docs/source/tutorial/algorithm_cp_apr.ipynb

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    "# CP-APR: Alternating Poisson Regression for fitting CP to sparse count data\n",
    "\n",
    "```\n",
    "Copyright 2025 National Technology & Engineering Solutions of Sandia,\n",
    "LLC (NTESS). Under the terms of Contract DE-NA0003525 with NTESS, the\n",
    "U.S. Government retains certain rights in this software.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up a sample problem\n",
    "We follow the general procedure outlined by E. C. Chi and T. G. Kolda, On Tensors, Sparsity, and Nonnegative Factorizations, arXiv:1112.2414 [math.NA], December 2011 (http://arxiv.org/abs/1112.2414)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import pyttb as ttb\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pick the shape and rank\n",
    "sz = (10, 8, 6)\n",
    "R = 5\n",
    "\n",
    "# Generate factor matrices with a few large entries in each column\n",
    "# this will be the basis of our solution.\n",
    "np.random.seed(0)  # Set seed for reproducibility\n",
    "A = []\n",
    "for n in range(len(sz)):\n",
    "    A.append(np.random.uniform(size=(sz[n], R)))\n",
    "    for r in range(R):\n",
    "        p = np.random.permutation(sz[n])\n",
    "        nbig = round((1 / R) * sz[n])\n",
    "        A[-1][p[0:nbig], r] *= 100\n",
    "weights = np.random.uniform(size=(R,))\n",
    "S = ttb.ktensor(A, weights)\n",
    "S.normalize(sort=True, normtype=1)\n",
    "\n",
    "X = S.to_tensor()\n",
    "X.data = np.floor(np.abs(X.data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Call CP-APR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute a solution\n",
    "short_tutorial = 2  # Cut off solve early for demo\n",
    "M = ttb.cp_apr(X, R, printitn=10, stoptime=short_tutorial);"
   ]
  }
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