ML-Kurs-SS2023/slides/intro_python.md

---
title: |
  | Introduction to Data Analysis and Machine Learning in Physics:  
  | 1. Introduction to python  

author: "Martino Borsato, Jörg Marks, Klaus Reygers"
date: "Studierendentage, 11-14 April 2022"
---

## Outline of the $1^{st}$ day

* Technical instructions for your interactions with the CIP pool, like
   * using the jupyter hub
   * using python locally in your own linux environment (anaconda)
   * access the CIP pool from your own windows or linux system
   * transfer data from and to the CIP pool

  Can be found in [\textcolor{violet}{CIPpoolAccess.PDF}](https://www.physi.uni-heidelberg.de/~marks/root_einfuehrung/Folien/CIPpoolAccess.pdf)\normalsize

* Summary of NumPy

* Plotting with matplotlib

* Input / output of data

* Summary of pandas

* Fitting with iminuit and pyROOT


## A glimpse into python classes

 The following python classes are important to data analysis and machine
 learning will be used during the course
 
 * [\textcolor{violet}{NumPy}](https://numpy.org/doc/stable/user/basics.html) - python library adding support for large,
   multi-dimensional arrays and matrices, along with high-level
   mathematical functions to operate on these arrays

 * [\textcolor{violet}{matplotlib}](https://matplotlib.org/stable/tutorials/index.html) - a python plotting library

 * [\textcolor{violet}{SciPy}](https://docs.scipy.org/doc/scipy/reference/tutorial/index.html) - extension of NumPy by a collection of
   mathematical algorithms for minimization, regression, 
   fourier transformation, linear algebra and image processing

 * [\textcolor{violet}{iminuit}](https://iminuit.readthedocs.io/en/stable/) -
   python wrapper to the data fitting toolkit
   [\textcolor{violet}{Minuit2}](https://root.cern.ch/doc/master/Minuit2Page.html)
   developed at CERN by F. James in the 1970ies 

 * [\textcolor{violet}{pyROOT}](https://root.cern/manual/python/) - python wrapper to the C++ data analysis toolkit
   ROOT used at the LHC

 * [\textcolor{violet}{scikit-learn}](https://scikit-learn.org/stable/) - machine learning library written in
   python, which makes use extensively of NumPy for high-performance
   linear algebra algorithms
   
## NumPy
 
   \textcolor{blue}{NumPy} (Numerical Python) is an open source Python library,
   which contains multidimensional array and matrix data structures and methods
   to efficiently operate on these. The core object is
   a homogeneous n-dimensional array object,  \textcolor{blue}{ndarray}, which
   allows for a wide variety of \textcolor{blue}{fast operations and mathematical calculations
   with arrays and matrices} due to the extensive usage of compiled code.  

   * It is heavily used in numerous scientific python packages

   * `ndarray` 's  have a fixed size at creation $\rightarrow$ changing size
     leads to recreation

   * Array elements are all required to be of the same data type

   * Facilitates advanced mathematical operations on large datasets

   * See for a summary, e.g.     
 \small
[\textcolor{violet}{https://cs231n.github.io/python-numpy-tutorial/\#numpy}](https://cs231n.github.io/python-numpy-tutorial/#numpy) \normalsize

\vfill
 
::: columns
:::: {.column width=30%}

::::
:::

::: columns
:::: {.column width=35%}

`c = []`

`for i in range(len(a)):`

    `c.append(a[i]*b[i])`

::::

:::: {.column width=35%}

with NumPy

`c = a * b`

::::
:::

<!---
It seem we need to indent by hand.
I don't manage to align under the bullet text
If we do it with column the vertical space is with code sections not good
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code high lightning.
See the different versions of the same page in the following
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## NumPy - array basics

* numpy arrays build a grid of \textcolor{blue}{same type} values, which are indexed.
  The *rank* is the dimension of the array.
  There are methods to create  and preset arrays.

