Try PyDSTool integrator, cgeneralize simulations in notebook
This commit is contained in:
Michael Soukup
parent
4c5c4ca124
commit
8df782ab92
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib notebook\n",
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"\n",
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"import numpy as np\n",
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"from scipy.integrate import odeint\n",
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"import matplotlib.pyplot as plt\n",
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"from matplotlib import animation\n",
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"plt.rcParams[\"animation.html\"] = \"jshtml\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"m1 = 1\n",
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"m2 = 1\n",
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"c1 = 0.1\n",
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"c2 = 0.1\n",
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"c3 = 0.1\n",
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"a1 = 0.1\n",
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"a2 = 0.1\n",
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"a3 = 0.1\n",
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"k1 = 0.05\n",
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"k2 = 0.21\n",
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"k3 = 0.11\n",
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"C1 = 0.15\n",
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"C2 = 0.30\n",
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"omega = 0.1\n",
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"\n",
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"f1 = lambda t: C1*np.cos(omega*t)\n",
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"f2 = lambda t: C2*np.cos(omega*t)\n",
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"\n",
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"def deriv(X, t):\n",
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" \"\"\"Return the derivatives dx/dt and d2x/dt2.\"\"\"\n",
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" x1, x2, xd1, xd2 = X\n",
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" F1 = f1(t)\n",
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" F2 = f2(t)\n",
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" xdd1 = F1 - xd1*(c1 + c2) + xd2*c2 - x1*(k1 + k2) + x2*k2 - a1*x1**3 + a2*(x2 - x1)**3\n",
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" xdd2 = F2 - xd2*(c2 + c3) + xd1*c1 - x2*(k2 + k3) + x1*k2 - a3*x2**3 + a2*(x2 - x1)**3\n",
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" return xd1, xd2, xdd1/m1, xdd2/m2\n",
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"\n",
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"\n",
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"def solve_duffing(tmax, dt_per_period, t_trans, x0, v0):\n",
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" \"\"\"Solve the Duffing equation with the standard odeint solver.\n",
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" \n",
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" Find the numerical solution to the Duffing equation using a suitable\n",
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" time grid: tmax is the maximum time (s) to integrate to; t_trans is\n",
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" the initial time period of transient behaviour until the solution\n",
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" settles down (if it does) to some kind of periodic motion (these data\n",
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" points are dropped) and dt_per_period is the number of time samples\n",
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" (of duration dt) to include per period of the driving motion (frequency\n",
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" omega).\n",
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" \n",
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" Returns the time grid, t (after t_trans), position, x, and velocity,\n",
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" xdot, dt, and step, the number of array points per period of the driving\n",
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" motion.\n",
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" \n",
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" \"\"\"\n",
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" # Time point spacings and the time grid\n",
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"\n",
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" period = 2*np.pi/omega\n",
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" dt = 2*np.pi/omega / dt_per_period\n",
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" step = int(period / dt)\n",
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" t = np.arange(0, tmax, dt)\n",
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" # Initial conditions: x, xdot\n",
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" X0 = x0 + v0\n",
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" X = odeint(deriv, X0, t)\n",
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" idx = int(t_trans / dt)\n",
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" return t[idx:], X[idx:], dt, step"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Set up the motion for a oscillator with initial positions and velocities\n",
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"x0, v0 = (0.5, -0.5), (0.5, -0.1)\n",
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"tmax, t_trans = 150, 0\n",
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"dt_per_period = 100"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# Solve the equation of motion.\n",
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"t, X, dt, pstep = solve_duffing(tmax, dt_per_period, t_trans, x0, v0)\n",
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"print(\"# samples: %d\" % len(t))\n",
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"print(\"dt: %.4f\" % dt)\n",
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"print(\"Steps per period: %d\" % pstep)\n",
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"x1, x2, xd1, xd2 = X.T"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"fig1, ((ax11, ax12), (ax21, ax22)) = plt.subplots(nrows=2, ncols=2)\n",
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"\n",
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"ax11.plot(t, x1)\n",
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"ax11.set_xlabel(r'$x_1$')\n",
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"ax12.plot(t, x2)\n",
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"ax12.set_xlabel(r'$x_2$')\n",
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"ax21.plot(t, xd1)\n",
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"ax21.set_xlabel(r'$v_1$')\n",
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"ax22.plot(t, xd2)\n",
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"ax22.set_xlabel(r'$v_2$')\n",
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"plt.tight_layout()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": false
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},
