{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "84b00e35-7bd9-418c-a3e1-0b698907e5ea",
   "metadata": {},
   "source": [
    "# Denoising and regularization: `rgz` and `cdf` modules (Checked: D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1413b178-74ef-443f-99fc-864b9c1ee0a5",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "> **NOTE:** This tutorial assumes familiarity with the concepts explained in  [Conceptual and mathematical background of higher-order Fourier analysis](concept-background) and that the ``HoFa`` package has already been installed, see [Installation](../getting_started/installation).\n",
    "\n",
    "> **HOW TO READ THIS NOTEBOOK:** This notebook starts from a simplified version of the algorithm and progressively introduces the full generality of the implementation. Readers interested only in usage may skip to [How the algorithm is implemented in practice](#denoising--how-the-algorithm-is-implemented), while readers interested in design choices may follow the full narrative.\n",
    "\n",
    "In this notebook we are going learn how the ``HoFa`` package removes $U^k$ noise from a function, and we are going to explain the implementation details of the regularization algorithm. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bf0f243-9dee-4d50-a474-b071cd926258",
   "metadata": {},
   "source": [
    "## The algorithm: a minimal but representative formulation\n",
    "\n",
    "We begin by presenting the algorithm in a deliberately restricted form. This version captures the full logical structure of the method while avoiding additional choices and tunable components that, although important in practice, are not essential for understanding how the algorithm works. The general implementation provided by the package follows the same core steps and introduces further flexibility only where meaningful alternatives arise. By starting from this minimal formulation, we can focus on the underlying mechanism of the algorithm before discussing how it can be extended, customized, and optimized.\n",
    "\n",
    "Throughout this section, it is useful to keep in mind that every component introduced here has a direct counterpart in the full implementation. Later sections will revisit each step and show how it can be modified or replaced to accommodate different variants of the algorithm.\n",
    "\n",
    "Let us recall below with pseudocode the basic version we are interested in.\n",
    "\n",
    "<a id=\"basic-regularization\"></a>**Basic** $U^3$ **regularization algorithm**\n",
    "\n",
    "_Input:_ $f: Z \\to \\mathbb{C}$, $\\rho, \\varepsilon {>0}$\n",
    "\n",
    "1. $M \\leftarrow f(x) \\otimes \\overline{f(y)} \\in \\mathbb{C}^{Z \\times Z}$\n",
    "\n",
    "2. For each $t \\in Z$:\n",
    "    - $M(\\cdot + t, \\cdot) \\leftarrow K_\\varepsilon(M(\\cdot + t, \\cdot))$\n",
    "\n",
    "3. $(\\mu_1, v_1), \\ldots, (\\mu_{|Z|}, v_{|Z|}) \\leftarrow \\mathrm{Eigdecomp}(M)$ \n",
    "\n",
    "\n",
    "_Output:_ $f_{\\text{reg}} \\leftarrow\\sum_{\\mu_i \\ge \\rho} \\langle f, v_i \\rangle v_i$, eigenvalues $\\leftarrow \\{\\mu_1,\\ldots, \\mu_{|Z|}\\}$, and eigenvectors $\\leftarrow \\{v_{1},\\ldots, v_{|Z|}\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8aafb2c-3d5f-4faf-8b71-ba9fe78bdb81",
   "metadata": {},
   "source": [
    "To better understand how the algorithm works, we now walk through its basic formulation step by step on a simple example. By explicitly computing the intermediate quantities, we expose the internal logic that is otherwise hidden by the implementation. This perspective will be useful when we later introduce more general variants of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dce28c0d-591d-47b2-9ca7-8f6ec2c407bc",
   "metadata": {},
   "source": [
    "## Manual execution of the basic algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0138073b-67fe-4184-9d37-a28272c44bb5",
   "metadata": {},
   "source": [
    "We consider the following illustrative problem, which will serve as a running example throughout this section.\n",
    "\n",
    "<a id=\"denoising--problem-statement\"></a>\n",
    "### Problem statement\n",
    "\n",
    "We want to transmit the periodic linear chirp $f_s(x)=\\sin(2\\pi x^2/n)$ defined for any integer $x$ (note the periodicity property $f_s(x+n)=f_s(x)$). However, our communication channel introduces noise, and what is received is a convex combination $f=tf_r+(1-t)f_s$ where $f_r(x)$ follows a uniform distribution $\\text{Unif}([-1,1))$ independently for every integer $x$ and the amount of noise is $t=30$%.\n",
    "\n",
    "This formulation intentionally simple and is chosen to highlight the core behavior of the algorithm rather than edge cases.\n",
    "\n",
    "### Objective\n",
    "\n",
    "Under these assumptions, we aim to compute an estimate of $f_s$.\n",
    "\n",
    "In the following, we use this example to manually execute the algorithm step by step, making explicit the intermediate quantities involved in the computation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8418738b-5b82-4a0f-801f-a098d140ef41",
   "metadata": {},
   "source": [
    "First of all, let us import the necessary modules. Recall that we are assuming that the ``HoFa`` package is already installed, see [Installation](../getting_started/installation). For a quick installation, run the following command:\n",
    "\n",
    "```console\n",
    "(hofavenv) $ pip install hofa\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6d10f400-49e2-40bf-b6c3-96fcd9a96f26",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the necessary packages to use hofa\n",
    "import hofa.cdf as cdf\n",
    "import hofa.rgz as rgz\n",
    "\n",
    "# and visualize its results\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=2)\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa17a1c0-25c1-43b0-969c-98883a57966b",
   "metadata": {},
   "source": [
    "### Modelization of the example problem\n",
    "\n",
    "**Setup:**\n",
    "\n",
    "* $f_s(x):\\mathbb{Z}\\to \\mathbb{R}$ is defined as $x\\mapsto \\sin(2\\pi x^2/n)$,\n",
    "* $f_r:\\mathbb{Z}\\to \\mathbb{R}$ is defined as $f_r(x)\\sim \\text{Unif}([-1,1))$ independently for every $x\\in \\mathbb{Z}$,\n",
    "* $f:=t f_r+(1-t)f_s$ for $t=0.3$.\n",
    "\n",
    "**Goal:** Recover $f_s$ using only $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "90ac52b8-a05b-4b7e-8a01-8799bfdf8904",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 173 # Feel free to change this\n",
    "x = np.arange(n)\n",
    "f_s = np.sin(2*np.pi*x**2/n)\n",
    "# Due to implementation reasons of auxiliary functions, \n",
    "# it is convenient to work with complex numbers\n",
    "f_s = f_s.astype(complex) \n",
    "\n",
    "# For reproducibility reasons, we fix a random seed, but feel free to change this.\n",
    "np.random.seed(123)\n",
    "f_r = np.random.uniform(-1, 1, size=len(x))\n",
    "\n",
    "# And finally we construct the only function we are going to work with, f.\n",
    "# To do that, we fix t=0.3, but again, feel free to change it and test the limits of the algorithm.\n",
    "t = 0.3\n",
    "f = t*f_r+(1-t)*f_s"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdf53855-5ed9-4d30-aeee-9a725da1bcf1",
   "metadata": {},
   "source": [
    "### The algorithm step by step\n",
    "\n",
    "Now that we have defined our function, it is time to implement [Basic $U^3$ regularization algorithm](#basic-regularization). To do so, not that the first step is to compute $f\\otimes \\overline{f}$. The module `rgz` provides us with the method `hofa.rgz.t_prod_itself` to compute such matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2ef8f7fd-7832-45c3-8b86-689442406b6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.01+0.j, -0.01-0.j, -0.01-0.j,  0.03+0.j,  0.06+0.j],\n",
       "       [-0.01+0.j,  0.01+0.j,  0.01+0.j, -0.03+0.j, -0.05+0.j],\n",
       "       [-0.01+0.j,  0.01+0.j,  0.  +0.j, -0.02+0.j, -0.03+0.j],\n",
       "       [ 0.03+0.j, -0.03-0.j, -0.02-0.j,  0.07+0.j,  0.13+0.j],\n",
       "       [ 0.06+0.j, -0.05-0.j, -0.03-0.j,  0.13+0.j,  0.27+0.j]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = rgz.t_prod_itself(f) # We compute the matrix\n",
    "M[:5,:5] # And we visualize only the first 5x5 upper left corner"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01cf83be-28a3-4702-b655-b556c00fbd2a",
   "metadata": {},
   "source": [
    "We see that the result is a real symmetric matrix $M_{n\\times n}(\\mathbb{R})$. In general, if the map $f$ takes complex values then the resulting matrix will be self-adjoint."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42e4e55e-297d-4ed8-ab2c-c5c14410e8e6",
   "metadata": {},
   "source": [
    "The second step in [Basic $U^3$ regularization algorithm](#basic-regularization) consists in changing the $Z$-diagonals of $M$ for a _Fourier regularized version_. Note that the $Z$-diagonals are not the usual diagonals of a matrix as they are defined using modular arithmetic. That is, if $M=(m_{i,j})_{i,j=0,\\ldots,n-1}$ , a $Z$-diagonal of height $t=0,\\ldots,n-1$ a collection of $m_{i,j}$ are in the same diagonal if $i-j$ equal the same integer $t$ **modulo $n$**. This part is important, so let us draw a diagram where we highlight the different diagonals. For simplicity, imagine now that $n=6$ instead of $n=173$ as we have above. Thus, the matrix $M$ is 6x6 and its $Z$-diagonals are as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ac26f753-592f-4825-ade7-b252954afeb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap, BoundaryNorm\n",
    "\n",
    "matrix = np.array([\n",
    "    [0, 1, 2, 3, 4, 5],\n",
    "    [5, 0, 1, 2, 3, 4],\n",
    "    [4, 5, 0, 1, 2, 3],\n",
    "    [3, 4, 5, 0, 1, 2],\n",
    "    [2, 3, 4, 5, 0, 1],\n",
    "    [1, 2, 3, 4, 5, 0]\n",
    "])\n",
    "\n",
    "colors = [\"red\", \"blue\", \"green\", \"yellow\", \"purple\", \"orange\"]\n",
    "\n",
    "cmap = ListedColormap(colors)\n",
    "norm = BoundaryNorm(np.arange(-0.5, 6.5, 1), cmap.N)\n",
    "\n",
    "plt.figure(figsize=(4, 4))\n",
    "plt.imshow(matrix, cmap=cmap, norm=norm, alpha=0.7)\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "for i in range(6):\n",
    "    for j in range(6):\n",
    "        plt.text(j, i, 'm['+str(i)+','+str(j)+']',\n",
