{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import ode\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define bloch and B_eff functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bloch_ode(t,M,T1,T2):\n",
    "    B = B_eff(t)\n",
    "    return np.array([M[1]*B[2] - M[2]*B[1] - M[0]/T2,\n",
    "                     M[2]*B[0] - M[0]*B[2] - M[1]/T2,\n",
    "                     M[0]*B[1] - M[1]*B[0] - (M[2]-1)/T1])\n",
    "\n",
    "def B_eff(t):\n",
    "    if t < 0.25:\n",
    "        return np.array([0, 0, 0])\n",
    "    elif t < 1.25:\n",
    "        return np.array([1.8*np.sinc(t-0.75), 0, 0])\n",
    "    elif t < 1.50:\n",
    "        return np.array([0, 0, 0])\n",
    "    elif t < 3.00:\n",
    "        return np.array([0, 0, 2*np.pi])\n",
    "    else:\n",
    "        return np.array([0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Integrate ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.array([0])\n",
    "M = np.array([[0, 0, 1]])\n",
    "dt= 0.005\n",
    "r = ode(bloch_ode)\n",
    "r.set_integrator('dopri5')\n",
    "r.set_initial_value(M[0],t[0])\n",
    "r.set_f_params(1500, 50)\n",
    "while r.successful() and r.t < 5:\n",
    "    t = np.append(t,r.t+dt)\n",
    "    M = np.append(M, np.array([r.integrate(t[-1])]),axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, ax = plt.subplots(figsize=(12,12))\n",
    "ax.plot(t,M[:,0], label='Mx')\n",
    "ax.plot(t,M[:,1], label='My')\n",
    "ax.plot(t,M[:,2], label='Mz')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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