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"outputs": [],
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"source": [
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"%%capture\n",
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"fig2, ((ax11, ax12), (ax21, ax22)) = plt.subplots(nrows=2, ncols=2)\n",
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"\n",
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"# Positions\n",
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"ax11.set_xlabel(r'$x_1$')\n",
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"ax11.set_ylabel(r'$x_2$')\n",
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"ln11, = ax11.plot([], [])\n",
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"ax11.set_xlim([np.min(x1), np.max(x1)])\n",
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"ax11.set_ylim([np.min(x2), np.max(x2)])\n",
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"\n",
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"# Velocities\n",
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"ax12.set_xlabel(r'$v_1$')\n",
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"ax12.set_ylabel(r'$v_2$')\n",
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"ln12, = ax12.plot([], [])\n",
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"ax12.set_xlim([np.min(xd1), np.max(xd1)])\n",
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"ax12.set_ylim([np.min(xd2), np.max(xd2)])\n",
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"\n",
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"# Phase spaces\n",
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"ax21.set_xlabel(r'$\\mathbf{x}$')\n",
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"ax21.set_ylabel(r'$\\mathbf{v}$')\n",
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"ln21a, = ax21.plot([], [])\n",
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"ln21b, = ax21.plot([], [])\n",
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"ax21.set_xlim([min(np.min(x1), np.min(x2)), max(np.max(x1), np.max(x2))])\n",
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"ax21.set_ylim([min(np.min(xd1), np.min(xd2)), max(np.max(xd1), np.max(xd2))])\n",
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"\n",
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"# F(t)\n",
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"F1 = f1(t)\n",
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"F2 = f2(t)\n",
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"ax22.set_xlabel(r'$t$')\n",
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"ax22.set_ylabel(r'$\\mathbf{F}(t)$')\n",
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"ln22a, = ax22.plot([], [])\n",
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"ln22b, = ax22.plot([], [])\n",
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"ax22.set_xlim([t[0], t[-1]])\n",
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"ax21.set_ylim([min(np.min(F1), np.min(F2)), max(np.max(F1), np.max(F2))])\n",
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"\n",
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"plt.tight_layout()\n",
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"\n",
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"def animate(i):\n",
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" ln11.set_data(x1[:i], x2[:i])\n",
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" ln12.set_data(xd1[:i], xd2[:i])\n",
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" ln21a.set_data(x1[:i], xd1[:i])\n",
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" ln21b.set_data(x2[:i], xd2[:i])\n",
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" ln22a.set_data(t[:i], F1[:i])\n",
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" ln22b.set_data(t[:i], F2[:i])\n",
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" \n",
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"\n",
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"anim = animation.FuncAnimation(fig2, animate, frames=len(t), interval=100, repeat_delay=1000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"anim"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"anaconda-cloud": {},
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
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}
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pydstool_integrator.py
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pydstool_integrator.py
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"""Simulate duffing model with PyDSTool integrator.
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See
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https://github.com/robclewley/pydstool/blob/master/examples/forced_spring.py
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for forced-spring example.
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"""
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import numpy as np
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import PyDSTool
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def simulate(T, t_trans, steps, x0, v0, omega, p):
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x1, x2 = x0
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xd1, xd2 = v0
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C1, C2, m1, m2, c1, c2, c3, k1, k2, k3, a1, a2, a3 = p
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args = PyDSTool.args(name='duffing-stuffing')
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args.varspecs = {
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'x1': 'xd1',
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'x2': 'xd2',
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'xd1': 'C1*F(t)/m1 - xd1*(c1 + c3) + xd2*c3 - x1*(k1 + k3) + x2*k3 - a1*pow(x1, 3) + a3*pow(x2 - x1, 3)',
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'xd2': 'C2*F(t)/m2 - xd2*(c2 + c3) + xd1*c3 - x2*(k2 + k3) + x1*k3 - a2*pow(x2, 3) + a3*pow(x2 - x1, 3)'
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}
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args.fnspecs = {
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'F': (['t'], 'cos(omega*t)')
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}
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args.pars = {
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'omega': omega,
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'C1': C1, 'C2': C2,
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'm1': m1, 'm2': m2,
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'c1': c1, 'c2': c2, 'c3': c3,
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'k1': k1, 'k2': k2, 'k3': k3,
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'a1': a1, 'a2': a2, 'a3': a3
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}
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args.ics = {
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'x1': x0[0], 'x2': x0[1],
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'xd1': v0[0], 'xd2': v0[1]
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}
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args.xdomain = {
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'x1': [-10, 10], 'x2': [-10, 10],
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'xd1': [-1e6, 1e6], 'xd2': [-1e6, 1e6]
