ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_sampleShift::getShifted Interface Reference

Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is shifted by the specified input amount along the specified axis dim.
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Detailed Description

Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is shifted by the specified input amount along the specified axis dim.

Here, ndim stands for the number of dimensions (data attributes) of the input sample and nsam represents the number of data points in the sample.
If the input amount is the negative of the mean of the sample, then the returned sample will have a mean of zero.

Parameters
[in]sample: The input contiguous array of shape (nsam), (ndim, nsam), or (nsam, ndim) of,
  1. type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
  2. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the sample to be shifted.
[in]dim: The input scalar of type integer of default kind IK, whose value represents the dimension of the input sample containing different nsam observations:
  1. If dim = 1, the input sample is assumed to have the shape (nsam, ndim).
  2. If dim = 2, the input sample is assumed to have the shape (ndim, nsam).
(optional. It must be present if and only if the input arguments the condition rank(sample) > 1 holds.)
[in]amount: The input scalar or the contiguous vector of the same type and kind as sample, representing the amount by which the input sample must be shifted.
  1. If the input rank(sample) = 1, then amount must be a scalar.
  2. If the input rank(sample) = 2, then amount must be a vector of size ndim.
If the sample is to be shifted toward the origin to have a mean of zero, then the input amount corresponds to the negative of the current mean of the sample that is returned by procedures collectively represented by the generic interface getMean.
Note that the size of the input amount must be consistent with the size of the input sample:
  1. If the input argument dim = 1 then, size(amount) == size(sample, 2) == ndim must hold.
  2. If the input argument dim = 2 then, size(amount) == size(sample, 1) == ndim must hold.
[in]operation: The input scalar constant that can be any of the following:
  1. The constant transHerm implying that a Hermitian transpose of the input sample must be returned.
    In other words, the actions getShifted(sample, dim, transHerm) and transpose(conjg(getShifted(sample, dim))) are equivalent.
    Specifying transHerm for source of type other than complex is identical to specifying transSymm for source of type other than complex.
(optional, default = .false.. It can be present only if the condition rank(sample) == 2 holds.)
Returns
sampleShifted : The output object of the same type and kind and rank as sample, containing the shifted sample.
  1. If the input sample is a vector, then sampleShifted has the same shape and size as that of sample.
  2. If the input sample is a matrix of shape (nrow, ncol), then
    1. sampleShifted has the shape (nrow, ncol) if operation is missing.
    2. sampleShifted has the shape (ncol, nrow) if operation = transHerm.


Possible calling interfaces ⛓

use pm_sampleShift, only: getShifted
sampleShifted(:) = getShifted(sample(:), amount)
sampleShifted(:,:) = getShifted(sample(:,:), dim, amount(:))
sampleShifted(:,:) = getShifted(sample(:,:), dim, amount(:), operation)
pm_sampleShift::getShifted
Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is shifted by the specified i...
Definition: pm_sampleShift.F90:197
pm_sampleShift
This module contains classes and procedures for shifting univariate or multivariate samples by arbitr...
Definition: pm_sampleShift.F90:59
Warning
The condition 1 <= dim .and. dim <= rank(sample) must hold for the corresponding input arguments.
The condition size(amount) == size(sample, 3 - dim) .or. rank(sample) /= 2 must hold for the corresponding input 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.
See also
getMean
setMean
getShifted
setShifted


