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{
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"cells": [
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{
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"cell_type": "markdown",
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||||
"id": "b705b060",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
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||||
}
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||||
},
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"source": [
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"# Steepest Descent Method\n",
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"\n",
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"Instructor: Dr.Yuhui Deng\n",
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"\n",
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""
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]
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},
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||||
{
|
||||
"cell_type": "markdown",
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||||
"id": "f576c3bd",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "subslide"
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||||
}
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||||
},
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"source": [
|
||||
"## Problem Description\n",
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"\n",
|
||||
"Problem: \n",
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"\n",
|
||||
"$\\begin{align*} \n",
|
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"min(fx) \\\\\n",
|
||||
"s.t. \\ x \\in \\mathbb{R}^n\n",
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"\\end{align*}$\n",
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"where\n",
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"\n",
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"* $f: \\mathbb{R}^n \\rightarrow \\mathbb{R}$\n",
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"* No constraints are placed on the variables $X$\n"
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]
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},
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{
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||||
"cell_type": "markdown",
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"id": "c6e94df1",
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||||
"metadata": {
|
||||
"slideshow": {
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||||
"slide_type": "slide"
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||||
}
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||||
},
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"source": [
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"# One Dimential Function\n",
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"\n",
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"$$min \\ f(x)=x^2 - 4x + 7$$\n",
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"\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": 4,
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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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|
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@ -12,283 +66,132 @@
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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||||
"execution_count": null,
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||||
"id": "8ce3dbbd-a698-448b-a2c6-772286c745d5",
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||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "f63728b9362047df80c1bf76167f6bf5",
|
||||
"version_major": 2,
|
||||
"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='-2 * x * sin(-(pi/4) * x)+10', description='Expressio…"
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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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||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "2ded251d4d034c058f83d613618e3a7d",
|
||||
"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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||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "b9e00497c1cd4bc484bf7ea793aa3d78",
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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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"outputs": [],
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"source": [
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"gd1 = gd_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": 6,
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"execution_count": null,
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"id": "a1765810-6cd8-4e1a-aaa6-7691a7b2a42e",
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||||
"metadata": {},
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||||
"outputs": [
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||||
{
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||||
"data": {
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||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "4101fea885e6435e8283e6da6f4f68e9",
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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=(Dropdown(options=(('(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x…"
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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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||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "1a7d3fe1bd72408684d18ad75e2754ce",
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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": {
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||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "be733631b99b4b09939ed99c1723b03b",
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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": {
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||||
"application/vnd.jupyter.widget-view+json": {
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||||
"model_id": "41c863b04c314bbd8df1353e7fc92ec1",
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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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"outputs": [],
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"source": [
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"gd2 = gd_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": 7,
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"id": "88e5e47f-3a02-4919-a74e-a4758c56390a",
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"execution_count": null,
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"id": "06b73a46-f6d5-420d-a668-abaf2c6127a3",
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"metadata": {},
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"outputs": [],
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"source": [
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"expr = sympify(gd2.wg_expr.value)"
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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": "e7504cf8-514c-444a-bd62-91a13b067cf6",
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"metadata": {},
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||||
"outputs": [],
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"source": [
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"expr"
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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": "ff3f9fa9-9071-45c5-a939-d5f0bbe7b37e",
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy import *\n",
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"from sympy.abc import x\n",
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"expr = \"(x - 2)**2 + 3\"\n",
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"ex = sympify(expr)\n",
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"solve(ex, x)"
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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": 1,
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"id": "61e0d2b8-41c8-4790-8b25-2df6ba4c3625",
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"metadata": {},
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"outputs": [],
