{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Simple Way to Draw a Curve"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.384879Z",
"iopub.status.busy": "2024-04-17T07:35:03.384795Z",
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"shell.execute_reply": "2024-04-17T07:35:03.708527Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"from lets_plot import *\n",
"LetsPlot.setup_html()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.722327Z",
"iopub.status.busy": "2024-04-17T07:35:03.722169Z",
"iopub.status.idle": "2024-04-17T07:35:03.723670Z",
"shell.execute_reply": "2024-04-17T07:35:03.723496Z"
}
},
"outputs": [],
"source": [
"BG_CLR = '#253494'\n",
"EC_CLR = '#ffffcc'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.724860Z",
"iopub.status.busy": "2024-04-17T07:35:03.724709Z",
"iopub.status.idle": "2024-04-17T07:35:03.726177Z",
"shell.execute_reply": "2024-04-17T07:35:03.725993Z"
}
},
"outputs": [],
"source": [
"# Curve parametrized equation\n",
"def ec_eq(*, a=0, b=0):\n",
" return lambda x, y: y ** 2 - x ** 3 - a * x - b"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.727343Z",
"iopub.status.busy": "2024-04-17T07:35:03.727227Z",
"iopub.status.idle": "2024-04-17T07:35:03.728785Z",
"shell.execute_reply": "2024-04-17T07:35:03.728605Z"
}
},
"outputs": [],
"source": [
"def level(X, Y, *, eq, c=1):\n",
" level_map = lambda z: np.exp(-c * np.abs(z))\n",
" return level_map(eq(X, Y))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.729910Z",
"iopub.status.busy": "2024-04-17T07:35:03.729800Z",
"iopub.status.idle": "2024-04-17T07:35:03.732091Z",
"shell.execute_reply": "2024-04-17T07:35:03.731908Z"
}
},
"outputs": [],
"source": [
"dx, dy = 1.0 / 30.0, 1.0 / 10.0\n",
"\n",
"x = np.arange(-3, 3, dx)\n",
"y = np.arange(-3, 3, dy)\n",
"X, Y = np.meshgrid(x, y)\n",
"curve_eq = ec_eq(a=-1, b=0)\n",
"Z = level(X, Y, eq=curve_eq, c=10)\n",
"\n",
"df = pd.DataFrame(dict(x=X.reshape(-1), y=Y.reshape(-1), z=Z.reshape(-1)))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.733183Z",
"iopub.status.busy": "2024-04-17T07:35:03.733071Z",
"iopub.status.idle": "2024-04-17T07:35:03.735021Z",
"shell.execute_reply": "2024-04-17T07:35:03.734839Z"
}
},
"outputs": [],
"source": [
"theme_layer = scale_color_gradient(low=BG_CLR, high=EC_CLR) + scale_fill_gradient(low=BG_CLR, high=EC_CLR) + \\\n",
" xlim(df.x.min(), df.x.max()) + ylim(df.y.min(), df.y.max()) + ggsize(600, 450) + \\\n",
" theme_void() + theme(panel_background=element_rect(color=BG_CLR, fill=BG_CLR))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.735958Z",
"iopub.status.busy": "2024-04-17T07:35:03.735845Z",
"iopub.status.idle": "2024-04-17T07:35:03.769452Z",
"shell.execute_reply": "2024-04-17T07:35:03.769215Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_point(aes(x='x', y='y', color='z'), data=df[df.z > 0.5].sort_values(by='z')) + \\\n",
" coord_fixed() + theme_layer + \\\n",
" ggtitle('Elliptic Curve by Points')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.770502Z",
"iopub.status.busy": "2024-04-17T07:35:03.770409Z",
"iopub.status.idle": "2024-04-17T07:35:03.847672Z",
"shell.execute_reply": "2024-04-17T07:35:03.847461Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_bin2d(aes(x='x', y='y', fill='z'), data=df, stat='identity', color=BG_CLR) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by 2D-Bins')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.850727Z",
"iopub.status.busy": "2024-04-17T07:35:03.850619Z",
"iopub.status.idle": "2024-04-17T07:35:03.927553Z",
"shell.execute_reply": "2024-04-17T07:35:03.927339Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_tile(aes(x='x', y='y', fill='z'), data=df, color=BG_CLR) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Tiles')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:03.930422Z",
"iopub.status.busy": "2024-04-17T07:35:03.930247Z",
"iopub.status.idle": "2024-04-17T07:35:04.006380Z",
"shell.execute_reply": "2024-04-17T07:35:04.006160Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_raster(aes(x='x', y='y', fill='z'), data=df) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Raster')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:04.009311Z",
"iopub.status.busy": "2024-04-17T07:35:04.009206Z",
"iopub.status.idle": "2024-04-17T07:35:04.054848Z",
"shell.execute_reply": "2024-04-17T07:35:04.054647Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_contour(aes(x='x', y='y', z='z', color='..level..'), data=df, bins=4) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Contours')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2024-04-17T07:35:04.055985Z",
"iopub.status.busy": "2024-04-17T07:35:04.055909Z",
"iopub.status.idle": "2024-04-17T07:35:04.108422Z",
"shell.execute_reply": "2024-04-17T07:35:04.108218Z"
}
},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ggplot() + \\\n",
" geom_contourf(aes(x='x', y='y', z='z', fill='..level..'), data=df, binwidth=.3) + \\\n",
" theme_layer + \\\n",
" ggtitle('Elliptic Curve by Filled Contours')"
]
}
],
"metadata": {
"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": "3.10.13"
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