GitHub Repository: robertopucp/1eco35_2022_2
Path: blob/main/Lab1/Python_Lab_1.ipynb
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Kernel: Python 3 (ipykernel)

Laboratorio 1 Python

1.0 Types of variables

In [12]:

a1 = 3.141
a1 = 3.141
a1 = 3.141
a1 = 3.141
a1 = 3.141
a1 = 3.141
a1 = 3.141
a1 = 3.141
a1 = 3.141

type(a1)

## Ctrl + Enter

Out[12]:

float

In [ ]:

# Añadir nueva liena de codigo botón: B 
# Borrar linea de codigo con: DD
# recuperar : Z

# pasar de código a comentario : Ctrl + /

# unir celdas de código : Shift + M
# dividir celdas de código : Ctrl + Shit + -

# seleccionar varias lineas de codigo  Shift + tecla hacia abajo o arriba

In [17]:

# from float to int 

c = int(a1)
type(c)

Out[17]:

int

In [18]:

b1 = 10000
type(b1)

# from int to float 

float(b1)

b2 = 8
type(b2)

Out[18]:

int

In [20]:

c1 = "My first python code"  # "My first python code" usando doble comilla
print(c1)  # show that varaible's content
type(c1) # providing varaibles's type

Out[20]:

My first python code

str

In [2]:

# including a space using \n

c1 = "First python code"
c2 = "at R y python Class"
print(c1,'\n',c2)

Out[2]:

First python code 
 at R y python Class

In [22]:

# join string 

print(c1 + " : " + c2)

Out[22]:

First python code : at R y python Class

In [23]:

# f-string

print(f'{c1} : semester 2022-1')

Out[23]:

First python code : semester 2022-1

In [1]:

d = 2022

In [3]:

print(f'{c1} : semester {d}-1')

Out[3]:

First python code : semester 2022-1

In [23]:

print('{} : semester {}-1'.format(c1,d))

Out[23]:

First python code : semester 2022-1

In [25]:

# Substr elements from string

c1[0:5]

Out[25]:

'First'

In [17]:

#first character
print('Fisrt letter is :',c1[0])

Out[17]:

Fisrt letter is : F

In [35]:

#first word
print('Fisrt word is :',c1[0:5])

Out[35]:

Fisrt word is : First

1.2 Boolean

It’s used to represent the truth value of an expression.

In [26]:

"a" == "a"

Out[26]:

True

In [27]:

1 > 1

Out[27]:

False

In [28]:

z1 = (1==1)
z1

Out[28]:

True

In [29]:

int(z1)  # true is 1 in numerical system

Out[29]:

1

In [30]:

z2 = (10 > 20) 
int(z2) # false is 0 in numerical system

Out[30]:

0

1.3 Tuple

It is an ordered and immutable Python object

In [31]:

T1 = (1,4,8,10,20,15,4,5,3,8)

type(T1)

Out[31]:

tuple

In [52]:

# aritmethic operations

print('Suma:', sum(T1),"\n", "Minimo:", min(T1), '\n', "Maximo:", max(T1))

Out[52]:

Suma: 78 
 Minimo: 1 
 Maximo: 20

In [53]:

len(T1) # lenght of tuple

Out[53]:

10

Indexing Tuple

In [32]:

T1 = (1,4,8,10,20,15,4,5,3,8)

####  0,1,2, 3, 4 

T1[0]

Out[32]:

4

In [62]:

T1[0:5] # desde la posición 0 hasta el 4

Out[62]:

(1, 4, 8, 10, 20)

In [30]:

T1[1] # get tuple's element

Out[30]:

4

In [31]:

T1[0:3]

Out[31]:

(1, 4, 8)

In [33]:

# It is not possible to change
T1[0] = 4

Out[33]:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Input In [33], in <cell line: 2>()
      1 # It is not possible to change
----> 2 T1[0] = 4
TypeError: 'tuple' object does not support item assignment

In [35]:

T1 = (1,4,8,10,20,15,4,5,3,8)
#                   -3,-2,-1
T1[-3:-1]

Out[35]:

(5, 3)

In [36]:

#position
T1.index(8)

Out[36]:

2

1.4 List

It is an ordered and mutable Python container.

