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initial set of slides corresponding to 2022 version
2023-03-10 14:19:06 +01:00
---
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
If we do it without code section the vertical space is ok, but there is no
code high lightning.
See the different versions of the same page in the following
-->
## 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
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