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FEM MiniProject ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"James Wright\n",
"\n",
"ASEN 5007"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"plt.rcParams.update({\n",
" 'font.family': 'serif',\n",
" 'font.serif': 'cmr10',\n",
" 'mathtext.fontset': 'cm',\n",
" 'axes.unicode_minus': False,\n",
" 'font.size': 11,\n",
" 'figure.dpi': 150,\n",
" 'lines.linewidth': 0.5,\n",
" 'axes.grid': True\n",
"})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction\n",
"## How to run the code.\n",
"\n",
"Simply load the included `*.ipynb` file in Jupyter Lab \n",
"(or any other software that can run the Jupyter Notebook).\n",
"The only software requirements are `numpy` and `matplotlib`. \n",
"If you get errors related to `matplotlib`, I'd first comment out the\n",
"`plt.rcParams.update(....)` command above, then retry."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code Overview\n",
"\n",
"I have a series of helper functions, followed by two formation and \n",
"assembly functions, and finally a function that wraps around the \n",
"formation and assembly functions.\n",
"\n",
"### Helper Functions\n",
"#### Lagrange Polynomial Functions\n",
"\n",
" - `lagrangeFESolution` takes in the values at nodes and computes the \n",
" solution (and it's derivative) at arbitrary specified points. ie.\n",
" $$ u^h(x) = \\sum_{A=0}^{n_\\text{node}} d_A N_A(x)$$\n",
" $$ \\frac{\\text{d}u^h}{\\text{d}x}(x) = \\sum_{A=0}^{n_\\text{node}} d_A N_{A,x}(x)$$\n",
" where $N_A(x)$ and $N_{A,x}$ are calculated on a per element basis\n",
" - `lagrangePoly` returns the values of shape function and it's derivative at arbitrary \n",
"points in parent space (though used in this code for quadrature points). $N_a(\\xi_q)$\n",
"\n",
"#### Other Helper Functions\n",
" - `build1Dconnectivity`, which builds the connectivity array for the problem.\n",
" Note that this array is in the _inverse_ order as in the notes. ie. A = IEN(e,a)\n",
" - `buildX_Xi` builds the $x_{,\\xi}$ correction factor for every element.\n",
" - `buildShapeFunctions` builds an array of the shape function (and it's derivatives) \n",
" evaluated at quadrature points in parent space: $N_a(\\xi_q)$ and $N_{a,\\xi}(\\xi_q)$.\n",
" Each row is the $a^{\\text{th}}$ shape function, and every column in \n",
" the $q^\\text{th}$ quadrature point.\n",
" - `xi2x` maps local element space to global space; $x(\\xi_q^e)$. This is used when\n",
" evaluating $\\kappa(x^e(\\xi_q))$ and $f(x^e(\\xi_q))$.\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Primary Functions\n",
" \n",
" - `element_formation` forms the array of $\\mathbf{k}_{ab}^e$ and $\\mathbf{f}_a^e$ matrices/vectors.\n",
" - `element_assembly` takes the array of $\\mathbf{k}_{ab}^e$ and $\\mathbf{f}_a^e$ matrices/vectors and \n",
" assembles them into the $\\mathbf{K}_{AB}$ matrix and $\\mathbf{F}_A$ vector.\n",
" \n",
" Finally, the `One_Dim_Model_Problem` function wraps the `element_formation` and `element_assembly`\n",
