sparsetensorviz/notebooks/Example_Rank4-binsparse.ipynb

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    "# Examples of \"bundling\" dimensions into groups to form the custom Binsparse levels\n",
    "\n",
    "Custom formats: https://graphblas.org/binsparse-specification/#custom_formats\n",
    "\n",
    "### Data of bundled groups\n",
    "- `Sparse(n1)`\n",
    "  - pointers array (or scalar `k` for ELLPACK-like compression) if not initial level\n",
    "  - indices for `n1` dimensions\n",
    "- `Dense(n2)`\n",
    "  - N/A\n",
    "\n",
    "_Note that indices grouped together in this scheme are all the same length, so they can be stored as separate 1-d arrays or a single 2-d array_"
   ]
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    "# Examples for rank 4 array\n",
    "\n",
    "Pass COO-like data to `SparseTensor` with one array of indices for each dimension.\n",
    "\n",
    "The default is to create CSF sparse data structure where all levels are Sparse."
   ]
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       "|S[2] -|S -----|\n",
       ".------.   .---.\n",
       "|i0 i1 |p2 |i2 |\n",
       "`------'   `---'\n",
       "================\n",
       ".-----.  0 .--.\n",
       "|0  0 |-+--|1 |\n",
       "`-----' `--|2 |\n",
       ".-----.  2 |--|\n",
       "|0  1 |----|0 |\n",
       "`-----'  3 `--'\n",
       ".-----.    .--.\n",
       "|1  0 |-+--|0 |\n",
       "`-----' `--|2 |\n",
       ".-----.  5 |--|\n",
       "|1  1 |-+--|0 |\n",
       "`-----' |--|1 |\n",
       "        `--|2 |\n",
       "         8 `--'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sparsetensorviz import SparseTensor\n",
    "import itertools\n",
    "import IPython\n",
    "\n",
    "indices = [\n",
    "    [0, 0, 1, 1, 0, 1, 1, 1],\n",
    "    [0, 0, 0, 0, 1, 1, 1, 1],\n",
    "    [1, 2, 0, 2, 0, 0, 1, 2],\n",
    "]\n",
    "sp = SparseTensor.from_binsparse(indices, structure=\"Sparse(2)-Sparse\")\n",
    "# Display as SVG diagram\n",
    "sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "833d4e98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0, 0, 1, 1]), array([0, 1, 0, 1]), array([1, 2, 0, 0, 2, 0, 1, 2])]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e3399807",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[None, array([0, 2, 3, 5, 8])]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.pointers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e0bdf4f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|S[2] -|S -----|\n",
      ".------.   .---.\n",
      "|i0 i1 |p2 |i2 |\n",
      "`------'   `---'\n",
      "================\n",
      ".-----.  0 .--.\n",
      "|0  0 |-+--|1 |\n",
      "`-----' `--|2 |\n",
      ".-----.  2 |--|\n",
      "|0  1 |----|0 |\n",
      "`-----'  3 `--'\n",
      ".-----.    .--.\n",
      "|1  0 |-+--|0 |\n",
      "`-----' `--|2 |\n",
      ".-----.  5 |--|\n",
      "|1  1 |-+--|0 |\n",
      "`-----' |--|1 |\n",
      "        `--|2 |\n",
      "         8 `--'\n"
     ]
    }
   ],
   "source": [
    "# Can also display as ASCII diagram\n",
    "print(sp)"
   ]
  },
  {
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   "execution_count": 5,
   "id": "1f3d5d9c-a512-43c1-aec6-2578d6dd8724",
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      "text/plain": [
       "|D -|S[2] -----|\n",
       ".~~~.   .------.\n",
       "┊i0 ┊p1 |i1 i2 |\n",
       "`~~~'   `------'\n",
       "================\n",
       ".~~.  0 .-----.\n",
       "┊0 ┊-+--|0  1 |\n",
       "`~~' |  `-----'\n",
       "     |  .-----.\n",
       "     |--|0  2 |\n",
       "     |  `-----'\n",
       "     |  .-----.\n",
       "     `--|1  0 |\n",
       "      3 `-----'\n",
       ".~~.    .-----.\n",
       "┊1 ┊-+--|0  0 |\n",
       "`~~' |  `-----'\n",
       "     |  .-----.\n",
       "     |--|0  2 |\n",
       "     |  `-----'\n",
       "     |  .-----.\n",
       "     |--|1  0 |\n",
       "     |  `-----'\n",
       "     |  .-----.\n",
       "     |--|1  1 |\n",
       "     |  `-----'\n",
       "     |  .-----.\n",
       "     `--|1  2 |\n",
       "      8 `-----'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example with a dense level\n",
    "SparseTensor.from_binsparse(indices, structure=\"Dense-S(2)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e5dd4568-7c48-404f-9ba2-f4f25ab0ce4f",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "|S -|S -----|S -----|\n",
       ".---.   .---.   .---.\n",
       "|i0 |p1 |i1 |p2 |i2 |\n",
       "`---'   `---'   `---'\n",
       "=====================\n",
       ".--.  0 .--.  0 .--.\n",
       "|0 |-+--|0 |-+--|1 |\n",
       "`--' |  `--' `--|2 |\n",
       "     |  .--.  2 |--|\n",
       "     `--|1 |----|0 |\n",
       "      2 `--'  3 `--'\n",
       ".--.    .--.    .--.\n",
       "|1 |-+--|0 |-+--|0 |\n",
       "`--' |  `--' `--|2 |\n",
       "     |  .--.  5 |--|\n",
       "     `--|1 |-+--|0 |\n",
       "      4 `--' |--|1 |\n",
       "             `--|2 |\n",
       "              8 `--'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The default structure is all levels Sparse(1), which is traditional compressed sparse fiber (CSF)\n",
