 \nL 233.152813 115.034847 \nL 236.760085 115.144424 \nL 240.367358 115.253656 \nL 243.974631 115.362546 \nL 247.581903 115.471099 \nL 251.189176 115.579319 \nL 254.796449 115.687209 \nL 258.403722 115.794772 \nL 259.626614 115.831219 \nL 262.010994 115.909022 \nL 265.618267 116.026458 \nL 269.22554 116.143461 \nL 272.832812 116.260037 \nL 276.440085 116.376191 \nL 280.047358 116.491929 \nL 283.654631 116.607255 \nL 287.261903 116.722175 \nL 290.869176 116.836693 \nL 294.476449 116.950814 \nL 298.083722 117.064542 \nL 301.690994 117.177884 \nL 305.298267 117.290842 \nL 308.90554 117.403421 \nL 312.512812 117.515627 \nL 316.120085 117.627463 \nL 319.727358 117.738934 \nL 323.334631 117.850044 \nL 326.941903 117.960796 \nL 330.549176 118.071196 \nL 334.156449 118.181247 \nL 337.763722 118.290953 \nL 341.370994 118.400318 \nL 344.978267 118.509346 \nL 345.304786 118.519219 \nL 348.58554 118.627822 \nL 352.192813 118.746828 \nL 355.800085 118.86539 \nL 359.407358 118.983511 \nL 363.014631 119.101199 \nL 366.621903 119.218458 \nL 370.229176 119.335292 \nL 373.836449 119.451709 \nL 377.443722 119.567711 \nL 381.050994 119.683305 \nL 384.658267 119.798495 \nL 388.26554 119.913286 \nL 391.872813 120.027683 \nL 395.480085 120.14169 \nL 399.087358 120.255312 \nL 402.694631 120.368553 \nL 406.301903 120.481418 \nL 409.909176 120.593912 \nL 413.516449 120.706037 \nL 417.123722 120.8178 \nL 420.730994 120.929203 \nL 424.338267 121.040252 \nL 427.94554 121.150949 \nL 429.781556 121.207219 \nL 431.552813 121.266673 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #482071; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_17\">\n <path d=\"M 431.552813 188.011217 \nL 427.94554 187.898823 \nL 424.338267 187.786714 \nL 420.730994 187.674885 \nL 417.123722 187.563336 \nL 413.516449 187.452063 \nL 409.909176 187.341064 \nL 406.301903 187.230337 \nL 402.694631 187.119879 \nL 399.087358 187.009688 \nL 395.480085 186.899762 \nL 391.872813 186.790098 \nL 388.26554 186.680694 \nL 384.658267 186.571547 \nL 381.050994 186.462656 \nL 377.443722 186.354019 \nL 373.836449 186.245632 \nL 370.229176 186.137495 \nL 366.621903 186.029604 \nL 363.014631 185.921958 \nL 359.407358 185.814555 \nL 356.199181 185.719219 \nL 355.800085 185.706536 \nL 352.192813 185.591897 \nL 348.58554 185.477558 \nL 344.978267 185.363517 \nL 341.370994 185.24977 \nL 337.763722 185.136315 \nL 334.156449 185.023149 \nL 330.549176 184.91027 \nL 326.941903 184.797676 \nL 323.334631 184.685363 \nL 319.727358 184.57333 \nL 316.120085 184.461573 \nL 312.512812 184.350091 \nL 308.90554 184.238881 \nL 305.298267 184.127941 \nL 301.690994 184.017268 \nL 298.083722 183.90686 \nL 294.476449 183.796714 \nL 290.869176 183.68683 \nL 287.261903 183.577203 \nL 283.654631 183.467832 \nL 280.047358 183.358716 \nL 276.440085 183.249851 \nL 272.832812 183.141235 \nL 269.22554 183.032867 \nL 269.170701 183.031219 \nL 265.618267 182.91706 \nL 262.010994 182.801442 \nL 258.403722 182.686129 \nL 254.796449 182.571118 \nL 251.189176 182.456406 \nL 247.581903 182.341991 \nL 243.974631 182.22787 \nL 240.367358 182.114041 \nL 236.760085 182.000501 \nL 233.152813 181.887247 \nL 229.54554 181.774278 \nL 225.938267 181.661589 \nL 222.330994 181.54918 \nL 218.723722 181.437048 \nL 215.116449 181.325189 \nL 211.509176 181.213603 \nL 207.901903 181.102285 \nL 204.294631 180.991235 \nL 200.687358 180.88045 \nL 197.080085 180.769928 \nL 193.472812 180.659665 \nL 189.86554 180.549661 \nL 186.258267 180.439913 \nL 183.073742 180.343219 \nL 182.650994 180.329492 \nL 179.043722 180.21237 \nL 175.436449 180.095562 \nL 171.829176 179.979067 \nL 168.221903 179.86288 \nL 164.614631 179.747 \nL 161.007358 179.631424 \nL 157.400085 179.516149 \nL 153.792813 179.401172 \nL 150.18554 179.286491 \nL 146.578267 179.172103 \nL 142.970994 179.058006 \nL 139.363722 178.944196 \nL 135.756449 178.830672 \nL 132.149176 178.717431 \nL 128.541903 178.604471 \nL 124.934631 178.491788 \nL 121.327358 178.379382 \nL 117.720085 178.267248 \nL 114.112812 178.155386 \nL 110.50554 178.043793 \nL 106.898267 177.932465 \nL 103.290994 177.821402 \nL 99.683722 177.710601 \nL 97.878983 177.655219 \nL 96.076449 177.596068 \nL 92.469176 177.47784 \nL 88.861903 177.359933 \nL 85.254631 177.242345 \nL 81.647358 177.125072 \nL 78.040085 177.008112 \nL 74.432812 176.891463 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #453882; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 100.083431 \nL 78.040085 100.195867 \nL 81.647358 100.308019 \nL 85.254631 100.419889 \nL 88.861903 100.53148 \nL 92.469176 100.642794 \nL 96.076449 100.753834 \nL 99.683722 100.864601 \nL 103.290994 100.975099 \nL 106.898267 101.08533 \nL 110.50554 101.195295 \nL 114.112812 101.304999 \nL 117.720085 101.414442 \nL 121.327358 101.523626 \nL 124.934631 101.632555 \nL 128.541903 101.741231 \nL 132.149176 101.849655 \nL 135.756449 101.957829 \nL 139.363722 102.065757 \nL 142.970994 102.173439 \nL 146.578267 102.280878 \nL 150.18554 102.388077 \nL 150.291221 102.391219 \nL 153.792812 102.502533 \nL 157.400085 102.616916 \nL 161.007358 102.731001 \nL 164.614631 102.844792 \nL 168.221903 102.95829 \nL 171.829176 103.071498 \nL 175.436449 103.184419 \nL 179.043722 103.297056 \nL 182.650994 103.40941 \nL 186.258267 103.521485 \nL 189.86554 103.633282 \nL 193.472812 103.744805 \nL 197.080085 103.856055 \nL 200.687358 103.967035 \nL 204.294631 104.077748 \nL 207.901903 104.188195 \nL 211.509176 104.298379 \nL 215.116449 104.408303 \nL 218.723722 104.517968 \nL 222.330994 104.627376 \nL 225.938267 104.73653 \nL 229.54554 104.845433 \nL 233.152813 104.954085 \nL 236.760085 105.06249 \nL 237.31669 105.079219 \nL 240.367358 105.17725 \nL 243.974631 105.292913 \nL 247.581903 105.408272 \nL 251.189176 105.523327 \nL 254.796449 105.638083 \nL 258.403722 105.752541 \nL 262.010994 105.866705 \nL 265.618267 105.980577 \nL 269.22554 106.09416 \nL 272.832812 106.207455 \nL 276.440085 106.320467 \nL 280.047358 106.433196 \nL 283.654631 106.545647 \nL 287.261903 106.65782 \nL 290.869176 106.769719 \nL 294.476449 106.881345 \nL 298.083722 106.992702 \nL 301.690994 107.103792 \nL 305.298267 107.214616 \nL 308.90554 107.325177 \nL 312.512812 107.435478 \nL 316.120085 107.54552 \nL 319.727358 107.655305 \nL 323.334631 107.764837 \nL 323.413028 107.767219 \nL 326.941903 107.881834 \nL 330.549176 107.998687 \nL 334.156449 108.115228 \nL 337.763722 108.23146 \nL 341.370994 108.347384 \nL 344.978267 108.463005 \nL 348.58554 108.578324 \nL 352.192813 108.693345 \nL 355.800085 108.808069 \nL 359.407358 108.9225 \nL 363.014631 109.03664 \nL 366.621903 109.150491 \nL 370.229176 109.264057 \nL 373.836449 109.37734 \nL 377.443722 109.490341 \nL 381.050994 109.603064 \nL 384.658267 109.715511 \nL 388.26554 109.827684 \nL 391.872813 109.939586 \nL 395.480085 110.051219 \nL 399.087358 110.162585 \nL 402.694631 110.273687 \nL 406.301903 110.384527 \nL 408.605642 110.455219 \nL 409.909176 110.497994 \nL 413.516449 110.616269 \nL 417.123722 110.734223 \nL 420.730994 110.851857 \nL 424.338267 110.969176 \nL 427.94554 111.086181 \nL 431.552813 111.202876 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #453882; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_18\">\n <path d=\"M 431.552813 201.651897 \nL 427.94554 201.539101 \nL 424.338267 201.426516 \nL 420.730994 201.314141 \nL 417.123722 201.201974 \nL 413.516449 201.090015 \nL 409.909176 200.97826 \nL 406.301903 200.86671 \nL 402.694631 200.755363 \nL 399.087358 200.644218 \nL 395.480085 200.533273 \nL 391.872813 200.422527 \nL 388.26554 200.311979 \nL 384.658267 200.201627 \nL 381.050994 200.09147 \nL 377.443722 199.981508 \nL 373.836449 199.871738 \nL 370.229176 199.76216 \nL 366.621903 199.652772 \nL 363.014631 199.543573 \nL 359.407358 199.434562 \nL 355.800085 199.325737 \nL 352.192813 199.217098 \nL 350.269588 199.159219 \nL 348.58554 199.105967 \nL 344.978267 198.991985 \nL 341.370994 198.878219 \nL 337.763722 198.764668 \nL 334.156449 198.651332 \nL 330.549176 198.538208 \nL 326.941903 198.425295 \nL 323.334631 198.312591 \nL 319.727358 198.200097 \nL 316.120085 198.087809 \nL 312.512812 197.975727 \nL 308.90554 197.863849 \nL 305.298267 197.752174 \nL 301.690994 197.640701 \nL 298.083722 197.529429 \nL 294.476449 197.418355 \nL 290.869176 197.30748 \nL 287.261903 197.196801 \nL 283.654631 197.086317 \nL 280.047358 196.976027 \nL 276.440085 196.865931 \nL 272.832812 196.756026 \nL 269.22554 196.646311 \nL 265.618267 196.536786 \nL 263.456891 196.471219 \nL 262.010994 196.425132 \nL 258.403722 196.310224 \nL 254.796449 196.195537 \nL 251.189176 196.081069 \nL 247.581903 195.966819 \nL 243.974631 195.852785 \nL 240.367358 195.738966 \nL 236.760085 195.625361 \nL 233.152813 195.511969 \nL 229.54554 195.398787 \nL 225.938267 195.285815 \nL 222.330994 195.173051 \nL 218.723722 195.060493 \nL 215.116449 194.948142 \nL 211.509176 194.835994 \nL 207.901903 194.724049 \nL 204.294631 194.612306 \nL 200.687358 194.500763 \nL 197.080085 194.389419 \nL 193.472812 194.278273 \nL 189.86554 194.167323 \nL 186.258267 194.056569 \nL 182.650994 193.946008 \nL 179.043722 193.835641 \nL 177.32927 193.783219 \nL 175.436449 193.722409 \nL 171.829176 193.606623 \nL 168.221903 193.491063 \nL 164.614631 193.375725 \nL 161.007358 193.260609 \nL 157.400085 193.145714 \nL 153.792813 193.031037 \nL 150.18554 192.916577 \nL 146.578267 192.802334 \nL 142.970994 192.688305 \nL 139.363722 192.574489 \nL 135.756449 192.460885 \nL 132.149176 192.347491 \nL 128.541903 192.234307 \nL 124.934631 192.12133 \nL 121.327358 192.00856 \nL 117.720085 191.895994 \nL 114.112812 191.783633 \nL 110.50554 191.671473 \nL 106.898267 191.559515 \nL 103.290994 191.447757 \nL 99.683722 191.336198 \nL 96.076449 191.224836 \nL 92.469176 191.11367 \nL 91.870451 191.095219 \nL 88.861903 190.997804 \nL 85.254631 190.88119 \nL 81.647358 190.764804 \nL 78.040085 190.648645 \nL 74.432812 190.532711 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #355f8d; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 86.442733 \nL 78.040085 86.55556 \nL 81.647358 86.668176 \nL 85.254631 86.780583 \nL 88.861903 86.89278 \nL 92.469176 87.004771 \nL 96.076449 87.116556 \nL 99.683722 87.228136 \nL 103.290994 87.339513 \nL 106.898267 87.450688 \nL 110.50554 87.561663 \nL 114.112812 87.672439 \nL 117.720085 87.783016 \nL 121.327358 87.893397 \nL 124.934631 88.003583 \nL 128.541903 88.113574 \nL 132.149176 88.223373 \nL 135.756449 88.332979 \nL 139.363722 88.442396 \nL 142.970994 88.551623 \nL 146.578267 88.660662 \nL 150.18554 88.769514 \nL 153.792812 88.87818 \nL 156.219834 88.951219 \nL 157.400085 88.988539 \nL 161.007358 89.102553 \nL 164.614631 89.216351 \nL 168.221903 89.329934 \nL 171.829176 89.443302 \nL 175.436449 89.556457 \nL 179.043722 89.669401 \nL 182.650994 89.782135 \nL 186.258267 89.894661 \nL 189.86554 90.006979 \nL 193.472812 90.119092 \nL 197.080085 90.231 \nL 200.687358 90.342705 \nL 204.294631 90.454208 \nL 207.901903 90.56551 \nL 211.509176 90.676613 \nL 215.116449 90.787517 \nL 218.723722 90.898226 \nL 222.330994 91.008738 \nL 225.938267 91.119056 \nL 229.54554 91.229182 \nL 233.152813 91.339115 \nL 236.760085 91.448858 \nL 240.367358 91.558411 \nL 243.031235 91.639219 \nL 243.974631 91.669288 \nL 247.581903 91.784229 \nL 251.189176 91.898949 \nL 254.796449 92.013449 \nL 258.403722 92.127731 \nL 262.010994 92.241797 \nL 265.618267 92.355647 \nL 269.22554 92.469283 \nL 272.832812 92.582707 \nL 276.440085 92.69592 \nL 280.047358 92.808923 \nL 283.654631 92.921718 \nL 287.261903 93.034305 \nL 290.869176 93.146687 \nL 294.476449 93.258865 \nL 298.083722 93.37084 \nL 301.690994 93.482612 \nL 305.298267 93.594185 \nL 308.90554 93.705558 \nL 312.512812 93.816733 \nL 316.120085 93.927712 \nL 319.727358 94.038495 \nL 323.334631 94.149084 \nL 326.941903 94.25948 \nL 329.157356 94.327219 \nL 330.549176 94.371932 \nL 334.156449 94.487751 \nL 337.763722 94.603344 \nL 341.370994 94.718715 \nL 344.978267 94.833863 \nL 348.58554 94.948791 \nL 352.192813 95.0635 \nL 355.800085 95.177991 \nL 359.407358 95.292266 \nL 363.014631 95.406327 \nL 366.621903 95.520174 \nL 370.229176 95.633809 \nL 373.836449 95.747233 \nL 377.443722 95.860448 \nL 381.050994 95.973456 \nL 384.658267 96.086256 \nL 388.26554 96.198852 \nL 391.872813 96.311243 \nL 395.480085 96.423432 \nL 399.087358 96.53542 \nL 402.694631 96.647207 \nL 406.301903 96.758796 \nL 409.909176 96.870187 \nL 413.516449 96.981382 \nL 414.614481 97.015219 \nL 417.123722 97.096465 \nL 420.730994 97.213112 \nL 424.338267 97.329531 \nL 427.94554 97.445724 \nL 431.552813 97.56169 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #355f8d; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_19\">\n <path d=\"M 431.552813 220.096282 \nL 427.94554 219.984232 \nL 424.338267 219.872334 \nL 420.730994 219.760587 \nL 417.123722 219.64899 \nL 413.516449 219.537543 \nL 409.909176 219.426246 \nL 406.301903 219.315096 \nL 402.694631 219.204094 \nL 399.087358 219.093239 \nL 395.480085 218.982531 \nL 391.872813 218.871968 \nL 388.26554 218.761549 \nL 384.658267 218.651275 \nL 381.050994 218.541144 \nL 377.443722 218.431156 \nL 373.836449 218.32131 \nL 370.229176 218.211605 \nL 366.621903 218.102042 \nL 363.014631 217.992618 \nL 362.441063 217.975219 \nL 359.407358 217.879768 \nL 355.800085 217.766401 \nL 352.192813 217.65319 \nL 348.58554 217.540135 \nL 344.978267 217.427236 \nL 341.370994 217.314492 \nL 337.763722 217.201903 \nL 334.156449 217.089466 \nL 330.549176 216.977182 \nL 326.941903 216.865051 \nL 323.334631 216.75307 \nL 319.727358 216.64124 \nL 316.120085 216.529559 \nL 312.512812 216.418028 \nL 308.90554 216.306645 \nL 305.298267 216.195409 \nL 301.690994 216.084321 \nL 298.083722 215.973378 \nL 294.476449 215.862582 \nL 290.869176 215.75193 \nL 287.261903 215.641422 \nL 283.654631 215.531058 \nL 280.047358 215.420836 \nL 276.440085 215.310757 \nL 275.6687 215.287219 \nL 272.832812 215.197467 \nL 269.22554 215.083422 \nL 265.618267 214.969537 \nL 262.010994 214.85581 \nL 258.403722 214.742241 \nL 254.796449 214.628828 \nL 251.189176 214.515573 \nL 247.581903 214.402472 \nL 243.974631 214.289527 \nL 240.367358 214.176735 \nL 236.760085 214.064097 \nL 233.152813 213.951611 \nL 229.54554 213.839277 \nL 225.938267 213.727094 \nL 222.330994 213.615062 \nL 218.723722 213.503179 \nL 215.116449 213.391445 \nL 211.509176 