" functions, and then solves the system $\\mathbf{K}_{AB}\\mathbf{d}=\\mathbf{F}_A$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def lagrangeFESolution(k, nodes, solution, x, derivative=False):\n",
" \"\"\"Return the FE solution evaulated at x locations\"\"\"\n",
" nelm = int((nodes.size-1)/k)\n",
" connectivity = build1Dconnectivity(k, nelm)\n",
" monomial = np.zeros((k+1, x.size))\n",
" FEsolution = np.zeros_like(x)\n",
" gradFEsolution = np.zeros_like(x)\n",
" for e in range(nelm):\n",
" elmNodes = connectivity[e,:]\n",
" elementFilter = ((x >= nodes[elmNodes[ 0]]) & \n",
" (x <= nodes[elmNodes[-1]]))\n",
" for a in elmNodes:\n",
" Na = 1\n",
" monomial = np.zeros((k+1, x.size))\n",
" for i, (n, node) in enumerate(zip(elmNodes, nodes[elmNodes])):\n",
" if a == n: continue\n",
" monomial[i,:] = (x-node) / (nodes[a] - node)\n",
" Na *= monomial[i,:]\n",
" Na *= elementFilter\n",
" FEsolution += solution[a]*Na\n",
"\n",
" if derivative:\n",
" if k==1:\n",
" h = nodes[elmNodes[1]] - nodes[elmNodes[0]]\n",
" Na_xi = np.ones_like(x)*(1/h)\n",
" if a==elmNodes[0]:\n",
" Na_xi *= -1\n",
" else:\n",
" Na_xi = 0\n",
" for ni, nodei in zip(elmNodes, nodes[elmNodes]):\n",
" if a == ni: continue\n",
" weight = 1/(nodes[a] - nodei)\n",
" product = 1\n",
" for j, (nj, nodej) in enumerate(zip(elmNodes, nodes[elmNodes])):\n",
" if nj in [ni, a]: continue\n",
" product *= monomial[j,:]\n",
" Na_xi += weight*product\n",
" Na_xi *= elementFilter\n",
" gradFEsolution += solution[a]*Na_xi\n",
" \n",
" if derivative:\n",
" return FEsolution, gradFEsolution\n",
" else:\n",
" return FEsolution\n",
"\n",
"def lagrangePoly(q, k, a):\n",
" \"\"\"Evaluate Lagrange polynomials and derivatives at locations q\n",
" \n",
" Parent space from [-1,1]\n",
" \n",
" q : np.ndarray\n",
" Quadrature point locations\n",
" k: int\n",
" The degree polynomial. Locations of nodes are determined from this\n",
" a: int\n",
" Shape function for which node location in xi\n",
" \n",
" Returns:\n",
" Na : np.ndarray\n",
" Shape function evaulated at quadrature points\n",
" Na_xi : np.ndarray\n",
" Shape function derivatives evaulated at quadrature points\n",
" \"\"\"\n",
" if a not in range(k+1): \n",
" raise RuntimeError(f'A k={k} order polynomial does not have an a={a} shape function')\n",
" xis = np.linspace(-1, 1, k+1)\n",
" Na = 1\n",
" monomial = np.zeros((k+1, q.size))\n",
" for i, xi in enumerate(xis):\n",
" if a == i: continue\n",
" monomial[i,:] = (q-xi) / (xis[a] - xi)\n",
" Na *= monomial[i,:]\n",
"\n",
" if k==1:\n",
" Na_xi = np.ones_like(q)*0.5\n",
" if a==0:\n",
" Na_xi *= -1\n",
" else:\n",
" Na_xi = 0\n",
" for i, xii in enumerate(xis):\n",
" if a == i: continue\n",
" weight = 1/(xis[a] - xii)\n",
" product = 1\n",
" for j, xij in enumerate(xis):\n",
" if j in [i, a]: continue\n",
" product *= monomial[j,:]\n",
" Na_xi += weight*product\n",
"\n",
" return Na, Na_xi"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def build1Dconnectivity(k, nelm):\n",
" \"\"\"Build the connectivity array for 1D elements\"\"\"\n",
" k = int(k)\n",
" nelm = int(nelm)\n",
" connectivity = np.outer(np.ones(nelm), np.arange(k+1))\n",
" connectivity += (np.arange(nelm)*k)[:,None]\n",
