update
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test/
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "af1d5646-4b13-4039-9f76-8042bc9dbda3",
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"metadata": {},
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"outputs": [],
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"source": [
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"from optimization.gd import gradient_descent_1d, gradient_descent_2d"
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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": null,
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"id": "0a5c51d2-8b18-4143-b6f1-73a909ccb623",
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"metadata": {},
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"outputs": [],
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"source": [
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"gd2 = gradient_descent_2d()"
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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": 3,
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"id": "f254549d-d9b0-43ac-a502-e65b7c462d05",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"plotly.graph_objs._scatter3d.Scatter3d"
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]
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},
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"execution_count": 3,
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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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"source": [
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"import plotly.graph_objects as go\n",
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"go.Scatter3d"
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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": null,
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"id": "8c0f6766-4f41-419b-94a0-916a379ebcd1",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
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||||
}
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||||
],
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"metadata": {
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"kernelspec": {
|
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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||||
},
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"language_info": {
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||||
"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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Binary file not shown.
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "af1d5646-4b13-4039-9f76-8042bc9dbda3",
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"metadata": {},
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"outputs": [],
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"source": [
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"from optimization.gd import gradient_descent_1d, gradient_descent_2d"
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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": 3,
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"id": "0a5c51d2-8b18-4143-b6f1-73a909ccb623",
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||||
"metadata": {},
|
||||
"outputs": [
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||||
{
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||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "923a9d77eecb4d78ade9e3113cf636c0",
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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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"VBox(children=(HBox(children=(VBox(children=(Text(value='x**3 - x**(1/2)', description='Expression:', style=De…"
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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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||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "c2252623a38940f0a80471ec28e491d3",
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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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"Output()"
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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": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "778d4e34c4ae4b0d8f2f1b4e0d3c1173",
|
||||
"version_major": 2,
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"version_minor": 0
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||||
},
|
||||
"text/plain": [
|
||||
"Output()"
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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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"source": [
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"gd1 = gradient_descent_1d()"
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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": 4,
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"id": "15c6e757-cde3-422b-be7e-3f55b7752142",
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"metadata": {},
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"outputs": [
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{
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"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "298df33c058b49e6927e582d532bb87b",
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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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"VBox(children=(HBox(children=(VBox(children=(Text(value='(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2', description…"
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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": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "47315c498b9a46fd9948fd7a53d3e80a",
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||||
"version_major": 2,
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"version_minor": 0
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||||
},
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||||
"text/plain": [
|
||||
"Output()"
