Generate and return .true. if the two input values are sufficiently close to each other within the specified tolerances.
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Detailed Description

Generate and return .true. if the two input values are sufficiently close to each other within the specified tolerances.

See the documentation of pm_mathCompare for extensive details of possible testing modes.

Parameters

[in]	x	: The input scalar, or array of the same rank as other array-like arguments, of, type `complex` of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128) or, type `real` of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), whose proximity to the input `y` will be tested based on the specified method and tolerances.
[in]	y	: The input scalar, or array of the same rank as other array-like arguments, of the same type and kind as the input `x`, whose proximity to the input `x` will be tested based on the specified method and tolerances.
[in]	method	: The input scalar, or array of the same rank as other array-like arguments, of, type reference_type or, type strong_type or, type weak_type or, type mean_type, whose presence is solely used to determine the scaling of the relative tolerance for the proximity test. If `method = reference_type()`, then the input `x` will be taken as the reference value. (optional, default = WEAK)
[in]	reltol	: The input positive scalar, or array of the same rank as other array-like arguments, of type `real` of the same kind as the input argument `x`, representing the relative tolerance to be used in the proximity test. (optional, default = `epsilon(x)`)
[in]	abstol	: The input positive scalar, or array of the same rank as other array-like arguments, of type `real` of the same kind as the input argument `x`, representing the absolute tolerance to be used in the proximity test. (optional, default = `tiny(x)`)

Returns: close : The output scalar, or array of the same rank as other array-like arguments, of type logical of default kind LK.
It is .true. if and only if the two input values x and y is close to each other according to the specified testing method and tolerances.

Possible calling interfaces ⛓

: use pm_mathCompare, only: isClose

use pm_kind, only: LK

logical(LK) :: close

close = isClose(x, y, reltol = reltol, abstol = abstol)

close = isClose(x, y, method, reltol = reltol, abstol = abstol)

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:535

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

Warning: The condition 0. <= abstol must hold for the corresponding arguments.
The condition 0. <= reltol must hold for the corresponding arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.; The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks: The procedures under discussion are elemental.

Note: A -Inf value is considered not close to a +Inf in all circumstances.
Two +Inf values or two -Inf values are considered close to each other in all circumstances.
A NaN value is considered not close to any other value including another NaN in all circumstances.

See also: pm_test

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK

4 use pm_kind, only: RKS, RKD, RKH ! all processor types and kinds are supported.

5 use pm_kind, only: CKS, CKD, CKH ! all processor types and kinds are supported.

6 use pm_io, only: display_type

7 use pm_except, only: getInfNeg

8 use pm_except, only: getInfPos

9 use pm_except, only: getNAN

10 use pm_mathCompare, only: isClose

11 use pm_mathCompare, only: REFERENCE, STRONG, WEAK, MEAN

12

13 implicit none

14

15 type(display_type) :: disp

16 disp = display_type(file = "main.out.F90")

17

18 call disp%skip

19 call disp%show("isClose(0., [0., tiny(0.), epsilon(0.), 1.])")

20 call disp%show( isClose(0., [0., tiny(0.), epsilon(0.), 1.]) )

21 call disp%skip

22

23 call disp%skip

24 call disp%show("isClose(0., [0., tiny(0.), epsilon(0.), 1.], MEAN)")

25 call disp%show( isClose(0., [0., tiny(0.), epsilon(0.), 1.], MEAN) )

26 call disp%skip

27

28 call disp%skip

29 call disp%show("isClose(0., [0., tiny(0.), epsilon(0.), 1.], WEAK)")

30 call disp%show( isClose(0., [0., tiny(0.), epsilon(0.), 1.], WEAK) )

31 call disp%skip

32

33 call disp%skip

34 call disp%show("isClose(0., [0., tiny(0.), epsilon(0.), 1.], STRONG)")

35 call disp%show( isClose(0., [0., tiny(0.), epsilon(0.), 1.], STRONG) )

36 call disp%skip

37

38 call disp%skip

39 call disp%show("isClose(0., [0., tiny(0.), epsilon(0.), 1.], REFERENCE)")

40 call disp%show( isClose(0., [0., tiny(0.), epsilon(0.), 1.], REFERENCE) )

41 call disp%skip

42

43 call disp%skip

44 call disp%show("isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.])")

45 call disp%show( isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.]) )

46 call disp%skip

47

48 call disp%skip

49 call disp%show("isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], MEAN)")

50 call disp%show( isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], MEAN) )

51 call disp%skip

52

53 call disp%skip

54 call disp%show("isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], WEAK)")

55 call disp%show( isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], WEAK) )

56 call disp%skip

57

58 call disp%skip

59 call disp%show("isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], STRONG)")

60 call disp%show( isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], STRONG) )

61 call disp%skip

62

63 call disp%skip

64 call disp%show("isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], REFERENCE)")

65 call disp%show( isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], REFERENCE) )

66 call disp%skip

67

68 call disp%skip

69 call disp%show("isClose(getInfNeg(mold = 0.), [1., getInfNeg(0.), getInfPos(0.), getNAN(0.)])")