    "SparseTensor.from_binsparse(indices)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51842351",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Display all standard sparse structures\n",
    "\n",
    "Hyphonated connecting lines indicate pointers that don't need stored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "03f416ee-3b94-4044-8f4f-6e6f5d76b199",
   "metadata": {},
   "outputs": [],
   "source": [
    "def display_header(st):\n",
    "    binsparse_groups = \", \".join(st.binsparse_groups)\n",
    "    taco_structure = \", \".join(st.taco_structure)\n",
    "    text = (\n",
    "        \"```\\n\"\n",
    "        f\"binsparse_groups = [{binsparse_groups}]\\n\\n\"\n",
    "        f\"taco_structure   = [{taco_structure}]\\n\\n\"\n",
    "        \"```\"\n",
    "        # f\"Erik's structure = {st.structure}\\n\\n\"\n",
    "    )\n",
    "    IPython.display.display(IPython.display.Markdown(text))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "232210ab",
   "metadata": {},
   "outputs": [
    {
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      "text/markdown": [
       "# `S[4]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
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       "```\n",
       "binsparse_groups = [Sparse(4)]\n",
       "\n",
       "taco_structure   = [compressed-nonunique, singleton, singleton, singleton]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|S[4] -------|\n",
       ".------------.\n",
       "|i0 i1 i2 i3 |\n",
       "`------------'\n",
       "==============\n",
       ".-----------.\n",
       "|0  0  0  1 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|0  0  0  2 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|0  1  0  0 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|0  1  0  2 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|0  1  1  0 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|1  1  1  0 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|1  1  1  1 |\n",
       "`-----------'\n",
       ".-----------.\n",
       "|1  1  1  2 |\n",
       "`-----------'"
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       "# `S[3]-S[1]`"
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       "```\n",
       "binsparse_groups = [Sparse(3), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, singleton, singleton, compressed]\n",
       "\n",
       "```"
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      "text/plain": [
       "|S[3] ----|S -----|\n",
       ".---------.   .---.\n",
       "|i0 i1 i2 |p3 |i3 |\n",
       "`---------'   `---'\n",
       "===================\n",
       ".--------.  0 .--.\n",
       "|0  0  0 |-+--|1 |\n",
       "`--------' `--|2 |\n",
       ".--------.  2 |--|\n",
       "|0  1  0 |-+--|0 |\n",
       "`--------' `--|2 |\n",
       ".--------.  4 |--|\n",
       "|0  1  1 |----|0 |\n",
       "`--------'  5 `--'\n",
       ".--------.    .--.\n",
       "|1  1  1 |-+--|0 |\n",
       "`--------' |--|1 |\n",
       "           `--|2 |\n",
       "            8 `--'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "# `S[2]-S[2]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(2), Sparse(2)]\n",
       "\n",
       "taco_structure   = [compressed, singleton, compressed-nonunique, singleton]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/plain": [
       "|S[2] -|S[2] -----|\n",
       ".------.   .------.\n",
       "|i0 i1 |p2 |i2 i3 |\n",
       "`------'   `------'\n",
       "===================\n",
       ".-----.  0 .-----.\n",
       "|0  0 |-+--|0  1 |\n",
       "`-----' |  `-----'\n",
       "        |  .-----.\n",
       "        `--|0  2 |\n",
       "         2 `-----'\n",
       ".-----.    .-----.\n",
       "|0  1 |-+--|0  0 |\n",
       "`-----' |  `-----'\n",
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       "        |--|0  2 |\n",
       "        |  `-----'\n",
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       "        `--|1  0 |\n",
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       "`-----' |  `-----'\n",
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       "        |--|1  1 |\n",
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       "         8 `-----'"
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     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/markdown": [
       "# `S[2]-D[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(2), Dense(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, singleton, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
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     "metadata": {},
     "output_type": "display_data"
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      "text/plain": [
       "|S[2] -|D -----|S -----|\n",
       ".------.   .~~~.   .---.\n",
       "|i0 i1 |p2 ┊i2 ┊p3 |i3 |\n",
       "`------'   `~~~'   `---'\n",
       "========================\n",
       ".-----.  0 .~~.  0 .--.\n",
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       "`-----' ┊  `~~' `--|2 |\n",
       "        ┊  .~~.  2 `--'\n",
       "        `~~┊1 ┊)\n",
       "         2 `~~'\n",
       ".-----.    .~~.  2 .--.\n",
       "|0  1 |~+~~┊0 ┊-+--|0 |\n",
