From 6d4d726447977b62dd78186db249bfe7ce1e6f92 Mon Sep 17 00:00:00 2001 From: TerenceLiu98 Date: Wed, 2 Nov 2022 20:53:36 +0800 Subject: [PATCH] update --- .../interactive-checkpoint.ipynb | 71123 +--------------- algorithm/interactive.ipynb | 97 +- .../.ipynb_checkpoints/gd-checkpoint.py | 308 +- .../__pycache__/gd.cpython-39.pyc | Bin 15502 -> 5828 bytes algorithm/optimization/gd.py | 308 +- algorithm/optimization/gd1d.py | 101 + algorithm/optimization/gd2d.py | 489 + algorithm/optimization/gd2d_test.py | 129 + algorithm/optimization/gd_new.py | 276 + 9 files changed, 1197 insertions(+), 71634 deletions(-) create mode 100644 algorithm/optimization/gd1d.py create mode 100644 algorithm/optimization/gd2d.py create mode 100644 algorithm/optimization/gd2d_test.py create mode 100644 algorithm/optimization/gd_new.py diff --git a/algorithm/.ipynb_checkpoints/interactive-checkpoint.ipynb b/algorithm/.ipynb_checkpoints/interactive-checkpoint.ipynb index c15b92b..987e34b 100644 --- a/algorithm/.ipynb_checkpoints/interactive-checkpoint.ipynb +++ b/algorithm/.ipynb_checkpoints/interactive-checkpoint.ipynb @@ -2,29 +2,29 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "id": "af1d5646-4b13-4039-9f76-8042bc9dbda3", "metadata": {}, "outputs": [], "source": [ - "from optimization.gd import *" + "from optimization.gd_new import *" ] }, { "cell_type": "code", - "execution_count": 2, - "id": "0a5c51d2-8b18-4143-b6f1-73a909ccb623", + "execution_count": 5, + "id": "8ce3dbbd-a698-448b-a2c6-772286c745d5", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "e47aabe79e0c4d0b805af9c8c5ddcd2c", + "model_id": "f63728b9362047df80c1bf76167f6bf5", "version_major": 2, "version_minor": 0 }, "text/plain": [ - "VBox(children=(HBox(children=(VBox(children=(Text(value='x**3 - x**(1/2)', description='Expression:', style=Te…" + "VBox(children=(HBox(children=(VBox(children=(Text(value='-2 * x * sin(-(pi/4) * x)+10', description='Expressio…" ] }, "metadata": {}, @@ -33,7 +33,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "3932d46cd01e4aa7954a96b578cba8c0", + "model_id": "2ded251d4d034c058f83d613618e3a7d", "version_major": 2, "version_minor": 0 }, @@ -47,7 +47,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "277e5f45abc84761bdcfc0f30b9aa434", + "model_id": "b9e00497c1cd4bc484bf7ea793aa3d78", "version_major": 2, "version_minor": 0 }, @@ -60,24 +60,24 @@ } ], "source": [ - "gd1 = gradient_descent_1d(environ=\"jupyterlab\")" + "gd1 = gd_1d()" ] }, { "cell_type": "code", - "execution_count": 3, - "id": "15c6e757-cde3-422b-be7e-3f55b7752142", + "execution_count": 6, + "id": "a1765810-6cd8-4e1a-aaa6-7691a7b2a42e", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "754a54a9b7294fde9ca6943c1164e7a8", + "model_id": "4101fea885e6435e8283e6da6f4f68e9", "version_major": 2, "version_minor": 0 }, "text/plain": [ - "VBox(children=(HBox(children=(Dropdown(index=2, options=(('(sin(x1) - 2) + (sin(x2) - 2) ** 2', '(sin(x1) - 2)…" + "VBox(children=(HBox(children=(Dropdown(options=(('(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x…" ] }, "metadata": {}, @@ -86,7 +86,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "e57f04a5d4474dc1bb12258dca317e12", + "model_id": "1a7d3fe1bd72408684d18ad75e2754ce", "version_major": 2, "version_minor": 0 }, @@ -100,7 +100,21 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "f690ccc4bc1741238bd81db935677a74", + "model_id": "be733631b99b4b09939ed99c1723b03b", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Output()" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "41c863b04c314bbd8df1353e7fc92ec1", "version_major": 2, "version_minor": 0 }, @@ -113,70969 +127,162 @@ } ], "source": [ - "gd2 = gradient_descent_2d(environ=\"jupyterlab\")" + "gd2 = gd_2d()" ] }, { "cell_type": "code", - "execution_count": 24, - "id": "f49bfc36-b6fd-408f-91ba-270a58854b2e", - "metadata": {}, - "outputs": [ - { - "ename": "ValueError", - "evalue": "operands could not be broadcast together with shapes (63,) (186,186) ", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m/tmp/ipykernel_153593/2094296290.