foreng_math_sets

Uses

- foreng_env

Interfaces

public interface intersection

Compute the intersection of two sets

public function intersection_int(A, B) result(inters)

Arguments

Type Intent Optional Attributes Name

integer, intent(in), dimension(:) :: A
set A

integer, intent(in), dimension(:) :: B
set B

Return Value integer, dimension(:), allocatable

$A \cap B$

public function intersection_r32(A, B) result(inters)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:)	::	A	set A
real(kind=real32),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real32), dimension(:), allocatable

$A \cap B$

public function intersection_r64(A, B) result(inters)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:)	::	A	set A
real(kind=real64),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real64), dimension(:), allocatable

$A \cap B$

public interface union

Compute the union of two sets

public function union_int(A, B) result(union_set)

Arguments

Type Intent Optional Attributes Name

integer, intent(in), dimension(:) :: A
set A

integer, intent(in), dimension(:) :: B
set B

Return Value integer, dimension(:), allocatable

$A \cup B$

public function union_r32(A, B) result(union_set)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:)	::	A	set A
real(kind=real32),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real32), dimension(:), allocatable

$A \cup B$

public function union_r64(A, B) result(union_set)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:)	::	A	set A
real(kind=real64),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real64), dimension(:), allocatable

$A \cup B$

public interface belongs_to

Check if $x \in \textrm{A}$
$x$ belongs to $A$ if there is at least one element $y$ in $A$ for which $x = y$

public function belongs_to_int(x, A) result(bool)

Check if a value $x$ belongs to a set $\textrm{A}$

Arguments

Type Intent Optional Attributes Name

integer, intent(in) :: x

integer, dimension(:) :: A

Return Value logical

public function belongs_to_r32(x, A, eps) result(bool)

Check if a value $x$ belongs to a set within a certain tolerance $\epsilon$ . If $\epsilon$ is not specified, it will automatically calculated using the $\verb|array_epsilon|$ function

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	x
real(kind=real32),			dimension(:)	::	A
real(kind=real32),		optional		::	eps	$x = y \iff \textrm{abs}(x - y) < \epsilon$

Return Value logical

public function belongs_to_r64(x, A, eps) result(bool)

Check if a value $x$ belongs to a set within a certain tolerance $\epsilon$ . If $\epsilon$ is not specified, it will automatically calculated using the $\verb|array_epsilon|$ function

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	x
real(kind=real64),			dimension(:)	::	A
real(kind=real64),		optional		::	eps	$x = y \iff \textrm{abs}(x - y) < \epsilon$

Return Value logical

public interface array_epsilon

public function array_epsilon_r32(array) result(eps)

Arguments

Type Intent Optional Attributes Name

real(kind=real32), intent(in), dimension(:) :: array

Return Value real(kind=real32)
public function array_epsilon_r64(array) result(eps)

Arguments

Type Intent Optional Attributes Name

real(kind=real64), intent(in), dimension(:) :: array

Return Value real(kind=real64)

public interface abs_max_val

public function abs_max_val_r32(array) result(abs_max_val)

Arguments

Type Intent Optional Attributes Name

real(kind=real32), intent(in), dimension(:) :: array

Return Value real(kind=real32)
public function abs_max_val_r64(array) result(abs_max_val)

Arguments

Type Intent Optional Attributes Name

real(kind=real64), intent(in), dimension(:) :: array

Return Value real(kind=real64)

Functions

public function intersection_int(A, B) result(inters)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		dimension(:)	::	A	set A
integer,	intent(in),		dimension(:)	::	B	set B

Return Value integer, dimension(:), allocatable

$A \cap B$

public function intersection_r32(A, B) result(inters)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:)	::	A	set A
real(kind=real32),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real32), dimension(:), allocatable

$A \cap B$

public function intersection_r64(A, B) result(inters)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:)	::	A	set A
real(kind=real64),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real64), dimension(:), allocatable

$A \cap B$

public function union_int(A, B) result(union_set)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in),		dimension(:)	::	A	set A
integer,	intent(in),		dimension(:)	::	B	set B

Return Value integer, dimension(:), allocatable

$A \cup B$

public function union_r32(A, B) result(union_set)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:)	::	A	set A
real(kind=real32),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real32), dimension(:), allocatable