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"source": [
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"from optimization.common import *"
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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": 2,
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"id": "cc84e26c-7135-427b-9a5b-c39b6b495fe5",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle \\operatorname{Plane}\\left(\\operatorname{Point3D}\\left(1, 1, 1\\right), \\left( 1, \\ 4, \\ 7\\right)\\right)$"
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],
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"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "e2a6bc45f7354f529c8475f034416135",
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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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"Plane(Point3D(1, 1, 1), (1, 4, 7))"
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"VBox(children=(HBox(children=(Text(value='-2 * x * sin(-(pi/4) * x)+10', description='Expression:', style=Text…"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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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": "c2c3118f55d241e68649a094a6bb3836",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"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": "cdc830df33fe4705b448245a1d64c335",
|
||||
"version_major": 2,
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||||
"version_minor": 0
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||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
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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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||||
"from sympy import Plane, Point3D\n",
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"Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))\n",
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"Plane((1, 1, 1), (2, 3, 4), (2, 2, 2))\n",
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"Plane(Point3D(1, 1, 1), normal_vector=(1,4,7))"
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||||
"a = func_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": null,
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||||
"id": "b0563398-5a79-47aa-9c31-474a518daa0d",
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||||
"metadata": {},
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||||
"outputs": [],
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||||
"source": [
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||||
"from sympy import Point3D, Plane\n",
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"a = Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))\n",
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"a.normal_vector\n",
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"a = Plane(Point3D(1, 1, 1), normal_vector=(1, 4, 7))\n",
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"a.normal_vector"
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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": "cf7ed01e-f42a-4a3d-8c2f-e0e7dfa682c5",
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"metadata": {},
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||||
"outputs": [],
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||||
"source": [
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"from sympy.vector import CoordSys3D, gradient\n",
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"from sympy import symbols, sympify, lambdify, diff\n",
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"expr = sympify(\"(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)\")\n",
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"x1, x2 = symbols(\"x1\"), symbols(\"x2\")\n",
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"gradient(expr)"
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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": "bdbceb9a-42f0-42e3-a2cb-573b4d82e4af",
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"metadata": {},
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"outputs": [],
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||||
"source": [
|
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"from sympy.vector import CoordSys3D\n",
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"R = CoordSys3D('R')\n",
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"v = (1 - 8*R.x +7*R.x**2 - (7/3)*R.x**3 + (1/4 * R.x**4) * R.y**2 * np.exp(1)**(-R.y))"
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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": "af76a657-c281-41b4-83c3-c3f73376d948",
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"metadata": {},
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"outputs": [],
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||||
"source": [
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"from sympy.vector import CoordSys3D, Del\n",
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"R = CoordSys3D('R')\n",
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"delop = Del()\n",
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"gradient_field = delop((1 - 8*R.x +7*R.x**2 - (7/3)*R.x**3 + (1/4 * R.x**4) * R.y**2 * np.exp(1)**(-R.y)))\n",
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"gradient_field"
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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": "d987886f-1231-487a-88dc-47e8a45d728c",
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"metadata": {},
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"outputs": [],
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"source": [
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"import sympy\n",
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"\n",
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"#define symbolic vars, function\n",
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"x,y=sympy.symbols('x y')\n",
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"fun= sympify(\"(1 - 8 * x + 7 * x**2 - (7/3) * x**3 + (1/4) * x**4) * y**2 * E**(-y)\")\n",
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"#fun=3*x**2-5*y**2\n",
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"#take the gradient symbolically\n",
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"gradfun=[sympy.diff(fun,var) for var in (x1,x2)]\n",
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"numgradfun=sympy.lambdify([x,y],gradfun)\n",
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"graddat=numgradfun(xx1_o,xx2_o)"
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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": "da34c7be-025f-4326-8138-9e78e2043b7e",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import plotly.figure_factory as ff\n",
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"import math\n",
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"\n",
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"X,Y=np.meshgrid(np.arange(0,5, 0.25),np.arange(0,5, 0.25))\n",
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"graddat=numgradfun(X,Y)\n",
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"\n",
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"\n",
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"fig = ff.create_quiver(X, Y, graddat[0], graddat[1],scale=.05, arrow_scale=.1, angle=math.pi/6)\n",
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"fig.update_traces(line_color=\"red\")\n",
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"fig.update_layout(height=800)\n",
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"fig.show()"
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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": "62504d86-9dc8-42b2-b052-d7acfe8be5e0",
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"metadata": {},
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"outputs": [],
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||||
"source": [
|
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"fig.data[0][\"x\"]"
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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": "415a2abd-3ea4-48ee-9923-c9897105ad27",
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||||
"metadata": {},
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||||
