PythonDataScience_01 - Jake VanderPlas

Question 1

In welcher Sprache ist Python geschrieben?

Answer 1

The standard Python implementation is written in C. This means that every Python object is simply a cleverly-disguised C structure, which contains not only its value, but other information as well.

This means that there is some overhead in storing an integer in Python as compared to an integer in a compiled language like C

Question 2

Was kann eine Liste aus der Python-Datenstruktur speichern?

Answer 2

Durch dynamische Typisierung kann ich heterogene Listen erstellen mit Integern, Strings oder Boolean.

Das erhöht aber auch den Speicherbedarf, da jedes als einzelne Python-Objekt gespeichert wird.

Bei C wäre es nur ein Pointer auf einen Speicherplatz.

Question 3

Wenn ich eine homogene Liste (Integer Array) erstellen möchte, was benutze ich am besten?

Answer 3

Das ndarray aus dem NumPy-Paket.

import numpy as np

In [8]:

integer array:
np.array([1, 4, 2, 5, 3])

Out[8]:

array([1, 4, 2, 5, 3])

Question 4

Wie kann ich explizit den Datentyp in einem Numpy-Array festlegen?

Ein Array 1,2,3,4 mit Datentyp float32

Answer 4

In [10]:

np.array([1, 2, 3, 4], dtype=’float32’)

Out[10]:

array([1., 2., 3., 4.], dtype=float32)

Question 5

Wie kann ich mit Numpy ein multidimensionales Array erstellen?

array([[2, 3, 4],
[4, 5, 6],
[6, 7, 8]])

Answer 5

In [11]:

nested lists result in multi-dimensional arrays
np.array([range(i, i + 3) for i in [2, 4, 6]])

Out[11]:

array([[2, 3, 4],
[4, 5, 6],
[6, 7, 8]])

Question 6

Numpy: Create a length-10 integer array filled with zeros

Answer 6

Create a length-10 integer array filled with zeros
np.zeros(10, dtype=int)

Out[12]:

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

Question 7

Numpy: Create a 3x5 floating-point array filled with ones

Answer 7

Create a 3x5 floating-point array filled with ones
np.ones((3, 5), dtype=float)

Out[13]:

array([[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.]])

Question 8

Numpy: Create a 3x5 array filled with 3.14

Answer 8

Create a 3x5 array filled with 3.14
np.full((3, 5), 3.14)

Out[14]:

array([[3.14, 3.14, 3.14, 3.14, 3.14],
[3.14, 3.14, 3.14, 3.14, 3.14],
[3.14, 3.14, 3.14, 3.14, 3.14]])

Question 9

Numpy: # Create an array filled with a linear sequence
# Starting at 0, ending at 20, stepping by 2
# (this is similar to the built-in range() function)

Answer 9

np.arange(0, 20, 2)

Out[15]:

array([0, 2, 4, 6, 8, 10, 12, 14, 16, 18])

Question 10

Numpy: Create an array of five values evenly spaced between 0 and 1

Answer 10

np.linspace(0, 1, 5)

Out[16]:

array([0. , 0.25, 0.5 , 0.75, 1.])

Question 11

Numpy:

Create a 3x3 array of uniformly distributed
# random values between 0 and 1

Answer 11

np.random.random((3, 3))

Out[17]:

array([[0.99844933, 0.52183819, 0.22421193],
[0.08007488, 0.45429293, 0.20941444],
[0.14360941, 0.96910973, 0.946117]])

Question 12

Numpy

Create a 3x3 array of normally distributed random values
# with mean 0 and standard deviation 1

Answer 12

np.random.normal(0, 1, (3, 3))

Out[18]:

array([[1.51772646, 0.39614948, -0.10634696],
[0.25671348, 0.00732722, 0.37783601],
[0.68446945, 0.15926039, -0.70744073]])

Question 13

Numpy

Create a 3x3 array of random integers in the interval [0, 10)

Answer 13

np.random.randint(0, 10, (3, 3))

Out[19]:

array([[2, 3, 4],
[5, 7, 8],
[0, 5, 0]])

Question 14

Numpy

Create a 3x3 identity matrix

Answer 14

np.eye(3)

Out[20]:

array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])

Question 15

Numpy

Create an uninitialized array of three integers
# The values will be whatever happens to already exist at that memory location

Answer 15

np.empty(3)

Out[21]:

array([1., 1., 1.])

Question 16

Wie kann ich ein 1-,2- und 3-Dimensionales Array x1, x2 und x3 mit Zufallszahlen bis 10 erstellen?

Answer 16

np.random.seed(0) # seed for reproducibility
x1 = np.random.randint(10, size=6) # One-dimensional array
x2 = np.random.randint(10, size=(3, 4)) # Two-dimensional array
x3 = np.random.randint(10, size=(3, 4, 5)) # Three-dimensional array

Question 17

Each array has attributes ndim (the number of dimensions), shape (the size of each dimension), and size (the total size of the array):

Wie kann ich das von x3 anzeigen lassen?