" return connectivity.astype(np.uint32)\n",
"\n",
"def buildX_Xi(connectivity, x):\n",
" \"\"\"Build per-element mapping of dx/dxi\"\"\"\n",
" x_xi = np.zeros(connectivity.shape[0])\n",
" for i in range(connectivity.shape[0]):\n",
" x_xi[i] = x[connectivity[i,-1]] - x[connectivity[i,0]]\n",
" return x_xi/2\n",
"\n",
"def buildShapeFunctions(k, q):\n",
" \"\"\"Array of values of shape functions evaluated at points q\"\"\"\n",
" Na = np.zeros((k+1, q.size))\n",
" Na_xi = np.zeros((k+1, q.size))\n",
" for a in range(k+1):\n",
" Na[a,:], Na_xi[a,:] = lagrangePoly(q, k, a)\n",
" return Na, Na_xi\n",
"\n",
"def xi2x(xi, x, x_xi, e, connectivity):\n",
" \"\"\"Map xi -> x\"\"\"\n",
" return x[connectivity[e,0]] + x_xi[e]*(xi+1)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def elementFormation(k, kappa, f, connectivity, x):\n",
" \"\"\"Form keab and fea array of element matrices\"\"\"\n",
" nelm = connectivity.shape[0]\n",
" q, w = np.polynomial.legendre.leggauss( int(2*(k)-1) )\n",
" Na, Na_xi = buildShapeFunctions(k, q)\n",
" x_xi = buildX_Xi(connectivity, x)\n",
" \n",
" keab = np.zeros((nelm, k+1, k+1))\n",
" fea = np.zeros((nelm, k+1))\n",
" for e in range(nelm):\n",
" xe = xi2x(q, x, x_xi, e, connectivity)\n",
" kappae = kappa(xe)\n",
" fe = f(xe)\n",
" for a in range(k+1):\n",
" for b in range(k+1):\n",
" keab[e,a,b] = np.sum(kappae*Na_xi[a,:]*Na_xi[b,:]*w*(1/x_xi[e]))\n",
" \n",
" fea[e,a] = np.sum(fe*Na[a,:]*w*x_xi[e])\n",
" return keab, fea\n",
"\n",
"def elementAssembly(keab, fea, connectivity, g0, gL):\n",
" \"\"\"Assemble keab and fea into KAB and FA, respectively\"\"\"\n",
" nelm = keab.shape[0]\n",
" nshg = connectivity.max() + 1\n",
" k1 = keab.shape[1]\n",
" KAB = np.zeros((nshg, nshg))\n",
" FA = np.zeros(nshg)\n",
" for e in range(nelm):\n",
" for a in range(k1):\n",
" A = connectivity[e, a]\n",
" if A != 0 and A != nshg-1:\n",
" FA[A] += fea[e,a]\n",
" for b in range(k1):\n",
" B = connectivity[e, b]\n",
" if B == 0:\n",
" FA[A] -= keab[e,a,b]*g0\n",
" elif B == nshg-1:\n",
" FA[A] -= keab[e,a,b]*gL\n",
" else:\n",
" KAB[A,B] += keab[e,a,b]\n",
" else:\n",
" # Fill in values for Dirchilet BC's\n",
" KAB[A,A] = 1\n",
" FA[A] = g0 if A==0 else gL\n",
" return KAB, FA"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"def One_Dim_Model_Problem(k, nelm, kappa, f, g0, gL, L):\n",
" nnodes = nelm*k + 1 \n",
" nodes = np.linspace(0, L, nnodes)\n",
" connectivity = build1Dconnectivity(k, nelm)\n",
" keab, fea = elementFormation(k, kappa, f, connectivity, nodes)\n",
" KAB, FA = elementAssembly(keab, fea, connectivity, g0, gL)\n",
" solution = np.linalg.solve(KAB,FA)\n",
" return nodes, solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Manufactured Solution:\n",
"\n",
"Given the problem\n",
"\n",
"$$-\\frac{\\text{d}}{\\text{d}x} \\left (\\kappa(x) \n",
"\\frac{\\text{d}u}{\\text{d}x}(x) \\right) = f(x) \\quad \\forall x\\in(0,L) \n",
"$$\n",
"\n",
"$$ u(0) = g_0, \\quad u(L) = g_L, \\quad g_0,g_L \\in \\mathbb{R}\n",
"$$\n",
"\n",
"$$ \\quad \\kappa:(0,L) \\rightarrow \\mathbb{R}^+ \\quad f:(0,L) \\rightarrow \\mathbb{R}\n",