"outputs": [],
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||||
"source": [
|
||||
"import numpy as np\n",
|
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"import matplotlib.pyplot as plt\n",
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"\n",
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"X,Y=np.meshgrid(np.arange(0,5, 0.1),np.arange(0,5,0.1))\n",
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"graddat=numgradfun(X,Y)\n",
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"\n",
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"plt.figure()\n",
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"plt.quiver(X,Y,graddat[0],graddat[1])\n",
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"plt.show()"
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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": "2c60be92-8c74-4f46-b7fc-bb9d7150cbe0",
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"id": "98061d97-555e-486a-a07d-1b8c37cd2471",
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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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"celltoolbar": "Slideshow",
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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{
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"cells": [
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{
|
||||
"cell_type": "markdown",
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||||
"id": "b705b060",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
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||||
}
|
||||
},
|
||||
"source": [
|
||||
"# Steepest Descent Method\n",
|
||||
"\n",
|
||||
"Instructor: Dr.Yuhui Deng\n",
|
||||
"\n",
|
||||
""
|
||||
]
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||||
},
|
||||
{
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||||
"cell_type": "markdown",
|
||||
"id": "f576c3bd",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "subslide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"## Problem Description\n",
|
||||
"\n",
|
||||
"Problem: \n",
|
||||
"\n",
|
||||
"$\\begin{align*} \n",
|
||||
"min(fx) \\\\\n",
|
||||
"s.t. \\ x \\in \\mathbb{R}^n\n",
|
||||
"\\end{align*}$\n",
|
||||
"where\n",
|
||||
"\n",
|
||||
"* $f: \\mathbb{R}^n \\rightarrow \\mathbb{R}$\n",
|
||||
"* No constraints are placed on the variables $X$\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "c6e94df1",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"# One Dimential Function\n",
|
||||
"\n",
|
||||
"$$min \\ f(x)=x^2 - 4x + 7$$\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"execution_count": null,
|
||||
"id": "af1d5646-4b13-4039-9f76-8042bc9dbda3",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
|
|
@ -12,120 +66,20 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"execution_count": null,
|
||||
"id": "8ce3dbbd-a698-448b-a2c6-772286c745d5",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "5715c7beff3c4ab58a001fecee2e6ba9",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(VBox(children=(Text(value='-2 * x * sin(-(pi/4) * x)+10', description='Expressio…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "60025f1dfc974c4ba4765136faa526e8",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "52d1cde962ba4b7dad5c4e581fc5aee1",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"gd1 = gd_1d()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"execution_count": null,
|
||||
"id": "a1765810-6cd8-4e1a-aaa6-7691a7b2a42e",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "f6ef2a67373b4552b4d866c633e8b9a7",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(Dropdown(options=(('(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "ece751b11bc643a196bc17d87d90499e",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "17c95b2c789044439b3e4412a41cdff4",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "8452902c477d4e25a51e0cb937babf6e",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"gd2 = gd_2d()"
|
||||
]
|
||||
|
|
@ -133,13 +87,111 @@
|
|||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "48944e3c-932a-4733-b77d-a2b50cee2e5a",
|
||||
"id": "06b73a46-f6d5-420d-a668-abaf2c6127a3",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"expr = sympify(gd2.wg_expr.value)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "e7504cf8-514c-444a-bd62-91a13b067cf6",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"expr"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "ff3f9fa9-9071-45c5-a939-d5f0bbe7b37e",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from sympy import *\n",
|
||||
"from sympy.abc import x\n",
|
||||
"expr = \"(x - 2)**2 + 3\"\n",
|
||||
"ex = sympify(expr)\n",
|
||||
"solve(ex, x)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"id": "61e0d2b8-41c8-4790-8b25-2df6ba4c3625",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from optimization.common import *"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"id": "cc84e26c-7135-427b-9a5b-c39b6b495fe5",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "e2a6bc45f7354f529c8475f034416135",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(Text(value='-2 * x * sin(-(pi/4) * x)+10', description='Expression:', style=Text…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "c2c3118f55d241e68649a094a6bb3836",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "cdc830df33fe4705b448245a1d64c335",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"a = func_1d()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "98061d97-555e-486a-a07d-1b8c37cd2471",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"celltoolbar": "Slideshow",
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3 (ipykernel)",
|
||||
"language": "python",
|
||||
|
|
|
|||
|
|
@ -0,0 +1,506 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "9b492ee6",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"# Steepest Descent Method\n",
|
||||
"\n",
|
||||
"Instructor: Dr.Yuhui Deng"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"id": "2472b8ca",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "f7a7d3f014ca4f599b561ca1e4e5e9ff",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(Text(value='x1^2 + x2^2', description='Expression:', style=TextStyle(description…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "5739708475934a0aa0fc6172f98ec6be",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<optimization.common.contourPlot2d at 0x147a89a30>"
|
||||
]
|
||||
},
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"from optimization.common import *\n",
|
||||
"contourPlot2d(environ=\"notebook\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "1d34025b",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"## Problem Description\n",
|
||||
"\n",
|
||||
"$\\textbf{Problem:}\\left\\{\\begin{align*}\n",
|
||||
"\\min \\ f(x) \\\\\n",
|
||||
"s.t. \\ x \\in \\mathbb{R}^n\n",
|
||||
"\\end{align*} \\right.$\n",
|
||||
"\n",
|
||||
"where: \n",
|
||||
"* $f: \\mathbb{R}^n \\mapsto \\mathbb{R}$\n",
|
||||
"* No constraints are placed on the variables $x$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "6f867a65",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"### One Dimentional Function\n",
|
||||
"\n",
|
||||
"$$\\min \\ f(x) = x^2 - 4x + 7$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"id": "302d9c60",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "fragment"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "cf33688620c54a4d85cb0f9dbce63fe3",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(Text(value='(x - 2)**2 + 3', description='Expression:', style=TextStyle(descript…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "aa0a66db4d33470fbe7a091588bb27a6",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "3a84ef2c3bd14854b81d4cb48005991f",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<optimization.common.funcPlot1d at 0x1674d2eb0>"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"funcPlot1d(environ=\"notebook\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "e2ce7e95",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "fragment"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"$$x_{k+1} = x_{k} + a \\cdot d \\quad d = \\left\\{\\begin{align*} +1 &\\text{ left} \\\\ -1 &\\text{ right}\\end{align*}\\right. \\ a \\geq 0$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"id": "a4827f0c",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "578d548bc16c45caa29f47f60b58acf0",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(VBox(children=(Text(value='sin(x) + sin((10.0 / 3.0) * x)', description='Express…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "ead520028b844ef78e0932d537ac7172",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "16060b8b5ae04f31833395b3b1f4259c",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<optimization.gd_new.gd_1d at 0x1675023a0>"