In [31]:

L1 = []
print(L1)
type(L1)

Out[31]:

[]

list

In [37]:

dis1 = [ "ATE", 'BARRANCO','BREÑA', 'CALLAO', 'CARABAYLLO' ] 
dis1

Out[37]:

['ATE', 'BARRANCO', 'BREÑA', 'CALLAO', 'CARABAYLLO']

In [38]:

dis2 = ['ATE', 'BARRANCO','BREÑA', 'CALLAO', 'CARABAYLLO','CHACLACAYO','CHORRILLOS','CIENEGUILLA'
        ,'COMAS','EL_AGUSTINO','INDEPENDENCIA']

In [39]:

len(dis2) # numero de elementos

Out[39]:

11

In [40]:

dis2[0] = "CALLAO"
print(dis2)

Out[40]:

['CALLAO', 'BARRANCO', 'BREÑA', 'CALLAO', 'CARABAYLLO', 'CHACLACAYO', 'CHORRILLOS', 'CIENEGUILLA', 'COMAS', 'EL_AGUSTINO', 'INDEPENDENCIA']

In [41]:

# Idenxing

print(dis2[1])

Out[41]:

BARRANCO

In [42]:

dis2[2:5]   # (5-1=4)

Out[42]:

['BREÑA', 'CALLAO', 'CARABAYLLO']

In [83]:

dis2[3:7]

Out[83]:

['CALLAO', 'CARABAYLLO', 'CHACLACAYO', 'CHORRILLOS']

In [44]:

dis2[-5:-1]

Out[44]:

['CHORRILLOS', 'CIENEGUILLA', 'COMAS', 'EL_AGUSTINO']

In [2]:

num = [13,5,5,8,9,10,5,8,13,1,20]
num.sort()
print(num)

Out[2]:

[1, 5, 5, 5, 8, 8, 9, 10, 13, 13, 20]

In [3]:

# append new elements 

num.append(102)

In [5]:

# append new list

num2 = [10,20,30]
num.extend(num2)
print(num)

Out[5]:

[1, 5, 5, 5, 8, 8, 9, 10, 13, 13, 20, 102, 10, 20, 30]

In [46]:

print(num.index(102))

Out[46]:

11

In [47]:

print("Suma:", sum(num),'\n', "Minimo:", min(num), '\n', "Maximo:", max(num))

Out[47]:

Suma: 259 
 Minimo: 1 
 Maximo: 102

1.5 Diccionario

In [64]:

Postal_code = { 'Majes': 40520 , 'Mollendo': 40701, 'Islay': 40704, 'Cotahuasi': 40801, 'Alca': 40802  }

type(Postal_code)

# dict de diccionario 
# 'Majes', 'Mollendo' son llaves

Out[64]:

dict

In [49]:

Postal_code

Out[49]:

{'Majes': 40520,
 'Mollendo': 40701,
 'Islay': 40704,
 'Cotahuasi': 40801,
 'Alca': 40802}

In [50]:

Postal_code.keys()

Out[50]:

dict_keys(['Majes', 'Mollendo', 'Islay', 'Cotahuasi', 'Alca'])

In [51]:

# Get information from key
Postal_code['Alca']

Out[51]:

40802

In [52]:

# Get information from key
Postal_code.get('Alca')

Out[52]:

40802

In [53]:

# Drop key
Postal_code.pop('Islay')
Postal_code

Out[53]:

{'Majes': 40520, 'Mollendo': 40701, 'Cotahuasi': 40801, 'Alca': 40802}

In [57]:

# add new elements 

Postal_code.update( { "CHARCANA" :  [1,2] } )

#diccioanrio dentro de otro diccionario
Postal_code.update( {"LOMAS": {"UBIGEO": 40311, "Poverty Rate" : "18.2%", "Population" : "20 mil"}})

In [58]:

Postal_code

Out[58]:

{'Majes': 40520,
 'Mollendo': 40701,
 'Islay': 40704,
 'Cotahuasi': 40801,
 'Alca': 40802,
 'CHARCANA': [1, 2],
 'LOMAS': {'UBIGEO': 40311, 'Poverty Rate': '18.2%', 'Population': '20 mil'}}

In [62]:

Postal_code.get('LOMAS').get('Poverty Rate')

Out[62]:

'18.2%'

In [63]:

Postal_code['LOMAS']['Poverty Rate'] # forna mas usada

Out[63]:

'18.2%'

In [62]:

Postal_code['LOMAS']

['Poverty Rate']

Out[62]:

'18.2%'

In [62]:

# keys
cities = ['Fray Martin','Santa Rosa de Puquio','Cuchicorral','Santiago de Punchauca','La Cruz (11 Amigos)','Cerro Cañon','Cabaña Suche','San Lorenzo','Jose Carlos Mariategui','Pascal','La Esperanza','Fundo Pancha Paula','Olfa','Rio Seco','Paraiso','El Rosario','Cerro Puquio','La Campana','Las Animas','Vetancio','Roma Alta','San Jose','San Pedro de Carabayllo','Huacoy','Fundo Pampa Libre','Ex Fundo Santa Ines','Reposo','Carmelito','Santa Elena','Don Luis','Santa Ines Parcela','Asociacion Santa Ines','Roma Baja','Residencial Santa Lucia','San Francisco','Santa Margarita - Molinos','Sipan Peru','Fundo Cuadros','Bello Horizonte','El Hueco','Ex Fundo Mariategui','Naranjito','Vista Hermosa','El Sabroso de Jose Carlos Mariategui','Granja Carabayllo','Agropecuario Valle el Chillon','Camino Real','Copacabana','El Trebol','Tablada la Virgen','San Fernando de Carabayllo','San Fernando de Copacabana','La Manzana','Chacra Grande','Torres de Copacabana','San Pedro de Carabayllo','San Lorenzo','Chaclacayo','Chorrillos','Cieneguilla','Lindero','Pichicato','San Isidro','San Vicente','Piedra Liza','Santa Rosa de Chontay (Chontay)','La Libertad','El Agustino','Independencia','Jesus Maria','La Molina','La Victoria','Lince','Las Palmeras','Chosica','Lurin','Los Almacigos','Rinconada del Puruhuay','Fundo Santa Genoveva','Los Maderos','Casco Viejo','Vista Alegre','Buena Vista Alta','Lomas Pucara','Fundo la Querencia','Magdalena del Mar','Pueblo Libre','Miraflores','Pachacamac','Puente Manchay','Tambo Inga','Pampa Flores','Manchay Alto Lote B','Invasion Cementerio','Manchay Bajo','Santa Rosa de Mal Paso','Cardal','Jatosisa','Tomina','Pucusana','Honda','Quipa','Los Pelicanos','Playa Puerto Bello','Ñaves','Granja Santa Elena','Alvatroz II','Poseidon - Lobo Varado','Playa Minka Mar','Playa Acantilado','Puente Piedra','Punta Hermosa','Capilla Lucumo','Cucuya','Pampapacta','Avicola San Cirilo de Loma Negra - 03','Avicola San Cirilo de Loma Negra - 02','Avicola San Cirilo de Loma Negra - 01','Pampa Mamay','Cerro Botija','Agricultores y Ganaderos','Pampa Malanche Avicola Puma','Punta Negra','Chancheria','Rimac','San Bartolo','Plantel 41','Granja 4','Granja 5','Granja 07','Granja 44','Granja 47','Santa Maria I','Las Torres Santa Fe','San Francisco de Borja','San Isidro','San Juan de Lurigancho','Ciudad de Dios','San Luis','Barrio Obrero Industrial','San Miguel','Santa Anita - los Ficus','Santa Maria del Mar','Don Bruno','Santa Rosa','Santiago de Surco','Surquillo','Villa el Salvador','Villa Maria del Triunfo', 'Pueblo libre']
# values
postal_code1 = [15001,15003,15004,15006,15018,15019,15046,15072,15079,15081,15082,15083,15088,15123,15004,15011,15012,15019,15022,15023,15026,15476,15479,15483,15487,15491,15494,15498,15047,15049,15063,15082,15083,15121,15122,15313,15316,15318,15319,15320,15321,15324,15320,15320,15320,15320,15320,15320,15121,15320,15320,15121,15320,15320,15121,15121,15122,15122,15121,15121,15121,15320,15320,15320,15320,15320,15320,15121,15121,15121,15320,15121,15319,15121,15121,15121,15320,15320,15121,15121,15121,15121,15320,15320,15320,15122,15122,15122,15122,15122,15122,15122,15122,15121,15121,15122,15122,15121,15121,15122,15122,15121,15122,15122,15122,15472,15476,15054,15056,15057,15058,15063,15064,15066,15067,15593,15594,15593,15593,15593,15593,15593,15593,15593,15311,15312,15313,15314,15316,15324,15326,15327,15328,15332,15003,15004,15006,15007,15008,15009,15011,15018,15022,15311,15328,15331,15332,15333,15046, 15001]