\footnotesize

```python
	 myA = np.array([2, 5 , 11])             # create rank 1 array (vector like)
	 type(myA)                               # <class ‘numpy.ndarray’>
	 myA.shape                               # (3,)
	 print(myA[2])                           # 11   access 3. element
	 myA[0] = 12                             # set 1. element to 12
	 myB = np.array([[1,5],[7,9]])           # create  rank 2 array
	 myB.shape                               # (2,2)
	 print(myB[0,0],myB[0,1],myB[1,1])       # 1 5 9
	 myC = np.arange(6)                      # create rank 1 set to 0 - 5
	 myC.reshape(2,3)                        # change rank to (2,3)

	 zero = np.zeros((2,5))                  # 2 rows, 5 columns, set to 0
	 one = np.ones((2,2))                    # 2 rows, 2 columns, set to 1
	 five = np.full((2,2), 5)                # 2 rows, 2 columns, set to 5
	 e = np.eye(2)                           # create 2x2 identity matrix
```
\normalsize


##  NumPy - array indexing (1)

* select slices of a numpy array

\footnotesize
```python
     a = np.array([[1,2,3,4],
                   [5,6,7,8],                # 3 rows 4 columns array
                   [9,10,11,12]])
     b = a[:2, 1:3]                          # subarray of 2 rows and
         array([[2, 3],                      # column 1 and 2
                [6, 7]])
```		    
\normalsize

* a slice of an array points into the same data, *modifying* changes the original array!
	 
\footnotesize
```python
     b[0, 0] = 77	                         # b[0,0] and a[0,1] are 77

     r1_row = a[1, :]                        # get 2nd row ->  rank 1
     r1_row.shape	                         # (4,)
     r2_row = a[1:2, :]                      # get 2nd row -> rank 2
     r2_row.shape                            # (1,4)
     a=np.array([[1,2],[3,4],[5,6]])         # set a , 3 rows 2 cols
     d=a[[0, 1, 2], [0, 1, 1]]               # d contains [1 4 6]
     e=a[[1, 2], [1, 1]]                     # e contains [4 6]
     np.array([a[0,0],a[1,1],a[2,0]])        # address elements explicitly
```
\normalsize


##  NumPy - array indexing (2)

 
* integer array indexing by setting an array of indices $\rightarrow$ selecting/changing elements

\footnotesize
```python
     a = np.array([[1,2,3,4],
                   [5,6,7,8],                # 3 rows 4 columns array
                   [9,10,11,12]])
     p_a = np.array([0,2,0])                 # Create an array of indices
     s = a[np.arange(3), p_a]                # number the rows, p_a points to cols
     print (s)                               # s contains [1 7 9]
     a[np.arange(3),p_a] += 10               # add 10 to corresponding elements
     x=np.array([[8,2],[7,4]])               # create 2x2 array
     bool = (x > 5)                          # bool : array of boolians
                                             #   [[True False]
                                             #    [True False]]
     print(x[x>5])                           # select elements, prints [8 7]
```		    
\normalsize

* data type in numpy - create according to input numbers or set explicitly

\footnotesize

```python
     x = np.array([1.1, 2.1])                # create float array 
     print(x.dtype)                          # print  float64
     y=np.array([1.1,2.9],dtype=np.int64)    # create float array [1 2]
```
\normalsize


## NumPy - functions

* math functions operate elementwise either as operator overload or as methods

\footnotesize
```python
     x=np.array([[1,2],[3,4]],dtype=np.float64)    # define 2x2 float array
     y=np.array([[3,1],[5,1]],dtype=np.float64)    # define 2x2 float array
     s = x + y                                     # elementwise sum 
     s = np.add(x,y)
     s = np.subtract(x,y)
     s = np.multiply(x,y)                          # no matrix multiplication!
     s = np.divide(x,y)
     s = np.sqrt(x), np.exp(x), ...
     x @ y , or np.dot(x, y)                       # matrix product
     np.sum(x, axis=0)                             # sum of each column
     np.sum(x, axis=1)                             # sum of each row
     xT = x.T                                      # transpose of x
     x = np.linspace(0,2*pi,100)                   # get equal spaced points in x

     r = np.random.default_rng(seed=42)            # constructor random number class
     b = r.random((2,3))                           # random 2x3 matrix
```
\normalsize



##

*  broadcasting in  numpy
  \vspace{0.4cm}
  
   The term broadcasting describes how numpy treats arrays with different
   shapes during arithmetic operations

   * add a scalar $b$ to a 1D array $a = [a_1,a_2,a_3]$ $\rightarrow$ expand $b$ to
     $[b,b,b]$
     \vspace{0.2cm}