213.27986 \nL 207.901903 213.168421 \nL 204.294631 213.05713 \nL 200.687358 212.945985 \nL 197.080085 212.834986 \nL 193.472812 212.724131 \nL 189.86554 212.613421 \nL 189.402834 212.599219 \nL 186.258267 212.499115 \nL 182.650994 212.384419 \nL 179.043722 212.269885 \nL 175.436449 212.155512 \nL 171.829176 212.041298 \nL 168.221903 211.927243 \nL 164.614631 211.813347 \nL 161.007358 211.699609 \nL 157.400085 211.586027 \nL 153.792812 211.472601 \nL 150.18554 211.35933 \nL 146.578267 211.246214 \nL 142.970994 211.133252 \nL 139.363722 211.020443 \nL 135.756449 210.907786 \nL 132.149176 210.795281 \nL 128.541903 210.682926 \nL 124.934631 210.570722 \nL 121.327358 210.458668 \nL 117.720085 210.346762 \nL 114.112812 210.235004 \nL 110.50554 210.123394 \nL 106.898267 210.01193 \nL 103.635167 209.911219 \nL 103.290994 209.900201 \nL 99.683722 209.784716 \nL 96.076449 209.669396 \nL 92.469176 209.554239 \nL 88.861903 209.439245 \nL 85.254631 209.324413 \nL 81.647358 209.209742 \nL 78.040085 209.095231 \nL 74.432812 208.980879 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #1e9b8a; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 67.998481 \nL 78.040085 68.110554 \nL 81.647358 68.222474 \nL 85.254631 68.334244 \nL 88.861903 68.445863 \nL 92.469176 68.557332 \nL 96.076449 68.668651 \nL 99.683722 68.779823 \nL 103.290994 68.890846 \nL 106.898267 69.001723 \nL 110.50554 69.112454 \nL 114.112812 69.223038 \nL 117.720085 69.333478 \nL 121.327358 69.443774 \nL 124.934631 69.553926 \nL 128.541903 69.663935 \nL 132.149176 69.773802 \nL 135.756449 69.883528 \nL 139.363722 69.993113 \nL 142.970994 70.102557 \nL 144.047715 70.135219 \nL 146.578267 70.214837 \nL 150.18554 70.328228 \nL 153.792812 70.441462 \nL 157.400085 70.554539 \nL 161.007358 70.667461 \nL 164.614631 70.780228 \nL 168.221903 70.892841 \nL 171.829176 71.0053 \nL 175.436449 71.117606 \nL 179.043722 71.229761 \nL 182.650994 71.341764 \nL 186.258267 71.453616 \nL 189.86554 71.565319 \nL 193.472812 71.676872 \nL 197.080085 71.788277 \nL 200.687358 71.899534 \nL 204.294631 72.010645 \nL 207.901903 72.121609 \nL 211.509176 72.232427 \nL 215.116449 72.3431 \nL 218.723722 72.453629 \nL 222.330994 72.564015 \nL 225.938267 72.674257 \nL 229.54554 72.784358 \nL 230.819115 72.823219 \nL 233.152813 72.897076 \nL 236.760085 73.011144 \nL 240.367358 73.125053 \nL 243.974631 73.238803 \nL 247.581903 73.352396 \nL 251.189176 73.465831 \nL 254.796449 73.57911 \nL 258.403722 73.692233 \nL 262.010994 73.805201 \nL 265.618267 73.918016 \nL 269.22554 74.030677 \nL 272.832812 74.143185 \nL 276.440085 74.255541 \nL 280.047358 74.367746 \nL 283.654631 74.479801 \nL 287.261903 74.591706 \nL 290.869176 74.703462 \nL 294.476449 74.815069 \nL 298.083722 74.926529 \nL 301.690994 75.037842 \nL 305.298267 75.149008 \nL 308.90554 75.260029 \nL 312.512812 75.370905 \nL 316.120085 75.481637 \nL 317.083907 75.511219 \nL 319.727358 75.595369 \nL 323.334631 75.710088 \nL 326.941903 75.824646 \nL 330.549176 75.939043 \nL 334.156449 76.05328 \nL 337.763722 76.167358 \nL 341.370994 76.281278 \nL 344.978267 76.395039 \nL 348.58554 76.508644 \nL 352.192813 76.622093 \nL 355.800085 76.735387 \nL 359.407358 76.848525 \nL 363.014631 76.96151 \nL 366.621903 77.074342 \nL 370.229176 77.187021 \nL 373.836449 77.299548 \nL 377.443722 77.411925 \nL 381.050994 77.524151 \nL 384.658267 77.636228 \nL 388.26554 77.748155 \nL 391.872813 77.859935 \nL 395.480085 77.971567 \nL 399.087358 78.083052 \nL 402.694631 78.194391 \nL 402.851016 78.199219 \nL 406.301903 78.309712 \nL 409.909176 78.425056 \nL 413.516449 78.540237 \nL 417.123722 78.655255 \nL 420.730994 78.770111 \nL 424.338267 78.884806 \nL 427.94554 78.99934 \nL 431.552813 79.113715 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #1e9b8a; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_20\">\n <path d=\"M 431.552813 245.071342 \nL 427.94554 244.961449 \nL 424.455305 244.855219 \nL 424.338267 244.851559 \nL 420.730994 244.738747 \nL 417.123722 244.626049 \nL 413.516449 244.513465 \nL 409.909176 244.400995 \nL 406.301903 244.288638 \nL 402.694631 244.176394 \nL 399.087358 244.064262 \nL 395.480085 243.952242 \nL 391.872813 243.840334 \nL 388.26554 243.728537 \nL 384.658267 243.61685 \nL 381.050994 243.505275 \nL 377.443722 243.393809 \nL 373.836449 243.282453 \nL 370.229176 243.171206 \nL 366.621903 243.060068 \nL 363.014631 242.949038 \nL 359.407358 242.838117 \nL 355.800085 242.727303 \nL 352.192813 242.616597 \nL 348.58554 242.505998 \nL 344.978267 242.395505 \nL 341.370994 242.285119 \nL 337.763722 242.174838 \nL 337.514517 242.167219 \nL 334.156449 242.061738 \nL 330.549176 241.948537 \nL 326.941903 241.83545 \nL 323.334631 241.722478 \nL 319.727358 241.60962 \nL 316.120085 241.496877 \nL 312.512812 241.384247 \nL 308.90554 241.27173 \nL 305.298267 241.159326 \nL 301.690994 241.047035 \nL 298.083722 240.934855 \nL 294.476449 240.822787 \nL 290.869176 240.71083 \nL 287.261903 240.598984 \nL 283.654631 240.487248 \nL 280.047358 240.375622 \nL 276.440085 240.264106 \nL 272.832812 240.152699 \nL 269.22554 240.041401 \nL 265.618267 239.930212 \nL 262.010994 239.81913 \nL 258.403722 239.708157 \nL 254.796449 239.59729 \nL 251.189176 239.486531 \nL 250.951053 239.479219 \nL 247.581903 239.372931 \nL 243.974631 239.259239 \nL 240.367358 239.145664 \nL 236.760085 239.032205 \nL 233.152813 238.918861 \nL 229.54554 238.805632 \nL 225.938267 238.692518 \nL 222.330994 238.579518 \nL 218.723722 238.466632 \nL 215.116449 238.353859 \nL 211.509176 238.2412 \nL 207.901903 238.128653 \nL 204.294631 238.016219 \nL 200.687358 237.903896 \nL 197.080085 237.791685 \nL 193.472812 237.679586 \nL 189.86554 237.567597 \nL 186.258267 237.455718 \nL 182.650994 237.343949 \nL 179.043722 237.23229 \nL 175.436449 237.12074 \nL 171.829176 237.009299 \nL 168.221903 236.897966 \nL 164.760015 236.791219 \nL 164.614631 236.786613 \nL 161.007358 236.672328 \nL 157.400085 236.55816 \nL 153.792812 236.44411 \nL 150.18554 236.330177 \nL 146.578267 236.21636 \nL 142.970994 236.10266 \nL 139.363722 235.989076 \nL 135.756449 235.875607 \nL 132.149176 235.762253 \nL 128.541903 235.649013 \nL 124.934631 235.535888 \nL 121.327358 235.422876 \nL 117.720085 235.309978 \nL 114.112812 235.197193 \nL 110.50554 235.084521 \nL 106.898267 234.971961 \nL 103.290994 234.859512 \nL 99.683722 234.747175 \nL 96.076449 234.634949 \nL 92.469176 234.522833 \nL 88.861903 234.410828 \nL 85.254631 234.298933 \nL 81.647358 234.187147 \nL 78.93717 234.103219 \nL 78.040085 234.074678 \nL 74.432812 233.95993 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #fde725; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 43.023743 \nL 78.040085 43.133652 \nL 81.647358 43.243456 \nL 82.03377 43.255219 \nL 85.254631 43.355949 \nL 88.861903 43.468664 \nL 92.469176 43.581264 \nL 96.076449 43.693751 \nL 99.683722 43.806125 \nL 103.290994 43.918386 \nL 106.898267 44.030534 \nL 110.50554 44.142571 \nL 114.112812 44.254496 \nL 117.720085 44.366309 \nL 121.327358 44.478012 \nL 124.934631 44.589604 \nL 128.541903 44.701086 \nL 132.149176 44.812458 \nL 135.756449 44.923721 \nL 139.363722 45.034875 \nL 142.970994 45.145921 \nL 146.578267 45.256858 \nL 150.18554 45.367688 \nL 153.792812 45.47841 \nL 157.400085 45.589025 \nL 161.007358 45.699534 \nL 164.614631 45.809936 \nL 168.221903 45.920232 \nL 168.973716 45.943219 \nL 171.829176 46.03291 \nL 175.436449 46.146129 \nL 179.043722 46.259233 \nL 182.650994 46.372222 \nL 186.258267 46.485096 \nL 189.86554 46.597857 \nL 193.472812 46.710503 \nL 197.080085 46.823037 \nL 200.687358 46.935457 \nL 204.294631 47.047766 \nL 207.901903 47.159962 \nL 211.509176 47.272047 \nL 215.116449 47.38402 \nL 218.723722 47.495882 \nL 222.330994 47.607634 \nL 225.938267 47.719276 \nL 229.54554 47.830809 \nL 233.152813 47.942232 \nL 236.760085 48.053546 \nL 240.367358 48.164751 \nL 243.974631 48.275849 \nL 247.581903 48.386838 \nL 251.189176 48.49772 \nL 254.796449 48.608496 \nL 255.536434 48.631219 \nL 258.403722 48.721673 \nL 262.010994 48.835382 \nL 265.618267 48.948974 \nL 269.22554 49.062451 \nL 272.832813 49.175812 \nL 276.440085 49.289058 \nL 280.047358 49.402189 \nL 283.654631 49.515205 \nL 287.261903 49.628108 \nL 290.869176 49.740897 \nL 294.476449 49.853573 \nL 298.083722 49.966137 \nL 301.690994 50.078587 \nL 305.298267 50.190926 \nL 308.90554 50.303154 \nL 312.512812 50.41527 \nL 316.120085 50.527275 \nL 319.727358 50.63917 \nL 323.334631 50.750955 \nL 326.941903 50.862631 \nL 330.549176 50.974197 \nL 334.156449 51.085654 \nL 337.763722 51.197003 \nL 341.370994 51.308244 \nL 341.726863 51.319219 \nL 344.978267 51.422233 \nL 348.58554 51.536418 \nL 352.192813 51.650486 \nL 355.800085 51.764436 \nL 359.407358 51.87827 \nL 363.014631 51.991987 \nL 366.621903 52.105588 \nL 370.229176 52.219074 \nL 373.836449 52.332445 \nL 377.443722 52.445702 \nL 381.050994 52.558844 \nL 384.658267 52.671872 \nL 388.26554 52.784787 \nL 391.872813 52.897588 \nL 395.480085 53.010277 \nL 399.087358 53.122854 \nL 402.694631 53.235319 \nL 406.301903 53.347673 \nL 409.909176 53.459915 \nL 413.516449 53.572047 \nL 417.123722 53.684068 \nL 420.730994 53.79598 \nL 424.338267 53.907782 \nL 427.54932 54.007219 \nL 427.94554 54.019824 \nL 431.552813 54.13459 \n\" clip-path=\"url(#p145acf6924)\" style=\"fill: none; stroke: #fde725; stroke-width: 1.5\"/>\n </g>\n <g id=\"patch_3\">\n <path d=\"M 74.432812 277.111219 \nL 74.432812 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_4\">\n <path d=\"M 431.552813 277.111219 \nL 431.552813 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_5\">\n <path d=\"M 74.432812 277.111219 \nL 431.552813 277.111219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_6\">\n <path d=\"M 74.432812 10.999219 \nL 431.552813 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n </g>\n </g>\n <defs>\n <clipPath id=\"p145acf6924\">\n <rect x=\"74.432812\" y=\"10.999219\" width=\"357.12\" height=\"266.112\"/>\n </clipPath>\n </defs>\n</svg>\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"contour_plot(XMx2, yMx2, rescale=10**10)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Jeżeli funkcja kosztu ma kształt taki, jak na powyższym wykresie, to łatwo sobie wyobrazić, że znalezienie minimum lokalnego przy użyciu metody gradientu prostego musi stanowć nie lada wyzwanie: algorytm szybko znajdzie „rynnę”, ale „zjazd” wzdłuż „rynny” w poszukiwaniu minimum będzie odbywał się bardzo powoli.\n",
"\n",
"Jak temu zaradzić?\n",
"\n",
"Spróbujemy przekształcić dane tak, żeby funkcja kosztu miała „ładny”, regularny kształt."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Skalowanie"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Będziemy dążyć do tego, żeby każda z cech przyjmowała wartości w podobnym zakresie.\n",
"\n",
"W tym celu przeskalujemy wartości każdej z cech, dzieląc je przez wartość maksymalną:\n",
"\n",
"$$ \\hat{x_i}^{(j)} := \\frac{x_i^{(j)}}{\\max_j x_i^{(j)}} $$"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 1.00 \\leq x_0 \\leq 1.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle 0.29 \\leq x_1 \\leq 1.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle 0.06 \\leq x_2 \\leq 1.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"XMx2_scaled = XMx2 / np.amax(XMx2, axis=0)\n",
"\n",
"show_mins_and_maxs(XMx2_scaled)\n"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"457.840312pt\" height=\"314.667469pt\" viewBox=\"0 0 457.840312 314.667469\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n <cc:Work>\n <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n <dc:date>2022-10-14T11:23:02.698988</dc:date>\n <dc:format>image/svg+xml</dc:format>\n <dc:creator>\n <cc:Agent>\n <dc:title>Matplotlib v3.6.1, https://matplotlib.org/</dc:title>\n </cc:Agent>\n </dc:creator>\n </cc:Work>\n </rdf:RDF>\n </metadata>\n <defs>\n <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n <g id=\"patch_1\">\n <path d=\"M 0 314.667469 \nL 457.840312 314.667469 \nL 457.840312 0 \nL 0 0 \nz\n\" style=\"fill: #ffffff\"/>\n </g>\n <g id=\"axes_1\">\n <g id=\"patch_2\">\n <path d=\"M 74.432812 277.111219 \nL 431.552813 277.111219 \nL 431.552813 10.999219 \nL 74.432812 10.999219 \nz\n\" style=\"fill: #ffffff\"/>\n </g>\n <g id=\"matplotlib.axis_1\">\n <g id=\"xtick_1\">\n <g id=\"line2d_1\">\n <defs>\n <path id=\"m68d512d3be\" d=\"M 0 0 \nL 0 3.5 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </defs>\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"74.432812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_1\">\n <!-- −100000 -->\n <g transform=\"translate(51.155469 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-2212\" d=\"M 678 2272 \nL 4684 2272 \nL 4684 1741 \nL 678 1741 \nL 678 2272 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-31\" d=\"M 794 531 \nL 1825 531 \nL 1825 4091 \nL 703 3866 \nL 703 4441 \nL 1819 4666 \nL 2450 4666 \nL 2450 531 \nL 3481 531 \nL 3481 0 \nL 794 0 \nL 794 531 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \nQ 1547 4250 1301 3770 \nQ 1056 3291 1056 2328 \nQ 1056 1369 1301 889 \nQ 1547 409 2034 409 \nQ 2525 409 2770 889 \nQ 3016 1369 3016 2328 \nQ 3016 3291 2770 3770 \nQ 2525 4250 2034 4250 \nz\nM 2034 4750 \nQ 2819 4750 3233 4129 \nQ 3647 3509 3647 2328 \nQ 3647 1150 3233 529 \nQ 2819 -91 2034 -91 \nQ 1250 -91 836 529 \nQ 422 1150 422 2328 \nQ 422 3509 836 4129 \nQ 1250 4750 2034 4750 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"401.904297\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_2\">\n <g id=\"line2d_2\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"119.072812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_2\">\n <!-- −75000 -->\n <g transform=\"translate(98.976719 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-37\" d=\"M 525 4666 \nL 3525 4666 \nL 3525 4397 \nL 1831 0 \nL 1172 0 \nL 2766 4134 \nL 525 4134 \nL 525 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-35\" d=\"M 691 4666 \nL 3169 4666 \nL 3169 4134 \nL 1269 4134 \nL 1269 2991 \nQ 1406 3038 1543 3061 \nQ 1681 3084 1819 3084 \nQ 2600 3084 3056 2656 \nQ 3513 2228 3513 1497 \nQ 3513 744 3044 326 \nQ 2575 -91 1722 -91 \nQ 1428 -91 1123 -41 \nQ 819 9 494 109 \nL 494 744 \nQ 775 591 1075 516 \nQ 1375 441 1709 441 \nQ 2250 441 2565 725 \nQ 2881 1009 2881 1497 \nQ 2881 1984 2565 2268 \nQ 2250 2553 1709 2553 \nQ 1456 2553 1204 2497 \nQ 953 2441 691 2322 \nL 691 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_3\">\n <g id=\"line2d_3\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"163.712812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_3\">\n <!