simulation_MP_analytical.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analytical Marchenko-Pastur Simulation\n",
    "\n",
    "In what follows, we look at the behaviour of the RG of the stochastic field theory of the **analytical** Marchenko–Pastur (MP) distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from pde import CartesianGrid, MemoryStorage, ScalarField\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "from ssd import SSD, MarchenkoPastur, TranslatedInverseMarchenkoPastur\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functional Renormalization Group\n",
    "\n",
    "We here simulate the behaviour of the functional RG."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "# Parameters of the distribution\n",
    "ratio = 0.8\n",
    "mu = [0.0, 1.0, 0.0]\n",
    "xinf = 0.0\n",
    "xsup = 1.0\n",
    "nval = 1000\n",
    "nsteps = 500\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then visualize the corresponding Marchenko-Pastur distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the Marchenko-Pastur distribution\n",
    "mp = MarchenkoPastur(L=ratio)\n",
    "x = np.linspace(0, mp.max * 1.1, num=10000)\n",
    "y_0 = np.array([mp(xi) for xi in x])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.plot(x, y_0, 'r-', label='MP')\n",
    "ax.set_xlabel('eigenvalues')\n",
    "ax.set_ylabel('density')\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then show the inverse distribution for reference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the inverse Marchenko-Pastur distribution\n",
    "mp_inv = TranslatedInverseMarchenkoPastur(L=ratio)\n",
    "x = np.linspace(0, 1 / mp.min, num=10000)\n",
    "y_0 = np.array([mp_inv(xi) for xi in x])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.plot(x, y_0, 'r-', label='MP (inverse)')\n",
    "\n",
    "ax.set_xlabel('momenta')\n",
    "ax.set_ylabel('density')\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "\n",
    "We can finally simulate the evolution of the FRG equation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0.0/0.1 [00:00<?, ?it/s]              /home/rf265700/Code/stochastic-signal-detection/venv/lib/python3.10/site-packages/pde/fields/base.py:511: RuntimeWarning: overflow encountered in power\n",
      "  op(self.data, other, out=result.data)\n",
      "/home/rf265700/Code/stochastic-signal-detection/venv/lib/python3.10/site-packages/pde/fields/base.py:511: RuntimeWarning: overflow encountered in multiply\n",
      "  op(self.data, other, out=result.data)\n",
      "/home/rf265700/Code/stochastic-signal-detection/venv/lib/python3.10/site-packages/pde/fields/base.py:505: RuntimeWarning: invalid value encountered in divide\n",
      "  op(self.data, other.data, out=result.data)\n",
      "100%|██████████| 0.1/0.1 [00:00<00:00,  4.70s/it]\n"
     ]
    }
   ],
   "source": [
    "# Define the grid\n",
    "grid = CartesianGrid(\n",
    "    [[xinf, xsup]],  # range of x coordinates\n",
    "    [nval],  # number of points in x direction\n",
    "    periodic=False,  # periodicity in x direction\n",
    ")\n",
    "expression = f'{mu[0]} + {mu[1]} * x + {mu[2]} * x**2'\n",
    "state = ScalarField.from_expression(grid, expression)  # initial state\n",
    "bc = 'auto_periodic_neumann'\n",
    "\n",
    "# Initialize a storage\n",
    "t_range = [0.0, 0.1]\n",
    "dt = (t_range[1] - t_range[0]) / nsteps\n",
    "dt_viz = dt * nsteps / 5\n",
    "storage = MemoryStorage()\n",
    "storage_viz = MemoryStorage()\n",
    "trackers = [\n",
    "    'progress',\n",
    "    'steady_state',\n",
    "    storage.tracker(interval=dt),\n",
    "    storage_viz.tracker(interval=dt_viz),\n",
    "]\n",
    "\n",
    "# Define the PDE and solve\n",
    "eq = SSD(dist=mp_inv, noise=0.0, bc=bc)\n",
    "_ = eq.solve(state, t_range=t_range, dt=dt, tracker=trackers)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualisation\n",
    "\n",
    "We finally visualise the results, as functions of the stochastic time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the simulation at fixed time steps\n",
    "fig, ax = plt.subplots(nrows=len(storage_viz), figsize=(8, 6), sharex=True)\n",
    "cmap = plt.get_cmap('tab10')\n",
    "for n, (time, field) in enumerate(storage_viz.items()):\n",
    "\n",
    "    # Collect data\n",
    "    x = field.grid.axes_coords[0]\n",
    "    y_0 = field.data\n",
    "\n",
    "    # Plot the field\n",
    "    ax[n].plot(x, y_0, color=cmap(n), label=rf'$\\tau$ = {time:.3f}')\n",
    "    ax[n].set_xlabel(r'$\\overline{\\chi}$')\n",
    "    ax[n].set_ylabel(r'$\\overline{\\mathcal{U}}^{~\\prime}$')\n",
    "    ax[n].legend(loc='best')\n",
    "    ax[n].ticklabel_format(axis='y',\n",
    "                           style='sci',\n",
    "                           scilimits=(0, 0),\n",
    "                           useMathText=True)\n",
    "plt.show()\n",
    "plt.close(fig)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the evolution of the field in a given position\n",
    "t = []\n",
    "y_0 = []\n",
    "y_1 = []\n",
    "for time, field in storage.items():\n",
    "\n",
    "    # Collect data\n",
    "    t.append(time)\n",
    "    y_0.append(field.data[0])\n",
    "    y_1.append(field.data[-1])\n",
    "fig, ax = plt.subplots(ncols=2, figsize=(16, 6))\n",
    "ax[0].plot(t, y_0, 'k-')\n",
    "ax[0].set_xlabel('k')\n",
    "ax[0].invert_xaxis()\n",
    "ax[0].set_ylabel(rf'$\\overline{{\\mathcal{{U}}}}^{{~\\prime}}[{xinf}]$')\n",
    "ax[0].ticklabel_format(axis='y',\n",
    "                       style='sci',\n",
    "                       scilimits=(0, 0),\n",
    "                       useMathText=True)\n",
    "ax[1].plot(t, y_1, 'k-')\n",
    "ax[1].set_xlabel('k')\n",
    "ax[1].invert_xaxis()\n",
    "ax[1].set_ylabel(rf'$\\overline{{\\mathcal{{U}}}}^{{~\\prime}}[{xsup}]$')\n",
    "ax[1].ticklabel_format(axis='y',\n",
    "                       style='sci',\n",
    "                       scilimits=(0, 0),\n",
    "                       useMathText=True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}