    "                 ha=\"center\", va=\"center\", color=\"black\")\n",
    "\n",
    "plt.title('Different Z-Diagonals in the case of period n=6')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcefa8dd-9a17-4e84-b480-18f1430632bf",
   "metadata": {},
   "source": [
    "There are many ways of operating on the $Z$-diagonals of a matriz but currently, there are no fast `numpy` or `scipy` method that can vectorize an operation through them. The solution given in `hofa.rgz` is to create an auxiliary matrix where the $Z$-diagonals of a function are moved to the rows using `hofa.rgz.move_diag_to_rows` so that we can operate with them easily, and then a function to put them back in their original positions `hofa.rgz.move_rows_to_diag`. Let us see in action how these methods in action on our toy example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8a9f33d7-84c2-4c79-9230-e7b69cc10d5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.01+0.j,  0.01+0.j,  0.  +0.j,  0.07+0.j,  0.27+0.j],\n",
       "       [-0.01-0.j,  0.01+0.j, -0.02+0.j,  0.13+0.j,  0.26+0.j],\n",
       "       [-0.01-0.j, -0.03+0.j, -0.03+0.j,  0.13+0.j,  0.5 +0.j],\n",
       "       [ 0.03+0.j, -0.05+0.j, -0.03+0.j,  0.25+0.j,  0.41+0.j],\n",
       "       [ 0.06+0.j, -0.05+0.j, -0.06+0.j,  0.2 +0.j,  0.26+0.j]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_diag_to_rows = rgz.move_diag_to_rows(M)\n",
    "M_diag_to_rows[:5,:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f171ebc9-e164-449f-8850-8ad0e74e3ad9",
   "metadata": {},
   "source": [
    "Note that, e.g., the main diagonal is now the first row in the `M_diag_to_rows` matrix.\n",
    "\n",
    "To put it back to its original state, we can use `hofa.rgz.move_rows_to_diag`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a58b72d5-616c-48a6-8fe8-2994f0d568f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " All elements correctly reorganized: True\n"
     ]
    }
   ],
   "source": [
    "M_back_to_position = rgz.move_rows_to_diag(M_diag_to_rows)\n",
    "print(f\" All elements correctly reorganized: {np.all(M == M_back_to_position)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "643b45d8-6618-4040-92b2-455463730e53",
   "metadata": {},
   "source": [
    "The actual implementation of both these functions currently use [Broadcasting](https://numpy.org/doc/stable/user/basics.broadcasting.html) and [Advanced indexing](https://numpy.org/doc/2.2/user/basics.indexing.html#advanced-indexing) to handle not only the case of 1-dimensional $n$-periodic function but also the general case of any number of dimensions with different periods, see [Coding theory example](#denoising--coding-theory)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed82d7da-cb7b-4cbf-8387-fb93e6efc968",
   "metadata": {},
   "source": [
    "But remember that what we want is to create a new matrix where we have changed the $Z$-diagonals by applying the Denoising operator $K_\\varepsilon$, see [Basic $U^3$ regularization algorithm](#basic-regularization). Remember that this operator uses a small constant $\\varepsilon$ defined by the user, so let us fix one such constant and define the denoising operator $K_\\varepsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "09693ebe-7d79-4f77-a261-8dfd6814f521",
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 0.03\n",
    "\n",
    "def denoising_operator(diag : np.ndarray):\n",
    "    \"\"\"\n",
    "    Modifies the function `diag` on the finite abelian group Z to produce K_epsilon(diag).\n",
    "\n",
    "    Parameters:\n",
    "        diag (function): The function defined on Z.\n",
    "\n",
    "    Returns:\n",
    "        function: The modified function K_epsilon(diag).\n",
    "    \"\"\"\n",
    "    # Compute all Fourier coefficients of diag\n",
    "    fourier_coeffs = np.fft.fftn(diag,norm=\"forward\")\n",
    "\n",
    "    # Modify Fourier coefficients as per the algorithm\n",
    "    modified_coeffs = (np.maximum(np.abs(fourier_coeffs)-epsilon,0))*np.exp(1j*np.angle(fourier_coeffs))\n",
    "\n",
    "    # Return the new function K_epsilon(diag) using the modified Fourier coefficients\n",
    "    return np.fft.ifftn(modified_coeffs, norm=\"forward\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d47fb420-2c7f-4412-8002-ee2c6a6932d2",
   "metadata": {},
   "source": [
    "Now, we need to apply this operator on every $Z$-diagonal of our $Z$-matrix $M$. To do so, we have the method `hofa.rgz.apply_on_diag`. This method essentially uses `hofa.rgz.move_diag_to_rows` to put all diagonals as rows, applies an operator to each diagonal, and puts the diagonals back in their original places with `hofa.rgz.move_rows_to_diag`.\n",
    "\n",
    "> **Note:** This is one of the places where performance could be enhanced by providing native methods written in C for handling $Z$-diagonals. Note that this process of applying an operator on every $Z$-diagonal can be parallelized, as we will see in the appropriate tutorial where we deal with the `PyTorch` implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "26206187-b4bf-4629-857f-b2e55bf5f5fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.21+2.78e-17j, 0.22-1.39e-17j, 0.21+6.94e-18j, 0.2 -2.78e-17j],\n",
       "       [0.22+7.98e-17j, 0.24+9.45e-17j, 0.22+6.25e-17j, 0.21-5.20e-17j],\n",
       "       [0.21+5.38e-17j, 0.22-6.25e-17j, 0.25-6.94e-18j, 0.21-4.16e-17j],\n",
       "       [0.2 -1.39e-17j, 0.21+1.18e-16j, 0.21+4.86e-17j, 0.26-4.16e-17j]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_diags_reg = rgz.apply_on_diag(M, denoising_operator)\n",
    "\n",
    "# Similarly as before, we compute the same for our toy example M_g\n",
    "M_g_diags_reg = rgz.apply_on_diag(M, denoising_operator)\n",
    "M_g_diags_reg[:4,:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffae9400-5c59-4616-9c10-3d09802fafa8",
   "metadata": {},
   "source": [
    "After this strange-looking operation we are ready to see where the magic starts. Precisely, we need now to compute the eigendecomposition of $M$. \n",
    "\n",
    "> **Note**: We prefer to use a different normalization for eigenvalues and eigenvectors other than the one of `np.linalg.eigh`. The reason is that if we treat $M$ as a **kernel operator**, we should normalize the application of $M$ on a vector dividing by the length of the vector. That is, as a kernel operator $M$ applied on a vector $v$ should be defined as $\\tfrac{1}{n}Mv$. This is consistent with e.g. normalizing the forward Fourier transform $\\widehat{f}(\\chi)=\\tfrac{1}{n}\\sum_{x=0}^{n-1} f(x)\\overline{\\chi(x)}$ as we always do in the ``HoFa`` package. In practive this means that we have to divide the eigenvalues resulting from `np.linalg.eigh` by $n$ and multiply the eigenvectors by $\\sqrt{n}$ (so that they have norm 1 when we compute the normalized $L^2$ norm $\\|f\\|_2^2=\\tfrac{1}{N}\\sum_{x=0}^{n-1} |f(x)|^2$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cc1f4174-3bad-4eb5-a72d-d86db7711546",
   "metadata": {},
   "outputs": [],
   "source": [
    "eivals, eivects = np.linalg.eigh(M_diags_reg)\n",
    "\n",
    "# To normalize eigenvalues and eigenvectors we need to do\n",
    "# the following\n",
    "eivals = eivals/n\n",
    "eivects = eivects*np.sqrt(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c015a47d-70bc-4535-8edc-8f639ebe94ec",
   "metadata": {},
   "source": [
    "The magic here occurs when we look at the eigenvalues of `M_diags_reg`. Recall that these are ordered increasingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "795bcd8e-cafc-4039-b8f5-2447533cd0bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 300x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3, 2))\n",
    "plt.plot(eivals, marker='o', linestyle='None')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7e334f3-c625-4cf1-a60c-760d636a255a",
   "metadata": {},
   "source": [
    "Note that there is something strange here, there two eigenvalues whose absolute value is significantly greater than the rest. The deep reason for this is that, with respect to this algorithm, we are seeing our function $f_s(x)=\\sin(2\\pi x^2/n)$ as a combination of two higher-order characters\n",
    "\n",
    "$$\\sin(2\\pi x^2/n) = \\frac{e^{2\\pi i x^2/n}-e^{-2\\pi i x^2/n}}{2i}.$$\n",
    "\n",
    "> **Note:** that we have computed this using only $f=tf_r+(1-t)f_s$, the algorithm has not seen $f_s$ but nevertheless it has been able to recognize not only the quadratic structure, but also the fact that it comes from 2 _higher-order characters_.\n",
    "\n",
    "Our [Basic $U^3$ regularization algorithm](#basic-regularization) tells us that projecting the function $f$ to the eigenspace generated by the eigenvectors corresponding to these two eigenvalues keeps precisely the quadratic component of the function $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "66a0f368-f14a-4d01-ad07-45fba94e0c85",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we compute the projection of f on that eigenvector\n",
    "f_reg = np.mean(f*eivects[:,-1].conjugate())*eivects[:,-1]+np.mean(f*eivects[:,-2].conjugate())*eivects[:,-2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a125a12b-d620-4ec3-831e-1371988ff0de",
   "metadata": {},
   "source": [
    "And to conclude let us plot this function together with the original function $f$ that we feeded the algorithm with and the real quadratic component $(1-t)f_s$ that is hidden within $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "17d12d71-56fb-4ac4-95b2-931b07beecaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# And now let us print the original function f_s*(1-t), the modified version\n",
    "# f, and the output of our algorithm f_reg. (For simplicity we only plot\n",
    "# the real part of those functions).\n",
    "fig, ax = plt.subplots(figsize=(12, 5))\n",
    "\n",
    "# Plot original (1-t)*f_s in light green\n",
    "ax.plot(x, np.real(f_s*(1-t)), linestyle='-', color='lightgreen', marker='o', markersize=6, linewidth=1, alpha=0.6, label=r'$(1-t)*f_s$')\n",
    "\n",
    "# Plot modified function in red\n",
    "ax.plot(x, np.real(f), linestyle='-', color='red', marker='o', markersize=6, linewidth=1, alpha=0.6, label=r'$f = t*f_r+(1-t)*f_s$')\n",
    "\n",
    "# Plot recovered function in blue\n",
    "ax.plot(x, np.real(f_reg), linestyle='-', color='blue', marker='o', markersize=3, linewidth=1, alpha=0.6, label=r'$f_{\\text{reg}}$')\n",
