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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Building interactive plots using bqplot and ipywidgets
bqplot is built on top of the ipywidgets framework
ipwidgets and bqplot widgets can be seamlessly integrated to build interactive plots
bqplot figure widgets can be stacked with UI controls available in ipywidgets by using Layout classes (Box, HBox, VBox) in ipywidgets
(Note that only Figure objects (not Mark objects) inherit from DOMWidget class and can be combined with other widgets from ipywidgets)
Trait attributes of widgets can be linked using callbacks. Callbacks should be registered using the observe method
Please follow these links for detailed documentation on
Step1:  Update the plot on a button click
Step2:  Let's look at an example where we link a plot to a dropdown menu
Step3:  Let's now create a scatter plot where we select X and Y data from the two dropdown menus
Step4:  In the example below, we'll look at plots of trigonometic functions
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Python Code:
import numpy as np
import ipywidgets as widgets
import bqplot.pyplot as plt
Explanation: Building interactive plots using bqplot and ipywidgets
bqplot is built on top of the ipywidgets framework
ipwidgets and bqplot widgets can be seamlessly integrated to build interactive plots
bqplot figure widgets can be stacked with UI controls available in ipywidgets by using Layout classes (Box, HBox, VBox) in ipywidgets
(Note that only Figure objects (not Mark objects) inherit from DOMWidget class and can be combined with other widgets from ipywidgets)
Trait attributes of widgets can be linked using callbacks. Callbacks should be registered using the observe method
Please follow these links for detailed documentation on:
1. Layout and Styling of Jupyter Widgets
*  Linking Widgets
<br>Let's look at examples of linking plots with UI controls
End of explanation
y = np.random.randn(100).cumsum() # simple random walk
# create a button
update_btn = widgets.Button(description='Update', button_style='success')
# create a figure widget
fig1 = plt.figure(animation_duration=750)
line = plt.plot(y)
# define an on_click function
def on_btn_click(btn):
    # update the y attribute of line mark
    line.y = np.random.randn(100).cumsum() # another random walk
# register the on_click function
update_btn.on_click(on_btn_click)
    
# stack button and figure using VBox
widgets.VBox([fig1, update_btn])
Explanation: Update the plot on a button click
End of explanation
import pandas as pd
# create a dummy time series for 5 dummy stock tickers
dates = pd.date_range(start='20180101', end='20181231')
n = len(dates)
tickers = list('ABCDE')
prices = pd.DataFrame(np.random.randn(n, 5).cumsum(axis=0), columns=tickers)
# create a dropdown menu for tickers
dropdown = widgets.Dropdown(description='Ticker', options=tickers)
# create figure for plotting time series
current_ticker = dropdown.value
fig_title_tmpl = '"{}" Time Series' # string template for title of the figure 
fig2 = plt.figure(title=fig_title_tmpl.format(current_ticker))
fig2.layout.width = '900px'
time_series = plt.plot(dates, prices[current_ticker])
plt.xlabel('Date')
plt.ylabel('Price')
# 1. create a callback which updates the plot when dropdown item is selected
def update_plot(*args):
    selected_ticker = dropdown.value
    
    # update the y attribute of the mark by selecting 
    # the column from the price data frame
    time_series.y = prices[selected_ticker]
    
    # update the title of the figure
    fig2.title = fig_title_tmpl.format(selected_ticker)
# 2. register the callback by using the 'observe' method
dropdown.observe(update_plot, 'value')
# stack the dropdown and fig widgets using VBox
widgets.VBox([dropdown, fig2])
Explanation: Let's look at an example where we link a plot to a dropdown menu
End of explanation
# create two dropdown menus for X and Y attributes of scatter
x_dropdown = widgets.Dropdown(description='X', options=tickers, value='A')
y_dropdown = widgets.Dropdown(description='Y', options=tickers, value='B')
# create figure for plotting the scatter
x_ticker = x_dropdown.value
y_ticker = y_dropdown.value
# set up fig_margin to allow space to display color bar
fig_margin = dict(top=20, bottom=40, left=60, right=80)
fig3 = plt.figure(animation_duration=1000, fig_margin=fig_margin)
# custom axis options for color data
axes_options = {'color': {'tick_format': '%m/%y', 
                          'side': 'right',
                          'num_ticks': 5}}
scatter = plt.scatter(x=prices[x_ticker], 
                      y=prices[y_ticker],
                      color=dates, # represent chronology using color scale
                      stroke='black',
                      colors=['red'],
                      default_size=32,
                      axes_options=axes_options)
plt.xlabel(x_ticker)
plt.ylabel(y_ticker)
# 1. create a callback which updates the plot when dropdown item is selected
def update_scatter(*args):
    x_ticker = x_dropdown.value
    y_ticker = y_dropdown.value
    
    # update the x and y attributes of the mark by selecting
    # the column from the price data frame
    with scatter.hold_sync():
        scatter.x = prices[x_ticker]
        scatter.y = prices[y_ticker]
    
    # update the title of the figure
    plt.xlabel(x_ticker)
    plt.ylabel(y_ticker)
# 2. register the callback by using the 'observe' method
x_dropdown.observe(update_scatter, 'value')
y_dropdown.observe(update_scatter, 'value')
# stack the dropdown and fig widgets using VBox
widgets.VBox([widgets.HBox([x_dropdown, y_dropdown]), fig3])
Explanation: Let's now create a scatter plot where we select X and Y data from the two dropdown menus
End of explanation
funcs = dict(sin=np.sin, cos=np.cos, tan=np.tan, sinh=np.sinh, tanh=np.tanh)
dropdown = widgets.Dropdown(options=funcs, description='Function')
fig = plt.figure(title='sin(x)', animation_duration=1000)
# create x and y data attributes for the line chart
x = np.arange(-10, 10, .1)
y = np.sin(x)
line = plt.plot(x, y ,'m')
def update_line(*args):
    f = dropdown.value
    fig.title = f'{f.__name__}(x)'
    line.y = f(line.x)
    
dropdown.observe(update_line, 'value')
widgets.VBox([dropdown, fig])
Explanation: In the example below, we'll look at plots of trigonometic functions
End of explanation
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