7. Visualization

Yi-Ju Tseng

Visualization

  • Visualization with Matplotlib
  • Simple Line Plots
  • Simple Scatter Plots
  • Visualizing Errors
  • Density and Contour Plots
  • Histograms, Binnings, and Density
  • Customizing Plot Legends and Colorbars
  • Multiple Subplots

Visualization with Matplotlib

What is Matplotlib?

  • Matplotlib is a multi-platform data visualization library for Python
  • Created by John Hunter in 2002, with version 0.1 released in 2003.
  • Large user and developer base, making it a powerful and ubiquitous tool for scientific visualization.
  • Despite newer visualization tools, Matplotlib remains a vital part of the data science stack.

Importing Matplotlib

# !pip3 install matplotlib
import matplotlib as mpl
import matplotlib.pyplot as plt

The plt interface is most commonly used

Load other important library

import numpy as np
import pandas as pd

Setting Plot Styles

Use plt.style.use('style') to set the visual style of your plots

plt.style.use('seaborn-v0_8-whitegrid')

Stylesheets

Figure

The figure (an instance of the class plt.Figure) = container that contains all the objects representing axes, graphics, text, and labels.

plt is from import matplotlib.pyplot as plt

fig = plt.figure()
<Figure size 960x480 with 0 Axes>

How to View Your Plots - (1/3)

  • From a Python script:
    Use plt.show() at the end to display figures.
    plt is from import matplotlib.pyplot as plt
  • plt.plot(x,y) for x and y axis
x = np.linspace(0, 10, 100) #(start, stop, num)
fig = plt.figure() # new instance
plt.plot(x, np.sin(x)) # plot
plt.show() # display figure

How to View Your Plots - (1/3)

How to View Your Plots - (2/3)

  • From an IPython shell:
    Use %matplotlib magic command to enable interactive plotting.
    plt.show() is not required.

How to View Your Plots - (3/3)

  • From a Jupyter (IPython) notebook:
    Use %matplotlib inline for static images or
    %matplotlib notebook for interactive plots
# %matplotlib inline
x = np.linspace(0, 10, 100)
plt.plot(x, np.sin(x), '-')
plt.plot(x, np.cos(x), '--');

Saving Figures

Save figures using fig.savefig():

fig.savefig('my_figure.png')
  • File format is inferred from the file extension.
  • Supported formats include: PNG, JPG, PDF, TIFF, and more.
fig.canvas.get_supported_filetypes()
{'eps': 'Encapsulated Postscript',
 'jpg': 'Joint Photographic Experts Group',
 'jpeg': 'Joint Photographic Experts Group',
 'pdf': 'Portable Document Format',
 'pgf': 'PGF code for LaTeX',
 'png': 'Portable Network Graphics',
 'ps': 'Postscript',
 'raw': 'Raw RGBA bitmap',
 'rgba': 'Raw RGBA bitmap',
 'svg': 'Scalable Vector Graphics',
 'svgz': 'Scalable Vector Graphics',
 'tif': 'Tagged Image File Format',
 'tiff': 'Tagged Image File Format',
 'webp': 'WebP Image Format'}

Visualization

  • Visualization with Matplotlib
  • Simple Line Plots
  • Simple Scatter Plots
  • Visualizing Errors
  • Density and Contour Plots
  • Histograms, Binnings, and Density
  • Customizing Plot Legends and Colorbars
  • Multiple Subplots

Simple Line Plots

Plotting a Simple Function

Plotting a sine curve with plt.plot(x,y), plt is from import matplotlib.pyplot as plt

plt.plot(x, np.sin(x))

Multiple Lines in One Plot

Call plt.plot multiple times to overlay lines:

plt.plot(x, np.sin(x))
plt.plot(x, np.cos(x))

Customizing Line Color

plt.plot() with color parameter

plt.plot(x, np.sin(x - 0), color='blue')        # by name
plt.plot(x, np.sin(x - 1), color='g')           # short code (r, g, b, c, m, y, k)
plt.plot(x, np.sin(x - 2), color='0.75')        # grayscale
plt.plot(x, np.sin(x - 3), color='#FFDD44')     # hex code
plt.plot(x, np.sin(x - 4), color=(1.0,0.2,0.3)) # RGB tuple
plt.plot(x, np.sin(x - 5), color='chartreuse')  # HTML color name