|
||||
]
|
||||
},
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"gd_1d(environ=\"notebook\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "f55e58dd",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"### Multi Dimentional Function\n",
|
||||
"\n",
|
||||
"$$(1 - 8 \\cdot x_1 + 7 \\cdot x_1^2 - \\frac{7x_{1}^{3}}{3} + \\frac{x^{4}}{4}) \\cdot x_2^2 \\cdot e^{(-x_2)}$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"id": "7c589589",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "fragment"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "5d9c8974d7c04f4dbdb7aa333ae7d172",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(Text(value='(1 - 8 * x1 + 7 * x1^2 - (7/3) * x1^3 + (1/4) * x1^4) * x2^2 * E^(-x…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "909764ee6cd94053a17da64592bb11e5",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "ba448ff14b8f454b8f4b6d3cb8f92c9e",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<optimization.common.funcPlot2d at 0x167583b50>"
|
||||
]
|
||||
},
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"funcPlot2d(environ=\"notebook\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "1a5b2203",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "subslide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"Some Questions:\n",
|
||||
"\n",
|
||||
"1. How many choices for the searching direction?\n",
|
||||
"2. Which direction will you choose?\n",
|
||||
"3. How far will you walk?\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"id": "f28bd167",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "subslide"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "bd08d4c9d0014062a1e0654177dfbd55",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"VBox(children=(HBox(children=(Dropdown(options=(('(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "26123777d5214fa28d4bfd16d9afe3b8",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "176568fccd1f49d79abc66fff51859d6",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "7f1d7ace2eef4a5480c72444f52fd4c1",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Output()"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<optimization.gd_new.gd_2d at 0x167c26b20>"
|
||||
]
|
||||
},
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"gd_2d(environ=\"notebook\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d585d6de",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "subslide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"### Multi Dimentional Function\n",
|
||||
"\n",
|
||||
"**Descent Direction** If a direction vector $d$ has the property that at least for sufficiently small $\\alpha > 0$, \n",
|
||||
"$$f(x + \\alpha d) < f(x)$$\n",
|
||||
"then $d$ is said a **descent direction** for function $f$ at point $x$."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "3adf3a40",
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "subslide"
|
||||
}
|
||||
},
|
||||
"source": [
|
||||
"### Multi Dimentional Function\n",
|
||||
"\n",
|
||||
"梯度取极值"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "49f800ef",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Multi Dimentional Function\n",
|
||||
"\n",
|
||||
"**When exact line search is used**, the steepest descent method obtains\n",
|
||||
"$$x^{k+1} = x^{k} - \\alpha_{k} \\nabla f(x^k)$$\n",
|
||||
"where $\\alpha_k$ is the solution of the one-dimensional minimization problem: \n",
|
||||
"$$\\min_{\\alpha > 0} F(\\alpha) \\equiv f(x^{k} - \\alpha \\nabla f(x^k))$$\n",
|
||||
"So,\n",
|
||||
"$$\\begin{align*}F^{\\prime} = 0 \\Rightarrow - \\nabla f(x^k - \\alpha_k \\nabla f(x^k))^T \\nabla f(x^k) = 0 \\\\\n",
|
||||
"\\Rightarrow \\nabla f(x^{k+1})^T \\nabla f(x^k) = 0\n",
|
||||
"\\end{align*}$$\n",
|
||||
"\n",
|
||||
"This means that **every pair of $\\nabla f(x^{k+1})$ and $\\nabla f(x^k)$ are vertical.** Hence $\\{x^k\\}$ usually takes a zigzag path to approach the solution $x^{*}$. By this fact, we may better understand the reason why steepest descent method progresses slowly when the contours of $f$ are flat, see Section 4.7 (Appendix 2)."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "1b5fb35c",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"celltoolbar": "Slideshow",
|
||||
"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
|
||||
}
|
||||
|
|
@ -1,138 +0,0 @@
|
|||
import copy
|
||||
import time
|
||||
import sympy
|
||||
import numpy as np
|
||||
from scipy.misc import derivative
|
||||
from sympy import symbols, sympify, lambdify, diff
|
||||
|
||||
import ipywidgets as widgets
|
||||
from IPython.display import display, clear_output
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import plotly.graph_objects as go
|
||||
import plotly.io as pio
|
||||
|
||||
import warnings
|
||||
warnings.filterwarnings("ignore")
|
||||
|
||||
|
||||
class gradient_descent_2d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Dropdown(options=[("(sin(x1) - 2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) + (sin(x2) - 2) ** 2"),
|
||||
("(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2"),
|
||||
("(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2")],
|
||||
value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", descrption="Expression")
|
||||
self.wg_x0 = widgets.Text(value="5,5",
|
||||
description="Startpoint:")
|
||||
self.wg_lr = widgets.FloatText(value="1e-1",
|
||||
description="step size:")
|
||||
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_x0, self.wg_lr])
|
||||
self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
|
||||
self.exp_box = widgets.HBox([self.wg_expr])
|
||||
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.exp_box, 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, 0.1)
|
||||
xx2 = np.arange(np.array(self.xn_list)[:, 1].min() * 0.5, np.array(self.xn_list)[:, 1].max() * 1.5, 0.1)
|
||||
xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1)
|
||||
xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1)
|
||||
xx1_o, xx2_o = xx1, xx2
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
xx1_tangent, xx2_tangent = np.meshgrid(xx1_tangent, xx2_tangent)
|
||||
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])
|
||||
partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
|
||||
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
|
||||
plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn
|
||||
z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
|
||||
|
||||
frames, steps = [], []
|
||||
for k in range(len(f_xn)):
|
||||
tmp_trace1 = go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn)
|
||||
tmp_trace2 = go.Surface(x=xx1_tangent, y=xx2_tangent, z=z[k], showscale=True, opacity=0.5)
|
||||
frame = go.Frame(dict(data=[tmp_trace1, tmp_trace2], name=f'frame{k+1}'), traces=[1, 2])
|
||||
frames.append(frame)
|
||||
step = dict(
|
||||
method="update",
|
||||
args=[{"visible": [True]},
|
||||
{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
|
||||
)
|
||||
steps.append(step)
|
||||
|
||||
sliders = [dict(steps= [dict(method= 'animate',
|
||||
args= [[f'frame{k+1}'],
|
||||
dict(mode= 'immediate',
|
||||
frame= dict( duration=0, redraw= True ),
|
||||
transition=dict( duration=0)
|
||||
)
|
||||
],
|
||||
#label='Date : {}'.format(date_range[k])
|
||||
) for k in range(0,len(frames))],
|
||||
transition= dict(duration=0),
|
||||
x=0,
|
||||
y=0,
|
||||
currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
|
||||
len=1.0)
|
||||
]
|
||||
|
||||
trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=False, opacity=0.6)
|
||||
trace2 = go.Scatter3d(x=None, y=None, z=None)
|
||||
fig = go.Figure(data=[trace1, trace2], frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
|
||||
dict(label="Pause", method="animate", args=[[None], \
|
||||
dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
|
||||
margin=dict(r=20, l=10, b=10, t=10), sliders=sliders)
|
||||
fig.show()
|
||||
|
|
@ -0,0 +1,188 @@
|
|||
import math
|
||||
import copy
|
||||
import time
|
||||
import sympy
|
||||
import numpy as np
|
||||
from scipy.misc import derivative
|
||||
from sympy import symbols, sympify, lambdify, diff, solve
|
||||
|
||||
import ipywidgets as widgets
