analysis/tx.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c622d507-01b1-41b8-a29b-dd2566858f74",
   "metadata": {},
   "source": [
    "# Transaction sizes and frequencies"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5797d3b8-fffd-438d-bf21-7be3c1123c73",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "91ddef2c-2566-453b-be8d-d4f216a22182",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: data.table\n",
      "\n",
      "Loading required package: ggplot2\n",
      "\n",
      "Loading required package: magrittr\n",
      "\n",
      "Loading required package: MASS\n",
      "\n"
     ]
    }
   ],
   "source": [
    "require(data.table)\n",
    "require(ggplot2)\n",
    "require(magrittr)\n",
    "require(MASS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dccd3cb-29a6-4fce-963a-efb3e3b7ba0f",
   "metadata": {},
   "source": [
    "## Transaction size distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cb69f26-25cd-4a5c-83a9-60b7e2d10e04",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Read export from `cardano-db-sync`\n",
    "\n",
    "```sql\n",
    "\\copy (select size from tx where size > 0 and block_id >= 5000000 and valid_contract) to tx-size-raw.csv header csv\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "834b4f0d-cf82-473d-9546-27d99853623f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      Size      \n",
       " Min.   :   55  \n",
       " 1st Qu.:  374  \n",
       " Median :  706  \n",
       " Mean   : 1940  \n",
       " 3rd Qu.: 1761  \n",
       " Max.   :16384  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "txSize <- fread(\"tx-size-raw.csv\")\n",
    "colnames(txSize) <- c(\"Size\")\n",
    "txSize %>% summary"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60013b44-c1a5-4c55-843c-7485fd89bd41",
   "metadata": {},
   "source": [
    "### Approximate by a log-normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "05c2a926-c12e-4448-9928-029ce9cff06f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.83295397274088"
      ],
      "text/latex": [
       "6.83295397274088"
      ],
      "text/markdown": [
       "6.83295397274088"
      ],
      "text/plain": [
       "[1] 6.832954"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meanLogTxSize <- txSize[, mean(log(`Size`))]\n",
    "meanLogTxSize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5751657f-7c87-415c-976b-e1344643387a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.12749843748005"
      ],
      "text/latex": [
       "1.12749843748005"
      ],
      "text/markdown": [
       "1.12749843748005"
      ],
      "text/plain": [
       "[1] 1.127498"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sdLogTxSize <- txSize[, sd(log(`Size`))]\n",
    "sdLogTxSize"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96c5beb2-19e1-40c5-8010-227a4f314a3d",
   "metadata": {},
   "source": [
    "### Plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0f1a15e5-29a4-43f7-877d-1486a527ad1c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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wAAkATBDgAAQBIEOwAAAEkQ7AAAACRBsAMAAJAEwQ4AAEASBDsAAABJEOwAAAAk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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(txSize, aes(x = `Size`)) +\n",
    "  geom_histogram(binwidth=100) +\n",
    "  geom_line(\n",
    "      data=data.table(Size=1:16384, Count=100*txSize[, .N] * dlnorm(1:16384, meanlog=meanLogTxSize), sdlog=sdLogTxSize),\n",
    "      aes(x=`Size`, y=`Count`),\n",
    "      color=\"darkviolet\", linewidth=1\n",
    "  ) +\n",
    "  xlab(\"Tx Size [B]\") +\n",
    "  ylab(\"Count of Txs\") +\n",
    "  ggtitle(\"Tx Size Distribution (post-Byron)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9c51ba71-128c-458b-be13-42eb845f31e8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ggsave(\"tx-size.png\", width=8, height=6, units=\"in\", dpi=150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b454d760-dec8-45c2-82bb-90ae6b128ee9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "ggsave(\"tx-size.svg\", width=8, height=6, units=\"in\", dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e70f969-e966-4007-a11f-ef3bc0fe152a",
   "metadata": {},
   "source": [
    "## Distribution of transactions per block"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1e194b0-6ae4-49c4-a0f4-9a93a35e0a97",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Read export from `cardano-db-sync`\n",
    "\n",
    "```sql\n",
    "\\copy (select count(*) from tx where block_id >= 5000000 and valid_contract group by block_id) to tx-block-raw.csv header csv;\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "02c8d1e2-2dc8-4557-8c35-6d0164a9c0fe",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    Txs/blk      \n",
       " Min.   :  1.00  \n",
       " 1st Qu.:  5.00  \n",
       " Median : 12.00  \n",
       " Mean   : 16.97  \n",
       " 3rd Qu.: 24.00  \n",
       " Max.   :385.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "txFreq <- fread(\"tx-block-raw.csv\")\n",
    "colnames(txFreq) <- c(\"Txs/blk\")\n",
    "txFreq %>% summary"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8893edef-6b65-4b76-9585-70a1ef3110e3",
   "metadata": {},
   "source": [
    "### Approximate by an exponential distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "24b61ff7-7686-4ed1-8409-21083cd8c42f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "16.9690326193426"
      ],
      "text/latex": [
       "16.9690326193426"
      ],
      "text/markdown": [
       "16.9690326193426"
      ],
      "text/plain": [
       "[1] 16.96903"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "meanTxFreq <- txFreq[, mean(`Txs/blk`)]\n",
    "meanTxFreq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3cae8e8-5f61-4536-a526-637a5b3c85da",
   "metadata": {},
   "source": [
    "### Plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "adb85dd0-39e1-4fb2-b08c-ac74beb86c2f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 2764 rows containing non-finite values (`stat_bin()`).”\n",
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 2 rows containing missing values (`geom_bar()`).”\n",
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 250 rows containing missing values (`geom_line()`).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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fv2LSwsrLPS6bp1644dO9a3b19l1YZz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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(txFreq, aes(x=`Txs/blk`)) +\n",
    "  geom_histogram(binwidth=1) +\n",
    "  geom_line(\n",
    "      data=data.table(Size=1:400, Count=1*txFreq[, .N] * dexp(1:400, 1/meanTxFreq)),\n",
    "      aes(x=`Size`, y=`Count`),\n",
    "      color=\"darkviolet\", linewidth=1\n",
    "  ) +\n",
    "  xlim(0, 150) +\n",
    "  xlab(\"Transactions in Block\") +\n",
    "  ylab(\"Blocks\") +\n",
    "  ggtitle(\"Transactions per Block Distribution (post-Byron)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bde619a7-6980-4310-88f4-2aeaceeb36b2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 2764 rows containing non-finite values (`stat_bin()`).”\n",
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 2 rows containing missing values (`geom_bar()`).”\n",
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 250 rows containing missing values (`geom_line()`).”\n"
     ]
    }
   ],
   "source": [
    "ggsave(\"tx-freq.png\", width=8, height=6, units=\"in\", dpi=150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9b503d53-e1fd-4d42-808c-0578b8ad6bbd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 2764 rows containing non-finite values (`stat_bin()`).”\n",
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 2 rows containing missing values (`geom_bar()`).”\n",
      "Warning message:\n",
      "“\u001b[1m\u001b[22mRemoved 250 rows containing missing values (`geom_line()`).”\n"
     ]
    }
   ],
   "source": [
    "ggsave(\"tx-freq.svg\", width=8, height=6, units=\"in\", dpi=150)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "r-minimal kernel",
   "language": "r",
   "name": "r-minimal"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.2.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}