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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": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "0cab52875285496a989f685de24515cb",
|
||||
"version_major": 2,
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||||
"version_minor": 0
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},
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||||
"text/plain": [
|
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"Output()"
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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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"source": [
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"gd2 = gradient_descent_2d()"
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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": null,
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"id": "120ecde5-cee1-47c0-b1bc-c99b0cb1098e",
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||||
"metadata": {},
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||||
"outputs": [],
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||||
"source": []
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||||
}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.4"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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import copy
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import time
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import sympy
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import numpy as np
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from scipy.misc import derivative
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from sympy import symbols, sympify, lambdify, diff
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import ipywidgets as widgets
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from IPython.display import display, clear_output
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from tqdm import tqdm
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import plotly.graph_objects as go
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import plotly.io as pio
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pio.renderers.default = 'iframe' # or 'notebook' or 'colab' or 'jupyterlab'
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import warnings
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warnings.filterwarnings("ignore")
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class gradient_descent_1d(object):
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def __init__(self):
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self.wg_expr = widgets.Text(value="x**3 - x**(1/2)",
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description="Expression:",
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style={'description_width': 'initial'})
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self.wg_x0 = widgets.FloatText(value="2",
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description="Startpoint:",
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style={'description_width': 'initial'})
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self.wg_lr = widgets.FloatText(value="1e-1",
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description="learning rate:",
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style={'description_width': 'initial'})
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self.wg_epsilon = widgets.FloatText(value="1e-5",
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description="criterion:",
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style={'description_width': 'initial'})
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self.wg_max_iter = widgets.IntText(value="1000",
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description="max iteration",
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style={'description_width': 'initial'})
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self.button_compute = widgets.Button(description="Compute")
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self.button_plot = widgets.Button(description="Plot")
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self.compute_output = widgets.Output()
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self.plot_output = widgets.Output()
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self.params_lvbox = widgets.VBox([self.wg_expr, self.wg_x0, self.wg_lr])
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self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
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self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
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self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
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self.config = widgets.VBox([self.params_box, self.button_box],
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layout=widgets.Layout(
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display='flex',
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flex_flow='column',
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border='solid 2px',
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align_items='stretch',
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width='auto'
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))
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self.initialization()
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def initialization(self):
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display(self.config)
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self.button_compute.on_click(self.compute)
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display(self.compute_output)
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self.button_plot.on_click(self.plot)
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display(self.plot_output)
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def compute(self, *args):
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with self.compute_output:
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xn = self.wg_x0.value
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x = symbols("x")
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expr = sympify(self.wg_expr.value)