"$$\n",
"\n",
"Let \n",
"\n",
"$$L = 2\\pi, \\quad u(x)=\\cos(x), \\quad \\kappa(x) = e^{x/4}\n",
"$$\n",
"\n",
"Then\n",
"\n",
"$$\\frac{\\text{d}u}{\\text{d}x} = -\\sin(x), \\quad \n",
"\\frac{\\text{d}\\kappa}{\\text{d}x} = \\frac{e^{x/4}}{4}, \\quad\n",
"g_0 = g_L = 1\n",
"$$\n",
"\n",
"Plug this into the ODE above to get an expression for $f(x)$:\n",
"\n",
"$$f(x) = \\frac{\\text{d}}{\\text{d}x} \\left (e^{x/4}\n",
"\\sin(x) \\right) \\quad \\forall x\\in(0,2\\pi) \n",
"$$\n",
"\n",
"$$\\therefore f(x) = \\frac{e^{x/4}}{4}\\sin(x) + \\cos(x)e^{x/4}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"f = lambda x: np.exp(x/4)*0.25*np.sin(x) + np.cos(x)*np.exp(x/4)\n",
"kappa = lambda x: np.exp(x/4)\n",
"\n",
"u = lambda x: np.cos(x)\n",
"du = lambda x: -np.sin(x)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fbdc46eb5d0>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"k = 2\n",
"nelm = 5\n",
"nodes, solution = One_Dim_Model_Problem(k, nelm, kappa, f, 1, 1, 2*np.pi)\n",
"\n",
"x = np.linspace(0,2*np.pi,1000)\n",
"FEsolution, gradFEsolution = lagrangeFESolution(k, nodes, solution, x, derivative=True)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, FEsolution, label=r'$u^h$')\n",
"ax.plot(x, u(x), linestyle=':', linewidth=1, label=r'$u$')\n",
"ax.plot(x, gradFEsolution, label=r\"$\\frac{\\mathrm{d}u^h}{\\mathrm{d}x}$\")\n",
"ax.plot(x, du(x), linestyle=':', linewidth=1, label=r\"$\\frac{\\mathrm{d}u}{\\mathrm{d}x}$\")\n",
"ax.legend()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def H1Error(u, du, FEMsolution, gradFEMsolution, x):\n",
" L = x.max() - x.min()\n",
" e = u(x) - FEMsolution\n",
" de = du(x) - gradFEMsolution\n",
" f1f2 = np.trapz(e**2, x)\n",
" df1df2 = np.trapz(de**2, x)\n",
" return np.sqrt(f1f2 + (L**2)*df1df2)\n",
"\n",
"\n",
"x = np.linspace(0,2*np.pi, 2000)\n",
"nelms = np.geomspace(1,100, 10, dtype=np.uint32)\n",
"Error = {}\n",
"for k in range(1,5):\n",
" kstr = str(k)\n",
" Error[kstr] = []\n",
" for nelm in nelms:\n",
" nodes, solution = One_Dim_Model_Problem(k, nelm, kappa, f, 1, 1, 2*np.pi)\n",
" FEMsolution, gradFEMsolution = lagrangeFESolution(k, nodes, solution, x, derivative=True)\n",
" Error[kstr].append(H1Error(u, du, FEMsolution, gradFEMsolution, x))"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fbdc47f8650>"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"plotkwargs = {'1':'black', '2':'green', '3':'red', '4':'blue'}\n",
"\n",
"for k, errors in Error.items():\n",
" ax.plot(nelms, errors, color=plotkwargs[k], label='$k='f'{k}''$')\n",
"\n",
"for k, errors in Error.items():\n",
" ax.plot(nelms, Error[k][0]*(1/nelms)**int(k), linestyle='--', alpha=0.5, color=plotkwargs[k])\n",
" \n",
"ax.set_yscale('log')\n",
"ax.set_xscale('log')\n",
"ax.set_xlabel(r'$n_\\mathrm{elm}$')\n",
"ax.set_ylabel(r'$\\Vert u - u^h \\Vert_{\\mathrm{H}^1}$')\n",
"ax.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The expected rate of convergence is given by\n",
"\n",
"$$\\Vert u - u^h \\Vert_{\\mathrm{H}^1} \\leq C \\left ( \\frac{h}{L} \\right)^r $$\n",
"\n",
"where $C$ is some problem dependent constant. \n",