       "`-----' ┊  `~~' `--|2 |\n",
       "        ┊  .~~.  4 |--|\n",
       "        `~~┊1 ┊----|0 |\n",
       "         4 `~~'  5 `--'\n",
       ".-----.    .~~.\n",
       "|1  1 |~+~~┊0 ┊)\n",
       "`-----' ┊  `~~'\n",
       "        ┊  .~~.  5 .--.\n",
       "        `~~┊1 ┊-+--|0 |\n",
       "         6 `~~' |--|1 |\n",
       "                `--|2 |\n",
       "                 8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `S[2]-S[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(2), Sparse(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, singleton, compressed, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
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     "output_type": "display_data"
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       "|S[2] -|S -----|S -----|\n",
       ".------.   .---.   .---.\n",
       "|i0 i1 |p2 |i2 |p3 |i3 |\n",
       "`------'   `---'   `---'\n",
       "========================\n",
       ".-----.  0 .--.  0 .--.\n",
       "|0  0 |----|0 |-+--|1 |\n",
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       ".-----.    .--.  2 |--|\n",
       "|0  1 |-+--|0 |-+--|0 |\n",
       "`-----' |  `--' `--|2 |\n",
       "        |  .--.  4 |--|\n",
       "        `--|1 |----|0 |\n",
       "         3 `--'  5 `--'\n",
       ".-----.    .--.    .--.\n",
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       "                `--|2 |\n",
       "                 8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `D[1]-S[3]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(1), Sparse(3)]\n",
       "\n",
       "taco_structure   = [dense, compressed-nonunique, singleton, singleton]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
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     "output_type": "display_data"
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       "|D -|S[3] --------|\n",
       ".~~~.   .---------.\n",
       "┊i0 ┊p1 |i1 i2 i3 |\n",
       "`~~~'   `---------'\n",
       "===================\n",
       ".~~.  0 .--------.\n",
       "┊0 ┊-+--|0  0  1 |\n",
       "`~~' |  `--------'\n",
       "     |  .--------.\n",
       "     |--|0  0  2 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     |--|1  0  0 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     |--|1  0  2 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     `--|1  1  0 |\n",
       "      5 `--------'\n",
       ".~~.    .--------.\n",
       "┊1 ┊-+--|1  1  0 |\n",
       "`~~' |  `--------'\n",
       "     |  .--------.\n",
       "     |--|1  1  1 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     `--|1  1  2 |\n",
       "      8 `--------'"
      ]
     },
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    {
     "data": {
      "text/markdown": [
       "# `D[1]-S[2]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(1), Sparse(2), Sparse(1)]\n",
       "\n",
       "taco_structure   = [dense, compressed, singleton, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
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     "output_type": "display_data"
    },
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       "|D -|S[2] -----|S -----|\n",
       ".~~~.   .------.   .---.\n",
       "┊i0 ┊p1 |i1 i2 |p3 |i3 |\n",
       "`~~~'   `------'   `---'\n",
       "========================\n",
       ".~~.  0 .-----.  0 .--.\n",
       "┊0 ┊-+--|0  0 |-+--|1 |\n",
       "`~~' |  `-----' `--|2 |\n",
       "     |  .-----.  2 |--|\n",
       "     |--|1  0 |-+--|0 |\n",
       "     |  `-----' `--|2 |\n",
       "     |  .-----.  4 |--|\n",
       "     `--|1  1 |----|0 |\n",
       "      3 `-----'  5 `--'\n",
       ".~~.    .-----.    .--.\n",
       "┊1 ┊----|1  1 |-+--|0 |\n",
       "`~~'  4 `-----' |--|1 |\n",
       "                `--|2 |\n",
       "                 8 `--'"
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      "text/markdown": [
       "# `D[2]-S[2]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
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     "metadata": {},
     "output_type": "display_data"
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       "```\n",
       "binsparse_groups = [Dense(2), Sparse(2)]\n",
       "\n",
       "taco_structure   = [dense, dense, compressed-nonunique, singleton]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|D[2] -|S[2] -----|\n",
       ".~~ ~~~.   .------.\n",
       "┊i0 i1 ┊p2 |i2 i3 |\n",
       "`~~ ~~~'   `------'\n",
       "===================\n",
       ".~~ ~~.  0 .-----.\n",
       "┊0  0 ┊-+--|0  1 |\n",
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       "        |  .-----.\n",
       "        `--|0  2 |\n",
       "         2 `-----'\n",
       "    ~~.    .-----.\n",
       "    1 ┊-+--|0  0 |\n",
       "    ~~' |  `-----'\n",
       ".~~ ~~. |  .-----.\n",
       "┊1  0 ┊)|--|0  2 |\n",
       "`~~ ~~' |  `-----'\n",
       "        |  .-----.\n",
       "        `--|1  0 |\n",
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       "    ~~.  5 .-----.\n",
       "    1 ┊-+--|1  0 |\n",
       "    ~~' |  `-----'\n",
       "        |  .-----.\n",
       "        |--|1  1 |\n",
