438 lines
23 KiB
Python
438 lines
23 KiB
Python
import copy
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import time
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import sympy
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import numpy as np
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from scipy.misc import derivative
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from sympy import symbols, sympify, lambdify, diff
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import ipywidgets as widgets
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from IPython.display import display, clear_output
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from tqdm import tqdm
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import matplotlib.pyplot as plt
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import plotly.graph_objects as go
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import plotly.io as pio
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import warnings
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warnings.filterwarnings("ignore")
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class gradient_descent_1d(object):
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def __init__(self, environ:str="jupyterlab"):
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pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
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self.wg_expr = widgets.Text(value="x**3 - x**(1/2)",
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description="Expression:",
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style={'description_width': 'initial'})
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self.wg_x0 = widgets.FloatText(value="2",
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description="Startpoint:",
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style={'description_width': 'initial'})
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self.wg_lr = widgets.FloatText(value="1e-1",
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description="step size:",
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style={'description_width': 'initial'})
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self.wg_epsilon = widgets.FloatText(value="1e-5",
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description="criterion:",
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style={'description_width': 'initial'})
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self.wg_max_iter = widgets.IntText(value="1000",
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description="max iteration",
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style={'description_width': 'initial'})
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self.button_compute = widgets.Button(description="Compute")
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self.button_plot = widgets.Button(description="Plot")
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self.compute_output = widgets.Output()
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self.plot_output = widgets.Output()
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self.params_lvbox = widgets.VBox([self.wg_expr, self.wg_x0, self.wg_lr])
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self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
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self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
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self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
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self.config = widgets.VBox([self.params_box, self.button_box])
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self.initialization()
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def initialization(self):
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display(self.config)
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self.button_compute.on_click(self.compute)
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display(self.compute_output)
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self.button_plot.on_click(self.plot)
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display(self.plot_output)
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def compute(self, *args):
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with self.compute_output:
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xn = self.wg_x0.value
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x = symbols("x")
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expr = sympify(self.wg_expr.value)
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f = lambdify(x, expr)
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df = lambdify(x, diff(expr, x))
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self.xn_list, self.df_list = [], []
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for n in tqdm(range(0, self.wg_max_iter.value)):
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gradient = df(xn)
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self.xn_list.append(xn)
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self.df_list.append(gradient)
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if abs (gradient < self.wg_epsilon.value):
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clear_output(wait=True)
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print("Found solution of {} after".format(expr), n, "iterations")
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print("x* = {}".format(xn))
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return None
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xn = xn - self.wg_lr.value * gradient
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clear_output(wait=True)
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display("Exceeded maximum iterations. No solution found.")
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return None
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def plot(self, *args):
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with self.plot_output:
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clear_output(wait=True)
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x0 = float(self.wg_x0.value)
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x = symbols("x")
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expr = sympify(self.wg_expr.value)
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f = lambdify(x, sympify(expr), "numpy")
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xx1 = np.arange(np.array(self.xn_list).min()*0.5, np.array(self.xn_list).max()*1.5, 0.05)
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fx = f(xx1)
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f_xn = f(np.array(self.xn_list))
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fig = go.Figure()
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fig.add_scatter(x=xx1, y=fx)
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frames = []
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frames.append({'data':copy.deepcopy(fig['data']),'name':f'frame{0}'})
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fig.add_traces(go.Scatter(x=None, y=None, mode="lines + markers", line={"color":"#de1032", "width":5}))
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frames = [go.Frame(data= [go.Scatter(x=np.array(self.xn_list)[:k], y=f_xn)],traces= [1],name=f'frame{k+2}')for k in range(len(f_xn))]
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fig.update(frames=frames)
