Minor updates
This commit is contained in:
Adam Wojdyla
parent
929bf13185
commit
ebf9e510f2
134
jupyter.ipynb
134
jupyter.ipynb
@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 18,
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"execution_count": 11,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -13,7 +13,7 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/var/folders/tq/jq5nwbnj7v10tls99x99qbh40000gn/T/ipykernel_66956/17056051.py:11: DeprecationWarning: Importing display from IPython.core.display is deprecated since IPython 7.14, please import from IPython display\n",
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"/var/folders/t3/dwnz0lh916ng4w7bzf0z56ym0000gn/T/ipykernel_43951/17056051.py:11: DeprecationWarning: Importing display from IPython.core.display is deprecated since IPython 7.14, please import from IPython display\n",
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" from IPython.core.display import display, HTML\n"
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]
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},
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@ -47,7 +47,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"execution_count": 12,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -80,13 +80,17 @@
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"source": [
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"Metodę SVD zastosujemy do kompresji obrazów. SVD dokonuje dekompozycji macierzy prostokątnej $M$ na trzy części.\n",
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"$M=U\\Sigma V^T$ -\n",
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"- $U$ - macierz, w której kolumny są wektorami własnymi macierzy $MM^T$ (lewe wektory osobliwe - 'left singular vectors')\n",
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"- $\\Sigma$ - macierz diagonalna, która na swojej diagonalii ma nieujemne wartości osobliwe (pierwiastki wartości własnych) macierzy $M^TM$ uporządkowane nierosnąco\n",
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"- $V$ - macierz, w której kolumny są wektorami własnymi macierzy $M^TM$ (prawe wektory osobliwe - 'right singular vectors')\n",
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"- $U$ - macierz, w której kolumny są wektorami własnymi macierzy $MM^T$ (lewe wektory osobliwe - 'left singular vectors'). Wektory te tworzą układ ortonormalny.\n",
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"- $\\Sigma$ - macierz diagonalna, która na swojej diagonalii ma nieujemne wartości osobliwe (szczególne), czyli pierwiastki wartości własnych macierzy $M^TM$ uporządkowane nierosnąco\n",
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"- $V$ - macierz, w której kolumny są wektorami własnymi macierzy $M^TM$ (prawe wektory osobliwe - 'right singular vectors'). Wektory te tworzą układ ortonormalny.\n",
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"\n",
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"SVD polega na rekonstrukcji oryginalnej macierzy jako kombinacji liniowej kilku macierzy rangi jeden. Macierz rangi jeden można wyrazić jako iloczyn zewnętrzny dwóch wektorów kolumnowych. \n",
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"\n",
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"$M=\\sigma_1u_1v_1^T+\\sigma_2u_2v_2^T+\\sigma_3u_3v_3^T+\\sigma_3u_3v_3^T+....$ . \n",
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"$M=\\sigma_1u_1v_1^T+\\sigma_2u_2v_2^T+\\sigma_3u_3v_3^T+\\sigma_3u_3v_3^T+....$ .\n",
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"\n",
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"$rank M=r$ .\n",
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"$M=\\sum_{i=1}^{r} \\sigma_iu_iv_i^T$\n",
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"\n",
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"Macierz o randze r będzie miała r takich wyrazów.\n",
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"\n",
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"Tutaj $\\sigma_1,\\sigma_2,\\sigma_3 ...$ są wartościami osobliwymi. $u_1,u_2,u_3 ...$ i $v_1,v_2,v_3 ...$ są kolejnymi kolumnami (wektorami własnymi) z macierzy U i V.\n",
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@ -109,7 +113,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"execution_count": 13,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -150,7 +154,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"execution_count": 14,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -185,7 +189,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"execution_count": 15,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -223,7 +227,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": 18,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -244,15 +248,17 @@
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"\n",
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"list_widget = widgets.Dropdown(options=list(gray_images.keys()))\n",
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"int_slider_widget = widgets.IntSlider(min=1,max=compute_k_max('cat'))\n",
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"\n",
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"def update_k_max(*args):\n",
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" img_name=list_widget.value\n",
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" int_slider_widget.max = compute_k_max(img_name)\n",
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"\n",
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"list_widget.observe(update_k_max,'value')\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": 33,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -279,7 +285,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"execution_count": 34,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -289,7 +295,7 @@
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "3909141856c04409b28f9d02306ef5a6",
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"model_id": "93aa562a15a44f30bb5fda5ee40fbf5f",
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"version_major": 2,
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"version_minor": 0
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},
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@ -306,7 +312,7 @@
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"<function __main__.print_matrices(img_name, k)>"
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]
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},
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"execution_count": 25,
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"execution_count": 34,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -317,7 +323,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"execution_count": 36,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -327,7 +333,7 @@
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "7ca89c134f914dc9bcd4372a352eae5a",
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"model_id": "bce351d98f7b471eaebc4e9a02d4396b",
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"version_major": 2,
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"version_minor": 0
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},
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@ -356,7 +362,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": 37,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -411,7 +417,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -446,7 +452,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 29,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -470,66 +476,26 @@
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},
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{
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"cell_type": "code",
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"execution_count": 30,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "de4cb84649574a71b1f36d77a7f6e893",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"interactive(children=(Dropdown(description='img_name', options=('cat', 'astro', 'coffee', 'koala', 'orange'), …"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"<function __main__.print_matrices(img_name, k)>"
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]
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},
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"execution_count": 30,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"interact(print_matrices, img_name=list_widget, k=int_slider_widget)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 31,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "be1b04fae0ac4bd4916d48fc5b6eb7d6",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"interactive(children=(Dropdown(description='img_name', options=('cat', 'astro', 'coffee', 'koala', 'orange'), …"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"outputs": [],
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"source": [
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"interact(compress_show_color_images_reshape,img_name=list_widget,k=int_slider_widget);"
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]
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@ -558,7 +524,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 32,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -596,7 +562,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 33,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -620,28 +586,13 @@
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},
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{
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"cell_type": "code",
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"execution_count": 34,
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "25bd4e6560f841569923087e4eae6e8c",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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"interactive(children=(Dropdown(description='img_name', options=('cat', 'astro', 'coffee', 'koala', 'orange'), …"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"outputs": [],
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"source": [
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"interact(compress_show_color_images_layer,img_name=list_widget,k=int_slider_widget);"
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]
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@ -649,7 +600,22 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": []
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}
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