-- −50000 -->\n <g transform=\"translate(143.616719 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_4\">\n <g id=\"line2d_4\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"208.352812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_4\">\n <!-- −25000 -->\n <g transform=\"translate(188.256719 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-32\" d=\"M 1228 531 \nL 3431 531 \nL 3431 0 \nL 469 0 \nL 469 531 \nQ 828 903 1448 1529 \nQ 2069 2156 2228 2338 \nQ 2531 2678 2651 2914 \nQ 2772 3150 2772 3378 \nQ 2772 3750 2511 3984 \nQ 2250 4219 1831 4219 \nQ 1534 4219 1204 4116 \nQ 875 4013 500 3803 \nL 500 4441 \nQ 881 4594 1212 4672 \nQ 1544 4750 1819 4750 \nQ 2544 4750 2975 4387 \nQ 3406 4025 3406 3419 \nQ 3406 3131 3298 2873 \nQ 3191 2616 2906 2266 \nQ 2828 2175 2409 1742 \nQ 1991 1309 1228 531 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_5\">\n <g id=\"line2d_5\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"252.992813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_5\">\n <!-- 0 -->\n <g transform=\"translate(249.811563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-30\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_6\">\n <g id=\"line2d_6\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"297.632812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_6\">\n <!-- 25000 -->\n <g transform=\"translate(281.726562 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-32\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_7\">\n <g id=\"line2d_7\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"342.272813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_7\">\n <!-- 50000 -->\n <g transform=\"translate(326.366563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-35\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_8\">\n <g id=\"line2d_8\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"386.912813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_8\">\n <!-- 75000 -->\n <g transform=\"translate(371.006563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-37\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_9\">\n <g id=\"line2d_9\">\n <g>\n <use xlink:href=\"#m68d512d3be\" x=\"431.552813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_9\">\n <!-- 100000 -->\n <g transform=\"translate(412.465313 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-31\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"318.115234\"/>\n </g>\n </g>\n </g>\n <g id=\"text_10\">\n <!-- $\\theta_1$ -->\n <g transform=\"translate(247.542813 305.387781) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-Oblique-3b8\" d=\"M 2913 2219 \nL 925 2219 \nQ 791 1284 928 888 \nQ 1100 400 1566 400 \nQ 2034 400 2391 891 \nQ 2703 1322 2913 2219 \nz\nM 3009 2750 \nQ 3094 3638 2984 3950 \nQ 2813 4444 2353 4444 \nQ 1875 4444 1525 3956 \nQ 1250 3563 1034 2750 \nL 3009 2750 \nz\nM 2444 4913 \nQ 3194 4913 3494 4250 \nQ 3794 3591 3566 2422 \nQ 3341 1256 2781 594 \nQ 2225 -72 1475 -72 \nQ 722 -72 425 594 \nQ 128 1256 353 2422 \nQ 581 3591 1134 4250 \nQ 1691 4913 2444 4913 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-Oblique-3b8\" transform=\"translate(0 0.234375)\"/>\n <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(61.181641 -16.171875) scale(0.7)\"/>\n </g>\n </g>\n </g>\n <g id=\"matplotlib.axis_2\">\n <g id=\"ytick_1\">\n <g id=\"line2d_10\">\n <defs>\n <path id=\"m51eecf25d4\" d=\"M 0 0 \nL -3.5 0 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </defs>\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_11\">\n <!-- −100000 -->\n <g transform=\"translate(20.878125 280.910437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"401.904297\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_2\">\n <g id=\"line2d_11\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"243.847219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_12\">\n <!-- −75000 -->\n <g transform=\"translate(27.240625 247.646437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_3\">\n <g id=\"line2d_12\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"210.583219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_13\">\n <!-- −50000 -->\n <g transform=\"translate(27.240625 214.382437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_4\">\n <g id=\"line2d_13\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"177.319219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_14\">\n <!-- −25000 -->\n <g transform=\"translate(27.240625 181.118437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_5\">\n <g id=\"line2d_14\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"144.055219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_15\">\n <!-- 0 -->\n <g transform=\"translate(61.070312 147.854437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-30\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_6\">\n <g id=\"line2d_15\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"110.791219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_16\">\n <!-- 25000 -->\n <g transform=\"translate(35.620312 114.590437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-32\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_7\">\n <g id=\"line2d_16\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"77.527219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_17\">\n <!-- 50000 -->\n <g transform=\"translate(35.620312 81.326437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-35\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_8\">\n <g id=\"line2d_17\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"44.263219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_18\">\n <!-- 75000 -->\n <g transform=\"translate(35.620312 48.062437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-37\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_9\">\n <g id=\"line2d_18\">\n <g>\n <use xlink:href=\"#m51eecf25d4\" x=\"74.432812\" y=\"10.999219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_19\">\n <!-- 100000 -->\n <g transform=\"translate(29.257812 14.798437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-31\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"318.115234\"/>\n </g>\n </g>\n </g>\n <g id=\"text_20\">\n <!-- $\\theta_2$ -->\n <g transform=\"translate(14.798437 149.505219) rotate(-90) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-Oblique-3b8\" transform=\"translate(0 0.234375)\"/>\n <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(61.181641 -16.171875) scale(0.7)\"/>\n </g>\n </g>\n </g>\n <g id=\"PathCollection_1\">\n <path d=\"M 269.22554 159.345211 \nL 268.189954 158.839219 \nL 265.618267 157.726598 \nL 263.14934 156.151219 \nL 262.010994 155.499505 \nL 259.320475 153.463219 \nL 258.403722 152.834043 \nL 255.991394 150.775219 \nL 254.796449 149.842318 \nL 252.916539 148.087219 \nL 251.189176 146.601214 \nL 249.98858 145.399219 \nL 247.581903 143.165215 \nL 247.153153 142.711219 \nL 244.679292 140.023219 \nL 243.974631 139.273074 \nL 242.446211 137.335219 \nL 240.367358 134.967851 \nL 240.124715 134.647219 \nL 238.622177 131.959219 \nL 237.27358 129.271219 \nL 240.367358 128.222611 \nL 242.312872 129.271219 \nL 243.974631 130.066337 \nL 246.758935 131.959219 \nL 247.581903 132.462236 \nL 250.339815 134.647219 \nL 251.189176 135.258442 \nL 253.538293 137.335219 \nL 254.796449 138.354104 \nL 256.534288 140.023219 \nL 258.403722 141.679622 \nL 259.410151 142.711219 \nL 262.010994 145.185417 \nL 262.208909 145.399219 \nL 264.489114 148.087219 \nL 265.618267 149.326463 \nL 266.735413 150.775219 \nL 268.890803 153.463219 \nL 269.22554 153.997057 \nL 270.284866 156.151219 \nL 270.461432 158.839219 \nL 269.22554 159.345211 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_2\">\n <path d=\"M 272.832812 164.553243 \nL 272.23375 164.215219 \nL 269.22554 162.642259 \nL 267.521588 161.527219 \nL 265.618267 160.366787 \nL 263.532001 158.839219 \nL 262.010994 157.79674 \nL 259.954269 156.151219 \nL 258.403722 154.985224 \nL 256.633493 153.463219 \nL 254.796449 151.973303 \nL 253.483794 150.775219 \nL 251.189176 148.793232 \nL 250.45373 148.087219 \nL 247.581903 145.470693 \nL 247.510602 145.399219 \nL 244.946828 142.711219 \nL 243.974631 141.751659 \nL 242.415741 140.023219 \nL 240.367358 137.896422 \nL 239.880331 137.335219 \nL 237.652931 134.647219 \nL 236.760085 133.576425 \nL 235.575371 131.959219 \nL 233.569496 129.271219 \nL 233.152813 128.592942 \nL 232.112161 126.583219 \nL 231.256476 123.895219 \nL 233.152813 121.883387 \nL 236.760085 123.157858 \nL 238.000818 123.895219 \nL 240.367358 125.199854 \nL 242.398444 126.583219 \nL 243.974631 127.584302 \nL 246.205466 129.271219 \nL 247.581903 130.246252 \nL 249.66638 131.959219 \nL 251.189176 133.136201 \nL 252.907093 134.647219 \nL 254.796449 136.21576 \nL 255.999045 137.335219 \nL 258.403722 139.4547 \nL 258.985791 140.023219 \nL 261.834733 142.711219 \nL 262.010994 142.878897 \nL 264.344032 145.399219 \nL 265.618267 146.683407 \nL 266.862638 148.087219 \nL 269.22554 150.585307 \nL 269.387862 150.775219 \nL 271.446184 153.463219 \nL 272.832812 155.160587 \nL 273.546943 156.151219 \nL 275.263933 158.839219 \nL 276.440085 160.791786 \nL 276.816317 161.527219 \nL 277.174365 164.215219 \nL 276.440085 165.080393 \nL 272.832812 164.553243 \nz\n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_3\">\n <path d=\"M 280.047358 172.354731 \nL 279.90361 172.279219 \nL 276.440085 170.563471 \nL 274.813099 169.591219 \nL 272.832812 168.471635 \nL 270.463809 166.903219 \nL 269.22554 166.125347 \nL 266.572363 164.215219 \nL 265.618267 163.561752 \nL 262.983507 161.527219 \nL 262.010994 160.811102 \nL 259.605053 158.839219 \nL 258.403722 157.898283 \nL 256.378811 156.151219 \nL 254.796449 154.843951 \nL 253.266235 153.463219 \nL 251.189176 151.6654 \nL 250.240783 150.775219 \nL 247.581903 148.377216 \nL 247.283579 148.087219 \nL 244.524069 145.399219 \nL 243.974631 144.875131 \nL 241.895468 142.711219 \nL 240.367358 141.194313 \nL 239.278528 140.023219 \nL 236.760085 137.43414 \nL 236.670748 137.335219 \nL 234.390043 134.647219 \nL 233.152813 133.257206 \nL 232.092927 131.959219 \nL 229.845299 129.271219 \nL 229.54554 128.883923 \nL 227.938813 126.583219 \nL 225.938267 123.925858 \nL 225.917253 123.895219 \nL 224.492655 121.207219 \nL 223.191365 118.519219 \nL 222.418103 115.831219 \nL 225.938267 114.143778 \nL 229.54554 115.323102 \nL 230.471513 115.831219 \nL 233.152813 117.219551 \nL 235.252553 118.519219 \nL 236.760085 119.402503 \nL 239.407487 121.207219 \nL 240.367358 121.828387 \nL 243.16771 123.895219 \nL 243.974631 124.462042 \nL 246.6631 126.583219 \nL 247.581903 127.27478 \nL 249.972186 129.271219 \nL 251.189176 130.242962 \nL 253.14524 131.959219 \nL 254.796449 133.346934 \nL 256.215942 134.647219 \nL 258.403722 136.570222 \nL 259.207701 137.335219 \nL 262.010994 139.898911 \nL 262.137291 140.023219 \nL 264.810145 142.711219 \nL 265.618267 143.494326 \nL 267.423499 145.399219 \nL 269.22554 147.213589 \nL 270.027731 148.087219 \nL 272.547155 150.775219 \nL 272.832812 151.089662 \nL 274.799541 153.463219 \nL 276.440085 155.332558 \nL 277.100495 156.151219 \nL 279.191465 158.839219 \nL 280.047358 159.961925 \nL 281.12707 161.527219 \nL 282.924299 164.215219 \nL 283.654631 165.451781 \nL 284.412597 166.903219 \nL 285.356442 169.591219 \nL 285.112497 172.279219 \nL 283.654631 173.064215 \nL 280.047358 172.354731 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_4\">\n <path d=\"M 290.869176 183.158192 \nL 290.577169 183.031219 \nL 287.261903 181.660097 \nL 284.634692 180.343219 \nL 283.654631 179.874859 \nL 280.047358 177.802166 \nL 279.827849 177.655219 \nL 276.440085 175.464547 \nL 275.737361 174.967219 \nL 272.832812 172.979313 \nL 271.891158 172.279219 \nL 269.22554 170.36058 \nL 268.235309 169.591219 \nL 265.618267 167.620721 \nL 264.730666 166.903219 \nL 262.010994 164.770624 \nL 261.348131 164.215219 \nL 258.403722 161.819914 \nL 258.065618 161.527219 \nL 254.885713 158.839219 \nL 254.796449 158.764666 \nL 251.879924 156.151219 \nL 251.189176 155.552572 \nL 248.931759 153.463219 \nL 247.581903 152.253571 \nL 246.030878 150.775219 \nL 243.974631 148.875696 \nL 243.169273 148.087219 \nL 240.367358 145.426017 \nL 240.34065 145.399219 \nL 237.730478 142.711219 \nL 236.760085 141.745103 \nL 235.133237 140.023219 \nL 233.152813 137.998036 \nL 232.540961 137.335219 \nL 230.058129 134.647219 \nL 229.54554 134.088399 \nL 227.71475 131.959219 \nL 225.938267 129.973772 \nL 225.346684 129.271219 \nL 223.130108 126.583219 \nL 222.330994 125.607923 \nL 221.020579 123.895219 \nL 218.897829 121.207219 \nL 218.723722 120.965707 \nL 217.093291 118.519219 \nL 215.208685 115.831219 \nL 215.116449 115.674067 \nL 213.761744 113.143219 \nL 212.421489 110.455219 \nL 211.509176 108.139266 \nL 211.378054 107.767219 \nL 211.300374 105.079219 \nL 211.509176 104.65279 \nL 215.116449 103.484619 \nL 218.723722 104.413874 \nL 220.184078 105.079219 \nL 222.330994 106.009965 \nL 225.707449 107.767219 \nL 225.938267 107.881795 \nL 229.54554 110.088544 \nL 230.082972 110.455219 \nL 233.152813 112.478797 \nL 234.075766 113.143219 \nL 236.760085 115.012364 \nL 237.844604 115.831219 \nL 240.367358 117.675618 \nL 241.437967 118.519219 \nL 243.974631 120.456603 \nL 244.891285 121.207219 \nL 247.581903 123.344792 \nL 248.23105 123.895219 \nL 251.189176 126.330875 \nL 251.47747 126.583219 \nL 254.604658 129.271219 \nL 254.796449 129.433584 \nL 257.580766 131.959219 \nL 258.403722 132.681351 \nL 260.503937 134.647219 \nL 262.010994 136.013283 \nL 263.38352 137.335219 \nL 265.618267 139.421645 \nL 266.226785 140.023219 \nL 268.991829 142.711219 \nL 269.22554 142.939775 \nL 271.584418 145.399219 \nL 272.832812 146.655527 \nL 274.172374 148.087219 \nL 276.440085 150.429366 \nL 276.756464 150.775219 \nL 279.157038 153.463219 \nL 280.047358 154.444312 \nL 281.500996 156.151219 \nL 283.654631 158.582131 \nL 283.869188 158.839219 \nL 285.987246 161.527219 \nL 287.261903 163.099297 \nL 288.107861 164.215219 \nL 290.099316 166.903219 \nL 290.869176 167.982648 \nL 291.93148 169.591219 \nL 293.639771 172.279219 \nL 294.476449 173.718596 \nL 295.139866 174.967219 \nL 