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fig.update_layout(updatemenus=[dict(type="buttons",buttons=[dict(label="Play",method="animate",args=[None])])])
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fig.show()
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class gradient_descent_2d(object):
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def __init__(self, environ:str="jupyterlab"):
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pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
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self.wg_expr = widgets.Dropdown(options=[("(sin(x1) - 2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) + (sin(x2) - 2) ** 2"),
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("(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** (1/2) + (sin(x2) - 2) ** 2"),
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("(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", "(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2")],
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value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", descrption="Expression")
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self.wg_x0 = widgets.Text(value="5,5",
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description="Startpoint:")
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self.wg_lr = widgets.FloatText(value="1e-1",
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description="step size:")
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self.wg_epsilon = widgets.FloatText(value="1e-5",
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description="criterion:")
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self.wg_max_iter = widgets.IntText(value="1000",
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description="max iteration")
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self.button_compute = widgets.Button(description="Compute")
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self.button_plot = widgets.Button(description="Plot")
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self.compute_output = widgets.Output()
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self.plot_output = widgets.Output()
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self.params_lvbox = widgets.VBox([self.wg_x0, self.wg_lr])
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self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
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self.exp_box = widgets.HBox([self.wg_expr])
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self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
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self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
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self.config = widgets.VBox([self.exp_box, self.params_box, self.button_box])
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self.initialization()
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def initialization(self):
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display(self.config)
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self.button_compute.on_click(self.compute)
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display(self.compute_output)
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self.button_plot.on_click(self.plot)
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display(self.plot_output)
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def compute(self, *args):
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with self.compute_output:
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x0 = np.array(self.wg_x0.value.split(","), dtype=float)
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xn = x0
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x1 = symbols("x1")
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x2 = symbols("x2")
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expr = sympify(self.wg_expr.value)
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self.xn_list, self.df_list = [], []
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for n in tqdm(range(0, self.wg_max_iter.value)):
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gradient = np.array([diff(expr, x1).subs(x1, xn[0]).subs(x2, xn[1]),
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diff(expr, x2).subs(x1, xn[0]).subs(x2, xn[1])], dtype=float)
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self.xn_list.append(xn)
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self.df_list.append(gradient)
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if np.linalg.norm(gradient, ord=2) < self.wg_epsilon.value:
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clear_output(wait=True)
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print("Found solution of {} after".format(expr), n, "iterations")
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print("x* = [{}, {}]".format(xn[0], xn[1]))
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return None
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xn = xn - self.wg_lr.value * gradient
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clear_output(wait=True)
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display("Exceeded maximum iterations. No solution found.")
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return None
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def plot(self, *args):
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with self.plot_output:
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clear_output(wait=True)
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x0 = np.array(self.wg_x0.value.split(","), dtype=float)
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x1 = symbols("x1")
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x2 = symbols("x2")
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expr = sympify(self.wg_expr.value)
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xx1 = np.arange(np.array(self.xn_list)[:, 0].min() * 0.5, np.array(self.xn_list)[:, 0].max() * 1.5, 0.1)
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xx2 = np.arange(np.array(self.xn_list)[:, 1].min() * 0.5, np.array(self.xn_list)[:, 1].max() * 1.5, 0.1)
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xx1_tangent = np.arange(np.array(self.xn_list)[:, 0].min(), np.array(self.xn_list)[:, 0].max(), 0.1)
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xx2_tangent = np.arange(np.array(self.xn_list)[:, 1].min(), np.array(self.xn_list)[:, 1].max(), 0.1)
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xx1_o, xx2_o = xx1, xx2
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xx1, xx2 = np.meshgrid(xx1, xx2)
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xx1_tangent, xx2_tangent = np.meshgrid(xx1_tangent, xx2_tangent)
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f = lambdify((x1, x2), expr, "numpy")
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fx = f(xx1, xx2)
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f_xn = f(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1])
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partial_x1 = lambdify((x1, x2), diff(expr, x1), "numpy")
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partial_x2 = lambdify((x1, x2), diff(expr, x2), "numpy")
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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
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z = [lambdify((x1, x2), plane[i], "numpy")(xx1_tangent, xx2_tangent) for i in range(0, len(plane))]