       "        |  `-----'\n",
       "        |  .-----.\n",
       "        `--|1  2 |\n",
       "         8 `-----'"
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    {
     "data": {
      "text/markdown": [
       "# `D[3]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
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     "metadata": {},
     "output_type": "display_data"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(3), Sparse(1)]\n",
       "\n",
       "taco_structure   = [dense, dense, dense, compressed]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|D[3] ----|S -----|\n",
       ".~~ ~~ ~~~.   .---.\n",
       "┊i0 i1 i2 ┊p3 |i3 |\n",
       "`~~ ~~ ~~~'   `---'\n",
       "===================\n",
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       "    ~~ ~~' `--|2 |\n",
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       "       1 ┊----|0 |\n",
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       ".~~ ~~ ~~.\n",
       "┊1  0  0 ┊)\n",
       "`~~ ~~ ~~'\n",
       "       ~~.  5\n",
       "       1 ┊)\n",
       "       ~~'\n",
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       "            8 `--'"
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     "data": {
      "text/markdown": [
       "# `D[2]-S[1]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(2), Sparse(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [dense, dense, compressed, compressed]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|D[2] -|S -----|S -----|\n",
       ".~~ ~~~.   .---.   .---.\n",
       "┊i0 i1 ┊p2 |i2 |p3 |i3 |\n",
       "`~~ ~~~'   `---'   `---'\n",
       "========================\n",
       ".~~ ~~.  0 .--.  0 .--.\n",
       "┊0  0 ┊----|0 |-+--|1 |\n",
       "`~~ ~~'  1 `--' `--|2 |\n",
       "    ~~.    .--.  2 |--|\n",
       "    1 ┊-+--|0 |-+--|0 |\n",
       "    ~~' |  `--' `--|2 |\n",
       ".~~ ~~. |  .--.  4 |--|\n",
       "┊1  0 ┊)`--|1 |----|0 |\n",
       "`~~ ~~'  3 `--'  5 `--'\n",
       "    ~~.  3 .--.    .--.\n",
       "    1 ┊----|1 |-+--|0 |\n",
       "    ~~'  4 `--' |--|1 |\n",
       "                `--|2 |\n",
       "                 8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `D[1]-S[1]-S[2]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(1), Sparse(1), Sparse(2)]\n",
       "\n",
       "taco_structure   = [dense, compressed, compressed-nonunique, singleton]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
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     "output_type": "display_data"
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       "|D -|S -----|S[2] -----|\n",
       ".~~~.   .---.   .------.\n",
       "┊i0 ┊p1 |i1 |p2 |i2 i3 |\n",
       "`~~~'   `---'   `------'\n",
       "========================\n",
       ".~~.  0 .--.  0 .-----.\n",
       "┊0 ┊-+--|0 |-+--|0  1 |\n",
       "`~~' |  `--' |  `-----'\n",
       "     |       |  .-----.\n",
       "     |       `--|0  2 |\n",
       "     |        2 `-----'\n",
       "     |  .--.    .-----.\n",
       "     `--|1 |-+--|0  0 |\n",
       "      2 `--' |  `-----'\n",
       "             |  .-----.\n",
       "             |--|0  2 |\n",
       "             |  `-----'\n",
       "             |  .-----.\n",
       "             `--|1  0 |\n",
       "              5 `-----'\n",
       ".~~.    .--.    .-----.\n",
       "┊1 ┊----|1 |-+--|1  0 |\n",
       "`~~'  3 `--' |  `-----'\n",
       "             |  .-----.\n",
       "             |--|1  1 |\n",
       "             |  `-----'\n",
       "             |  .-----.\n",
       "             `--|1  2 |\n",
       "              8 `-----'"
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     },
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "# `D[1]-S[1]-D[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(1), Sparse(1), Dense(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [dense, compressed, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "|D -|S -----|D -----|S -----|\n",
       ".~~~.   .---.   .~~~.   .---.\n",
       "┊i0 ┊p1 |i1 |p2 ┊i2 ┊p3 |i3 |\n",
       "`~~~'   `---'   `~~~'   `---'\n",
       "=============================\n",
       ".~~.  0 .--.  0 .~~.  0 .--.\n",
       "┊0 ┊-+--|0 |~+~~┊0 ┊-+--|1 |\n",
       "`~~' |  `--' ┊  `~~' `--|2 |\n",
       "     |       ┊  .~~.  2 `--'\n",
       "     |       `~~┊1 ┊)\n",
       "     |        2 `~~'\n",
       "     |  .--.    .~~.  2 .--.\n",
       "     `--|1 |~+~~┊0 ┊-+--|0 |\n",
       "      2 `--' ┊  `~~' `--|2 |\n",
       "             ┊  .~~.  4 |--|\n",
       "             `~~┊1 ┊----|0 |\n",
       "              4 `~~'  5 `--'\n",
       ".~~.    .--.    .~~.\n",
       "┊1 ┊----|1 |~+~~┊0 ┊)\n",
       "`~~'  3 `--' ┊  `~~'\n",
       "             ┊  .~~.  5 .--.\n",
       "             `~~┊1 ┊-+--|0 |\n",
       "              6 `~~' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
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    },
    {
     "data": {
      "text/markdown": [
       "# `D[1]-S[1]-S[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(1), Sparse(1), Sparse(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [dense, compressed, compressed, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "|D -|S -----|S -----|S -----|\n",
