{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# [Chapter 3](https://github.com/Ziaeemehr/spikes/blob/main/docs/examples/chap_03.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### **Two-dimensional systems and state space**\n", "\n", "Code by : Abolfazl Ziaeemehr \n", "- https://github.com/Ziaeemehr\n", "\n", "\"Open" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# uncomment and run this line to install the package on colab\n", "# !pip install \"git+https://github.com/Ziaeemehr/spikes.git\" -q" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sympy as sp\n", "import numpy as np\n", "from sympy import lambdify\n", "import matplotlib.pyplot as plt\n", "from scipy.linalg import eig, inv\n", "from scipy.integrate import odeint\n", "from IPython.display import display, Math\n", "from spikes.solver import solve_linear_system_numerical" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "#### Analytical Solution for $\\frac{d\\vec{X}}{dt} = A\\vec{X} + \\vec{B}$\n", "\n", "Let's derive the analytical solution step-by-step for the differential equation $\\frac{d\\vec{X}}{dt} = A\\vec{X} + \\vec{B}$, assuming $\\lambda_1 \\neq \\lambda_2$.\n", "\n", "##### Steps to Solve Analytically\n", "\n", "1. Find the Equilibrium State\n", "The equilibrium state $\\vec{X}_{eq}$ is given by:\n", "$$\n", "\\vec{X}_{eq} = -A^{-1} \\vec{B}\n", "$$\n", "\n", "2. Determine the Eigenvalues and Eigenvectors\n", "The eigenvalues $\\lambda_1$ and $\\lambda_2$ are solutions to the characteristic equation:\n", "$$\n", "\\det(A - \\lambda I) = 0\n", "$$\n", "where $I$ is the identity matrix.\n", "\n", "Let's denote the eigenvectors corresponding to $\\lambda_1$ and $\\lambda_2$ as $\\vec{v}_1$ and $\\vec{v}_2$, respectively.\n", "\n", "3. General Solution\n", "The general solution for the system $\\frac{d\\vec{X}}{dt} = A\\vec{X}$ can be written as:\n", "$$\n", "\\vec{X}(t) = c_1 \\vec{v}_1 e^{\\lambda_1 t} + c_2 \\vec{v}_2 e^{\\lambda_2 t}\n", "$$\n", "where $c_1$ and $c_2$ are constants determined by initial conditions.\n", "\n", "4. Incorporate the Equilibrium State\n", "To incorporate $\\vec{B}$, we use the transformation $\\vec{X} = \\vec{X}_{hom} + \\vec{X}_{eq}$, where $\\vec{X}_{hom}$ is the homogeneous solution. Thus:\n", "$$\n", "\\vec{X}(t) = \\vec{X}_{hom}(t) + \\vec{X}_{eq}\n", "$$\n", "$$\n", "\\vec{X}(t) = c_1 \\vec{v}_1 e^{\\lambda_1 t} + c_2 \\vec{v}_2 e^{\\lambda_2 t} + \\vec{X}_{eq}\n", "$$\n", "\n", "This gives us the analytical solution in the form:\n", "$$\n", "\\vec{X}(t) = \\begin{pmatrix} \n", "a_1 e^{\\lambda_1 t} + a_2 e^{\\lambda_2 t} \\\\ \n", "b_1 e^{\\lambda_1 t} + b_2 e^{\\lambda_2 t} \n", "\\end{pmatrix} + \\vec{X}_{eq}\n", "$$\n", "\n", "\n", "\n", "5. General Solution for Repeated Eigenvalues\n", "\n", "The general solution when $\\lambda_1 = \\lambda_2 = \\lambda$ is:\n", "$$\n", "\\vec{X}(t) = (c_1 + c_2 t) e^{\\lambda t} \\vec{v} + \\vec{X}_{eq}\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[0;31mSignature:\u001b[0m \u001b[0msolve_linear_system_numerical\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mSource:\u001b[0m \n", "\u001b[0;32mdef\u001b[0m \u001b[0msolve_linear_system_numerical\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;34m\"\"\"\u001b[0m\n", "\u001b[0;34m Solves the differential equation dX/dt = AX + B.\u001b[0m\n", "\u001b[0;34m\u001b[0m\n", "\u001b[0;34m Parameters:\u001b[0m\n", "\u001b[0;34m A (numpy.ndarray): Coefficient matrix.\u001b[0m\n", "\u001b[0;34m B (numpy.ndarray): Constant vector.\u001b[0m\n", "\u001b[0;34m X0 (numpy.ndarray): Initial condition vector.\u001b[0m\n", "\u001b[0;34m t (numpy.ndarray): Array of time points at which to solve.\u001b[0m\n", "\u001b[0;34m\u001b[0m\n", "\u001b[0;34m Returns:\u001b[0m\n", "\u001b[0;34m numpy.ndarray: Array of solution vectors at each time point.