70 call disp%show( isClose(getInfNeg(mold = 0.), [1., getInfNeg(0.), getInfPos(0.), getNAN(0.)]) )

71 call disp%skip

72

73 call disp%skip

74 call disp%show("isClose(getNAN(0.), getNAN(0.))")

75 call disp%show( isClose(getNAN(0.), getNAN(0.)) )

76 call disp%skip

77

78 call disp%skip

79 call disp%show("isClose((0., 0.), cmplx(tiny(0.), tiny(0.)))")

80 call disp%show( isClose((0., 0.), cmplx(tiny(0.), tiny(0.))) )

81 call disp%skip

82

83 call disp%skip

84 call disp%show("isClose((0., 0.), cmplx(epsilon(0.), epsilon(0.)))")

85 call disp%show( isClose((0., 0.), cmplx(epsilon(0.), epsilon(0.))) )

86 call disp%skip

87

88 call disp%skip

89 call disp%show("isClose((1., 1.), (1., 1.) + cmplx(epsilon(0.), epsilon(0.)), reltol = 2 * epsilon(0.))")

90 call disp%show( isClose((1., 1.), (1., 1.) + cmplx(epsilon(0.), epsilon(0.)), reltol = 2 * epsilon(0.)) )

91 call disp%skip

92

93 call disp%skip

94 call disp%show("isClose((0., 0.), cmplx(tiny(0.), tiny(0.)), abstol = 2 * tiny(0.))")

95 call disp%show( isClose((0., 0.), cmplx(tiny(0.), tiny(0.)), abstol = 2 * tiny(0.)) )

96 call disp%skip

97

98end program example

pm_except::getInfNeg
Generate and return an IEEE-compliant negative infinity.
Definition: pm_except.F90:1719

pm_except::getInfPos
Generate and return an IEEE-compliant positive infinity.
Definition: pm_except.F90:1189

pm_except::getNAN
Generate and return an IEEE-compliant quiet NAN (Not a Number).
Definition: pm_except.F90:2414

pm_io::show
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_except
This module contains procedures and generic interfaces for testing for exceptional cases at runtime.
Definition: pm_except.F90:46

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:843

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:571

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_mathCompare::WEAK
type(weak_type), parameter WEAK
This is a convenience constant object of type weak_type() that is exclusively provided to distinguish...
Definition: pm_mathCompare.F90:387

pm_mathCompare::STRONG
type(strong_type), parameter STRONG
This is a convenience constant object of type strong_type() that is exclusively provided to distingui...
Definition: pm_mathCompare.F90:327

pm_mathCompare::REFERENCE
type(reference_type), parameter REFERENCE
This is a convenience constant object of type reference_type() that is exclusively provided to distin...
Definition: pm_mathCompare.F90:267

pm_mathCompare::MEAN
type(mean_type), parameter MEAN
This is a convenience constant object of type mean_type() that is exclusively provided to distinguish...
Definition: pm_mathCompare.F90:447

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1

2isClose(0., [0., tiny(0.), epsilon(0.), 1.])

3T, T, F, F

4

5

6isClose(0., [0., tiny(0.), epsilon(0.), 1.], MEAN)

7T, T, F, F

8

9

10isClose(0., [0., tiny(0.), epsilon(0.), 1.], WEAK)

11T, T, F, F

12

13

14isClose(0., [0., tiny(0.), epsilon(0.), 1.], STRONG)

15T, T, F, F

16

17

18isClose(0., [0., tiny(0.), epsilon(0.), 1.], REFERENCE)

19T, T, F, F

20

21

22isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.])

23T, T, T, F

24

25

26isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], MEAN)

27T, T, T, F

28

29

30isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], WEAK)

31T, T, T, F

32

33

34isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], STRONG)

35T, T, T, F

36

37

38isClose(1., 1. + [0., tiny(0.), epsilon(0.), 1.], REFERENCE)

39T, T, T, F

40

41

42isClose(getInfNeg(mold = 0.), [1., getInfNeg(0.), getInfPos(0.), getNAN(0.)])

43F, T, F, F

44

45

46isClose(getNAN(0.), getNAN(0.))

47F

48

49

50isClose((0., 0.), cmplx(tiny(0.), tiny(0.)))

51F

52

53

54isClose((0., 0.), cmplx(epsilon(0.), epsilon(0.)))

55F

56

57

58isClose((1., 1.), (1., 1.) + cmplx(epsilon(0.), epsilon(0.)), reltol = 2 * epsilon(0.))

59T

60

61

62isClose((0., 0.), cmplx(tiny(0.), tiny(0.)), abstol = 2 * tiny(0.))

63T

64

65

Test:: test_pm_mathCompare

Todo:: The implementations of the procedures of this generic interface can be improved to ensure robustness against possible rare cases of overflows and underflow as discussed in the documentation of pm_mathCompare.

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 08:49 PM, August 10, 2021, Dallas, TX

Definition at line 535 of file pm_mathCompare.F90.

The documentation for this interface was generated from the following file:

src/fortran/main/pm_mathCompare.F90