Customizing Line Style

plt.plot() with linestyle parameter

plt.plot(x, x + 0, linestyle='solid')
plt.plot(x, x + 1, linestyle='dashed')
plt.plot(x, x + 2, linestyle='dashdot')
plt.plot(x, x + 3, linestyle='dotted')
# Short codes:
plt.plot(x, x + 4, linestyle='-')   # solid
plt.plot(x, x + 5, linestyle='--')  # dashed
plt.plot(x, x + 6, linestyle='-.')  # dashdot
plt.plot(x, x + 7, linestyle=':')   # dotted

Customizing Line Color and Style

plt.plot(x, x + 0, '-g')  # solid green
plt.plot(x, x + 1, '--c') # dashed cyan
plt.plot(x, x + 2, '-.k') # dashdot black
plt.plot(x, x + 3, ':r')  # dotted red

Adjusting Axes Limits

plt.axis([xmin, xmax, ymin, ymax]), limits are arranged into a list

plt.axis([-1, 11, -1.5, 1.5])

Adding Titles, Labels, and Legends

plt.title(), plt.xlabel(), plt.ylabel()

plt.plot(x, np.sin(x))
plt.title("A Sine Curve")
plt.xlabel("x")
plt.ylabel("sin(x)")
Text(0, 0.5, 'sin(x)')

Adding Titles, Labels, and Legends

Add a legend for multiple lines with plt.plot() + label parameter and call plt.legend()

plt.plot(x, np.sin(x), '-g', label='sin(x)')
plt.plot(x, np.cos(x), ':b', label='cos(x)')
plt.legend()

Hands-on - Line Plot

Setting:

  1. Load library
import matplotlib
import matplotlib.pyplot as plt
  1. 中文問題….
# colab顯示繁體中文 問題：matplotlib繪圖，會發生中文無法顯示的問題
# 先下載台北黑體字型
!gdown '1eGAsTN1HBpJAkeVM57_C7ccp7hbgSz3_' --output TaipeiSansTCBeta-Regular.ttf
# 新增字體
matplotlib.font_manager.fontManager.addfont('TaipeiSansTCBeta-Regular.ttf')
# 將 font-family 設為 Taipei Sans TC Beta
# 設定完後，之後的圖表都可以顯示中文了
matplotlib.rc('font', family='Taipei Sans TC Beta')

Hands-on - Line Plot

Data: 空氣品質監測日平均值(一般污染物)

# https://data.moenv.gov.tw/dataset/detail/AQX_P_19
# https://drive.google.com/drive/folders/1OrMlB4hP8nnW_0bYwoHRO6DRXWNk1qvy?usp=sharing
!gdown '1P3qrYrynZhXDC13dVo5KhDXmld5OGZz1' --output 202310.csv
!gdown '1P1Kv1ZmPOYyi83DJKUIPoksM31vJJiS5' --output 202311.csv
!gdown '1P0mojOXgvVbXImnRTPQemm7dCkLDLKAC' --output 202312.csv
!gdown '1OwAf366l-iItXV4foJemw5QdMuD3JgMc' --output 202401.csv

Hands-on - Line Plot

Data

df202401 = pd.read_csv('202401.csv') 
df202312 = pd.read_csv('202312.csv') 
df202311 = pd.read_csv('202311.csv') 
df202310 = pd.read_csv('202310.csv') 
df_air = pd.concat([df202401,df202312,df202311,df202310],axis=0)
print(df_air.head())
   "siteid" "sitename"  "itemid" "itemname" "itemengname" "itemunit"  \
0        80         關山         4       懸浮微粒          PM10      μg/m3   
1        80         關山         5       氮氧化物           NOx        ppb   
2        80         關山         6       一氧化氮            NO        ppb   
3        80         關山         7       二氧化氮           NO2        ppb   
4        80         關山        10         風速    WIND_SPEED      m/sec   

  "monitordate" "concentration"  
0    2024-01-01              33  
1    2024-01-01             3.8  
2    2024-01-01             0.5  
3    2024-01-01             3.2  
4    2024-01-01             2.2