\u001b[0m\n", "\u001b[0;34m \"\"\"\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;31m# Equilibrium state\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mX_eq\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;31m# Eigenvalues and eigenvectors\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0meigenvalues\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0meigenvectors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0meig\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;31m# Solve for the constants a1, a2, b1, b2\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msystem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mA\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mX\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0msol\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0modeint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msystem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m\"x\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0msol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"xeq\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mX_eq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"ev\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0meigenvalues\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"evec\"\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0meigenvectors\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mFile:\u001b[0m ~/git/workshops/spikes/spikes/solver.py\n", "\u001b[0;31mType:\u001b[0m function" ] } ], "source": [ "solve_linear_system_numerical??" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Numerical solution" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(100, 2)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B_np = np.array([7, 1])\n", "X0_np = np.array([0, 0])\n", "A_np = np.array([[-9, -5], [1, -3]])\n", "t_range = np.linspace(0, 3, 100)\n", "solution_num = solve_linear_system_numerical(\n", " A_np, B_np, X0_np, t_range\n", ")\n", "solution_num[\"x\"].shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Analytical solution" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_1(t) = \\frac{1}{2} + \\frac{3 e^{- 4 t}}{4} - \\frac{5 e^{- 8 t}}{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle x_2(t) = \\frac{1}{2} - \\frac{3 e^{- 4 t}}{4} + \\frac{e^{- 8 t}}{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Equilibrium state: [0.5 0.5]\n", "Eigenvalues: [-8.+0.j -4.+0.j]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "t = sp.Symbol('t')\n", "x1, x2 = sp.Function('x1')(t), sp.Function('x2')(t)\n", "A = sp.Matrix(A_np)\n", "X = sp.Matrix([x1, x2])\n", "B = sp.Matrix(B_np)\n", "X0 = sp.Matrix(X0_np)\n", "\n", "dx_dt = A * X + B\n", "system = [sp.Eq(sp.diff(x1, t), dx_dt[0]), sp.Eq(sp.diff(x2, t), dx_dt[1])]\n", "sol_hom = sp.dsolve(system)\n", "\n", "t0 = 0\n", "constants = sp.solve(\n", " [sol.rhs.subs(t, t0) - x0 for sol, x0 in zip(sol_hom, X0)]\n", ")\n", "\n", "sol_hom_constants = [sol.rhs.subs(constants) for sol in sol_hom]\n", "final_solution = [sol_hom for sol_hom in sol_hom_constants]\n", "\n", "# display solutions\n", "for i, sol in enumerate(final_solution, 1):\n", " display(Math(f'x_{i}(t) = {sp.latex(sol)}'))\n", " \n", "# evaluate solution\n", "x_functions = [lambdify((t,), sol, \"numpy\") for sol in final_solution]\n", "x_values = [x_func(t_range) for x_func in x_functions]\n", "\n", "# plot solutions\n", "plt.figure(figsize=(5,3))\n", "for i in range(2):\n", " plt.plot(t_range, x_values[i], label=f'$X_{i} a$', alpha=0.5)\n", " \n", "# plot numerical solution to compare\n", "for i in range(2):\n", " plt.plot(t_range, solution_num['x'][:, i], label=f'$X_{i} num$', ls='--', alpha=0.5)\n", " \n", "plt.legend(loc='upper right');\n", "print(\"Equilibrium state:\", solution_num['xeq'])\n", "print(\"Eigenvalues:\", solution_num['ev'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can define the above process as a function `solve_system_of_equations` that takes in the coefficient matrix `A` (any size) , rhs of `B` and initial conditions `X0` and time range `t_range`. The function will return the final analytical solution and evalution of the function at fiven time interval.