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f = lambdify(x, expr)
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df = lambdify(x, diff(expr, x))
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self.xn_list, self.df_list = [], []
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for n in tqdm(range(0, self.wg_max_iter.value)):
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gradient = df(xn)
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self.xn_list.append(xn)
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self.df_list.append(gradient)
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if abs (gradient < self.wg_epsilon.value):
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clear_output(wait=True)
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print("Found solution of {} after".format(expr), n, "iterations")
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print("x* = {}".format(xn))
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return None
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xn = xn - self.wg_lr.value * gradient
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clear_output(wait=True)
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display("Exceeded maximum iterations. No solution found.")
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return None
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def plot(self, *args):
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with self.plot_output:
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clear_output(wait=True)
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x0 = float(self.wg_x0.value)
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x = symbols("x")
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expr = sympify(self.wg_expr.value)
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f = lambdify(x, sympify(expr), "numpy")
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xx1 = np.arange(np.array(self.xn_list).min()*0.5, np.array(self.xn_list).max()*1.5, 0.05)
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fx = f(xx1)
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f_xn = f(np.array(self.xn_list))
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fig = go.Figure()
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fig.add_scatter(x=xx1, y=fx)
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frames = []
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frames.append({'data':copy.deepcopy(fig['data']),'name':f'frame{0}'})
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fig.add_traces(go.Scatter(x=None, y=None, mode="lines + markers", line={"color":"#de1032", "width":5}))
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frames = [go.Frame(data= [go.Scatter(x=np.array(self.xn_list)[:k], y=f_xn)],traces= [1],name=f'frame{k+2}')for k in range(len(f_xn))]
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fig.update(frames=frames)
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fig.update_layout(updatemenus=[dict(type="buttons",buttons=[dict(label="Play",method="animate",args=[None])])])
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fig.show()
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class gradient_descent_2d(object):
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def __init__(self):
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self.wg_expr = widgets.Text(value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2",
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description="Expression:") #style={'description_width': 'initial'})
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self.wg_x0 = widgets.Text(value="5,5",
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description="Startpoint:")
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self.wg_lr = widgets.FloatText(value="1e-1",
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description="learning rate:")
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self.wg_epsilon = widgets.FloatText(value="1e-5",
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description="criterion:")
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self.wg_max_iter = widgets.IntText(value="1000",
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description="max iteration")
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self.button_compute = widgets.Button(description="Compute")
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self.button_plot = widgets.Button(description="Plot")
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self.compute_output = widgets.Output()
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self.plot_output = widgets.Output()
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self.params_lvbox = widgets.VBox([self.wg_expr, self.wg_x0, self.wg_lr])
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self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
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self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
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self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
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self.config = widgets.VBox([self.params_box, self.button_box])
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self.initialization()
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def initialization(self):
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display(self.config)
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self.button_compute.on_click(self.compute)
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display(self.compute_output)
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self.button_plot.on_click(self.plot)
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display(self.plot_output)
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def compute(self, *args):
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with self.compute_output:
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x0 = np.array(self.wg_x0.value.split(","), dtype=float)
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xn = x0
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x1 = symbols("x1")
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x2 = symbols("x2")