Hands-on - Line Plot

Data Clean: Remove the quotes of column headers

new_headers = []
for header in df_air.columns: # data.columns is your list of headers
    header = header.strip('"') # Remove the quotes off each header
    new_headers.append(header) # Save the new strings without the quotes
df_air.columns = new_headers # Replace the old headers with the new list
print(df_air.head())
   siteid sitename  itemid itemname itemengname itemunit monitordate  \
0      80       關山       4     懸浮微粒        PM10    μg/m3  2024-01-01   
1      80       關山       5     氮氧化物         NOx      ppb  2024-01-01   
2      80       關山       6     一氧化氮          NO      ppb  2024-01-01   
3      80       關山       7     二氧化氮         NO2      ppb  2024-01-01   
4      80       關山      10       風速  WIND_SPEED    m/sec  2024-01-01   

  concentration  
0            33  
1           3.8  
2           0.5  
3           3.2  
4           2.2

Hands-on - Line Plot

Data Clean: Data type

df_air['concentration'].dtypes
dtype('O')
df_air['concentration'][0:5]
0     33
1    3.8
2    0.5
3    3.2
4    2.2
Name: concentration, dtype: object

pd.to_numeric(List or Series, errors={‘ignore’, ‘raise’, ‘coerce’})

df_air['concentration'] = pd.to_numeric(df_air['concentration'], 
                                        errors="coerce")
df_air['concentration'].dtypes
dtype('float64')

Hands-on - Line Plot

Data Clean: Data type

df_air['monitordate'].dtypes
dtype('O')

pd.to_datetime(List or Series, errors={‘ignore’, ‘raise’, ‘coerce’},format=)

# Parse String To DateTime
df_air['DateTime']=pd.to_datetime(df_air['monitordate'],
                              format='%Y-%m-%d')
df_air.dtypes
siteid                    int64
sitename                 object
itemid                    int64
itemname                 object
itemengname              object
itemunit                 object
monitordate              object
concentration           float64
DateTime         datetime64[ns]
dtype: object

Hands-on - Line Plot

請試著呈現林口測站在2024/1/1~2024/1/15的PM2.5濃度

Hint:

  • Subset, Boolean masking
  • pd.to_datetime(List or Series, errors={‘ignore’, ‘raise’, ‘coerce’},format=)
  • df.sort_values(by=column) (df can be any DataFrame)
       siteid sitename  itemid itemname itemengname itemunit monitordate  \
978         9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-01   
1262        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-02   
3105        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-03   
3337        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-04   
4521        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-05   
5502        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-06   
7452        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-07   
7901        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-08   
8853        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-09   
9946        9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-10   
11105       9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-11   
12241       9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-12   
13228       9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-13   
15186       9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-14   
15416       9       林口      33    細懸浮微粒       PM2.5    μg/m3  2024-01-15   

       concentration   DateTime  
978             24.0 2024-01-01  
1262            13.0 2024-01-02  
3105            15.1 2024-01-03  
3337            15.9 2024-01-04  
4521            23.5 2024-01-05  
5502            20.6 2024-01-06  
7452            20.2 2024-01-07  
7901            12.6 2024-01-08  
8853             5.8 2024-01-09  
9946            27.3 2024-01-10  
11105           19.7 2024-01-11  
12241           10.1 2024-01-12  
13228            4.5 2024-01-13  
15186            6.3 2024-01-14  
15416           19.2 2024-01-15

Hands-on - Line Plot

請試著呈現林口測站在2024/1/1~2024/1/15的PM2.5濃度，要呈現figure legend，也要呈現x y 軸的名字

Ref:

Line Plot - Seaborn

sns.lineplot(x,y), x and y are data for each axis

import seaborn as sns
sns.lineplot(x=pm25Linkou2024['DateTime'], 
              y=pm25Linkou2024['concentration'])

Line Plot - Seaborn

sns.lineplot(data, x, y), x and y are column names for each axis

sns.lineplot(data = pm25Linkou2024, x='DateTime', y='concentration')

Simple Scatter Plots

What is a Scatter Plot?

  • A scatter plot displays individual data points as dots, circles, or other shapes, rather than connecting them with lines.
  • Useful for visualizing the relationship between two or more variables.

