Data Types#

from datascience import *
from cs104 import *
import numpy as np

%matplotlib inline

1. Table Review: Art sales in the UK#

This data comes from the Getty Provenance Index, which currently contains more than 2.3 million records taken from source material such as archival inventories, auction catalogs, and dealer stock books.

Sir Anthony van Dyck - Portrait of Antoine Triest

Recall: you can open the raw .csv files within Jupyter’s file system. From inside Jupyter, locate the CSV file from the File Browser on the left-hand side of the window. Double click to view as a formatted table, and right-click and select “Open With -> Editor” to view as an editable text file.

art = Table().read_table('data/UK_art_subset.csv')
art.show(5)

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1839	Christie's	A rich equipage halting on the bank of a river, where fi ...	K. du Jardin	Painting	14
1839	Christie's	A breeze, with men-of-war and boats; a clear and beautif ...	Backhuysen	Painting	13
1837	Enoch & Redfern	A Mythological Subject, representing Apollo playing on a ...	Rubens	Painting	1
1803	Edwards (Edward)	This picture represents an Alchemist with other Figures; ...	Teniers	Painting	18
1838	Christie's	A dance of cupids; admirably coloured	V. Dyck	Painting	12

... (1098 rows omitted)

Review: Remove the unhelpful columns (e.g. 'auction_house') with the drop method, and save the result table in no_house variable.

no_house = art.drop('auction_house')
no_house.show(5)

lot_sale_year	title	artist_name	object_type	pounds
1839	A rich equipage halting on the bank of a river, where fi ...	K. du Jardin	Painting	14
1839	A breeze, with men-of-war and boats; a clear and beautif ...	Backhuysen	Painting	13
1837	A Mythological Subject, representing Apollo playing on a ...	Rubens	Painting	1
1803	This picture represents an Alchemist with other Figures; ...	Teniers	Painting	18
1838	A dance of cupids; admirably coloured	V. Dyck	Painting	12

... (1098 rows omitted)

art.sort('artist_name', descending=True).show(4)

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1839	Rainy (Alexander)	The late Admiral Lord Exmouth, going into Action at Algi ...	[Sir William Beechey]	Painting	37
1839	Christie's	The Infant placing a wreath of flowers on the head of th ...	Zurbaran	Painting	39
1805	Coxe (Peter)	Ditto [Landscape and Figures], the Companion	Zuccarelli	Painting	14
1836	Christie's	A landscape, with a waterfall and figures	Zuccarelli	Painting	17

... (1099 rows omitted)

Find non-painting objects using Table.where(...) and the predicate are.not_equal_to().

not_a_painting = art.where('object_type', are.not_equal_to('Painting'))
not_a_painting

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1859	Phillips (Harry)	A set of three finely modelled bronzes of the Venus de M ...	G. Zoffoli	Sculpture	16
1859	Phillips (Harry)	Another [finely modelled Old Florentine Bronze] of A Fem ...	Florentine	Sculpture	22
1859	Phillips (Harry)	Milton dictating his Paradise Lost.	Nash	Drawing	51
1836	Foster (Edward)	Portrait of himself, in chalks, glazed, capital.	La Tour	Drawing	56

Now, a quick recap of where and the predicate tests to select rows.

art.where("auction_house", are.equal_to("Christie's"))

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1839	Christie's	A rich equipage halting on the bank of a river, where fi ...	K. du Jardin	Painting	14
1839	Christie's	A breeze, with men-of-war and boats; a clear and beautif ...	Backhuysen	Painting	13
1838	Christie's	A dance of cupids; admirably coloured	V. Dyck	Painting	12
1838	Christie's	Susannah & the elders	Dietrich	Painting	13
1838	Christie's	A harbour-scene, with a royal yacht, vessels, boats, and ...	Backhuyzen	Painting	35
1838	Christie's	Interior of a Flemish cathedral, with figures by Francks	P. Neefs	Painting	25
1838	Christie's	A river-scene, with buildings and figures; a brilliant s ...	V. der Neer	Painting	23
1838	Christie's	A Dutch river near a town, with vessels and figures -- b ...	V. der Neer	Painting	53
1838	Christie's	A mountainous landscape, with classical figures; circular	G. Poussin	Painting	13
1838	Christie's	A cavalier seated smoking, in conversation with a female ...	Mieris	Painting	28

