{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8bbfdb92",
   "metadata": {},
   "source": [
    "# Moment Matrix Example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe918261",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "df2d21a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2025-08-05 14:15:36,039 \t DEBUG \t CRISTAL.__init__.<module> \t CRISTAL version 0.0.1 (date: 2025-08-01) loaded successfully.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from cristal import IMPLEMENTED_INVERSION_OPTIONS, IMPLEMENTED_POLYNOMIAL_BASIS, DyCF, PolynomialsBasisGenerator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "531d643d",
   "metadata": {},
   "source": [
    "## Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "39bd8616",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = 8  # Data dimension\n",
    "n = 5  # Degree of the polynomial basis\n",
    "N = 1000  # Number of samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "deb7a911",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cd7dedd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "data = np.random.random((N, d))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8730a0cb",
   "metadata": {},
   "source": [
    "## Method 1: Using DyCF"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86eb82ae",
   "metadata": {},
   "source": [
    "### Create a DyCF instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "460f3b31",
   "metadata": {},
   "outputs": [],
   "source": [
    "dycf = DyCF(n, inv_opt=IMPLEMENTED_INVERSION_OPTIONS.PINV)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9afe087a",
   "metadata": {},
   "source": [
    "### Fit the DyCF model to the data to compute the moments matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ca13b241",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<cristal.christoffel.DyCF at 0x1df40ad8ad0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dycf.fit(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f491c3e6",
   "metadata": {},
   "source": [
    "### Access the moments matrix and its inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "63d97675",
   "metadata": {},
   "outputs": [],
   "source": [
    "moments_matrix = dycf.moments_matrix.moments_matrix\n",
    "inversed_moments_matrix = dycf.moments_matrix.inverse_moments_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71934885",
   "metadata": {},
   "source": [
    "## Method 2: By computing the design matrix X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b5530dd",
   "metadata": {},
   "source": [
    "### Generate the monomials combinations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d4727469",
   "metadata": {},
   "outputs": [],
   "source": [
    "monomials = np.asarray(PolynomialsBasisGenerator.generate_combinations(n, d), dtype=np.int8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6ebf8f6",
   "metadata": {},
   "source": [
    "### Compute the vectors design matrix X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2da49624",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = PolynomialsBasisGenerator.make_design_matrix(data, monomials, IMPLEMENTED_POLYNOMIAL_BASIS.MONOMIALS.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17c456eb",
   "metadata": {},
   "source": [
    "### Construct the moments matrix M and its inverse M_inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "53741232",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = np.dot(X.T, X) / N\n",
    "M_inv = IMPLEMENTED_INVERSION_OPTIONS.PINV.value.invert(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8eb257b",
   "metadata": {},
   "source": [
    "## Equality check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2452ea93",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(True, True)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(moments_matrix, M, atol=1e-16), np.allclose(inversed_moments_matrix, M_inv, atol=1e-16)"
   ]
  }
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