$A \cup B$

public function union_r64(A, B) result(union_set)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:)	::	A	set A
real(kind=real64),	intent(in),		dimension(:)	::	B	set B

Return Value real(kind=real64), dimension(:), allocatable

$A \cup B$

public function belongs_to_int(x, A) result(bool)

Check if a value $x$ belongs to a set $\textrm{A}$

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	x
integer,			dimension(:)	::	A

Return Value logical

public function belongs_to_r32(x, A, eps) result(bool)

Check if a value $x$ belongs to a set within a certain tolerance $\epsilon$ . If $\epsilon$ is not specified, it will automatically calculated using the $\verb|array_epsilon|$ function

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in)			::	x
real(kind=real32),			dimension(:)	::	A
real(kind=real32),		optional		::	eps	$x = y \iff \textrm{abs}(x - y) < \epsilon$

Return Value logical

public function belongs_to_r64(x, A, eps) result(bool)

Check if a value $x$ belongs to a set within a certain tolerance $\epsilon$ . If $\epsilon$ is not specified, it will automatically calculated using the $\verb|array_epsilon|$ function

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	x
real(kind=real64),			dimension(:)	::	A
real(kind=real64),		optional		::	eps	$x = y \iff \textrm{abs}(x - y) < \epsilon$

Return Value logical

public function array_epsilon_r32(array) result(eps)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:)	::	array

Return Value real(kind=real32)

public function array_epsilon_r64(array) result(eps)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:)	::	array

Return Value real(kind=real64)

public function abs_max_val_r32(array) result(abs_max_val)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real32),	intent(in),		dimension(:)	::	array

Return Value real(kind=real32)

public function abs_max_val_r64(array) result(abs_max_val)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:)	::	array

foreng_math_sets Module

Contents

Interfaces

Functions

Uses

Contents

Interfaces

Functions

Interfaces

public interface intersection

public function intersection_int(A, B) result(inters)

Arguments

Return Value integer, dimension(:), allocatable

public function intersection_r32(A, B) result(inters)

Arguments

Return Value real(kind=real32), dimension(:), allocatable

public function intersection_r64(A, B) result(inters)

Arguments

Return Value real(kind=real64), dimension(:), allocatable

public interface union

public function union_int(A, B) result(union_set)

Arguments

Return Value integer, dimension(:), allocatable

public function union_r32(A, B) result(union_set)

Arguments

Return Value real(kind=real32), dimension(:), allocatable

public function union_r64(A, B) result(union_set)

Arguments

Return Value real(kind=real64), dimension(:), allocatable

public interface belongs_to

public function belongs_to_int(x, A) result(bool)

Arguments

Return Value logical

public function belongs_to_r32(x, A, eps) result(bool)

Arguments

Return Value logical

public function belongs_to_r64(x, A, eps) result(bool)

Arguments

Return Value logical

public interface array_epsilon

public function array_epsilon_r32(array) result(eps)

Arguments

Return Value real(kind=real32)

public function array_epsilon_r64(array) result(eps)

Arguments

Return Value real(kind=real64)

public interface abs_max_val

public function abs_max_val_r32(array) result(abs_max_val)

Arguments

Return Value real(kind=real32)

public function abs_max_val_r64(array) result(abs_max_val)

Arguments

Return Value real(kind=real64)

Functions

public function intersection_int(A, B) result(inters)

Arguments

Return Value integer, dimension(:), allocatable

public function intersection_r32(A, B) result(inters)

Arguments

Return Value real(kind=real32), dimension(:), allocatable

public function intersection_r64(A, B) result(inters)

Arguments

Return Value real(kind=real64), dimension(:), allocatable

public function union_int(A, B) result(union_set)

Arguments

Return Value integer, dimension(:), allocatable

public function union_r32(A, B) result(union_set)

Arguments

Return Value real(kind=real32), dimension(:), allocatable

public function union_r64(A, B) result(union_set)

Arguments

Return Value real(kind=real64), dimension(:), allocatable

public function belongs_to_int(x, A) result(bool)

Arguments

Return Value logical

public function belongs_to_r32(x, A, eps) result(bool)

Arguments

Return Value logical

public function belongs_to_r64(x, A, eps) result(bool)

Arguments