... (776 rows omitted)

art.where("pounds", are.above(900))

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1804	Coxe (Peter)	King Charles I. his Queen and Family, from the Orleans' ...	Vandyck	Painting	1575
1859	Phillips (Harry)	A Landscape, with full length Portraits of Pierre Both, ...	Albert Cuyp	Painting	966
1840	Christie's	The Holy Family; a composition of four figures, as large ...	Rubens	Painting	945

art.where("lot_sale_year", are.between(1815, 1835))

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1823	Christie's	The Four Seasons, exemplified in Four beautiful small Ca ...	David Teniers	Painting	189
1819	Christie's	A pair Historical, Edward and Eleonora, and companion, v ...	A. Kauffman	Painting	48

art.where("title", are.containing('river'))

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1839	Christie's	A rich equipage halting on the bank of a river, where fi ...	K. du Jardin	Painting	14
1838	Christie's	A river-scene, with buildings and figures; a brilliant s ...	V. der Neer	Painting	23
1838	Christie's	A Dutch river near a town, with vessels and figures -- b ...	V. der Neer	Painting	53
1838	Christie's	A Grand Italian Landscape, with buildings near a river; ...	Berghem	Painting	164
1840	Christie's	The manege; numerous figures near a stable, and distant ...	J. Ostade	Painting	26
1849	Christie's	A grand landscape, with a river, with a cavalier and gyp ...	Van Uden	Painting	18
1836	Christie's	A brown horse standing near a river, in a landscape, wit ...	Cuyp	Painting	28
1838	Christie's	A Flemish town on fire on the bank of the river, moonlight	V. der Neer	Painting	45
1838	Christie's	A windmill and cottages on the bank of a river, with boa ...	Ostade	Painting	22
1836	Christie's	Landscape, with a river; on the perforated rocky bank of ...	Claude	Painting	98

... (21 rows omitted)

What else can we learn from these data sets?#

Think-pair-share: Display the most expensive items sold after 1850?

Recall: method chaining let’s us combine multiple steps into a single line

art.where('lot_sale_year', are.above(1850)).sort('pounds', descending=True).show(5)

lot_sale_year	auction_house	title	artist_name	object_type	pounds
1859	Phillips (Harry)	A Landscape, with full length Portraits of Pierre Both, ...	Albert Cuyp	Painting	966
1859	Phillips (Harry)	The Disgrace of Clarendon.	E.M. Ward, R.A.	Painting	845
1859	Phillips (Harry)	View of Windsor Castle. The celebrated picture pain ...	Patrick Nasmyth	Painting	588
1859	Phillips (Harry)	The Wood. Nymph chanting her Hymn to the Rising Sun.	J. Danby, R.A.	Painting	378
1859	Phillips (Harry)	L'Umana Fragilita. A strange but wonderfully imagina ...	Salvator Rosa	Painting	346

... (39 rows omitted)

How much is £966 in 1859 in today’s USD?

The pound had an average inflation of 3.15% per year, meaning it is around £155,000 today.

pounds_2023 = 155000
dollars_2023 = pounds_2023 * 1.25
dollars_2023

193750.0

2. Data Types#

Type#

Can ask for the type of a value or variable with the built-in Python function type

type(3)

int

temperature = 98.6
type(temperature)

float

prof_name = "Katie"
type(prof_name)

str

this_class_is_fun = True
type(this_class_is_fun)

bool

Floats#

Some decisions made from Python. What type of value is produced by multiplying a float by an int?

answer = 0.75 * 2
answer
type(answer)

float

A computer cannot represent every real number exactly. That would require infinite memory because some numbers have an infinite number of digits.

