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@Sin-tel
Last active December 18, 2024 22:00
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "9b931400-1b08-4c2f-916f-4a4fab513ebb",
"metadata": {},
"outputs": [],
"source": [
"from fractions import Fraction\n",
"import math\n",
"\n",
"import numpy as np\n",
"import scipy\n",
"\n",
"import matplotlib.pyplot as plt\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d5a23e83-6213-46dd-bbff-e5c9dfdf7bce",
"metadata": {},
"outputs": [],
"source": [
"# arbitrary cutoff point\n",
"c_limit = 10_000"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6af30c89-2caa-4e2f-a50a-6d8a6f8b6917",
"metadata": {},
"outputs": [],
"source": [
"# generate farey series up to some integer limit\n",
"def farey(n: int) -> list[Fraction]:\n",
" l: list[Fraction] = []\n",
" # We know first two terms are\n",
" # 0/1 and 1/n\n",
" x1 = 0\n",
" y1 = 1\n",
" x2 = 1\n",
" y2 = n\n",
"\n",
" l.append(Fraction(y2, x2))\n",
"\n",
" # For next terms to be evaluated\n",
" x = 0\n",
" y = 0\n",
" while True:\n",
" # Using recurrence relation to\n",
" # find the next term\n",
" x = math.floor((y1 + n) / y2) * x2 - x1\n",
" y = math.floor((y1 + n) / y2) * y2 - y1\n",
"\n",
" if y == 1:\n",
" break\n",
"\n",
" if x*y < c_limit:\n",
" l.append(Fraction(y, x))\n",
"\n",
" # Update x1, y1, x2 and y2 for\n",
" # next iteration\n",
" x1 = x2\n",
" x2 = x\n",
" y1 = y2\n",
" y2 = y\n",
"\n",
" # we forgot 1\n",
" l.append(Fraction(1,1))\n",
" return l\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d203b87e-4c16-4d42-a2fc-dad39e4e69e1",
"metadata": {},
"outputs": [],
"source": [
"def weight(n, d):\n",
" return 1.0 / np.sqrt(n*d)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d0aecd70-cddb-400a-9808-e5b898297128",
"metadata": {},
"outputs": [],
"source": [
"def cents(n, d):\n",
" return 1200*np.log2(n/d)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "f143b169-fab9-444f-8ec9-632d8f680167",
"metadata": {},
"outputs": [],
"source": [
"# the Renyi entropy power\n",
"# n.b. you can't set this to 1 since that's only defined in the limit\n",
"# use some number like 7 to get something close to min-entropy\n",
"alpha = 2.0"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "8ab49800-7bf5-469b-8f6b-51420ee05288",
"metadata": {},
"outputs": [],
"source": [
"f_list = farey(1000)\n",
"n = np.array([f.numerator for f in f_list])\n",
"d = np.array([f.denominator for f in f_list])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "2b266655-e6e2-4e77-b3f2-87f12537c04e",
"metadata": {},
"outputs": [],
"source": [
"x_start = 0\n",
"x_end = 2400\n",
"x = np.arange(x_start, x_end+1, 1)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "1f17ff9b-5d54-4e23-9798-730f7239d287",
"metadata": {},
"outputs": [],
"source": [
"k = np.zeros_like(x).astype(np.float64)\n",
"k_alpha = np.zeros_like(x).astype(np.float64)\\\n",
"\n",
"# crude rounding to get the coordinate\n",
"c = np.round(cents(n, d)).astype(np.int64)\n",
"\n",
"# splat the dirac deltas\n",
"for i in range(len(d)):\n",
" if c[i] < x_start or c[i] > x_end:\n",
" continue\n",
" k[c[i]] += weight(n[i], d[i])\n",
" k_alpha[c[i]] += weight(n[i], d[i])**alpha"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "1d2aca1c-1a5f-46d1-bc86-71bd6553adee",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x, k)\n",
"plt.plot(x, k_alpha)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7517d3ce-09ac-4f2c-99ad-a442e4e1ab91",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 300x200 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# define spreading function\n",
"\n",
"std = 12 # cents spread\n",
"s_range = round(std*5)\n",
"x_s = np.arange(-s_range, s_range, 1)\n",
"s = np.exp(-(x_s**2) / (2*std**2))\n",
"\n",
"plt.figure(figsize=(3, 2))\n",
"plt.plot(x_s, s)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "b10b5a62-fb74-4404-b2a5-2bef5ae4da34",
"metadata": {},
"outputs": [],
"source": [
"prod_k_s = scipy.signal.convolve(k, s, mode = 'same')\n",
"prod_k_s_alpha = scipy.signal.convolve(k_alpha, s**alpha, mode = 'same')\n",
"entropy = (1 / (1-alpha)) * np.log(prod_k_s_alpha / (prod_k_s**alpha))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "60c41c6d-8ad2-4c4a-8b31-5ecb74b02e8a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1000x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10, 5))\n",
"plt.plot(x, entropy)\n",
"plt.xlim([x_start, x_end])\n",
"plt.xticks([0, 702, 1200, 1902, 2400])\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d512aa7e-6d33-42e3-a09d-9cbb45a617d7",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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