Answer 17

print(“x3 ndim: “, x3.ndim)
print(“x3 shape:”, x3.shape)
print(“x3 size: “, x3.size)

x3 ndim: 3
x3 shape: (3, 4, 5)
x3 size: 60

Question 18

To index from the end of the array, you can use…

In [5]:

x1

Out[5]:

array([5, 0, 3, 3, 7, 9])

Answer 18

To index from the end of the array, you can use negative indices:

In [8]:

x1[-1]

Out[8]:

9

Question 19

In a multi-dimensional array, items can be accessed using a …

In [10]:

x2

Out[10]:

array([[3, 5, 2, 4],
[7, 6, 8, 8],
[1, 6, 7, 7]])

Answer 19

In a multi-dimensional array, items can be accessed using a comma-separated tuple of indices:

x2[0, 0]

Out[11]:

3

Question 20

Wie kann ich die ersten 5 Elemente von array x anzeigen lassen?

Answer 20

x[:5] # first five elements

Out[17]:

array([0, 1, 2, 3, 4])

Question 21

Wie kann ich die Elemente ab index 5 anzeigen lassen?

Answer 21

x[5:] # elements after index 5

Out[18]:

array([5, 6, 7, 8, 9])

Question 22

Wie kann ich jedes zweite Element anzeigen lassen?

x = np.arange(10)
x

Out[16]:

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

Answer 22

x[::2] # every other element

Out[20]:

array([0, 2, 4, 6, 8])

Question 23

Wie kann ich mir von array x den Index 4 bis 7 anzeigen lassen?

Answer 23

x[4:7] # middle sub-array

Out[19]:

array([4, 5, 6])

Question 24

Wie kann ich mir jedes zweite Element anzeigen lassen? Startpunkt ist Index 1

x = np.arange(10)
x

Out[16]:

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

Answer 24

x[1::2] # every other element, starting at index 1

Out[21]:

array([1, 3, 5, 7, 9])

Question 25

Wie kann ich mir die Elemente von hinten bis vorne anzeigen lassen?

Answer 25

x[::-1] # all elements, reversed

Out[22]:

array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])

Question 26

Wie kann ich mir die erste Reihe von x2 anzeigen lassen?

Answer 26

print(x2[0, :]) # first row of x2

[12 5 2 4]

print(x2[0]) # equivalent to x2[0, :]

Question 27

Wie kann ich mir die erste Spalte von x2 anzeigen lassen?

Answer 27

print(x2[:, 0]) # first column of x2

[12 7 1]

Question 28

Wie unterscheiden sich Python Listen und NumPy Listen?

Answer 28

One important–and extremely useful–thing to know about array slices is that they return views rather than copies of the array data. This is one area in which NumPy array slicing differs from Python list slicing: in lists, slices will be copies.

Question 29

Another useful type of operation is reshaping of arrays. The most flexible way of doing this is with the reshape method. For example, if you want to put the numbers 1 through 9 in a 3×3 grid, you can do the following:

Answer 29

In [38]:

grid = np.arange(1, 10).reshape((3, 3))
print(grid)

[[1 2 3]
[4 5 6]
[7 8 9]]

Question 30

Another common reshaping pattern is the conversion of a one-dimensional array into a two-dimensional row or column matrix. This can be done with the reshape method, or more easily done by making use of the newaxis keyword within a slice operation:

Answer 30

In [39]: x = np.array([1, 2, 3])

row vector via reshape
x.reshape((1, 3))

Out[39]: array([[1, 2, 3]])

row vector via newaxis

In [40]: x[np.newaxis, :]

Out[40]: array([[1, 2, 3]])

column vector via reshape

In [41]: x.reshape((3, 1))

Out[41]:

array([[1],
[2],
[3]])

column vector via newaxis

In [42]: x[:, np.newaxis]

Out[42]:

array([[1],
[2],
[3]])

Question 31

Concatenation of two arrays in NumPy

x = np.array([1, 2, 3])
y = np.array([3, 2, 1])

Answer 31

np.concatenate([x, y])

Out[43]: array([1, 2, 3, 3, 2, 1])

Question 32

Concatenation of two-dimensional arrays:

grid = np.array([[1, 2, 3],
[4, 5, 6]])

Answer 32

concatenate along the first axis
np.concatenate([grid, grid])

array([[1, 2, 3],
[4, 5, 6],
[1, 2, 3],
[4, 5, 6]])

Question 33

Concatenation along the second axis?

grid = np.array([[1, 2, 3],
[4, 5, 6]])

Answer 33

concatenate along the second axis (zero-indexed)
np.concatenate([grid, grid], axis=1)

Out[47]:

array([[1, 2, 3, 1, 2, 3],
[4, 5, 6, 4, 5, 6]])

Question 34

Eine 4x4 Matrix mit Zahlen von 0 bis 15

Answer 34

grid = np.arange(16).reshape((4, 4))
grid

Out[51]:

array([[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11],
[12, 13, 14, 15]])

Question 35

Das Array x = [1, 2, 3, 99, 99, 3, 2, 1] folgendermaßen aufteilen:

[1 2 3] [99 99] [3 2 1]

Answer 35

x = [1, 2, 3, 99, 99, 3, 2, 1]
x1, x2, x3 = np.split(x, [3, 5])
print(x1, x2, x3)

[1 2 3] [99 99] [3 2 1]

Question 36

Kopiere die ersten 2 Reihen und 2 Spalten eines Array als x2_sub_copy

Answer 36

x2_sub_copy = x2[:2, :2].copy()

Question 37

Was sind ufuncs?

Answer 37

NumPy’s universal functions (ufuncs)

Vektorisierte Operationen in NumPy werden durch ufuncs implementiert.