Addition of examples

examples/example.ipynb

@@ -0,0 +1,172 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "458048cb-959b-4c1e-a4bf-08f64f0af712",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy\n",
+    "from pca import pca\n",
+    "from pcp import pcp\n",
+    "from spcp import spcp"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c6d850e2-665d-4d2c-b9fc-959351de0b18",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "rank = 5\n",
+    "n = 1000\n",
+    "m = 100\n",
+    "\n",
+    "# Create low-rank with random bases\n",
+    "x = (numpy.random.randn(m, rank)).astype(numpy.float32)\n",
+    "y = (numpy.random.randn(n, rank)).astype(numpy.float32)\n",
+    "b = y @ x.T"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d11962f0-7815-4b44-a240-b82cf56d6f41",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Create uniform noise pattern (m = l + s)\n",
+    "d = numpy.random.uniform(low=-1, high=1, size=(n, n)).astype(numpy.float32)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3b3071fd-ce85-4b80-8f4f-3416ac6040f0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = b + d"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d6ebd91b-8ae7-41bc-8959-915bccf01d4b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Initiate PCA\n",
+    "pca_object = pca(verbose=False, rank=rank)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7c9fb551-3717-4a07-ad4e-d9ba58a311b7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Run PCA\n",
+    "pca_object.run(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a4a88548-1830-47ae-be75-6d1b268028d7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "print('Fit: ', linalg.norm(pca_object.b - b, \"fro\") / linalg.norm(b, \"fro\")*100, ' %')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e701526c-9a8a-4aae-89e4-734e2cc62b7e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Initiate PCP\n",
+    "pcp_object = pcp(verbose=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e25ee615-dc4c-4a0f-b63c-8c3ca7bf9107",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Run PCP\n",
+    "pcp_object.run(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5126cc98-6359-4f62-8475-fa7f48d04e1b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "print('Fit: ', linalg.norm(pcp_object.b - b, \"fro\") / linalg.norm(b, \"fro\")*100, ' %')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "46cdc0df-d382-4348-a83c-b7e17ff250fb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Initiate SPCP\n",
+    "spcp_object = spcp(verbose=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14c6f0ef-077f-4657-8db2-67c0797b8386",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Run SPCP\n",
+    "spcp_object.run(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "96570952-cd7d-4449-9779-d140000324f1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "print('Fit: ', linalg.norm(spcp_object.b - b, \"fro\") / linalg.norm(b, \"fro\")*100, ' %')"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}