Files
plateflow/Bendpoint Kruemmung.ipynb
Franz Innerbichler 9cbf31608b Formulas iPyNB added
2025-12-30 15:10:43 +01:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 42,
"id": "9d327064-7af3-4932-a9a9-351b2844638a",
"metadata": {},
"outputs": [],
"source": [
"import sympy as sp\n",
"import numpy as np\n",
"import matplotlib"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "36eb1531-9115-43e2-855d-af239a17b757",
"metadata": {},
"outputs": [],
"source": [
"a,d,b,c,x,g,z, trueb, = sp.symbols(\"a d b c x g z trueb\")"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "ae3356c6-7afc-4763-824e-349d84e05558",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle a + \\frac{- a + d}{e^{b \\left(c - x\\right)} + 1}$"
],
"text/plain": [
"a + (-a + d)/(exp(b*(c - x)) + 1)"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = a+(d-a)/(1+sp.exp(b*(c-x)))\n",
"f"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "74c80174-8c90-4a5c-b806-c45824ac7a01",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p1 = sp.plot(f.subs({a: 0.5, b: 1, c: 0, d: 5}), (x,-7,7), show=False)\n",
"x2 = sp.Symbol('x2 y')\n",
"p2 = sp.plot_implicit(sp.Eq(x2,(3)), legend=True, show = False)\n",
"p3 = sp.plot_implicit(sp.Eq(x2,(-3)), legend=True, show = False)\n",
"p4 = sp.plot_implicit(sp.Eq(x2,(-1.31696)), legend=True, show = False, line_color = \"red\")\n",
"p5 = sp.plot_implicit(sp.Eq(x2,(1.31696)), legend=True, show = False, line_color=\"red\")\n",
"\n",
"p1.append(p2[0])\n",
"p1.append(p3[0])\n",
"p1.append(p4[0])\n",
"p1.append(p5[0])\n",
"p1.show()"
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "a4ba0f5f-d37b-4fca-8104-c0156a4aac2e",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{b \\left(- a + d\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{2}}$"
],
"text/plain": [
"b*(-a + d)*exp(b*(c - x))/(exp(b*(c - x)) + 1)**2"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df1 = f.diff(x)\n",
"df1"
]
},
{
"cell_type": "code",
"execution_count": 47,
"id": "df4df7d7-477f-4d6c-aacb-88d4b95b7813",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\\frac{b \\left(- a + d\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{2}}\n"
]
}
],
"source": [
"print(sp.latex(df1))"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "76d73d1a-337e-4f6b-9df1-3388307151e3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x11feeaab0>"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.plot(df1.subs({a: 0, b: 1, c: 0.517, d: 6}),(x,-7,7))"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "6ff6cf1c-d79a-4f8d-8acf-de9bc1a2ade4",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{b^{2} \\left(1 - e^{b \\left(c - x\\right)}\\right) \\left(a - d\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}}$"
],
"text/plain": [
"b**2*(1 - exp(b*(c - x)))*(a - d)*exp(b*(c - x))/(exp(b*(c - x)) + 1)**3"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df2 = f.diff(x,2).simplify()\n",
"df2"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "aba3542c-98b8-4e45-a4e6-7d1bf0df8f6a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\\frac{b^{2} \\left(1 - e^{b \\left(c - x\\right)}\\right) \\left(a - d\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}}\n"
]
}
],
"source": [
"print(sp.latex(df2))"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "8c4d3d6e-339c-4840-a690-e9b391cab76b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x11fd4a660>"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.plot(df2.subs({a: 0, b: 1, c: 0.517, d: 6}),(x,-7,7))"
]
},
{
"cell_type": "markdown",
"id": "980af1a4-7e85-4d7f-b070-552edace131a",
"metadata": {},
"source": [
"Berechne, wo die 2. Ableitung bei x=3 ist in %"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "d3240da7-6fab-491e-987f-8d017da14e54",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle -0.204457873304717$"
],
"text/plain": [
"-0.204457873304717"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df2.subs({a: 0, b: 1, c: 0, d: 5, x: 3}).evalf()"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "a1f65e93-ebe6-4471-94f0-b841df1149ae",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle -0.481125224323624$"
],
"text/plain": [
"-0.481125224323624"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df2.subs({a: 0, b: 1, c: 0, d: 5, x: 1.31696}).evalf()"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "bcf70b76-bd1c-47e1-b983-89d819549b79",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"42.495817095349445"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"-0.204458/-0.481125*100"
]
},
{
"cell_type": "markdown",
"id": "b0f4eb2a-fe40-46ea-bc92-4aece83a1ff8",
"metadata": {},
"source": [
"## Approach 3\n"
]
},
{
"cell_type": "code",
"execution_count": 55,
"id": "978d063f-34e1-476a-ba59-a2a5c4dea762",
"metadata": {},
"outputs": [],
"source": [
"K = df2/(1+df1**2)**(3/2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e6607d65-1aeb-4d18-8dc7-3173affd82be",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 56,
"id": "0544598c-c6cd-4758-84e4-ed989028ae9c",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle - \\frac{b^{3} \\left(1 - e^{b \\left(c - x\\right)}\\right) \\left(a - d\\right) e^{b \\left(c - x\\right)}}{\\left(\\frac{b^{2} \\left(- a + d\\right)^{2} e^{2 b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}} + 1\\right)^{1.5} \\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}} + \\frac{3 b^{3} \\left(1 - e^{b \\left(c - x\\right)}\\right) \\left(a - d\\right) e^{2 b \\left(c - x\\right)}}{\\left(\\frac{b^{2} \\left(- a + d\\right)^{2} e^{2 b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}} + 1\\right)^{1.5} \\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}} + \\frac{b^{3} \\left(a - d\\right) e^{2 b \\left(c - x\\right)}}{\\left(\\frac{b^{2} \\left(- a + d\\right)^{2} e^{2 b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}} + 1\\right)^{1.5} \\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}} + \\frac{b^{2} \\left(1 - e^{b \\left(c - x\\right)}\\right) \\left(a - d\\right) \\left(\\frac{3.0 b^{3} \\left(- a + d\\right)^{2} e^{2 b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}} - \\frac{6.0 b^{3} \\left(- a + d\\right)^{2} e^{3 b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{5}}\\right) e^{b \\left(c - x\\right)}}{\\left(\\frac{b^{2} \\left(- a + d\\right)^{2} e^{2 b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}} + 1\\right)^{2.5} \\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}}$"