296.242628 177.655219 \nL 296.916962 180.343219 \nL 295.942617 183.031219 \nL 294.476449 183.66478 \nL 290.869176 183.158192 \nz\n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_5\">\n <path d=\"M 305.298267 197.536201 \nL 301.762126 196.471219 \nL 301.690994 196.450754 \nL 298.083722 194.807335 \nL 296.107369 193.783219 \nL 294.476449 192.966012 \nL 291.137588 191.095219 \nL 290.869176 190.949633 \nL 287.261903 188.717637 \nL 286.800672 188.407219 \nL 283.654631 186.3439 \nL 282.764284 185.719219 \nL 280.047358 183.860412 \nL 278.90959 183.031219 \nL 276.440085 181.275166 \nL 275.205134 180.343219 \nL 272.832812 178.595398 \nL 271.626327 177.655219 \nL 269.22554 175.827673 \nL 268.153667 174.967219 \nL 265.618267 172.977964 \nL 264.77149 172.279219 \nL 262.010994 170.051713 \nL 261.46707 169.591219 \nL 258.403722 167.053891 \nL 258.229959 166.903219 \nL 255.102236 164.215219 \nL 254.796449 163.95667 \nL 252.063576 161.527219 \nL 251.189176 160.768286 \nL 249.070187 158.839219 \nL 247.581903 157.515634 \nL 246.116022 156.151219 \nL 243.974631 154.203067 \nL 243.196063 153.463219 \nL 240.367358 150.834555 \nL 240.306117 150.775219 \nL 237.565022 148.087219 \nL 236.760085 147.315132 \nL 234.851081 145.399219 \nL 233.152813 143.736002 \nL 232.150792 142.711219 \nL 229.54554 140.109668 \nL 229.462488 140.023219 \nL 226.93563 137.335219 \nL 225.938267 136.29807 \nL 224.420625 134.647219 \nL 222.330994 132.433274 \nL 221.902422 131.959219 \nL 219.503518 129.271219 \nL 218.723722 128.402112 \nL 217.166441 126.583219 \nL 215.116449 124.258144 \nL 214.810468 123.895219 \nL 212.617936 121.207219 \nL 211.509176 119.866883 \nL 210.4475 118.519219 \nL 208.315012 115.831219 \nL 207.901903 115.288732 \nL 206.35359 113.143219 \nL 204.342553 110.455219 \nL 204.294631 110.384812 \nL 202.616339 107.767219 \nL 200.829655 105.079219 \nL 200.687358 104.833341 \nL 199.366008 102.391219 \nL 197.982723 99.703219 \nL 197.080085 97.680718 \nL 196.805084 97.015219 \nL 196.153532 94.327219 \nL 196.161785 91.639219 \nL 197.080085 89.986539 \nL 200.687358 89.050381 \nL 204.294631 89.876947 \nL 207.901903 91.182174 \nL 208.84005 91.639219 \nL 211.509176 92.895415 \nL 214.202903 94.327219 \nL 215.116449 94.796855 \nL 218.723722 96.891741 \nL 218.912867 97.015219 \nL 222.330994 99.188471 \nL 223.085143 99.703219 \nL 225.938267 101.60116 \nL 227.049806 102.391219 \nL 229.54554 104.121189 \nL 230.844376 105.079219 \nL 233.152813 106.740774 \nL 234.497847 107.767219 \nL 236.760085 109.452865 \nL 238.032978 110.455219 \nL 240.367358 112.251063 \nL 241.467883 113.143219 \nL 243.974631 115.129545 \nL 244.817157 115.831219 \nL 247.581903 118.083002 \nL 248.092695 118.519219 \nL 251.189176 121.106584 \nL 251.304284 121.207219 \nL 254.394058 123.895219 \nL 254.796449 124.238703 \nL 257.410543 126.583219 \nL 258.403722 127.452995 \nL 260.384362 129.271219 \nL 262.010994 130.730102 \nL 263.321146 131.959219 \nL 265.618267 134.065785 \nL 266.225577 134.647219 \nL 269.078577 137.335219 \nL 269.22554 137.474253 \nL 271.796585 140.023219 \nL 272.832812 141.025211 \nL 274.500149 142.711219 \nL 276.440085 144.625663 \nL 277.191086 145.399219 \nL 279.838383 148.087219 \nL 280.047358 148.301947 \nL 282.344896 150.775219 \nL 283.654631 152.14767 \nL 284.855449 153.463219 \nL 287.261903 156.031358 \nL 287.369535 156.151219 \nL 289.706661 158.839219 \nL 290.869176 160.144793 \nL 292.044467 161.527219 \nL 294.385688 164.215219 \nL 294.476449 164.323948 \nL 296.523144 166.903219 \nL 298.083722 168.803921 \nL 298.69971 169.591219 \nL 300.745637 172.279219 \nL 301.690994 173.530229 \nL 302.720849 174.967219 \nL 304.624847 177.655219 \nL 305.298267 178.65217 \nL 306.375283 180.343219 \nL 308.029148 183.031219 \nL 308.90554 184.555954 \nL 309.5314 185.719219 \nL 310.749758 188.407219 \nL 311.77997 191.095219 \nL 312.391346 193.783219 \nL 311.715388 196.471219 \nL 308.90554 197.918724 \nL 305.298267 197.536201 \nz\n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_6\">\n <path d=\"M 319.727358 215.61981 \nL 318.933657 215.287219 \nL 316.120085 214.140885 \nL 312.74751 212.599219 \nL 312.512812 212.494826 \nL 308.90554 210.589572 \nL 307.722651 209.911219 \nL 305.298267 208.551793 \nL 303.086123 207.223219 \nL 301.690994 206.403541 \nL 298.708904 204.535219 \nL 298.083722 204.151865 \nL 294.545424 201.847219 \nL 294.476449 201.803228 \nL 290.869176 199.341576 \nL 290.614703 199.159219 \nL 287.261903 196.79954 \nL 286.815736 196.471219 \nL 283.654631 194.185923 \nL 283.120862 193.783219 \nL 280.047358 191.504434 \nL 279.517559 191.095219 \nL 276.440085 188.758529 \nL 275.995238 188.407219 \nL 272.832812 185.951431 \nL 272.544881 185.719219 \nL 269.22554 183.086156 \nL 269.158762 183.031219 \nL 265.862944 180.343219 \nL 265.618267 180.146773 \nL 262.63403 177.655219 \nL 262.010994 177.144167 \nL 259.45506 174.967219 \nL 258.403722 174.087206 \nL 256.320694 172.279219 \nL 254.796449 170.978653 \nL 253.226329 169.591219 \nL 251.189176 167.821088 \nL 250.167976 166.903219 \nL 247.581903 164.61692 \nL 247.142156 164.215219 \nL 244.169325 161.527219 \nL 243.974631 161.351673 \nL 241.283544 158.839219 \nL 240.367358 157.998829 \nL 238.419806 156.151219 \nL 236.760085 154.603771 \nL 235.575991 153.463219 \nL 233.152813 151.168641 \nL 232.750243 150.775219 \nL 229.993109 148.087219 \nL 229.54554 147.652715 \nL 227.300816 145.399219 \nL 225.938267 144.05613 \nL 224.617419 142.711219 \nL 222.330994 140.424573 \nL 221.942093 140.023219 \nL 219.346426 137.335219 \nL 218.723722 136.693571 \nL 216.802985 134.647219 \nL 215.116449 132.884754 \nL 214.25894 131.959219 \nL 211.742126 129.271219 \nL 211.509176 129.01905 \nL 209.335044 126.583219 \nL 207.901903 125.010767 \nL 206.918426 123.895219 \nL 204.520902 121.207219 \nL 204.294631 120.948374 \nL 202.245107 118.519219 \nL 200.687358 116.714455 \nL 199.950661 115.831219 \nL 197.720019 113.143219 \nL 197.080085 112.36406 \nL 195.568626 110.455219 \nL 193.472812 107.873662 \nL 193.389393 107.767219 \nL 191.381738 105.079219 \nL 189.86554 103.097073 \nL 189.345627 102.391219 \nL 187.435428 99.703219 \nL 186.258267 98.046959 \nL 185.554181 97.015219 \nL 183.790409 94.327219 \nL 182.650994 92.567295 \nL 182.075996 91.639219 \nL 180.529705 88.951219 \nL 179.043722 86.355528 \nL 178.99335 86.263219 \nL 177.769926 83.575219 \nL 176.663789 80.887219 \nL 175.754136 78.199219 \nL 175.436449 76.461707 \nL 175.275297 75.511219 \nL 175.436449 73.209541 \nL 175.4895 72.823219 \nL 178.289614 70.135219 \nL 179.043722 69.861366 \nL 182.650994 69.866431 \nL 183.790278 70.135219 \nL 186.258267 70.696958 \nL 189.86554 71.957091 \nL 191.876603 72.823219 \nL 193.472812 73.491726 \nL 197.080085 75.233708 \nL 197.580922 75.511219 \nL 200.687358 77.193523 \nL 202.414917 78.199219 \nL 204.294631 79.269274 \nL 206.951523 80.887219 \nL 207.901903 81.453433 \nL 211.245339 83.575219 \nL 211.509176 83.739105 \nL 215.116449 86.13562 \nL 215.297874 86.263219 \nL 218.723722 88.628945 \nL 219.1694 88.951219 \nL 222.330994 91.196638 \nL 222.92731 91.639219 \nL 225.938267 93.83479 \nL 226.585681 94.327219 \nL 229.54554 96.539763 \nL 230.156357 97.015219 \nL 233.152813 99.308166 \nL 233.649377 99.703219 \nL 236.760085 102.136831 \nL 237.073301 102.391219 \nL 240.367358 105.022799 \nL 240.435477 105.079219 \nL 243.706753 107.767219 \nL 243.974631 107.983927 \nL 246.913476 110.455219 \nL 247.581903 111.007474 \nL 250.072374 113.143219 \nL 251.189176 114.084491 \nL 253.18851 115.831219 \nL 254.796449 117.212268 \nL 256.266255 118.519219 \nL 258.403722 120.388274 \nL 259.309405 121.207219 \nL 262.010994 123.610146 \nL 262.321272 123.895219 \nL 265.262137 126.583219 \nL 265.618267 126.906382 \nL 268.135923 129.271219 \nL 269.22554 130.276828 \nL 270.988649 131.959219 \nL 272.832812 133.688757 \nL 273.822322 134.647219 \nL 276.440085 137.140068 \nL 276.638703 137.335219 \nL 279.359836 140.023219 \nL 280.047358 140.694629 \nL 282.044852 142.711219 \nL 283.654631 144.307032 \nL 284.721509 145.399219 \nL 287.261903 147.953737 \nL 287.390575 148.087219 \nL 289.946432 150.775219 \nL 290.869176 151.73146 \nL 292.485891 153.463219 \nL 294.476449 155.554776 \nL 295.0262 156.151219 \nL 297.498014 158.839219 \nL 298.083722 159.476863 \nL 299.903998 161.527219 \nL 301.690994 163.498625 \nL 302.319507 164.215219 \nL 304.666941 166.903219 \nL 305.298267 167.629515 \nL 306.944633 169.591219 \nL 308.90554 171.875363 \nL 309.240683 172.279219 \nL 311.416359 174.967219 \nL 312.512812 176.309654 \nL 313.572735 177.655219 \nL 315.700587 180.343219 \nL 316.120085 180.88883 \nL 317.704525 183.031219 \nL 319.727358 185.690013 \nL 319.748762 185.719219 \nL 321.589951 188.407219 \nL 323.334631 190.875292 \nL 323.48397 191.095219 \nL 325.167582 193.783219 \nL 326.892422 196.471219 \nL 326.941903 196.557969 \nL 328.353716 199.159219 \nL 329.777951 201.847219 \nL 330.549176 203.466208 \nL 331.031274 204.535219 \nL 331.992296 207.223219 \nL 332.696942 209.911219 \nL 332.927756 212.599219 \nL 332.124421 215.287219 \nL 330.549176 216.719154 \nL 326.941903 217.29162 \nL 323.334631 216.695025 \nL 319.727358 215.61981 \nz\n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_7\">\n <path d=\"M 348.58554 242.831877 \nL 344.978267 241.852282 \nL 341.370994 240.543095 \nL 337.763722 239.058254 \nL 333.018654 236.791219 \nL 326.941903 233.617176 \nL 319.727358 229.420942 \nL 310.193466 223.351219 \nL 305.298267 220.077389 \nL 298.083722 215.024578 \nL 290.869176 209.745716 \nL 280.571314 201.847219 \nL 276.440085 198.580625 \nL 265.618267 189.735412 \nL 254.578501 180.343219 \nL 243.974631 170.923255 \nL 230.929178 158.839219 \nL 222.514572 150.775219 \nL 217.101711 145.399219 \nL 211.509176 139.792772 \nL 200.687358 128.487455 \nL 189.86554 116.614286 \nL 182.196355 107.767219 \nL 175.436449 99.599766 \nL 167.227899 88.951219 \nL 163.34962 83.575219 \nL 159.687933 78.199219 \nL 156.283035 72.823219 \nL 153.185731 67.447219 \nL 150.18554 61.304876 \nL 149.410399 59.383219 \nL 148.49569 56.695219 \nL 147.782562 54.007219 \nL 147.386651 51.319219 \nL 147.532951 48.631219 \nL 148.725105 45.943219 \nL 150.18554 44.620883 \nL 153.792812 43.599909 \nL 157.400085 43.795414 \nL 161.007358 44.562394 \nL 165.377513 45.943219 \nL 168.221903 47.037493 \nL 171.948897 48.631219 \nL 179.043722 52.198065 \nL 182.650994 54.15706 \nL 189.86554 58.436825 \nL 199.687598 64.759219 \nL 204.294631 67.872696 \nL 211.509176 72.966804 \nL 218.723722 78.284145 \nL 229.060181 86.263219 \nL 233.152813 89.518785 \nL 243.974631 98.41054 \nL 254.925272 107.767219 \nL 265.618267 117.312325 \nL 278.471177 129.271219 \nL 284.089654 134.647219 \nL 294.476449 144.929827 \nL 305.350014 156.151219 \nL 316.120085 167.858235 \nL 324.685946 177.655219 \nL 329.205952 183.031219 \nL 334.156449 189.103527 \nL 341.860093 199.159219 \nL 347.524098 207.223219 \nL 349.311522 209.911219 \nL 352.667242 215.287219 \nL 355.800085 220.86756 \nL 358.206441 226.039219 \nL 359.407358 228.982139 \nL 360.140289 231.415219 \nL 360.706086 234.103219 \nL 360.904928 236.791219 \nL 360.482216 239.479219 \nL 359.407358 241.427984 \nL 358.514941 242.167219 \nL 355.800085 243.267452 \nL 352.192813 243.393853 \nL 348.58554 242.831877 \nL 348.58554 242.831877 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_8\">\n <path d=\"M 378.696497 277.111219 \nL 377.443722 276.764293 \nL 371.036962 274.423219 \nL 370.229176 274.114875 \nL 363.014631 270.863311 \nL 359.315084 269.047219 \nL 352.192813 265.220216 \nL 344.8256 260.983219 \nL 336.163866 255.607219 \nL 330.549176 251.983428 \nL 319.727358 244.64911 \nL 308.90554 236.912167 \nL 294.452234 226.039219 \nL 283.654631 217.538431 \nL 271.033684 207.223219 \nL 261.447351 199.159219 \nL 251.189176 190.27392 \nL 236.760085 177.363597 \nL 222.330994 163.942243 \nL 207.901903 149.981028 \nL 193.472812 135.448915 \nL 182.428242 123.895219 \nL 171.829176 112.374419 \nL 160.638091 99.703219 \nL 151.592968 88.951219 \nL 146.578267 82.791212 \nL 138.816945 72.823219 \nL 132.149176 63.739042 \nL 127.296692 56.695219 \nL 123.793698 51.319219 \nL 120.498428 45.943219 \nL 117.441264 40.567219 \nL 114.112812 33.871977 \nL 112.408334 29.815219 \nL 111.411995 27.127219 \nL 110.50554 24.285531 \nL 109.942639 21.751219 \nL 109.584419 19.063219 \nL 109.561636 16.375219 \nL 110.040302 13.687219 \nL 110.50554 12.593447 \nL 111.612489 10.999219 \nL 111.612489 10.999219 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 132.903482 10.999219 \nL 135.756449 12.042204 \nL 139.79997 13.687219 \nL 146.578267 16.821416 \nL 153.792812 20.57183 \nL 161.007358 24.623853 \nL 169.536815 29.815219 \nL 175.436449 33.567011 \nL 186.258267 40.810177 \nL 193.57293 45.943219 \nL 204.599534 54.007219 \nL 215.196627 62.071219 \nL 225.938267 70.56251 \nL 238.52251 80.887219 \nL 248.07714 88.951219 \nL 258.403722 97.928887 \nL 272.832812 110.885521 \nL 287.261903 124.354022 \nL 301.690994 138.363213 \nL 313.995815 150.775219 \nL 321.758371 158.839219 \nL 329.333163 166.903219 \nL 336.711144 174.967219 \nL 343.882678 183.031219 \nL 350.83749 191.095219 \nL 355.800085 196.9923 \nL 364.052319 207.223219 \nL 370.288072 215.287219 \nL 378.060527 226.039219 \nL 383.456828 234.103219 \nL 386.81041 239.479219 \nL 388.437146 242.167219 \nL 391.872813 248.44339 \nL 394.044655 252.919219 \nL 395.480085 256.140608 \nL 396.307119 258.295219 \nL 397.213844 260.983219 \nL 397.976174 263.671219 \nL 398.538627 266.359219 \nL 398.813118 269.047219 \nL 398.650896 271.735219 \nL 397.779443 274.423219 \nL 395.639949 277.111219 \nL 395.639949 277.111219 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_9\">\n <path d=\"M 338.214156 277.111219 \nL 330.549176 271.614716 \nL 319.727358 263.623294 \nL 308.90554 255.383062 \nL 294.476449 244.036195 \nL 278.97347 231.415219 \nL 269.22554 223.279281 \nL 253.674226 209.911219 \nL 243.974631 201.380944 \nL 229.54554 188.377887 \nL 215.086093 174.967219 \nL 200.687358 161.223072 \nL 184.625384 145.399219 \nL 175.436449 136.11996 \nL 161.007358 121.157808 \nL 146.070074 105.079219 \nL 135.756449 93.598983 \nL 124.698106 80.887219 \nL 113.473007 67.447219 \nL 104.862213 56.695219 \nL 98.627104 48.631219 \nL 92.469176 40.389799 \nL 84.974285 29.815219 \nL 77.855815 19.063219 \nL 74.432812 13.540126 \nL 74.432812 13.540126 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 171.56257 10.999219 \nL 179.043722 