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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:
 Using Layout Templates
As we showed in containers exercises, multiple widgets can be arranged together using HBox and VBox. It is also possible to use the flexible GridBox specification. However, use of the specification involves some understanding of CSS properties and may impose a steep learning curve. Here, we will describe layout templates built on top of GridBox that simplify creation of common widget layouts.
Step1:  2x2 Grid
You can easily create a layout with 4 widgets arranged in a 2x2 matrix using the TwoByTwoLayout widget
Step2:  If you don't define a widget for some of the slots, the layout will automatically re-configure itself by merging neighbouring cells
Step3:  You can pass merge=False in the argument of the TwoByTwoLayout constructor if you don't want this behavior
Step4:  You can add a missing widget even after the layout initialization
Step5:  You can also use the linking feature of widgets to update some property of a widget based on another widget
Step6:  You can easily create more complex layouts with custom widgets. For example, you can use a bqplot Figure widget to add plots
Step7:  AppLayout
AppLayout is a widget layout template that allows you to create an application-like widget arrangements. It consist of a header, a footer, two sidebars and a central pane
Step8:  However with the automatic merging feature, it's possible to achieve many other layouts
Step9:  You can also modify the relative and absolute widths and heights of the panes using pane_widths and pane_heights arguments. Both accept a sequence of three elements, each of which is either an integer (equivalent to the weight given to the row/column) or a string in the format '1fr' (denoting one portion of the free space available) or '100px' (absolute size).
Step10:  Grid layout
GridspecLayout is a N-by-M grid layout allowing for flexible layout definitions using an API similar to matplotlib's GridSpec.
You can use GridspecLayout to define a simple regularly-spaced grid. For example, to create a 4x3 layout
Step11:  To make a widget span several columns and/or rows, you can use slice notation
Step12:  You can still change properties of the widgets stored in the grid, using the same indexing notation.
Step13:  Note
Step14:  Note
Step15:  Creating scatter plots using GridspecLayout
In this examples, we will demonstrate how to use GridspecLayout and bqplot widget to create a multipanel scatter plot. To run this example you will need to install the bqplot package.
For example, you can use the following snippet to obtain a scatter plot across multiple dimensions
Step16:  Style attributes
You can specify extra style properties to modify the layout. For example, you can change the size of the whole layout using the height and width arguments.
Step17:  The gap between the panes can be increase or decreased with grid_gap argument
Step18:  Additionally, you can control the alignment of widgets within the layout using justify_content and align_items attributes
Step19:  For other alignment options it's possible to use common names (top and bottom) or their CSS equivalents (flex-start and flex-end)
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Python Code:
# Utils widgets
from ipywidgets import Button, Layout, jslink, IntText, IntSlider
def create_expanded_button(description, button_style):
    return Button(description=description, button_style=button_style, 
                  layout=Layout(height='auto', width='auto'))
top_left_button = create_expanded_button("Top left", 'info')
top_right_button = create_expanded_button("Top right", 'success')
bottom_left_button = create_expanded_button("Bottom left", 'danger')
bottom_right_button = create_expanded_button("Bottom right", 'warning')
top_left_text = IntText(description='Top left', layout=Layout(width='auto', height='auto'))
top_right_text = IntText(description='Top right', layout=Layout(width='auto', height='auto'))
bottom_left_slider = IntSlider(description='Bottom left', layout=Layout(width='auto', height='auto'))
bottom_right_slider = IntSlider(description='Bottom right', layout=Layout(width='auto', height='auto'))
Explanation: Using Layout Templates
As we showed in containers exercises, multiple widgets can be arranged together using HBox and VBox. It is also possible to use the flexible GridBox specification. However, use of the specification involves some understanding of CSS properties and may impose a steep learning curve. Here, we will describe layout templates built on top of GridBox that simplify creation of common widget layouts.