    "\n",
    "# Customize the plot\n",
    "ax.set_xlabel(\"x\")\n",
    "ax.set_title(f\"t (Amount of noise): {t:.2f}\")\n",
    "ax.set_ylim(-1,1)\n",
    "\n",
    "# Legend below the plot\n",
    "fig.subplots_adjust(bottom=0.25)  # Adjust layout to fit legend below\n",
    "ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=2, frameon=False)\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82349f72-dcf1-4df3-9280-eee96f2059ca",
   "metadata": {},
   "source": [
    "Before continue, the reader is encouraged to modify the above example with different functions, parameters $\\varepsilon,\\rho, t, n$ etc. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3c93266-943f-4be8-8319-16e7c9620445",
   "metadata": {},
   "source": [
    "The sequence of operations we have just carried out manually is exactly what the package implements internally. In practice, all of the steps above are encapsulated in a single function call to ``hofa.rgz.regularize()``, which performs the same computation while handling the necessary bookkeeping and numerical details. Moreover, it includes heuristics to compute the parameters $\\varepsilon,\\rho$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f22b81d3-f200-455b-9559-32fa75977fc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 5))\n",
    "\n",
    "ax.plot(x, np.real(f_s*(1-t)), linestyle='-', color='lightgreen', marker='o', markersize=6, linewidth=1, alpha=0.6, label=r'$(1-t)*f_s$')\n",
    "\n",
    "ax.plot(x, np.real(rgz.regularize(f,2).regularization), linestyle='-', color='purple', marker='o', markersize=3, linewidth=1, alpha=0.6, label=r'Using hofa.rgz.regularize')\n",
    "\n",
    "ax.set_ylim(-1,1)\n",
    "fig.subplots_adjust(bottom=0.25)  # Adjust layout to fit legend below\n",
    "ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=2, frameon=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34d4ca46-d139-486d-97c2-fe29580b8ccb",
   "metadata": {},
   "source": [
    "\n",
    "<a id=\"denoising--generalizing-the-algorithm\"></a>\n",
    "### Generalizing the algorithm\n",
    "\n",
    "While the basic formulation already captures the core idea of the algorithm, it is not the only reasonable way to instantiate it. Several aspects of the procedure admit alternative choices, leading to variants that differ in behavior, robustness, or computational cost. The package is designed to expose these degrees of freedom in a controlled way, allowing users to adapt the algorithm to specific problems while preserving the underlying structure described above. Let us now discuss where these alternatives may take place by pinpointing in the [Basic $U^3$ regularization algorithm](#basic-regularization) possible variants.\n",
    "\n",
    "_Input:_ $f: Z \\to \\mathbb{C}$, $\\rho, \\varepsilon {>0}$ <span style=\"border: 0px solid red; padding: 2px; display: inline-block; background-color: #f8d7da; border-radius: 5px; text-align: right; font-weight: bold;\"> &#8594; 1 </span>\n",
    "\n",
    "1. $M \\leftarrow f(x) \\otimes \\overline{f(y)} \\in \\mathbb{C}^{Z \\times Z}$\n",
    "\n",
    "2. For each $t \\in Z$:\n",
    "    - $M(\\cdot + t, \\cdot) \\leftarrow K_\\varepsilon(M(\\cdot + t, \\cdot))$ <span style=\"border: 0px solid red; padding: 2px; display: inline-block; background-color: #f8d7da; border-radius: 5px; text-align: right; font-weight: bold;\"> &#8594; 2 </span>\n",
    "\n",
    "3. $(\\mu_1, v_1), \\ldots, (\\mu_{|Z|}, v_{|Z|}) \\leftarrow \\mathrm{Eigdecomp}(M)$ <span style=\"padding: 2px; display: inline-block; background-color: #f8d7da; border-radius: 5px; text-align: right; font-weight: bold;\"> &#8594; 3 </span>\n",
    "\n",
    "\n",
    "_Output:_ $f_{\\text{reg}} \\leftarrow\\sum_{\\mu_i \\ge \\rho} \\langle f, v_i \\rangle v_i$, eigenvalues $\\leftarrow \\{\\mu_1,\\ldots, \\mu_{|Z|}\\}$, and eigenvectors $\\leftarrow \\{v_{1},\\ldots, v_{|Z|}\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab823b53-df47-4ed9-9d2f-4bd2536be4a5",
   "metadata": {},
   "source": [
    "<span style=\"border: 0px solid red; padding: 2px; display: inline-block; background-color: #f8d7da; border-radius: 5px; text-align: right; font-weight: bold;\"> &#8594; 1 </span> How can we choose these parameters $\\varepsilon$ and $\\rho$?\n",
    "\n",
    "<span style=\"border: 0px solid red; padding: 2px; display: inline-block; background-color: #f8d7da; border-radius: 5px; text-align: right; font-weight: bold;\"> &#8594; 2 </span> So far we used the map ``denoising_operator`` for regularizing the diagonals, which changes any diagonal $g \\mapsto \\sum \\mathrm{ReLU}(|\\widehat{g}(\\chi)|-\\varepsilon)\\tfrac{\\widehat{g}(\\chi)}{|\\widehat{g}(\\chi)|}\\chi$. But can we use other method such as simply $g \\mapsto \\sum_{|\\widehat{g}(\\chi)|\\ge \\varepsilon}\\widehat{g}(\\chi)\\chi$ ? and moreover, what if we want to do cubic or higher-order regularization? As explained in [Order increment principle, page 4, Figure 1](https://arxiv.org/pdf/2501.12287) we should replace $K_\\varepsilon$ with a lower order regularizer. For instance, if we want cubic regularization we should replace $K_\\varepsilon$ with the [Basic $U^3$ regularization algorithm](#basic-regularization) itself! \n",
    "\n",
    "<span style=\"border: 0px solid red; padding: 2px; display: inline-block; background-color: #f8d7da; border-radius: 5px; text-align: right; font-weight: bold;\"> &#8594; 3 </span> Last but not least, we have to compute the eigendecomposition of a matrix. But we are typically interested only in the largest eigenvalues and eigenvectors. Moreover, the size of the largest eigenvalues needed depend on this last cutoff parameter $\\rho$. Hence, in general we do not want to compute the full eigendecomposition using `numpy.linalg.eigh`, is there anything better?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e220cc47-8a12-468e-b879-c3508673695e",
   "metadata": {},
   "source": [
    "All these question will be adressed below, where we will see how to precisely handle all of these issues."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85788d1c-4887-473b-82c8-34f149d5b070",
   "metadata": {},
   "source": [
    "<a id=\"denoising--how-the-algorithm-is-implemented\"></a>\n",
    "## How the algorithm is implemented in practice"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e423c611-88f7-4ba3-8294-283e0471cd00",
   "metadata": {},
   "source": [
    "So far, we have explored the basic version of the algorithm and walked through its steps manually to build intuition. The version implemented in the package follows the same core logic but adds flexibility and tunable components that allow it to handle a wider range of practical scenarios.  \n",
    "\n",
    "Let us now present the **full algorithm** in pseudocode and explain how its different parts are implemented. We start with the main function that encapsulates the internal logic, then describe auxiliary functions and classes that provide additional control for advanced users. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9909a85-66ef-4908-ad93-fb6d67ca027d",
   "metadata": {},
   "source": [
    "To understand this pseudocode, recall that this is a **recursive** algorithm. Let us denote by $K(f,k)$ its output for a function $f$ if we want regularization of order $k$.\n",
    "\n",
    "<a id=\"general-regularization\"></a>**General** $U^k$ **regularization algorithm**\n",
    "\n",
    "_Input:_ Function to regularize: $f: Z \\to \\mathbb{C}$ and order of regularization: $k$ (a positive integer)\n",
    "\n",
    "0. If $k==1$:\n",
    "\n",
    "    _Output_: $K(f,1)$: Fourier regularization on $f$, absolute value squared of Fourier coefficients $|\\widehat{f}(\\chi)|^2$, and all Fourier characters $\\{\\chi\\}$.\n",
    "\n",
    "2. $M \\leftarrow f(x) \\otimes \\overline{f(y)} \\in \\mathbb{C}^{Z \\times Z}$\n",
    "\n",
    "3. For each $t \\in Z$:\n",
    "    - Replace the $Z$-diagonal $M(\\cdot + t, \\cdot)$ in the $Z$-diagonal with the $k-1$-regularized version $K((M(\\cdot + t, \\cdot),k-1)$.\n",
    "\n",
    "4. $(\\mu_1, v_1), \\ldots, (\\mu_{|Z|}, v_{|Z|}) \\leftarrow \\mathrm{Eigdecomp}(M)$ \n",
    "\n",
    "_Output_ $K(f,k)$:  is the **weighted** projection of $f$ in terms of the $\\mu_i$ to the eigenspaces $v_i$, the eigenvalues $\\{\\mu_i\\}$, and the eigenvectors $\\{v_i\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e85170d8-97a9-43c0-983e-337baacfa3d9",
   "metadata": {},
   "source": [
    "The pseudocode above captures the logical flow of the full algorithm, highlighting its core steps and optional variant points. Each step corresponds directly to one or more functions or classes in the package, with the main workflow implemented in the `regularize()` function.  \n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def regularize(f : np.ndarray, per_layer_regularizers : List[LayerRegularizer] | int = 2, rng : int | np.random.Generator | None = None) -> RegularizationResult:\n",
    "```\n",
    "\n",
    "The signature of this function reflects the flexibility illustrated in the pseudocode: it accepts both simple parameters for standard usage and objects that encapsulate specific algorithmic variants, allowing advanced users to control individual steps. In other words, the main function is a **direct, ready-to-use realization** of the algorithm, where each argument corresponds to a concept from the pseudocode:\n",
    "\n",
    "- Core input: the function ``f``.\n",
    "- Regularization component: the variable ``per_layer_regularizers`` which represent either an ``int`` for default regularization of some order or a ``List[LayerRegularizer]`` to allow flexibility and fine-tunning of the regularization process.\n",
    "- Output: final result of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27cb0b21-a26d-44c3-ab6c-500caa86489f",
   "metadata": {},
   "source": [
    "### Exploring auxiliary functions\n",
    "\n",
    "While the `regularize()` function serves as the main entry point, its role is primarily to perform setup, validate inputs, and orchestrate the overall workflow. The actual computations and algorithmic decisions are carried out by a set of **auxiliary functions** that implement the core steps highlighted in the pseudocode, the most important ones being:\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def regularize_after_setup(f : np.ndarray, per_layer_regularizers : List[LayerRegularizer])\n",
