324 lines
72 KiB
Plaintext
324 lines
72 KiB
Plaintext
|
{
|
||
|
|
"cells": [
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 2,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import sympy as sp\n",
|
||
|
|
"import matplotlib.pyplot as plt\n",
|
||
|
|
"from sympy.plotting import plot\n",
|
||
|
|
"from sympy.polys.polyfuncs import horner\n",
|
||
|
|
"\n",
|
||
|
|
"sp.init_printing()\n",
|
||
|
|
"\n",
|
||
|
|
"%matplotlib inline"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 3,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"x, s = sp.symbols(\"x, sigma\")\n",
|
||
|
|
"s = sp.sympify(1)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 4,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"full = sp.exp(- (x/s)**2)\n",
|
||
|
|
"approx = full.series(x, x0=0, n=5).removeO()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 5,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"x_vals = (-2 *s, -1.6*s, 0, 1.6*s, 2 * s)\n",
|
||
|
|
"y_vals = list(full.subs(x, e) for e in x_vals)\n",
|
||
|
|
"y_vals[0] = 0\n",
|
||
|
|
"y_vals[-1] = 0"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle \\begin{cases} - 0.27606958941084 x^{3} - 0.80213917882168 x^{2} + 6.93889390390723 \\cdot 10^{-18} x + 1.0 & \\text{for}\\: x \\geq -2 \\wedge x \\leq 0 \\\\0.27606958941084 x^{3} - 0.80213917882168 x^{2} + 6.93889390390723 \\cdot 10^{-18} x + 1.0 & \\text{for}\\: x \\geq 0 \\wedge x \\leq 2 \\end{cases}$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"⎧ 3 2 \n",
|
||
|
|
"⎪- 0.27606958941084⋅x - 0.80213917882168⋅x + 6.93889390390723e-18⋅x + 1.0 f\n",
|
||
|
|
"⎨ \n",
|
||
|
|
"⎪ 3 2 \n",
|
||
|
|
"⎩ 0.27606958941084⋅x - 0.80213917882168⋅x + 6.93889390390723e-18⋅x + 1.0 f\n",
|
||
|
|
"\n",
|
||
|
|
" \n",
|
||
|
|
"or x ≥ -2 ∧ x ≤ 0\n",
|
||
|
|
" \n",
|
||
|
|
" \n",
|
||
|
|
"or x ≥ 0 ∧ x ≤ 2 "
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"spline = sp.interpolating_spline(3, x, x_vals, y_vals)\n",
|
||
|
|
"spline"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 7,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle - 0.27606958941084 x^{3} - 0.80213917882168 x^{2} + 6.93889390390723 \\cdot 10^{-18} x + 1.0$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
" 3 2 \n",
|
||
|
|
"- 0.27606958941084⋅x - 0.80213917882168⋅x + 6.93889390390723e-18⋅x + 1.0"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 7,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"spline.args[0][0]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"p1 = plot(full, show=False, xlim=(0, 3), ylim=(-0.1, 1.1))\n",
|
||
|
|
"p2 = plot(spline, show=False, line_color='r')\n",
|
||
|
|
"p1.append(p2[0])\n",
|
||
|
|
"p1.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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\n",
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle -0.2441961116159$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"-0.244196111615900"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"spline.subs(x, 1.99).evalf() * 255"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 42,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def bellCurveApproximation(x, inverseWidth):\n",
|
||
|
|
" if x < 0:\n",
|
||
|
|
" x = -x\n",
|
||
|
|
"\n",
|
||
|
|
" nx = x * inverseWidth * 4\n",
|
||
|
|
" if nx > 2:\n",
|
||
|
|
" return 0\n",
|
||
|
|
"\n",
|
||
|
|
" x2 = nx * nx\n",
|
||
|
|
" x3 = x2 * nx\n",
|
||
|
|
" res = 0.27606958941084 * x3 - 0.80213917882168 * x2 + 1\n",
|
||
|
|
" \n",
|
||
|
|
" return 0 if res < 0 else res"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 43,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[<matplotlib.lines.Line2D at 0x7f4a503fd190>]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 43,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot([bellCurveApproximation(i, 1 / (51 / 2)) for i in range(51)])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 25,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def extract_blue(v):\n",
|
||
|
|
" return (v >> 16) & 255"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 36,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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\n",
|
||
|
|
"text/latex": [
|
||
|
|
"$\\displaystyle 0.35294117647058826$"
|
||
|
|
],
|
||
|
|
"text/plain": [
|
||
|
|
"0.35294117647058826"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 36,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"v = [extract_blue(e) for e in data[0]]\n",
|
||
|
|
"v.count(0) / len(v)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 27,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"[<matplotlib.lines.Line2D at 0x7f4a4fe84340>]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 27,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.plot([extract_blue(e) for e in data[0]])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.8.10"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|