Scatter Plots with plt.plot()

plt.plot(x,y,marker,color), marker for shapes, color for color

x = np.linspace(0, 10, 30)
y = np.sin(x)
plt.plot(x, y, 'o', color='black')

Scatter Plots - marker shape

'o', '.', ',', 'x', '+', 'v', '^', '', 's', 'd' …

rng = np.random.RandomState(0)
for marker in ['o', '.', ',', 'x', '+', 'v', '^', '', 's', 'd']:
    plt.plot(rng.rand(5), rng.rand(5), marker, label=f"marker='{marker}'")
plt.legend()

Line styles and marker shape

Combine marker and line styles for more complex plots

plt.plot(x, y, '-ok') # solid, circle, black

Line styles and marker shape

Customize markers and lines with additional arguments

plt.plot(x, y, '-p', color='gray', # solid, pentagon
         markersize=15, linewidth=4,
         markerfacecolor='white',
         markeredgecolor='gray',
         markeredgewidth=2)

Scatter Plots with plt.scatter

plt.scatter(x, y) allowing individual control over each point’s size, color, and other properties.

plt.scatter(x, y, marker='o')

Varying color and size - Bubble chart

Data:

rng = np.random.RandomState(0)
x = rng.randn(100)
y = rng.randn(100)
colors = rng.rand(100)
sizes = 1000 * rng.rand(100)

Parameters:

  • c: color for each point
  • s size
  • alpha transparency
  • cmap colormap (more details later)

with varying color and size - Bubble chart

plt.scatter(x, y, c=colors, s=sizes, alpha=0.3, cmap='viridis')
plt.colorbar()  # Show color scale

Visualizing Multidimensional Data

Iris dataset, visualizing four features at once.

Data:

# !pip3 install scikit-learn
from sklearn.datasets import load_iris
iris = load_iris()
features = iris.data.T
print(features)
[[5.1 4.9 4.7 4.6 5.  5.4 4.6 5.  4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1
  5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.  5.  5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.
  5.5 4.9 4.4 5.1 5.  4.5 4.4 5.  5.1 4.8 5.1 4.6 5.3 5.  7.  6.4 6.9 5.5
  6.5 5.7 6.3 4.9 6.6 5.2 5.  5.9 6.  6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1
  6.3 6.1 6.4 6.6 6.8 6.7 6.  5.7 5.5 5.5 5.8 6.  5.4 6.  6.7 6.3 5.6 5.5
  5.5 6.1 5.8 5.  5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3
  6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.  6.9 5.6 7.7 6.3 6.7 7.2
  6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.  6.9 6.7 6.9 5.8 6.8
  6.7 6.7 6.3 6.5 6.2 5.9]
 [3.5 3.  3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 3.7 3.4 3.  3.  4.  4.4 3.9 3.5
  3.8 3.8 3.4 3.7 3.6 3.3 3.4 3.  3.4 3.5 3.4 3.2 3.1 3.4 4.1 4.2 3.1 3.2
  3.5 3.6 3.  3.4 3.5 2.3 3.2 3.5 3.8 3.  3.8 3.2 3.7 3.3 3.2 3.2 3.1 2.3
  2.8 2.8 3.3 2.4 2.9 2.7 2.  3.  2.2 2.9 2.9 3.1 3.  2.7 2.2 2.5 3.2 2.8
  2.5 2.8 2.9 3.  2.8 3.  2.9 2.6 2.4 2.4 2.7 2.7 3.  3.4 3.1 2.3 3.  2.5
  2.6 3.  2.6 2.3 2.7 3.  2.9 2.9 2.5 2.8 3.3 2.7 3.  2.9 3.  3.  2.5 2.9
  2.5 3.6 3.2 2.7 3.  2.5 2.8 3.2 3.  3.8 2.6 2.2 3.2 2.8 2.8 2.7 3.3 3.2
  2.8 3.  2.8 3.  2.8 3.8 2.8 2.8 2.6 3.  3.4 3.1 3.  3.1 3.1 3.1 2.7 3.2
  3.3 3.  2.5 3.  3.4 3. ]
 [1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.5 1.3 1.4
  1.7 1.5 1.7 1.5 1.  1.7 1.9 1.6 1.6 1.5 1.4 1.6 1.6 1.5 1.5 1.4 1.5 1.2
  1.3 1.4 1.3 1.5 1.3 1.3 1.3 1.6 1.9 1.4 1.6 1.4 1.5 1.4 4.7 4.5 4.9 4.
  4.6 4.5 4.7 3.3 4.6 3.9 3.5 4.2 4.  4.7 3.6 4.4 4.5 4.1 4.5 3.9 4.8 4.
  4.9 4.7 4.3 4.4 4.8 5.  4.5 3.5 3.8 3.7 3.9 5.1 4.5 4.5 4.7 4.4 4.1 4.
  4.4 4.6 4.  3.3 4.2 4.2 4.2 4.3 3.  4.1 6.  5.1 5.9 5.6 5.8 6.6 4.5 6.3
  5.8 6.1 5.1 5.3 5.5 5.  5.1 5.3 5.5 6.7 6.9 5.  5.7 4.9 6.7 4.9 5.7 6.
  4.8 4.9 5.6 5.8 6.1 6.4 5.6 5.1 5.6 6.1 5.6 5.5 4.8 5.4 5.6 5.1 5.1 5.9
  5.7 5.2 5.  5.2 5.4 5.1]
 [0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 0.2 0.2 0.1 0.1 0.2 0.4 0.4 0.3
  0.3 0.3 0.2 0.4 0.2 0.5 0.2 0.2 0.4 0.2 0.2 0.2 0.2 0.4 0.1 0.2 0.2 0.2
  0.2 0.1 0.2 0.2 0.3 0.3 0.2 0.6 0.4 0.3 0.2 0.2 0.2 0.2 1.4 1.5 1.5 1.3
  1.5 1.3 1.6 1.  1.3 1.4 1.  1.5 1.  1.4 1.3 1.4 1.5 1.  1.5 1.1 1.8 1.3
  1.5 1.2 1.3 1.4 1.4 1.7 1.5 1.  1.1 1.  1.2 1.6 1.5 1.6 1.5 1.3 1.3 1.3
  1.2 1.4 1.2 1.  1.3 1.2 1.3 1.3 1.1 1.3 2.5 1.9 2.1 1.8 2.2 2.1 1.7 1.8
  1.8 2.5 2.  1.9 2.1 2.  2.4 2.3 1.8 2.2 2.3 1.5 2.3 2.  2.  1.8 2.1 1.8
  1.8 1.8 2.1 1.6 1.9 2.  2.2 1.5 1.4 2.3 2.4 1.8 1.8 2.1 2.4 2.3 1.9 2.3
  2.5 2.3 1.9 2.  2.3 1.8]]

Visualizing Multidimensional Data

x/y positions, size, and color all encode different data dimensions.

plt.scatter(features[0], features[1], alpha=0.2,
            s=100*features[3], c=iris.target, cmap='viridis')
plt.xlabel(iris.feature_names[0])
plt.ylabel(iris.feature_names[1])
Text(0, 0.5, 'sepal width (cm)')

Visualizing Multidimensional Data

Text(0, 0.5, 'sepal width (cm)')

plot vs. scatter: Efficiency Note

  • For small datasets, both plt.plot and plt.scatter work well.
  • For large datasets (thousands of points or more), plt.plot is more efficient because all points are rendered with the same style.
  • plt.scatter is less efficient for large datasets since it allows per-point customization and must render each point individually.

Hands-on - Scatter Plot

試著看看空氣污染資料中，NO2濃度與SO2濃度有沒有相關？

Hint: multiple records on the same date - df.groupby()

Ref:

Hands-on - Scatter Plot

使用泡泡圖呈現NO2與SO2的關係，並用風速（WIND_SPEED）當作泡泡大小，觀察這些資料是否有相關

Visualizing Errors

Why Show Error Bars?