In [63]:

# Return a dictionarie
ct_pc = dict( zip( cities , postal_code1) )

In [64]:

ct_pc

Out[64]:

{'Fray Martin': 15001,
 'Santa Rosa de Puquio': 15003,
 'Cuchicorral': 15004,
 'Santiago de Punchauca': 15006,
 'La Cruz (11 Amigos)': 15018,
 'Cerro Cañon': 15019,
 'Cabaña Suche': 15046,
 'San Lorenzo': 15122,
 'Jose Carlos Mariategui': 15079,
 'Pascal': 15081,
 'La Esperanza': 15082,
 'Fundo Pancha Paula': 15083,
 'Olfa': 15088,
 'Rio Seco': 15123,
 'Paraiso': 15004,
 'El Rosario': 15011,
 'Cerro Puquio': 15012,
 'La Campana': 15019,
 'Las Animas': 15022,
 'Vetancio': 15023,
 'Roma Alta': 15026,
 'San Jose': 15476,
 'San Pedro de Carabayllo': 15121,
 'Huacoy': 15483,
 'Fundo Pampa Libre': 15487,
 'Ex Fundo Santa Ines': 15491,
 'Reposo': 15494,
 'Carmelito': 15498,
 'Santa Elena': 15047,
 'Don Luis': 15049,
 'Santa Ines Parcela': 15063,
 'Asociacion Santa Ines': 15082,
 'Roma Baja': 15083,
 'Residencial Santa Lucia': 15121,
 'San Francisco': 15122,
 'Santa Margarita - Molinos': 15313,
 'Sipan Peru': 15316,
 'Fundo Cuadros': 15318,
 'Bello Horizonte': 15319,
 'El Hueco': 15320,
 'Ex Fundo Mariategui': 15321,
 'Naranjito': 15324,
 'Vista Hermosa': 15320,
 'El Sabroso de Jose Carlos Mariategui': 15320,
 'Granja Carabayllo': 15320,
 'Agropecuario Valle el Chillon': 15320,
 'Camino Real': 15320,
 'Copacabana': 15320,
 'El Trebol': 15121,
 'Tablada la Virgen': 15320,
 'San Fernando de Carabayllo': 15320,
 'San Fernando de Copacabana': 15121,
 'La Manzana': 15320,
 'Chacra Grande': 15320,
 'Torres de Copacabana': 15121,
 'Chaclacayo': 15122,
 'Chorrillos': 15121,
 'Cieneguilla': 15121,
 'Lindero': 15121,
 'Pichicato': 15320,
 'San Isidro': 15004,
 'San Vicente': 15320,
 'Piedra Liza': 15320,
 'Santa Rosa de Chontay (Chontay)': 15320,
 'La Libertad': 15320,
 'El Agustino': 15121,
 'Independencia': 15121,
 'Jesus Maria': 15121,
 'La Molina': 15320,
 'La Victoria': 15121,
 'Lince': 15319,
 'Las Palmeras': 15121,
 'Chosica': 15121,
 'Lurin': 15121,
 'Los Almacigos': 15320,
 'Rinconada del Puruhuay': 15320,
 'Fundo Santa Genoveva': 15121,
 'Los Maderos': 15121,
 'Casco Viejo': 15121,
 'Vista Alegre': 15121,
 'Buena Vista Alta': 15320,
 'Lomas Pucara': 15320,
 'Fundo la Querencia': 15320,
 'Magdalena del Mar': 15122,
 'Pueblo Libre': 15122,
 'Miraflores': 15122,
 'Pachacamac': 15122,
 'Puente Manchay': 15122,
 'Tambo Inga': 15122,
 'Pampa Flores': 15122,
 'Manchay Alto Lote B': 15122,
 'Invasion Cementerio': 15121,
 'Manchay Bajo': 15121,
 'Santa Rosa de Mal Paso': 15122,
 'Cardal': 15122,
 'Jatosisa': 15121,
 'Tomina': 15121,
 'Pucusana': 15122,
 'Honda': 15122,
 'Quipa': 15121,
 'Los Pelicanos': 15122,
 'Playa Puerto Bello': 15122,
 'Ñaves': 15122,
 'Granja Santa Elena': 15472,
 'Alvatroz II': 15476,
 'Poseidon - Lobo Varado': 15054,
 'Playa Minka Mar': 15056,
 'Playa Acantilado': 15057,
 'Puente Piedra': 15058,
 'Punta Hermosa': 15063,
 'Capilla Lucumo': 15064,
 'Cucuya': 15066,
 'Pampapacta': 15067,
 'Avicola San Cirilo de Loma Negra - 03': 15593,
 'Avicola San Cirilo de Loma Negra - 02': 15594,
 'Avicola San Cirilo de Loma Negra - 01': 15593,
 'Pampa Mamay': 15593,
 'Cerro Botija': 15593,
 'Agricultores y Ganaderos': 15593,
 'Pampa Malanche Avicola Puma': 15593,
 'Punta Negra': 15593,
 'Chancheria': 15593,
 'Rimac': 15311,
 'San Bartolo': 15312,
 'Plantel 41': 15313,
 'Granja 4': 15314,
 'Granja 5': 15316,
 'Granja 07': 15324,
 'Granja 44': 15326,
 'Granja 47': 15327,
 'Santa Maria I': 15328,
 'Las Torres Santa Fe': 15332,
 'San Francisco de Borja': 15003,
 'San Juan de Lurigancho': 15006,
 'Ciudad de Dios': 15007,
 'San Luis': 15008,
 'Barrio Obrero Industrial': 15009,
 'San Miguel': 15011,
 'Santa Anita - los Ficus': 15018,
 'Santa Maria del Mar': 15022,
 'Don Bruno': 15311,
 'Santa Rosa': 15328,
 'Santiago de Surco': 15331,
 'Surquillo': 15332,
 'Villa el Salvador': 15333,
 'Villa Maria del Triunfo': 15046,
 'Pueblo libre': 15001}