End of explanation
from ipywidgets import TwoByTwoLayout
layout = dict(height='300px')
TwoByTwoLayout(top_left=top_left_button,
               top_right=top_right_button,
               bottom_left=bottom_left_button,
               bottom_right=bottom_right_button,
               layout=layout)
Explanation: 2x2 Grid
You can easily create a layout with 4 widgets arranged in a 2x2 matrix using the TwoByTwoLayout widget:
End of explanation
TwoByTwoLayout(top_left=top_left_button,
               bottom_left=bottom_left_button,
               bottom_right=bottom_right_button,
               layout=layout)
Explanation: If you don't define a widget for some of the slots, the layout will automatically re-configure itself by merging neighbouring cells
End of explanation
TwoByTwoLayout(top_left=top_left_button,
               bottom_left=bottom_left_button,
               bottom_right=bottom_right_button,
               merge=False,
               layout=layout)
Explanation: You can pass merge=False in the argument of the TwoByTwoLayout constructor if you don't want this behavior
End of explanation
layout_2x2 = TwoByTwoLayout(top_left=top_left_button,
                            bottom_left=bottom_left_button,
                            bottom_right=bottom_right_button,
                            layout=layout)
layout_2x2
layout_2x2.top_right = top_right_button
Explanation: You can add a missing widget even after the layout initialization:
End of explanation
app = TwoByTwoLayout(top_left=top_left_text, top_right=top_right_text,
                     bottom_left=bottom_left_slider, bottom_right=bottom_right_slider)
                     
link_left = jslink((app.top_left, 'value'), (app.bottom_left, 'value'))
link_right = jslink((app.top_right, 'value'), (app.bottom_right, 'value'))
app.bottom_right.value = 30
app.top_left.value = 25
app
Explanation: You can also use the linking feature of widgets to update some property of a widget based on another widget:
End of explanation
import bqplot as bq
import numpy as np
size = 100
np.random.seed(0)
x_data = range(size)
y_data = np.random.randn(size)
y_data_2 = np.random.randn(size)
y_data_3 = np.cumsum(np.random.randn(size) * 100.)
x_ord = bq.OrdinalScale()
y_sc = bq.LinearScale()
bar = bq.Bars(x=np.arange(10), y=np.random.rand(10), scales={'x': x_ord, 'y': y_sc})
ax_x = bq.Axis(scale=x_ord)
ax_y = bq.Axis(scale=y_sc, tick_format='0.2f', orientation='vertical')
fig = bq.Figure(marks=[bar], axes=[ax_x, ax_y], padding_x=0.025, padding_y=0.025,
                layout=Layout(width='auto', height='90%'))
from ipywidgets import FloatSlider
max_slider = FloatSlider(min=0, max=10, default_value=2, description="Max: ",
                         layout=Layout(width='auto', height='auto'))
min_slider = FloatSlider(min=-1, max=10, description="Min: ",
                         layout=Layout(width='auto', height='auto'))
app = TwoByTwoLayout(top_left=min_slider,
                     bottom_left=max_slider, 
                     bottom_right=fig,
                     align_items="center", 
                     height='700px')
jslink((y_sc, 'max'), (max_slider, 'value'))
jslink((y_sc, 'min'), (min_slider, 'value'))
jslink((min_slider, 'max'), (max_slider, 'value'))
jslink((max_slider, 'min'), (min_slider, 'value'))
max_slider.value = 1.5
app
Explanation: You can easily create more complex layouts with custom widgets. For example, you can use a bqplot Figure widget to add plots:
End of explanation
from ipywidgets import AppLayout, Button, Layout
header_button = create_expanded_button('Header', 'success')
left_button = create_expanded_button('Left', 'info')
center_button = create_expanded_button('Center', 'warning')
right_button = create_expanded_button('Right', 'info')
footer_button = create_expanded_button('Footer', 'success')
AppLayout(header=header_button,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=right_button,
          footer=footer_button,
          layout=layout)
Explanation: AppLayout
AppLayout is a widget layout template that allows you to create an application-like widget arrangements. It consist of a header, a footer, two sidebars and a central pane:
End of explanation
AppLayout(header=None,
          left_sidebar=None,
          center=center_button,
          right_sidebar=None,
          footer=None,
          layout=layout)
AppLayout(header=header_button,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=right_button,
          footer=None,
          layout=layout)
AppLayout(header=None,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=right_button,
          footer=None,
          layout=layout)
AppLayout(header=header_button,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=None,
          footer=footer_button,
          layout=layout)
AppLayout(header=header_button,
          left_sidebar=None,
          center=center_button,
          right_sidebar=right_button,
          footer=footer_button,
          layout=layout)
AppLayout(header=header_button,
          left_sidebar=None,
          center=center_button,
          right_sidebar=None,
          footer=footer_button,
          layout=layout)
AppLayout(header=header_button,
          left_sidebar=left_button,
          center=None,
          right_sidebar=right_button,
          footer=footer_button,
          layout=layout)
Explanation: However with the automatic merging feature, it's possible to achieve many other layouts:
End of explanation
AppLayout(header=header_button,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=right_button,
          footer=footer_button,
          pane_widths=[3, 3, 1],
          pane_heights=[1, 5, '60px'],
          layout=layout)
Explanation: You can also modify the relative and absolute widths and heights of the panes using pane_widths and pane_heights arguments. Both accept a sequence of three elements, each of which is either an integer (equivalent to the weight given to the row/column) or a string in the format '1fr' (denoting one portion of the free space available) or '100px' (absolute size).
End of explanation
from ipywidgets import GridspecLayout
grid = GridspecLayout(4, 3, layout=layout)
for i in range(4):
    for j in range(3):
        grid[i, j] = create_expanded_button('Button {} - {}'.format(i, j), 'warning')
grid
Explanation: Grid layout
GridspecLayout is a N-by-M grid layout allowing for flexible layout definitions using an API similar to matplotlib's GridSpec.