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expr = sympify(self.wg_expr.value)
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self.xn_list, self.df_list = [], []
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for n in tqdm(range(0, self.wg_max_iter.value)):
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gradient = np.array([diff(expr, x1).subs(x1, xn[0]).subs(x2, xn[1]),
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diff(expr, x2).subs(x1, xn[0]).subs(x2, xn[1])], dtype=float)
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self.xn_list.append(xn)
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self.df_list.append(gradient)
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if np.linalg.norm(gradient, ord=2) < self.wg_epsilon.value:
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clear_output(wait=True)
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print("Found solution of {} after".format(expr), n, "iterations")
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print("x* = [{}, {}]".format(xn[0], xn[1]))
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return None
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xn = xn - self.wg_lr.value * gradient
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clear_output(wait=True)
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display("Exceeded maximum iterations. No solution found.")
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return None
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def plot(self, *args):
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with self.plot_output:
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clear_output(wait=True)
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x0 = np.array(self.wg_x0.value.split(","), dtype=float)
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x1 = symbols("x1")
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x2 = symbols("x2")
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expr = sympify(self.wg_expr.value)
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xx1 = np.arange(np.array(self.xn_list)[:, 0].min()*0.5, np.array(self.xn_list)[:, 0].max()*1.5, 0.05)
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xx2 = np.arange(np.array(self.xn_list)[:, 1].min()*0.5, np.array(self.xn_list)[:, 1].max()*1.5, 0.05)
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xx1, xx2 = np.meshgrid(xx1, xx2)
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f = lambdify((x1, x2), expr, "numpy")
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fx = f(xx1, xx2)
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f_xn = f(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1])
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fig = go.Figure()
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fig.add_surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.9)
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fig.update_traces(contours_z=dict(show=True, usecolormap=True, highlightcolor="limegreen", project_z=True))
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frames = []
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frames.append({'data':copy.deepcopy(fig['data']),'name':f'frame{0}'})
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line_marker=dict(color="#de1032", width=5)
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fig.add_traces(go.Scatter3d(x=None, y=None, z=None, mode='lines+markers', line={"color":"#de1032", "width":5}))
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frames = [go.Frame(data= [go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1],z=f_xn)],traces= [1],name=f'frame{k+2}')for k in range(len(f_xn))]
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fig.update(frames=frames)
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fig.update_layout(updatemenus=[dict(type="buttons",
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buttons=[dict(label="Play",
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method="animate",
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args=[None])])])
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fig.show()
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@ -0,0 +1,202 @@
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import copy
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import time
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import sympy
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import numpy as np
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from scipy.misc import derivative
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from sympy import symbols, sympify, lambdify, diff
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import ipywidgets as widgets
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from IPython.display import display, clear_output
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from tqdm import tqdm
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import plotly.graph_objects as go
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import plotly.io as pio
|
||||
pio.renderers.default = 'iframe' # or 'notebook' or 'colab' or 'jupyterlab'
|
||||
|
||||
import warnings
|
||||
warnings.filterwarnings("ignore")
|
||||
|
||||
class gradient_descent_1d(object):
|
||||
def __init__(self):
|
||||
self.wg_expr = widgets.Text(value="x**3 - x**(1/2)",
|
||||
description="Expression:",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_x0 = widgets.FloatText(value="2",
|
||||
description="Startpoint:",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_lr = widgets.FloatText(value="1e-1",
|
||||
description="learning rate:",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_epsilon = widgets.FloatText(value="1e-5",
|
||||
description="criterion:",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_max_iter = widgets.IntText(value="1000",
|
||||
description="max iteration",
|
||||
style={'description_width': 'initial'})
|
||||
|
||||
self.button_compute = widgets.Button(description="Compute")
|
||||
self.button_plot = widgets.Button(description="Plot")
|
||||
|
||||
self.compute_output = widgets.Output()
|
||||
self.plot_output = widgets.Output()
|
||||
self.params_lvbox = widgets.VBox([self.wg_expr, self.wg_x0, self.wg_lr])
|
||||
self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
|
||||