],
"text/plain": [
"-b**3*(1 - exp(b*(c - x)))*(a - d)*exp(b*(c - x))/((b**2*(-a + d)**2*exp(2*b*(c - x))/(exp(b*(c - x)) + 1)**4 + 1)**1.5*(exp(b*(c - x)) + 1)**3) + 3*b**3*(1 - exp(b*(c - x)))*(a - d)*exp(2*b*(c - x))/((b**2*(-a + d)**2*exp(2*b*(c - x))/(exp(b*(c - x)) + 1)**4 + 1)**1.5*(exp(b*(c - x)) + 1)**4) + b**3*(a - d)*exp(2*b*(c - x))/((b**2*(-a + d)**2*exp(2*b*(c - x))/(exp(b*(c - x)) + 1)**4 + 1)**1.5*(exp(b*(c - x)) + 1)**3) + b**2*(1 - exp(b*(c - x)))*(a - d)*(3.0*b**3*(-a + d)**2*exp(2*b*(c - x))/(exp(b*(c - x)) + 1)**4 - 6.0*b**3*(-a + d)**2*exp(3*b*(c - x))/(exp(b*(c - x)) + 1)**5)*exp(b*(c - x))/((b**2*(-a + d)**2*exp(2*b*(c - x))/(exp(b*(c - x)) + 1)**4 + 1)**2.5*(exp(b*(c - x)) + 1)**3)"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dK = K.diff(x)\n",
"dK"
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "2a05085e-333b-4733-9ac4-0e86cfb66912",
"metadata": {},
"outputs": [],
"source": [
"# sp.solve(dK)"
]
},
{
"cell_type": "markdown",
"id": "1b788546-5fd4-4882-8c9a-174303100e66",
"metadata": {},
"source": [
"## Approach 2"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "3dd4162c-a6dd-4095-950b-8a44d8d6d060",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle - \\frac{b^{3} \\left(a - d\\right) \\left(\\left(e^{b \\left(c - x\\right)} + 1\\right)^{2} - 6 \\left(e^{b \\left(c - x\\right)} + 1\\right) e^{b \\left(c - x\\right)} + 6 e^{2 b \\left(c - x\\right)}\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}}$"
],
"text/plain": [
"-b**3*(a - d)*((exp(b*(c - x)) + 1)**2 - 6*(exp(b*(c - x)) + 1)*exp(b*(c - x)) + 6*exp(2*b*(c - x)))*exp(b*(c - x))/(exp(b*(c - x)) + 1)**4"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df3 = f.diff(x, 3).simplify()\n",
"df3"
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "f2eb92ba-dda7-4024-88e9-417a4100a271",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"- \\frac{b^{3} \\left(a - d\\right) \\left(\\left(e^{b \\left(c - x\\right)} + 1\\right)^{2} - 6 \\left(e^{b \\left(c - x\\right)} + 1\\right) e^{b \\left(c - x\\right)} + 6 e^{2 b \\left(c - x\\right)}\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{4}}\n"
]
}
],
"source": [
"print(sp.latex(df3))"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "045ab4ba-068a-49ef-bbe0-f70830b17b21",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[log((2 - sqrt(3))*exp(b*c))/b, log((sqrt(3) + 2)*exp(b*c))/b]"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nullst = sp.solve(df3, x)\n",
"nullst"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "8d2f2c44-339f-4126-870d-1d17370c6a04",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\\left[ \\frac{\\log{\\left(\\left(2 - \\sqrt{3}\\right) e^{b c} \\right)}}{b}, \\ \\frac{\\log{\\left(\\left(\\sqrt{3} + 2\\right) e^{b c} \\right)}}{b}\\right]\n"
]
}
],
"source": [
"print(sp.latex(nullst))"
]
},
{
"cell_type": "markdown",
"id": "2724f2ad-a934-4560-8260-04bf9aa6f4fe",
"metadata": {},
"source": [
"Solving = setting to 0: Set exp(b*(c-x)+1) as z in df3; denominator and b^3(a-d) can be ignored"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "0f8eb3d2-5f3c-4b76-b64a-8fcf9633a56a",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle z^{2} - 4 z + 1$"
],
"text/plain": [
"z**2 - 4*z + 1"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zfun2 = ((z+1)**2-6*(z+1)*z+6*z**2)\n",
"zfun2.simplify()"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "70ea6da1-bf03-4dac-b501-b79a3f6c1819",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0.267949192431123, 3.73205080756888]"
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zfunsim2 = (z**2-4*z+1)\n",
"iniGuess = [0.5,5]\n",
"nst_bx2 = [sp.nsolve(zfunsim2, z,i) for i in iniGuess]\n",
"nst_bx2"
]
},
{
"cell_type": "code",
"execution_count": 70,
"id": "11045911-2294-4bb1-8515-635de2e2a35c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(-1.3169578969248157)"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(0.267949192431123)"
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "81be7854-7420-4b59-b0e4-a3ff9f60e8cc",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(1.3169578969248175)"
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(3.73205080756888)"
]
},
{
"cell_type": "code",
"execution_count": 72,
"id": "1087a144-4f58-4bce-98e4-1cf4df32939a",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x11fd5af30>"
]
},
"execution_count": 72,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.plot(df3.subs({a: 0, b: 1, c: 0.517, d: 6}),(x,-7,7))"
]
},
{
"cell_type": "code",
"execution_count": 74,
"id": "c19aad29-aa8b-40e2-8c0e-50912136d4f1",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 0.267949192431123$"
],
"text/plain": [
"0.267949192431123"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nst_bx2[0].subs({a: 0, b: 1, c: 0.517, d: 6}).evalf()"
]
},
{
"cell_type": "code",
"execution_count": 75,
"id": "a70992c8-6495-4274-87b0-4d51b5dd2ee9",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 3.73205080756888$"
],
"text/plain": [
"3.73205080756888"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nst_bx2[1].subs({a: 0, b: 1, c: 0.517, d: 6}).evalf()"
]
},
{
"cell_type": "code",
"execution_count": 82,
"id": "598d076f-5ccc-434e-a02a-31cb831817ec",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\log{\\left(e^{b c} \\right)}}{b} + \\frac{\\log{\\left(2 - \\sqrt{3} \\right)}}{b}$"
],
"text/plain": [
"log(exp(b*c))/b + log(2 - sqrt(3))/b"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nullst[0].simplify().expand()"
]
},
{
"cell_type": "markdown",
"id": "233870f5-7000-4338-aade-64a32483d1d1",
"metadata": {},
"source": [
"log(exp(bc)/b = c"
]
},
{
"cell_type": "code",
"execution_count": 83,
"id": "5e703c88-0718-423a-b2d6-2b7b932c5cae",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(-1.3169578969248164)"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(2-np.sqrt(3))"
]
},
{
"cell_type": "code",
"execution_count": 84,
"id": "59afbf5c-0449-4860-9984-90b734671415",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\log{\\left(e^{b c} \\right)}}{b} + \\frac{\\log{\\left(\\sqrt{3} + 2 \\right)}}{b}$"
],
"text/plain": [
"log(exp(b*c))/b + log(sqrt(3) + 2)/b"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nullst[1].simplify().expand()"
]
},
{
"cell_type": "code",
"execution_count": 86,