    "\n",
    "def regularize_and_decompose(f : np.ndarray, K : Callable , layer_regularizer : LayerRegularizer)\n",
    "```\n",
    "\n",
    "The function ``regularize_after_setup()`` is in charge of doing the main **recursion step**, while ``regularize_and_decompose()`` implements **steps 1., 2., and 3.** of the [General $U^k$ regularization algorithm](#general-regularization)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e44a2e4-7d74-437e-8830-ddcef9d944f1",
   "metadata": {},
   "source": [
    "Beyond these core functions, the implementation is decomposed into several smaller auxiliary functions that correspond to individual steps or sub-steps of the algorithm. This decomposition serves two purposes: it keeps the main logic readable and maintainable, and it allows advanced users to inspect or customize specific operations in isolation.\n",
    "\n",
    "In typical usage, these auxiliary functions are invoked internally by the core functions and do not need to be called directly. Nevertheless, they are exposed as part of the public API to facilitate experimentation, debugging, or fine-grained control over specific stages of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be97ab9e-06fa-400d-be87-7b39349541c2",
   "metadata": {},
   "source": [
    "#### Auxiliary functions\n",
    "\n",
    "The following auxiliary functions implement individual steps of the algorithm and are primarily intended for advanced usage:\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def weighed_projection(f : np.ndarray, eigvals : np.ndarray, eigvects : np.ndarray, layer_regularizer : LayerRegularizer)\n",
    "```\n",
    "- Implements the _Output_ step of the algorithm where we need to compute the projection of a function to certain eigenspaces weighted by some parameters which depends on the eigenvalues\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def default_reg_list(k : int)\n",
    "```\n",
    "\n",
    "- Gives a list of default tested ``LayerRegularizer`` s of a certain length.\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def move_diag_to_rows(M : np.ndarray)\n",
    "```\n",
    "\n",
    "- Auxiliary function that re-organizes the $Z$-diagonals of a matrix into rows\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def move_rows_to_diag(M : np.ndarray)\n",
    "```\n",
    "\n",
    "- Auxiliary function that re-organizes the rows of a matrix as $Z$-diagonals. Inverse operation of ``move_diag_to_rows``.\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def apply_on_diag(M : np.ndarray , K : Callable)\n",
    "```\n",
    "\n",
    "- Function to apply a certain operator into the $Z$-diagonals of a matrix.\n",
    "\n",
    "``` python\n",
    "# In the module hofa.rgz\n",
    "def t_prod_itself(g : np.ndarray)\n",
    "```\n",
    "\n",
    "- Function to apply create, from a function, the corresponding matrix of **step 1.** of [General $U^k$ regularization algorithm](#general-regularization).\n",
    "\n",
    "Each of these functions is called internally by the core workflow, but can also be used independently to customize or extend specific stages of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28070ed3-ea04-4dd4-a424-4a7c63f72c62",
   "metadata": {},
   "source": [
    "### Encapsulating fine-tuning and algorithmic variants\n",
    "\n",
    "To support fine-grained control over the algorithm, the package introduces an abstract base class ``LayerRegularizer`` that defines the common interface and encapsulates the choices and behaviors that may vary between different algorithmic variants. This abstract class appears throughout the functions presented above. Rather than hard-coding specific choices into each function, the algorithm delegates these decisions to the particular implementations of such class, allowing the same workflow to support multiple variants, tuning strategies, and extensions in a consistent and modular way.\n",
    "\n",
    "For most users, the default concrete implementation ``StandardLayerRegularizer`` provided by the package is sufficient and can be used directly without modification. Advanced users, however, may subclass the abstract class to customize specific aspects of the algorithm while preserving compatibility with the rest of the pipeline.\n",
    "\n",
    "Finally, there is the class ``RegularizationResult`` which is nothing but a ``NamedTuple`` containing the result of the main regularization algorithm. Its signature is as follows:\n",
    "\n",
    "```python\n",
    "class RegularizationResult(NamedTuple):\n",
    "    regularization : np.ndarray\n",
    "    eigenvalues : np.ndarray\n",
    "    eigenvectors : np.ndarray\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7967c73d-8a9a-44b6-a958-37121ff37d24",
   "metadata": {},
   "source": [
    "As the [General $U^k$ regularization algorithm](#general-regularization) is **recursive** in nature, note that we may want different behaviour _at different heights_. For instance, we may want to use a faster method for computing eigendecomposition of matrices when we have to repeat that operation many times, but we may want a more precise one when we are at a higher level and the computing time will not be affected much. This is why ``hofa.rgz.regularize()`` takes as a value a ``List[LayerRegularizer]``. Note that the **length** of such list of ``LayerRegularizer`` will determine the order of regularization of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31f7d262-36da-4b57-b95e-961c6c07ee9b",
   "metadata": {},
   "source": [
    "Before examining the concrete implementations, it is helpful to step back and look at how the abstract class fits into the overall structure of the algorithm.\n",
    "\n",
    "The diagram below illustrates the role of the abstract class as a mediator between the high-level workflow and the low-level algorithmic choices. Rather than embedding variant-specific logic directly into each function, the algorithm delegates these decisions to an object that implements a common interface. This design allows the same core workflow to support multiple behaviors while remaining easy to extend and reason about.\n",
    "\n",
    "The accompanying example walks through a simplified execution of the algorithm and highlights when and how the abstract class is queried during the process."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3c4adcb-41cd-4d17-9167-dcfcaedfd1cf",
   "metadata": {},
   "source": [
    "#### Interaction between workflow and variant logic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4768aea-62be-4da9-b3b4-eae2332bb2bd",
   "metadata": {},
   "source": [
    "In the next diagram we are going to see the main workflow of a call to ``regularize`` and how the different ``LayerRegularizers`` provide the variant-specific behavior required at each decision point. To best illustrate this, let us consider the case of **cubic** regularization (i.e. for the $U^4$ norm). Hence `per_layer_regularizers` is a `List[LayerRegularizer]` with `len(per_layer_regularizers)` equal to 3.\n",
    "``` python\n",
    "hofa.rgz.regularize(f , [per_layer_regularizers[0], \n",
    "                         per_layer_regularizers[1], \n",
    "                         per_layer_regularizers[2]])\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5760f67-2b4b-4fa4-bae5-bdb6dbe83321",
   "metadata": {},
   "source": [
    "The steps that we need to follow to understand this diagram are marked with <span style=\"color:blue\">blue numbers</span>.\n",
    "\n",
    "| Function                     | Operator                                                                                     | Regularizer             |\n",
    "|-----------------------|---------------------------------------------------------------------------------------|---------------|\n",
    "| <span style=\"color:blue\">1.</span> $f$   | <span style=\"color:blue\">2.</span> $f\\otimes \\overline{f} = \\begin{pmatrix}\\ddots &  &  \\\\& \\Delta_t f &  \\\\&  & \\ddots\\end{pmatrix}$ | <span style=\"color:blue\">9.</span> per_layer_regularizers[2] |\n",
    "| <span style=\"color:blue\">3.</span> $\\Delta_tf$ for each $t\\in Z$   | <span style=\"color:blue\">4.</span> $\\Delta_tf\\otimes \\overline{\\Delta_tf} = \\begin{pmatrix}\\ddots &  &  \\\\& \\Delta_{t'}\\Delta_t f &  \\\\&  & \\ddots\\end{pmatrix}$ | <span style=\"color:blue\">8.</span> per_layer_regularizers[1] |\n",
    "| <span style=\"color:blue\">5.</span> $\\Delta_{t'}\\Delta_tf$ for $t,t'\\in Z$   | <span style=\"color:blue\">6.</span> No need of creating an operator, its eigenvectors are the Fourier characters and its eigenvalues are $\\vert\\widehat{\\Delta_{t'}\\Delta_tf}(\\chi)\\vert^2$ for $\\chi\\in\\widehat{Z}$. | <span style=\"color:blue\">7.</span> per_layer_regularizers[0] |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86267228-e6b8-4892-99ff-1469a405f7bb",
   "metadata": {},
   "source": [
    "<span style=\"color:blue\">1.</span> We begin with the function $f$ to do cubic regularization.\n",
    "\n",
    "<span style=\"color:blue\">2.</span> We construct the matrix $f\\otimes \\overline{f}$.\n",
    "\n",
    "<span style=\"color:blue\">3.</span> For each $Z$-diagonal of $f\\otimes \\overline{f}$, which corresponds to the function $\\Delta_tf$,\n",
    "\n",
    "<span style=\"color:blue\">4.</span> we construct the matrix $\\Delta_tf\\otimes \\overline{\\Delta_tf}$.\n",
    "\n",
    "<span style=\"color:blue\">5.</span> For each $Z$-diagonal of $\\Delta_tf\\otimes \\overline{\\Delta_tf}$, which corresponds to the function $\\Delta_{t'}\\Delta_tf$,\n",
    "\n",
    "<span style=\"color:blue\">6.</span> we compute its Fourier regularization. We **do not** need to construct the matrix $\\Delta_{t'}\\Delta_tf\\otimes \\overline{\\Delta_{t'}\\Delta_tf}$ as we already known that in this case we can take as eigenvalues the set $\\{|\\widehat{\\Delta_{t'}\\Delta_tf}(\\chi)|^2\\}_{\\chi\\in\\widehat{Z}}$ and $\\widehat{Z}$ as the set of eigenvectors.\n",
    "\n",