16.389039 \nL 189.900975 24.439219 \nL 200.687358 32.680247 \nL 215.116449 44.063383 \nL 230.588937 56.695219 \nL 240.367358 64.879969 \nL 255.824758 78.199219 \nL 265.618267 86.835685 \nL 280.047358 99.872994 \nL 294.476449 113.288467 \nL 311.127325 129.271219 \nL 319.727358 137.716083 \nL 335.318218 153.463219 \nL 344.978267 163.481564 \nL 355.800085 174.981264 \nL 370.445711 191.095219 \nL 382.181871 204.535219 \nL 389.01963 212.599219 \nL 397.851384 223.351219 \nL 404.257695 231.415219 \nL 410.473257 239.479219 \nL 418.381872 250.231219 \nL 424.338267 258.732922 \nL 431.097323 269.047219 \nL 431.552813 269.776607 \nL 431.552813 269.776607 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_10\">\n <path d=\"M 305.624697 277.111219 \nL 295.68634 269.047219 \nL 283.654631 259.124857 \nL 265.618267 243.886799 \nL 247.581903 228.23264 \nL 229.54554 212.156588 \nL 211.509176 195.652742 \nL 193.472812 178.71509 \nL 175.436449 161.331524 \nL 157.400085 143.453999 \nL 142.970994 128.78698 \nL 125.419314 110.455219 \nL 114.112812 98.334037 \nL 99.683722 82.475328 \nL 86.415654 67.447219 \nL 77.168335 56.695219 \nL 74.432812 53.471142 \nL 74.432812 53.471142 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 203.975346 10.999219 \nL 213.89224 19.063219 \nL 225.938267 29.017585 \nL 243.974631 44.286339 \nL 262.010994 59.971103 \nL 280.047358 76.077663 \nL 298.083722 92.611915 \nL 316.120085 109.579862 \nL 334.156449 127.000364 \nL 352.67812 145.399219 \nL 366.621903 159.611543 \nL 381.333211 174.967219 \nL 396.363603 191.095219 \nL 406.301903 202.004554 \nL 420.730994 218.280648 \nL 431.552813 230.85858 \nL 431.552813 230.85858 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_11\">\n <path d=\"M 267.005459 277.111219 \nL 265.618267 275.92239 \nL 263.882469 274.423219 \nL 262.010994 272.812859 \nL 260.768222 271.735219 \nL 258.403722 269.692473 \nL 257.662517 269.047219 \nL 254.796449 266.561351 \nL 254.565162 266.359219 \nL 251.484537 263.671219 \nL 251.189176 263.414039 \nL 248.418855 260.983219 \nL 247.581903 260.251576 \nL 245.36097 258.295219 \nL 243.974631 257.078575 \nL 242.310703 255.607219 \nL 240.367358 253.895151 \nL 239.267886 252.919219 \nL 236.760085 250.701421 \nL 236.23235 250.231219 \nL 233.205439 247.543219 \nL 233.152813 247.496483 \nL 230.201069 244.855219 \nL 229.54554 244.270839 \nL 227.203454 242.167219 \nL 225.938267 241.035092 \nL 224.212442 239.479219 \nL 222.330994 237.789354 \nL 221.227889 236.791219 \nL 218.723722 234.533737 \nL 218.249652 234.103219 \nL 215.282256 231.415219 \nL 215.116449 231.265076 \nL 212.334621 228.727219 \nL 211.509176 227.976998 \nL 209.392799 226.039219 \nL 207.901903 224.67925 \nL 206.456662 223.351219 \nL 204.294631 221.371941 \nL 203.526087 220.663219 \nL 200.687358 218.055177 \nL 200.600954 217.975219 \nL 197.698261 215.287219 \nL 197.080085 214.716574 \nL 194.803119 212.599219 \nL 193.472812 211.366831 \nL 191.912939 209.911219 \nL 189.86554 208.007848 \nL 189.027613 207.223219 \nL 186.258267 204.639729 \nL 186.147039 204.535219 \nL 183.288627 201.847219 \nL 182.650994 201.2494 \nL 180.437759 199.159219 \nL 179.043722 197.847691 \nL 177.591175 196.471219 \nL 175.436449 194.437069 \nL 174.748785 193.783219 \nL 171.912794 191.095219 \nL 171.829176 191.015868 \nL 169.10016 188.407219 \nL 168.221903 187.570924 \nL 166.291258 185.719219 \nL 164.614631 184.117299 \nL 163.486008 183.031219 \nL 161.007358 180.655093 \nL 160.684332 180.343219 \nL 157.899756 177.655219 \nL 157.400085 177.173592 \nL 155.127481 174.967219 \nL 153.792812 173.676462 \nL 152.358331 172.279219 \nL 150.18554 170.17099 \nL 149.592242 169.591219 \nL 146.836162 166.903219 \nL 146.578267 166.651559 \nL 144.099464 164.215219 \nL 142.970994 163.110421 \nL 141.365383 161.527219 \nL 139.363722 159.561189 \nL 138.633863 158.839219 \nL 135.908995 156.151219 \nL 135.756449 156.000498 \nL 133.206831 153.463219 \nL 132.149176 152.41485 \nL 130.50679 150.775219 \nL 128.541903 148.821365 \nL 127.808827 148.087219 \nL 125.117872 145.399219 \nL 124.934631 145.215881 \nL 122.449204 142.711219 \nL 121.327358 141.585218 \nL 119.782181 140.023219 \nL 117.720085 137.946988 \nL 117.116768 137.335219 \nL 114.462414 134.647219 \nL 114.112812 134.292962 \nL 111.826209 131.959219 \nL 110.50554 130.616785 \nL 109.191188 129.271219 \nL 106.898267 126.933319 \nL 106.557323 126.583219 \nL 103.94224 123.895219 \nL 103.290994 123.226771 \nL 101.337473 121.207219 \nL 99.683722 119.504581 \nL 98.733441 118.519219 \nL 96.131634 115.831219 \nL 96.076449 115.77401 \nL 93.556973 113.143219 \nL 92.469176 112.012095 \nL 90.982622 110.455219 \nL 88.861903 108.243396 \nL 88.408575 107.767219 \nL 85.851072 105.079219 \nL 85.254631 104.452694 \nL 83.306237 102.391219 \nL 81.647358 100.643466 \nL 80.761287 99.703219 \nL 78.221187 97.015219 \nL 78.040085 96.822996 \nL 75.705691 94.327219 \nL 74.432812 92.972181 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440256; stroke-width: 1.5\"/>\n <path d=\"M 242.511093 10.999219 \nL 243.974631 12.25529 \nL 245.630207 13.687219 \nL 247.581903 15.369013 \nL 248.740655 16.375219 \nL 251.189176 18.493553 \nL 251.842636 19.063219 \nL 254.796449 21.628792 \nL 254.93634 21.751219 \nL 258.010571 24.439219 \nL 258.403722 24.782033 \nL 261.072692 27.127219 \nL 262.010994 27.948615 \nL 264.127087 29.815219 \nL 265.618267 31.125698 \nL 267.173931 32.503219 \nL 269.22554 34.313165 \nL 270.213392 35.191219 \nL 272.832812 37.510902 \nL 273.245636 37.879219 \nL 276.265855 40.567219 \nL 276.440085 40.722162 \nL 279.267025 43.255219 \nL 280.047358 43.951812 \nL 282.261502 45.943219 \nL 283.654631 47.191529 \nL 285.249434 48.631219 \nL 287.261903 50.4412 \nL 288.230967 51.319219 \nL 290.869176 53.700715 \nL 291.20624 54.007219 \nL 294.166698 56.695219 \nL 294.476449 56.976087 \nL 297.111462 59.383219 \nL 298.083722 60.268058 \nL 300.050468 62.071219 \nL 301.690994 63.569664 \nL 302.98384 64.759219 \nL 305.298267 66.880797 \nL 305.911701 67.447219 \nL 308.832127 70.135219 \nL 308.90554 70.202834 \nL 311.729724 72.823219 \nL 312.512812 73.547049 \nL 314.622297 75.511219 \nL 316.120085 76.900574 \nL 317.509954 78.199219 \nL 319.727358 80.263304 \nL 320.392802 80.887219 \nL 323.269135 83.575219 \nL 323.334631 83.63649 \nL 326.122004 86.263219 \nL 326.941903 87.032921 \nL 328.970535 88.951219 \nL 330.549176 90.438332 \nL 331.814824 91.639219 \nL 334.156449 93.852623 \nL 334.65496 94.327219 \nL 337.483353 97.015219 \nL 337.763722 97.281624 \nL 340.293831 99.703219 \nL 341.370994 100.730225 \nL 343.100616 102.391219 \nL 344.978267 104.187472 \nL 345.903787 105.079219 \nL 348.58554 107.653268 \nL 348.703419 107.767219 \nL 351.480227 110.455219 \nL 352.192812 111.142941 \nL 354.250559 113.143219 \nL 355.800085 114.643645 \nL 357.017798 115.831219 \nL 359.407358 118.152658 \nL 359.78201 118.519219 \nL 362.530105 121.207219 \nL 363.014631 121.680623 \nL 365.265029 123.895219 \nL 366.621903 125.225284 \nL 367.997365 126.583219 \nL 370.229176 128.778006 \nL 370.72717 129.271219 \nL 373.443848 131.959219 \nL 373.836449 132.347604 \nL 376.144402 134.647219 \nL 377.443722 135.936722 \nL 378.84286 137.335219 \nL 381.050994 139.533643 \nL 381.539265 140.023219 \nL 384.221837 142.711219 \nL 384.658267 143.148419 \nL 386.889054 145.399219 \nL 388.26554 146.782494 \nL 389.55465 148.087219 \nL 391.872813 150.424105 \nL 392.218659 150.775219 \nL 394.864449 153.463219 \nL 395.480085 154.087819 \nL 397.499358 156.151219 \nL 399.087358 157.76735 \nL 400.133105 158.839219 \nL 402.694631 161.454138 \nL 402.765715 161.527219 \nL 405.372063 164.215219 \nL 406.301903 165.170781 \nL 407.975686 166.903219 \nL 409.909176 168.896264 \nL 410.578591 169.591219 \nL 413.171405 172.279219 \nL 413.516449 172.637352 \nL 415.745054 174.967219 \nL 417.123722 176.402526 \nL 418.318408 177.655219 \nL 420.730994 180.174452 \nL 420.891474 180.343219 \nL 423.43983 183.031219 \nL 424.338267 183.976109 \nL 425.983799 185.719219 \nL 427.94554 187.788528 \nL 428.527895 188.407219 \nL 431.058597 191.095219 \nL 431.552813 191.620414 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #440256; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_12\">\n <path d=\"M 217.702539 277.111219 \nL 215.116449 274.793802 \nL 214.705154 274.423219 \nL 211.71694 271.735219 \nL 211.509176 271.548438 \nL 208.742278 269.047219 \nL 207.901903 268.289639 \nL 205.772231 266.359219 \nL 204.294631 265.023557 \nL 202.806725 263.671219 \nL 200.687358 261.750252 \nL 199.845685 260.983219 \nL 197.080085 258.469784 \nL 196.88904 258.295219 \nL 193.946539 255.607219 \nL 193.472812 255.175228 \nL 191.012298 252.919219 \nL 189.86554 251.870689 \nL 188.082182 250.231219 \nL 186.258267 248.559101 \nL 185.156124 247.543219 \nL 182.650994 245.240523 \nL 182.234061 244.855219 \nL 179.321653 242.167219 \nL 179.043722 241.910846 \nL 176.421856 239.479219 \nL 175.436449 238.567858 \nL 173.525789 236.791219 \nL 171.829176 235.217997 \nL 170.633392 234.103219 \nL 168.221903 231.861322 \nL 167.744607 231.415219 \nL 164.864493 228.727219 \nL 164.614631 228.494079 \nL 161.997821 226.039219 \nL 161.007358 225.112657 \nL 159.134502 223.351219 \nL 157.400085 221.724541 \nL 156.274484 220.663219 \nL 153.792812 218.329787 \nL 153.417713 217.975219 \nL 150.572006 215.287219 \nL 150.18554 214.92246 \nL 147.73718 212.599219 \nL 146.578267 211.502627 \nL 144.905349 209.911219 \nL 142.970994 208.07628 \nL 142.076466 207.223219 \nL 139.363722 204.643474 \nL 139.250483 204.535219 \nL 136.441215 201.847219 \nL 135.756449 201.193469 \nL 133.636995 199.159219 \nL 132.149176 197.735256 \nL 130.835429 196.471219 \nL 128.541903 194.27071 \nL 128.036475 193.783219 \nL 125.246397 191.095219 \nL 124.934631 190.794886 \nL 122.469214 188.407219 \nL 121.327358 187.304531 \nL 119.694397 185.719219 \nL 117.720085 183.807975 \nL 116.921909 183.031219 \nL 114.152517 180.343219 \nL 114.112812 180.304622 \nL 111.401798 177.655219 \nL 110.50554 176.781852 \nL 108.653165 174.967219 \nL 106.898267 173.253014 \nL 105.906584 172.279219 \nL 103.290994 169.718162 \nL 103.162025 169.591219 \nL 100.434541 166.903219 \nL 99.683722 166.164886 \nL 97.711528 164.215219 \nL 96.076449 162.603497 \nL 94.990297 161.527219 \nL 92.469176 159.036229 \nL 92.270822 158.839219 \nL 89.567238 156.151219 \nL 88.861903 155.451224 \nL 86.869283 153.463219 \nL 85.254631 151.857011 \nL 84.172847 150.775219 \nL 81.647358 148.257062 \nL 81.477908 148.087219 \nL 78.799682 145.399219 \nL 78.040085 144.638371 \nL 76.126227 142.711219 \nL 74.432812 141.011065 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #450457; stroke-width: 1.5\"/>\n <path d=\"M 291.763757 10.999219 \nL 294.476449 13.432506 \nL 294.758865 13.687219 \nL 297.742037 16.375219 \nL 298.083722 16.682704 \nL 300.714474 19.063219 \nL 301.690994 19.94441 \nL 303.682326 21.751219 \nL 305.298267 23.21338 \nL 306.645669 24.439219 \nL 308.90554 26.489553 \nL 309.604574 27.127219 \nL 312.512812 29.77287 \nL 312.559114 29.815219 \nL 315.496451 32.503219 \nL 316.120085 33.07247 \nL 318.428639 35.191219 \nL 319.727358 36.379856 \nL 321.35673 37.879219 \nL 323.334631 39.694271 \nL 324.280789 40.567219 \nL 326.941903 43.015657 \nL 327.200882 43.255219 \nL 330.107995 45.943219 \nL 330.549176 46.350573 \nL 333.005873 48.631219 \nL 334.156449 49.696366 \nL 335.900047 51.319219 \nL 337.763722 53.049012 \nL 338.790577 54.007219 \nL 341.370994 56.408454 \nL 341.67752 56.695219 \nL 344.552221 59.383219 \nL 344.978267 59.781133 \nL 347.417103 62.071219 \nL 348.58554 63.165317 \nL 350.278656 64.759219 \nL 352.192813 66.556176 \nL 353.136932 67.447219 \nL 355.800085 69.953654 \nL 355.991984 70.135219 \nL 358.832168 72.823219 \nL 359.407358 73.366616 \nL 361.665328 75.511219 \nL 363.014631 76.789168 \nL 364.495514 78.199219 \nL 366.621903 80.218215 \nL 367.322775 80.887219 \nL 370.145455 83.575219 \nL 370.229176 83.655023 \nL 372.950803 86.263219 \nL 373.836449 87.109543 \nL 375.753475 88.951219 \nL 377.443722 90.570431 \nL 378.553514 91.639219 \nL 381.050994 94.037633 \nL 381.35096 94.327219 \nL 384.135292 97.015219 \nL 384.658267 97.519485 \nL 386.911022 99.703219 \nL 388.26554 101.012488 \nL 389.684404 102.391219 \nL 391.872813 104.511674 \nL 392.455475 105.079219 \nL 395.219002 107.767219 \nL 395.480085 108.021252 \nL 397.968361 110.455219 \nL 399.087358 111.546642 \nL 400.715651 113.143219 \nL 402.694631 115.078082 \nL 403.460904 115.831219 \nL 406.202142 118.519219 \nL 406.301903 118.617176 \nL 408.925697 121.207219 \nL 409.909176 122.175229 \nL 411.647457 123.895219 \nL 413.516449 125.739192 \nL 414.367449 126.583219 \nL 417.084919 129.271219 \nL 417.123722 129.309672 \nL 419.783237 131.959219 \nL 420.730994 132.90066 \nL 422.480026 134.647219 \nL 424.338267 136.497417 \nL 425.175309 137.335219 \nL 427.867541 140.023219 \nL 427.94554 140.101235 \nL 430.541185 142.711219 \nL 431.552813 143.725432 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #450457; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_13\">\n <path d=\"M 152.885302 277.111219 \nL 150.18554 274.617471 \nL 149.976071 274.423219 \nL 147.077237 271.735219 \nL 146.578267 271.27311 \nL 144.184381 269.047219 \nL 142.970994 267.921305 \nL 141.294219 266.359219 \nL 139.363722 264.564459 \nL 138.406718 263.671219 \nL 135.756449 261.202603 \nL 135.521847 260.983219 \nL 132.647122 258.295219 \nL 132.149176 257.830148 \nL 129.778541 255.607219 \nL 128.541903 254.450027 \nL 126.91245 252.919219 \nL 124.934631 251.064964 \nL 124.04882 250.231219 \nL 121.327358 247.674986 \nL 121.187622 247.543219 \nL 118.338153 244.855219 \nL 117.720085 244.273062 \nL 115.493154 242.167219 \nL 114.112812 240.864639 \nL 112.650449 239.479219 \nL 110.50554 237.45137 \nL 109.810011 236.791219 \nL 106.972939 234.103219 \nL 106.898267 234.032421 \nL 104.148714 231.415219 \nL 103.290994 230.600489 \nL 101.326619 228.727219 \nL 99.683722 227.163779 \nL 98.506628 226.039219 \nL 96.076449 223.722321 \nL 95.688718 223.351219 \nL 92.879016 220.663219 \nL 92.469176 220.271342 \nL 90.077217 217.975219 \nL 88.861903 216.811042 \nL 87.277362 215.287219 \nL 85.254631 213.346063 \nL 84.479429 212.599219 \nL 81.683946 209.911219 \nL 81.647358 209.876002 \nL 78.902129 207.223219 \nL 78.040085 206.391961 \nL 76.122099 204.535219 \nL 74.432812 202.903313 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #450559; stroke-width: 1.5\"/>\n <path d=\"M 356.54654 10.999219 \nL 359.407358 13.643609 \nL 359.45435 13.687219 \nL 362.349254 16.375219 \nL 363.014631 16.99188 \nL 365.240718 19.063219 \nL 366.621903 20.345745 \nL 368.129502 21.751219 \nL 370.229176 23.704641 \nL 371.015639 24.439219 \nL 373.836449 27.068536 \nL 373.899158 27.127219 \nL 376.76989 29.815219 \nL 377.443722 30.44501 \nL 379.637148 32.503219 \nL 381.050994 33.827166 \nL 382.501929 35.191219 \nL 384.658267 37.214257 \nL 385.364262 37.879219 \nL 388.223541 40.567219 \nL 388.26554 40.606731 \nL 391.069593 43.255219 \nL 391.872813 44.012301 \nL 393.913336 45.943219 \nL 395.480085 47.422737 \nL 396.754798 48.631219 \nL 399.087358 50.838009 \nL 399.594006 51.319219 \nL 402.426952 54.007219 \nL 402.694631 54.261186 \nL 405.249975 56.695219 \nL 406.301903 57.695118 \nL 408.07088 59.383219 \nL 409.909176 61.133817 \nL 410.889693 62.071219 \nL 413.516449 64.577255 \nL 413.706436 64.759219 \nL 416.51196 67.447219 \nL 417.123722 68.032572 \nL 419.312622 70.135219 \nL 420.730994 71.494848 \nL 422.11135 72.823219 \nL 424.338267 74.961792 \nL 424.908166 75.511219 \nL 427.699404 78.199219 \nL 427.94554 78.436297 \nL 430.480135 80.887219 \nL 431.552813 81.922299 \n\" clip-path=\"url(#pff26c45cfe)\" style=\"fill: none; stroke: #450559; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_14\"/>\n <g id=\"PathCollection_15\"/>\n <g id=\"PathCollection_16\"/>\n <g id=\"PathCollection_17\"/>\n <g id=\"PathCollection_18\"/>\n <g id=\"PathCollection_19\"/>\n <g id=\"PathCollection_20\"/>\n <g id=\"patch_3\">\n <path d=\"M 74.432812 277.111219 \nL 74.432812 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_4\">\n <path d=\"M 431.552813 277.111219 \nL 431.552813 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_5\">\n <path d=\"M 74.432812 277.111219 \nL 431.552813 277.111219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_6\">\n <path d=\"M 74.432812 10.999219 \nL 431.552813 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n </g>\n </g>\n <defs>\n <clipPath id=\"pff26c45cfe\">\n <rect x=\"74.432812\" y=\"10.999219\" width=\"357.12\" height=\"266.112\"/>\n </clipPath>\n </defs>\n</svg>\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"contour_plot(XMx2_scaled, yMx2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Normalizacja średniej"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Będziemy dążyć do tego, żeby dodatkowo średnia wartość każdej z cech była w okolicach $0$.\n",
"\n",
"W tym celu oprócz przeskalowania odejmiemy wartość średniej od wartości każdej z cech:\n",
"\n",
"$$ \\hat{x_i}^{(j)} := \\frac{x_i^{(j)} - \\mu_i}{\\max_j x_i^{(j)}} $$"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 0.00 \\leq x_0 \\leq 0.00$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle -0.10 \\leq x_1 \\leq 0.62$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle -0.23 \\leq x_2 \\leq 0.70$"
],
"text/plain": [
"<IPython.core.display.Math object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"XMx2_norm = (XMx2 - np.mean(XMx2, axis=0)) / np.amax(XMx2, axis=0)\n",
"\n",
"show_mins_and_maxs(XMx2_norm)\n"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"457.840312pt\" height=\"314.667469pt\" viewBox=\"0 0 457.840312 314.667469\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n <cc:Work>\n <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n <dc:date>2022-10-14T11:23:08.721094</dc:date>\n <dc:format>image/svg+xml</dc:format>\n <dc:creator>\n <cc:Agent>\n <dc:title>Matplotlib v3.6.1, https://matplotlib.org/</dc:title>\n </cc:Agent>\n </dc:creator>\n </cc:Work>\n </rdf:RDF>\n </metadata>\n <defs>\n <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n </defs>\n <g id=\"figure_1\">\n <g id=\"patch_1\">\n <path d=\"M 0 314.667469 \nL 457.840312 314.667469 \nL 457.840312 0 \nL 0 0 \nz\n\" style=\"fill: #ffffff\"/>\n </g>\n <g id=\"axes_1\">\n <g id=\"patch_2\">\n <path d=\"M 74.432812 277.111219 \nL 431.552813 277.111219 \nL 431.552813 10.999219 \nL 74.432812 10.999219 \nz\n\" style=\"fill: #ffffff\"/>\n </g>\n <g id=\"matplotlib.axis_1\">\n <g id=\"xtick_1\">\n <g id=\"line2d_1\">\n <defs>\n <path id=\"m495bae0224\" d=\"M 0 0 \nL 0 3.5 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </defs>\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"74.432812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_1\">\n <!-- −100000 -->\n <g transform=\"translate(51.155469 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-2212\" d=\"M 678 2272 \nL 4684 2272 \nL 4684 1741 \nL 678 1741 \nL 678 2272 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-31\" d=\"M 794 531 \nL 1825 531 \nL 1825 4091 \nL 703 3866 \nL 703 4441 \nL 1819 4666 \nL 2450 4666 \nL 2450 531 \nL 3481 531 \nL 3481 0 \nL 794 0 \nL 794 531 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \nQ 1547 4250 1301 3770 \nQ 1056 3291 1056 2328 \nQ 1056 1369 1301 889 \nQ 1547 409 2034 409 \nQ 2525 409 2770 889 \nQ 3016 1369 3016 2328 \nQ 3016 3291 2770 3770 \nQ 2525 4250 2034 4250 \nz\nM 2034 4750 \nQ 2819 4750 3233 4129 \nQ 3647 3509 3647 2328 \nQ 3647 1150 3233 529 \nQ 2819 -91 2034 -91 \nQ 1250 -91 836 529 \nQ 422 1150 422 2328 \nQ 422 3509 836 4129 \nQ 1250 4750 2034 4750 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"401.904297\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_2\">\n <g id=\"line2d_2\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"119.072812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_2\">\n <!-- −75000 -->\n <g transform=\"translate(98.976719 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-37\" d=\"M 525 4666 \nL 3525 4666 \nL 3525 4397 \nL 1831 0 \nL 1172 0 \nL 2766 4134 \nL 525 4134 \nL 525 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n <path id=\"DejaVuSans-35\" d=\"M 691 4666 \nL 3169 4666 \nL 3169 4134 \nL 1269 4134 \nL 1269 2991 \nQ 1406 3038 1543 3061 \nQ 1681 3084 1819 3084 \nQ 2600 3084 3056 2656 \nQ 3513 2228 3513 1497 \nQ 3513 744 3044 326 \nQ 2575 -91 1722 -91 \nQ 1428 -91 1123 -41 \nQ 819 9 494 109 \nL 494 744 \nQ 775 591 1075 516 \nQ 1375 441 1709 441 \nQ 2250 441 2565 725 \nQ 2881 1009 2881 1497 \nQ 2881 1984 2565 2268 \nQ 2250 2553 1709 2553 \nQ 1456 2553 1204 2497 \nQ 953 2441 691 2322 \nL 691 4666 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_3\">\n <g id=\"line2d_3\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"163.712812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_3\">\n <!-- −50000 -->\n <g transform=\"translate(143.616719 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_4\">\n <g id=\"line2d_4\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"208.352812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_4\">\n <!-- −25000 -->\n <g transform=\"translate(188.256719 291.709656) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-32\" d=\"M 1228 531 \nL 3431 531 \nL 3431 0 \nL 469 0 \nL 469 531 \nQ 828 903 1448 1529 \nQ 2069 2156 2228 2338 \nQ 2531 2678 2651 2914 \nQ 2772 3150 2772 3378 \nQ 2772 3750 2511 3984 \nQ 2250 4219 1831 4219 \nQ 1534 4219 1204 4116 \nQ 875 4013 500 3803 \nL 500 4441 \nQ 881 4594 1212 4672 \nQ 1544 4750 1819 4750 \nQ 2544 4750 2975 4387 \nQ 3406 4025 3406 3419 \nQ 3406 3131 3298 2873 \nQ 3191 2616 2906 2266 \nQ 2828 2175 2409 1742 \nQ 1991 1309 1228 531 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_5\">\n <g id=\"line2d_5\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"252.992813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_5\">\n <!-- 0 -->\n <g transform=\"translate(249.811563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-30\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_6\">\n <g id=\"line2d_6\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"297.632812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_6\">\n <!-- 25000 -->\n <g transform=\"translate(281.726562 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-32\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_7\">\n <g id=\"line2d_7\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"342.272813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_7\">\n <!-- 50000 -->\n <g transform=\"translate(326.366563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-35\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_8\">\n <g id=\"line2d_8\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"386.912813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_8\">\n <!-- 75000 -->\n <g transform=\"translate(371.006563 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-37\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_9\">\n <g id=\"line2d_9\">\n <g>\n <use xlink:href=\"#m495bae0224\" x=\"431.552813\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_9\">\n <!-- 100000 -->\n <g transform=\"translate(412.465313 291.709656) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-31\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"318.115234\"/>\n </g>\n </g>\n </g>\n <g id=\"text_10\">\n <!-- $\\theta_1$ -->\n <g transform=\"translate(247.542813 305.387781) scale(0.1 -0.1)\">\n <defs>\n <path id=\"DejaVuSans-Oblique-3b8\" d=\"M 2913 2219 \nL 925 2219 \nQ 791 1284 928 888 \nQ 1100 400 1566 400 \nQ 2034 400 2391 891 \nQ 2703 1322 2913 2219 \nz\nM 3009 2750 \nQ 3094 3638 2984 3950 \nQ 2813 4444 2353 4444 \nQ 1875 4444 1525 3956 \nQ 1250 3563 1034 2750 \nL 3009 2750 \nz\nM 2444 4913 \nQ 3194 4913 3494 4250 \nQ 3794 3591 3566 2422 \nQ 3341 1256 2781 594 \nQ 2225 -72 1475 -72 \nQ 722 -72 425 594 \nQ 128 1256 353 2422 \nQ 581 3591 1134 4250 \nQ 1691 4913 2444 4913 \nz\n\" transform=\"scale(0.015625)\"/>\n </defs>\n <use xlink:href=\"#DejaVuSans-Oblique-3b8\" transform=\"translate(0 0.234375)\"/>\n <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(61.181641 -16.171875) scale(0.7)\"/>\n </g>\n </g>\n </g>\n <g id=\"matplotlib.axis_2\">\n <g id=\"ytick_1\">\n <g id=\"line2d_10\">\n <defs>\n <path id=\"me0e6bd0d09\" d=\"M 0 0 \nL -3.5 0 \n\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </defs>\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"277.111219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_11\">\n <!-- −100000 -->\n <g transform=\"translate(20.878125 280.910437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-31\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"401.904297\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_2\">\n <g id=\"line2d_11\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"243.847219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_12\">\n <!-- −75000 -->\n <g transform=\"translate(27.240625 247.646437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-37\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_3\">\n <g id=\"line2d_12\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"210.583219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_13\">\n <!-- −50000 -->\n <g transform=\"translate(27.240625 214.382437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_4\">\n <g id=\"line2d_13\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"177.319219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_14\">\n <!-- −25000 -->\n <g transform=\"translate(27.240625 181.118437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-2212\"/>\n <use xlink:href=\"#DejaVuSans-32\" x=\"83.789062\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"147.412109\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"211.035156\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"274.658203\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"338.28125\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_5\">\n <g id=\"line2d_14\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"144.055219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_15\">\n <!-- 0 -->\n <g transform=\"translate(61.070312 147.854437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-30\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_6\">\n <g id=\"line2d_15\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"110.791219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_16\">\n <!-- 25000 -->\n <g transform=\"translate(35.620312 114.590437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-32\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_7\">\n <g id=\"line2d_16\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"77.527219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_17\">\n <!-- 50000 -->\n <g transform=\"translate(35.620312 81.326437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-35\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_8\">\n <g id=\"line2d_17\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"44.263219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_18\">\n <!-- 75000 -->\n <g transform=\"translate(35.620312 48.062437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-37\"/>\n <use xlink:href=\"#DejaVuSans-35\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_9\">\n <g id=\"line2d_18\">\n <g>\n <use xlink:href=\"#me0e6bd0d09\" x=\"74.432812\" y=\"10.999219\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n </g>\n </g>\n <g id=\"text_19\">\n <!-- 100000 -->\n <g transform=\"translate(29.257812 14.798437) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-31\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"63.623047\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"127.246094\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"190.869141\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"254.492188\"/>\n <use xlink:href=\"#DejaVuSans-30\" x=\"318.115234\"/>\n </g>\n </g>\n </g>\n <g id=\"text_20\">\n <!