   * add a  scalar $b$ to a 2D [2,3] array  $a =[[a_{11},a_{12},a_{13}],[a_{21},a_{22},a_{23}]]$
     $\rightarrow$ expand $b$ to $b =[[b,b,b],[b,b,b]]$ and add element wise
     \vspace{0.2cm}

   * add 1D array $b = [b_1,b_2,b_3]$ to a 2D [2,3] array $a=[[a_{11},a_{12},a_{13}],[a_{21},a_{22},a_{23}]]$   $\rightarrow$  1D array is broadcast
     across each row of the 2D array $b =[[b_1,b_2,b_3],[b_1,b_2,b_3]]$ and added  element wise 
 \vspace{0.2cm}

   Arithmetic operations can only be performed when the shape of each
   dimension in the arrays are equal or one has the dimension size of 1. Look
   [\textcolor{violet}{here}](https://numpy.org/doc/stable/user/basics.broadcasting.html) for more details 

\footnotesize
```python
     # Add a vector to each row of a matrix
     x = np.array([[1,2,3], [4,5,6]]) # x has shape (2, 3)
     v = np.array([1,2,3])            # v has shape (3,)
     x + v     # [[2 4 6]
               #  [5 7 9]]    
```
\normalsize

## Plot data

A popular library to present data is the `pyplot` module of `matplotlib`.

* Drawing a function in one plot

\footnotesize
::: columns
:::: {.column width=35%}
```python
import numpy as np
import matplotlib.pyplot as plt
# generate 100 points from 0 to 2 pi
x = np.linspace( 0, 10*np.pi, 100 )
f = np.sin(x)**2
# plot function
plt.plot(x,f,'blueviolet',label='sine')
plt.xlabel('x [radian]')
plt.ylabel('f(x)')
plt.title('Plot sin^2')
plt.legend(loc='upper right')
plt.axis([0,30,-0.1,1.2]) # limit the plot range

# show the plot
plt.show()
```
::::
:::: {.column width=40%}
![](figures/matplotlib_Figure_1.png)
::::
:::

\normalsize

##
* Drawing subplots in one canvas

\footnotesize
::: columns
:::: {.column width=35%}
```python
...
g = np.exp(-0.2*x)
# create figure
plt.figure(num=2,figsize=(10.0,7.5),dpi=150,facecolor='lightgrey')
plt.suptitle('1 x 2 Plot')
# create subplot and plot first one
plt.subplot(1,2,1)
# plot first one
plt.title('exp(x)')
plt.xlabel('x')
plt.ylabel('g(x)')
plt.plot(x,g,'blueviolet')
# create subplot and plot second one 
plt.subplot(1,2,2)
plt.plot(x,f,'orange')
plt.plot(x,f*g,'red')
plt.legend(['sine^2','exp*sine'])
# show the plot
plt.show()
```
::::
:::: {.column width=40%}
\vspace{3cm}
![](figures/matplotlib_Figure_2.png)
::::
:::
\normalsize

## Image data 

The `image` class of the `matplotlib` library can be used to load the image
to numpy arrays and to render the image.

* There are 3 common formats for the numpy array  

  * (M, N) scalar data used for greyscale images

  * (M, N, 3) for RGB images (each pixel has an array with RGB color attached) 

  * (M, N, 4) for RGBA images (each pixel has an array with RGB color
    and transparency attached)


  The method `imread` loads the image into an `ndarray`, which can be
  manipulated.

  The method `imshow` renders the image data

 \vspace {2cm}
 
##
* Drawing pixel data and images

\footnotesize
::: columns
:::: {.column width=50%}

```python
....
# create data array with pixel postion and RGB color code
width, height = 400, 400
data = np.zeros((height, width, 3), dtype=np.uint8)
# red patch in the center
data[175:225, 175:225] = [255, 0, 0] 
x = np.random.randint(0,width-1,100)
y = np.random.randint(0,height-1,100)
data[x,y]= [0,255,0] # random green pixel
plt.imshow(data)
plt.show()
....
import matplotlib.image as mpimg
#read image into numpy array
pic = mpimg.imread('picture.jpg')
mod_pic = pic[:,:,0] # grab slice 0 of the colors
plt.imshow(mod_pic)  # use default color code also
plt.colorbar()       # try cmap='hot' 
plt.show()
```
::::
:::: {.column width=25%} 
![](figures/matplotlib_Figure_3.png)
\vspace{1cm}
![](figures/matplotlib_Figure_4.png)
::::
::: 
\normalsize


## Input / output

For the analysis of measured data efficient input \/ output plays an
important role. In numpy, `ndarrays` can be saved and read in from files.
`load()` and `save()` functions handle numpy binary files (.npy extension)
which contain  data, shape, dtype and other information required to
reconstruct the `ndarray` of the disk file.

