{
"cells": [
{
"cell_type": "markdown",
"id": "d8d05291",
"metadata": {},
"source": [
"# principal\n",
"Principal Components Analysis (PCA) example.\n",
"\n",
"Example of using TPrincipal as a stand alone class.\n",
"\n",
"I create n-dimensional data points, where c = trunc(n / 5) + 1\n",
"are correlated with the rest n - c randomly distributed variables.\n",
"\n",
"Based on principal.C by Rene Brun and Christian Holm Christensen\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Juan Fernando, Jaramillo Botero \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:27 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "2f51431f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:13.442328Z",
"iopub.status.busy": "2026-05-19T20:27:13.442176Z",
"iopub.status.idle": "2026-05-19T20:27:14.400939Z",
"shell.execute_reply": "2026-05-19T20:27:14.397845Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"*************************************************\n",
"* Principal Component Analysis *\n",
"* *\n",
"* Number of variables: 10 *\n",
"* Number of data points: 10000 *\n",
"* Number of dependent variables: 3 *\n",
"* *\n",
"*************************************************\n"
]
}
],
"source": [
"from ROOT import TPrincipal, gRandom, TBrowser, vector\n",
"\n",
"\n",
"n = 10\n",
"m = 10000\n",
"\n",
"c = int(n / 5) + 1\n",
"\n",
"print (\"\"\"*************************************************\n",
"* Principal Component Analysis *\n",
"* *\n",
"* Number of variables: {0:4d} *\n",
"* Number of data points: {1:8d} *\n",
"* Number of dependent variables: {2:4d} *\n",
"* *\n",
"*************************************************\"\"\".format(n, m, c))"
]
},
{
"cell_type": "markdown",
"id": "eaaf8f2b",
"metadata": {},
"source": [
"Initilase the TPrincipal object. Use the empty string for the\n",
"final argument, if you don't wan't the covariance\n",
"matrix. Normalising the covariance matrix is a good idea if your\n",
"variables have different orders of magnitude."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f0f7f6e0",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:14.412406Z",
"iopub.status.busy": "2026-05-19T20:27:14.412257Z",
"iopub.status.idle": "2026-05-19T20:27:14.536487Z",
"shell.execute_reply": "2026-05-19T20:27:14.536046Z"
}
},
"outputs": [],
"source": [
"principal = TPrincipal(n, \"ND\")"
]
},
{
"cell_type": "markdown",
"id": "09bda92c",
"metadata": {},
"source": [
"Use a pseudo-random number generator"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "cac7f84a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:14.546379Z",
"iopub.status.busy": "2026-05-19T20:27:14.546238Z",
"iopub.status.idle": "2026-05-19T20:27:14.649361Z",
"shell.execute_reply": "2026-05-19T20:27:14.648945Z"
}
},
"outputs": [],
"source": [
"randomNum = gRandom"
]
},
{
"cell_type": "markdown",
"id": "9116f62b",
"metadata": {},
"source": [
"Make the m data-points\n",
"Make a variable to hold our data\n",
"Allocate memory for the data point"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "8ae375f9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:14.651724Z",
"iopub.status.busy": "2026-05-19T20:27:14.651519Z",
"iopub.status.idle": "2026-05-19T20:27:14.922471Z",
"shell.execute_reply": "2026-05-19T20:27:14.922065Z"
}
},
"outputs": [],
"source": [
"data = vector('double')()\n",
"for i in range(m):\n",
" # First we create the un-correlated, random variables, according\n",
" # to one of three distributions\n",
" for j in range(n - c):\n",
" if j % 3 == 0:\n",
" data.push_back(randomNum.Gaus(5, 1))\n",
" elif j % 3 == 1:\n",
" data.push_back(randomNum.Poisson(8))\n",
" else:\n",
" data.push_back(randomNum.Exp(2))\n",
"\n",
" # Then we create the correlated variables\n",
" for j in range(c):\n",
" data.push_back(0)\n",
" for k in range(n - c - j):\n",