       ".~~~.   .---.   .---.   .---.\n",
       "┊i0 ┊p1 |i1 |p2 |i2 |p3 |i3 |\n",
       "`~~~'   `---'   `---'   `---'\n",
       "=============================\n",
       ".~~.  0 .--.  0 .--.  0 .--.\n",
       "┊0 ┊-+--|0 |----|0 |-+--|1 |\n",
       "`~~' |  `--'  1 `--' `--|2 |\n",
       "     |  .--.    .--.  2 |--|\n",
       "     `--|1 |-+--|0 |-+--|0 |\n",
       "      2 `--' |  `--' `--|2 |\n",
       "             |  .--.  4 |--|\n",
       "             `--|1 |----|0 |\n",
       "              3 `--'  5 `--'\n",
       ".~~.    .--.    .--.    .--.\n",
       "┊1 ┊----|1 |----|1 |-+--|0 |\n",
       "`~~'  3 `--'  4 `--' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
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    },
    {
     "data": {
      "text/markdown": [
       "# `S[1]-S[3]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Sparse(3)]\n",
       "\n",
       "taco_structure   = [compressed, compressed-nonunique, singleton, singleton]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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       "|S -|S[3] --------|\n",
       ".---.   .---------.\n",
       "|i0 |p1 |i1 i2 i3 |\n",
       "`---'   `---------'\n",
       "===================\n",
       ".--.  0 .--------.\n",
       "|0 |-+--|0  0  1 |\n",
       "`--' |  `--------'\n",
       "     |  .--------.\n",
       "     |--|0  0  2 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     |--|1  0  0 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     |--|1  0  2 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     `--|1  1  0 |\n",
       "      5 `--------'\n",
       ".--.    .--------.\n",
       "|1 |-+--|1  1  0 |\n",
       "`--' |  `--------'\n",
       "     |  .--------.\n",
       "     |--|1  1  1 |\n",
       "     |  `--------'\n",
       "     |  .--------.\n",
       "     `--|1  1  2 |\n",
       "      8 `--------'"
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      "text/markdown": [
       "# `S[1]-S[2]-S[1]`"
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       "<IPython.core.display.Markdown object>"
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       "```\n",
       "binsparse_groups = [Sparse(1), Sparse(2), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, compressed, singleton, compressed]\n",
       "\n",
       "```"
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       "|S -|S[2] -----|S -----|\n",
       ".---.   .------.   .---.\n",
       "|i0 |p1 |i1 i2 |p3 |i3 |\n",
       "`---'   `------'   `---'\n",
       "========================\n",
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      "text/markdown": [
       "# `S[1]-D[1]-S[2]`"
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       "<IPython.core.display.Markdown object>"
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       "```\n",
       "binsparse_groups = [Sparse(1), Dense(1), Sparse(2)]\n",
       "\n",
       "taco_structure   = [compressed, dense, compressed-nonunique, singleton]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|S -|D -----|S[2] -----|\n",
       ".---.   .~~~.   .------.\n",
       "|i0 |p1 ┊i1 ┊p2 |i2 i3 |\n",
       "`---'   `~~~'   `------'\n",
       "========================\n",
       ".--.  0 .~~.  0 .-----.\n",
       "|0 |~+~~┊0 ┊-+--|0  1 |\n",
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       "     ┊        2 `-----'\n",
       "     ┊  .~~.    .-----.\n",
       "     `~~┊1 ┊-+--|0  0 |\n",
       "      2 `~~' |  `-----'\n",
       ".--.    .~~. |  .-----.\n",
       "|1 |~+~~┊0 ┊)|--|0  2 |\n",
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       "     ┊       |  .-----.\n",
       "     ┊       `--|1  0 |\n",
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       "     ┊  .~~.  5 .-----.\n",
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    {
     "data": {
      "text/markdown": [
       "# `S[1]-D[2]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Dense(2), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, dense, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
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     "output_type": "display_data"
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       "|S -|D[2] -----|S -----|\n",
       ".---.   .~~ ~~~.   .---.\n",
       "|i0 |p1 ┊i1 i2 ┊p3 |i3 |\n",
       "`---'   `~~ ~~~'   `---'\n",
       "========================\n",
       ".--.  0 .~~ ~~.  0 .--.\n",
       "|0 |~+~~┊0  0 ┊-+--|1 |\n",
       "`--' ┊  `~~ ~~' `--|2 |\n",
       "     ┊      ~~.  2 `--'\n",
       "     ┊      1 ┊)\n",
       "     ┊      ~~'\n",
       "     ┊  .~~ ~~.  2 .--.\n",
       "     `~~┊1  0 ┊-+--|0 |\n",
       "      2 `~~ ~~' `--|2 |\n",
       "            ~~.  4 |--|\n",
       "            1 ┊----|0 |\n",
       "            ~~'  5 `--'\n",
       ".--.    .~~ ~~.\n",
       "|1 |~+~~┊0  0 ┊)\n",
       "`--' ┊  `~~ ~~'\n",
       "     ┊      ~~.  5\n",
       "     ┊      1 ┊)\n",
       "     ┊      ~~'\n",
       "     ┊  .~~ ~~.  5\n",
       "     `~~┊1  0 ┊)\n",
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       "            ~~.  5 .--.\n",