"For smooth problems, $r=k$.\n",
"\n",
"The slope of the line plotting the error $\\Vert u - u^h \\Vert_{\\mathrm{H}^1}$ for \n",
"constant $k$ on a log-log plot is equal to $r$. \n",
"Above, the dashed lines correspond to\n",
"$(n_\\text{elm})^{-k}\\left [\\Vert u - u^h \\Vert_{\\mathrm{H}^1}\\right]_{n_\\text{elm}=1}$,\n",
"which are the expected convergence rates for a given $k$.\n",
"Since all the error plots have the same slope as their corresponding \n",
"expected convergence rate, the problem is converging as expected."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fbdc42a0c10>"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"plotkwargs = {'1':'black', '2':'green', '3':'red', '4':'blue'}\n",
"\n",
"for k, errors in Error.items():\n",
" ax.plot(nelms*int(k) +1, errors, color=plotkwargs[k], label='$k='f'{k}''$')\n",
"\n",
"ax.set_yscale('log')\n",
"ax.set_xscale('log')\n",
"ax.set_xlabel(r'$n_\\mathrm{dofs}$')\n",
"ax.set_ylabel(r'$\\Vert u - u^h \\Vert_{\\mathrm{H}^1}$')\n",
"ax.legend()\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 3"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7fbdb80f3f90>"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"R = 0.025\n",
"hmax = 1500\n",
"L = 2\n",
"g0 = gL = 30\n",
"kappa = lambda x: 385\n",
"f = lambda x: (2/R)*hmax*np.exp(-100*(x/L - 0.5)**2)\n",
"\n",
"k = 5\n",
"nelm = 10\n",
"nodes, solution = One_Dim_Model_Problem(k, nelm, kappa, f, g0, gL, L)\n",
"\n",
"x = np.linspace(0,L,1000)\n",
"FEsolution = lagrangeFESolution(k, nodes, solution, x)\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, FEsolution, label='FEM Solution')\n",
"ax.scatter(nodes, solution, s=3, label='Raw FEM Solution')"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"79.01138808347842"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"FEsolution.max()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Therefore the maximum temperature is 79 degrees."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 4"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fbdc430dad0>]"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Amin = 0.00002\n",
"Amax = 0.0001\n",
"E = 200e9\n",
"L = 0.1\n",
"g0 = 0\n",
"gL = 0.00002\n",
"kappa = lambda x: Amax - (Amax-Amin)*np.exp(-50*(x/L - 0.5)**2)\n",
"f = lambda x: 0\n",
"\n",
"k = 5\n",
"nelm = 100\n",
"nodes, solution = One_Dim_Model_Problem(k, nelm, kappa, f, g0, gL, L)\n",
"\n",
"x = np.linspace(0,L,1000)\n",
"FEsolution, gradFEsolution = lagrangeFESolution(k, nodes, solution, x, derivative=True)\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, E*gradFEsolution, label='Gradient FEM Solution')"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"126.10198669804062"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(E*gradFEsolution).max()/1e6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Therefore the maximum stress is 126 MPa"
]
}
],
"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": "3.7.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
numpy
matplotlib
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