pm_arrayComplement Module Reference

This module contains procedures and generic interfaces for computing the absolute or relative complement of one set in another set. More...

Data Types
interface	getComplement
	Generate and return an array of elements of setB that are not in setA. More...
interface	getComplementRange
	Generate and return the complement of the input set setA with respect to an array of elements of the sorted set comprised of a range of integer values constructed by the triple start, stop, step. More...

Variables
character(*, SK), parameter	MODULE_NAME = "@pm_arrayComplement"

Detailed Description

This module contains procedures and generic interfaces for computing the absolute or relative complement of one set in another set.

In mathematical terminology, the complement of set \(A\) in set \(B\) is denoted by \(B \backslash A\), or \(B \cap A^{C}\), or less frequently by \(B - A\).
Read \(B \backslash A\) as the set of elements in B that do not appear in A.

1. If the set \(B\) contains all elements of the set \(A\), then \(B \backslash A\) is the absolute complement of \(A\).
2. If the set \(B\) does not contain all elements of the set \(A\), then \(B \backslash A\) is the relative complement of \(A\) (with respect to \(B\)).

An example Venn diagram illustration of \(B \backslash A\) is the red region in the following graph,

Note

This module contains two generic interfaces for computing the difference of two unsorted or two similarly-sorted sets.
If the sets are similarly sorted, use getComplement with sorted = .true. input argument.
Computing the difference of two sorted sets is significantly faster than computing the difference of two similarly-sorted sets.

Developer Remark:

The two generic interfaces of this module getComplement and getComplementRange are intentionally kept separately from each other under different names.

Test:

test_pm_arrayComplement

Todo:

High Priority: The two function interfaces of this module can be merged into a single generic interface.

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

Fatemeh Bagheri, Wednesday 12:24 PM, August 11, 2021, Dallas, TX

Variable Documentation

MODULE_NAME

character(*, SK), parameter pm_arrayComplement::MODULE_NAME = "@pm_arrayComplement"

Definition at line 69 of file pm_arrayComplement.F90.