" data[n - c + j] += data[k]\n",
"\n",
" # Finally we're ready to add this datapoint to the PCA\n",
" principal.AddRow(data.data())\n",
" data.clear()"
]
},
{
"cell_type": "markdown",
"id": "c38b79a0",
"metadata": {},
"source": [
"Do the actual analysis"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "929801a2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:14.934421Z",
"iopub.status.busy": "2026-05-19T20:27:14.934281Z",
"iopub.status.idle": "2026-05-19T20:27:15.041866Z",
"shell.execute_reply": "2026-05-19T20:27:15.040820Z"
}
},
"outputs": [],
"source": [
"principal.MakePrincipals()"
]
},
{
"cell_type": "markdown",
"id": "b4d8cd9e",
"metadata": {},
"source": [
"Print out the result on"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "01456efb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:15.064411Z",
"iopub.status.busy": "2026-05-19T20:27:15.064237Z",
"iopub.status.idle": "2026-05-19T20:27:15.172879Z",
"shell.execute_reply": "2026-05-19T20:27:15.172223Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" Variable # | Mean Value | Sigma | Eigenvalue\n",
"-------------+------------+------------+------------\n",
" 0 | 4.994 | 0.9926 | 0.3856 \n",
" 1 | 8.011 | 2.824 | 0.112 \n",
" 2 | 2.017 | 1.992 | 0.1031 \n",
" 3 | 4.998 | 0.9952 | 0.1022 \n",
" 4 | 8.019 | 2.794 | 0.09998 \n",
" 5 | 1.976 | 2.009 | 0.0992 \n",
" 6 | 4.996 | 0.9996 | 0.09794 \n",
" 7 | 35.01 | 5.147 | 1.162e-16 \n",
" 8 | 30.01 | 5.041 | 2.795e-16 \n",
" 9 | 28.04 | 4.644 | 4.235e-16 \n",
"\n"
]
}
],
"source": [
"principal.Print()"
]
},
{
"cell_type": "markdown",
"id": "7000aed7",
"metadata": {},
"source": [
"Test the PCA"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9c066720",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:15.174143Z",
"iopub.status.busy": "2026-05-19T20:27:15.174023Z",
"iopub.status.idle": "2026-05-19T20:27:15.339084Z",
"shell.execute_reply": "2026-05-19T20:27:15.338443Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : created default TCanvas with name c1\n"
]
}
],
"source": [
"principal.Test()"
]
},
{
"cell_type": "markdown",
"id": "a6621249",
"metadata": {},
"source": [
"Make some histograms of the original, principal, residue, etc data"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "cfd98e68",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:15.340458Z",
"iopub.status.busy": "2026-05-19T20:27:15.340325Z",
"iopub.status.idle": "2026-05-19T20:27:15.484025Z",
"shell.execute_reply": "2026-05-19T20:27:15.483359Z"
}
},
"outputs": [],
"source": [
"principal.MakeHistograms()"
]
},
{
"cell_type": "markdown",
"id": "a7b061d9",
"metadata": {},
"source": [
"Make two functions to map between feature and pattern space\n",
"Start a browser, so that we may browse the histograms generated\n",
"above"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "dcf6db8a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:15.485747Z",
"iopub.status.busy": "2026-05-19T20:27:15.485619Z",
"iopub.status.idle": "2026-05-19T20:27:15.599337Z",
"shell.execute_reply": "2026-05-19T20:27:15.598642Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Writing on file \"pca.C\" ... done\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning in : The ROOT browser cannot run in batch mode\n"
]
}
],
"source": [
"principal.MakeCode()\n",
"b = TBrowser(\"principalBrowser\", principal)"
]
},
{
"cell_type": "markdown",
"id": "dd56328a",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "66b0a820",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:27:15.600762Z",
"iopub.status.busy": "2026-05-19T20:27:15.600639Z",
"iopub.status.idle": "2026-05-19T20:27:15.789248Z",
"shell.execute_reply": "2026-05-19T20:27:15.788865Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.12.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}