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frames, steps = [], []
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for k in range(len(f_xn)):
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tmp_trace1 = go.Scatter3d(x=np.array(self.xn_list)[:k,0], y=np.array(self.xn_list)[:k,1], z=f_xn)
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tmp_trace2 = go.Surface(x=xx1_tangent, y=xx2_tangent, z=z[k], showscale=True, opacity=0.5)
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frame = go.Frame(dict(data=[tmp_trace1, tmp_trace2], name=f'frame{k+1}'), traces=[1, 2])
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frames.append(frame)
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step = dict(
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method="update",
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args=[{"visible": [True]},
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{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
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)
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steps.append(step)
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sliders = [dict(steps= [dict(method= 'animate',
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args= [[f'frame{k+1}'],
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dict(mode= 'immediate',
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frame= dict( duration=0, redraw= True ),
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transition=dict( duration=0)
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)
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],
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#label='Date : {}'.format(date_range[k])
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) for k in range(0,len(frames))],
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transition= dict(duration=0),
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x=0,
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y=0,
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currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
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len=1.0)
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]
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trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=False, opacity=0.8)
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trace2 = go.Scatter3d(x=None, y=None, z=None)
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trace3 = go.Surface(x=None, y=None, z=None, showscale=False, opacity=0.5, colorscale='Blues')
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fig = go.Figure(data=[trace1, trace2, trace3], frames=frames)
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fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
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dict(label="Pause", method="animate", args=[[None], \
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dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
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margin=dict(r=20, l=10, b=10, t=10), sliders=sliders)
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fig.show()
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class gradient_descent_2d_custom(object):
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def __init__(self, environ:str="jupyterlab"):
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pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
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self.wg_expr = widgets.Text(value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", description="Expression:")
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self.wg_x0 = widgets.Text(value="5,5", description="Startpoint:")
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self.wg_lr = widgets.FloatText(value="1e-1", description="step size:")
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self.wg_epsilon = widgets.FloatText(value="1e-5", description="criterion:")
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self.wg_max_iter = widgets.IntText(value="1000", description="max iteration")
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self.button_compute = widgets.Button(description="Compute")
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self.button_plot = widgets.Button(description="Plot")
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self.compute_output = widgets.Output()
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self.plot_output = widgets.Output()
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self.params_lvbox = widgets.VBox([self.wg_expr, self.wg_x0, self.wg_lr])
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self.params_rvbox = widgets.VBox([self.wg_epsilon, self.wg_max_iter])
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self.params_box = widgets.HBox([self.params_lvbox, self.params_rvbox], description="Parameters")
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self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
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self.config = widgets.VBox([self.params_box, self.button_box])
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self.initialization()
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def initialization(self):
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display(self.config)
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self.button_compute.on_click(self.compute)
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display(self.compute_output)
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self.button_plot.on_click(self.plot)
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display(self.plot_output)
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def compute(self, *args):
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with self.compute_output:
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x0 = np.array(self.wg_x0.value.split(","), dtype=float)
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xn = x0
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x1 = symbols("x1")
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x2 = symbols("x2")
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expr = sympify(self.wg_expr.value)
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self.xn_list, self.df_list = [], []
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for n in tqdm(range(0, self.wg_max_iter.value)):
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gradient = np.array([diff(expr, x1).subs(x1, xn[0]).subs(x2, xn[1]),
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diff(expr, x2).subs(x1, xn[0]).subs(x2, xn[1])], dtype=float)
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self.xn_list.append(xn)
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self.df_list.append(gradient)
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if np.linalg.norm(gradient, ord=2) < self.wg_epsilon.value:
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clear_output(wait=True)
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print("Found solution of {} after".format(expr), n, "iterations")
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print("x* = [{}, {}]".format(xn[0], xn[1]))
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return None
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xn = xn - self.wg_lr.value * gradient
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clear_output(wait=True)
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display("Exceeded maximum iterations. No solution found.")