"id": "9ab449ce-bab6-4dae-9e27-e915d9bc2615",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(1.3169578969248166)"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(np.sqrt(3)+2)"
]
},
{
"cell_type": "code",
"execution_count": 91,
"id": "078a0476-0e93-4dc8-8a43-c159e2a91f64",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 0.267949192431123$"
],
"text/plain": [
"0.267949192431123"
]
},
"execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nst_bx2[0]"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "997d7a59-1ab1-4f93-a9d5-26322cdcd0a6",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 88,
"id": "f31016f0-d50a-4237-b191-72abcd778d68",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 3.73205080756888$"
],
"text/plain": [
"3.73205080756888"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nst_bx2[1]"
]
},
{
"cell_type": "code",
"execution_count": 92,
"id": "bf446e9c-dcb8-40e2-837a-fe1f94b21f46",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(-1.3169578985337886)"
]
},
"execution_count": 92,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(0.267949192)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"id": "45328449-e68b-4c44-bb99-f7b61dd3387e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.float64(1.3169578948967422)"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.log(3.7320508)"
]
},
{
"cell_type": "markdown",
"id": "4032701a-7e24-4e51-9eab-04c82a362da4",
"metadata": {},
"source": [
"## Sebaugh et al 2007 Differentiate on b first, then on x"
]
},
{
"cell_type": "code",
"execution_count": 112,
"id": "7d4c0dee-8d64-4f9f-8b98-41418f4e62c7",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle - \\frac{\\left(- a + d\\right) \\left(c - x\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{2}}$"
],
"text/plain": [
"-(-a + d)*(c - x)*exp(b*(c - x))/(exp(b*(c - x)) + 1)**2"
]
},
"execution_count": 112,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_b = f.diff(b)\n",
"df_b"
]
},
{
"cell_type": "code",
"execution_count": 113,
"id": "1003c19b-4524-4761-a689-63c68b575572",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p1 = sp.plot(df_b.subs({a: 0.212, b: 1.359, c: 0.517, d: 1.38}),(x,-7,7), legend=True, show = False, label = \"Sebaugh\", title = \"comparison of Sebaugh and approach 2\", xlabel = \"log-dilution\")\n",
"p2 = sp.plot(df2.subs({a: 0.212, b: 1.359, c: 0.517, d: 1.38}),(x,-7,7), legend=True, show = False, label = \"2nd approach\", line_color = \"red\")\n",
"p1.append(p2[0])\n",
"p1.show()"
]
},
{
"cell_type": "code",
"execution_count": 98,
"id": "43cbe6d8-85e7-4c9e-a9c3-23f460e6b2fb",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\left(1 - e^{b \\left(c - x\\right)}\\right) \\left(a - d\\right) \\left(c - x\\right)^{2} e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}}$"
],
"text/plain": [
"(1 - exp(b*(c - x)))*(a - d)*(c - x)**2*exp(b*(c - x))/(exp(b*(c - x)) + 1)**3"
]
},
"execution_count": 98,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_b2 = f.diff(b,2).simplify()\n",
"df_b2"
]
},
{
"cell_type": "code",
"execution_count": 99,
"id": "f5193d32-faf4-40ae-8fbd-838e3d11e846",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x11fe2cda0>"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.plot(df_b2.subs({a: 0.212, b: 1.359, c: 0.517, d: 1.38}),(x,-7,7))"
]
},
{
"cell_type": "code",
"execution_count": 100,
"id": "5fb9c722-1d91-4d58-8e3a-e64fea2695d5",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\left(2 b \\left(a - d\\right) \\left(c - x\\right) e^{b \\left(c - x\\right)} + \\left(e^{b \\left(c - x\\right)} + 1\\right) \\left(- a - b \\left(a - d\\right) \\left(c - x\\right) + d\\right)\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}}$"
],
"text/plain": [
"(2*b*(a - d)*(c - x)*exp(b*(c - x)) + (exp(b*(c - x)) + 1)*(-a - b*(a - d)*(c - x) + d))*exp(b*(c - x))/(exp(b*(c - x)) + 1)**3"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_bx = df_b.diff(x).simplify()\n",
"df_bx"
]
},
{
"cell_type": "code",
"execution_count": 101,
"id": "23e2092f-348a-4d84-8ca8-2108de6bf2ef",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\\frac{\\left(2 b \\left(a - d\\right) \\left(c - x\\right) e^{b \\left(c - x\\right)} + \\left(e^{b \\left(c - x\\right)} + 1\\right) \\left(- a - b \\left(a - d\\right) \\left(c - x\\right) + d\\right)\\right) e^{b \\left(c - x\\right)}}{\\left(e^{b \\left(c - x\\right)} + 1\\right)^{3}}\n"
]
}
],
"source": [
"print(sp.latex(df_bx))"
]
},
{
"cell_type": "code",
"execution_count": 102,
"id": "562d0d9a-1d26-4831-867b-f49a66e58df8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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xQmQdsWOwIyI7YLAjIrcjCMLFEbu+nooNEtfYMdgRke0x2BGR2ymrtbQ6UchliArs2xG7AS0jdhV1etTrjX362kTk+hjsiMjtiDti+wf0XasTkcbLAxovDwBAPqdjicjGGOyIyO2I69vE9W59TXxdBjsisjUGOyJyO+KO1Og+OnHicuJJF/lcZ0dENsZgR0Ruxxrs+nh9nejizlg2KSYi22KwIyK3U1DdCKDvzoi9nPi63BlLRLbGYEdEbufiVKyXJK8/oKXlCZsUE5GtMdgRkVtpajahrFYPQPqp2AvVjTCazJLUQESuicGOiNzKhZZpWF+1EgHeHpLUEO7vCZVSDqNZQLG2SZIaiMg1MdgRkVspqLZMf0YFekEmk0lSg1wuQ3SgZRqY6+yIyJYY7IjIrVyQuNWJyNryhOvsiMiGGOyIyK2IO2KlWl8nimk5o5YtT4jIlhjsiMitSL0jVhTVMhVb2BI0iYhsgcGOiNyKuMZO6hE7MdhdYLAjIhtisCMit1JQ1TIVK/Eau6iWYFlYw2BHRLbDYEdEbkPb2AxtYzOAiyNmUukfYHn98lo9mppNktZCRK6DwY6I3EZhyzRsPx8VfNRKSWsJ8PaAj0oBgKN2RGQ7DHZE5DbEABUl8TQsAMhksovTsVxnR0Q2wmBHRG5DDFADHCDYAdxAQUS2x2BHRG5DHLGLlnh9nai/NdixSTER2QaDHRG5DTFASb0jVsQROyKyNQY7InIbhTVNAKTvYSdiyxMisjUGOyJyG9apWIlPnRBFcSqWiGyMwY6I3Ia+2Qy5DIjQOEawE3vZler00BvZy46Ieo/BjojcSpi/J1RKx/jWF+SjgpeHpZddccs0MRFRbzjGdzcioj4SGeAYo3WA2MuOGyiIyHYY7IjIrfR3oGAHcJ0dEdkWgx0RuRVHGrEDLu1lxxE7Iuo9Bjsiciv9AzylLqEVtjwhIltisCMit+JoI3aciiUiW2KwIyK30t9BjhMTiWv+OBVLRLbAYEdELq/BYLT+2vFG7CxTsSW6JhiMZomrISJnx2BHRC6vWGvpEeerVsDf00PialoL9lVBrZRDEIASLXvZEVHvMNgRkU0tX74ccXFx8PT0RHJyMnbt2tXhtZs2bcLNN9+MkJAQ+Pv7Iy0tDd98802b6zZu3IiEhASo1WokJCRg8+bN3apJDEyOcuLEpVr3suM6OyLqHQY7IrKZ9evXY/78+Vi0aBFycnIwceJETJkyBfn5+e1ev3PnTtx8883YunUrsrOzccMNN+DWW29FTk6O9Zo9e/Zg5syZyMjIwKFDh5CRkYEZM2bgp59+6nJdRS07TsM16t69QTsRp4e5M5aIeksmCIIgdRFE5BpSU1ORlJSEFStWWJ+Lj4/H9OnTsXTp0i7dY/jw4Zg5cyb+8pe/AABmzpwJnU6Hbdu2Wa+55ZZbEBgYiLVr13bpnn/dnI3n7kjBHz7Pwmv3pHXjHfWNZ/51GOsPFGDBzVfhyZuGSF0OETkxjtgRkU0YDAZkZ2cjPT291fPp6enIysrq0j3MZjNqa2sRFBRkfW7Pnj1t7jl58uRO76nX66HT6ayP/AodACBc41g97ETiiF0RR+yIqJcY7IjIJioqKmAymRAWFtbq+bCwMJSUlHTpHm+88Qbq6+sxY8YM63MlJSXdvufSpUuh0Wisj83f/AAAiHTANXYAENHSNLmImyeIqJcY7IjIpmQyWauPBUFo81x71q5di8WLF2P9+vUIDQ3t1T0XLlwIrVZrfcSNSAbguCN2/TliR0Q2opS6ACJyDcHBwVAoFG1G0srKytqMuF1u/fr1mD17NjZs2IBJkya1+r3w8PBu31OtVkOttmyUMJkFVNQZADjwiF1L4CyuaexyECYiag9H7IjIJlQqFZKTk5GZmdnq+czMTIwfP77Dz1u7di0efPBBrFmzBlOnTm3z+2lpaW3u+e2333Z6z0tV1OnRbLLsEQvxc+xdsfUGE3SNxitcTUTUMY7YEZHNLFiwABkZGUhJSUFaWhpWrVqF/Px8zJ07F4BlirSwsBCffvopAEuou//++/HWW29h3Lhx1pE5Ly8vaDQaAMBTTz2Fa6+9Fq+++ipuv/12bNmyBdu3b8fu3bu7VNOlLUSUCsf8t6ynhwJBPipU1RtQpG2ExtuxmigTkfNwzO9yROSUZs6ciWXLlmHJkiUYPXo0du7cia1btyImJgYAUFxc3Kqn3XvvvQej0Yh58+YhIiLC+njqqaes14wfPx7r1q3Dxx9/jFGjRmH16tVYv349UlNTu1RToZOcwSpOx3KdHRH1BvvYEZFLe2/HGfz13wdRsGwGtFot/P39pS6pXXM+PYDMo6X4v+kjkDEuRupyiMhJccSOiFyas4yARV6ygYKIqKcY7IjIpRXWOEdvODYpJiJbYLAjIpfmLEEpQgx2bFJMRL3AYEdELq3QSYJd/wBuniCi3mOwIyKXVac3QtvYLHUZXRLR0jy5VNcEk5l72oioZxjsiMhliRsR/DwVEldyZaF+aijkMjSbBFTU6aUuh4icFIMdEbkscRo2wkGPEruUUiFHWMvJGJyOJaKeYrAjIpclBrvwllYijs66gcJJdvISkeNhsCMil1XSssM0wkmCndjypFjLETsi6hkGOyJyWeLIV5i/kwS7lgDqLDt5icjxMNgRkcsq0bVMxTpLsBNH7DgVS0Q9xGBHRC6rWOtcI3bilDGnYomopxjsiMglCYJgHflyls0T4oidsxyDRkSOh8GOiFySrtGIxmYTAOcZsRODXUWdHnqjSeJqiMgZMdgRkUsqbllfF+jtAU8Px29QDIi1Wr4tl/DMWCLqAQY7InJJ4vq6cCdoTiySyWSI1LCXHRH1HIMdEbkkcX1dpJOsrxNFBFjq5ekTRNQTDHZE5JJKtM516oRIHLHjzlgi6gkGOyJyScVOduqEKII7Y4moFxjsiMgllejEYOc8a+yAi1PHJRyxI6IeYLAjIpckrlFzthG7cGuTYo7YEVH3MdgRkcsRBOGSXbHOFezEEcZSHYMdEXUfgx0RuZxavRENBkuDX2ebihWDaHVDM5qa2aSYiLqHwY6IXI7Y6iTA2wNeKudoTizy91TCu6VmNikmou5isCMilyO2Cgl3kqPELiWTybjOjoh6jMGOiFxOiZO2OhGJdZfouDOWiLqHwY6IXI61h12Ac62vE4X7i02KOWJHRN3DYEdELkecio1wwqlY4JIROwY7IuomBjsicjnO2upExDV2RNRTDHZE5HIurrFzzqlYjtgRUU8x2BGRy7m4xo4jdkTkXhjsiMil1DY1o05vBOCc7U6AiyONFXV6GIxmiashImfCYEdELkWcvvT3VMJHrZS4mp4J9PaASmn59syjxYioOxjsiMiliNOXkU7a6gSwNCm+2MuOwY6Iuo7BjohcivXUCSfdESsSp5G5zo6IuoPBjohcSrGTnzohurgzlqdPEFHXMdgRkUsR19iJpzc4q3ANT58gou5jsCMil1Lk5K1OROxlR0Q9wWBHRC5FnLp09qnYMK6xI6IeYLAjIpfiemvsGOyIqOsY7IjIZdTpjahtamlO7KTHiYnEYFdW2wSjiU2KiahrGOyIyGWI07B+nkr4OmlzYlE/XzWUchnMAlBep5e6HCJyEgx2RGRTy5cvR1xcHDw9PZGcnIxdu3Z1eG1xcTHuueceDB06FHK5HPPnz29zzerVqyGTydo8mpraTlG6yjQsACjkMq6zI6JuY7AjIptZv3495s+fj0WLFiEnJwcTJ07ElClTkJ+f3+71er0eISEhWLRoEa6++uoO7+vv74/i4uJWD0/PtuFNDEDOPg0rCuc6OyLqJgY7IrKZN998E7Nnz8bDDz+M+Ph4LFu2DNHR0VixYkW718fGxuKtt97C/fffD41G0+F9ZTIZwsPDWz3aIwagSBcYsQMuBjuO2BFRVzHYEZFNGAwGZGdnIz09vdXz6enpyMrK6tW96+rqEBMTg6ioKEybNg05OTntXiceJxbi4wGdTtfq4Ywi/Hn6BBF1D4MdEdlERUUFTCYTwsLCWj0fFhaGkpKSHt932LBhWL16Nb788kusXbsWnp6emDBhAk6dOtXmWnFkK3v3d9BoNNZHdHR0j19fShyxI6LuYrAjIpuSyWStPhYEoc1z3TFu3Djcd999uPrqqzFx4kR88cUXuOqqq/DOO++0uVacip199x3QarXWR0FBQY9fX0oRLWsFucaOiLrKufsBEJHDCA4OhkKhaDM6V1ZW1mYUrzfkcjnGjBnT7ohdUY1lynJAsB/8/f1s9ppS4YgdEXUXR+yIyCZUKhWSk5ORmZnZ6vnMzEyMHz/eZq8jCAJyc3MRERHR6vl6vRE6a3Ni19g8IbZtKdU1wWwWJK6GiJwBR+yIyGYWLFiAjIwMpKSkIC0tDatWrUJ+fj7mzp0LAFi4cCEKCwvx6aefWj8nNzcXgGWDRHl5OXJzc6FSqZCQkAAAePHFFzFu3DgMGTIEOp0Ob7/9NnJzc/Huu++2eu0SnWVUy1ethJ+nRx+8W/sL8VNDLgOMZgEV9XqE+rlGYCUi+2GwIyKbmTlzJiorK7FkyRIUFxdjxIgR2Lp1K2JiYgBYGhJf3tMuMTHR+uvs7GysWbMGMTExyMvLAwDU1NTgkUceQUlJCTQaDRITE7Fz506MHTu21X1KXKg5schDIUeInxqlOj1KtE0MdkR0RTJBEDi+T0ROb8OBAvzxX4cxcUgwPpud2ur3dDodNBoNtFot/P39JaqwZ25/90ccKqjBqoxkpA9vv38fEZGIa+yIyCWII3bh/q41qmXtZafjBgoiujIGOyJyCcUtwSciwDWOExNxZywRdQeDHRG5BFdcYwdcfD/sZUdEXcFgR0QuwToV62LB7uKIHY8VI6IrY7AjIpcgrkFzvRE7nj5BRF3HYEdETq+p2YSqegMAIMLftdbYRVyyxo5NDIjoShjsiMjplbaM1nl5KODv5VrtOUP91QAAvdGMmoZmiashIkfHYEdETq/4ko0TMplM4mpsS61UINhXBYA7Y4noyhjsiMjpuerGCZH4vkp03EBBRJ1jsCMip1fs6sGuZd0gR+yI6EoY7IjI6ZW0tAJxtR2xIvayI6KuYrAjIqdX7KLHiYl4+gQRdRWDHRE5PbGHXbjGtVqdiDhiR0RdxWBHRE6v2EWPExPx9Aki6ioGOyJyagajGRV1egCuu3lCPH2CTYqJ6EoY7IjIqZXVNkEQAJVCjiBvldTl2IW4drDBYEKt3ihxNUTkyBjsiMipievOwjRqyOWu1ZxY5KVSIMDbAwBQXMN1dkTUMQY7InJq4sYJVzsj9nLiqJ34fomI2sNgR0ROzdVPnRBd3BnLDRRE1DEGOyJyaq6+I1YktnIp4lQsEXWCwY6InJr7jdgx2BFRxxjsiMipFbv4cWIiay87rrEjok4w2BGRU7s4Yufamye4xo6IuoLBjoiclsksoLTW0pzY1UfsLm1STETUEQY7InJaFXV6mMwCFHIZgn3VUpdjV+JUbG2TEXVsUkxEHWCwIyKnJY5ehfqpoXDR5sQiX7USfp5KAJyOJaKOMdgRkdMSA46r74gVidPNnI4loo4w2BGR03KXHnaicK6zI6IrYLAjIqdl3RHr4seJiSLZy46IroDBjoiclvuN2HEqlog6x2BHRE7LXU6dEF1cY8fNE0TUPgY7InJaxTr3OHVCJK6x41QsEXWEwY6InJIgCCjVWpoTu9+IHYMdEbWPwY6InFJVvQEGkxkyGRDq5x7BTgyw2sZmNBjYpJiI2mKwIyKnJI5aBfuqoVK6x7cyf08P+KrFJsUctSOittzjuyERuZwSN9sRKwpnyxMi6gSDHZELam5uRkFBAU6cOIGqqiqpy7GLYp3Yw869gp0YZIsY7IioHQx2RC6irq4O7733Hq6//npoNBrExsYiISEBISEhiImJwZw5c7B//36py7QZ8Tgxtxux8xdH7NjyhIjaYrAjcgF///vfERsbi/fffx833ngjNm3ahNzcXJw4cQJ79uzBCy+8AKPRiJtvvhm33HILTp06JXXJvSausQtzs2DHnbFE1Bml1AUQUe9lZWXh+++/x8iRI9v9/bFjx+Khhx7CypUr8eGHH2LHjh0YMmRIH1dpW+67xo697IioYwx2RC5gw4YN1l/X1tbCz8+v3evUajUee+yxvirLrtztnFhRRABH7IioY5yKJXIxEydORElJidRl2JUgCG53TqyIx4oRUWcY7IhcTEpKClJTU3H8+PFWz+fk5OBXv/qV3V9/+fLliIuLg6enJ5KTk7Fr164Ory0uLsY999yDoUOHQi6XY/78+e1et3HjRiQkJECtViMhIQFr/vVvNDabALjPqROiiJYRyuqGZjS1fA2IiEQMdkQu5oMPPsBDDz2Ea665Brt378bJkycxY8YMpKSkQK1W2/W1169fj/nz52PRokXIycnBxIkTMWXKFOTn57d7vV6vR0hICBYtWoSrr7663Wv27NmDmTNnIiMjA4cOHUJGRgYefvKPAIBAbw94eijs9n4ckb+XEl4t75nr7IjocjJBEASpiyAi21u6dCmWLFkCk8mEyZMn48UXX0RSUpJdXzM1NRVJSUlYsWKF9bn4+HhMnz4dS5cu7fRzr7/+eowePRrLli1r9fzMmTOh0+mwbds263PX3PUoLgy6DfER/tj21MQr1qXT6aDRaKDVauHv79+9N+WAbnz9B5ytqMfaOeOQNqif1OUQkQPhiB2RiykuLsaTTz6J//u//0NCQgI8PDwwa9Ysu4c6g8GA7OxspKent3o+PT0dWVlZPb7vnj172txz6OhUAB2vr9Pr9dDpdK0ersR6+oSO6+yIqDUGOyIXM3DgQOzatQsbNmxAdnY2Nm3ahMceewyvvvqqXV+3oqICJpMJYWFhrZ4PCwvr1WaOkpKSNvcUvDQAOl5ft3TpUmg0GusjOjq6x6/viCJaWp5wZywRXY7BjsjFfPzxx8jJycHUqVMBAJMnT8b333+Pt956q09anchkslYfC4LQ5rne3lPbbPk4ooPjxBYuXAitVmt9FBQU9Or1HY11Z2wNgx0RtcY+dkQuZtasWW2eS0pKQlZWll13xQYHB0OhULQZnSsrK2sz4tYd4eHhbe5ZUW8EoO5wxE6tVtt9o4iUwnn6BBF1gCN2RG4iNjYWP/74o93ur1KpkJycjMzMzFbPZ2ZmYvz48T2+b1paWpt7Xjx1wr2aE4siuMaOiDrAETsiF5Cfn48BAwZc8brAwEAAQGFhIfr372/zOhYsWICMjAykpKQgLS0Nq1atQn5+PubOnQvAMkVaWFiITz/91Po5ubm5AIC6ujqUl5cjNzcXKpUKCQkJAICnnnoK1157LV599VXcfvvt2LJlCxplcZDD/XrYiaybJzhiR0SX4YgdkQsYM2YM5syZg3379nV4jVarxfvvv48RI0Zg06ZNdqlj5syZWLZsGZYsWYLRo0dj586d2Lp1K2JiYgBYduxe3tMuMTERiYmJyM7Oxpo1a5CYmNhqynj8+PFYt24dPv74Y4waNQof/3Mt5J4+ANw32EW2jFRW1BmgN7JJMRFdxD52RC7gkUcegZ+fHz7++GN4eHggJSUFkZGR8PT0RHV1NY4ePYojR44gJSUFzz33HKZMmSJ1yT12uqwOk97cAT+1Ej+/OLlLn+NqfewEQcCw57+G3mjGrj/dgOggb6lLIiIHwalYIhewevVqFBQU4KWXXkJYWBgiIiJQUVGBxsZGBAcH495778XkyZMxYsQIqUvtNXH60V1H6wDLLuEIjSfyKhtQVNPIYEdEVgx2RC6gf//+yMnJwS233IK6ujq8/PLLCA0NlbosuyjWWjYMuHOwAyzvP6+yASU6rrMjoou4xo7IBfzhD3/AbbfdhvHjx0Mmk+Hzzz/H/v370djoersmL+6Ide9gxybFRNQeBjsiFzBv3jzk5ORg2rRpEAQB7777LtLS0uDv74/4+HjMmjULr7zySqvzVp1VkXUq1j1bnYi4M5aI2sOpWCIXMXz4cAwfPhwfffQR9u7dCx8fHxw+fBi5ubnIzc3Fli1b8Ne//hW1tbVSl9or4lRs/wD3HrGLtDYpdr1RWSLqOQY7Ihdz+vRp669TU1ORmppq/dgVNsEX1ViCjLs2JxaFcyqWiNrBqVgiN9LbM1sdgXg+aqSbj9hF8FgxImoHgx0ROQ1dUzNq9UYAHLET