  • Error bars represent the uncertainty or variability in your data.
  • They help communicate the reliability and precision of measurements.
  • For example, reporting a measurement as \[74 \pm 5\] is much more informative than just 74

Basic Error Bars with plt.errorbar

plt.errorbar(x, y, yerr=error size, fmt = style): add error bars to your plots

  • yerr specifies the vertical error bar size
  • fmt controls the marker and line style (same as in plt.plot)

Data:

x = np.linspace(0, 10, 50) #(start,end,num)
dy = 0.8
y = np.sin(x) + dy * np.random.randn(50)

Basic Error Bars with plt.errorbar

Plot: plt.errorbar(x, y, yerr=error size, fmt = style)

plt.errorbar(x, y, yerr=dy, fmt='.k')
plt.show()

Customizing Error Bars

You can adjust the appearance for clarity, especially in crowded plots in plt.errorbar():

  • ecolor: color of the error bars
  • elinewidth: width of error bar lines
  • capsize: size of the error bar caps

Customizing Error Bars

plt.errorbar(
    x, y, yerr=dy, fmt='o', color='black',
    ecolor='lightgray', elinewidth=3, capsize=0
)
plt.show()

Horizontal and One-Sided Error Bars

Add horizontal error bars using xerr in plt.errorbar()

plt.errorbar(x, y, xerr=0.5, fmt='o')

Summary: Common Error Bar Options

Parameter Description
yerr Vertical error bar sizes
xerr Horizontal error bar sizes
fmt Format string for marker/line style
ecolor Color of error bars
elinewidth Line width of error bars
capsize Size of caps at the ends of error bars

Key Takeaways

  • Use error bars to show uncertainty in your data.
  • plt.errorbar is flexible and customizable for both simple and advanced needs.
  • See the Matplotlib documentation for more options.

Density and Contour Plots

Introduction

  • Density and contour plots are useful for visualizing three-dimensional data in two dimensions using contours (lines) or color-coded regions.
  • Matplotlib provides three main functions for this purpose:
    • plt.contour() for contour lines
    • plt.contourf() for filled contours
    • plt.imshow() for displaying images

Creating a Contour Plot

  • Contour plots require a function \[ z = f(x, y) \] evaluated on a grid.
  • Use np.meshgrid to create the grid:
def f(x, y):
    return np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)
x = np.linspace(0, 5, 50)
y = np.linspace(0, 5, 40)
X, Y = np.meshgrid(x, y)
Z = f(X, Y)
print(Z)
[[-0.83907153 -0.83470697 -0.8216586  ...  0.8956708   0.68617261
   0.41940746]
 [-0.83907153 -0.8275558  -0.80744041 ...  0.93467448  0.77467433
   0.55894214]
 [-0.83907153 -0.820263   -0.79266951 ...  0.98503397  0.88847607
   0.73757604]
 ...
 [-0.83907153 -0.48696962 -0.02692065 ...  0.98525345  0.79584263
   0.46799565]
 [-0.83907153 -0.47558005 -0.00130271 ...  0.93488414  0.6993547
   0.37933079]
 [-0.83907153 -0.46410908  0.02431613 ...  0.89579384  0.65690314
   0.40107702]]

Basic contour plot

plt.contour(X, Y, Z, colors)

plt.contour(X, Y, Z, colors='black')

Negative values are dashed lines, positive values are solid lines

Color-Coded Contour Plot

  • cmap: to specify a colormap
  • set the number of contour levels 20
plt.contour(X, Y, Z, 20, cmap='RdGy')

Filled Contour Plot

  • plt.contourf() for filled contours
  • add a colorbar plt.colorbar() for reference:
plt.contourf(X, Y, Z, 20, cmap='RdGy')
plt.colorbar()

Displaying Data as an Image

  • plt.imshow to display the grid as an image
    • does not accept x and y grids; set extent manually.
    • The default origin for imshow is the upper left; set origin='lower' for consistency with contour plots.
plt.imshow(Z, extent=[0, 5, 0, 5], origin='lower', cmap='RdGy')
plt.colorbar()

Combining Contour and Image Plots

Overlay contours on an image for richer visualization: plt.clabel()- label contour lines

contours = plt.contour(X, Y, Z, 3, colors='black')
plt.clabel(contours, inline=True, fontsize=8)
plt.imshow(Z, extent=[0, 5, 0, 5], origin='lower', cmap='RdGy', alpha=0.5)
plt.colorbar()

Summary Table: Key Functions

Function Description
plt.contour Draws contour lines
plt.contourf Draws filled contours
plt.imshow Displays a 2D array as an image
plt.colorbar Adds a colorbar to the plot
plt.clabel Adds labels to contour lines

Histograms, Binnings, and Density

What is a Histogram?

