{ "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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\n", "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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\n", "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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\n", "text/plain": [ "
" ] }, "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": [ "[]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "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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"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": [ "[]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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