pm_arrayMembership Module Reference

This module contains procedures and generic interfaces for assessing whether particular value(s) or any values or all values within a collection are members of another collection of values, or within a range of values that specifies a mathematical set.
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Data Types
interface	operator(.allin.)
	Generate and return .true. if all elements of the input array-like val are members of the input array-like object Set, otherwise, return .false.. More...
interface	operator(.allinrange.)
	Generate and return .true. if all elements of the input array-like object val are within a range specified by the input vector Set(1:2), otherwise, return .false.. More...
interface	operator(.anyin.)
	Generate and return .true. if any elements of the input array-like val are members of the input array-like object Set, otherwise, return .false.. More...
interface	operator(.anyinrange.)
	Generate and return .true. if any elements of the input array-like object val are within a range specified by the input vector Set(1:2), otherwise, return .false.. More...
interface	operator(.in.)
	Generate and return .true. if the input value val is a member of the input array-like object set, otherwise, return .false.. More...
interface	operator(.inrange.)
	Generate and return .true. if the input value val is within a range specified by the input array-like object set(1:2), otherwise, return .false.. More...

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

Detailed Description

This module contains procedures and generic interfaces for assessing whether particular value(s) or any values or all values within a collection are members of another collection of values, or within a range of values that specifies a mathematical set.

In mathematics, an element or member of a set is any one of the distinct objects that belong to that set.
The relation is an element of, also called set membership, is denoted by the symbol \(\in\).
Writing \(x\in A\) means that \(x\) is an element of \(A\).
Equivalent expressions are \(x\) is a member of \(A\), \(x\) belongs to \(A\), \(x\) is in \(A\) and \(x\) lies in \(A\).
The expressions \(A\) includes \(x\) and \(A\) contains \(x\) are also used to mean set membership, although it is more frequently used to mean instead \(x\) is a subset of \(A\).
Logician George Boolos strongly urged that contains be used for membership only, and includes for the subset relation only.
For the relation \(\in\), the converse relation \(\in^T\) may be written \(A\ni x\) meaning \(A\) contains or includes \(x\).
The negation of set membership is denoted by the symbol \(\notin\).
Writing \(x\notin A\) means that \(x\) is not an element of \(A\).

Note

The functionalities of the generic interfaces .allin. and .allinrange. of this module are similar to that of the set-theoretic subset operation \(\subset\).
In mathematics, set \(A\) is a subset of a set \(B\) if all elements of \(A\) are also elements of \(B\).
Then, \(B\) is then a superset of \(A\).
It is possible for \(A\) and \(B\) to be equal.
If they are unequal, then \(A\) is a proper subset of \(B\).
The relationship of one set being a subset of another is called inclusion (or sometimes containment).
The statement \(A\) is a subset of \(B\) may also be expressed as \(B\) includes (or contains) \(A\) or \(A\) is included (or contained) in \(B\).
A \(k\)-subset is a subset with \(k\) elements.

The functionalities of the generic interfaces .anyin. and .anyinrange. of this module are similar to testing whether the output of set-theoretic intersection operation \(A\cap B\) is non-empty.
In set theory, the intersection of two sets \(A\) and \(B\), denoted by \(A\cap B\) is the set containing any elements of \(A\) that also belong to \(B\) or equivalently, any elements of \(B\) that also belong to \(A\).

See also

operator(.in.)
operator(.allin.)
operator(.anyin.)
operator(.inrange.)
operator(.anyinrange.)
operator(.allinrange.)
operator(.divmul.)
operator(.subadd.)
getMinMax
setMinMax
pm_arraySearch
pm_arrayFind

Test:

test_pm_arrayMembership

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_arrayMembership::MODULE_NAME = "@pm_arrayMembership"

Definition at line 80 of file pm_arrayMembership.F90.