Aaa ped-4- Data manipulation: Numpy

Data manipulation:
Numpy
AAA-Python Edition

Plan
●
1- Numpy: ndarray
●
2- indexing
●
3- Operations with ndarray
●
4- File saving and loading
●
5- Structures with dtype

3
1-Numpy:ndarray
[By Amina Delali]
Numpy
●
Numpy for Numerical Python, a library for numerical computing
in Python.
●
It defnes:
●
ndarray : multidimentioanl array
●
Fast Mathematical functions and operations with ndarray
including reading and writing array data from/to disk
●
Linear algebra, random number generation,
and Fourrier transform capabilities
●
A C API for connecting NumPy with libraries written in C, C++,
or FORTRAN.
●
We will focus int this course on the 3 frst points.

4
1-Numpy:ndarray
[By Amina Delali]
ndarray
●
ndarray is a multidimensional array object = a generic
multidimensional container for data of the same type.
a is a list
b is an ndarray
Import Numpy to use “array” function
array function used to transform
a list to an ndarray

5
1-Numpy:ndarray
[By Amina Delali]
ndarray
●
ndarray is characterized by its shape and dimension
Number of external
Brackets = dimension
(=3)
The ndarray d is a 3 dimensional array, composed of: 2 elements of dimesion 2.
Each dimension 2 element is composed of: 3 elements of dimension 1
Each dimension 1 element is composed of: 3 elements of dimension 0
==> the shape of d = 2 x 3 x 3
2 elements of dimension 2
(a 2 dimensionl element has2 external brackets)
3 elements of
dimension 1
3 elements
of dimension 0 =scalars

6
1-Numpy:ndarray
[By Amina Delali]
Creating ndarray
●
like array function, other functions exist to create an ndarray
Since b is an ndarray, it will not be copied.
g and b will refer to the same element
Modifying the first element of g, will
modify also the first element of b
Using array function, the array b
will be copied in a new element h
Modifying the second element of h
will not modify the second element of b

7
1-Numpy:ndarray
[By Amina Delali]
Creating ndarray
Identity matrix (2 dimensions:
rows and columns)
1. 0. 0.
0. 1. 0.
0. 0. 1.
1 in diagonal,
0 elsewhereRange from 1 to (9-1)
with step 3
Axis 0 == lines
Axis 1 == columns
id1
0 1 2
0
1
2

8
1-Numpy:ndarray
[By Amina Delali]
Creating ndarray
●
Each of the following functions has two versions: function-name
and function-nam_like
We can specify in
these functions the
dtype argument
(the values type)

9
1-Numpy:ndarray
[By Amina Delali]
dtype
●
The ndarray can be created specifying a type "dtype"
●
The types can be:
●
int : signed (i1, i2, i4 or i8) and unsigned (u1, u2, u4 or u8)
●
foat: f2, f4 or f, f8 or d, f16 or g
●
complex: c8, c16, c32
●
boolean: ?
●
object: O
●
String: S . Fixed length ASCII String type, (S"number" for a
stirng of "number" byte size)
●
Unicode: U . Fixed length Unicode type, (U"number" for unicode
of "number" of certain_byte size )
These codes can be used
as arguments: dtype=”i8”
The float fill
value(3.2) is
converted
to int

10
2-Indexing
[By Amina Delali]
indexes
●
ndarray can be indexed by: integers, arrays, slices,and Boolean
c[0]==[1,2,3]
1 2 3
4 5 6
0
1
0 1 2
1 2 3
4 5 6
0
1
0 1 2
1 2 3
4 5 6
0
1
0 1 2
Ind == [1, 1]
c[ind]==[[4,5,6],[4,5,6]]
1 2 3
4 5 6
0
1
0 1 2
C[ : ,0:2]==[[1,2],[4,5]]
“ : “
0:2
c

11
2-Indexing
[By Amina Delali]
indexes
●
ndarray can be indexed by: integers, arrays, slices,and Boolean
1 2 3
4 5 6
0
1
0 1 2
1 2 3
4 5 6
0
1
0 1 2
False False False
False False False
0
1
0 1 2
c
ind2
Assigning one value(True)
to the entire line (0)
ind2
ind2
Assigning one value
(True) to one cell (1,0)
True True True
False False False
0
1
0 1 2
True True True
True False False
0
1
0 1 2
Selecting values from c
corresponding to True in
ind2

12
2-Indexing
[By Amina Delali]
Slices and copies
●
Using slices to create arrays from other ndarrays doesn't create
copies.To have distinct arrays, we have to use the method copy
1 2 3
4 5 6
0
1
0 1 2
c
part
1 2
4 5
0
1
0 1
1 1000
4 5
0
1
0 1
1 1000 3
4 5 6
0
1
0 1 2c

