Sort a Data Set¶

sorted_list(data)¶

Sorts all elements in a data set in increasing order via quicksort

Parameters: data (list of int or float) – List of numbers to analyze
Returns: order – List of all elements from a data set sorted in increasing order
Return type: list of int or float

Notes

Set of numbers: \(a_i = \{ a_1, a_2, \cdots, a_n \}\)
Sorted version of set: \(A_i = ( A_1, A_2, \cdots, A_n )\)
- For all terms in \(A_i\): \(A_{n-1} \leq A_n\)
Monotonic Function

Examples

Import sorted_list function from regressions library

>>> from regressions.statistics.sort import sorted_list

Sort the set [5, 2, 9, 8]

>>> order_1 = sorted_list([5, 2, 9, 8])
>>> print(order_1)
[2, 5, 8, 9]

Sort the set [11, 3, 52, 25, 21, 25, 6]

>>> order_2 = sorted_list([11, 3, 52, 25, 21, 25, 6])
>>> print(order_2)
[3, 6, 11, 21, 25, 25, 52]

sorted_dimension(data, dimension=1)¶

Sorts all elements in a multidimensional data set in increasing order, according to particular dimension

Parameters

data (list of lists of int or float) – List of lists of numbers to analyze
dimension (int, default=1) – Number representing the dimension to use for sorting

Returns

order – List of lists of numbers sorted in increasing order, based on only one dimension of the nested list

Return type

list of lists of int or float

Notes

Set of ordered pairs of numbers: \(a_i = \{ ( a_{1,1}, a_{1,2}, \cdots, a_{1,j}, a_{1,n} ), ( a_{2,1}, a_{2,2}, \cdots, a_{2,j}, a_{2,n} ), \cdots, \\ ( a_{m,1}, a_{m,2}, \cdots, a_{m,j}, a_{m,n} ) \}\)
Sorted version of set according to the values in the \(j\)th position: \(A_i = ( ( A_{1,1}, A_{1,2}, \cdots, A_{1,j}, A_{1,n} ), ( A_{2,1}, A_{2,2}, \cdots, A_{2,j}, A_{2,n} ), \cdots, \\ ( A_{m,1}, A_{m,2}, \cdots, A_{m,j}, A_{m,n} ) )\)
- For all terms in \(A_i\): \(A_{n-1,j} \leq A_{n,j}\)
Monotonic Function

Examples

Import sorted_dimension function from regressions library

>>> from regressions.statistics.sort import sorted_dimension

Sort the set [[1, 3, 5], [9, 2, 4], [6, 1, 8]] according to its second dimension

>>> order_1 = sorted_dimension([[1, 3, 5], [9, 2, 4], [6, 1, 8]], 2)
>>> print(order_1)
[[6, 1, 8], [9, 2, 4], [1, 3, 5]]

Sort the set [[1, 3, 5], [9, 2, 4], [6, 1, 8]] according to its third dimension

>>> order_2 = sorted_dimension([[1, 3, 5], [9, 2, 4], [6, 1, 8]], 3)
>>> print(order_2)
[[9, 2, 4], [1, 3, 5], [6, 1, 8]]