self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
|
||||
self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
|
||||
self.config = widgets.VBox([self.params_box, self.button_box],
|
||||
layout=widgets.Layout(
|
||||
display='flex',
|
||||
flex_flow='column',
|
||||
border='solid 2px',
|
||||
align_items='stretch',
|
||||
width='auto'
|
||||
))
|
||||
self.initialization()
|
||||
|
||||
|
||||
def initialization(self):
|
||||
display(self.config)
|
||||
self.button_compute.on_click(self.compute)
|
||||
display(self.compute_output)
|
||||
self.button_plot.on_click(self.plot)
|
||||
display(self.plot_output)
|
||||
|
||||
def compute(self, *args):
|
||||
with self.compute_output:
|
||||
xn = self.wg_x0.value
|
||||
x = symbols("x")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
f = lambdify(x, expr)
|
||||
df = lambdify(x, diff(expr, x))
|
||||
self.xn_list, self.df_list = [], []
|
||||
|
||||
for n in tqdm(range(0, self.wg_max_iter.value)):
|
||||
gradient = df(xn)
|
||||
self.xn_list.append(xn)
|
||||
self.df_list.append(gradient)
|
||||
if abs (gradient < self.wg_epsilon.value):
|
||||
clear_output(wait=True)
|
||||
print("Found solution of {} after".format(expr), n, "iterations")
|
||||
print("x* = {}".format(xn))
|
||||
return None
|
||||
xn = xn - self.wg_lr.value * gradient
|
||||
clear_output(wait=True)
|
||||
display("Exceeded maximum iterations. No solution found.")
|
||||
return None
|
||||
|
||||
def plot(self, *args):
|
||||
with self.plot_output:
|
||||
clear_output(wait=True)
|
||||
x0 = float(self.wg_x0.value)
|
||||
x = symbols("x")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
f = lambdify(x, sympify(expr), "numpy")
|
||||
xx1 = np.arange(np.array(self.xn_list).min()*0.5, np.array(self.xn_list).max()*1.5, 0.05)
|
||||
fx = f(xx1)
|
||||
f_xn = f(np.array(self.xn_list))
|
||||
|
||||
fig = go.Figure()
|
||||
fig.add_scatter(x=xx1, y=fx)
|
||||
frames = []
|
||||
frames.append({'data':copy.deepcopy(fig['data']),'name':f'frame{0}'})
|
||||
fig.add_traces(go.Scatter(x=None, y=None, mode="lines + markers", line={"color":"#de1032", "width":5}))
|
||||
frames = [go.Frame(data= [go.Scatter(x=np.array(self.xn_list)[:k], y=f_xn)],traces= [1],name=f'frame{k+2}')for k in range(len(f_xn))]
|
||||
fig.update(frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons",buttons=[dict(label="Play",method="animate",args=[None])])])
|
||||
fig.show()
|
||||
|
||||
|
||||
class gradient_descent_2d(object):
|
||||
def __init__(self):
|
||||
|
||||
self.wg_expr = widgets.Text(value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2",
|
||||
description="Expression:") #style={'description_width': 'initial'})
|
||||
self.wg_x0 = widgets.Text(value="5,5",
|
||||
description="Startpoint:")
|
||||
self.wg_lr = widgets.FloatText(value="1e-1",
|
||||
description="learning rate:")
|
||||
self.wg_epsilon = widgets.FloatText(value="1e-5",
|
||||
description="criterion:")
|
||||
self.wg_max_iter = widgets.IntText(value="1000",
|
||||
description="max iteration")
|
||||
self.button_compute = widgets.Button(description="Compute")
|
||||
self.button_plot = widgets.Button(description="Plot")
|
||||
|
||||
self.compute_output = widgets.Output()
|
||||
self.plot_output = widgets.Output()
|
||||
self.params_lvbox = widgets.VBox([self.wg_expr, self.wg_x0, self.wg_lr])
|
||||
self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
|
||||
self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
|
||||
self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
|
||||
self.config = widgets.VBox([self.params_box, self.button_box])
|
||||
self.initialization()
|
||||
|
||||
def initialization(self):
|
||||
display(self.config)
|
||||
self.button_compute.on_click(self.compute)
|
||||
display(self.compute_output)
|
||||
self.button_plot.on_click(self.plot)
|
||||
display(self.plot_output)
|
||||
|
||||
def compute(self, *args):
|
||||
with self.compute_output:
|
||||
x0 = np.array(self.wg_x0.value.split(","), dtype=float)
|
||||
xn = x0
|
||||
x1 = symbols("x1")
|
||||
x2 = symbols("x2")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
self.xn_list, self.df_list = [], []
|
||||
|
||||
for n in tqdm(range(0, self.wg_max_iter.value)):
|
||||
gradient = np.array([diff(expr, x1).subs(x1, xn[0]).subs(x2, xn[1]),
|
||||
diff(expr, x2).subs(x1, xn[0]).subs(x2, xn[1])], dtype=float)
|
||||
self.xn_list.append(xn)
|
||||
self.df_list.append(gradient)
|
||||
if np.linalg.norm(gradient, ord=2) < self.wg_epsilon.value:
|
||||
clear_output(wait=True)
|
||||
print("Found solution of {} after".format(expr), n, "iterations")
|
||||
print("x* = [{}, {}]".format(xn[0], xn[1]))
|
||||
return None
|
||||
xn = xn - self.wg_lr.value * gradient
|
||||
clear_output(wait=True)
|
||||
display("Exceeded maximum iterations. No solution found.")
|
||||
return None
|
||||
|
||||
def plot(self, *args):
|
||||
with self.plot_output:
|
||||
clear_output(wait=True)
|
||||
x0 = np.array(self.wg_x0.value.split(","), dtype=float)
|
||||
x1 = symbols("x1")
|
||||
x2 = symbols("x2")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
xx1 = np.arange(np.array(self.xn_list)[:, 0].min()*0.5, np.array(self.xn_list)[:, 0].max()*1.5, 0.05)
|
||||
xx2 = np.arange(np.array(self.xn_list)[:, 1].min()*0.5, np.array(self.xn_list)[:, 1].max()*1.5, 0.05)
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
|
||||
f = lambdify((x1, x2), expr, "numpy")
|
||||
fx = f(xx1, xx2)
|
||||
f_xn = f(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1])
|
||||
|
||||
fig = go.Figure()
|
||||
fig.add_surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.9)
|
||||
fig.update_traces(contours_z=dict(show=True, usecolormap=True, highlightcolor="limegreen", project_z=True))
|
||||
|
||||
frames = []
|
||||
frames.append({'data':copy.deepcopy(fig['data']),'name':f'frame{0}'})
|
||||
|
||||
line_marker=dict(color="#de1032", width=5)
|
||||
fig.add_traces(go.Scatter3d(x=None, y=None, z=None, mode='lines+markers', line={"color":"#de1032", "width":5}))
|
||||
|
||||
frames = [go.Frame(data= [go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1],z=f_xn)],traces= [1],name=f'frame{k+2}')for k in range(len(f_xn))]
|
||||
fig.update(frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons",
|
||||
buttons=[dict(label="Play",
|
||||
method="animate",
|
||||
args=[None])])])
|
||||
fig.show()
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue