Generate and return the Fractional rank of the input scalar string or contiguous array of rank 1 in ascending order or in the order specified by the input procedure isSorted() using the Quicksort algorithm such that array(rank) will be in ascending order (or in the requested order as specified by isSorted(). More...

Detailed Description

Generate and return the Fractional rank of the input scalar string or contiguous array of rank 1 in ascending order or in the order specified by the input procedure isSorted() using the Quicksort algorithm such that array(rank) will be in ascending order (or in the requested order as specified by isSorted().

This kind of ranking of values is widely known as fractional (1 2.5 2.5 4) ranking.
In Fractional ranking, items that compare equal receive the same ranking number, which is the mean of what they would have under ordinal rankings; equivalently, the ranking number of 1 plus the number of items ranked above it plus half the number of items equal to it.
This strategy has the property that the sum of the ranking numbers is the same as under ordinal ranking.
For this reason, it is used in computing Borda counts and ranking statistics (e.g., Spearman Correlation).
Thus if A ranks ahead of B and C (which compare equal) which are both ranked ahead of D, then A gets ranking number 1 (first), B and C each get ranking number 2.5 (average of joint second/third) and D gets ranking number 4 (fourth).
That is, if A < B == C < D, then the sequence ABCD has the Fractional ranking 1223.
Example:
Suppose the data set is 1.0, 1.0, 2.0, 3.0, 3.0, 4.0, 5.0, 5.0, 5.0.
The ordinal ranks are 1, 2, 3, 4, 5, 6, 7, 8, 9.
For v = 1.0, the Fractional rank is the average of the ordinal ranks: (1 + 2) / 2 = 1.5.
In a similar manner, for v = 5.0, the Fractional rank is (7 + 8 + 9) / 3 = 8.0.
Thus the Fractional ranks are: 1.5, 1.5, 3.0, 4.5, 4.5, 6.0, 8.0, 8.0, 8.0

Parameters

[in]

array

: The input contiguous array of rank 1 of either

type css_pdt (parameterized container of string of kind any supported by the processor (e.g., SK, SKA, SKD , or SKU)) or,
type css_type (container of string of default kind SK) or,
type character of kind any supported by the processor (e.g., SK, SKA, SKD , or SKU) of arbitrary length type parameter or,
type integer of kind any supported by the processor (e.g., IK, IK8, IK16, IK32, or IK64) or,
type logical of kind any supported by the processor (e.g., LK) or,
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),

or,

a scalar of type character of kind any supported by the processor (e.g., SK, SKA, SKD , or SKU) of arbitrary length type parameter,

whose elements rankings will be computed and returned.

isSorted

: The external user-specified function that takes two input scalar arguments of the same type and kind as the input array.
It returns a scalar logical of default kind LK that is .true. if the first input scalar argument is sorted with respect to the second input argument according to the user-defined sorting condition within isSorted(), otherwise, it is .false..
If array is a Fortran string (i.e., a scalar character), then both input arguments to isSorted() are single character(1,SKG) where SKG is the kind of array.
The following illustrates the generic interface of isSorted() when the rank of the input array is 1,

function isSorted(a,b) result (sorted)
    use pm_kind, only: SK, IK, LK, CK, RK
    TYPE(KIND)  , intent(in)    :: a, b
    logical(LK)                 :: sorted
end function

where TYPE(KIND) represents the type and kind of the input argument array, which can be one of the following,

use pm_container, only: css_type, css_pdt
use pm_kind, only: SK, IK, LK, CK, RK
character(*, SK)    , intent(in)    :: a, b
integer(IK)         , intent(in)    :: a, b
logical(LK)         , intent(in)    :: a, b
complex(CK)         , intent(in)    :: a, b
real(RK)            , intent(in)    :: a, b
type(css_type)      , intent(in)    :: a, b
type(css_pdt(SK))   , intent(in)    :: a, b

where the kinds SK, IK, LK, CK, RK, can refer to any kind type parameter that is supported by the processor.
The following illustrates the generic interface of isSorted() when the input array is a scalar string,

function isSorted(a,b) result (sorted)
    character(1,SKG), intent(in)    :: a, b
    logical(LK)                     :: sorted
end function

where SKG represents the kind of the input string argument array.
This user-defined equivalence check is extremely useful where a user-defined sorting criterion other than simple ascending order is needed, for example, when the case-sensitivity of an input string or array of strings is irrelevant or when sorting of the absolute values matters excluding the signs of the numbers, or when descending order is desired.
In such cases, user can define a custom sorting condition within the user-defined external function isSorted to achieve the goal.
(optional, the default sorting condition is ascending order, that is a < b.)

Returns: rank(1:size(array) : The output contiguous array of rank 1 of type real of default kind RK containing the ranks of the corresponding elements of array.
The size of rank must match that of array (or its length type parameter if array is a scalar string).
Read rank(i) as the Fractional rank of the ith element of array.

Possible calling interfaces ⛓

: use pm_arrayRank, only: getRankFractional

rank(1:size(array)) = getRankFractional(array)

rank(1:size(array)) = getRankFractional(array, isSorted)

pm_arrayRank::getRankFractional
Generate and return the Fractional rank of the input scalar string or contiguous array of rank 1 in a...
Definition: pm_arrayRank.F90:2706

pm_arrayRank
This module contains procedures and generic interfaces for obtaining various rankings of elements of ...
Definition: pm_arrayRank.F90:137

Warning: Note that the definition of isSorted(), if present, must be such that isSorted() .and. .not. isSorted() is equivalent to an equality check for two elements of the input array. This equality check is used to identify ties within the Standard ranking of the input array.; 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.; The procedures under this generic interface are always impure when the input argument isSorted is present.

See also: setSelected
getRankDense
setRankDense
getRankOrdinal
setRankOrdinal
getRankFractional
setRankFractional
getRankStandard
setRankStandard
getRankModified
setRankModified
setSorted
setSorted

Example usage ⛓

: 1program example

2

3 use pm_io, only: display_type

4 use pm_kind, only: SK, IK, LK, CK, RK ! all other processor kinds are also supported.

5 use pm_distUnif, only: setUnifRand

6 use pm_arrayRank, only: getRankFractional

7 use pm_str, only: getTrimmedTZ

8 use pm_val2str, only: getStr

9

10 implicit none

11

12 integer(IK) , parameter :: NP = 5_IK

13

14 ! Vector of indices of the sorted array.

15

16 integer(IK) :: i

17 real(RK) , allocatable :: rank(:)

18 character(:, SK) , allocatable :: string_SK

19 character(9, SK) , allocatable :: vector_SK(:)

20 real(RK) :: vector_RK(NP)

21 integer(IK) :: vector_IK(NP)

22 logical(LK) :: vector_LK(NP)

23

24 type(display_type) :: disp

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

26

27 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

28 ! Define the unsorted arrays.

29 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

30

31 !call setUnifRand(vector_SK, SK_"aaaaaaaaa", SK_"zzzzzzzzz")

32 call setUnifRand(vector_RK, -0.5_RK, +0.5_RK)

33 call setUnifRand(vector_IK, 1_IK, 2_IK**NP)

34 call setUnifRand(vector_LK)

35

36 call disp%skip()

37 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

38 call disp%show("!Sort string of characters in ascending order.")

39 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

40 call disp%skip()

41

42 string_SK = SK_"ParaMonte"

43 call allocateRank(len(string_SK))

44

45 call disp%skip()

46 call disp%show("string_SK")

47 call disp%show( string_SK, deliml = SK_"""" )

48 call disp%show("rank = getRankFractional(string_SK)")

49 rank = getRankFractional(string_SK)

50 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

51 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

52 call disp%skip()

53

54 call disp%skip()

55 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

56 call disp%show("!Sort array of strings of the same length in ascending order.")

57 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

58 call disp%skip()

59

60 vector_SK = [ "ParaMonte" &

61 , "V.2 " &

62 , "is " &

63 , "a " &

64 , "Parallel " &

65 , "Monte " &

66 , "Carlo " &

67 , "and " &

68 , "a " &

69 , "Machine " &

70 , "Learning " &

71 , "Library. " &

72 ]

73

74 call allocateRank(size(vector_SK))

75 call disp%skip()

76 call disp%show("vector_SK")

77 call disp%show( vector_SK, deliml = SK_"""" )

78 call disp%show("rank = getRankFractional(vector_SK)")

79 rank = getRankFractional(vector_SK)

80 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

81 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

82 call disp%skip()

83

84 call disp%skip()

85 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

86 call disp%show("!Sort vector of integers of arbitrary kinds in ascending order.")

87 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

88 call disp%skip()

89

90 call allocateRank(size(vector_IK))

91 call disp%skip()

92 call disp%show("vector_IK")

93 call disp%show( vector_IK )

94 call disp%show("rank = getRankFractional(vector_IK)")

95 rank = getRankFractional(vector_IK)

96 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

97 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

98 call disp%skip()

99

100 call allocateRank(size(vector_IK))

101 call disp%skip()

102 call disp%show("vector_IK = [1_IK, 2_IK, 3_IK, 2_IK, 1_IK]")

103 vector_IK = [1_IK, 2_IK, 3_IK, 2_IK, 1_IK]

104 call disp%show("rank = getRankFractional(vector_IK)")

105 rank = getRankFractional(vector_IK)

106 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

107 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

108 call disp%skip()

109

110 call disp%skip()

111 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

112 call disp%show("!Sort vector of logicals of arbitrary kinds in ascending order.")

113 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

114 call disp%skip()

115

116 call allocateRank(size(vector_LK))

117 call disp%skip()

118 call disp%show("vector_LK")

119 call disp%show( vector_LK )

120 call disp%show("rank = getRankFractional(vector_LK)")

121 rank = getRankFractional(vector_LK)

122 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

123 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

124 call disp%skip()

125

126 call disp%skip()

127 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

128 call disp%show("!Sort arrays of reals of arbitrary kinds in ascending order.")

129 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

130 call disp%skip()

131

132 call allocateRank(size(vector_RK))

133 call disp%skip()

134 call disp%show("vector_RK")

135 call disp%show( vector_RK )

136 call disp%show("rank = getRankFractional(vector_RK)")

137 rank = getRankFractional(vector_RK)

138 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

139 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

140 call disp%skip()

141

142 block

143 real, allocatable :: vector_RK(:)

144 vector_RK = [1.0, 1.0, 2.0, 3.0, 3.0, 4.0, 5.0, 5.0, 5.0]

145 call allocateRank(size(vector_RK))

146 call disp%skip()

147 call disp%show("vector_RK")

148 call disp%show( vector_RK )

149 call disp%show("rank = getRankFractional(vector_RK)")

150 rank = getRankFractional(vector_RK)

151 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

152 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

153 call disp%skip()

154 end block

155

156 call disp%skip()

157 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

158 call disp%show("!Sort according to an input user-defined comparison function.")

159 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

160 call disp%skip()

161

162 vector_IK = int([(i, i = 1_IK, NP)], kind = IK)

163 call allocateRank(size(vector_IK))

164 call disp%skip()

165 call disp%show("!Sort in DESCENDING (decreasing) order via an input custom-designed `isSorted()` function.")

166 call disp%skip()

167 call disp%show("vector_IK")

168 call disp%show( vector_IK )

169 call disp%show("rank = getRankFractional(vector_IK, isSorted_IK)")

170 rank = getRankFractional(vector_IK, isSorted_IK)

171 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

172 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

173 call disp%skip()

174

175 call random_number(vector_RK); vector_RK = vector_RK - 0.5_RK

176 call allocateRank(size(vector_RK))

177 call disp%skip()

178 call disp%show("!Sort in ascending order solely based on the magnitude of numbers using a custom comparison function.")

179 call disp%skip()

180 call disp%show("vector_RK")

181 call disp%show( vector_RK )

182 call disp%show("rank = getRankFractional(vector_RK, isSorted_RK)")

183 rank = getRankFractional(vector_RK, isSorted_RK)

184 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

185 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

186 call disp%skip()

187

188 string_SK = "ParaMonte"

189 call allocateRank(len(string_SK))

190 call disp%skip()

191 call disp%show("!Sort string in ascending order without case-sensitivity via a custom-designed input comparison function.")

192 call disp%skip()

193 call disp%show("string_SK")

194 call disp%show( string_SK, deliml = SK_"""" )

195 call disp%show("rank = getRankFractional(string_SK, isSorted_SK)")

196 rank = getRankFractional(string_SK, isSorted_SK)

197 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

198 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

199 call disp%skip()

200

201#if PDT_ENABLED

202 call disp%skip()

203 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

204 call disp%show("!Sort array of strings of varying length in ascending order.")

205 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")

206 call disp%skip()

207

208 block

209 use pm_container, only: css_pdt

210 type(css_pdt) , allocatable :: cssvec(:)

211 cssvec =[ css_pdt("ParaMonte") &

212 , css_pdt("V.2") &

213 , css_pdt("is") &

214 , css_pdt("a") &

215 , css_pdt("Parallel") &

216 , css_pdt("Monte") &

217 , css_pdt("Carlo") &

218 , css_pdt("and") &

219 , css_pdt("a") &

220 , css_pdt("Machine") &

221 , css_pdt("Learning") &

222 , css_pdt("Library.") &

223 ]

224 call allocateRank(size(cssvec))

225 call disp%skip()

226 call disp%show("cssvec")

227 call disp%show( cssvec, deliml = SK_"""" )

228 call disp%show("rank = getRankFractional(cssvec)")

229 rank = getRankFractional(cssvec)

230 call disp%show("getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))")

231 call disp%show( getTrimmedTZ(getStr(rank, format = SK_"(*(g0,:,', '))")) )

232 call disp%skip()

233 end block

234#endif

235

236contains

237

238 function isSorted_IK(a,b) result(isSorted)

239 use pm_kind, only: LK, IK

240 integer(IK) , intent(in) :: a, b

241 logical(LK) :: isSorted

242 isSorted = a > b

243 end function

244

245 function isSorted_RK(a,b) result(isSorted)

246 use pm_kind, only: LK, IK

247 integer(IK) , intent(in) :: a, b

248 logical(LK) :: isSorted

249 isSorted = abs(a) < abs(b)

250 end function

251

252 function isSorted_SK(a,b) result(isSorted)

253 use pm_strASCII, only: getStrLower

254 use pm_kind, only: LK, SK

255 character(1, SK), intent(in) :: a, b

256 logical(LK) :: isSorted

257 isSorted = getStrLower(a) < getStrLower(b)

258 end function

259

260 subroutine allocateRank(size)

261 integer, intent(in) :: size

262 if (allocated(rank)) deallocate(rank)

263 allocate(rank(size))

264 end subroutine

265

266end program example

pm_distUnif::setUnifRand
Return a uniform random scalar or contiguous array of arbitrary rank of randomly uniformly distribute...
Definition: pm_distUnif.F90:11083

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_strASCII::getStrLower
Generate and return the input string where the uppercase English alphabets are all converted to lower...
Definition: pm_strASCII.F90:4092

pm_str::getTrimmedTZ
Generate and return a vector of single-characters each element of which corresponds to one character ...
Definition: pm_str.F90:1449

pm_val2str::getStr
Generate and return the conversion of the input value to an output Fortran string,...
Definition: pm_val2str.F90:167

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

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_strASCII
This module contains the uncommon and hardly representable ASCII characters as well as procedures for...
Definition: pm_strASCII.F90:61

pm_str
This module contains classes and procedures for various string manipulations and inquiries.
Definition: pm_str.F90:49

pm_val2str
This module contains the generic procedures for converting values of different types and kinds to For...
Definition: pm_val2str.F90:58

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

2!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

3!Sort string of characters in ascending order.

4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

5

6

7string_SK

8"ParaMonte"

9rank = getRankFractional(string_SK)

10getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

112., 3.5, 8., 3.5, 1., 7., 6., 9., 5.

12

13

14!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

15!Sort array of strings of the same length in ascending order.

16!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

17

18

19vector_SK

20"ParaMonte", "V.2 ", "is ", "a ", "Parallel ", "Monte ", "Carlo ", "and ", "a ", "Machine ", "Learning ", "Library. "

21rank = getRankFractional(vector_SK)

22getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

236., 8., 12., 9.5, 7., 5., 1., 11., 9.5, 4., 2., 3.

24

25

26!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

27!Sort vector of integers of arbitrary kinds in ascending order.

28!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

29

30

31vector_IK

32+6, +32, +28, +29, +17

33rank = getRankFractional(vector_IK)

34getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

351., 5., 3., 4., 2.

36

37

38vector_IK = [1_IK, 2_IK, 3_IK, 2_IK, 1_IK]

39rank = getRankFractional(vector_IK)

40getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

411.5, 3.5, 5., 3.5, 1.5

42

43

44!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

45!Sort vector of logicals of arbitrary kinds in ascending order.

46!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

47

48

49vector_LK

50F, F, T, T, T

51rank = getRankFractional(vector_LK)

52getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

531.5, 1.5, 4., 4., 4.

54

55

56!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

57!Sort arrays of reals of arbitrary kinds in ascending order.

58!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

59

60

61vector_RK

62+0.18057849512577595, -0.18096351796249610, +0.16591992473318706, -0.38846759183403767, +0.26438055969664975E-1

63rank = getRankFractional(vector_RK)

64getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

655., 2., 4., 1., 3.

66

67

68vector_RK

69+1.00000000, +1.00000000, +2.00000000, +3.00000000, +3.00000000, +4.00000000, +5.00000000, +5.00000000, +5.00000000

70rank = getRankFractional(vector_RK)

71getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

721.5, 1.5, 3., 4.5, 4.5, 6., 8., 8., 8.

73

74

75!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

76!Sort according to an input user-defined comparison function.

77!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

78

79

80!Sort in DESCENDING (decreasing) order via an input custom-designed `isSorted()` function.

81

82vector_IK

83+1, +2, +3, +4, +5

84rank = getRankFractional(vector_IK, isSorted_IK)

85getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

865., 4., 3., 2., 1.

87

88

89!Sort in ascending order solely based on the magnitude of numbers using a custom comparison function.

90

91vector_RK

92-0.17083296690461525, +0.28656530278302694, +0.10973993140036642, +0.48530256689881779, +0.20698253293536628

93rank = getRankFractional(vector_RK, isSorted_RK)

94getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

952., 1., 4., 5., 3.

96

97

98!Sort string in ascending order without case-sensitivity via a custom-designed input comparison function.

99

100string_SK

101"ParaMonte"

102rank = getRankFractional(string_SK, isSorted_SK)

103getTrimmedTZ(getStr(rank, format = SK_'(*(g0,:,', '))'))

1047., 1.5, 8., 1.5, 4., 6., 5., 9., 3.

105

106

Test:: test_pm_arrayRank

Bug:: Status: Unresolved
Source: Intel Classic Fortran Compiler ifort version 2021.5
Description: See pm_arraySplit for the description of a relevant bug in PDT name aliasing when compiled with Intel ifort 2021.5 that also applies to this module.
Remedy (as of ParaMonte Library version 2.0.0): See pm_arraySplit for the remedy.

Todo:: Low Priority: The current bypass for the PDT name aliasing bug can be reverted back to PDT name aliasing once the ifort bug is resolved.

Todo:: Low Priority: A test should be implemented for arrays of size that can be represented only by an IKD integer.

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.
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Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, April 21, 2017, 1:54 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas Austin

Definition at line 2706 of file pm_arrayRank.F90.

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

src/fortran/main/pm_arrayRank.F90