    "<span style=\"color:blue\">7.</span> The object `per_layer_regularizers[0]` will be in charge of performing the Fourier regularization for each of the $\\Delta_{t'}\\Delta_t f$ functions. Thus, it will be feeded with functions of the form $\\Delta_{t'}\\Delta_t f$ and it will have to return a Fourier-regularize version of them. Note that it would be convenient that `per_layer_regularizers[0]` has access at some point to $\\Delta_t f$ and $f$, i.e., to the function whose multiplicative derivatives result in the function that `per_layer_regularizers[0]` has to regularize.\n",
    "\n",
    "<span style=\"color:blue\">8.</span> After `per_layer_regularizers[0]` has regularized all diagonals of the matrix $\\Delta_t f(x)\\otimes \\overline{\\Delta_t f(x)}$ from step <span style=\"color:blue\">4.</span>, the algorithm must then decompose the resulting matrix. Let us denote this regularized matrix as $\\mathcal{K}(\\Delta_t f(x)\\otimes \\overline{\\Delta_t f(x)},1)$. The object `per_layer_regularizers[1]` is in charge of controlling this process for each of the $\\Delta_t f(x)$, i.e., deciding which eigendecomposition method to use for $\\mathcal{K}(\\Delta_t f(x)\\otimes \\overline{\\Delta_t f(x)},1)$ and how to project to the different eigenspaces the functions $\\Delta_t f(x)$ according to some weights. Again, it would be useful if `per_layer_regularizers[1]` had access to $f$.\n",
    "\n",
    "<span style=\"color:blue\">9.</span> After all diagonals of the matrix from step <span style=\"color:blue\">2.</span> are regularized, we have a matrix which we denote by $\\mathcal{K}(f(x)\\otimes \\overline{ f(x)},2)$. Then the object `per_layer_regularizers[2]` is in charge of computing the eigendecomposition of $\\mathcal{K}(f(x)\\otimes \\overline{ f(x)},2)$ and to then project $f$ to the corresponding eigenspaces according to some weights which depend on the corresponding eigenvalues."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78a5e273-a03c-4b05-89b1-56d1e796e6c1",
   "metadata": {},
   "source": [
    "Therefore, we saw that each (implementation of) ``LayerRegularizer`` will perform a certain regularization based on its relative position position in the list ``per_layer_regularizers``. That is, it will have to compute eigenvalues and eigenvectors of a certain matrix and then it will have to compute the weights of the different eigenspaces. Moreover, it would be convenient that each regularizer has access not only to the function to regularize, e.g. $\\Delta_{t'}\\Delta_t f$ for `per_layer_regularizers[0]`, but also to all the functions whose multiplicative derivatives used in the computation of that function, i.e., $\\Delta_t f$ and $f$ for `per_layer_regularizers[0]`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bcc2ea9-9700-4cd6-967e-6a2caded1122",
   "metadata": {},
   "source": [
    "### Abstract class ``LayerRegularizer``"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4b1f588-8932-4c1a-b0ba-258702080e5d",
   "metadata": {},
   "source": [
    "We are now ready to understand the abstract class `LayerRegularizer` and how its implementation affect the execution of the ``regularize`` function.\n",
    "\n",
    "````python\n",
    "# In hofa.rgz\n",
    "class LayerRegularizer(ABC):\n",
    "    \n",
    "    @abstractmethod\n",
    "    def __init__(self):\n",
    "        pass\n",
    "\n",
    "    @abstractmethod\n",
    "    def setup(self, f : np.ndarray, depth : int, layer : int):\n",
    "        pass\n",
    "\n",
    "    @abstractmethod\n",
    "    def update(self, f : np.ndarray, height : int):\n",
    "        pass\n",
    "\n",
    "    @abstractmethod\n",
    "    def alpha(self, eigs : np.ndarray):\n",
    "        pass\n",
    "\n",
    "    @abstractmethod\n",
    "    def eigh(self, M : np.ndarray):\n",
    "        pass\n",
    "````\n",
    "Let us now explain each of those methods in depth."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11b2022a-ea78-4dd3-ad1a-f2d686e703d2",
   "metadata": {},
   "source": [
    "#### Constructor\n",
    "\n",
    "````python\n",
    "def __init__(self):\n",
    "````\n",
    "The constructor. It can have a different signature to accept parameters in order to define several version of similar implementations of `LayerRegularizer`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "257c8db4-4fb0-448a-9bac-ed0ac48771a3",
   "metadata": {},
   "source": [
    "#### Setup method\n",
    "\n",
    "````python\n",
    "def setup(self, f : np.ndarray, depth : int, layer : int):\n",
    "````\n",
    "This method will be called once for each regularizer at the begining of the regularization process. The variable `f` is the function to regularize, `depth`=k represents that we want to regularize `f` for the $U^{k+1}$ norm, and `layer` represents the position of this regularizer in the regularization process. That is, `layer` will be a number between $0$ and $k-1$. If `layer`=0 it means that this regularizer will do the role of Fourier regularizer (step <span style=\"color:blue\">7.</span> above in case for $k=3$), `layer`=1 means that it will do $U^3$ regularization, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "974a9410-34ef-484c-a052-c4c81591501a",
   "metadata": {},
   "source": [
    "#### Update\n",
    "\n",
    "````python\n",
    "def update(self, f : np.ndarray, height : int):\n",
    "````\n",
    "This method will be called once per multiplicative derivative that sits above the one that a particular regularizer has to handle. For example, `per_layer_regularizers[0]` in the above example will be called with\n",
    "- per_layer_regularizers[0].update($f$, 3),\n",
    "- per_layer_regularizers[0].update($\\Delta_t f$, 2), and finally\n",
    "- per_layer_regularizers[0].update($\\Delta_{t'}\\Delta_t f$, 1)\n",
    "\n",
    "before it has to regularize the function $\\Delta_{t'}\\Delta_t f$. In between, it may be receive different calls to `update` but it can be certain that by the time `per_layer_regularizers[0]` has to regularize $\\Delta_{t'}\\Delta_t f$, the latest times `update` was called with `height` equal to 1,2,3 are precisely calls corresponding to the multiplicative derivatives that sit above the particular function to regularize. These calls may be used to update internal states of `per_layer_regularizers[0]` in order to perform the regularization.\n",
    "\n",
    "In general, if a particular `LayerRegularizer` was called in `setup` with `depth`=$k$ and `layer`=$l$, it will be called once with ``update``($f$,$k$), $|Z|$ times with update($\\Delta_t f$, $k-1$),..., and $|Z|^{k-l-1}$ times with ``update``($\\Delta_{t_1}\\cdots\\Delta_{t_{k-l-1}}f$, $l$). It is guaranteed that by the time a particular `LayerRegularizer` has to regularize $\\Delta_{t_1}\\cdots\\Delta_{t_{k-l-1}}f$, the last calls to `update` with the sequence of numbers $\\{k,k-1,\\ldots,l\\}$ in the second argument contains exactly the multiplicative derivatives that were used to create $\\Delta_{t_1}\\cdots\\Delta_{t_{k-l-1}}f$. This can be used to boost efficiency as typically we do not need to keep in memory all multplicative derivatives."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eebc05d-0d1d-4630-82b6-9d52b9d70fb4",
   "metadata": {},
   "source": [
    "#### Eigendecomposition\n",
    "\n",
    "````python\n",
    "def eigh(self, M : np.ndarray):\n",
    "````\n",
    "Consider the case of `per_layer_regularizers[2]` from the above diagram. Note that after regularizing all the diagonals of the matrix $f\\otimes \\overline{f}$, we need first to compute its eigendecomposition. As later `per_layer_regularizers[2]` will apply some weights on the different eigenspaces, it makes no sense that it computes the full eigendecomposition. Thus, the user is allowed to program here a method that computes only the largest eigenvalues and eigenvectors that will be used later.\n",
    "\n",
    "The case of `per_layer_regularizers[0]` is special as this method will be ignored. Remember that we know that a valid eigendecomposotion in the case of the $U^2$ norm can be computed using the Fourier transform. Hence, the Fast Fourier Transform is used in this case."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ccc7c42-e30a-4d43-a31c-4b23b2db090a",
   "metadata": {},
   "source": [
    "#### The weighting function\n",
    "\n",
    "````python\n",
    "def alpha(self, eigs : np.ndarray):\n",
    "````\n",
    "This is the method for computing the weights of the different eigenspaces. Those weigths will be used with the eigenvalues and eigenvectors of `LayerRegularizer.eigh` in order to regularize a function by projecting to the appropriate eigenspaces. Note that in the case of `per_layer_regularizers[0]` the variable `eigs` in the call of `alpha` will be the squared modules of the Fourier coefficients of the function to regularize."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "759d9881-7d47-497a-a68b-4dccb4781d68",
   "metadata": {},
   "source": [
    "### Default implementation: `StandardLayerRegularizer`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "895a9f05-ff1e-4760-9ada-58805eba9955",
   "metadata": {},
   "source": [
    "Having defined the abstract interface ``LayerRegularizer``, we now turn to the default concrete implementation ``StandardLayerRegularizer`` provided by the package. This implementation realizes a commonly useful variant of the algorithm and serves both as a practical, ready-to-use component and as a reference for understanding how the abstract methods are intended to be implemented.\n",
    "\n",
    "The default use of ``regularize`` use this class, so users can benefit from the full algorithmic capabilities without interacting directly with the abstract class ``LayerRegularizer``. At the same time, the structure of this implementation illustrates how fine-tuning and variant-specific behavior are encapsulated, making it a useful starting point for users who wish to extend or customize the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "006a8aa3-52bd-4aa2-904c-011d362fc6b7",
   "metadata": {},
   "source": [
    "```python\n",
    "# In hofa.rgz\n",
    "class StandardLayerRegularizer(Regularizer):\n",
    "    \n",
    "    def __init__(self, \n",
    "                 alpha_method : Callable = hofa.cdf.relu ,  \n",
    "                 param : float | int = 1.2,  \n",
    "                 mode : str = 'dynamic-original', \n",
    "                 lin_alg_method : str = 'sparse',\n",
    "                 num_eigen : str | int = 'dynamic'\n",
    "                ):\n",