  • Graphical representation of the distribution of numerical data.
  • It divides data into bins (intervals) and shows the frequency (count) of data points in each bin.
  • Useful as a first step in understanding a dataset.

Creating a Simple Histogram

plt.hist(data) displays the distribution of data in default bins

data = np.random.randn(1000)
plt.hist(data)
plt.show()

Customizing Histograms

Options to control calculation and display:

  • bins: Number of bins
  • alpha: Transparency
  • histtype: Type of histogram (e.g., 'stepfilled')
  • color, edgecolor: Color settings
plt.hist(data, bins=30, alpha=0.5,
         histtype='stepfilled', color='steelblue',
         edgecolor='none')
plt.show()

Customizing Histograms

plt.hist(data, bins=30, alpha=0.5,
         histtype='stepfilled', color='steelblue',
         edgecolor='none')
plt.show()

Comparing Multiple Distributions

Overlay several histograms using transparency for comparison.

Data:

x1 = np.random.normal(0, 0.8, 1000)
x2 = np.random.normal(-2, 1, 1000)
x3 = np.random.normal(3, 2, 1000)

Comparing Multiple Distributions

Use dict(parameters) to set parameters

kwargs = dict(histtype='stepfilled', alpha=0.3, bins=40)
plt.hist(x1, **kwargs)
plt.hist(x2, **kwargs)
plt.hist(x3, **kwargs)
plt.show()

Two-Dimensional Histograms

plt.hist2d(x, y)

Data

mean = [0, 0]
cov = [[1, 1], [1, 2]]
x, y = np.random.multivariate_normal(mean, cov, 10000).T

Figure

plt.hist2d(x, y, bins=30, cmap='Blues')
cb = plt.colorbar()
cb.set_label('counts in bin')
plt.show()

Two-Dimensional Histograms

Hexagonal Binning

plt.hexbin(x,y) use hexagons for 2D binning

plt.hexbin(x, y, gridsize=30, cmap='Blues')
cb = plt.colorbar(label='count in bin')
plt.show()

Summary: Histogram and Binning

Function Description
plt.hist 1D histogram plot
plt.hist2d 2D histogram plot
plt.hexbin 2D hexagonal bin plot

Hands-on - Histogram

看看新竹與前鎮一氧化碳(CO)的資料分布是否有差異（疊在一張圖中）

Customizing Plot Legends and Colorbars

Creating a Simple Legend

  • Legends assign meaning to plot elements, making visualizations clearer and more informative.
  • The simplest way to add a legend is with plt.legend().
  • Any plot element with a label will appear in the legend.

Creating a Simple Legend

x = np.linspace(0, 10, 1000)
fig = plt.figure()
plt.plot(x, np.sin(x), '-b', label='Sine')
plt.plot(x, np.cos(x), '--r', label='Cosine')
plt.axis('equal')
plt.legend()

  • By default, all labeled elements are included in the legend

Customizing Legend Placement and Appearance

  • Location: Control legend placement with the loc parameter (e.g., 'upper left', 'lower center').
  • Frame: Remove the legend box with frameon=False.
  • Columns: Use ncol to arrange legend entries in multiple columns.
  • Aesthetics: Customize with options like fancybox, shadow, framealpha, and borderpad.

Legend Placement and Appearance

For more options, see the plt.legend docstring.

plt.plot(x, np.cos(x), '--r', label='Cosine')
plt.legend(loc='upper left', frameon=False)

Legend Placement and Appearance

plt.plot(x, np.cos(x), '--r', label='Cosine')
plt.plot(x, np.sin(x), '-b', label='Sine')
plt.legend(frameon=False, loc='lower center', ncol=2)

Choosing Elements for the Legend

To control which elements appear, pass specific plot objects and labels to legend()

y = np.sin(x[:, np.newaxis] + np.pi * np.arange(0, 2, 0.5))
lines = plt.plot(x, y)
plt.legend(lines[:2], ['first', 'second'])

Choosing Elements for the Legend

Or only label the elements you want in the legend

plt.plot(x, y[:, 0], label='first')
plt.plot(x, y[:, 1], label='second')
plt.plot(x, y[:, 2:])
plt.legend(framealpha=1, frameon=True)

Key Points

  • Use label in plotting commands and call legend() to create legends.
  • Customize legends with location, columns, frame, and more.
  • Control legend entries by labeling only desired elements or passing specific objects.