       "            1 ┊-+--|0 |\n",
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       "                 8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `S[1]-D[1]-S[1]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Dense(1), Sparse(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, dense, compressed, compressed]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|S -|D -----|S -----|S -----|\n",
       ".---.   .~~~.   .---.   .---.\n",
       "|i0 |p1 ┊i1 ┊p2 |i2 |p3 |i3 |\n",
       "`---'   `~~~'   `---'   `---'\n",
       "=============================\n",
       ".--.  0 .~~.  0 .--.  0 .--.\n",
       "|0 |~+~~┊0 ┊----|0 |-+--|1 |\n",
       "`--' ┊  `~~'  1 `--' `--|2 |\n",
       "     ┊  .~~.    .--.  2 |--|\n",
       "     `~~┊1 ┊-+--|0 |-+--|0 |\n",
       "      2 `~~' |  `--' `--|2 |\n",
       ".--.    .~~. |  .--.  4 |--|\n",
       "|1 |~+~~┊0 ┊)`--|1 |----|0 |\n",
       "`--' ┊  `~~'  3 `--'  5 `--'\n",
       "     ┊  .~~.  3 .--.    .--.\n",
       "     `~~┊1 ┊----|1 |-+--|0 |\n",
       "      4 `~~'  4 `--' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `S[1]-S[1]-S[2]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Sparse(1), Sparse(2)]\n",
       "\n",
       "taco_structure   = [compressed, compressed, compressed-nonunique, singleton]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
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     "output_type": "display_data"
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       "|S -|S -----|S[2] -----|\n",
       ".---.   .---.   .------.\n",
       "|i0 |p1 |i1 |p2 |i2 i3 |\n",
       "`---'   `---'   `------'\n",
       "========================\n",
       ".--.  0 .--.  0 .-----.\n",
       "|0 |-+--|0 |-+--|0  1 |\n",
       "`--' |  `--' |  `-----'\n",
       "     |       |  .-----.\n",
       "     |       `--|0  2 |\n",
       "     |        2 `-----'\n",
       "     |  .--.    .-----.\n",
       "     `--|1 |-+--|0  0 |\n",
       "      2 `--' |  `-----'\n",
       "             |  .-----.\n",
       "             |--|0  2 |\n",
       "             |  `-----'\n",
       "             |  .-----.\n",
       "             `--|1  0 |\n",
       "              5 `-----'\n",
       ".--.    .--.    .-----.\n",
       "|1 |----|1 |-+--|1  0 |\n",
       "`--'  3 `--' |  `-----'\n",
       "             |  .-----.\n",
       "             |--|1  1 |\n",
       "             |  `-----'\n",
       "             |  .-----.\n",
       "             `--|1  2 |\n",
       "              8 `-----'"
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    {
     "data": {
      "text/markdown": [
       "# `S[1]-S[1]-D[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Sparse(1), Dense(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, compressed, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "|S -|S -----|D -----|S -----|\n",
       ".---.   .---.   .~~~.   .---.\n",
       "|i0 |p1 |i1 |p2 ┊i2 ┊p3 |i3 |\n",
       "`---'   `---'   `~~~'   `---'\n",
       "=============================\n",
       ".--.  0 .--.  0 .~~.  0 .--.\n",
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       "     |       ┊  .~~.  2 `--'\n",
       "     |       `~~┊1 ┊)\n",
       "     |        2 `~~'\n",
       "     |  .--.    .~~.  2 .--.\n",
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       "      2 `--' ┊  `~~' `--|2 |\n",
       "             ┊  .~~.  4 |--|\n",
       "             `~~┊1 ┊----|0 |\n",
       "              4 `~~'  5 `--'\n",
       ".--.    .--.    .~~.\n",
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       "             ┊  .~~.  5 .--.\n",
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     "data": {
      "text/markdown": [
       "# `S[1]-S[1]-S[1]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Sparse(1), Sparse(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, compressed, compressed, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
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     "output_type": "display_data"
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       "|S -|S -----|S -----|S -----|\n",
       ".---.   .---.   .---.   .---.\n",
       "|i0 |p1 |i1 |p2 |i2 |p3 |i3 |\n",
       "`---'   `---'   `---'   `---'\n",
       "=============================\n",
       ".--.  0 .--.  0 .--.  0 .--.\n",
       "|0 |-+--|0 |----|0 |-+--|1 |\n",
       "`--' |  `--'  1 `--' `--|2 |\n",
       "     |  .--.    .--.  2 |--|\n",
       "     `--|1 |-+--|0 |-+--|0 |\n",
       "      2 `--' |  `--' `--|2 |\n",
       "             |  .--.  4 |--|\n",
       "             `--|1 |----|0 |\n",
       "              3 `--'  5 `--'\n",
       ".--.    .--.    .--.    .--.\n",
       "|1 |----|1 |----|1 |-+--|0 |\n",
       "`--'  3 `--'  4 `--' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "indices = [\n",
    "    [0, 0, 0, 0, 0, 1, 1, 1],\n",
    "    [0, 0, 1, 1, 1, 1, 1, 1],\n",
    "    [0, 0, 0, 0, 1, 1, 1, 1],\n",
    "    [1, 2, 0, 2, 0, 0, 1, 2],\n",
    "]\n",
    "sparsities = [\"S\", \"C\", \"DC\"]\n",
    "for sparsity in itertools.product(sparsities, sparsities, sparsities, [\"S\"]):\n",