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[0mpartial_x1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlambdify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdiff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m,\u001b[0m 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0].max()*1.5, 0.05)\n", - "xx2 = np.arange(np.array(gd2.xn_list)[:, 1].min()*0.5, np.array(gd2.xn_list)[:, 1].max()*1.5, 0.05)\n", - "xx1_o, xx2_o = xx1, xx2\n", - "xx1, xx2 = np.meshgrid(xx1, xx2)\n", - "fx = f(xx1, xx2)\n", - "expr = sympify(gd2.wg_expr.value)\n", - "partial_x1 = lambdify((x1, x2), diff(expr, x1), \"numpy\")\n", - "partial_x2 = lambdify((x1, x2), diff(expr, x2), \"numpy\")\n", - "plane = partial_x1(np.array(gd2.xn_list)[:, 0], np.array(gd2.xn_list)[:, 1]) * (x1 - np.array(gd2.xn_list)[:, 0]) + \\\n", - " partial_x2(np.array(gd2.xn_list)[:, 0], np.array(gd2.xn_list)[:, 1]) * (x2 - np.array(gd2.xn_list)[:, 0]) + \\\n", - " fx\n", - "z = lambdify((x1, x2), plane[0][10], \"numpy\")(xx1, xx2)\n", - "\n", - "trace0 = go.Surface(x=xx1, y=xx2, z=z)" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "a493e2f6-6b4a-4e30-9816-6580ac9d0123", - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - 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" - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig = go.Figure(trace0)\n", - "fig.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "e3909c55-8d69-4476-9d38-6c7f5986d3aa", + "execution_count": 7, + "id": "88e5e47f-3a02-4919-a74e-a4758c56390a", "metadata": {}, "outputs": [ { "data": { + "text/latex": [ + "$\\displaystyle \\operatorname{Plane}\\left(\\operatorname{Point3D}\\left(1, 1, 1\\right), \\left( 1, \\ 4, \\ 7\\right)\\right)$" + ], "text/plain": [ - "array([-1.67866985e+00, -2.54965667e+00, -3.59746536e+00, -4.35129259e+00,\n", - " -4.12200838e+00, -3.12277143e+00, -2.19419969e+00, -1.57072577e+00,\n", - " -1.16291457e+00, -8.84107882e-01, -6.84378894e-01, -5.36050326e-01,\n", - " -4.23070981e-01, -3.35534592e-01, -2.66942015e-01, -2.12796420e-01,\n", - " -1.69850594e-01, -1.35682940e-01, -1.08445337e-01, -8.67045898e-02,\n", - " -6.93372252e-02, -5.54562438e-02, -4.43580658e-02, -3.54829054e-02,\n", - " -2.83845083e-02, -2.27066768e-02, -1.81648654e-02, -1.45316486e-02,\n", - " -1.16251941e-02, -9.30009141e-03, -7.44004042e-03, -5.95201559e-03,\n", - " -4.76160389e-03, -3.80927873e-03, -3.04742073e-03, -2.43793544e-03,\n", - " -1.95034776e-03, -1.56027791e-03, -1.24822217e-03, -9.98577657e-04,\n", - " -7.98862085e-04, -6.39089647e-04, -5.11271707e-04, -4.09017360e-04,\n", - " -3.27213885e-04, -2.61771107e-04, -2.09416885e-04, -1.67533507e-04,\n", - " -1.34026806e-04, -1.07221445e-04, -8.57771556e-05, -6.86217244e-05,\n", - " -5.48973795e-05, -4.39179036e-05, -3.51343229e-05, -2.81074583e-05,\n", - " -2.24859666e-05, -1.79887733e-05, -1.43910187e-05, -1.15128149e-05,\n", - " -9.21025194e-06, -7.36820155e-06, -5.89456124e-06])" + "Plane(Point3D(1, 1, 1), (1, 4, 7))" ] }, - "execution_count": 32, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "partial_x1(np.array(gd2.xn_list)[:, 0], np.array(gd2.xn_list)[:, 1])" + "from sympy import Plane, Point3D\n", + "Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))\n", + "Plane((1, 1, 1), (2, 3, 4), (2, 2, 2))\n", + "Plane(Point3D(1, 1, 1), normal_vector=(1,4,7))" ] }, { "cell_type": "code", "execution_count": null, - "id": "3442b03b-1bb3-4694-8715-1b465b78dc63", + "id": "b0563398-5a79-47aa-9c31-474a518daa0d", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import