\footnotesize
```python
   r = np.random.default_rng()       # instanciate random number generator
   a = r.random((4,3))               # random 4x3 array
   np.save('myBinary.npy', a)        # write array a to binary file myBinary.npy
   b = np.arange(12)                 
   np.savez('myComp.npz', a=a, b=b)  # write a and b in compressed binary file  
   ......
   b = np.load('myBinary.npy')       # read content of myBinary.npy into b
```
\normalsize
   
The storage and retrieval of array data in text file format is done
with `savetxt()` and `loadtxt()` methods. Parameter controling delimiter,
line separators, file header and footer can be specified.

\footnotesize
```python
   x = np.array([1,2,3,4,5,6,7])       # create ndarray 
   np.savetxt('myText.txt',x,fmt='%d') # write array x to text file myText.txt
   .....
   y = np.loadtxt('myText.txt',dtype=int)  # read content of myText.txt in y
```
\normalsize


## Exercise 1

i) Display a numpy array as figure of a blue cross. The size should be 200
   by 200 pixel. Use as array format (M, N, 3), where the first 2 specify
   the pixel positions and the last 3 the rbg color from 0:255.
   - Draw in addition a red square of arbitrary position into the figure.
   - Draw a circle in the center of the figure. Try to create a mask which
     selects the inner part of the circle using the indexing.
     
   \small
   [Solution:  01_intro_ex_1a_sol.py](https://www.physi.uni-heidelberg.de/~reygers/lectures/2021/ml/solutions/01_intro_ex_1a_sol.py) \normalsize
   
ii) Read data which contains pixels from the binary file horse.py into a
    numpy array. Display the data and the following transformations in 4
    subplots: scaling and translation, compression in x and y, rotation
    and mirroring.
    
    \small
    [Solution: 01_intro_ex_1b_sol.py](https://www.physi.uni-heidelberg.de/~reygers/lectures/2021/ml/solutions/01_intro_ex_1b_sol.py) \normalsize 
      

## Pandas

[\textcolor{violet}{pandas}](https://pandas.pydata.org/pandas-docs/stable/getting_started/index.html) is a software library written in Python for
\textcolor{blue}{data manipulation and analysis}. 

 \vspace{0.4cm}

\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* Offers data structures and operations for manipulating numerical tables with
  integrated indexing
  
* Imports data from various file formats, e.g. comma-separated values, JSON,
  SQL or Excel

* Tools for reading and writing data structures, allows analyzing, filtering,
  spliting, merging and joining 

* Built on top of `NumPy`

* Visualize the data with `matplotlib`

* Most machine learning tools support `pandas` $\rightarrow$ 
  it is widely used to preprocess data sets for machine learning
  
## Pandas micro introduction

Goal: Exploring, cleaning, transforming, and visualization of data.
The basic indexable objects are

\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* `Series` -> vector (list) of data elements of arbitrary  type
 
* `DataFrame` -> tabular arangement of data elements of column wise
                 arbitrary type
		 
   Both allow cleaning data by removing of `empty` or `nan` data entries
		 
\footnotesize
```python
     import numpy as np
     import pandas as pd                    # use together with numpy
     s = pd.Series([1, 3, 5, np.nan, 6, 8]) # create a Series of float64
     r = pd.Series(np.random.randn(4))      # Series of random numbers float64 
     dates = pd.date_range("20130101", periods=3) # index according to dates
     df = pd.DataFrame(np.random.randn(3,4),index=dates,columns=list("ABCD"))
     print (df)                             # print the DataFrame
                        A         B         C         D
          2013-01-01  1.618395  1.210263 -1.276586 -0.775545
          2013-01-02  0.676783 -0.754161 -1.148029 -0.244821
          2013-01-03 -0.359081  0.296019  1.541571  0.235337

     new_s = s.dropna() # return a new Data Frame with no empty cells	  
```
\normalsize

##

\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* pandas data can be saved in different file formats (CSV, JASON, html, XML,
  Excel, OpenDocument, HDF5 format, .....). `NaN` entries are kept
  in the output file.