    "    structure = \"-\".join(sparsity)\n",
    "    st = SparseTensor(indices, shape=(2, 2, 2, 3), structure=structure, as_binsparse=True)\n",
    "    if \"expanded\" in \" \".join(st.binsparse_groups):\n",
    "        continue\n",
    "    abbvs = []\n",
    "    for abbv, n in st.binsparse_structure:\n",
    "        abbvs.append(f\"{abbv}[{n}]\")\n",
    "    IPython.display.display(IPython.display.Markdown(f\"# `{'-'.join(abbvs)}`\"))\n",
    "    display_header(st)\n",
    "    IPython.display.display(st)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44c45d8f-b109-4965-8dd8-d88122788164",
   "metadata": {},
   "source": [
    "The visualization via `sparsetensorviz` admits an \"expanded sparse\" level denoted by `Sparse(n, expanded=1)`.\n",
    "This is a Sparse level that is followed by a Dense level and has values duplicated to expand to match the dense level.\n",
    "\n",
    "This is not yet part of the standard binsparse formats (I think), because the regular `Sparse(n)` level without duplicates is preferred.\n",
    "\n",
    "Similarly, I don't know if these are valid TACO formats."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "34660901-7de1-40ea-b192-49b2c7a5ae3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "# `SE[2]-D[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(2, expanded=1), Dense(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed-nonunique, singleton, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "|SE[2] |D -----|S -----|\n",
       ".------.   .~~~.   .---.\n",
       "|i0 i1 |p2 ┊i2 ┊p3 |i3 |\n",
       "`------'   `~~~'   `---'\n",
       "========================\n",
       ".-----.  0 .~~.  0 .--.\n",
       "|0  0 |~~~~┊0 ┊-+--|1 |\n",
       "`-----'  1 `~~' `--|2 |\n",
       ".-----.    .~~.  2 `--'\n",
       "|0  0 |~~~~┊1 ┊)\n",
       "`-----'  2 `~~'\n",
       ".-----.    .~~.  2 .--.\n",
       "|0  1 |~~~~┊0 ┊-+--|0 |\n",
       "`-----'  3 `~~' `--|2 |\n",
       ".-----.    .~~.  4 |--|\n",
       "|0  1 |~~~~┊1 ┊----|0 |\n",
       "`-----'  4 `~~'  5 `--'\n",
       ".-----.    .~~.\n",
       "|1  1 |~~~~┊0 ┊)\n",
       "`-----'  5 `~~'\n",
       ".-----.    .~~.  5 .--.\n",
       "|1  1 |~~~~┊1 ┊-+--|0 |\n",
       "`-----'  6 `~~' |--|1 |\n",
       "                `--|2 |\n",
       "                 8 `--'"
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     "data": {
      "text/markdown": [
       "# `SE[1]-D[1]-S[2]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
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     "metadata": {},
     "output_type": "display_data"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1, expanded=1), Dense(1), Sparse(2)]\n",
       "\n",
       "taco_structure   = [compressed-nonunique, dense, compressed-nonunique, singleton]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
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     "output_type": "display_data"
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       "|SE |D -----|S[2] -----|\n",
       ".---.   .~~~.   .------.\n",
       "|i0 |p1 ┊i1 ┊p2 |i2 i3 |\n",
       "`---'   `~~~'   `------'\n",
       "========================\n",
       ".--.  0 .~~.  0 .-----.\n",
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       "             |  .-----.\n",
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       ".--.    .~~.    .-----.\n",
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       ".--.    .~~. |  .-----.\n",
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       "             |  .-----.\n",
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       "              5 `-----'\n",
       ".--.    .~~.  5 .-----.\n",
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       "             |  .-----.\n",
       "             |--|1  1 |\n",
       "             |  `-----'\n",
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      "text/markdown": [
       "# `SE[1]-D[2]-S[1]`"
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       "<IPython.core.display.Markdown object>"
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1, expanded=1), Dense(2), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed-nonunique, dense, dense, compressed]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|SE |D[2] -----|S -----|\n",
       ".---.   .~~ ~~~.   .---.\n",
       "|i0 |p1 ┊i1 i2 ┊p3 |i3 |\n",
       "`---'   `~~ ~~~'   `---'\n",
       "========================\n",
       ".--.  0 .~~ ~~.  0 .--.\n",
       "|0 |~~~~┊0  0 ┊-+--|1 |\n",
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       "            ~~.  2 `--'\n",
       "            1 ┊)\n",
       "            ~~'\n",
       ".--.    .~~ ~~.  2 .--.\n",
       "|0 |~~~~┊1  0 ┊-+--|0 |\n",
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       "            ~~.  4 |--|\n",
       "            1 ┊----|0 |\n",
       "            ~~'  5 `--'\n",
       ".--.    .~~ ~~.\n",
       "|1 |~~~~┊0  0 ┊)\n",
       "`--'  3 `~~ ~~'\n",
       "            ~~.  5\n",
       "            1 ┊)\n",
       "            ~~'\n",
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       "            ~~.  5 .--.\n",
       "            1 ┊-+--|0 |\n",
       "            ~~' |--|1 |\n",