13
2-Indexing
[By Amina Delali]
Slices and copies
●
Using slices to create arrays from other ndarrays doesn't create
copies.To have distinct arrays, we have to use the method copy
1 2 3
4 5 6
0
1
0 1 2
c
part2
1 2
4 5
0
1
0 1
1 1000
4 5
0
1
0 1
1 2 3
4 5 6
0
1
0 1 2c

14
3-Operationswith
Ndarrays
[By Amina Delali]
Arithmetic operations & Linear Algebra
●
1 2 3
4 5 6
0
1
0 1 2 *
@
1 0 0
0 1 0
0
1
0 1 2
1 0 0
0 1 0
0 0 1
0
1
0 1 2
1 0 0
0 5 0
0
1
0 1 2
0 1 2
0
1
1 2 3
4 5 6
c @ indentity== c

15
3-Operationswith
Ndarrays
[By Amina Delali]
Element wise multiplication vs Matrix multiplication
1 2 3
4 5 6
0
1
0 1 2
*
1 -1 0
-5 1 2
0
1
0 1 2
1 -2 0
-20 5 12
0
1
0 1 2
1 * 1 == 1 6 * 2 == 12
Element wise multiplication
Matrix multiplication
@
1 -1
0 -5
1 2
0
1
2
0 1
4 -5
10 -17
0
1
0 1
Line 0 * Column 0 == Cell ( 0 , 0 ):
1 * 1 + 2 * 0 + 3 * 1 == 4
1 2 3
4 5 6
0
1
0 1 2
Line 1 * Column 1 == Cell ( 1 , 1 )
4 * -1 + 5 * -5 + 6 * 2 = -17

16
3-Operationswith
Ndarrays
[By Amina Delali]
Arithmetic and Logical operations
Same operation can be done
With: - , / , *

17
3-Operationswith
Ndarrays
[By Amina Delali]
Arithmetic and Logical operations
The result is an ndarray ( each value
Greater than 3 will produce a True value)
●
We can use logical operations to select certain elements of an array

18
3-Operationswith
Ndarrays
[By Amina Delali]
Linear Algebra
●
We already seen the matrix multiplication using dot method
or np.dot function or the operator @
●
There are other functions related to linear Algebra as: diag,trace,
inv, solve, … etc.
●
as for sacalrs, matrices have inverse regarding the matrix
multiplication operation:
is the Identity matrix
●
A system of linear equations can be represented by matrices:
for example:
And the solution will be :
mat∗mat
−1
=I
I
mat∗x= y

19
3-Operationswith
Ndarrays
[By Amina Delali]
Linear Algebra
A square matrix means:
number of rows ==
number of columns
The solution must be equal to
the inverse matrix of mat

20
3-Operationswith
Ndarrays
[By Amina Delali]
Some functions and methods
● Numpy defnes a list of element wise functions applicable to:
●
One ndarray, as: sqrt, exp, modf, log, sign, ceil and floor,
cos, logical_not, … etc
●
Two ndarray as: add, mod, maximum... etc
Access to the
first ndarray
1 for positive elements, -1 for negative
elements and 0 for 0 values

21
3-Operationswith
Ndarrays
[By Amina Delali]
● There is a list of functions that permit the generation of ndarrays
with certain values. For example: randn, meshgrid, and where
If a value from c is greater
than 3 it will return “G”
else it will return “L”
Each value from the generated range
Can be associated with all values

22
3-Operationswith
Ndarrays
[By Amina Delali]
● With the function append we can create a new ndarray by
appending new values
The given values must have
the same dimension as
the first argument”
c didn’t change

23
3-Operationswith
Ndarrays
[By Amina Delali]
●
ndarray objects defne a list of useful methods like: mean, sum,
cumsum, max, sort,T, ...etc
Lines 0,1 become
columns 0,1.
And columns 0,1,2
become lines 0,1,2

24
4-Arraysaving
andloading
[By Amina Delali]
Save and Load
● It is possible to save and load ndarrays into binray format
If the extensions “npy”
or “npz” are not specified
they will be added.
The extension has to be
specified in loading data
Access to the arrays
with the names
used in the saving

25
5-Structureswith
dtype
[By Amina Delali]
● dtype constructor can be used to create structured type.
name and type
Each myType element is defined by
two values: “code” and “Value”
Initialized by tuples of two values
corresponding to myType definition

References
●
Wes McKinney. Python for data analysis: Data wrangling
with Pandas, NumPy, and IPython. O’Reilly Media, Inc, 2018.
●
SciPy.org. Data type objects. On-line at
https://docs.scipy.org/doc/numpy-
1.13.0/reference/arrays.dtypes.html. Accessed on 05-10-
2018.

Aaa ped-4- Data manipulation: Numpy

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