19hV1OlhMJolroaIHAWDHRE5DXG0TuPlAR+1e68kCfJWQaWQQxCAslqO2hGRBYMdETmNIq24vs69p2EBQC6XIUyjBsCdsUR0EYMdETkNccSuf4B7T8OK2MuOiC7HYEdETsO6I9bNN06IItjyhIguw2BHRE7j4lQsR+yAixsoOGJHRCIGOyJyGpyKbS3CvyXY1TDYEZEFgx0ROQ1unmgtoiXgFusY7IjIgsGOiJyCIAjWKcdIjtgBuDhyKa49JCJisCMip1BZb4DBaIZMBoT5c8QOuBhwy2v10BtNEldDRI6AwY6InII4KhXiq4ZKyW9dABDo7QFPD8vXgr3siAhgsCMiJ1HUskEggtOwVjKZzDpqV8jpWCICgx0ROQmxV1t/9rBr5eI6O47YERGDHRE5CWtzYvawayVSww0URHQRgx0ROYWiljVkbHXSWiR3xhLRJRjsiMgpFNeIU7EcsbtUZMvUNNfYERHAYEdEToKbJ9rHXnZEdCkGOyJyeEaTGWW1Lc2JORXbSsQlmycEQZC4GiKSGoMdETm80lo9zALgoZAh2FctdTkORVxz2NhsQk1Ds8TVEJHUGOyIyOGJ04zhGk/I5TKJq3Esnh4KBPuqAHCdHREx2BGRE2Crk85xZywRiRjsiMjhFWu5vq4z7GVHRCIGOyJyeGJgieSO2HaJX5dinhdL5PYY7IjI4bHVSefYy46IRAx2ROTwxHNiORXbPvayIyIRgx0ROTxOxXYu8pJedkTk3hjsiMihNRpMqG7pzxbJXbHtEoNdaW0Tmk1miashIikx2BGRQxOnYb1VCvh7KSWuxjH181FBpZRDEIASbqAgcmsMdkTk0MTpxcgAL8hkbE7cHrlcZl1/yHV2RO6NwY6IHFqRVmxOzI0TnbGus9My2BG5MwY7InJohdWWoNKfGyc6xQ0URAQw2BGRgxN7s0UFMth1Rgx27GVH5N4Y7IjIoVlH7BjsOsU1dkQEMNgRkYO7UNMAAIgK9Ja4EscWySbFRAQGOyJyYCazgOKWNWNcY9c561RsdSMEQZC4GiKSCoMdEdnU8uXLERcXB09PTyQnJ2PXrl2dXr9jxw4kJyfD09MTAwcOxMqVK62/V6prgtEsQDAZ0T/IFzKZzPpoauImgUuJ58XWG0zQNRklroaIpMJgR0Q2s379esyfPx+LFi1CTk4OJk6ciClTpiA/P7/d68+dO4df/epXmDhxInJycvDnP/8ZTz75JDZu3Ajg4kYAc30ViosKUVxcbH14erL9yaW8VUoEensA4HQskTtjsCMim3nzzTcxe/ZsPPzww4iPj8eyZcsQHR2NFStWtHv9ypUrMWDAACxbtgzx8fF4+OGH8dBDD+H1118HcHHjhLm2AuHh4a0e1BbX2RERgx0R2YTBYEB2djbS09NbPZ+eno6srKx2P2fPnj1trp88eTIOHDiA5uZmXKi2bJwwVBcjJiYGUVFRmDZtGnJycjqtRa/XQ6fTtXq4AwY7ImKwIyKbqKiogMlkQlhYWKvnw8LCUFJS0u7nlJSUtHu90WhERUWFdSp22g3j8eWXX2Lt2rXw9PTEhAkTcOrUqQ5rWbp0KTQajfURHR3dy3fnHPpbe9lx/SGRu2KwIyKbuvw8V0EQOj3jtb3rxecvtEzF/uq6VFx99dWYOHEivvjiC1x11VV45513OrznwoULodVqrY+CgoKevh2nIm6gYJNiIvellLoAInINwcHBUCgUbUbnysrK2ozKicLDw9u9XqlUol+/fiisPg6gdXNiuVyOMWPGdDpip1aroVare/pWnFZ0S68/cQqbiNwPR+yIyCZUKhWSk5ORmZnZ6vnMzEyMHz++3c9JS0trc/23336LlJQUKJXKi8eJBVxsTiwIAnJzcxEREWHjd+D8oqzBjiN2RO6KwY6IbGbBggX44IMP8NFHH+HYsWN4+umnkZ+fj7lz5wKwTJHef//91uvnzp2L8+fPY8GCBTh27Bg++ugjfPjhh/jDH/6A8jo99EYzZBDw876dOHv2LHJzczF79mzk5uZa70kXiefpltfq0dRskrgaIpICp2KJyGZmzpyJyspKLFmyBMXFxRgxYgS2bt2KmJgYAEBxcXGrnnZxcXHYunUrnn76abz77ruIjIzE22+/jTvvvBM5+dUAAE9Bj8fmzkNJSQk0Gg0SExOxc+dOjB07VpL36MgCvD3gq1aiTm/EhepGDA71lbokIupjMoFnzxCRA/rqUBGeWJuDMbGB2DC3/ancrtLpdNBoNNBqtfD397dRhY7plmU7cbykFqt/OwbXDw2Vuhwi6mOciiUihySur+MZsd0jTscWcJ0dkVtisCMihySeOnHpjli6sijujCVyawx2ROSQxGAiBhXqGnHEjjtjidwTgx0ROSROxfaMdcSuiiN2RO6IwY6IHI4gCNYRpyhOxXZLdBBH7IjcGYMdETmcmoZmNBgsfdgiOWLXLeKIXWW9AfV6o8TVEFFfY7AjIocjTsOG+Knh6aGQuBrnovHygL+npUUpz4wlcj8MdkTkcMSNE1xf1zPcGUvkvhjsiMjhXGCrk16x9rKr4ogdkbthsCMih8ONE70THcQROyJ3xWBHRA5HXBsWxanYHmEvOyL3xWBHRA6noIrNiXtD/LoVcMSOyO0w2BGRQxEEwRrsBvRjsOsJ9rIjcl8MdkTkUKrqDag3mCCTcVdsT4lft5qGZtQ2NUtcDRH1JQY7InIo+S2jdeH+nuxh10N+nh4I8PYAwFE7InfDYEdEDkUMduLOTuqZaGsvOwY7InfCYEdEDsW6vo7Brlcu7ozlBgoid8JgR0QOJZ/BzibYpJjIPTHYEZFDEYMIg13vsEkxkXtisCMih8I1drbBJsVE7onBjogchsFoRrGWI3a2IG6eKKhqgCAIEldDRH2FwY6IHEZRTSPMAuDloUCwr0rqcpyaOOJZqzeipoG97IjcBYMdETmMSzdOyGQyiatxbp4eCoT5qwEAeZX1EldDRH2FwY6IHAbX19lWTD8fABe/rkTk+hjsiMhhFFiDHY8Ss4WYloB8vpLBjshdMNgRkcNgDzvbiunHYEfkbhjsiMhhMNjZ1oCWqdjzXGNH5DYY7IjIIQiCgPxKBjtbihVH7LjGjshtMNgRkUPQNjajVm8EAEQFMtjZQkyQZcSuvFaPBoNR4mqIqC8w2BGRQxCnYUP91PBSKSSuxjVovD2g8fIAwJ2xRO6CwY6IHALX19mHuIEir4LBjsgdMNgRkUNgsLOPi73suIGCyB0w2BGRQ8irsASPAf0Y7GyJveyI3AuDHRE5BHGqMC7YR+JKXIsYlLnGjsg9MNgRkUM419JrLbYfg50tiSN2PC+WyD0w2BGR5Or0RpTX6gEAsRyxsynx61lU04Rmk1niaojI3hjsiEhy4vq6IB+VtT0H2UaonxqeHnKYzAIKqxulLoeI7IzBjogkl2edhuXGCVuTyWTWncY8gYLI9THYEZHkxBG7uGBfiStxTQOCeGYskbtgsCMiyZ2z7ojliJ09WM+MZcsTIpfHYEdEkrNOxXLjhF3EWIMdR+yIXB2DHRFJTpyKZasT+xCnuM9WMNgRuToGOyKyqeXLlyMuLg6enp5ITk7Grl27Or1+6/YfUFlvAADcesM4rFy5ss01GzduREJCAtRqNRISErB582a71O6q4kJajhWrbGDLEyIXx2BHRDazfv16zJ8/H4sWLUJOTg4mTpyIKVOmID8/v93rz507h7vnPAkACPRSYNGffo8nn3wSGzdutF6zZ88ezJw5ExkZGTh06BAyMjIwY8YM/PTTT33ynlxBhL8nPD3kMJoFXGDLEyKXJhMEQZC6CCJyDampqUhKSsKKFSusz8XHx2P69OlYunRpm+ufeeYZbMouQHPKvRgbG4Qv5qZh7ty5OHToEPbs2QMAmDlzJnQ6HbZt22b9vFtuuQWBgYFYu3Ztl+rS6XTQaDTQarXw9/fv5bt0TlPe2oVjxTp8+EAKbooPk7ocIrITZVcuEgQBtbW19q4FAHC2og7f/FwKhQJQymVQKuRQymVQKGRQymRQyuVQKiz/VShkF6+RyS5eJ5e1vUYuh4dcBpVSAbWHHCqFHHK5rE/eE5E7MBgMOHDgAJ588knodDrr89dddx127tzZ6jnRrl27MCDpdpzSNyDCOwA6nQ4TJ07EBx98gMrKSnh4eODHH3/EvHnz2txz+fLl7d4TAPR6PfR6vfVj8ftXR9e7gyhvAUf0DTiSV4Ix/b2kLoeIesDPzw8yWefZpUsjduK/domIiIhIGl2ZdehSsOvLEbujRVpsyL4Ak0lAs9kMk1lo9etmswCzWUCzSYDJLMBoMl98ruUao8nyvMl86ecBRpMZfT3x7KGQw99TCX8vJfw9Paz/DfBWwe+Sj/29PBDgpUSQrxr9fFTwVSuvmMqdkU6nQ3R0NAoKCtx2SqynHP1rV1xcjGHDhiEzMxNjx461Pv/aa69h3bp1yM7ObvM5iYmJCPj1X1Bu8sbfZ1yNm4eHY+/evZg8eTJOnjyJsLAw9OvXDytXrsRdd91l/bz169fj8ccfR3l5ebu1XD5iV1xcjLFjx+Lo0aPo37+/Dd+18/jqUCEWbvoFKTGBWP3Q2Ct/QgtH/3PnyPi1653efv0EQUCd3oiahmZUNxhQ09iMmnqD5dcNzahpbIa2wYBavQl1TUbUG4yoa2pGnd6IBkPXNhm9NWt0ny5t6MqIXZemYmUyWZ/9oRzn749xw6Ltcm9BEGA0C9AbzdA3myz/NZqhN5qgb+7g15dc29RsRnVdA95Z/h7uvv+3aBZkaDCYUK83ol5vQr3BaP1Yb7T8oTABqDYC1bUAapsBNAO48uJltVKOYF81gv3UCPFVWX7tq0awrwrhGk9EBnghMsAL/XxUThkA/f39+Y2uhxz1a+fp6QmFQoHa2tpW9el0OkRGRrZbc//+/VGs0ECu9EBCbDj8/f1RX18PpVKJ2NhYeHh4ICIiAjqdrtXn19XVITw8vNtfBz8/P4f82vWFEbFmyNVnUVCPHn0NHPXPnTPg1653Lv/6GU1mVNQZUFbbhFKdHqW6JpTpmlBWa/l1qU6Pijo9qhsMaDZ1dzRHCciUkKstH6mVcvh5KuHn6QFftRI+agW8VUp4qxTwVikwqH+Iw/2/7VKwcxUymQweChk8FHL4qnv21nU6HV789Qq8/K9XOv2faTSZ0dBsQm2TEdqGZmgbLQ9dYzNqGg3Wj7WNRtQ0GKBrbEZ1QzMq6/SoN1iCZGFNIwprOg+BKqUckRpPRGi8WsKeJ6ICvRDbzwexwT4I9VM7ZfAj56NSqZCcnIzMzEz8+te/tj6fmZmJ22+/vd3PSUqbiH/LPABc7GH37bffIiUlBR4elufT0tKQmZmJp59+2vp53377LcaPH2+vt+KSxJYn5bV61DY1w8/TQ+KKiNpnMgso1jbi5IUa+Iy4Cct3nkdZgwkXqhtxoaoBJbommLuR17w8FAjyUSHA2wNBPioEequsHwd4WWbMfNWW8GYJcUr4qpXw9VRCrVTY743aiVsFu76kVMjhr5DD39MD/QO6t1C5wWBEZZ0B5XV6VNTqUVFnQEWd5V8g5bV6lOiaUFTTiLJaPQxGM/IqG5DXwVFB3ioFYvr5IC7Y2xr2Bof6YmiYH3x6GG6JOrJgwQJkZGQgJSUFaWlpWLVqFfLz8zF37lwAwMKFC1FYWIhPP/0UAHDzr+/Bv/+dB0+hCXlnTmLPnj348MMPW+12feqpp3Dttdfi1Vdfxe23344tW7Zg+/bt2L17tyTv0Vn5e3og2FeNijo9zlXUY1RUgNQlkZurbWrG2fJ6nCmvw5nyOpwuq8OZ8nqcr6y3jrQFT30aK3e3bZekkMsQ4qtGmL8aof6eCPVTI8zf0/pxiK/aGuK8VM4XznqDP9m7Sa1W44UXXoBarbbba3irlPAOUiI6qPNzMw1GM0pbQl6xtgmFNY0oqmlEQXUj8irqcaG6AQ0GE44V63CsuO1uwOggLwwN88ewcD8MDfdDfIQf4oJ9obDjbuG++Pq5Kmf42s2cOROVlZVYsmQJiouLMWLECGzduhUxMTEALGvdLu1p1+hh2ZRlrC7C6NH3IDIyEm+//TbuvPNO6zXjx4/HunXr8Nxzz+H555/HoEGDsH79eqSmpna5LvFr5shfu74wMMQHFXV6nC3verBzhj93jopfOwuzWUBeZT2OFutwtEiHI0U6HC/RoVSn7/BzPBQyRGg80VxTgomJCYgJ9kVUoBeig7wRFeCFfr5qu/6scmbsY+fCDEYzCqobkFdRj3MV9cirtPz3VGkdymrb/wvlo1JgZJQGV0cHYHRUAK6ODkCExpPTuWQXr359HCt+OIOMcTH4v+kj7PY67GNn8ezGw1i3vwBP3jgYC9KHSl0OuSBBsDTBPphfjYPnq/FLkWVgocFgavf6ED81BoX4YFCIr+UR6ouBwT6IDPBicOshjti5MJVSbv3LcrmqegOOl+hwoqQWJ0pqcbzlv/UGE/aercLes1XWa0P81BgdHYBxA/th3MAgxIf7swcg2cTpsjoAwODQtn9GyfYGtqyzO8MzY8lGmk1mHL6gRfb5Khw8X4Ps/GqUtzNwoFbKMSzcDwmRGiRE+iMhwg+DQ/yg8eZaT1tjsHNTQT4qjB8UjPGDgq3PmcwCTpfV4VBBDXIv1OBQQQ2Ol9SivFaPzKOlyDxaCgDQeHlgbFyQNeglRPhzRI965ExLsGvvHx9kewODLV/nc+UMdtQzZrOA4yW1yDpTgR9PV2DfuSrUXzYap5TLMLy/BkkDAnB1VAASIv0xMNgHSgVPMe0LDHZkpZDLMLRlvd2MMZaWM03NJhwp0uJAXjX2nq3E/rxqaBubWwW9UD81bhgaihuGheCaISE93nFM7sVgNON8lWXTD0fs+oY4Yneuoh5ms8CRd+oSXVMzdpwox/Zjpdh9qgKV9YZWvx/o7YExsUFIiglEckwgRvbXwNPDvTYsOBL+BKZOeXookBwThOSYIDx63SAYTWYcKdJh79lK7D1biZ/OVaGsVo/1Bwqw/kABPBQyjIkNws0JYZgyIgLhGk+p3wI5qPOV9TCZBfiqlQjzd+/F5X0lOsgbSrkMjc0mlOiaENnNHfvkPgqqGrD9WCm2HyvFT2erYLykv4iXhwJj44IwYXA/TBgczOU5Dobjojbw3//+F6mpqfDy8kJwcDDuuOMOqUuyG6VCjqujA/DodYPw8W/HIucvN+Oz2WPx2wmxiAv2QbNJQNaZSrz41VGkvfId7lqZhdU/nkOprqnDe+r1eowePRoymQy5ubl992acVF5eHmbPno24uDh4eXlh0KBBeOGFF2AwGK78yQ7ktHUa1seuU/nLly/HyJEjAQDXXnstdu3aZbfXcnQeCjkGtOy2P3eFdXZLly7FmDFj4Ofnh9DQUEyfPh0nTpzoizJdztKlSyGTyTB//nypS+lUibYJH+w6i9v+sRsT//Y9XvzqKH48XQmjWcCgEB88eu1ArHtkHA69kI5PHhqLR64dhOGRGpuHusLCQtx3333o168fvL29MXr06HZPrqH2ccSulzZu3Ig5c+bg5Zdfxo033ghBEPDzzz9LXVafUSsVmDgkBBOHhOCFWy0/LL47VoqvfynBgfPV2J9nebz4n6NIjQvCXcnRmDIyHN6qi3/0/vSnPyEyMhKHDh2S8J04j+PHj8NsNuO9997D4MGD8csvv2DOnDmor6/H66+/LnV5XXamvCXY2XEadv369Zg/fz7eeOMNPPnkk0hLS8OUKVNw9OhRDBgwwG6v68gGhvjgbEU9zpbXYcLg4A6v27FjB+bNm4cxY8bAaDRi0aJFSE9Px9GjR+Hj49OHFTu3/fv3Y9WqVRg1apTUpbRL29iM/xwuwpe5RdiXV2U9dlMuA8bEBmFSfBhuig/FwD5aB1tdXY0JEybghhtuwLZt2xAaGoozZ84gICCgT17fFbDdSS8YjUbExsbixRdfxOzZs6Uux+EUaxux7ecS/PfnYmSfr7Y+76tWYurICNyVEoWyo3vx+9//Hhs3bsTw4cORk5OD0aNHS1e0k3rttdewYsUKnD17VupSumz+uhz8O7cIf5w8FPNuGGyX10hNTUVSUhJeffVVa7uT1NRUTJ8+HUuXLrXLazq6pVuP4b2dZ/FAWgxevL3rLWbKy8sRGhqKHTt24Nprr7Vjha6jrq4OSUlJWL58OV566SWMHj0ay5Ytk7osCIKAA+ersXZfPrb+XIym5ovnoqbEBOK20ZH41cgIBPv2/RKJZ599Fj/++KNbj6z3FkfseuHgwYMoLCyEXC5HYmIiSkpKMHr0aLz++usYPny41OVJLkLjhYeuicND18ShsKYRm7Iv4F8HL+B8ZYN1TZ5QU4RHFr8HmQfX4vWGVqtFUFCQ1GV0y+ly+7Y6MRgMyM7OxrPPPtvq+fT0dGRlZdnlNZ2B+PU+WVrXrc/TarUA4HR/zqQ0b948TJ06FZMmTcJLL70kdTnQNjZjw4ECrNtfYF0KAQBDQn1xZ3IUpo2KQFRg543x7e3LL7/E5MmTcdddd2HHjh3o378/HnvsMcyZM0fSupwJg10viKMjixcvxptvvonY2Fi88cYbuO6663Dy5El+A7xE/wAvPHHTEDx+42DsO1eFDdkF2LjvHBAQifdzarH2yAkE3PAQSuuMUpfqdM6cOYN33nkHb7zxhtSldJnZLOBMmWWNl72CXUVFBUwmE8LCwlo9HxYWhpKSEru8pjO4KswPAHCqrLbLnyMIAhYsWIBrrrkGI0bYr5G0K1m3bh0OHjyI/fv3S10K8isb8NGP5/DFgQJro2AvDwWmjYrArLEDkDQgwGFaVp09exYrVqzAggUL8Oc//xn79u3Dk08+CbVajfvvv1/q8pwCN0+0Y/HixZDJZJ0+Dhw4ALPZMny9aNEi3HnnnUhOTsbHH38MmUyGDRs2SPwupHGlr51cLoei6hwGFO9E+E9v4/mpwxDbzxt1BjM0Y+/A3P+U4tHPDuDnC1qp30qf6+qfu0sVFRXhlltuwV133YWHH35Yosq7r1jXhMZmE5RymXUxv71c/gNLEASH+SEmBTFIV9QZUFXftQ03jz/+OA4fPtzqDF/qWEFBAZ566in885//hKendLMRB/KqMPezbFz3+vdYnZWHBoMJQ8P88NL0Efhp0U147a6rkRwT6FB/H8xmM5KSkvDyyy8jMTERjz76KObMmYMVK1ZIXZrT4IhdOx5//HHMmjWr02tiY2NRW2v5F29CQoL1ebVajYEDB7Y6D9OddPVr99JLL2Hfjzux/4ahAGTwjEuCT+JUeA1MxjdHSvHNkVJcd1UIHr9xMMbEusfIZ1e/dqKioiLccMMNSEtLw6pVq+xcnW2JjYljg33gYaempcHBwVAoFCgpKWm1NKKsrKzNKJ478VErERXohQvVjThVWovUgf06vf6JJ57Al19+iZ07dyIqKqqPqnRu2dnZKCsrQ3JysvU5k8mEnTt34h//+Af0ej0UCvv1edtzphLLtp/ET+cuniB0/dAQzL4mDtcMDnaoIHe5iIiIVj9TASA+Ph4bN26UqCLnw2DXjuDgYAQHd7xbTJScnAy1Wo0TJ07gmmuuAQA0NzcjLy/Peui5u+nq1+7tt99uteakqKgIkydPxj8+24jDzeHIPFmNHSfLseNkOVLjgvDHyUOR4uIBr6tfO8DSDuCGG26wjhLL5c41+G49SsyOO+1UKhWSk5ORmZmJm266yfp8ZmYmbr/9dru9rjMYEuqLC9WNOFlW12GwEwQBTzzxBDZv3owffvgBcXFxfVyl87rpppvadEf47W9/i2HDhuGZZ56xW6i7PNCpFHL8OrE/Zk+Ms07BO7oJEya0aatz8uRJt/2Z2hMMdr3g7++PuXPn4oUXXkB0dDRiYmLw2muvAQDuuusuiatzbJe3mvD1tfyAnzBiIOaNHo3zlfVYueMM/pV9AT+dq8JvVu7BpPhQ/HHyMAwNd45vUPZSVFSE66+/HgMGDMDrr7+O8vJy6++Fh4dLWFnXieu7BoXat23GggULkJGRYR2xe/bZZ5Gfn4+5c+fa9XUd3VVhfvj+RDlOlXa8zm7evHlYs2YNtmzZAj8/P+u6RI1GAy8vNjbujJ+fX5u1iD4+PujXr59d1ij+UqjFy1uPIetMJQBLoJs1Nhq/u34QIjTO9f/q6aefxvjx4/Hyyy9jxowZ2LdvH1atWuV0sxJSYrDrpddeew1KpRIZGRlobGxEamoq/ve//yEwMFDq0pxaTD8fLL1jFJ64cQje+d8pfHHgArYfK8N3x8twR2IUfp9+ldt2zf/2229x+vRpnD59us3UmLN0LzpRYgkUQ8P97fo6M2fORGVlJV555RUAQFZWFrZu3er2//ofIm6g6GRnrLim6frrr2/1/Mcff4wHH3zQXqVRNxTVNOL1b05gU04hAOcOdKIxY8Zg8+bNWLhwIZYsWYK4uDgsW7YM9957r9SlOQ32sSOncLqsDm98ewLbfrGMGnh5KPD4jYPx8MQ4qJU8k9CZCIKAkYu/RZ3eiG+fvrZPpoh0Op21j52/v33DpDM4fKEGt/3jRwT7qnDguZulLoe6qV5vxLvfn8aHu89Bb7Rs4ps+OhJ/mDxU8nYlJD2O2JFTGBzqixX3JSO3oAYv//cY9uVV4bVvTmDDgQL85dYE3DjMfRfDO5vCmkbU6Y3wUMgQF8wTDKQwKKT1ztggH5XEFVFXCIKAb46U4sWvjqBYazmmcWxcEJ6bGo9RUQHSFkcOw7lWXJPbGx0dgPWPjsNbs0YjzF+NvMoGPLT6AB7+ZD+KahqlLo+6QJyGHRTia7cdsdQ5cWcsgE7X2ZHjKKhqwOxPDmDuP7NRrG1CVKAXVmUkY/0j4xjqqBV+VyWnI5PJcPvo/vju99fj0esGQimXYfuxMqT/fSfW/JTvNOvM3NWJliDhLLv0XJX49T9Z1r0TKKhvmcwC3ttxBjf/fQf+d7wMHgoZ5t0wCJlPX4f04eEO3bqEpMFgR07LV63Ewinx+Hr+RCQNCECd3og/b/4Z97z/E/IrG6QujzpwceMEg52UhoRZpmM5Yue4zlXU466VWVi67Tiams0YNzAI256aiD9OHgYvFdcWU/sY7MjpDQ71w4a54/GXaQnw8lBgz9lKTF62E5/tyePonQOyBjuO2EnqqlDL11/8/0GOw2wWsPrHc5jy1k4czK+Br1qJv905CmvnjMPgUP69oc5x8wS5BIVchoeuicOk+DA8s/Ew9pytxPNbjmDHyQr87TejuDjcQTSbzDhTbpn644idtIZFWL7+x4p1bn/MmiMp0TZhwRe51p501wwOxqu/GYX+btreibqPI3bkUgb088bnD6fiL9MSoFLIsf1YKaa8tRNZpyukLo1gmVpqNgnwUSn4g0pig0N9oZTLoGsyoqhlhyVJ64cTZfjV27uQdaYSXh4K/N/tw/HpQ2P5d4W6hcGOXI68ZfRu87zxGBTig1KdHvd++BP+9vVxGE1mqctza+K031XhfpDLOUIkJbVSgcGhlnV2x4p0Elfj3ppNZryy7Tge/Hg/quoNGB7pj61PTURGWiz/nlC3MdiRyxoeqcFXT1yDu8dGQxCA5T+cwQMf70NVvUHq0twW19c5lvgIS7PmY8UMdlIpqmnErFV7sXLHGQDA/Wkx2Pi78ezxSD3GYEcuzVulxNI7RuEf9yTCW6XAj6crces7u/HzBa3Upbml49wR61DixXV2JQx2UtifV4Xb/rEb2eer4adWYvm9SVhy+wh4enDHK/Ucgx25hWmjIvHveRMQF+yDwppG3LkyC//KviB1WW5HHBkaZuczYkVr166Fp6cnioqKrM89/PDDGDVqFLRahvuLI3bcGdvX1u7Lxz3v70VFnQHxEf7475MT8auREVKXRS6AwY7cxlVhfvj3vAmYFB8Kg9GMP2w4hCVfHYXJzJYofaG63oDCltNBEiL7JtjNmjULQ4cOxZtvvgkAWLp0Kb755hts27YNGo2mT2pwZGKwy6usR4PBKHE17qHZZMYLW37Bwk0/o9kkYOrICGz8XRoG9OMZr2QbDHbkVjReHliVkYKnJ10FAPjox3P43T+z+UOtDxxtGa0bEOQNjZdHn7ymTCbDX//6V3zyyScAgJUrV+Lrr79G//79++T1HV2wrxohfmoIwsVpcrIfbWMzHvhoHz7Zcx4A8Pubr2pZJsLOY2Q7DHbkduRyGZ6aNATv3J0IlVKOb4+WYtaqvSirZcsHezpSZJn6HN5Ho3WiadOmYdiwYQCAzz//HMOHD+/T13d03EDRN4pqGnHXyixknamEj0qBVRnJeOKmIewfSDbHYEdu69arI7Hm4VQEenvg8AUtfv1uFk7yeCW7OdLSUmNE/76dAv3mm29w8uRJAEBoaGifvrYziL+kUTHZx/ESHe5YnoWTpXUI9VNjw9zxSB8eLnVZ5KIY7MitpcQGYfNjFzdV/GZFFrLPV0tdlkv6pdAyYtdX6+sA4ODBg7jrrrvw1ltvAQBeeumlPnttZ5HADRR2tedMJe5auQcluiYMDvXF5nkT+vTvALkfBjtye7HBPtj0u/FIjgmErsmI+z74CbtP8aQKW2owGHG2oh5A303F5uXlYerUqXj22Wcxa9YsAMCWLVuQnZ3dJ6/vLMRgd7xYx41ENrbt52I88NE+1DYZMTY2CP+am8ZTJMjuGOyIAAT6qPDZ7LGYOCQYjc0mPLR6P77+pUTqslzGseJaCAIQ6qdGqJ+n3V+vqqoKU6ZMwW233YY///nP1uenTJmCRYsW2f31ncnAEF94eShQbzDhXEWd1OW4jM05FzBvzUEYTGZMGRGOT2ePRYA3z6wm+2OwI2rhrVLigwdSMGVEOAwmM+atOYiN7HVnE0f7eONEUFAQjh07hvfee6/V8+vWrcPXX3/dJzU4C4VchhH9Lf9fDhWwt58trNuXjwVfHIJZAGakROEf9ySx6TD1GQY7okuolQq8c3ci7kqOgsks4PcbDuHzn85LXZbT+6XQsjB/eCR7xzmiUVEBAICfCxnseuuTrDw8u+lnCAKQMS4Gr9wxCgqe90p9iMGO6DJKhRyv3jkKv50QCwBYtPkXrNuXL21RTu5IsSUwiCND5FhGRVkC96ELNdIW4uRW7TyDF748AgCYMzEOS24fDjlDHfUxdkUkaodcLsNfpiVABhk++vEcnt30M+QyGWaMiZa6NKejN5pwssSydosjdo5JHLE7WqRDs8kMDwX/zd9dH+4+h5e3HgcAPHnjYDx981XsUUeS4N9eog7IZDI8Py0eD46PBQA8s+kwz5ftgaNFOhhMZgT5qBAVyB2BjigmyBt+nkrojWacKuUGiu76597z+L//HAUAzJ80BAvShzLUkWQY7Ig6IZPJ8MKtCbg/LQaCAPzxX4ew6SDDXXfkFtQAAEZHB/CHnYOSy2UY2dI4+jCnY7vliwMFeO7fvwAA5l43CE/dNETiisjdMdgRXYFMJsOLtw3HvakDWsLdYXx7hK1QuurSYEeOS5yOPcwNFF22JbcQz2w8DAB4cHwsnrmFI3UkPQY7oi6QyWT4v9tH4Dctu2UfX5uDPWcqpS7LKYjBLnFAgKR1UOfEDRQcseuazKOlWPDFIQgCcPfYAXjh1gSGOnIIDHZEXSSXy/DKHSNxc0IYDEYz5nx6AD9f4OhGZ6rqDThf2QDg4ogQOSYx2J0oqUVTs0niahzbgbwqPL7mIExmAXck9sdfp49gqCOHwWBH1A1KhRzv3J2I1Lgg1OmNeODjfThTzsXmAFBdXY2MjAxoNBpoNBpkZGRg9zHLesRBIT7QeHm0+RxBELB48WJERkbCy8sL119/PY4cOdLqmuuvvx4ymazVQzwijGynf4AX+vmo0GwScKRIJ3U5DutUaS1mf3IAeqMZNw4Lxd9+M4otTcihMNgRdZOnhwIfPJCCEf39UVVvwP0f7kOJtknqsiR3zz33IDc3F19//TW+/vpr5Obm4qXlnwEARkcHtvs5f/vb3/Dmm2/iH//4B/bv34/w8HDcfPPNqK1tfSD9nDlzUFxcbH1cfqIE9Z5MJkNSjOX/08Hz1RJX45iKtY24/6N90DY2I3FAAN69JwlKtoYhB8M/kUQ94OfpgdW/HYuBwT4orGnEQ6v3o05vlLosyRw7dgxff/01PvjgA6SlpSEtLQ3vv/8+ztdbvsWMbmd9nSAIWLZsGRYtWoQ77rgDI0aMwCeffIKGhgasWbOm1bXe3t4IDw+3PjQa9sOzh5SWYHfgfJXElTgebUMzHvhoH4q1TRgY4oMPHxgDLxWPCSPHw2BH1EPBvmp88tBYBPuqcLRYh8fXHITRZJa6LEns2bMHGo0Gqamp1ufGjk2FOnIoACCxnR2x586dQ0lJCdLT063PqdVqXHfddcjKymp17eeff47g4GAMHz4cf/jDH9qM6F1Or9dDp9O1etCVpcRagl32+WoIgiBxNY6jqdmEhz/dj5OldQjzV+PTh8YiyEcldVlE7WKwI+qF6CBvfPDAGHh6yPHDiXK88OURt/yBWFJSgtDQ0FbPna2oh1ztAwXMGBru1+7nAEBYWFir58PCwqy/BwD33nsv1q5dix9++AHPP/88Nm7ciDvuuKPTepYuXWpd66fRaBAdzRNDumJEfw1USjkq6i5uenF35pYzo/fnVcPPU4lPHhqLqEBvqcsi6hCDHVEvjY4OwFuzEiGTAZ//lI/3dp6VuiSbWbx4cZuNC5c/Dhw4AABtdgXuz7NM54UpGzo9ouryzxMEodVzc+bMwaRJkzBixAjMmjUL//rXv7B9+3YcPHiww3suXLgQWq3W+igoKOj2e3dHaqUCo1oaFR/gOjsAwLLvTuG/h4vhoZBhVUYKhoXzvGNybDwrlsgGJg8Px/NTE7DkP0fxyrbjiAr0wrRRkVKX1WuPP/74FXegxsbG4vDhwygtLW31/E9nLX3+Bmva3zEYHh4OwDJyFxERYX2+rKyszSjepZKSkuDh4YFTp04hKSmp3WvUajXUanWndVP7kmMDceB8NbLPV+E3yVFSlyOpf+cU4u3vTgEA/vrrkUgb1E/iioiujMGOyEYeuiYO+VUNWJ2VhwVfHEJkgBeSBrS/G9RZBAcHIzg4+IrXpaWlQavVYt++fRg7diwEQcCuE5bp1Kkp7R+xFBcXh/DwcGRmZiIxMREAYDAYsGPHDrz66qsdvtaRI0fQ3NzcKgyS7SS3/Jk9kOfeI3YH8qrwp39ZTpV49LqBmJHC6XxyDpyKJbKh56clYFK8pYHxo59lo1jbKHVJfSI+Ph633HIL5syZg7179+Kr/2WhstEMCCbcNmGU9bphw4Zh8+bNACxTsPPnz8fLL7+MzZs345dffsGDDz4Ib29v3HPPPQCAM2fOYMmSJThw4ADy8vKwdetW3HXXXUhMTMSECRMkea+uLrllZ+ypsjrUNBgkrkYaBVUNePSzbBhMZqQnhOGZycOkLomoyxjsiGxIIZfhrVmjMSzcD+W1ejzyabbbdPH//PPPMXLkSKSnp+OhZ5cCsJw2cWlLiBMnTkCrvXhax5/+9CfMnz8fjz32GFJSUlBYWIhvv/0Wfn6WzRYqlQrfffcdJk+ejKFDh+LJJ59Eeno6tm/fDoWCrSbsoZ+vGgODfQAAB/Pdb9RO19SMh1bvR2W9AcMj/bFs1mg2ICanIhPccQsfkZ0VVDXgtn/sRnVDM269OhJvzxrtVkcO/XHDIWzIvoDfXT8Iz9wi/WiHTqeDRqOBVquFvz8Xv1/JsxsPY93+AsyZGIdFUxOkLqfPmMwCHlq9HztOliPMX40t865BuMZT6rKIuoUjdkR2EB3kjeX3JkMpl+GrQ0VY/sMZqUvqU/tadsSOjQuSuBLqifGDLesqd5+ulLiSvvX6tyew42Q5PD3k+OD+MQx15JQY7IjsJG1QPyy+bTgAyw+MzKOlV/gM11CibcL5ygbIZRdPMiDnMr5l9+exYh0q6/QSV9M3tv1cjBUt/wD722+uxsgonm5CzonBjsiO7hsXg4xxMRAEYP66HJws7fzEBFfw0znLKM/wSA38PD0kroZ6IthXjWEtTaX3nHX9UbuTpbX4/YZDAICHr4nDbVc7f6sicl8MdkR29pdbEzBuYBDqDSY8/MkBaBuapS7JrnadqgAA9vxychNapmN/PF0hcSX2pW1sxqOfZaPBYML4Qf3w7BTp14QS9QaDHZGdeSjkWH5vMqICvZBf1YD563NgNrvmniVBELDrVDkA4NohIRJXQ70xYbAlmP/owuvszGYBC9bn4lxFPfoHeOGduxOh7OSUFCJnwD/BRH0gyEeFlfclQ62U4/sT5XirpZu9qzlVVodSnR5qpdx6oDw5p7Fx/aCUy5Bf1YCCKtc8N/bt/53Cd8fLoFLKsfK+ZPTz5Wkl5PwY7Ij6yIj+Giy9YyQA4K3vTuG7Y663mWLnSctoXerAfvD0YJ85Z+arVuLq6AAArjkdu/1oKZZtbzkubPoIbpYgl8FgR9SH7kiKwgNpMQCA+S1TQK5kZ8v6umuHXPkYMnJ84jq7nS3T667ibHkdnl6fCwC4Py0Gd/G4MHIhDHZEfWzR1ASkxASitsmIuZ9lo15vlLokm2hqNuGnlh2U117F9XWu4Iahlv+PO09WwGA0S1yNbdTpjXj0s2zU6o1IiQnEc27UgJncA4MdUR9TKeVYfm8SQvzUOFFai2c2HoYrHADz4+kK6I1mRGo8MSTUV+pyyAaujgpAsK8KdXoj9rc0nXZmgiDgjxsO4VRZHcL81Vh+XxJUSv4YJNfCP9FEEgj198SKe5OglMvwn8PF+HD3OalL6rXtLWsGJyWEudXxaa5MLpfhhqGhAIDvjpVJXE3vrdhxBtt+KYGHQobl9yYj1I8nS5DrYbAjkkhKbBCen2aZBlq67TiyzjjvAnWzWcD2lh/8NyeESVwN2dJN8S3B7nipU48s7zxZjte/OQEAWHzbcCTzVBRyUQx2RBK6Py0GdyT2h8ks4Ik1OSiqaZS6pB7JvVCD8lo9/NRKpMaxMbEruWZICFQKOc5XNuBMeZ3U5fRIfmUDnlibA7MAzBoTjXvGDpC6JCK7YbAjkpBMJsNffz0SCRH+qKw34Hf/zEZTs0nqsrpte8s5uNcNDeGaJRfjq1ZaTxHZ9nOJxNV0X6PBhEf/mQ1tYzOujg7Ai7cP51IBcmn8DkwkMS+VAu9lJEPj5YFDF7R4YcsRp5ryEgQB236x/MDnNKxrmjoqAgDw35+LJa6kewRBwLObDuNYsQ7BviqsvC8JaiX7K5JrY7AjcgDRQd54++5EyGXA+gMF+PynfKlL6rIjRTqcq6iHp4cck+IZ7FxRekIYlHIZjpfU4nSZ80zHfrj7HLbkFkEpl+Hde5IQofGSuiQiu2OwI3IQ110Vgj9OthxAvvjLI07TXuLLQ0UAgJuGhcFHrZS4GrKHAG8VrmlpOr3VSUbtfjxdgZe3HgMALJoaj9SBXPtJ7oHBjsiBzL1uIKaOioDRLOB3/zyIYq1jb6YwmwV81RLsbr06UuJqyJ6mjrRMx351qMjhlwoUVDXg8TUHYRaAO5Oi8OD4WKlLIuozDHZEDkQmk+G134zCsHA/VNTpMfczx95MceB8NYq1TfBTK3H9UJ424crSh4dDpZTjVFkdfi7USl1OhxoNJjz6WTaqG5oxKkqDv/56BDdLkFthsCNyMN4qJVZlpCDA27KZ4vl//+KwIyQbDhQAACaPCIenBxeluzKNlwcmDw8HAGw4cEHiatonCAKe2XgYR62bJZL555LcDoMdkQMa0M8b/7g7CXIZsCH7Aj7be17qktqobWrGfw5b1lvNGsND1N3BjJQoAMCW3EKHHEl+f9dZfHno4maJyABuliD3w2BH5KCuGRKMhVPiAQBLvjqKn85WSlxRa1tyi9DYbMLgUF928XcT4wcFI1LjCV2TEd+29C50FLtOleOVbccBAM9PS+BmCXJbDHZEDuzhiXG4fXQkjGYBj31+EIUOdDLFuv2WliyzxkRzDZObUMhl+E2yZdTunw40iny6rA7zPrdslvhNchTuT4uRuiQiyTDYETkwmUyGV+4YZT2Z4qGP96O2qVnqsnAgrwq/FOqgUshxR1KU1OVQH7onNQZKuQz7zlXhFwfYRFFVb8DsT/ZD12RE0oAAvDSdmyXIvTHYETk4L5UCHzyQglA/NU6U1uKxzw+i2WSWtKZVO88CAH6d2B9BPipJa6G+Fa7xtJ5E8dGP5yStRW80Ye5n2Thf2YCoQC+suj+FmyXI7THYETmByAAvfPjAGHh5KLDrVAVe+FK6Y8fOltch85hlfdWca+MkqYGk9dAEy//3rw4VoVTXJEkNgiBg4aafsS+vCn5qJT56cAyCfdWS1ELkSBjsiJzEyCgN3r47ETIZsOanfLy/66wkdby/6ywEAbhpWCgGh/pJUgNJ6+roAIyJDUSzScCKH85IUsPb353GpoOFUMhlePfeJFwVxj+LRACDHZFTuTkhDM9PTQAAvLz1OP6dU9inr3+uoh5ftPQwm3v9oD59bXIs8yddBcDyj4y+PiHls73n8fftJwEAi28bjmuvYnNsIhGDHZGT+e2EWOsRSb/fcAjfHinps9d+M/MkTGYB1w8NwZjYoD57XXI84wf1w9i4IBhMZrzzv9N99rpfHirCX7b8AgB48qYhyBjHHbBEl2KwI3IyMpkMf5mWgDuS+sNkFvD4mhzsPlVh99f9+YLWei7snyYPs/vrkWOTyWT4/c2WUbv1+wtwvERn99f84UQZFqzPhSAA96fF4OlJQ+z+mkTOhsGOyAnJ5TL87c5RuGV4OAwmM+Z8egD786rs9npGkxl/3vwzAGD66EgkRPrb7bXIeaQO7IdbhofDZBbsfvTdjpPlePSzbBjNAm67OhKLbx3OtiZE7WCwI3JSSoUcb909GhOHBKOx2YT7P9yHXafK7fJaq7Py8HOhFv6eSvx5arxdXoOc019uTYC3SoH9edX4ouXsYFvbfrQUcz45AL3RjEnxoXj9rqshlzPUEbWHwY7IiamVCqzKSMF1V4WgsdmE2asP4OtfbLvm7kRJLd741rJQ/c+/ikeon6dN70/OLTLAC0/dZJkSffGrozhbXmfT+//ncBHm/jMbBpMZU0aEY/m9yVAp+aOLqCP820Hk5LxUCrx/fwp+NdIyLfvY59n4JCvPJtNiuqZm/O6f2WhsNmHikGDMSIm2QcXkah6eOBDjBgahwWDC42ty0NRs6vU9BUHA8h9O4/E1Odbp13fuTmSoI7oC/g0hcgEqpRxvz0rEjJQomAXghS+PYOGmn6E39vwHrN5owhNrcnC2oh6RGk+8NSuR01/ULoVchrdmJSLIR4WjxTo8vuYgjL04HaXBYMQfNhzG374+AQB4cHws/j5zNJQK/sgiuhL+LSFyEUqFHK/eOQp//tUwyGXAuv0FmP5uFo4Vd3+3ot5owrzPD2LHyXJ4esix/L5kHh1GnQrz98TK+5KhVsqx/VgZFnxxqEf/sDhapMOt7+zGxoMXIJcBL942HItvGw4F/1FB1CUyQapziYjIbr5vaQtR3dAMD4UMj10/GI9cOxA+auUVP/dCdQPmfX4Qhy5ooVbK8dGDYzBhcHAfVG0/Op0OGo0GWq0W/v7c0WtP24+W4tF/ZsNkFjAmNhDv3pOEUP8rr8us1xvxzv9O48PdZ9FsEhDmr8bfZ47G+EHO/WePqK8x2BG5qLLaJvx508/YfqwMABDsq8aD42MwY0x0uxsgdE3N+HxvPpZ/fxq1eiMCvD3w7j1JTh/qAAa7vrbjZDke//wgavVG+KqVeOLGwZg1dgA0Xh5tri2qacSGAxewOuscqhuaAQDpCWF45c5RHCUm6gEGOyIXJggC/vtzMf729QnkVzUAAGQyYESkBvERfgj2VaNeb8SJ0loczK+BwWhZFzU6OgDv3J2I6CBvKcu3GQa7vne6rBa//+IQDl3QArCsA02NC8LgUF+olHJU1xtwpEiHI0UXlwrE9vPGc1MTMCkhTKqyiZwegx2RGzAYzfjP4SJ8tvc8cvJrOrzuqjBfPHLtINyR2N+lNkow2EnDbBbwr+wL+HD3OZworW33GpkMGBMThPvSYvCrEeHcIEHUSwx2RG6mTNeEPWcrkV/ZgMp6A3zVSkQEeGLcwH4YGOzjkt38GeykJQgCjhXX4tCFGuRV1MMsCPBWKTEs3A/JMYFdWoNHRF3DYEdELo/BjojcBce8icgmqqurkZGRAY1GA41Gg4yMDNTU1HT6OZs2bcLkyZMRHBwMmUyG3NzcNtfo9Xo88cQTCA4Oho+PD2677TZcuHDBPm+CiMjJMdgRkU3cc889yM3Nxddff42vv/4aubm5yMjI6PRz6uvrMWHCBLzyyisdXjN//nxs3rwZ69atw+7du1FXV4dp06bBZOr96QZERK6GU7FE1GvHjh1DQkIC9u7di9TUVADA3r17kZaWhuPHj2Po0KGdfn5eXh7i4uKQk5OD0aNHW5/XarUICQnBZ599hpkzZwIAioqKEB0dja1bt2Ly5Mldqo9TsUTkLjhiR0S9tmfPHmg0GmuoA4Bx48ZBo9EgKyurx/fNzs5Gc3Mz0tPTrc9FRkZixIgRnd5Xr9dDp9O1ehARuQMGOyLqtZKSEoSGhrZ5PjQ0FCUlJb26r0qlQmBgYKvnw8LCOr3v0qVLrWv9NBoNoqOje1wDEZEzYbAjog4tXrwYMpms08eBAwcAoN02KYIg2KV9ypXuu3DhQmi1WuujoKDA5jUQETmiKx8cSURu6/HHH8esWbM6vSY2NhaHDx9GaWlpm98rLy9HWFjPTxEIDw+HwWBAdXV1q1G7srIyjB8/vsPPU6vVUKvVPX5dIiJnxWBHRB0KDg5GcPCVz4pNS0uDVqvFvn37MHbsWADATz/9BK1W22kAu5Lk5GR4eHggMzMTM2bMAAAUFxfjl19+wd/+9rce35eIyFVxKpaIei0+Ph633HIL5syZg71792Lv3r2YM2cOpk2b1mpH7LBhw7B582brx1VVVcjNzcXRo0cBACdOnEBubq51/ZxGo8Hs2bPx+9//Ht999x1ycnJw3333YeTIkZg0aVLfvkkiIifAYEdENvH5559j5MiRSE9PR3p6OkaNGoXPPvus1TUnTpyAVqu1fvzll18iMTERU6dOBQDMmjULiYmJWLlypfWav//975g+fTpmzJiBCRMmwNvbG1999RUUCkXfvDEiIifCPnZE5PLYx46I3AVH7IiIiIhcBIMdERERkYtgsCMiIiJyEQx2RERERC6CwY6IiIjIRTDYEREREbkIBjsiIiIiF8FgR0REROQi2KCYiFyeIAiora2Fn58fZDKZ1OUQEdkNgx0RERGRi+BULBEREZGLYLAjIiIichEMdkREREQugsGOiIiIyEUw2BERERG5CAY7IiIiIhfBYEdERETkIv4fu6LqZ43z2bkAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x12829b2f0>"
]
},
"execution_count": 102,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.plot(df_bx.subs({a: 0.212, b: 1.359, c: 0.517, d: 1.38}),(x,-7,7))"
]
},
{
"cell_type": "markdown",
"id": "1b915cc9-7daf-4962-a52f-3274e11deb57",
"metadata": {},
"source": [
"replacing exp(b(c-x)) with z"
]
},
{
"cell_type": "code",
"execution_count": 103,
"id": "608c1d9a-e40e-49bd-a545-b6ec6ca7da75",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle z \\left(z \\log{\\left(z \\right)} - z - \\log{\\left(z \\right)} - 1\\right)$"
],
"text/plain": [
"z*(z*log(z) - z - log(z) - 1)"
]
},
"execution_count": 103,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zfun = 2*sp.log(z)*z**2+(z**2+z)*(-1-sp.log(z))\n",
"zfun.simplify()"
]
},
{
"cell_type": "code",
"execution_count": 105,
"id": "fd227fb9-a451-4ed4-8509-c5fba66f4a47",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0.213652452390022, 4.68049857988291]"
]
},
"execution_count": 105,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zfuns = z*(z*sp.log(z)-z-sp.log(z)-1)\n",
"iniGuess = [0.5,5]\n",
"nst_bx = [sp.nsolve(zfuns,z,i) for i in iniGuess]\n",
"nst_bx"
]
},
{
"cell_type": "code",
"execution_count": 106,
"id": "48017871-7862-4652-90ba-873bda41d325",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<lambdifygenerated-47>:2: RuntimeWarning: divide by zero encountered in log\n",
" return z*(z*log(z) - z - log(z) - 1)\n",
"<lambdifygenerated-47>:2: RuntimeWarning: invalid value encountered in scalar multiply\n",
" return z*(z*log(z) - z - log(z) - 1)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x1282bff50>"
]
},
"execution_count": 106,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.plot(zfuns, (z,0,5))"
]
},
{
"cell_type": "code",
"execution_count": 107,
"id": "dd40d14b-59f2-4266-a46a-6576003e39e0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"z \\left(z \\log{\\left(z \\right)} - z - \\log{\\left(z \\right)} - 1\\right)\n"
]
}
],
"source": [
"print(sp.latex(zfuns))"
]
},
{
"cell_type": "code",
"execution_count": 108,
"id": "90d9fa1f-1996-4019-a6f9-2c494c9b95b8",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle -1.54340463841821$"
],
"text/plain": [
"-1.54340463841821"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sp.log(0.213652452390022)"
]
},
{
"cell_type": "markdown",
"id": "66c84984-2063-4658-a963-17b0516cdc88",
"metadata": {},
"source": [
"## Use true slope"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ab2f01a5-2cfc-40d5-a2d2-a97d85a10654",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 109,
"id": "c671916e-753a-4e02-8238-c4b1483405e0",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{b \\left(- a + d\\right)}{4}$"
],
"text/plain": [
"b*(-a + d)/4"
]
},
"execution_count": 109,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df1.subs({x: c})"
]
},
{
"cell_type": "markdown",
"id": "bd61349a-da84-4072-8ba7-bd551d002fed",
"metadata": {},
"source": [
"... is the true slope at EC50"
]
},
{
"cell_type": "code",
"execution_count": 129,
"id": "90c0d2cd-1d2f-4c9e-8a94-121c1a3f5319",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p1 = sp.plot(df_b.subs({a: 1.38, b: 1.359, c: 0, d: 0.212}),(x,-3.5, 3.5), legend=True, show = False, label = \"Sebaugh\", title = \"comparison of bend points\", xlabel = \"log-dilution\")\n",
"p2 = sp.plot(df2.subs({a: 0.212, b: 1.359, c: 0, d: 1.38}),(x,-3.5, 3.5), legend=True, show = False, label = \"2nd der on x\", line_color = \"red\")\n",
"p3 = sp.plot(K.subs({a: 0.212, b: 1.359, c: 0, d: 1.38}),(x,-3.5, 3.5), legend=True, show = False, label = \"max curvature\", line_color = \"green\")\n",
"p1.append(p2[0])\n",
"p1.append(p3[0])\n",
"p1.show()"
]
},
{
"cell_type": "code",
"execution_count": 122,
"id": "435f9637-41dd-4c47-af2d-953f9408c76f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x12894eed0>"
]
},
"execution_count": 122,
"metadata": {},
"output_type": "execute_result"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "7b42aad2-e2ce-416e-87a3-1c5b2eaa73b0",
"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": "3.12.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}