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       "                 8 `--'"
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     "data": {
      "text/markdown": [
       "# `SE[1]-D[1]-S[1]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
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      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1, expanded=1), Dense(1), Sparse(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed-nonunique, dense, compressed, compressed]\n",
       "\n",
       "```"
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       "<IPython.core.display.Markdown object>"
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       "|SE |D -----|S -----|S -----|\n",
       ".---.   .~~~.   .---.   .---.\n",
       "|i0 |p1 ┊i1 ┊p2 |i2 |p3 |i3 |\n",
       "`---'   `~~~'   `---'   `---'\n",
       "=============================\n",
       ".--.  0 .~~.  0 .--.  0 .--.\n",
       "|0 |~~~~┊0 ┊----|0 |-+--|1 |\n",
       "`--'  1 `~~'  1 `--' `--|2 |\n",
       ".--.    .~~.    .--.  2 |--|\n",
       "|0 |~~~~┊1 ┊-+--|0 |-+--|0 |\n",
       "`--'  2 `~~' |  `--' `--|2 |\n",
       ".--.    .~~. |  .--.  4 |--|\n",
       "|1 |~~~~┊0 ┊)`--|1 |----|0 |\n",
       "`--'  3 `~~'  3 `--'  5 `--'\n",
       ".--.    .~~.  3 .--.    .--.\n",
       "|1 |~~~~┊1 ┊----|1 |-+--|0 |\n",
       "`--'  4 `~~'  4 `--' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `D[1]-SE[1]-D[1]-S[1]`"
      ],
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       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Dense(1), Sparse(1, expanded=1), Dense(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [dense, compressed-nonunique, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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       "|D -|SE ----|D -----|S -----|\n",
       ".~~~.   .---.   .~~~.   .---.\n",
       "┊i0 ┊p1 |i1 |p2 ┊i2 ┊p3 |i3 |\n",
       "`~~~'   `---'   `~~~'   `---'\n",
       "=============================\n",
       ".~~.  0 .--.  0 .~~.  0 .--.\n",
       "┊0 ┊-+--|0 |~~~~┊0 ┊-+--|1 |\n",
       "`~~' |  `--'  1 `~~' `--|2 |\n",
       "     |  .--.    .~~.  2 `--'\n",
       "     |--|0 |~~~~┊1 ┊)\n",
       "     |  `--'  2 `~~'\n",
       "     |  .--.    .~~.  2 .--.\n",
       "     |--|1 |~~~~┊0 ┊-+--|0 |\n",
       "     |  `--'  3 `~~' `--|2 |\n",
       "     |  .--.    .~~.  4 |--|\n",
       "     `--|1 |~~~~┊1 ┊----|0 |\n",
       "      4 `--'  4 `~~'  5 `--'\n",
       ".~~.    .--.    .~~.\n",
       "┊1 ┊-+--|1 |~~~~┊0 ┊)\n",
       "`~~' |  `--'  5 `~~'\n",
       "     |  .--.    .~~.  5 .--.\n",
       "     `--|1 |~~~~┊1 ┊-+--|0 |\n",
       "      6 `--'  6 `~~' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
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    {
     "data": {
      "text/markdown": [
       "# `S[1]-SE[1]-D[1]-S[1]`"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/markdown": [
       "```\n",
       "binsparse_groups = [Sparse(1), Sparse(1, expanded=1), Dense(1), Sparse(1)]\n",
       "\n",
       "taco_structure   = [compressed, compressed-nonunique, dense, compressed]\n",
       "\n",
       "```"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
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     "output_type": "display_data"
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      "text/plain": [
       "|S -|SE ----|D -----|S -----|\n",
       ".---.   .---.   .~~~.   .---.\n",
       "|i0 |p1 |i1 |p2 ┊i2 ┊p3 |i3 |\n",
       "`---'   `---'   `~~~'   `---'\n",
       "=============================\n",
       ".--.  0 .--.  0 .~~.  0 .--.\n",
       "|0 |-+--|0 |~~~~┊0 ┊-+--|1 |\n",
       "`--' |  `--'  1 `~~' `--|2 |\n",
       "     |  .--.    .~~.  2 `--'\n",
       "     |--|0 |~~~~┊1 ┊)\n",
       "     |  `--'  2 `~~'\n",
       "     |  .--.    .~~.  2 .--.\n",
       "     |--|1 |~~~~┊0 ┊-+--|0 |\n",
       "     |  `--'  3 `~~' `--|2 |\n",
       "     |  .--.    .~~.  4 |--|\n",
       "     `--|1 |~~~~┊1 ┊----|0 |\n",
       "      4 `--'  4 `~~'  5 `--'\n",
       ".--.    .--.    .~~.\n",
       "|1 |-+--|1 |~~~~┊0 ┊)\n",
       "`--' |  `--'  5 `~~'\n",
       "     |  .--.    .~~.  5 .--.\n",
       "     `--|1 |~~~~┊1 ┊-+--|0 |\n",
       "      6 `--'  6 `~~' |--|1 |\n",
       "                     `--|2 |\n",
       "                      8 `--'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for sparsity in itertools.product(sparsities, sparsities, sparsities, [\"S\"]):\n",
    "    structure = \"-\".join(sparsity)\n",
    "    st = SparseTensor(indices, shape=(2, 2, 2, 3), structure=structure, as_binsparse=True)\n",
    "    if \"expanded\" not in \" \".join(st.binsparse_groups):\n",
    "        continue\n",
    "    abbvs = []\n",
    "    for abbv, n in st.binsparse_structure:\n",
    "        abbvs.append(f\"{abbv}[{n}]\")\n",
    "    IPython.display.display(IPython.display.Markdown(f\"# `{'-'.join(abbvs)}`\"))\n",
    "    display_header(st)\n",
    "    IPython.display.display(st)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07f40f47",
   "metadata": {},
   "source": [
    "# voilà!"
   ]
  }
 ],
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