1 / 3

0.3333333333333333

What happens when we run the next cell?

# 2 / 0

Scientific Notation#

Represent some numbers as \(b \times 10^e\).

Examples:

1.23e5 is \(1.23 \times 10^5\).
6.667e-07 is \(6.67 \times 10^{-7}\).

2 / 3000

0.0006666666666666666

2 / 3000000

6.666666666666667e-07

0.000000000000000123456789

1.23456789e-16

0.000000000000000000000000000000000000000000000000000000000000000000000123456789

1.23456789e-70

Rounding Errors#

Since numbers aren’t always represented exactly, small errors may creap when we operated on floats. Too small for us to worry about in this class.

0.6666666666666666 - 0.6666666666666666123456789 # a little less than 0 

0.0

2 ** 0.5

1.4142135623730951

2 ** 0.5 * 2 ** 0.5 # should be 2.0 

2.0000000000000004

2 ** 0.5 * 2 ** 0.5 - 2 # should be 0 

4.440892098500626e-16

Strings#

String values capture text data (sequences of characters). Use single quotes or double quotes around strings.

'Painting'

'Painting'

"Painting"

'Painting'

Variables vs Strings#

print("painting") # String value

painting = 4      # variable named painting
print(painting)

painting
4

Why both single and double quotes?

'Don't always use single quotes'

  Cell In[30], line 1
    'Don't always use single quotes'
         ^
SyntaxError: invalid syntax

"Don't always use single quotes"

"Don't always use single quotes"

'cs' + '104' # concatenation

'cs104'

'cs' + ' ' +  '104' # spaces aren't added for you

'cs 104'

Conversions#

Can only concatenate multiple strings.

number = 104
'cs' + number

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[34], line 2
      1 number = 104
----> 2 'cs' + number

TypeError: can only concatenate str (not "int") to str

Convert numbers to strings when you want to use them to build larger strings.

'cs' + str(number)

'cs104'

Can convert from string back to numbers as well.

int('3')

float('3.0')

3.0

int(str(number)) * 2

3. Arrays#

Array: sequence of values, all the same type, “boxed up”

Table operation: column

not_a_painting.column('pounds')

array([16, 22, 51, 56])

Arithmetic operations are broadcast on arrays.

What’s the price in dollars for each of these items?

price_in_pounds = not_a_painting.column('pounds')
price_in_dollars = price_in_pounds * 1.25
price_in_dollars

array([20.  , 27.5 , 63.75, 70.  ])

Suppose the art auction house adds 5 pounds to each item’s price.

price_in_pounds + 5

array([21, 27, 56, 61])

fives = make_array(5,10,15,20)
fives

array([ 5, 10, 15, 20])

price_in_pounds + fives

array([21, 32, 66, 76])

We can call other built-in Python functions on these arrays as well.

len(price_in_pounds)

max(price_in_pounds)

min(price_in_pounds)

sum(price_in_pounds)

np.mean(price_in_pounds)

36.25

price_in_pounds + make_array(1,2) #Error because not the same shapes 

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[49], line 1
----> 1 price_in_pounds + make_array(1,2) #Error because not the same shapes 

ValueError: operands could not be broadcast together with shapes (4,) (2,) 

price_in_pounds + make_array(1,2, 3, 4)

array([17, 24, 54, 60])

Index into array to retrieve items. Indices start at 0.

price_in_pounds.item(0)

price_in_pounds.item(1)

price_in_pounds.item(3)

Think of item(n) as asking for the item that has n items before it.

The price of the most expensive piece of art sold:

top_price = art.sort('pounds', descending=True).column('pounds').item(0)
top_price

CSCI 104: Data Science and Computing for All

Data Types

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