   * csv file
     \footnotesize
     ```python
     df.to_csv("myFile.csv")  # Write the DataFrame df to a csv file 
     ```
      \normalsize

   * HDF5 output
  
     \footnotesize
     ```python  
     df.to_hdf("myFile.h5",key='df',mode='w') # Write the DataFrame df to HDF5
     s.to_hdf("myFile.h5", key='s',mode='a')	  
     ```
     \normalsize

   * Writing to an excel file
  
     \footnotesize
     ```python  
     df.to_excel("myFile.xlsx", sheet_name="Sheet1")
     ```
     \normalsize

* Deleting file with data in python
  
\footnotesize
```python  
     import os
     os.remove('myFile.h5')
```
\normalsize

##

\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* read in data from various formats
 
   * csv file

     \footnotesize

     ```python
      .......
      df = pd.read_csv('heart.csv')  # read csv data table
      print(df.info())
         <class 'pandas.core.frame.DataFrame'>
         RangeIndex: 303 entries, 0 to 302
         Data columns (total 14 columns):
         #   Column    Non-Null Count  Dtype  
         ---  ------    --------------  -----  
         0   age       303 non-null    int64  
         1   sex       303 non-null    int64  
         2   cp        303 non-null    int64
         print(df.head(5))       # prints the first 5 rows of the data table 
         print(df.describe())    # shows a quick statistic summary of your data
     ```
\normalsize

   * Reading an excel file

     \footnotesize
     ```python  
     df = pd.read_excel("myFile.xlsx","Sheet1", na_values=["NA"])
     ```
     \normalsize

     \textcolor{olive}{There are many options specifying details for IO.}

##

\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* Various functions exist to select and view data from pandas objects

  * Display column and index

    \footnotesize

     ```python
     df.index                    # show datetime index of df
     DatetimeIndex(['2013-01-01','2013-01-02','2013-01-03'],
                   dtype='datetime64[ns]',freq='D')
     df.column                   # show columns info
     Index(['A', 'B', 'C', 'D'], dtype='object')
     ```
     \normalsize
     
  * `DataFrame.to_numpy()` gives a `NumPy` representation of the underlying data

    \footnotesize

     ```python
     df.to_numpy()       # one dtype for the entire array, not per column!
     [[-0.62660101 -0.67330526  0.23269168 -0.67403546]
     [-0.53033339  0.32872063 -0.09893568  0.44814084]
     [-0.60289996 -0.22352548 -0.43393248  0.47531456]]
     ```
     \normalsize
     
     Does not include the index or column labels in the output
     
  * more on viewing 

    \footnotesize

    ```python
    df.T                                   # transpose the DataFrame df
    df.sort_values(by="B")                 # Sorting by values of a column of df
    df.sort_index(axis=0,ascending=False)  # Sorting by index descending values
    df.sort_index(axis=0,ascending=False)  # Display columns in inverse order
			
    ```
    \normalsize
    
##

\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* Selecting data of pandas objects $\rightarrow$ keep or reduce dimensions

  * get a named column as a Series

    \footnotesize

     ```python
     df["A"]           # selects a column A from df, simular to  df.A
     df.iloc[:, 1:2]   # slices column A explicitly from df, df.loc[:, ["A"]]
     ```
     \normalsize

  * select rows of a DataFrame 

    \footnotesize

     ```python
     df[0:2]                   # selects row 0 and 1 from df, 
     df["20130102":"20130103"] # use indices endpoint are included!
     df.iloc[3]                # Select with the position of the passed integers
     df.iloc[1:3, :]           # selects row 1 and 2 from df
     ```
     \normalsize

  * select by label

     \footnotesize

     ```python
     df.loc["20130102":"20130103",["C","D"]] # selects row 1 and 2 and only C and D
     df.loc[dates[0], "A"]                   # selects a single value (scalar)
     ```
     \normalsize

  *  select by lists of integer position (as in `NumPy`)

     \footnotesize

     ```python
     df.iloc[[0, 2], [1, 3]] # select row 1 and 3 and col B and D
     df.iloc[1, 1]           # get a value explicitly

     ```
     \normalsize

  *  select according to expressions

     \footnotesize

     ```python
     df.query('B<C')         # select rows where B < C
     df1=df[(df["B"]==0)&(df["D"]==0)] # conditions on rows
     ```
     \normalsize