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}
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#args.tdomain = [0, T]
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args.tdata = [0, T]
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# Integrator
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ds = PyDSTool.Generator.Vode_ODEsystem(args)
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traj = ds.compute('experiment')
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pts = traj.sample(dt=(T-t_trans)/steps, precise=True)
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return np.stack([
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pts['x1'][-steps:],
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pts['x2'][-steps:],
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pts['xd1'][-steps:],
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pts['xd2'][-steps:]
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])
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def test():
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C1 = 1.5e5
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C2 = 1.5e5
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m1 = 1.0 #1e-3
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m2 = 1.0 #1e-3
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c1 = 9647.403
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c2 = 10282.101
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c3 = 0.000
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k1 = 2326809592.681
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k2 = 2643039774.512
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k3 = 0.000
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a1 = 0.000
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a2 = 0.000
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a3 = 0.000
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p = (
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C1, C2,
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m1, m2,
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c1, c2, c3,
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k1, k2, k3,
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a1, a2, a3
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)
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omega = 2*np.pi*5e3
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x0, v0 = (0.00001, 0.00002), (0.000001, 0.0002)
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T = 0.6
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t_trans = 0.1
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steps = 100
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return simulate(T, t_trans, steps, x0, v0, omega, p)
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if __name__ == '__main__':
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X = test()
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print(X.shape)
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print(X.mean(axis=1))
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print(X.std(axis=1))
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print(X)
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#pars = {'D1': 1.0 , 'D2': 10.0, 'A': 2.1, 'B': 3.5, 'lambda': 5}
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#
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#tdomain = [0,50]
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#
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#icdict = {'X1': 1.087734, 'X2': 1.087734, 'X3': 4.124552, \
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# 'Y1': 1.8488063, 'Y2': 1.8488063, 'Y3': 1.0389936}
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#
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## Set up model
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#X1str = 'D1*(X2 - 2*X1 + X3) + lambda*(A - (B+1)*X1 + pow(X1,2)*Y1)'
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#X2str = 'D1*(X3 - 2*X2 + X1) + lambda*(A - (B+1)*X2 + pow(X2,2)*Y2)'
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#X3str = 'D1*(X1 - 2*X3 + X2) + lambda*(A - (B+1)*X3 + pow(X3,2)*Y3)'
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#Y1str = 'D2*(Y2 - 2*Y1 + Y3) + lambda*(B*X1 - pow(X1,2)*Y1)'
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#Y2str = 'D2*(Y3 - 2*Y2 + Y1) + lambda*(B*X2 - pow(X2,2)*Y2)'
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#Y3str = 'D2*(Y1 - 2*Y3 + Y2) + lambda*(B*X3 - pow(X3,2)*Y3)'
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#
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#DSargs = args(name='Brusselator')
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#DSargs.tdomain = tdomain
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#DSargs.pars = pars
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#DSargs.varspecs = {'X1': X1str, 'X2': X2str, 'X3': X3str, 'Y1': Y1str, 'Y2': Y2str, 'Y3': Y3str}
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#DSargs.xdomain = {'X1': [0, 50], 'X2': [0, 50], 'X3': [0, 50], 'Y1': [0, 50], 'Y2': [0, 50], 'Y3': [0, 50]}
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#DSargs.ics = icdict
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#
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#testDS = Generator.Vode_ODEsystem(DSargs)
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#
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## Set up continuation class
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#PyCont = ContClass(testDS)
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#
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#PCargs = args(name='EQ1', type='EP-C')
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#PCargs.freepars = ['lambda']
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#PCargs.StepSize = 5e-3
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#PCargs.LocBifPoints = ['BP','LP']
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#PCargs.verbosity = 2
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#PCargs.SaveEigen = True
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#PyCont.newCurve(PCargs)
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#
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#print('Computing curve...')
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#start = clock()
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#PyCont['EQ1'].forward()
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#print('done in %.3f seconds!' % (clock()-start))
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#
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## Plot
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#PyCont['EQ1'].display(('lambda','X1'), stability=True)
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#PyCont.plot.toggleAll('off', byname='P1')
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#show()
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2
requirements.txt
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2
requirements.txt
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scipy>=0.5.1,<1.0
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PyDSTool
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