Point3D, Plane\n", + "a = Plane(Point3D(1, 1, 1), Point3D(2, 3, 4), Point3D(2, 2, 2))\n", + "a.normal_vector\n", + "a = Plane(Point3D(1, 1, 1), normal_vector=(1, 4, 7))\n", + "a.normal_vector" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cf7ed01e-f42a-4a3d-8c2f-e0e7dfa682c5", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy.vector import CoordSys3D, gradient\n", + "from sympy import symbols, sympify, lambdify, diff\n", + "expr = sympify(\"(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x2**2 * E**(-x2)\")\n", + "x1, x2 = symbols(\"x1\"), symbols(\"x2\")\n", + "gradient(expr)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bdbceb9a-42f0-42e3-a2cb-573b4d82e4af", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy.vector import CoordSys3D\n", + "R = CoordSys3D('R')\n", + "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))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "af76a657-c281-41b4-83c3-c3f73376d948", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy.vector import CoordSys3D, Del\n", + "R = CoordSys3D('R')\n", + "delop = Del()\n", + "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", + "gradient_field" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d987886f-1231-487a-88dc-47e8a45d728c", + "metadata": {}, + "outputs": [], + "source": [ + "import sympy\n", + "\n", + "#define symbolic vars, function\n", + "x,y=sympy.symbols('x y')\n", + "fun= sympify(\"(1 - 8 * x + 7 * x**2 - (7/3) * x**3 + (1/4) * x**4) * y**2 * E**(-y)\")\n", + "#fun=3*x**2-5*y**2\n", + "#take the gradient symbolically\n", + "gradfun=[sympy.diff(fun,var) for var in (x1,x2)]\n", + "numgradfun=sympy.lambdify([x,y],gradfun)\n", + "graddat=numgradfun(xx1_o,xx2_o)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "da34c7be-025f-4326-8138-9e78e2043b7e", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import plotly.figure_factory as ff\n", + "import math\n", + "\n", + "X,Y=np.meshgrid(np.arange(0,5, 0.25),np.arange(0,5, 0.25))\n", + "graddat=numgradfun(X,Y)\n", + "\n", + "\n", + "fig = ff.create_quiver(X, Y, graddat[0], graddat[1],scale=.05, arrow_scale=.1, angle=math.pi/6)\n", + "fig.update_traces(line_color=\"red\")\n", + "fig.update_layout(height=800)\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "62504d86-9dc8-42b2-b052-d7acfe8be5e0", + "metadata": {}, + "outputs": [], + "source": [ + "fig.data[0][\"x\"]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "415a2abd-3ea4-48ee-9923-c9897105ad27", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "X,Y=np.meshgrid(np.arange(0,5, 0.1),np.arange(0,5,0.1))\n", + "graddat=numgradfun(X,Y)\n", + "\n", + "plt.figure()\n", + "plt.quiver(X,Y,graddat[0],graddat[1])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2c60be92-8c74-4f46-b7fc-bb9d7150cbe0", "metadata": {}, "outputs": [], "source": [] @@ -71097,7 +304,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.13" + "version": "3.9.13" } }, "nbformat": 4, diff --git a/algorithm/interactive.ipynb b/algorithm/interactive.ipynb index b6ac3b7..31aa33f 100644 --- a/algorithm/interactive.ipynb +++ b/algorithm/interactive.ipynb @@ -7,24 +7,24 @@ "metadata": {}, "outputs": [], "source": [ - "from optimization.gd import *" + "from optimization.gd_new import *" ] }, { "cell_type": "code", "execution_count": 2, - "id": "0a5c51d2-8b18-4143-b6f1-73a909ccb623", + "id": "8ce3dbbd-a698-448b-a2c6-772286c745d5", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "0bcac263607a46d19fead8b1cf79e498", + "model_id": "5715c7beff3c4ab58a001fecee2e6ba9", "version_major": 2, "version_minor": 0 }, "text/plain": [ - "VBox(children=(HBox(children=(VBox(children=(Text(value='x**3 - x**(1/2)', description='Expression:', style=Te…" + "VBox(children=(HBox(children=(VBox(children=(Text(value='-2 * x * sin(-(pi/4) * x)+10', description='Expressio…" ] }, "metadata": {}, @@ -33,7 +33,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "3f64c031482d41799291390431aa3264", + "model_id": "60025f1dfc974c4ba4765136faa526e8", "version_major": 2, "version_minor": 0 }, @@ -47,7 +47,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "0504d25c3aab477ca0acf3d054dbaf92", + "model_id": "52d1cde962ba4b7dad5c4e581fc5aee1", "version_major": 2, "version_minor": 0 }, @@ -60,24 +60,24 @@ } ], "source": [ - "gd1 = gradient_descent_1d(environ=\"jupyterlab\")" + "gd1 = gd_1d()" ] }, { "cell_type": "code", - "execution_count": 5, - "id": "15c6e757-cde3-422b-be7e-3f55b7752142", + "execution_count": 3, + "id": "a1765810-6cd8-4e1a-aaa6-7691a7b2a42e", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "fca48b98af304f1d821c948d8dcc8629", + "model_id": "f6ef2a67373b4552b4d866c633e8b9a7", "version_major": 2, "version_minor": 0 }, "text/plain": [ - "VBox(children=(HBox(children=(Dropdown(index=2, options=(('(sin(x1) - 2) + (sin(x2) - 2) ** 2', '(sin(x1) - 2)…" + "VBox(children=(HBox(children=(Dropdown(options=(('(1 - 8 * x1 + 7 * x1**2 - (7/3) * x1**3 + (1/4) * x1**4) * x…" ] }, "metadata": {}, @@ -86,7 +86,7 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "f25a00c1bb294530973475c7a5c8bb10", + "model_id": "ece751b11bc643a196bc17d87d90499e", "version_major": 2, "version_minor": 0 }, @@ -100,7 +100,21 @@ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "4afc98f7c6954a58aba389526ba09164", + "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 }, @@ -113,66 +127,13 @@ } ], "source": [ - "gd2 = gradient_descent_2d(environ=\"jupyterlab\")" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "694b7e27-cc21-44f4-9a89-7a6b97725a64", - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "f1d170fccfee4e5891a3c33ad564c197", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "VBox(children=(Text(value='(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2', description='Expression:'), Text(value='(…" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "e6a5a98d84b54da7b1ac6deaa408ed5d", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "Output()" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "5b35d3e6383947cfb24f1663388ef556", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "Output()" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "gd2_race = gradient_descent_2d_race(environ=\"jupyterlab\")" + "gd2 = gd_2d()" ] }, { "cell_type": "code", "execution_count": null, - "id": "d6001078-5cf2-402e-b37e-a6dad90674a6", + "id": "48944e3c-932a-4733-b77d-a2b50cee2e5a", "metadata": {}, "outputs": [], "source": [] diff --git a/algorithm/optimization/.ipynb_checkpoints/gd-checkpoint.py b/algorithm/optimization/.ipynb_checkpoints/gd-checkpoint.py index de0e56e..572adfe 100644 --- a/algorithm/optimization/.ipynb_checkpoints/gd-checkpoint.py +++ b/algorithm/optimization/.ipynb_checkpoints/gd-checkpoint.py @@ -17,88 +17,6 @@ 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"): @@ -178,7 +96,7 @@ class gradient_descent_2d(object): 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)[:, 0]) + f_xn + 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 = [], [] @@ -210,229 +128,11 @@ class gradient_descent_2d(object): len=1.0) ] - trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=False, opacity=0.8) + 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=0.5, colorscale='Blues') - fig = go.Figure(data=[trace1, trace2, trace3], frames=frames) + 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() - -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() - - - \ No newline at end of file + fig.show() \ 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