You can use GridspecLayout to define a simple regularly-spaced grid. For example, to create a 4x3 layout:
End of explanation
grid = GridspecLayout(4, 3, layout=layout)
grid[:3, 1:] = create_expanded_button('One', 'success')
grid[:, 0] = create_expanded_button('Two', 'info')
grid[3, 1] = create_expanded_button('Three', 'warning')
grid[3, 2] = create_expanded_button('Four', 'danger')
grid
Explanation: To make a widget span several columns and/or rows, you can use slice notation:
End of explanation
grid = GridspecLayout(4, 3, layout=layout)
grid[:3, 1:] = create_expanded_button('One', 'success')
grid[:, 0] = create_expanded_button('Two', 'info')
grid[3, 1] = create_expanded_button('Three', 'warning')
grid[3, 2] = create_expanded_button('Four', 'danger')
grid
grid[0, 0].description = "I am the blue one"
Explanation: You can still change properties of the widgets stored in the grid, using the same indexing notation.
End of explanation
grid = GridspecLayout(4, 3, layout=layout)
grid[:3, 1:] = create_expanded_button('One', 'info')
grid[:, 0] = create_expanded_button('Two', 'info')
grid[3, 1] = create_expanded_button('Three', 'info')
grid[3, 2] = create_expanded_button('Four', 'info')
grid
grid[3, 1] = create_expanded_button('New button!!', 'danger')
Explanation: Note: It's enough to pass an index of one of the grid cells occupied by the widget of interest. Slices are not supported in this context.
If there is already a widget that conflicts with the position of the widget being added, it will be removed from the grid:
End of explanation
grid[:3, 1:] = create_expanded_button('I am new too!!!!!', 'warning')
Explanation: Note: Slices are supported in this context.
End of explanation
import bqplot as bq
import numpy as np
from ipywidgets import GridspecLayout, Button, Layout
n_features = 5
data = np.random.randn(100, n_features)
data[:50, 2] += 4 * data[:50, 0] **2
data[50:, :] += 4
A = np.random.randn(n_features, n_features)/5
data = np.dot(data,A)
scales_x = [bq.LinearScale() for i in range(n_features)]
scales_y = [bq.LinearScale() for i in range(n_features)]
gs = GridspecLayout(n_features, n_features)
for i in range(n_features):
    for j in range(n_features):
        
        if i != j:
            sc_x = scales_x[j]
            sc_y = scales_y[i]
            scatt = bq.Scatter(x=data[:, j], y=data[:, i], scales={'x': sc_x, 'y': sc_y}, default_size=1)
            gs[i, j] = bq.Figure(marks=[scatt], layout=Layout(width='auto', height='auto'),
                                 fig_margin=dict(top=0, bottom=0, left=0, right=0))
        else:
            sc_x = scales_x[j]
            sc_y = bq.LinearScale()
        
            hist = bq.Hist(sample=data[:,i], scales={'sample': sc_x, 'count': sc_y})
            
            gs[i, j] = bq.Figure(marks=[hist], layout=Layout(width='auto', height='auto'),
                                 fig_margin=dict(top=0, bottom=0, left=0, right=0))
gs
Explanation: Creating scatter plots using GridspecLayout
In this examples, we will demonstrate how to use GridspecLayout and bqplot widget to create a multipanel scatter plot. To run this example you will need to install the bqplot package.
For example, you can use the following snippet to obtain a scatter plot across multiple dimensions:
End of explanation
AppLayout(header=None,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=right_button,
          footer=None,
          height="200px", width="50%")
Explanation: Style attributes
You can specify extra style properties to modify the layout. For example, you can change the size of the whole layout using the height and width arguments.
End of explanation
AppLayout(header=None,
          left_sidebar=left_button,
          center=center_button,
          right_sidebar=right_button,
          footer=None,
          height="200px", width="50%",
          grid_gap="10px")
Explanation: The gap between the panes can be increase or decreased with grid_gap argument:
End of explanation
from ipywidgets import Text, HTML
TwoByTwoLayout(top_left=top_left_button, top_right=top_right_button,
               bottom_right=bottom_right_button,
               justify_items='center',
               width="50%",
               align_items='center')
Explanation: Additionally, you can control the alignment of widgets within the layout using justify_content and align_items attributes:
End of explanation
TwoByTwoLayout(top_left=top_left_button, top_right=top_right_button,
               bottom_right=bottom_right_button,
               justify_items='center',
               width="50%",
               align_items='top')
Explanation: For other alignment options it's possible to use common names (top and bottom) or their CSS equivalents (flex-start and flex-end):
End of explanation
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