    "    ...\n",
    "                \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7f324f0-de72-4d2a-be97-63b65dacefc5",
   "metadata": {},
   "source": [
    "#### The `alpha_method` parameter\n",
    "\n",
    "The first argument in this constructor is `alpha_method`, that tells `StandardLayerRegularizer` which function it has to apply to the eigenvalues of the regularized matrix. Recall that each `Regularizer` is in charge of regularizing a particular type of function depending on its `layer` (given via the `setup` method). In most cases, for a function $g$ (in the above example this would be either $f$, $\\Delta_t f$, or $\\Delta_{t'}\\Delta_t f$ depending on whether `layer` equals 2, 1, or 0 respectively) this method will compute a series of eigenvalues and eigenvectors and it will have to return a weighted projection of $g$ to the eigenspaces weighted by some function. Recall that in case `layer`=0, the eigenvalues will be $\\{|\\widehat{g}(\\chi)|^2\\}_{\\chi\\in \\widehat{Z}}$ and the eigenvectors the set $\\widehat{Z}$. \n",
    "\n",
    "The way `StandardLayerRegularizer` computes the weights of the eigenspaces depending on the eigenvalues is by applying the `alpha_method` given in the constructor of `StandardLayerRegularizer` together with a parameter $\\tau>0$. Below we explain how this parameter is computed. It is **mandatory** that the method given in the constructor of `StandardLayerRegularizer` has precisely the signature \n",
    "````python\n",
    "def alpha_method(eigvals : np.ndarray, tau : int | float)\n",
    "````"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc0f2df1-dd24-4a69-a0e2-8fffe9439fa4",
   "metadata": {},
   "source": [
    "#### The `cdf` module"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2e028d8-0b1a-478c-bdc0-fa05599ae83a",
   "metadata": {},
   "source": [
    "The `hofa` package comes with a pre-defined set of functions that can act as regularizers. Let us see how they look like. Recall that these functions will be used on functions defined on $[-1,1)$. The philosophy of these functions is that they should be 0 (or near 0) for values of the form $[-1,\\varepsilon)$ for a small $\\varepsilon$ while they should be close to 1 for values in $[1-\\varepsilon,1)$. To better visualize them, we are going to put logaritmic scale on the $x$ axis. The bahaviour of these functions in the interval $[\\varepsilon,1-\\varepsilon)$ is an active area of reasearch, as it is not clear which is the optimal choice if there exists one or the optimal choices depending on the particular problem studied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a6fbcabb-784d-4290-a9c4-28570cd7367c",
   "metadata": {},
   "outputs": [],
   "source": [
    "N=500\n",
    "\n",
    "def plot_on_uniform_grid(cdf_function, param, label):\n",
    "    x = np.arange(N) / N \n",
    "    y = cdf_function(x,param) \n",
    "    plt.figure(figsize=(3, 3))\n",
    "    plt.xscale(\"log\")\n",
    "    plt.plot(x, y)\n",
    "    plt.title(\"Function \"+label+\" evaluated on [0,1)\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce7de936-b4c7-4799-8f1e-d3f2671e4d89",
   "metadata": {},
   "source": [
    "````python\n",
    "# In hofa.cdf\n",
    "def relu(eigvals : np.ndarray, epsilon : float)\n",
    "````\n",
    "\n",
    "This function does the operation $x\\mapsto 1-\\tfrac{\\varepsilon}{\\sqrt{\\max(\\varepsilon^2,x)}}$. The name \"relu\" comes from the fact that, if this is applied to the $|\\widehat{f}(\\chi)|^2$ then what we get is $\\max(|\\widehat{f}(\\chi)|-\\varepsilon,0)\\tfrac{\\widehat{f}(\\chi)}{|\\widehat{f}(\\chi)|}=\\text{ReLU}(|\\widehat{f}(\\chi)|-\\varepsilon)\\tfrac{\\widehat{f}(\\chi)}{|\\widehat{f}(\\chi)|}$, i.e., applying $\\text{ReLU}(\\cdot-\\varepsilon)$ to the magnitude of the Fourier coefficient while keeping its phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b4e9cfdb-f20a-4eab-92ee-f1e37426e57b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_on_uniform_grid(cdf.relu, 0.1, 'cdf.relu')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae46bd82-64aa-44fc-8073-1f0789d329cd",
   "metadata": {},
   "source": [
    "````python\n",
    "# In hofa.cdf\n",
    "def cutoff(eigvals : np.ndarray, epsilon : float)\n",
    "````\n",
    "This function does the operation $x\\mapsto 1_{x\\ge \\varepsilon^2)}$. As before, the idea is that when applied to $|\\widehat{f}(\\chi)|^2$ it is 1 only when $|\\widehat{f}(\\chi)|\\ge \\varepsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3910d798-578c-42b9-b3dc-545fb734f33a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_on_uniform_grid(cdf.cutoff, 0.1, 'cdf.cutoff')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c01af85-05b2-4a62-88e4-c6ee1eb00498",
   "metadata": {},
   "source": [
    "````python\n",
    "# In hofa.cdf\n",
    "def avg_cutoff(eigvals : np.ndarray, epsilon : float)\n",
    "````\n",
    "This function is an averaged version of the previous one over the interval $[\\rho,2\\rho]$. Hence, it equals $\\mathbb{E}_{\\varepsilon\\in[\\rho,2\\rho]}1_{\\sqrt{x}\\ge \\varepsilon}$. Equivalently, it is easy to deduce that it equals $\\min\\big(\\tfrac{\\sqrt{\\max(\\rho^2,x)}}{\\rho}-1,1\\big)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "53245087-7b45-4252-a75d-9894ebcdb079",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_on_uniform_grid(cdf.avg_cutoff, 0.1, 'cdf.avg_cutoff')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2b0bf73-06de-4469-b2a5-9faee4ef9b48",
   "metadata": {},
   "source": [
    "````python\n",
    "# In hofa.cdf\n",
    "def top_eig(eigvals : np.ndarray, n : int)\n",
    "````\n",
    "This function does not follow the pattern of the previous ones, as it does not assign a particular weight to the different eigenspaces but rather it masks for the top `n` eigenvalues. **Note** that an `StandardLayerRegularizer` class that uses it must also choose `mode='literal'` and provide such number."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dd98737-f7c6-41ed-b06e-4b2095e32829",
   "metadata": {},
   "source": [
    "````python\n",
    "# In hofa.cdf\n",
    "def u2_dual(eigvals : np.ndarray, unused : float)\n",
    "````\n",
    "Last but not least we have a function that corresponds to the $U^2$ dual operator. It turns out that this is probably the simplest of all, $x\\mapsto x$ (the parameter `unused` is ignored). (Recall that we are putting a logaritmic scale in the $x$ axis, that is why we do not see an straight line.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7c8582ce-8f87-444a-8467-03af169e9ecc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_on_uniform_grid(cdf.u2_dual, 0.1, 'cdf.u2_dual')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1608968-aa6b-4088-89f2-814581695182",
   "metadata": {},
   "source": [
    "#### The `param` and `mode` parameters\n",
    "\n",
    "As we just said, there is a parameter $\\tau$ that each `StandardLayerRegularizer` object will use to pass to the `alpha_method` to compute the weights of the different eigenspaces. Suppose that a particular `StandardLayerRegularizer` object is called during `setup` with `depth`=$k$ and `layer`=$l$. Let `param`=$C$, let $f$ be the original function to regularize and let $\\Delta_{t_1}\\cdots\\Delta_{t_{k-l-1}}f$ be the particular function the `StandardLayerRegularizer` object has to regularize of order $U^{l+1}$. The parameter $\\tau$ will then be computed as follows.\n",
    "\n",
    "* If `mode='literal'`, then $\\tau = C$,\n",
    "* If `mode='dynamic-original'` then $\\tau = C\\sigma^{2^{k-l-1}}\\sqrt{\\tfrac{\\log |Z|}{|Z|}}$ where $\\sigma^2 = \\text{Var}(f) = \\mathbb{E}_{x\\in Z} |f-\\mathbb{E}_{x\\in Z}f|^2$.\n",
    "* If `mode='dynamic-strict'` then $\\tau = C\\tilde{\\sigma}\\sqrt{\\tfrac{\\log |Z|}{|Z|}}$ where $\\tilde{\\sigma}^2 = \\text{Var}(\\Delta_{t_1}\\cdots\\Delta_{t_{k-l-1}}f)$.\n",
    "\n",
    "The heuristic explanation behind these options will be detailed in a forthcoming paper."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18cbe10a-81f7-4cbf-9688-0e808e8466ff",
   "metadata": {},
   "source": [
    "#### The `lin_alg_method` and the `num_eigen` parameters\n",
    "\n",
    "These are used to allow the user to choose between two different methods for obtaining the eigenvalues and eigenvectors of a matrix. Recall that if `layer`=0 during setup these values will be ignored and instead the Fast Fourier Transform will be used. The possibilities are as follows.\n",
    "\n",
    "* If `lin_alg_method='full'` then this regularizer will use `numpy.linalg.eigh` as the method for obtaining the eigenvalue decomposition. In this case, the parameter `num_eigen` is ignored.\n",
    "* If `lin_alg_method='sparse'` and `num_eigen` is an integer, then this regularizer will use the method `scipy.sparse.linalg.eigsh` with the number of eigenvalues being precisely the number passed in `num_eigen`.\n",
    "* If `lin_alg_method='sparse'` and `num_eigen='dynamic'`, then this regularizer will use the method `scipy.sparse.linalg.eigsh` with the number of eigenvalues computed dynamically by the formula $\\lfloor \\tfrac{|Z|}{C^2\\log|Z|}\\rfloor$ where the constant ``param=``$C$ as in the previous section."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58ff3153-5535-4e0c-a133-361cb29c7b6b",
   "metadata": {},
   "source": [
    "## Putting everything together: Chirps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9396e07-a23f-4582-bb6d-8f28f50c4205",
   "metadata": {},
   "source": [
    "Having described the main components of the package and how they interact, we now illustrate their use on a concrete example with [chirps](https://en.wikipedia.org/wiki/Chirp). This section demonstrates how the ``regularize`` function performs in a larger, more complicated example. We will follow the same structure as in our [toy example at the beginning](#denoising--problem-statement) but with some changes.\n",
    "\n",
    "### Problem statement\n",
    "\n",
    "We want to transmit a convex combination of a **periodic** linear chirp of period $n=1001$ and a **non-periodic** linear chirp defined for $\\{0,\\ldots,n-1\\}$.\n",
    "\n",
    "$$f_s(x)=\\tfrac{1}{2}\\sin(200\\pi x^2/n)+\\tfrac{1}{2}\\sin(5x^2/n)$$\n",
    "\n",