Why Use Colorbars?

  • Provide a key for interpreting the meaning of colors in plots
  • While legends are for discrete labels, colorbars are essential for continuous labels

Creating a Basic Colorbar

Data:

x = np.linspace(0, 10, 1000)
I = np.sin(x) * np.cos(x[:, np.newaxis])
print(I)
[[ 0.          0.01000984  0.02001868 ... -0.52711499 -0.53559488
  -0.54402111]
 [ 0.          0.01000934  0.02001768 ... -0.52708858 -0.53556805
  -0.54399386]
 [ 0.          0.01000784  0.02001467 ... -0.52700936 -0.53548755
  -0.54391209]
 ...
 [-0.         -0.0085063  -0.01701176 ...  0.44793914  0.4551453
   0.46230586]
 [-0.         -0.00845306 -0.01690528 ...  0.44513546  0.45229652
   0.45941226]
 [-0.         -0.00839897 -0.01679711 ...  0.44228718  0.44940242
   0.45647263]]

Creating a Basic Colorbar

Add plt.colorbar() after using color mapping:

plt.imshow(I)
plt.colorbar()

Customizing Colormaps

Specify a colormap with the cmap argument (check plt.cm namespace (e.g., plt.cm.viridis, plt.cm.RdBu))

plt.imshow(I, cmap='gray')

Types of Colormaps

  • Sequential colormaps: One continuous color sequence (e.g., binary, viridis).
  • Divergent colormaps: Two contrasting colors for positive/negative deviations (e.g., RdBu, PuOr).
  • Qualitative colormaps: No particular sequence, for categorical data (e.g., rainbow, jet).

Setting Color Limits and Extensions

  • Manually set color limits with plt.clim() (to focus on a specific data range)
  • Indicate out-of-bounds values using the extend in plt.colorbar()
plt.imshow(I, cmap='RdBu')
plt.colorbar(extend='both')
plt.clim(-1, 1)

Setting Color Limits and Extensions

Discrete Colorbars

Represent discrete values: plt.cm.get_cmap() with number of bins

plt.imshow(I, cmap=plt.cm.get_cmap('Blues', 6))
plt.colorbar()
plt.clim(-1, 1)

Key Points

  • Use colorbars for continuous data and choose colormaps thoughtfully for clarity and accessibility.
  • Customize colorbars with colormap selection, color limits, extensions, and discrete bins.
  • Always consider how your color choices will appear in grayscale or to colorblind viewers.

Multiple Subplots

Why Use Multiple Subplots?

  • Comparing data side by side is often helpful for analysis and presentation.
  • Matplotlib allows you to arrange multiple smaller plots (subplots) within a single figure.
  • There are 3 Ways to Create Subplots

1. Manual Placement with plt.axes

Create axes anywhere in the figure by specifying [left, bottom, width, height] in figure coordinates (0 to 1).

ax1 = plt.axes()  # Standard axes
ax2 = plt.axes([0.65, 0.65, 0.2, 0.2])  # Inset axes at top-right

2. Simple Grids with plt.subplot

Create a grid of subplots by specifying rows, columns, and plot index (starts at 1, goes left-to-right, top-to-bottom). plt.subplot(row, col, plot index)

for i in range(1, 7):
    plt.subplot(2, 3, i)
    plt.text(0.5, 0.5, str((2, 3, i)), fontsize=18, ha='center')

3. Flexible Layouts with plt.GridSpec

For more complex arrangements

grid = plt.GridSpec(2, 3, wspace=0.4, hspace=0.3)
plt.subplot(grid[0, 0])
plt.subplot(grid[0, 1:])
plt.subplot(grid[1, :2])
plt.subplot(grid[1, 2])

Summary Table

Method Use Case Access Pattern
plt.axes Manual, precise placement Variable names
plt.subplot Simple grid, small number of subplots Index (1-based)
plt.GridSpec Complex, flexible layouts Slicing, subplots