##


\setbeamertemplate{itemize item}{\color{red}\tiny$\blacksquare$}

* Selecting data of pandas objects continued

  * Boolean indexing

    \footnotesize

     ```python
     df[df["A"] > 0]           # select df where all values of column A are >0
     df[df > 0]                # select values from the entire DataFrame
     ```
     \normalsize

     more complex example
     
     \footnotesize
     
     ```python
     df2 = df.copy()                     # copy df
     df2["E"] = ["eight","one","four"]   # add column E
     df2[df2["E"].isin(["two", "four"])] # test if elements "two" and  "four" are
                                         # contained in Series column E
     ```
     \normalsize

  * Operations (in general exclude missing data)

    \footnotesize

     ```python
     df2[df2 > 0] = -df2   # All elements > 0 change sign
     df.mean(0)            # get column wise mean (numbers=axis)  
     df.mean(1)            # get row wise mean
     df.std(0)             # standard deviation according to axis
     df.cumsum()           # cumulative sum of each column
     df.apply(np.sin)      # apply function to each element of df
     df.apply(lambda x: x.max() - x.min()) # apply lambda function column wise
     df + 10               # add scalar 10
     df - [1, 2, 10 , 100] # subtract values of each column
     df.corr()             # Compute pairwise correlation of columns
     ```
     \normalsize


##  Pandas - plotting data

[\textcolor{violet}{Visualization}](https://pandas.pydata.org/pandas-docs/stable/user_guide/visualization.html) is integrated in pandas using mathplotlib. Here are only 2 examples

* Plot random data in histogramm and scatter plot

\footnotesize
```python
     # create DataFrame with random normal distributed data
     df = pd.DataFrame(np.random.randn(1000,4),columns=["a","b","c","d"])
     df = df + [1, 3, 8 , 10]  # shift mean to  1, 3, 8 , 10
     plt.figure()
     df.plot.hist(bins=20)     # histogram all 4 columns
     g1 = df.plot.scatter(x="a",y="c",color="DarkBlue",label="Group 1")
     df.plot.scatter(x="b",y="d",color="DarkGreen",label="Group 2",ax=g1)
```
\normalsize
   
::: columns
:::: {.column width=35%}
![](figures/pandas_histogramm.png)
::::
:::: {.column width=35%}
![](figures/pandas_scatterplot.png)
::::
:::

##  Pandas - plotting data

The function crosstab() takes one or more array-like objects as indexes or
columns and constructs a new DataFrame of variable counts on the inputs

\footnotesize
```python
   df = pd.DataFrame(           # create DataFrame of 2 categories
      {"sex":   np.array([0,0,0,0,1,1,1,1,0,0,0]),
       "heart": np.array([1,1,1,0,1,1,1,0,0,0,1])
      }  )                      # closing bracket goes on next line
   pd.crosstab(df2.sex,df2.heart)    # create cross table of possibilities
   pd.crosstab(df2.sex,df2.heart).plot(kind="bar",color=['red','blue']) # plot counts
```
\normalsize
::: columns
:::: {.column width=42%}
![](figures/pandas_crosstabplot.png)
::::
:::

## Exercise 2

Read the file [\textcolor{violet}{heart.csv}](https://www.physi.uni-heidelberg.de/~reygers/lectures/2021/ml/exercises/heart.csv) into a DataFrame.
[\textcolor{violet}{Information on the dataset}](https://archive.ics.uci.edu/ml/datasets/heart+Disease)

\setbeamertemplate{itemize item}{\color{red}$\square$}

  * Which columns do we have

  * Print the first 3 rows

  * Print the statistics summary and the correlations

  * Print mean values for each column with and without disease

  * Select the data according to `sex` and `target` (heart disease 0=no 1=yes). 

  * Plot the `age` distribution of male and female in one histogram

  * Plot the heart disease distribution according to chest pain type `cp`
  
  * Plot `thalach`  according to `target` in one histogramm

  * Plot `sex` and `target` in a histogramm figure    

  * Correlate `age` and `max heart rate` according to `target` 

  * Correlate `age` and `colesterol` according to `target` 

  \small
   [Solution: 01_intro_ex_2_sol.py](https://www.physi.uni-heidelberg.de/~reygers/lectures/2021/ml/solutions/01_intro_ex_2_sol.py) \normalsize