|
||||
from IPython.display import Image, display, clear_output
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
import plotly.io as pio
|
||||
import plotly.graph_objects as go
|
||||
import plotly.figure_factory as ff
|
||||
|
||||
class funcPlot1d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Text(value="(x - 2)**2 + 3",
|
||||
description="Expression:",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_x_range = widgets.Text(value="-10,10",
|
||||
description="X-axis range",
|
||||
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_box = widgets.HBox([self.wg_expr, self.wg_x_range])
|
||||
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:
|
||||
x = symbols("x")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
f = lambdify(x, expr)
|
||||
clear_output(wait=True)
|
||||
print(solve(expr, x))
|
||||
|
||||
|
||||
def plot(self, *args):
|
||||
with self.plot_output:
|
||||
fig = go.Figure()
|
||||
x_range = np.array(self.wg_x_range.value.split(","), dtype=float)
|
||||
x_num = np.arange(x_range[0], x_range[1], 0.1)
|
||||
expr = sympify(self.wg_expr.value)
|
||||
x = symbols("x")
|
||||
f = lambdify(x, expr)
|
||||
fx = f(x_num)
|
||||
fig.add_scatter(x=x_num, y=fx)
|
||||
clear_output(wait=True)
|
||||
fig.show()
|
||||
|
||||
class funcPlot2d(object):
|
||||
def __init__(self, environ:str="jupyterlab", type="default"):
|
||||
if type == "default":
|
||||
self.initialization_default(environ=environ)
|
||||
self.user_step = 1
|
||||
elif type == "custom":
|
||||
self.initlization_custom()
|
||||
self.compute_custom()
|
||||
else:
|
||||
return None
|
||||
def initialization_default(self, environ):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Text(value="(1 - 8 * x1 + 7 * x1^2 - (7/3) * x1^3 + (1/4) * x1^4) * x2^2 * E^(-x2)",
|
||||
description="Expression:",
|
||||
style={'description_width': 'initial'})
|
||||
self.button_plot_default = widgets.Button(description="3D Plot")
|
||||
|
||||
self.compute_output = widgets.Output()
|
||||
self.plot_default_output = widgets.Output()
|
||||
self.plot_contour_output = widgets.Output()
|
||||
self.exp_box = widgets.HBox([self.wg_expr])
|
||||
self.button_box = widgets.HBox([self.button_plot_default], description="operations")
|
||||
self.config = widgets.VBox([self.exp_box, self.button_box])
|
||||
display(self.config)
|
||||
|
||||
display(self.compute_output)
|
||||
self.button_plot_default.on_click(self.plot_default)
|
||||
img1 = self.plot_default_output
|
||||
display(img1)
|
||||
|
||||
def plot_default(self, *args):
|
||||
with self.plot_default_output:
|
||||
clear_output(wait=True)
|
||||
x1 = symbols("x1")
|
||||
x2 = symbols("x2")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
xx1 = np.arange(0, 5, 0.25)
|
||||
xx2 = np.arange(0, 5, 0.25)
|
||||
xx1_o, xx2_o = xx1, xx2
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
xx1_tangent, xx2_tangent = np.meshgrid(xx1_o, xx2_o)
|
||||
#xx1_tangent, xx2_tangent = array_mesh(np.arange(0, 5, 0.25), 10), array_mesh(np.arange(0, 5, 0.25), 10)
|
||||
f = lambdify((x1, x2), expr, "numpy")
|
||||
fx = f(xx1, xx2)
|
||||
## projection
|
||||
z_offset = (np.min(fx)) * np.ones(fx.shape)
|
||||
proj_z = lambda x, y, z: z
|
||||
colorsurfz = proj_z(xx1, xx2, fx)
|
||||
|
||||
from plotly.subplots import make_subplots
|
||||
fig = make_subplots(rows=1, cols=1, specs=[[{'type': 'surface'}]])
|
||||
fig.add_trace(go.Surface(contours = {"x": {"show": True}, "y":{"show": True}, "z":{"show": True}}, x=xx1, y=xx2, z=fx), row=1, col=1)
|
||||
fig.add_trace(go.Scatter3d(x=None, y=None, z=None), row=1, col=1)
|
||||
fig.add_trace(go.Surface(x=None, y=None, z=None, showlegend=False, showscale=False, colorscale='Blues'), row=1, col=1)
|
||||
frames = [go.Frame(data=[go.Surface(visible=True, showscale=False, opacity=0.8)],
|
||||
traces=[0])]
|
||||
fig.frames = frames
|
||||
self.fig_frames = frames
|
||||
|
||||
fig.update_layout(height=600, scene_aspectmode='manual', scene_aspectratio=dict(x=0, y=0, z=0), updatemenus=[dict(type="buttons")])
|
||||
fig.update_scenes(xaxis_visible=False,
|
||||
yaxis_visible=False,
|
||||
zaxis_visible=False)
|
||||
fig.update_scenes(camera_projection_type = "orthographic")
|
||||
fig.show()
|
||||
|
||||
class contourPlot2d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Text(value="x1^2 + x2^2",
|
||||
description="Expression:",
|
||||
style={'description_width': 'initial'})
|
||||
|
||||
self.button_plot = widgets.Button(description="Plot")
|
||||
|
||||
self.plot_output = widgets.Output()
|
||||
|
||||
self.params_box = widgets.HBox([self.wg_expr])
|
||||
self.button_box = widgets.HBox([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_plot.on_click(self.plot)
|
||||
display(self.plot_output)
|
||||
|
||||
|
||||
def plot(self, *args):
|
||||
with self.plot_output:
|
||||
clear_output(wait=True)
|
||||
x1 = symbols("x1")
|
||||
x2 = symbols("x2")
|
||||
expr = sympify(self.wg_expr.value)
|
||||
xx1 = np.arange(-5, 5, 0.5)
|
||||
xx2 = np.arange(-5, 5, 0.5)
|
||||
xx1_o, xx2_o = xx1, xx2 #np.arange(-5, 5, 0.5), np.arange(-5, 5, 0.5)
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
f = lambdify((x1, x2), expr, "numpy")
|
||||
fx = f(xx1, xx2)
|
||||
partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
|
||||
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
|
||||
|
||||
gradfun=[sympy.diff(expr,var) for var in (x1,x2)]
|
||||
numgradfun=sympy.lambdify([x1,x2], gradfun)
|
||||
x1_mesh, x2_mesh = np.meshgrid(xx1_o, xx2_o)
|
||||
graddat=numgradfun(x1_mesh, x2_mesh)
|
||||
|
||||
vec_field = ff.create_quiver(x1_mesh, x2_mesh, graddat[0], graddat[1], scale=.05, arrow_scale=.1, angle=math.pi/4)
|
||||
vec_field.update_traces(line_color="black")
|
||||
fig = go.Figure()
|
||||
fig.add_trace(go.Contour(x=xx1_o, y=xx2_o, z=fx))
|
||||
for d in vec_field.data:
|
||||
fig.add_trace(go.Scatter(visible=False, x=d['x'], y=d['y'], line_color="black"))
|
||||
fig.update_layout(
|
||||
updatemenus=[dict(type = "buttons",direction = "left",
|
||||
buttons=list([
|
||||
dict(args=[{"visible":["True", "True"]}], label="Gradient", method="update")]))], height=800)
|
||||
fig.show()
|
||||
|
|
@ -1,138 +0,0 @@
|
|||
import copy
|
||||
import time
|
||||
import sympy
|
||||
import numpy as np
|
||||
from scipy.misc import derivative
|
||||
from sympy import symbols, sympify, lambdify, diff
|
||||
|
||||
import ipywidgets as widgets
|
||||
from IPython.display import display, clear_output
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import plotly.graph_objects as go
|
||||
import plotly.io as pio
|
||||
|
||||
import warnings
|
||||
warnings.filterwarnings("ignore")
|
||||
|
||||
|
||||
class gradient_descent_2d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Dropdown(options=[("(sin(x1) - 2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) + (sin(x2) - 2) ** 2"),
|
||||
("(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2"),
|
||||
("(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2")],
|
||||
value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", descrption="Expression")
|
||||
self.wg_x0 = widgets.Text(value="5,5",
|
||||
description="Startpoint:")
|
||||
self.wg_lr = widgets.FloatText(value="1e-1",
|
||||
description="step size:")
|
||||
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_x0, self.wg_lr])
|
||||
self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
|
||||
self.exp_box = widgets.HBox([self.wg_expr])
|
||||
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.exp_box, 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, 0.1)
|
||||
xx2 = np.arange(np.array(self.xn_list)[:, 1].min() * 0.5, np.array(self.xn_list)[:, 1].max() * 1.5, 0.1)
|
||||
xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1)
|
||||
xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1)
|
||||
xx1_o, xx2_o = xx1, xx2
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
xx1_tangent, xx2_tangent = np.meshgrid(xx1_tangent, xx2_tangent)
|
||||
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])
|
||||
partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
|
||||
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
|
||||
plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn
|
||||
z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
|
||||
|
||||
frames, steps = [], []
|
||||
for k in range(len(f_xn)):
|
||||
tmp_trace1 = go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn)
|
||||
tmp_trace2 = go.Surface(x=xx1_tangent, y=xx2_tangent, z=z[k], showscale=True, opacity=0.5)
|
||||