-- $\\theta_2$ -->\n <g transform=\"translate(14.798437 149.505219) rotate(-90) scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-Oblique-3b8\" transform=\"translate(0 0.234375)\"/>\n <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(61.181641 -16.171875) scale(0.7)\"/>\n </g>\n </g>\n </g>\n <g id=\"PathCollection_1\">\n <path d=\"M 254.796449 159.077071 \nL 253.941246 158.839219 \nL 251.189176 157.983511 \nL 247.581903 156.57452 \nL 246.68643 156.151219 \nL 243.974631 154.709627 \nL 241.923553 153.463219 \nL 240.367358 152.382975 \nL 238.308953 150.775219 \nL 236.760085 149.364736 \nL 235.497697 148.087219 \nL 233.291534 145.399219 \nL 233.152813 145.172232 \nL 231.794583 142.711219 \nL 230.820705 140.023219 \nL 230.461465 137.335219 \nL 230.865978 134.647219 \nL 232.235833 131.959219 \nL 233.152813 130.959372 \nL 235.386992 129.271219 \nL 236.760085 128.57558 \nL 240.367358 127.480298 \nL 243.974631 127.038873 \nL 247.581903 127.116811 \nL 251.189176 127.614137 \nL 254.796449 128.45499 \nL 257.369208 129.271219 \nL 258.403722 129.639818 \nL 262.010994 131.244619 \nL 263.3806 131.959219 \nL 265.618267 133.278834 \nL 267.662784 134.647219 \nL 269.22554 135.849834 \nL 270.950658 137.335219 \nL 272.832812 139.24133 \nL 273.530721 140.023219 \nL 275.443019 142.711219 \nL 276.440085 144.608833 \nL 276.816712 145.399219 \nL 277.530487 148.087219 \nL 277.620239 150.775219 \nL 276.941949 153.463219 \nL 276.440085 154.333024 \nL 275.006032 156.151219 \nL 272.832812 157.788343 \nL 270.629109 158.839219 \nL 269.22554 159.315316 \nL 265.618267 159.948929 \nL 262.010994 160.059714 \nL 258.403722 159.744352 \nL 254.796449 159.077071 \nz\n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_2\">\n <path d=\"M 254.796449 164.887031 \nL 252.351388 164.215219 \nL 251.189176 163.868304 \nL 247.581903 162.552525 \nL 245.137676 161.527219 \nL 243.974631 160.995501 \nL 240.367358 159.133787 \nL 239.855373 158.839219 \nL 236.760085 156.891585 \nL 235.681499 156.151219 \nL 233.152813 154.236125 \nL 232.210767 153.463219 \nL 229.54554 151.024545 \nL 229.292513 150.775219 \nL 226.926336 148.087219 \nL 225.938267 146.774524 \nL 224.975313 145.399219 \nL 223.452935 142.711219 \nL 222.330994 140.095225 \nL 222.302219 140.023219 \nL 221.662896 137.335219 \nL 221.471493 134.647219 \nL 221.799355 131.959219 \nL 222.330994 130.394142 \nL 222.799182 129.271219 \nL 224.739138 126.583219 \nL 225.938267 125.459053 \nL 228.142614 123.895219 \nL 229.54554 123.149573 \nL 233.152813 121.809098 \nL 235.839426 121.207219 \nL 236.760085 121.040259 \nL 240.367358 120.743228 \nL 243.974631 120.776825 \nL 247.581903 121.097996 \nL 248.246344 121.207219 \nL 251.189176 121.732404 \nL 254.796449 122.624733 \nL 258.403722 123.728406 \nL 258.853734 123.895219 \nL 262.010994 125.164947 \nL 265.134777 126.583219 \nL 265.618267 126.823105 \nL 269.22554 128.839362 \nL 269.926497 129.271219 \nL 272.832812 131.235174 \nL 273.818044 131.959219 \nL 276.440085 134.092753 \nL 277.07075 134.647219 \nL 279.787348 137.335219 \nL 280.047358 137.634109 \nL 281.974585 140.023219 \nL 283.654631 142.466448 \nL 283.811535 142.711219 \nL 285.139772 145.399219 \nL 286.092266 148.087219 \nL 286.60962 150.775219 \nL 286.61922 153.463219 \nL 286.031345 156.151219 \nL 284.733813 158.839219 \nL 283.654631 160.232277 \nL 282.37114 161.527219 \nL 280.047358 163.185435 \nL 278.044617 164.215219 \nL 276.440085 164.853428 \nL 272.832812 165.797424 \nL 269.22554 166.286444 \nL 265.618267 166.389222 \nL 262.010994 166.161312 \nL 258.403722 165.648101 \nL 254.796449 164.887031 \nz\n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_3\">\n <path d=\"M 254.796449 172.680071 \nL 253.322674 172.279219 \nL 251.189176 171.663171 \nL 247.581903 170.456473 \nL 245.283874 169.591219 \nL 243.974631 169.06702 \nL 240.367358 167.463559 \nL 239.216308 166.903219 \nL 236.760085 165.629505 \nL 234.227381 164.215219 \nL 233.152813 163.573292 \nL 229.955847 161.527219 \nL 229.54554 161.244919 \nL 226.26732 158.839219 \nL 225.938267 158.578159 \nL 223.059007 156.151219 \nL 222.330994 155.483407 \nL 220.25094 153.463219 \nL 218.723722 151.836353 \nL 217.77997 150.775219 \nL 215.639226 148.087219 \nL 215.116449 147.334266 \nL 213.842397 145.399219 \nL 212.32855 142.711219 \nL 211.509176 140.923988 \nL 211.117202 140.023219 \nL 210.251401 137.335219 \nL 209.694403 134.647219 \nL 209.481428 131.959219 \nL 209.653264 129.271219 \nL 210.257413 126.583219 \nL 211.349528 123.895219 \nL 211.509176 123.623948 \nL 213.181968 121.207219 \nL 215.116449 119.172469 \nL 215.87027 118.519219 \nL 218.723722 116.575152 \nL 220.112529 115.831219 \nL 222.330994 114.852191 \nL 225.938267 113.66884 \nL 228.271012 113.143219 \nL 229.54554 112.897424 \nL 233.152813 112.479448 \nL 236.760085 112.325711 \nL 240.367358 112.409334 \nL 243.974631 112.706959 \nL 247.166456 113.143219 \nL 247.581903 113.203602 \nL 251.189176 113.933726 \nL 254.796449 114.834423 \nL 258.198214 115.831219 \nL 258.403722 115.89523 \nL 262.010994 117.203194 \nL 265.298059 118.519219 \nL 265.618267 118.655729 \nL 269.22554 120.36637 \nL 270.862228 121.207219 \nL 272.832812 122.287199 \nL 275.563687 123.895219 \nL 276.440085 124.448188 \nL 279.604724 126.583219 \nL 280.047358 126.904853 \nL 283.105859 129.271219 \nL 283.654631 129.731253 \nL 286.159964 131.959219 \nL 287.261903 133.028429 \nL 288.83977 134.647219 \nL 290.869176 136.937932 \nL 291.203038 137.335219 \nL 293.191129 140.023219 \nL 294.476449 142.006928 \nL 294.909701 142.711219 \nL 296.279347 145.399219 \nL 297.378515 148.087219 \nL 298.083722 150.472739 \nL 298.168537 150.775219 \nL 298.588479 153.463219 \nL 298.662302 156.151219 \nL 298.34997 158.839219 \nL 298.083722 159.824339 \nL 297.551934 161.527219 \nL 296.174692 164.215219 \nL 294.476449 166.503927 \nL 294.122595 166.903219 \nL 290.979786 169.591219 \nL 290.869176 169.666795 \nL 287.261903 171.657915 \nL 285.781377 172.279219 \nL 283.654631 173.025552 \nL 280.047358 173.933394 \nL 276.440085 174.5051 \nL 272.832812 174.778998 \nL 269.22554 174.787801 \nL 265.618267 174.559601 \nL 262.010994 174.118656 \nL 258.403722 173.486024 \nL 254.796449 172.680071 \nz\n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_4\">\n <path d=\"M 269.22554 185.72166 \nL 265.618267 185.282359 \nL 262.010994 184.699629 \nL 258.403722 183.983985 \nL 254.375816 183.031219 \nL 247.581903 181.000687 \nL 243.974631 179.724608 \nL 238.847304 177.655219 \nL 233.058001 174.967219 \nL 228.087463 172.279219 \nL 223.643876 169.591219 \nL 219.65327 166.903219 \nL 216.054902 164.215219 \nL 212.798423 161.527219 \nL 209.841748 158.839219 \nL 207.149429 156.151219 \nL 204.294631 152.953195 \nL 202.556065 150.775219 \nL 200.585579 148.087219 \nL 198.895559 145.399219 \nL 197.080085 142.075352 \nL 196.133014 140.023219 \nL 195.100929 137.335219 \nL 194.286194 134.647219 \nL 193.706789 131.959219 \nL 193.388677 129.271219 \nL 193.345637 126.583219 \nL 193.592815 123.895219 \nL 194.180147 121.207219 \nL 195.130147 118.519219 \nL 196.47877 115.831219 \nL 197.080085 114.907015 \nL 198.377245 113.143219 \nL 200.89559 110.455219 \nL 204.361663 107.767219 \nL 207.901903 105.768466 \nL 209.384019 105.079219 \nL 211.509176 104.216932 \nL 215.116449 103.04473 \nL 218.723722 102.174547 \nL 222.330994 101.591668 \nL 225.938267 101.222557 \nL 229.54554 101.050228 \nL 233.152813 101.059451 \nL 236.760085 101.236527 \nL 240.367358 101.569099 \nL 245.991428 102.391219 \nL 247.581903 102.675852 \nL 251.189176 103.462147 \nL 257.280062 105.079219 \nL 258.403722 105.414385 \nL 265.618267 107.936155 \nL 271.524236 110.455219 \nL 276.440085 112.852789 \nL 280.047358 114.836574 \nL 283.654631 116.99689 \nL 287.261903 119.362015 \nL 290.869176 121.966605 \nL 294.476449 124.853604 \nL 298.083722 128.076876 \nL 299.324129 129.271219 \nL 301.928728 131.959219 \nL 305.298267 135.976239 \nL 306.335508 137.335219 \nL 308.90554 141.161519 \nL 309.829044 142.711219 \nL 311.23202 145.399219 \nL 312.512812 148.29393 \nL 313.372885 150.775219 \nL 314.083701 153.463219 \nL 314.557587 156.151219 \nL 314.774743 158.839219 \nL 314.713095 161.527219 \nL 314.347967 164.215219 \nL 313.651681 166.903219 \nL 312.512812 169.743936 \nL 311.016422 172.279219 \nL 308.90554 175.011003 \nL 305.298267 178.252595 \nL 301.690994 180.60235 \nL 298.083722 182.329621 \nL 294.476449 183.644088 \nL 290.869176 184.611786 \nL 287.261903 185.32256 \nL 283.654631 185.792713 \nL 280.047358 186.034988 \nL 276.440085 186.095104 \nL 272.832812 185.986588 \nL 269.22554 185.72166 \nL 269.22554 185.72166 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_5\">\n <path d=\"M 265.618267 199.573102 \nL 263.370906 199.159219 \nL 262.010994 198.900446 \nL 258.403722 198.110795 \nL 254.796449 197.23092 \nL 251.968434 196.471219 \nL 251.189176 196.254948 \nL 247.581903 195.155779 \nL 243.974631 193.977566 \nL 243.423386 193.783219 \nL 240.367358 192.670201 \nL 236.760085 191.280297 \nL 236.30936 191.095219 \nL 233.152813 189.75562 \nL 230.121752 188.407219 \nL 229.54554 188.141994 \nL 225.938267 186.392336 \nL 224.611143 185.719219 \nL 222.330994 184.521979 \nL 219.603614 183.031219 \nL 218.723722 182.532714 \nL 215.116449 180.407256 \nL 215.012121 180.343219 \nL 211.509176 178.113265 \nL 210.814401 177.655219 \nL 207.901903 175.661046 \nL 206.922265 174.967219 \nL 204.294631 173.031559 \nL 203.306208 172.279219 \nL 200.687358 170.202583 \nL 199.940405 169.591219 \nL 197.080085 167.148021 \nL 196.802155 166.903219 \nL 193.891983 164.215219 \nL 193.472812 163.808248 \nL 191.193748 161.527219 \nL 189.86554 160.129277 \nL 188.675464 158.839219 \nL 186.325034 156.151219 \nL 186.258267 156.069503 \nL 184.190094 153.463219 \nL 182.650994 151.401153 \nL 182.196881 150.775219 \nL 180.395324 148.087219 \nL 179.043722 145.908211 \nL 178.736758 145.399219 \nL 177.27191 142.711219 \nL 175.946945 140.023219 \nL 175.436449 138.844262 \nL 174.801319 137.335219 \nL 173.830842 134.647219 \nL 173.020954 131.959219 \nL 172.381252 129.271219 \nL 171.922114 126.583219 \nL 171.829176 125.636196 \nL 171.663343 123.895219 \nL 171.603346 121.207219 \nL 171.749617 118.519219 \nL 171.829176 117.924589 \nL 172.130884 115.831219 \nL 172.763821 113.143219 \nL 173.66132 110.455219 \nL 174.842188 107.767219 \nL 175.436449 106.675944 \nL 176.38434 105.079219 \nL 178.317022 102.391219 \nL 179.043722 101.531731 \nL 180.747389 99.703219 \nL 182.650994 97.942946 \nL 183.76819 97.015219 \nL 186.258267 95.198878 \nL 187.606331 94.327219 \nL 189.86554 93.024786 \nL 192.62207 91.639219 \nL 193.472812 91.25342 \nL 197.080085 89.835267 \nL 199.752164 88.951219 \nL 200.687358 88.668751 \nL 204.294631 87.759023 \nL 207.901903 87.034951 \nL 211.509176 86.484646 \nL 213.552126 86.263219 \nL 215.116449 86.106443 \nL 218.723722 85.88449 \nL 222.330994 85.798039 \nL 225.938267 85.839515 \nL 229.54554 86.001897 \nL 232.947967 86.263219 \nL 233.152813 86.279493 \nL 236.760085 86.684733 \nL 240.367358 87.197211 \nL 243.974631 87.811166 \nL 247.581903 88.521243 \nL 249.502111 88.951219 \nL 251.189176 89.341465 \nL 254.796449 90.273468 \nL 258.403722 91.290132 \nL 259.53812 91.639219 \nL 262.010994 92.425242 \nL 265.618267 93.656512 \nL 267.456054 94.327219 \nL 269.22554 94.994575 \nL 272.832812 96.439248 \nL 274.191661 97.015219 \nL 276.440085 98.000579 \nL 280.047358 99.657045 \nL 280.14265 99.703219 \nL 283.654631 101.46355 \nL 285.430839 102.391219 \nL 287.261903 103.381655 \nL 290.278739 105.079219 \nL 290.869176 105.423747 \nL 294.476449 107.613283 \nL 294.720394 107.767219 \nL 298.083722 109.96942 \nL 298.800507 110.455219 \nL 301.690994 112.490818 \nL 302.587005 113.143219 \nL 305.298267 115.197646 \nL 306.107856 115.831219 \nL 308.90554 118.113496 \nL 309.387583 118.519219 \nL 312.444367 121.207219 \nL 312.512812 121.270479 \nL 315.266173 123.895219 \nL 316.120085 124.749881 \nL 317.897661 126.583219 \nL 319.727358 128.569475 \nL 320.355226 129.271219 \nL 322.620098 131.959219 \nL 323.334631 132.863628 \nL 324.70368 134.647219 \nL 326.635894 137.335219 \nL 326.941903 137.797866 \nL 328.372336 140.023219 \nL 329.965065 142.711219 \nL 330.549176 143.802534 \nL 331.379914 145.399219 \nL 332.626878 148.087219 \nL 333.724471 150.775219 \nL 334.156449 152.024529 \nL 334.639884 153.463219 \nL 335.373795 156.151219 \nL 335.936649 158.839219 \nL 336.318148 161.527219 \nL 336.50715 164.215219 \nL 336.491582 166.903219 \nL 336.258339 169.591219 \nL 335.793173 172.279219 \nL 335.080564 174.967219 \nL 334.156449 177.512823 \nL 334.100393 177.655219 \nL 332.762681 180.343219 \nL 331.098643 183.031219 \nL 330.549176 183.777681 \nL 328.980919 185.719219 \nL 326.941903 187.864137 \nL 326.369968 188.407219 \nL 323.334631 190.912818 \nL 323.086961 191.095219 \nL 319.727358 193.283521 \nL 318.85473 193.783219 \nL 316.120085 195.18695 \nL 313.219406 196.471219 \nL 312.512812 196.754695 \nL 308.90554 197.99974 \nL 305.298267 199.029578 \nL 304.745372 199.159219 \nL 301.690994 199.816582 \nL 298.083722 200.421814 \nL 294.476449 200.864054 \nL 290.869176 201.153184 \nL 287.261903 201.298302 \nL 283.654631 201.3078 \nL 280.047358 201.18943 \nL 276.440085 200.950365 \nL 272.832812 200.59725 \nL 269.22554 200.136253 \nL 265.618267 199.573102 \nz\n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_6\">\n <path d=\"M 280.047358 220.979319 \nL 272.832812 220.02314 \nL 265.618267 218.754204 \nL 258.403722 217.179216 \nL 251.105294 215.287219 \nL 242.384693 212.599219 \nL 236.760085 210.635428 \nL 229.54554 207.83672 \nL 222.330994 204.71731 \nL 216.323607 201.847219 \nL 211.099039 199.159219 \nL 204.294631 195.338284 \nL 197.38866 191.095219 \nL 193.341098 188.407219 \nL 186.258267 183.300378 \nL 182.471359 180.343219 \nL 179.043722 177.505183 \nL 173.221319 172.279219 \nL 170.446522 169.591219 \nL 167.808313 166.903219 \nL 162.975737 161.527219 \nL 160.743352 158.839219 \nL 156.692942 153.463219 \nL 153.136556 148.087219 \nL 150.064203 142.711219 \nL 147.497459 137.335219 \nL 146.38466 134.647219 \nL 144.563948 129.271219 \nL 143.834642 126.583219 \nL 142.970994 122.379934 \nL 142.772468 121.207219 \nL 142.456033 118.519219 \nL 142.280564 115.831219 \nL 142.252412 113.143219 \nL 142.378312 110.455219 \nL 142.665418 107.767219 \nL 143.127457 105.079219 \nL 143.78658 102.391219 \nL 144.639919 99.703219 \nL 145.697499 97.015219 \nL 146.987904 94.327219 \nL 148.556839 91.639219 \nL 150.388099 88.951219 \nL 153.792812 84.947577 \nL 155.150973 83.575219 \nL 158.171831 80.887219 \nL 161.768502 78.199219 \nL 166.112341 75.511219 \nL 168.221903 74.381098 \nL 171.829176 72.653564 \nL 175.436449 71.196474 \nL 179.043722 69.925626 \nL 182.650994 68.863492 \nL 188.586489 67.447219 \nL 189.86554 67.18797 \nL 193.472812 66.576141 \nL 197.080085 66.085375 \nL 204.294631 65.445475 \nL 211.509176 65.22826 \nL 218.723722 65.398202 \nL 225.938267 65.923646 \nL 233.152813 66.776296 \nL 240.367358 67.949054 \nL 247.581903 69.434834 \nL 254.796449 71.224743 \nL 262.010994 73.309865 \nL 269.22554 75.699966 \nL 276.440085 78.40525 \nL 283.654631 81.436378 \nL 290.869176 84.804501 \nL 298.083722 88.521283 \nL 303.610115 91.639219 \nL 308.90554 94.84955 \nL 312.512812 97.172453 \nL 