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return None
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def plot(self, *args):
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with self.plot_output:
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clear_output(wait=True)
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x0 = np.array(self.wg_x0.value.split(","), dtype=float)
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x1 = symbols("x1")
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x2 = symbols("x2")
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expr = sympify(self.wg_expr.value)
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xx1 = np.arange(np.array(self.xn_list)[:, 0].min()*0.5, np.array(self.xn_list)[:, 0].max()*1.5, 0.05)
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xx2 = np.arange(np.array(self.xn_list)[:, 1].min()*0.5, np.array(self.xn_list)[:, 1].max()*1.5, 0.05)
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xx1, xx2 = np.meshgrid(xx1, xx2)
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f = lambdify((x1, x2), expr, "numpy")
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fx = f(xx1, xx2)
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f_xn = f(np.array(self.xn_list)[:, 0], np.array(self.xn_list)[:, 1])
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frames, steps = [], []
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for k in range(len(f_xn)):
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#frame = go.Frame(data=[go.Surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.8)])
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#fig.add_trace(go.Scatter3d(x=np.array(self.xn_list)[:k, 0], y=np.array(self.xn_list)[:k, 1], z=f_xn))
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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])
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frames.append(frame)
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step = dict(
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method="update",
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args=[{"visible": [True]},
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{"title": "Slider switched to step: " + str(k+1)}], # layout attribute
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)
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steps.append(step)
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sliders = [dict(steps= [dict(method= 'animate',
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args= [[f'frame{k+1}'],
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dict(mode= 'immediate',
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frame= dict( duration=0, redraw= True ),
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transition=dict( duration=0)
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)
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],
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#label='Date : {}'.format(date_range[k])
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) for k in range(0,len(frames))],
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transition= dict(duration=0),
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x=0,
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y=0,
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currentvalue=dict(font=dict(size=12), visible=True, xanchor= 'center'),
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len=1.0)
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]
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trace1 = go.Surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.8)
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trace2 = go.Scatter3d(x=None, y=None, z=None)
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fig = go.Figure(data=[trace1, trace2], frames=frames)
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#fig.add_surface(x=xx1, y=xx2, z=fx, showscale=True, opacity=0.9)
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#fig.update_traces(contours_z=dict(show=True, usecolormap=True, highlightcolor="limegreen", project_z=True))
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#fig.update(frames=frames)
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fig.update_layout(updatemenus=[dict(type="buttons", buttons=[dict(label="Play", method="animate", args=[None, dict(fromcurrent=True)]), \
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dict(label="Pause", method="animate", args=[[None], dict(fromcurrent=True, mode='immediate', transition= {'duration': 0}, frame=dict(redraw=True, duration=0))])])],
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margin=dict(l=0, r=0, b=0, t=0), sliders=sliders)
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fig.show()
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class gradient_descent_2d_race(object):
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def __init__(self, environ:str="jupyterlab"):
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pio.renderers.default = environ # 'notebook' or 'colab' or 'jupyterlab'
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self.wg_expr = widgets.Text(value="(sin(x1) - 2) ** 2 + (sin(x2) - 2) ** 2", description="Expression:")
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self.wg_person_one = widgets.Text(value="(5, 5)", description="candidate 1:")
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self.wg_person_two = widgets.Text(value="(5, 5)", description="candidate 2:")
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self.button_compute = widgets.Button(description="Compute")
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self.button_plot = widgets.Button(description="Plot")
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self.compute_output = widgets.Output()
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self.plot_output = widgets.Output()
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self.button_box = widgets.HBox([self.button_compute, self.button_plot], description="operations")
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self.config = widgets.VBox([self.wg_expr, self.wg_person_one, self.wg_person_two, self.button_box])
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self.xn_list_p1, self.df_list_p1 = [], []
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self.xn_list_p2, self.df_list_p2 = [], []
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self.initialization()
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def initialization(self):
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display(self.config)
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self.button_compute.on_click(self.compute)
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display(self.compute_output)
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self.button_plot.on_click(self.plot)
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display(self.plot_output)
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def compute(self, *args):
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with self.compute_output:
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# person_one
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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()
|
|
|
|
|
|
|