frame = go.Frame(dict(data=[tmp_trace1, tmp_trace2], name=f'frame{k+1}'), traces=[1, 2])
|
||||
frames.append(frame)
|
||||
step = dict(
|
||||
method="update",
|
||||
args=[{"visible": [True]},
|
||||
{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
|
||||
)
|
||||
steps.append(step)
|
||||
|
||||
sliders = [dict(steps= [dict(method= 'animate',
|
||||
args= [[f'frame{k+1}'],
|
||||
dict(mode= 'immediate',
|
||||
frame= dict( duration=0, redraw= True ),
|
||||
transition=dict( duration=0)
|
||||
)
|
||||
],
|
||||
#label='Date : {}'.format(date_range[k])
|
||||
) for k in range(0,len(frames))],
|
||||
transition= dict(duration=0),
|
||||
x=0,
|
||||
y=0,
|
||||
currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
|
||||
len=1.0)
|
||||
]
|
||||
|
||||
trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=False, opacity=0.6)
|
||||
trace2 = go.Scatter3d(x=None, y=None, z=None)
|
||||
fig = go.Figure(data=[trace1, trace2], frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
|
||||
dict(label="Pause", method="animate", args=[[None], \
|
||||
dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
|
||||
margin=dict(r=20, l=10, b=10, t=10), sliders=sliders)
|
||||
fig.show()
|
||||
|
|
@ -1,101 +0,0 @@
|
|||
import copy
|
||||
import time
|
||||
import sympy
|
||||
import numpy as np
|
||||
from scipy.misc import derivative
|
||||
from sympy import symbols, sympify, lambdify, diff
|
||||
|
||||
import ipywidgets as widgets
|
||||
from IPython.display import display, clear_output
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import plotly.graph_objects as go
|
||||
import plotly.io as pio
|
||||
|
||||
import warnings
|
||||
warnings.filterwarnings("ignore")
|
||||
|
||||
class gradient_descent_1d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
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="step size:",
|
||||
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])
|
||||
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()
|
||||
|
|
@ -1,489 +0,0 @@
|
|||
import copy
|
||||
import time
|
||||
import sympy
|
||||
import numpy as np
|
||||
from scipy.misc import derivative
|
||||
from sympy import symbols, sympify, lambdify, diff
|
||||
|
||||
import ipywidgets as widgets
|
||||
from IPython.display import display, clear_output
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import plotly.graph_objects as go
|
||||
import plotly.io as pio
|
||||
|
||||
import warnings
|
||||
warnings.filterwarnings("ignore")
|
||||
|
||||
class gradient_descent_1d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
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="step size:",
|
||||
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])
|
||||
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, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Dropdown(options=[("(sin(x1) - 2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) + (sin(x2) - 2) ** 2"),
|
||||
("(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2"),
|
||||
("(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2")],
|
||||
value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", descrption="Expression")
|
||||
self.wg_x0 = widgets.Text(value="5,5",
|
||||
description="Startpoint:")
|
||||
self.wg_lr = widgets.FloatText(value="1e-1",
|
||||
description="step size:")
|
||||
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_x0, self.wg_lr])
|
||||
self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
|
||||
self.exp_box = widgets.HBox([self.wg_expr])
|
||||
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.exp_box, 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, 0.1)
|
||||
xx2 = np.arange(np.array(self.xn_list)[:, 1].min() * 0.5, np.array(self.xn_list)[:, 1].max() * 1.5, 0.1)
|
||||
xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1)
|
||||
xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1)
|
||||
xx1_o, xx2_o = xx1, xx2
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
xx1_tangent, xx2_tangent = np.meshgrid(xx1_tangent, xx2_tangent)
|
||||
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])
|
||||
partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
|
||||
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
|
||||
plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn
|
||||
z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
|
||||
|
||||
frames, steps = [], []
|
||||
for k in range(len(f_xn)):
|
||||
tmp_trace1 = go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn)
|
||||
tmp_trace2 = go.Surface(x=xx1_tangent, y=xx2_tangent, z=z[k], showscale=True, opacity=0.5)
|
||||
frame = go.Frame(dict(data=[tmp_trace1, tmp_trace2], name=f'frame{k+1}'), traces=[1, 2])
|
||||
frames.append(frame)
|
||||
step = dict(
|
||||
method="update",
|
||||
args=[{"visible": [True]},
|
||||
{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
|
||||
)
|
||||
steps.append(step)
|
||||
|
||||
sliders = [dict(steps= [dict(method= 'animate',
|
||||
args= [[f'frame{k+1}'],
|
||||
dict(mode= 'immediate',
|
||||
frame= dict( duration=0, redraw= True ),
|
||||
transition=dict( duration=0)
|
||||
)
|
||||
],
|
||||
#label='Date : {}'.format(date_range[k])
|
||||
) for k in range(0,len(frames))],
|
||||
transition= dict(duration=0),
|
||||
x=0,
|
||||
y=0,
|
||||
currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
|
||||
len=1.0)
|
||||
]
|
||||
|
||||
trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=False, opacity=0.6)
|
||||
trace2 = go.Scatter3d(x=None, y=None, z=None)
|
||||
trace3 = go.Surface(x=None, y=None, z=None, showscale=False, opacity=0.9, colorscale='Blues')
|
||||
fig = go.Figure(data=[trace1, trace2, trace3], frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
|
||||
dict(label="Pause", method="animate", args=[[None], \
|
||||
dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
|
||||
margin=dict(r=20, l=10, b=10, t=10), sliders=sliders)
|
||||
fig.show()
|
||||
|
||||
class gradient_descent_2d_custom(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
|
||||
self.wg_expr = widgets.Text(value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", description="Expression:")
|
||||
self.wg_x0 = widgets.Text(value="5,5", description="Startpoint:")
|
||||
self.wg_lr = widgets.FloatText(value="1e-1", description="step size:")
|
||||
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])
|
||||
|
||||
frames, steps = [], []
|
||||
for k in range(len(f_xn)):
|
||||
#frame = go.Frame(data=[go.Surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.8)])
|
||||
#fig.add_trace(go.Scatter3d(x=np.array(self.xn_list)[:k, 0], y=np.array(self.xn_list)[:k, 1], z=f_xn))
|
||||
frame = go.Frame(dict(data=[go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn)], name=f'frame{k+1}'), traces=[1])
|
||||
frames.append(frame)
|
||||
step = dict(
|
||||
method="update",
|
||||
args=[{"visible": [True]},
|
||||
{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
|
||||
)
|
||||
steps.append(step)
|
||||
|
||||
sliders = [dict(steps= [dict(method= 'animate',
|
||||
args= [[f'frame{k+1}'],
|
||||
dict(mode= 'immediate',
|
||||
frame= dict( duration=0, redraw= True ),
|
||||
transition=dict( duration=0)
|
||||
)
|
||||
],
|
||||
#label='Date : {}'.format(date_range[k])
|
||||
) for k in range(0,len(frames))],
|
||||
transition= dict(duration=0),
|
||||
x=0,
|
||||
y=0,
|
||||
currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
|
||||
len=1.0)
|
||||
]
|
||||
|
||||
trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.8)
|
||||
trace2 = go.Scatter3d(x=None, y=None, z=None)
|
||||
fig = go.Figure(data=[trace1, trace2], frames=frames)
|
||||
#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))
|
||||
#fig.update(frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
|
||||
dict(label="Pause", method="animate", args=[[None], dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
|
||||
margin=dict(l=0, r=0, b=0, t=0), sliders=sliders)
|
||||
fig.show()
|
||||
|
||||
class gradient_descent_2d_race(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Text(value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", description="Expression:")
|
||||
self.wg_person_one = widgets.Text(value="(5, 5)", description="candidate 1:")
|
||||
self.wg_person_two = widgets.Text(value="(5, 5)", description="candidate 2:")
|
||||
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.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
|
||||
self.config = widgets.VBox([self.wg_expr, self.wg_person_one, self.wg_person_two, self.button_box])
|
||||
self.xn_list_p1, self.df_list_p1 = [], []
