{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c70df536-cea0-4cdf-bd6a-601824a52768",
   "metadata": {},
   "source": [
    "# Custom Noise CBX\n",
    "\n",
    "This notebook showcases, how to use a custom noise function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33394a7d-caa6-4f01-aa88-4dd69d5c400d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from cbx.dynamics import CBO\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef05a88a-d000-4ea8-af21-714df66858fa",
   "metadata": {},
   "source": [
    "## Define the custom noise function\n",
    "\n",
    "In this case we select that the noise should be zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "319270d9-01d4-49c0-8ac5-ab94bd6c327b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def custom_noise(dyn):\n",
    "    return np.zeros(dyn.drift.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08dac699-4772-4409-8e25-2a398216a2f4",
   "metadata": {},
   "source": [
    "## Define a loss function and test the method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aae8cac4-7a04-41a2-b9ee-a0c8c26e27da",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.linalg.norm(x, axis=-1)\n",
    "\n",
    "x0 = np.random.normal(0,1,(4,7,26))\n",
    "dyn_cn = CBO(f, x=x0, noise=custom_noise, max_it=10, verbosity = 0)\n",
    "x_cn = dyn_cn.optimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "762bcbf2-6861-4c21-8475-3e6b45e35fdb",
   "metadata": {},
   "source": [
    "Using this noise is equivalent to specifying ``sigma=0`` with standard CBO. So let's test, if this is the case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1f11124-6a10-4e54-abef-4168cbfd6dbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "dyn = CBO(f, x=x0, sigma=0, max_it=10, verbosity = 0)\n",
    "x = dyn.optimize()\n",
    "print('L-infinty Error between the custom noise solution and standard CBO with sigma=0: ' + str(np.abs(x-x_cn).max()))"
   ]
  }
 ],
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