    "defined for any integer $x\\in\\{0,\\ldots,n-1\\}$. Similarly as above, imagine that our communication channel introduces noise, and what is received is a convex combination $f=tf_r+(1-t)f_s$ where $f_r(x)$ follows a uniform distribution $\\text{Unif}([-1,1))$ independently for every integer $x$ and the amount of noise is $t$, a parameter that we are going to vary in $[0,1)$.\n",
    "\n",
    "### Objective\n",
    "\n",
    "Under these assumptions, we aim to compute an estimate of $f_s$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afe43b05-732c-4c45-acc0-8cccf6db188c",
   "metadata": {},
   "source": [
    "This time, instead of using the default values of ``regularize``, let us use a different ``alpha_method``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7e8382f2-4843-449c-9d93-454142d5e4aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import moviepy as mpy\n",
    "import os\n",
    "\n",
    "N = 1001\n",
    "output_video = '_output/tutorial_denoising.mp4'\n",
    "\n",
    "def f_s(x : np.ndarray):\n",
    "    return 0.5*np.sin(2*100*np.pi*x**2/N)+0.5*np.sin((5*x**2)/N)\n",
    "\n",
    "# For the quadratic regularization we use now the average cutoff, and for computing the \n",
    "# eigendecomposition, we only use 6 dominant eigenvectors.\n",
    "# We fix the random number generator for reproducibility.\n",
    "list_reg = [\n",
    "    rgz.StandardLayerRegularizer(alpha_method = cdf.avg_cutoff, rng = 28),\n",
    "    rgz.StandardLayerRegularizer(alpha_method = cdf.avg_cutoff, rng = 28, num_eigen= 6)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f2c7684-8d59-401e-8362-e47d2577e457",
   "metadata": {},
   "source": [
    "### Strategy\n",
    "\n",
    "Let us run the ``regualrize()`` function on the noisy version of $f_s$ for values of $t$ in $[0,1)$. The resulting function will be our candidate for recovery of $f_s$. Let us plot the function to approximate, the noisy version, and the regularized result in a video. You can find the video on the folder ``_output``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "57dc9c82-c747-4124-9bfc-d5b267c53594",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MoviePy - Building video _output/tutorial_denoising.mp4.\n",
      "MoviePy - Writing video _output/tutorial_denoising.mp4\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "                                                                                                                       "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MoviePy - Done !\n",
      "MoviePy - video ready _output/tutorial_denoising.mp4\n",
      "Movie saved at _output/tutorial_denoising.mp4, individual frames deleted.\n"
     ]
    }
   ],
   "source": [
    "x_values = np.arange(N)\n",
    "rng = np.random.default_rng(123)\n",
    "r_values = rng.uniform(-1, 1, size=len(x_values))\n",
    "frames = 100\n",
    "\n",
    "# Function to generate a frame\n",
    "def generate_frame(t):\n",
    "\n",
    "    print(f\"t: {t:.2f}\",end='\\r')\n",
    "    \n",
    "    # Compute f(x) for the selected window\n",
    "    y_values = (1 - t) * f_s(x_values)\n",
    "    \n",
    "    # Compute the modified function f_mod(x) = (1-t)*f(x) + t*r(x) using the same r_values\n",
    "    y_values_mod = y_values + t * r_values\n",
    "\n",
    "    # Regularize with respect to quadratic Fourier analysis\n",
    "    y_values_quad_reg = rgz.regularize(y_values_mod,list_reg).regularization\n",
    "    \n",
    "    # Create the plot\n",
    "    fig, ax = plt.subplots(figsize=(12, 5))\n",
    "    \n",
    "    # Plot original function in light green with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values), linestyle='-', color='lightgreen', marker='o', markersize=6, linewidth=1, alpha=0.6, label=fr'$(1-t)*f_s(x)$')\n",
    "    \n",
    "    # Plot modified function in red with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values_mod), linestyle='-', color='red', marker='o', markersize=6, linewidth=1, alpha=0.6, label=r'$(1-t)f_s(x) + tf_r(x)$')\n",
    "\n",
    "    # Plot recovered function with fourier analysis in yellow with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values_quad_reg), linestyle='-', color='yellow', marker='o', markersize=3, linewidth=1, alpha=0.6, label=r'quadratic regularization')\n",
    "    \n",
    "    # Customize the plot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    l1_original = np.mean(np.abs(y_values))\n",
    "    ax.set_title(f\"t: {t:.2f}, \\\n",
    "    L1 original {l1_original:.5f},\\\n",
    "    L1 error quadratic reg. {np.mean(np.abs(y_values_quad_reg-y_values)):.5f}\")\n",
    "    ax.grid(True, linestyle=\"--\", alpha=0.6)\n",
    "    \n",
    "    # Fix y-axis range and ticks from -1 to 1\n",
    "    ax.set_ylim(-1, 1)\n",
    "    ax.set_yticks(np.linspace(-1, 1, 5))  # Keeps y-axis ticks fixed at [-1, -0.5, 0, 0.5, 1]\n",
    "    \n",
    "    # Legend below the plot\n",
    "    fig.subplots_adjust(bottom=0.25)  # Adjust layout to fit legend below\n",
    "    ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=2, frameon=False)\n",
    "    \n",
    "    # Save frame as image\n",
    "    filename = f\"_output/frame_{t:.2f}.png\"\n",
    "    plt.savefig(filename)\n",
    "    plt.close()\n",
    "    return filename\n",
    "\n",
    "# Generate frames\n",
    "frame_files = [generate_frame(t / (frames - 1)) for t in range(frames)]\n",
    "\n",
    "# Create movie\n",
    "clip = mpy.ImageSequenceClip(frame_files, fps=10)\n",
    "clip.write_videofile(output_video, codec='libx264')\n",
    "\n",
    "# Remove individual frame images\n",
    "for frame in frame_files:\n",
    "    os.remove(frame)\n",
    "\n",
    "print(f\"Movie saved at {output_video}, individual frames deleted.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d1c1388-448f-4254-82c1-addd696a1b8e",
   "metadata": {},
   "source": [
    "<a id=\"denoising--coding-theory\"></a>\n",
    "## Putting everything together: Coding theory"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4737ed17-1a65-4866-9f60-10eec7357f99",
   "metadata": {},
   "source": [
    "The previous example focused on the theory of chirps. In this section, we consider a different application that highlights the same algorithmic framework from a coding-theoretic perspective.\n",
    "\n",
    "While the underlying workflow and API remain unchanged, this example emphasizes structural aspects that may be of particular interest to readers with a background in coding theory or discrete signal models. The goal is to illustrate how the general design presented above naturally accommodates this setting, without introducing additional mathematical machinery beyond what is strictly necessary."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85669e4a-d686-4bf9-8788-e02174a470fa",
   "metadata": {},
   "source": [
    "### Problem statement\n",
    "\n",
    "We want to transmit a function $\\{0,1\\}^{7}\\to \\{-1,1\\}$ that can be expressed as a quadratic polynomial $\\mathbb{F}_2^{7}\\to \\mathbb{C}$\n",
    "\n",
    "$$f_s(x)= \\exp( \\pi i \\sum_{i=0}^{5} x_ix_{i+1}).$$\n",
    "\n",
    "Note that this functions equals $1$ when $\\sum_{i=0}^{5} x_ix_{i+1}$ is even and $-1$ when $\\sum_{i=0}^{5} x_ix_{i+1}$ is odd. Similar functions appear for example in the [Reed-Muller codes](https://en.wikipedia.org/wiki/Reed%E2%80%93Muller_code). \n",
    "\n",
    "Now imagine that we want to transmit the values of this function, but again out communication channel is noisy, and for a proportion $t\\in[0,1)$ of the values, it swaps $1$ and $-1$ with probability $1/2$. Let us denote this noisy version of $f_s$ by $f$.\n",
    "\n",
    "### Objective\n",
    "\n",
    "Under these assumptions, for different values of $t$, we aim to compute an estimate of $f_s$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b99e51d1-eedb-4466-8592-eb0a52a806a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import moviepy as mpy\n",
    "import os\n",
    "import itertools\n",
    "\n",
    "output_video2 = '_output/tutorial_denoising2.mp4'\n",
    "\n",
    "n = 7\n",
    "f_s = np.empty([2]*n).astype(complex)\n",
    "\n",
    "def quadratic_poly(x : np.ndarray):\n",
    "    return np.exp(np.pi*1j*np.sum(x[:-1]*x[1:]))\n",
    "\n",
    "for idx in itertools.product([0, 1], repeat=n):\n",
    "    f_s[idx] = np.real(quadratic_poly(np.array(idx)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59e2c93e-1c9f-48b5-91fa-9cec17632ebb",
   "metadata": {},
   "source": [
    "Now we create the function $f$ for every $t$ between $0$ and $1$ and we regularize it using our algorithm. \n",
    "\n",
    "### Strategy\n",
    "\n",
    "While our original signal takes either $1$ or $-1$, this is no longer the case for the case of our regularized version. Thus, we may simply take the real part of our regularization and take 1 if the number is positive and -1 if it is negative. This is how we reconstruct our signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ee88b6f2-7049-4401-97fd-55bf9c764867",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MoviePy - Building video _output/tutorial_denoising2.mp4.\n",
      "MoviePy - Writing video _output/tutorial_denoising2.mp4\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "                                                                                                                       "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MoviePy - Done !\n",
      "MoviePy - video ready _output/tutorial_denoising2.mp4\n",
      "Movie saved at _output/tutorial_denoising2.mp4, individual frames deleted.\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import math\n",
    "\n",
    "list_indices = list(itertools.product([0, 1], repeat=n))\n",
    "M = len(list_indices)\n",
    "rng = np.random.default_rng(4)\n",
    "rng.shuffle(list_indices)\n",
    "swapping_parameters = rng.integers(low = 0, high = 2, size = M)*2-1\n",
    "\n",
    "frames = 100\n",
    "x_values = range(M)\n",
    "\n",
    "# Function to generate a frame\n",
    "def generate_frame(t):\n",
    "\n",
    "    print(f\"t: {t:.2f}\",end='\\r')\n",
    "\n",
    "    # We compute the noisy version of f_s\n",
    "    elements_to_alter = math.floor(M*t)\n",
    "    multipliers = np.ones_like(f_s)\n",
    "    for i in range(elements_to_alter):\n",
    "        multipliers[list_indices[i]] *= swapping_parameters[i]\n",
    "    f = f_s*multipliers\n",
    "\n",
    "    # Regularize with respect to quadratic Fourier analysis\n",
    "    # Similarly as before, we fix the Random Number Generator for reproducibility\n",
    "    y_values_quad_reg = np.sign(np.real(rgz.regularize(f,2, rng = 28).regularization))\n",
    "    \n",
    "    # Create the plot\n",
    "    fig, ax = plt.subplots(figsize=(12, 5))\n",
    "    \n",
    "    # Plot original function in light green with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(f_s.flatten()), linestyle=None, color='lightgreen', marker='o', markersize=6, linewidth=1, alpha=0.6, label=fr'$(1-t)*f_s(x)$')\n",
    "    \n",
    "    # Plot modified function in red with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(f.flatten()), linestyle=None, color='red', marker='o', markersize=6, linewidth=1, alpha=0.6, label=r'$(1-t)f_s(x) + tf_r(x)$')\n",
    "\n",
    "    # Plot recovered function with fourier analysis in yellow with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values_quad_reg.flatten()), linestyle=None, color='yellow', marker='o', markersize=3, linewidth=1, alpha=0.6, label=r'quadratic regularization')\n",
    "    \n",
    "    # Customize the plot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    l1_original = np.mean(np.abs(f_s))\n",
    "    ax.set_title(f\"Perfectage of elements randomly swapped with probability 1/2: {elements_to_alter/M*100:.2f}%, \\\n",
    "    Percentage of failed reconstruction: {100*np.sum(y_values_quad_reg!=f_s)/M:.2f}%\")\n",
    "    ax.grid(True, linestyle=\"--\", alpha=0.6)\n",
    "    \n",
    "    # Fix y-axis range and ticks from -1 to 1\n",
    "    ax.set_ylim(-1.1, 1.1)\n",
    "    ax.set_yticks(np.linspace(-1, 1, 5))  # Keeps y-axis ticks fixed at [-1, -0.5, 0, 0.5, 1]\n",
    "    \n",
    "    # Legend below the plot\n",
    "    fig.subplots_adjust(bottom=0.25)  # Adjust layout to fit legend below\n",
    "    ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=2, frameon=False)\n",
    "    \n",
    "    # Save frame as image\n",
    "    filename = f\"_output/frame_{t:.2f}.png\"\n",
    "    plt.savefig(filename)\n",
    "    plt.close()\n",
    "    return filename\n",
    "\n",
    "# Generate frames\n",
    "frame_files = [generate_frame(t / (frames - 1)) for t in range(frames)]\n",
    "\n",
    "# Create movie\n",
    "clip = mpy.ImageSequenceClip(frame_files, fps=10)\n",
    "clip.write_videofile(output_video2, codec='libx264')\n",
    "\n",
    "# Remove individual frame images\n",
    "for frame in frame_files:\n",
    "    os.remove(frame)\n",
    "\n",
    "print(f\"Movie saved at {output_video2}, individual frames deleted.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d59548e8-770b-463d-bc47-66a2ef912ea4",
   "metadata": {},
   "source": [
    "Check the video we have just created, where up to a $t=50$% of **randomly swapped parameters** (that means that on average we have changed $25$% of the values) we get a **perfect reconstruction**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dad5bff5-e190-4509-aff6-4130577525ec",
   "metadata": {},
   "source": [
    "## Optional: deeper insights and extensions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c46cac0-b62f-4c1e-b296-8a67a2b13be5",
   "metadata": {},
   "source": [
    "Recall from [Theoretical Foundations and Extensions](theoretical_foundations_extensions) that we mentioned some family of functions called **nilsequences** that in a sense work similarly as **periodic quadratic polynomials** but cannot be represented as those. The ``hofa`` package can also deal with this kind of functions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3cd01e7-b9c9-419d-b80a-597897ef12aa",
   "metadata": {},
   "source": [
    "### A nilsequence\n",
    "\n",
    "A **2-step nilsequence** is a function which shares many properties with **periodic** quadratic polynomials (such as chirps or in general quadratic exponentials), but which cannot be decomposed or even approximated efficiently by functions of the form $e^{2\\pi i (ax^2+bx+c)/n}$ for integers $a,b,c$. Nevertheless, a 2-step nilsequence has the property that it also has a non-trivial $U^3$ norm. See [Theoretical Foundations and Extensions](theoretical_foundations_extensions) for a lengthier presentation of these functions. To define them, we need to consider the Heisenberg group\n",
    "\n",
    "$$G:=\\left(\\begin{matrix} 1 & \\mathbb{R} & \\mathbb{R}\\\\[0.1em]0  & 1 & \\mathbb{R}\\\\[0.1em] 0 & 0 & 1 \\end{matrix}\\right) \\text{ and the discrete Heisenberg group }  \\Gamma:=\\left(\\begin{matrix} 1 & \\mathbb{Z} & \\mathbb{Z}\\\\[0.1em]0  & 1 & \\mathbb{Z}\\\\[0.1em] 0 & 0 & 1 \\end{matrix}\\right)$$ \n",
    "\n",
    "The Heisenberg manifold is then $G/\\Gamma$. To define a nilsequence here, we let $r$ be an integer and we let \n",
    "\n",
    "$$M=\\left(\\begin{matrix} 1 & 2r/n & r/n^2\\\\[0.1em]0  & 1 & 1/n\\\\[0.1em] 0 & 0 & 1 \\end{matrix}\\right) $$\n",
    "\n",
    "Our nilsequence $f_s:\\mathbb{Z}\\to \\mathbb{C}$ is defined as follows. Let $\\{g\\Gamma\\}$ be thethe representative in $[0,1)$ of the top right corner of any element $g\\Gamma$ for $g\\in G$. Then $f_s(x)=\\exp(2\\pi i \\{M^x\\Gamma\\}) = \\exp(2\\pi i t x^2/n^2)$ for $x=0,\\ldots,n$. Note that, while this may look like a quadratic polynomial, it is not because we have a term $n^2$ in the denominator. This seemingly unimportant detail is important, and ultimately tells us that a more complicated representation using the Heisenberg nilmanifold is necessary.\n",
    "\n",
    "### Problem statement\n",
    "\n",
    "Similarly as with chirps, we will let $f_s(x)=\\exp(2\\pi i \\{M^x\\Gamma\\})$ for any integer $x$ and we will modify it by taking a convex combination $f=tf_r+(1-t)f_s$ where $t\\in[0,1)$ and $f_r(x)$ follows a uniform distribution $\\text{Unif}([-1,1))$ independently for every integer $x$.\n",
    "\n",
    "### Objective\n",
    "\n",
    "Recover $f_s$ from the noisy version $f$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a0c7d522-e4f8-4f6a-adae-d97c06bfa678",
   "metadata": {},
   "outputs": [],
   "source": [
    "import moviepy as mpy\n",
    "import os\n",
    "\n",
    "N = 1001\n",
    "output_video = '_output/tutorial_denoising3.mp4'\n",
    "t = 100\n",
    "\n",
    "def f_s(x : np.ndarray):\n",
    "    return np.exp(2*t*np.pi*1j*x**2/N**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0f250762-5de7-453e-9b85-ca2082996bf4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MoviePy - Building video _output/tutorial_denoising3.mp4.\n",
      "MoviePy - Writing video _output/tutorial_denoising3.mp4\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "                                                                                                                       "
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MoviePy - Done !\n",
      "MoviePy - video ready _output/tutorial_denoising3.mp4\n",
      "Movie saved at _output/tutorial_denoising3.mp4, individual frames deleted.\n"
     ]
    }
   ],
   "source": [
    "x_values = np.arange(N)\n",
    "rng = np.random.default_rng(123)\n",
    "r_values = rng.uniform(-1, 1, size=len(x_values))\n",
    "frames = 100\n",
    "\n",
    "# Function to generate a frame\n",
    "def generate_frame(t):\n",
    "\n",
    "    print(f\"t: {t:.2f}\",end='\\r')\n",
    "    \n",
    "    # Compute f(x) for the selected window\n",
    "    y_values = (1 - t) * f_s(x_values)\n",
    "    \n",
    "    # Compute the modified function f_mod(x) = (1-t)*f(x) + t*r(x) using the same r_values\n",
    "    y_values_mod = y_values + t * r_values\n",
    "\n",
    "    # Regularize with respect to quadratic Fourier analysis\n",
    "    y_values_quad_reg = rgz.regularize(y_values_mod,2).regularization\n",
    "    \n",
    "    # Create the plot\n",
    "    fig, ax = plt.subplots(figsize=(12, 5))\n",
    "    \n",
    "    # Plot original function in light green with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values), linestyle='-', color='lightgreen', marker='o', markersize=6, linewidth=1, alpha=0.6, label=fr'$(1-t)*f_s(x)$')\n",
    "    \n",
    "    # Plot modified function in red with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values_mod), linestyle='-', color='red', marker='o', markersize=6, linewidth=1, alpha=0.6, label=r'$(1-t)f_s(x) + tf_r(x)$')\n",
    "\n",
    "    # Plot recovered function with fourier analysis in yellow with thin, semi-transparent lines and dots\n",
    "    ax.plot(x_values, np.real(y_values_quad_reg), linestyle='-', color='yellow', marker='o', markersize=3, linewidth=1, alpha=0.6, label=r'quadratic regularization')\n",
    "    \n",
    "    # Customize the plot\n",
    "    ax.set_xlabel(\"x\")\n",
    "    l1_original = np.mean(np.abs(y_values))\n",
    "    ax.set_title(f\"t: {t:.2f}, \\\n",
    "    L1 original {l1_original:.5f},\\\n",
    "    L1 error quadratic reg. {np.mean(np.abs(y_values_quad_reg-y_values)):.5f}\")\n",
    "    ax.grid(True, linestyle=\"--\", alpha=0.6)\n",
    "    \n",
    "    # Fix y-axis range and ticks from -1 to 1\n",
    "    ax.set_ylim(-1, 1)\n",
    "    ax.set_yticks(np.linspace(-1, 1, 5))  # Keeps y-axis ticks fixed at [-1, -0.5, 0, 0.5, 1]\n",
    "    \n",
    "    # Legend below the plot\n",
    "    fig.subplots_adjust(bottom=0.25)  # Adjust layout to fit legend below\n",
    "    ax.legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=2, frameon=False)\n",
    "    \n",
    "    # Save frame as image\n",
    "    filename = f\"_output/frame_{t:.2f}.png\"\n",
    "    plt.savefig(filename)\n",
    "    plt.close()\n",
    "    return filename\n",
    "\n",
    "# Generate frames\n",
    "frame_files = [generate_frame(t / (frames - 1)) for t in range(frames)]\n",
    "\n",
    "# Create movie\n",
    "clip = mpy.ImageSequenceClip(frame_files, fps=10)\n",
    "clip.write_videofile(output_video, codec='libx264')\n",
    "\n",
    "# Remove individual frame images\n",
    "for frame in frame_files:\n",
    "    os.remove(frame)\n",
    "\n",
    "print(f\"Movie saved at {output_video}, individual frames deleted.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ddfb5d72-8137-4143-9d63-9416e357989f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.14.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