|
||||
self.xn_list_p2, self.df_list_p2 = [], []
|
||||
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:
|
||||
# person_one
|
||||
x0 = np.array(self.wg_person_one.value.split("(")[1].split(")")[0].split(","), dtype=float)
|
||||
xn = x0
|
||||
x1 = symbols("x1")
|
||||
x2 = symbols("x2")
|
||||
expr = sympify(self.wg_expr.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_p1.append(xn)
|
||||
self.df_list_p1.append(gradient)
|
||||
print("player one: x = [{}, {}]".format(xn[0], xn[1]))
|
||||
print("player one: gradient= {}".format(gradient))
|
||||
# person_two
|
||||
x0 = np.array(self.wg_person_two.value.split("(")[1].split(")")[0].split(","), dtype=float)
|
||||
xn = x0
|
||||
x1 = symbols("x1")
|
||||
x2 = symbols("x2")
|
||||
expr = sympify(self.wg_expr.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_p2.append(xn)
|
||||
self.df_list_p2.append(gradient)
|
||||
print("player two: x = [{}, {}]".format(xn[0], xn[1]))
|
||||
print("player two: gradient= {}".format(gradient))
|
||||
clear_output(wait=True)
|
||||
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_p1)[:, 0].min()*0.5, np.array(self.xn_list_p1)[:, 0].max()*1.5, 0.1)
|
||||
xx2 = np.arange(np.array(self.xn_list_p1)[:, 1].min()*0.5, np.array(self.xn_list_p1)[:, 1].max()*1.5, 0.1)
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
|
||||
f = lambdify((x1, x2), expr, "numpy")
|
||||
fx = f(xx1, xx2)
|
||||
f_xn_p1 = f(np.array(self.xn_list_p1)[:, 0], np.array(self.xn_list_p1)[:, 1])
|
||||
f_xn_p2 = f(np.array(self.xn_list_p2)[:, 0], np.array(self.xn_list_p2)[:, 1])
|
||||
|
||||
frames, steps = [], []
|
||||
for k in range(len(f_xn_p1)):
|
||||
tmp_trace1 = go.Scatter3d(x=np.array(self.xn_list_p1)[:k,0], y=np.array(self.xn_list_p1)[:k,1], z=f_xn_p1)
|
||||
tmp_trace2 = go.Scatter3d(x=np.array(self.xn_list_p2)[:k,0], y=np.array(self.xn_list_p2)[:k,1], z=f_xn_p2)
|
||||
frame = go.Frame(dict(data=[tmp_trace1, tmp_trace2], name=f'frame{k+1}'), traces=[1, 2])
|
||||
frames.append(frame)
|
||||
step = dict(
|
||||
method="update",
|
||||
args=[{"visible": [True]},
|
||||
{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
|
||||
)
|
||||
steps.append(step)
|
||||
|
||||
sliders = [dict(steps= [dict(method= 'animate',
|
||||
args= [[f'frame{k+1}'],
|
||||
dict(mode= 'immediate',
|
||||
frame= dict( duration=0, redraw= True ),
|
||||
transition=dict( duration=0)
|
||||
)
|
||||
],
|
||||
#label='Date : {}'.format(date_range[k])
|
||||
) for k in range(0,len(frames))],
|
||||
transition= dict(duration=0),
|
||||
x=0,
|
||||
y=0,
|
||||
currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
|
||||
len=1.0)
|
||||
]
|
||||
|
||||
trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.4)
|
||||
trace2 = go.Scatter3d(x=None, y=None, z=None)
|
||||
trace3 = go.Scatter3d(x=None, y=None, z=None)
|
||||
fig = go.Figure(data=[trace1, trace2, trace3], frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
|
||||
dict(label="Pause", method="animate", args=[[None], dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
|
||||
margin=dict(l=20, r=20, b=20, t=20), sliders=sliders)
|
||||
fig.show()
|
||||
|
||||
def plot2(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_p1)[:, 0].min()*0.5, np.array(self.xn_list_p1)[:, 0].max()*1.5, 0.1)
|
||||
xx2 = np.arange(np.array(self.xn_list_p1)[:, 1].min()*0.5, np.array(self.xn_list_p1)[:, 1].max()*1.5, 0.1)
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
|
||||
f = lambdify((x1, x2), expr, "numpy")
|
||||
fx = f(xx1, xx2)
|
||||
f_xn_p1 = f(np.array(self.xn_list_p1)[:, 0], np.array(self.xn_list_p1)[:, 1])
|
||||
f_xn_p2 = f(np.array(self.xn_list_p2)[:, 0], np.array(self.xn_list_p2)[:, 1])
|
||||
|
||||
frames, steps = [], []
|
||||
for k in range(len(f_xn_p1)):
|
||||
tmp_trace1 = go.Scatter3d(x=np.array(self.xn_list_p1)[:k,0], y=np.array(self.xn_list_p1)[:k,1], z=f_xn_p1)
|
||||
tmp_trace2 = go.Scatter3d(x=np.array(self.xn_list_p2)[:k,0], y=np.array(self.xn_list_p2)[:k,1], z=f_xn_p2)
|
||||
frame = go.Frame(dict(data=[tmp_trace1, tmp_trace2], name=f'frame{k+1}'), traces=[1, 2])
|
||||
frames.append(frame)
|
||||
step = dict(
|
||||
method="update",
|
||||
args=[{"visible": [True]},
|
||||
{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
|
||||
)
|
||||
steps.append(step)
|
||||
|
||||
sliders = [dict(steps= [dict(method= 'animate',
|
||||
args= [[f'frame{k+1}'],
|
||||
dict(mode= 'immediate',
|
||||
frame= dict( duration=0, redraw= True ),
|
||||
transition=dict( duration=0)
|
||||
)
|
||||
],
|
||||
#label='Date : {}'.format(date_range[k])
|
||||
) for k in range(0,len(frames))],
|
||||
transition= dict(duration=0),
|
||||
x=0,
|
||||
y=0,
|
||||
currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
|
||||
len=1.0)
|
||||
]
|
||||
|
||||
trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.4)
|
||||
trace2 = go.Scatter3d(x=None, y=None, z=None)
|
||||
trace3 = go.Scatter3d(x=None, y=None, z=None)
|
||||
fig = go.Figure(data=[trace1, trace2, trace3], frames=frames)
|
||||
fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
|
||||
dict(label="Pause", method="animate", args=[[None], dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
|
||||
margin=dict(l=20, r=20, b=20, t=20), sliders=sliders)
|
||||
fig.show()
|
||||
|
|
@ -1,129 +0,0 @@
|
|||
import copy
|
||||
import time
|
||||
import sympy
|
||||
import numpy as np
|
||||
from scipy.misc import derivative
|
||||
from sympy import symbols, sympify, lambdify, diff
|
||||
|
||||
import ipywidgets as widgets
|
||||
from IPython.display import Image, display, clear_output
|
||||
|
||||
from tqdm import tqdm
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
import plotly.graph_objects as go
|
||||
import plotly.io as pio
|
||||
|
||||
import warnings
|
||||
warnings.filterwarnings("ignore")
|
||||
|
||||
class gd_2d_test(object):
|
||||
def __init__(self, environ:str="jupyterlab", type="default"):
|
||||
if type == "default":
|
||||
self.initialization_default(environ=environ)
|
||||
self.compute_default()
|
||||
self.user_step = 1
|
||||
elif type == "custom":
|
||||
self.initlization_custom()
|
||||
self.compute_custom()
|
||||
else:
|
||||
return None
|
||||
|
||||
|
||||
def initialization_default(self, environ):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Dropdown(options=[("(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", "(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)"), ("(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2")], value="(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)", descrption="Expression")
|
||||
self.wg_x0 = widgets.Text(value="0,2", description="Startpoint:")
|
||||
self.wg_lr = widgets.FloatText(value="1e-1", description="step size:")
|
||||
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_default = widgets.Button(description="Plot")
|
||||
|
||||
self.compute_output = widgets.Output()
|
||||
self.plot_default_output = widgets.Output()
|
||||
self.params_lvbox = widgets.VBox([self.wg_x0, self.wg_lr])
|
||||
self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
|
||||
self.exp_box = widgets.HBox([self.wg_expr])
|
||||
self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
|
||||
self.button_box = widgets.HBox([self.button_compute, self.button_plot_default], description="operations")
|
||||
self.config = widgets.VBox([self.exp_box, self.params_box, self.button_box])
|
||||
display(self.config)
|
||||
|
||||
self.button_compute.on_click(self.compute_default)
|
||||
display(self.compute_output)
|
||||
self.button_plot_default.on_click(self.plot_default)
|
||||
img1 = self.plot_default_output
|
||||
display(img1)
|
||||
|
||||
|
||||
def compute_default(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_default(self, *args):
|
||||
with self.plot_default_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(0, 5, 0.1)
|
||||
xx2 = np.arange(0, 6, 0.1)
|
||||
#xx1 = np.arange(np.array(self.xn_list)[:, 0].min() * 0.5, np.array(self.xn_list)[:, 0].max() * 1.5, 0.1)
|
||||
#xx2 = np.arange(np.array(self.xn_list)[:, 1].min() * 0.5, np.array(self.xn_list)[:, 1].max() * 1.5, 0.1)
|
||||
xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1)
|
||||
xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1)
|
||||
xx1_o, xx2_o = xx1, xx2
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
xx1_tangent, xx2_tangent = np.meshgrid(xx1_o, xx2_o)
|
||||
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])
|
||||
partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
|
||||
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
|
||||
plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn
|
||||
z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
|
||||
|
||||
|
||||
from plotly.subplots import make_subplots
|
||||
import plotly.express as px
|
||||
df = px.data.tips()
|
||||
fig = px.density_contour(df, x="total_bill", y="tip")
|
||||
fig = make_subplots(rows=1, cols=2, specs=[[{'type': 'surface'}, {'type': 'xy'}]])
|
||||
fig.add_trace(go.Surface(contours = {"x": {"show": True}, "y":{"show": True}, "z":{"show": True}},x=xx1, y=xx2, z=fx), row=1, col=1)
|
||||
fig.add_trace(go.Scatter3d(x=None, y=None, z=None), row=1, col=1)
|
||||
fig.add_trace(go.Surface(x=None, y=None, z=None, showscale=False, colorscale='Blues'), row=1, col=1)
|
||||
fig.add_trace(go.Contour(x=xx1_o, y=xx2_o, z=fx), row=1, col=2)
|
||||
fig.add_trace(go.Scatter(x=None, y=None), row=1, col=2)
|
||||
frames = [go.Frame(data=[go.Surface(visible=True, showscale=False, opacity=0.8),
|
||||
go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn),
|
||||
go.Surface(x=xx1_tangent, y=xx2_tangent, z=z[k]),
|
||||
go.Contour(visible=True),
|
||||
go.Scatter(x=np.array(self.xn_list)[:k, 0], y=np.array(self.xn_list)[:k, 1])],
|
||||
traces=[0, 1, 2, 3, 4]) for k in range(len(f_xn))]
|
||||
fig.frames = frames
|
||||
fig.update_layout(autosize=False, height=800, updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True, transition= {'duration': 0}, frame=dict(redraw=True, duration=500))]), \
|
||||
dict(label="Pause", method="animate", args=[[None], \
|
||||
dict(fromcurrent=True, mode='immediate', transition={'duration': 0}, frame=dict(redraw=True, duration=0))])])])
|
||||
fig.show()
|
||||
|
|
@ -30,7 +30,7 @@ def array_mesh(data, n):
|
|||
class gd_1d(object):
|
||||
def __init__(self, environ:str="jupyterlab"):
|
||||
pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
|
||||
self.wg_expr = widgets.Text(value="-2 * x * sin(-(pi/4) * x)+10",
|
||||
self.wg_expr = widgets.Text(value="sin(x) + sin((10.0 / 3.0) * x)",
|
||||
description="Expression:",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_x0 = widgets.FloatText(value="2",
|
||||
|
|
@ -45,6 +45,9 @@ class gd_1d(object):
|
|||
self.wg_max_iter = widgets.IntText(value="1000",
|
||||
description="max iteration",
|
||||
style={'description_width': 'initial'})
|
||||
self.wg_x_range = widgets.Text(value="-5,5",
|
||||
description="X-axis range",
|
||||
style={"description_width": "initial"})
|
||||
|
||||
self.button_compute = widgets.Button(description="Compute")
|
||||
self.button_plot = widgets.Button(description="Plot")
|
||||
|
|
@ -52,7 +55,7 @@ class gd_1d(object):
|
|||
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_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter, self.wg_x_range])
|
||||
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])
|
||||
|
|
@ -93,11 +96,11 @@ class gd_1d(object):
|
|||
with self.plot_output:
|
||||
clear_output(wait=True)
|
||||
x0 = float(self.wg_x0.value)
|
||||
x_range = np.array(self.wg_x_range.value.split(","), dtype=float)
|
||||
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)
|
||||
xx1 = np.arange(0, 10, 0.05)
|
||||
xx1 = np.arange(x_range[0], x_range[1], 0.05)
|
||||
fx = f(xx1)
|
||||
f_xn = f(np.array(self.xn_list))
|
||||
|
||||
|
|
@ -133,8 +136,8 @@ class gd_2d(object):
|
|||
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_default = widgets.Button(description="Plot")
|
||||
self.button_plot_contour = widgets.Button(description="Plot contour")
|
||||
self.button_plot_default = widgets.Button(description="3D Plot")
|
||||
self.button_plot_contour = widgets.Button(description="Contour")
|
||||
|
||||
self.compute_output = widgets.Output()
|
||||
self.plot_default_output = widgets.Output()
|
||||
|
|
@ -197,13 +200,16 @@ class gd_2d(object):
|
|||
xx1_o, xx2_o = xx1, xx2
|
||||
xx1, xx2 = np.meshgrid(xx1, xx2)
|
||||
xx1_tangent, xx2_tangent = np.meshgrid(xx1_o, xx2_o)
|
||||
#xx1_tangent, xx2_tangent = array_mesh(np.arange(0, 5, 0.25), 10), array_mesh(np.arange(0, 5, 0.25), 10)
|
||||
self.xx1_tangent, self.xx2_tangent = xx1_tangent, xx2_tangent
|
||||
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])
|
||||
partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
|
||||
partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
|
||||
self.partial_x1, self.partial_x2 = partial_x1, partial_x2
|
||||
plane = partial_x1(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x1 - np.array(self.xn_list)[:, 0]) + partial_x2(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1]) * (x2 - np.array(self.xn_list)[:, 1]) + f_xn
|
||||
|
||||
z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
|
||||
self.z = z
|
||||
## projection
|
||||
|
|
@ -215,13 +221,13 @@ class gd_2d(object):
|
|||
fig = make_subplots(rows=1, cols=2, specs=[[{'type': 'surface'}, {'type': 'surface'}]])
|
||||
fig.add_trace(go.Surface(contours = {"x": {"show": True}, "y":{"show": True}, "z":{"show": True}}, x=xx1, y=xx2, z=fx), row=1, col=1)
|
||||
fig.add_trace(go.Scatter3d(x=None, y=None, z=None), row=1, col=1)
|
||||
fig.add_trace(go.Surface(x=xx1_tangent, y=xx2_tangent, z=z[0], showscale=False, colorscale='Blues'), row=1, col=1)
|
||||
fig.add_trace(go.Surface(x=None, y=None, z=None, showlegend=False, showscale=False, colorscale='Blues'), row=1, col=1)
|
||||
fig.add_trace(go.Surface(z=list(z_offset), x=xx1, y=xx2, showlegend=False, showscale=False, surfacecolor=colorsurfz), row=1, col=2)
|
||||
fig.add_trace(go.Scatter3d(x=None, y=None, z=None), row=1, col=2)
|
||||
fig.add_trace(go.Scatter3d(x=None, y=None, z=None), row=1, col=2)
|
||||
frames = [go.Frame(data=[go.Surface(visible=True, showscale=False, opacity=0.8),
|
||||
go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn),
|
||||
go.Surface(visible=True, x=xx1_tangent, y=xx2_tangent, z=z[k]),
|
||||
go.Surface(visible=False, x=xx1_tangent, y=xx2_tangent, z=z[k]),
|
||||
go.Surface(visible=True, showscale=False, opacity=0.8),
|
||||
go.Scatter3d(x=np.array(self.xn_list)[:k, 0], y=np.array(self.xn_list)[:k, 1], z=f_xn),
|
||||
go.Scatter3d(x=np.array(self.xn_list)[:k, 0].flatten(), y=np.array(self.xn_list)[:k, 1].flatten(), z=z_offset.flatten())],
|
||||
|
|
@ -231,9 +237,13 @@ class gd_2d(object):
|
|||
|
||||
button_play = dict(label="Play", method="animate", args=[None, dict(fromcurrent=True, transition=dict(duration=0), frame=dict(redraw=True, duration=1000))])
|
||||
button_pause = dict(label="Pause", method="animate", args=[[None], dict(fromcurrent=True, mode='immediate', transition={'duration': 0}, frame=dict(redraw=True, duration=0))])
|
||||
button_quiver = dict(label="Quiver", method="update", args=[{"visible": [False, False, False, False, False, True]}])
|
||||
button_tangent = dict(label="Tangent Plane", method="update", args=[{"visible": [True, True, True, True, True, True]}])
|
||||
fig.update_layout(scene_aspectmode='manual', scene_aspectratio=dict(x=0, y=0, z=0),
|
||||
height=800, updatemenus=[dict(type="buttons", buttons=[button_play, button_pause])])
|
||||
height=800, updatemenus=[dict(type="buttons", buttons=[button_play, button_pause, button_tangent])])
|
||||
fig.update_scenes(xaxis_visible=True,
|
||||
yaxis_visible=True,
|
||||
zaxis_visible=True)
|
||||
fig.update_scenes(camera_projection_type = "orthographic")
|
||||
fig.show()
|
||||
|
||||
def plot_contour(self, *args):
|
||||
|
|
@ -260,10 +270,10 @@ class gd_2d(object):
|
|||
|
||||
gradfun=[sympy.diff(expr,var) for var in (x1,x2)]
|
||||
numgradfun=sympy.lambdify([x1,x2], gradfun)
|
||||
x1_mesh, x2_mesh = np.meshgrid(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1])
|
||||
x1_mesh, x2_mesh = np.meshgrid(xx1_o, xx2_o)#np.meshgrid(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1])
|
||||
graddat=numgradfun(x1_mesh, x2_mesh)
|
||||
|
||||
vec_field = ff.create_quiver(x1_mesh, x2_mesh, graddat[0], graddat[1],scale=.05, arrow_scale=.1, angle=math.pi/6)
|
||||
vec_field = ff.create_quiver(x1_mesh, x2_mesh, graddat[0], graddat[1], scale=.05, arrow_scale=.4, angle=math.pi/3)
|
||||
vec_field.update_traces(line_color="black")
|
||||
fig = go.Figure()
|
||||
fig.add_trace(go.Contour(x=xx1_o, y=xx2_o, z=fx))
|
||||
|
|
@ -272,5 +282,5 @@ class gd_2d(object):
|
|||
fig.update_layout(
|
||||
updatemenus=[dict(type = "buttons",direction = "left",
|
||||
buttons=list([
|
||||
dict(args=[{"visible":["True", "True"]}], label="Quiver", method="update")]))], height=800)
|
||||
dict(args=[{"visible":["True", "True"]}], label="Gradient", method="update")]))], height=800)
|
||||
fig.show()
|
||||
Loading…
Reference in New Issue