1.6 Arrays and Matrix

In [2]:

import numpy as np

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

# A library is a collection of modules or a single module. Libraries are the tools we will use to make our program.

Out[2]:

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

In [67]:

# 1D array (vector)
a = np.array( [1, 2, 3, 4, 5] )


print(a)

Out[67]:

[1 2 3 4 5]

In [68]:

type(a)

Out[68]:

numpy.ndarray

In [80]:

np.mean(a)
np.sum(a)

Out[80]:

15

In [72]:

np.std(a)

Out[72]:

1.4142135623730951

Standar deviation in Python by default

\begin{equation} sd(x) = \sqrt{\frac{\sum(x_i-\bar{x})^2}{N-1}} \end{equation}

In [73]:

np.std(a,ddof=1)

Out[73]:

1.5811388300841898

Standar deviation in Python by default

\begin{equation} sd(x) = \sqrt{\frac{\sum(x_i-\bar{x})^2}{N}} \end{equation}

In [74]:

# 2D array
M = np.array( [ [1, 2, 3], [4, 5, 6] ] )

print(M)

Out[74]:

[[1 2 3]
 [4 5 6]]

In [78]:

# dimensiones

M.shape # numero de filas

Out[78]:

(2, 3)

In [77]:

print("Rows:",M.shape[0],"\n", "Columns: ", M.shape[1])

Out[77]:

Rows: 2 
 Columns:  3

In [86]:

# Create a 1D NumPy array with values from 0 to 20 (exclusively) incremented by 2:
y = np.arange( 0, 20, 2 )
print(y)

Out[86]:

[ 0  2  4  6  8 10 12 14 16 18]

In [90]:

# deafult one by one 

y = np.arange( 1, 11)
print(y)

list(range(11))

Out[90]:

[ 1  2  3  4  5  6  7  8  9 10]

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

In [92]:

# rep() equivalent in python

print( np.repeat(2, 4) )

print( np.repeat(range(11), 4) )

Out[92]:

[2 2 2 2]
[ 0  0  0  0  1  1  1  1  2  2  2  2  3  3  3  3  4  4  4  4  5  5  5  5
  6  6  6  6  7  7  7  7  8  8  8  8  9  9  9  9 10 10 10 10]

In [96]:

print( np.tile(np.array([0,1]), 4) )


# split array

np.array_split(np.arange( 0, 10), 4)

Out[96]:

[0 1 0 1 0 1 0 1]

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

Matrix

In [97]:

A = np.array([ np.arange(0,10), np.arange(10,20), np.arange(30,40), np.arange(-20,-10), np.arange(2,21,2)])

In [98]:

Out[98]:

array([[  0,   1,   2,   3,   4,   5,   6,   7,   8,   9],
       [ 10,  11,  12,  13,  14,  15,  16,  17,  18,  19],
       [ 30,  31,  32,  33,  34,  35,  36,  37,  38,  39],
       [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11],
       [  2,   4,   6,   8,  10,  12,  14,  16,  18,  20]])

In [99]:

A[2:5,:]  # rows selecrtion

Out[99]:

array([[ 30,  31,  32,  33,  34,  35,  36,  37,  38,  39],
       [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11],
       [  2,   4,   6,   8,  10,  12,  14,  16,  18,  20]])

In [100]:

A[:,0:6]  # columns selecrtion

Out[100]:

array([[  0,   1,   2,   3,   4,   5],
       [ 10,  11,  12,  13,  14,  15],
       [ 30,  31,  32,  33,  34,  35],
       [-20, -19, -18, -17, -16, -15],
       [  2,   4,   6,   8,  10,  12]])

In [101]:

M1 = np.zeros( (8, 2) )
print(M1)

Out[101]:

[[0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]]

In [102]:

M2 = np.ones( (8, 4) )
print(M2)

Out[102]:

[[1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]
 [1. 1. 1. 1.]]

Join matrix

In [103]:

M3 = np.hstack((M1,M2))  # stack horizontal 
M3

Out[103]:

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

In [104]:

M4 = np.array([[2,2,3,4,5,1],[1,5,5,9,8,2]])
print(M4)

Out[104]:

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

In [89]:

M5 = np.vstack((M3,M4)) # stack vertical 
print(M5)
M5.T

Out[89]:

[[0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [0. 0. 1. 1. 1. 1.]
 [2. 2. 3. 4. 5. 1.]
 [1. 5. 5. 9. 8. 2.]]

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

In [90]:

# Create a 1D NumPy array of ones of length 10:
w = np.ones(10)
print(w)

Out[90]:

[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]

In [105]:

# Create the identity matrix of size 8:
I = np.eye(8)
print(I)

Out[105]:

[[1. 0. 0. 0. 0. 0. 0. 0.]
 [0. 1. 0. 0. 0. 0. 0. 0.]
 [0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 1. 0. 0. 0. 0.]
 [0. 0. 0. 0. 1. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0.]
 [0. 0. 0. 0. 0. 0. 1. 0.]
 [0. 0. 0. 0. 0. 0. 0. 1.]]

In [106]:

I3 = I.reshape(32, 2)
print(I3)

Out[106]:

[[1. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 1.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [1. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 1.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [1. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 1.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [1. 0.]
 [0. 0.]
 [0. 0.]
 [0. 0.]
 [0. 1.]]

In [3]:

np.random.seed(175) # semilla aleatoria para producir numeros aleatorios 
#  permite que los numeros aleatorios no cambien al correr los códigos
# numpy random permite generar números aleatorios unicos 

x1 = np.random.rand(500) 
x2 = np.random.rand(500) # uniform distribution [0,1]
x3 = np.random.rand(500) # uniform distribution [0,1]
x4 = np.random.rand(500) # uniform distribution [0,1]
e = np.random.normal(0,1,500) # normal distribution mean = 0 and sd = 1

# Poblacional regression (Data Generating Process GDP)

Y = 1 + 0.8*x1 + 1.2*x2 + 0.5*x3 + 1.5*x4 + e

In [151]:

X = np.column_stack((np.ones(500),x1,x2,x3,x4))
X

Out[151]:

array([[1.        , 0.04475417, 0.40772643, 0.34264416, 0.02414698],
       [1.        , 0.28733056, 0.37711362, 0.50872145, 0.44327971],
       [1.        , 0.07313766, 0.12851589, 0.82887389, 0.42140717],
       ...,
       [1.        , 0.45844518, 0.72689186, 0.10918985, 0.68319966],
       [1.        , 0.03768319, 0.24451085, 0.94042077, 0.94862136],
       [1.        , 0.35377639, 0.60304925, 0.82421856, 0.49296456]])

In [152]:

beta = np.linalg.inv(X.T @ X) @ ((X.T) @ Y )
print(beta)

Out[152]:

[0.96104291 0.91288635 1.08981519 0.47300876 1.53537517]

References

Numpy

https://numpy.org/doc/stable/reference/arrays.html

https://www.kaggle.com/code/hkumls/intensive-python-tutorial-numpy/notebook