316.237326 99.703219 \nL 319.98021 102.391219 \nL 323.528454 105.079219 \nL 326.941903 107.807071 \nL 333.0946 113.143219 \nL 337.763722 117.59635 \nL 341.370994 121.313337 \nL 346.0038 126.583219 \nL 348.58554 129.793677 \nL 352.192813 134.708573 \nL 355.800085 140.343448 \nL 358.580397 145.399219 \nL 359.888586 148.087219 \nL 362.124123 153.463219 \nL 363.068272 156.151219 \nL 363.864126 158.839219 \nL 364.537091 161.527219 \nL 365.081806 164.215219 \nL 365.492591 166.903219 \nL 365.763427 169.591219 \nL 365.887928 172.279219 \nL 365.859313 174.967219 \nL 365.670378 177.655219 \nL 365.313457 180.343219 \nL 364.780389 183.031219 \nL 364.062474 185.719219 \nL 363.014631 188.739167 \nL 361.990971 191.095219 \nL 360.59951 193.783219 \nL 358.948396 196.471219 \nL 355.800085 200.569329 \nL 354.658117 201.847219 \nL 351.946598 204.535219 \nL 348.58554 207.331082 \nL 344.884931 209.911219 \nL 340.191571 212.599219 \nL 337.763722 213.791278 \nL 334.156449 215.370645 \nL 330.549176 216.69607 \nL 326.51892 217.975219 \nL 323.334631 218.81718 \nL 319.727358 219.632306 \nL 313.856913 220.663219 \nL 308.90554 221.2732 \nL 301.690994 221.775065 \nL 294.476449 221.87177 \nL 287.261903 221.596608 \nL 280.047358 220.979319 \nL 280.047358 220.979319 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_7\">\n <path d=\"M 283.654631 247.781222 \nL 276.440085 246.682438 \nL 269.22554 245.360752 \nL 262.010994 243.807199 \nL 254.796449 242.040027 \nL 245.701665 239.479219 \nL 240.367358 237.815082 \nL 233.152813 235.368151 \nL 225.938267 232.692229 \nL 218.723722 229.781728 \nL 211.509176 226.630877 \nL 204.294631 223.230265 \nL 197.080085 219.552138 \nL 189.304922 215.287219 \nL 182.650994 211.350087 \nL 175.436449 206.778474 \nL 168.216749 201.847219 \nL 160.947149 196.471219 \nL 153.792812 190.72481 \nL 148.029455 185.719219 \nL 142.279027 180.343219 \nL 136.972864 174.967219 \nL 132.067105 169.591219 \nL 127.574716 164.215219 \nL 123.457847 158.839219 \nL 119.710787 153.463219 \nL 116.327937 148.087219 \nL 113.303812 142.711219 \nL 110.50554 137.043015 \nL 108.346959 131.959219 \nL 106.408984 126.583219 \nL 104.857316 121.207219 \nL 103.678025 115.831219 \nL 102.906378 110.455219 \nL 102.558168 105.079219 \nL 102.54766 102.391219 \nL 102.651118 99.703219 \nL 102.872427 97.015219 \nL 103.290994 93.891575 \nL 103.696798 91.639219 \nL 104.315066 88.951219 \nL 105.073204 86.263219 \nL 105.976423 83.575219 \nL 107.034464 80.887219 \nL 108.28424 78.199219 \nL 110.50554 74.14876 \nL 111.324609 72.823219 \nL 114.112812 68.876169 \nL 115.244721 67.447219 \nL 117.720085 64.607099 \nL 121.327358 61.052521 \nL 124.934631 57.985667 \nL 128.541903 55.309657 \nL 132.149176 52.951676 \nL 135.756449 50.855939 \nL 140.120712 48.631219 \nL 142.970994 47.340446 \nL 146.578267 45.845958 \nL 150.18554 44.533223 \nL 154.085348 43.255219 \nL 161.007358 41.380247 \nL 164.614631 40.559377 \nL 171.829176 39.259402 \nL 179.043722 38.320411 \nL 186.258267 37.723336 \nL 193.472812 37.444996 \nL 200.687358 37.452984 \nL 207.901903 37.730014 \nL 215.116449 38.271052 \nL 222.330994 39.060944 \nL 229.54554 40.081031 \nL 236.760085 41.338899 \nL 245.894722 43.255219 \nL 251.189176 44.531235 \nL 258.403722 46.458367 \nL 265.694916 48.631219 \nL 273.776104 51.319219 \nL 281.122779 54.007219 \nL 287.890223 56.695219 \nL 294.476449 59.513552 \nL 301.690994 62.84875 \nL 308.90554 66.439664 \nL 316.120085 70.297644 \nL 323.334631 74.463897 \nL 330.549176 78.938422 \nL 337.763722 83.755518 \nL 344.978267 88.961285 \nL 352.192813 94.610484 \nL 358.205779 99.703219 \nL 363.014631 104.062742 \nL 366.879239 107.767219 \nL 372.101811 113.143219 \nL 376.929767 118.519219 \nL 381.361055 123.895219 \nL 385.406664 129.271219 \nL 389.085591 134.647219 \nL 392.403349 140.023219 \nL 395.480085 145.633226 \nL 397.94812 150.775219 \nL 400.179973 156.151219 \nL 402.046663 161.527219 \nL 403.532634 166.903219 \nL 404.628616 172.279219 \nL 405.326635 177.655219 \nL 405.5999 183.031219 \nL 405.568214 185.719219 \nL 405.419165 188.407219 \nL 405.148664 191.095219 \nL 404.752432 193.783219 \nL 404.225985 196.471219 \nL 403.564625 199.159219 \nL 402.694631 202.044877 \nL 401.789434 204.535219 \nL 400.657259 207.223219 \nL 399.087358 210.42301 \nL 397.859643 212.599219 \nL 395.480085 216.271202 \nL 394.234945 217.975219 \nL 391.872813 220.892705 \nL 388.26554 224.694734 \nL 384.658267 227.951895 \nL 383.718552 228.727219 \nL 380.16586 231.415219 \nL 376.095871 234.103219 \nL 371.392691 236.791219 \nL 370.229176 237.396554 \nL 365.859089 239.479219 \nL 363.014631 240.683075 \nL 359.163163 242.167219 \nL 352.192813 244.409322 \nL 348.58554 245.381196 \nL 341.370994 246.984093 \nL 337.763722 247.635018 \nL 330.549176 248.632685 \nL 323.334631 249.293072 \nL 316.120085 249.637893 \nL 308.90554 249.687038 \nL 301.690994 249.45876 \nL 294.476449 248.969838 \nL 287.261903 248.235726 \nL 283.654631 247.781222 \nL 283.654631 247.781222 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_8\">\n <path d=\"M 255.675354 277.111219 \nL 254.796449 276.884316 \nL 251.189176 275.913337 \nL 247.581903 274.90852 \nL 245.901653 274.423219 \nL 243.974631 273.859343 \nL 240.367358 272.767452 \nL 237.05643 271.735219 \nL 236.760085 271.64161 \nL 233.152813 270.4628 \nL 229.54554 269.252971 \nL 228.950627 269.047219 \nL 225.938267 267.991655 \nL 222.330994 266.696152 \nL 221.418472 266.359219 \nL 218.723722 265.351039 \nL 215.116449 263.970075 \nL 214.355786 263.671219 \nL 211.509176 262.537903 \nL 207.901903 261.071717 \nL 207.689589 260.983219 \nL 204.294631 259.549125 \nL 201.382717 258.295219 \nL 200.687358 257.991717 \nL 197.080085 256.381505 \nL 195.379281 255.607219 \nL 193.472812 254.727429 \nL 189.86554 253.031768 \nL 189.631152 252.919219 \nL 186.258267 251.277319 \nL 184.145795 250.231219 \nL 182.650994 249.480658 \nL 179.043722 247.637914 \nL 178.861926 247.543219 \nL 175.436449 245.733866 \nL 173.799575 244.855219 \nL 171.829176 243.782472 \nL 168.908984 242.167219 \nL 168.221903 241.781679 \nL 164.614631 239.723754 \nL 164.193087 239.479219 \nL 161.007358 237.604312 \nL 159.646346 236.791219 \nL 157.400085 235.429452 \nL 155.244497 234.103219 \nL 153.792812 233.196683 \nL 150.981261 231.415219 \nL 150.18554 230.903362 \nL 146.850719 228.727219 \nL 146.578267 228.546683 \nL 142.970994 226.12166 \nL 142.850119 226.039219 \nL 139.363722 223.624386 \nL 138.974674 223.351219 \nL 135.756449 221.055858 \nL 135.213295 220.663219 \nL 132.149176 218.412645 \nL 131.561473 217.975219 \nL 128.541903 215.691091 \nL 128.014935 215.287219 \nL 124.934631 212.887297 \nL 124.569627 212.599219 \nL 121.327358 209.997104 \nL 121.2217 209.911219 \nL 117.972784 207.223219 \nL 117.720085 207.010403 \nL 114.818117 204.535219 \nL 114.112812 203.922849 \nL 111.751975 201.847219 \nL 110.50554 200.731344 \nL 108.771087 199.159219 \nL 106.898267 197.430088 \nL 105.872346 196.471219 \nL 103.290994 194.012836 \nL 103.052788 193.783219 \nL 100.322265 191.095219 \nL 99.683722 190.45364 \nL 97.671353 188.407219 \nL 96.076449 186.752354 \nL 95.092521 185.719219 \nL 92.585513 183.031219 \nL 92.469176 182.903407 \nL 90.166286 180.343219 \nL 88.861903 178.861326 \nL 87.81263 177.655219 \nL 85.527528 174.967219 \nL 85.254631 174.637563 \nL 83.324974 172.279219 \nL 81.647358 170.180195 \nL 81.182023 169.591219 \nL 79.117051 166.903219 \nL 78.040085 165.463347 \nL 77.117198 164.215219 \nL 75.185685 161.527219 \nL 74.432812 160.447166 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 431.552813 257.369285 \nL 430.451188 258.295219 \nL 427.94554 260.291826 \nL 427.037543 260.983219 \nL 424.338267 262.937053 \nL 423.274552 263.671219 \nL 420.730994 265.344124 \nL 419.108505 266.359219 \nL 417.123722 267.545157 \nL 414.474087 269.047219 \nL 413.516449 269.566744 \nL 409.909176 271.421539 \nL 409.264817 271.735219 \nL 406.301903 273.118738 \nL 403.331438 274.423219 \nL 402.694631 274.691909 \nL 399.087358 276.127706 \nL 396.446001 277.111219 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 74.432812 31.643988 \nL 76.508334 29.815219 \nL 78.040085 28.537301 \nL 79.806922 27.127219 \nL 81.647358 25.732522 \nL 83.43509 24.439219 \nL 85.254631 23.18614 \nL 87.442161 21.751219 \nL 88.861903 20.86262 \nL 91.887822 19.063219 \nL 92.469176 18.732661 \nL 96.076449 16.784564 \nL 96.876623 16.375219 \nL 99.683722 14.998831 \nL 102.522503 13.687219 \nL 103.290994 13.346309 \nL 106.898267 11.835337 \nL 109.025992 10.999219 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 256.204303 10.999219 \nL 258.403722 11.602438 \nL 262.010994 12.628274 \nL 265.618267 13.687083 \nL 265.618712 13.687219 \nL 269.22554 14.800293 \nL 272.832812 15.945422 \nL 274.144813 16.375219 \nL 276.440085 17.137019 \nL 280.047358 18.368299 \nL 282.028143 19.063219 \nL 283.654631 19.641395 \nL 287.261903 20.958631 \nL 289.379157 21.751219 \nL 290.869176 22.316432 \nL 294.476449 23.719405 \nL 296.284374 24.439219 \nL 298.083722 25.165216 \nL 301.690994 26.65368 \nL 302.812527 27.127219 \nL 305.298267 28.190907 \nL 308.90554 29.764589 \nL 309.018909 29.815219 \nL 312.512812 31.396741 \nL 314.913321 32.503219 \nL 316.120085 33.067105 \nL 319.727358 34.786036 \nL 320.561025 35.191219 \nL 323.334631 36.557909 \nL 325.970937 37.879219 \nL 326.941903 38.372691 \nL 330.549176 40.239443 \nL 331.171087 40.567219 \nL 334.156449 42.162854 \nL 336.16777 43.255219 \nL 337.763722 44.134404 \nL 340.995884 45.943219 \nL 341.370994 46.156191 \nL 344.978267 48.239391 \nL 345.646037 48.631219 \nL 348.58554 50.381251 \nL 350.137745 51.319219 \nL 352.192813 52.579484 \nL 354.487061 54.007219 \nL 355.800085 54.836636 \nL 358.700116 56.695219 \nL 359.407358 57.155411 \nL 362.782695 59.383219 \nL 363.014631 59.53868 \nL 366.621903 61.991446 \nL 366.737563 62.071219 \nL 370.229176 64.51712 \nL 370.570132 64.759219 \nL 373.836449 67.115348 \nL 374.290417 67.447219 \nL 377.443722 69.789644 \nL 377.90283 70.135219 \nL 381.050994 72.543753 \nL 381.411557 72.823219 \nL 384.658267 75.381669 \nL 384.820569 75.511219 \nL 388.130797 78.199219 \nL 388.26554 78.310588 \nL 391.343324 80.887219 \nL 391.872813 81.338352 \nL 394.465235 83.575219 \nL 395.480085 84.466689 \nL 397.4999 86.263219 \nL 399.087358 87.701148 \nL 400.450524 88.951219 \nL 402.694631 91.04769 \nL 403.320156 91.639219 \nL 406.107825 94.327219 \nL 406.301903 94.51839 \nL 408.806153 97.015219 \nL 409.909176 98.137039 \nL 411.430779 99.703219 \nL 413.516449 101.893946 \nL 413.984304 102.391219 \nL 416.456236 105.079219 \nL 417.123722 105.821848 \nL 418.851755 107.767219 \nL 420.730994 109.929525 \nL 421.182577 110.455219 \nL 423.433607 113.143219 \nL 424.338267 114.250508 \nL 425.614809 115.831219 \nL 427.733135 118.519219 \nL 427.94554 118.796758 \nL 429.769095 121.207219 \nL 431.552813 123.625186 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_9\">\n <path d=\"M 138.765798 277.111219 \nL 135.756449 275.408867 \nL 134.033784 274.423219 \nL 132.149176 273.333355 \nL 129.416591 271.735219 \nL 128.541903 271.21812 \nL 124.934631 269.061614 \nL 124.910847 269.047219 \nL 121.327358 266.854699 \nL 120.526245 266.359219 \nL 117.720085 264.604535 \nL 116.243367 263.671219 \nL 114.112812 262.309678 \nL 112.059002 260.983219 \nL 110.50554 259.968619 \nL 107.970071 258.295219 \nL 106.898267 257.579779 \nL 103.973624 255.607219 \nL 103.290994 255.14151 \nL 100.066829 252.919219 \nL 99.683722 252.652082 \nL 96.24697 250.231219 \nL 96.076449 250.109687 \nL 92.511439 247.543219 \nL 92.469176 247.512431 \nL 88.861903 244.858269 \nL 88.857799 244.855219 \nL 85.28344 242.167219 \nL 85.254631 242.145289 \nL 81.786253 239.479219 \nL 81.647358 239.371133 \nL 78.363946 236.791219 \nL 78.040085 236.533561 \nL 75.01438 234.103219 \nL 74.432812 233.630161 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n <path d=\"M 371.137758 10.999219 \nL 373.836449 12.538996 \nL 375.826208 13.687219 \nL 377.443722 14.630674 \nL 380.40135 16.375219 \nL 381.050994 16.762577 \nL 384.658267 18.938164 \nL 384.863156 19.063219 \nL 388.26554 21.162572 \nL 389.209338 21.751219 \nL 391.872813 23.430783 \nL 393.455067 24.439219 \nL 395.480085 25.744267 \nL 397.603499 27.127219 \nL 399.087358 28.104557 \nL 401.657663 29.815219 \nL 402.694631 30.513258 \nL 405.62046 32.503219 \nL 406.301903 32.972051 \nL 409.494676 35.191219 \nL 409.909176 35.482691 \nL 413.282982 37.879219 \nL 413.516449 38.047021 \nL 416.987946 40.567219 \nL 417.123722 40.666968 \nL 420.612031 43.255219 \nL 420.730994 43.344557 \nL 424.157607 45.943219 \nL 424.338267 46.081908 \nL 427.626951 48.631219 \nL 427.94554 48.881249 \nL 431.022253 51.319219 \nL 431.552813 51.74492 \n\" clip-path=\"url(#pc77fd4bf65)\" style=\"fill: none; stroke: #440154; stroke-width: 1.5\"/>\n </g>\n <g id=\"PathCollection_10\"/>\n <g id=\"PathCollection_11\"/>\n <g id=\"PathCollection_12\"/>\n <g id=\"PathCollection_13\"/>\n <g id=\"PathCollection_14\"/>\n <g id=\"PathCollection_15\"/>\n <g id=\"PathCollection_16\"/>\n <g id=\"PathCollection_17\"/>\n <g id=\"PathCollection_18\"/>\n <g id=\"PathCollection_19\"/>\n <g id=\"PathCollection_20\"/>\n <g id=\"patch_3\">\n <path d=\"M 74.432812 277.111219 \nL 74.432812 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_4\">\n <path d=\"M 431.552813 277.111219 \nL 431.552813 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_5\">\n <path d=\"M 74.432812 277.111219 \nL 431.552813 277.111219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n <g id=\"patch_6\">\n <path d=\"M 74.432812 10.999219 \nL 431.552813 10.999219 \n\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n </g>\n </g>\n </g>\n <defs>\n <clipPath id=\"pc77fd4bf65\">\n <rect x=\"74.432812\" y=\"10.999219\" width=\"357.12\" height=\"266.112\"/>\n </clipPath>\n </defs>\n</svg>\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"contour_plot(XMx2_norm, yMx2)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Teraz funkcja kosztu ma wykres o bardzo regularnym kształcie – algorytm gradientu prostego zastosowany w takim przypadku bardzo szybko znajdzie minimum funkcji kosztu."
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.4"
},
"livereveal": {
"start_slideshow_at": "selected",
"theme": "white"
},
"vscode": {
"interpreter": {
"hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
}
}
},
"nbformat": 4,
"nbformat_minor": 4
}
Reference in New Issue View Git Blame Copy Permalink