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from spikes.solver import solve_system_of_equations" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x_1(t) = \\frac{1}{2} + \\frac{3 e^{- 4 t}}{4} - \\frac{5 e^{- 8 t}}{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle x_2(t) = \\frac{1}{2} - \\frac{3 e^{- 4 t}}{4} + \\frac{e^{- 8 t}}{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Equilibrium state: [0.5 0.5]\n", "Eigenvalues: [-8.+0.j -4.+0.j]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "B_np = np.array([7, 1])\n", "X0_np = np.array([0, 0])\n", "A_np = np.array([[-9, -5], [1, -3]])\n", "t_range = np.linspace(0, 3, 100)\n", "solution_num = solve_linear_system_numerical(\n", " A_np, B_np, X0_np, t_range\n", ")\n", "solution_num[\"x\"].shape\n", "\n", "final_solution, x_values = solve_system_of_equations(A_np, B_np, X0_np, t_range)\n", "for i, sol in enumerate(final_solution, 1):\n", " display(Math(f'x_{i}(t) = {sp.latex(sol)}'))\n", "\n", "# plot solutions\n", "plt.figure(figsize=(5,3))\n", "for i in range(2):\n", " plt.plot(t_range, x_values[i], label=f'$X_{i} a$', alpha=0.5)\n", " \n", "# plot numerical solution to compare\n", "for i in range(2):\n", " plt.plot(t_range, solution_num['x'][:, i], label=f'$X_{i} num$', ls='--', alpha=0.5)\n", " \n", "plt.legend(loc='upper right');\n", "print(\"Equilibrium state:\", solution_num['xeq'])\n", "print(\"Eigenvalues:\", solution_num['ev'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Direction Fields" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[0;31mSignature:\u001b[0m\n", "\u001b[0mplot_direction_field\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mx1_range\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mtuple\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0;34m=\u001b[0m \u001b[0;34m'x2'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0mtitle\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mstr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'Direction Field for the System $dX/dt = AX + B$'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n", "\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mDocstring:\u001b[0m\n", "Plots the direction field for the system dx/dt = A * X + B.\n", "\n", "Parameters:\n", "- A: 2x2 numpy array, the coefficient matrix for the linear system.\n", "- B: 1x2 numpy array, the constant vector.\n", "- x1_range: tuple, the range for x1 values (default: (-10, 10)).\n", "- x2_range: tuple, the range for x2 values (default: (-10, 10)).\n", "- num_points: int, the number of points per axis in the grid (default: 20).\n", "\u001b[0;31mFile:\u001b[0m ~/git/workshops/spikes/spikes/plot.py\n", "\u001b[0;31mType:\u001b[0m function" ] } ], "source": [ "from spikes.plot import plot_direction_field\n", "plot_direction_field?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from spikes.plot import plot_direction_field\n", "\n", "ax = plot_direction_field(A_np, B_np, x1_range=(-3,3), alpha=.5, color=\"b\")\n", "\n", "#plot a solution trajectory\n", "x0 = np.array([-2, -1])\n", "sol = solve_linear_system_numerical(A_np, B_np, x0, t_range)['x']\n", "ax.plot(sol[:, 0], sol[:, 1], 'r-')\n", "circle = plt.Circle(x0, 0.1, color='r', fill=False)\n", "ax.plot(x0[0], x0[1], 'ro');\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "jax", "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 4 }