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@AlexanderJChapa
AlexanderJChapa committed Sep 21, 2019
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677 changes: 677 additions & 0 deletions homework/AlexanderChapaHW3.ipynb
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470 changes: 470 additions & 0 deletions homework/AlexanderJChapa-F16.ipynb
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4 changes: 2 additions & 2 deletions lectures/4-Casadi-Transport.ipynb
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},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
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"name": "stderr",
"output_type": "stream",
"text": [
"/home/jgoppert/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/control/xferfcn.py:896: ComplexWarning: Casting complex values to real discards the imaginary part\n",
"/home/alexander/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/control/xferfcn.py:896: ComplexWarning: Casting complex values to real discards the imaginary part\n",
" num[i, j, np + 1 - len(numpoly):np + 1] = numpoly[::-1]\n"
]
},
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181 changes: 181 additions & 0 deletions lectures/AJC-MSD.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import casadi as ca"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$m\\ddot{x} + c\\dot{x}+k x = u$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\vec{x} = \\begin{bmatrix} x \\\\ \\dot{x} \\end{bmatrix}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\vec{u} = \\begin{bmatrix} u \\end{bmatrix}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\vec{y} = \\begin{bmatrix} x \\end{bmatrix}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\ddot{x} = (-c \\dot{x} - k x + u)/m$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\vec{\\dot{x}} = f(\\vec{x}) = \\begin{bmatrix} \\dot{x} \\\\ (-c \\dot{x} - k x + u)/m \\end{bmatrix}$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\dot{\\vec{x}} = A \\vec{x} + B \\vec{u}$\n",
"\n",
"$\\vec{y} = C \\vec{x} + D \\vec{u}$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"SX([x_1, ((u-((c*x_1)+(k*x_0)))/m)])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"m = ca.SX.sym('m')\n",
"c = ca.SX.sym('c')\n",
"k = ca.SX.sym('k')\n",
"p = ca.vertcat(m, c, k)\n",
"\n",
"u = ca.SX.sym('u')\n",
"xv = ca.SX.sym('x',2)\n",
"x = xv[0]\n",
"xd = xv[1]\n",
"\n",
"xv_dot = ca.vertcat(xd, (-c*xd - k*x + u)/m)\n",
"xv_dot\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"f_rhs = ca.Function('rha', [xv, u, p], [xv_dot], ['x','u','p'], ['x_dot'])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"DM([2, -7])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f_rhs([1,2], [0], [1,2,3])"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "could not broadcast input array from shape (2,1) into shape (2)",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-15-927dc80cd2d6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve_ivp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf_rhs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt_span\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my0\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt_eval\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m~/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/scipy/integrate/_ivp/ivp.py\u001b[0m in \u001b[0;36msolve_ivp\u001b[0;34m(fun, t_span, y0, method, t_eval, dense_output, events, vectorized, **options)\u001b[0m\n\u001b[1;32m 500\u001b[0m \u001b[0mstatus\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 501\u001b[0m \u001b[0;32mwhile\u001b[0m \u001b[0mstatus\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 502\u001b[0;31m \u001b[0mmessage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 503\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 504\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msolver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'finished'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/scipy/integrate/_ivp/base.py\u001b[0m in \u001b[0;36mstep\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 180\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 181\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 182\u001b[0;31m \u001b[0msuccess\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmessage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_step_impl\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 183\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 184\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0msuccess\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/scipy/integrate/_ivp/rk.py\u001b[0m in \u001b[0;36m_step_impl\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 141\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 142\u001b[0m y_new, f_new, error = rk_step(self.fun, t, y, self.f, h, self.A,\n\u001b[0;32m--> 143\u001b[0;31m self.B, self.C, self.E, self.K)\n\u001b[0m\u001b[1;32m 144\u001b[0m \u001b[0mscale\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0matol\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmaximum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my_new\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mrtol\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 145\u001b[0m \u001b[0merror_norm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merror\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mscale\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m~/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/scipy/integrate/_ivp/rk.py\u001b[0m in \u001b[0;36mrk_step\u001b[0;34m(fun, t, y, f, h, A, B, C, E, K)\u001b[0m\n\u001b[1;32m 65\u001b[0m \u001b[0mEquations\u001b[0m \u001b[0mI\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mNonstiff\u001b[0m \u001b[0mProblems\u001b[0m\u001b[0;31m\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mSec\u001b[0m\u001b[0;34m.\u001b[0m \u001b[0mII\u001b[0m\u001b[0;36m.4\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 66\u001b[0m \"\"\"\n\u001b[0;32m---> 67\u001b[0;31m \u001b[0mK\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 68\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 69\u001b[0m \u001b[0mdy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0ms\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mh\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: could not broadcast input array from shape (2,1) into shape (2)"
]
}
],
"source": [
"import scipy.integrate\n",
"import numpy as np\n",
"scipy.integrate.solve_ivp(\n",
" fun=lambda t, x: np.array(f_rhs(x, 1.0, [1,2,3])), \n",
" t_span=[0,1], y0=[0,0], t_eval = np.arange(0,1,0.1))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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"kernelspec": {
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}
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