Example usage ⛓

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_sampleMean, only: getMean
5 use pm_sampleShift, only: transHerm
6 use pm_sampleShift, only: getShifted
7 use pm_arraySpace, only: getLinSpace
8 use pm_io, only: display_type
9
10 implicit none
11
12 integer(IK) :: dim
13 type(display_type) :: disp
14 disp = display_type(file = "main.out.F90")
15
16 call disp%skip()
17 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
18 call disp%show("!Shift a 1D sample to have a zero mean.")
19 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
20 call disp%skip()
21
22 block
23 use pm_kind, only: TKG => RKS ! All kinds are supported.
24 real(TKG), allocatable :: sample(:)
25 call disp%show("sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)")
26 sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)
27 call disp%show("sample")
28 call disp%show( sample )
29 call disp%show("getMean(sample)")
30 call disp%show( getMean(sample) )
31 call disp%show("sample = getShifted(sample, -getMean(sample))")
32 sample = getShifted(sample, -getMean(sample))
33 call disp%show("sample")
34 call disp%show( sample )
35 call disp%show("getMean(sample)")
36 call disp%show( getMean(sample) )
37 call disp%skip()
38 end block
39
40 block
41 use pm_kind, only: TKG => RKS ! All kinds are supported.
42 complex(TKG), allocatable :: sample(:)
43 call disp%show("sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)")
44 sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)
45 call disp%show("sample")
46 call disp%show( sample )
47 call disp%show("getMean(sample)")
48 call disp%show( getMean(sample) )
49 call disp%show("sample = getShifted(sample, -getMean(sample))")
50 sample = getShifted(sample, -getMean(sample))
51 call disp%show("sample")
52 call disp%show( sample )
53 call disp%show("getMean(sample)")
54 call disp%show( getMean(sample) )
55 call disp%skip()
56 end block
57
58 call disp%skip()
59 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
60 call disp%show("!Shift a 2D sample to have a zero mean along the second dimension.")
61 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
62 call disp%skip()
63
64 block
65 use pm_kind, only: TKG => RKS ! All kinds are supported.
66 real(TKG), allocatable :: sample(:,:)
67 call disp%show("sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")
68 sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
69 call disp%show("sample")
70 call disp%show( sample )
71 call disp%show("dim = 2")
72 dim = 2
73 call disp%show("getMean(sample, dim)")
74 call disp%show( getMean(sample, dim) )
75 call disp%show("sample = getShifted(sample, dim, -getMean(sample, dim))")
76 sample = getShifted(sample, dim, -getMean(sample, dim))
77 call disp%show("sample")
78 call disp%show( sample )
79 call disp%show("getMean(sample, dim)")
80 call disp%show( getMean(sample, dim) )
81 call disp%skip()
82 end block
83
84 block
85 use pm_kind, only: TKG => RKS ! All kinds are supported.
86 complex(TKG), allocatable :: sample(:,:)
87 call disp%show("sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))")
88 sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))
89 call disp%show("sample")
90 call disp%show( sample )
91 call disp%show("dim = 2")
92 dim = 2
93 call disp%show("getMean(sample, dim)")
94 call disp%show( getMean(sample, dim) )
95 call disp%show("sample = getShifted(sample, dim, -getMean(sample, dim))")
96 sample = getShifted(sample, dim, -getMean(sample, dim))
97 call disp%show("sample")
98 call disp%show( sample )
99 call disp%show("getMean(sample, dim)")
100 call disp%show( getMean(sample, dim) )
101 call disp%skip()
102 end block
103
104 call disp%skip()
105 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
106 call disp%show("!Shift a 2D sample to have a zero mean along the second dimension, and transpose the result upon return.")
107 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
108 call disp%skip()
109
110 block
111 use pm_kind, only: TKG => RKS ! All kinds are supported.
112 real(TKG), allocatable :: sample(:,:)
113 call disp%show("sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")
114 sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
115 call disp%show("sample")
116 call disp%show( sample )
117 call disp%show("dim = 2")
118 dim = 2
119 call disp%show("getMean(sample, dim)")
120 call disp%show( getMean(sample, dim) )
121 call disp%show("sample = getShifted(sample, dim, -getMean(sample, dim), transHerm)")
122 sample = getShifted(sample, dim, -getMean(sample, dim), transHerm)
123 call disp%show("sample")
124 call disp%show( sample )
125 call disp%show("getMean(sample, 3_IK - dim)")
126 call disp%show( getMean(sample, 3_IK - dim) )
127 call disp%skip()
128 end block
129
130 block
131 use pm_kind, only: TKG => RKS ! All kinds are supported.
132 complex(TKG), allocatable :: sample(:,:)
133 call disp%show("sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))")
134 sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))
135 call disp%show("sample")
136 call disp%show( sample )
137 call disp%show("dim = 2")
138 dim = 2
139 call disp%show("getMean(sample, dim)")
140 call disp%show( getMean(sample, dim) )
141 call disp%show("sample = getShifted(sample, dim, -getMean(sample, dim), transHerm)")
142 sample = getShifted(sample, dim, -getMean(sample, dim), transHerm)
143 call disp%show("sample")
144 call disp%show( sample )
145 call disp%show("getMean(sample, 3_IK - dim)")
146 call disp%show( getMean(sample, 3_IK - dim) )
147 call disp%skip()
148 end block
149
150end program example
pm_arraySpace::getLinSpace
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Definition: pm_arraySpace.F90:108
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_sampleMean::getMean
Generate and return the (weighted) mean of an input sample of nsam observations with ndim = 1 or 2 at...
Definition: pm_sampleMean.F90:229
pm_arraySpace
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
Definition: pm_arraySpace.F90:33
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
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_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::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::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_sampleMean
This module contains classes and procedures for computing the first moment (i.e., the statistical mea...
Definition: pm_sampleMean.F90:104
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!Shift a 1D sample to have a zero mean.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)
7sample
8+0.00000000, +1.00000000, +2.00000000, +3.00000000, +4.00000000, +5.00000000, +6.00000000, +7.00000000, +8.00000000, +9.00000000, +10.0000000
9getMean(sample)
10+5.00000000
11sample = getShifted(sample, -getMean(sample))
12sample
13-5.00000000, -4.00000000, -3.00000000, -2.00000000, -1.00000000, +0.00000000, +1.00000000, +2.00000000, +3.00000000, +4.00000000, +5.00000000
14getMean(sample)
15+0.00000000
16
17sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)
18sample
19(+0.00000000, -0.00000000), (+1.00000000, -1.00000000), (+2.00000000, -2.00000000), (+3.00000000, -3.00000000), (+4.00000000, -4.00000000), (+5.00000000, -5.00000000), (+6.00000000, -6.00000000), (+7.00000000, -7.00000000), (+8.00000000, -8.00000000), (+9.00000000, -9.00000000), (+10.0000000, -10.0000000)
20getMean(sample)
21(+5.00000000, -5.00000000)
22sample = getShifted(sample, -getMean(sample))
23sample
24(-5.00000000, +5.00000000), (-4.00000000, +4.00000000), (-3.00000000, +3.00000000), (-2.00000000, +2.00000000), (-1.00000000, +1.00000000), (+0.00000000, +0.00000000), (+1.00000000, -1.00000000), (+2.00000000, -2.00000000), (+3.00000000, -3.00000000), (+4.00000000, -4.00000000), (+5.00000000, -5.00000000)
25getMean(sample)
26(+0.00000000, +0.00000000)
27
28
29!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
30!Shift a 2D sample to have a zero mean along the second dimension.
31!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
32
33sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
34sample
35+1.00000000, +3.00000000, +5.00000000, +7.00000000, +9.00000000
36+2.00000000, +4.00000000, +6.00000000, +8.00000000, +10.0000000
37dim = 2
38getMean(sample, dim)
39+5.00000000, +6.00000000
40sample = getShifted(sample, dim, -getMean(sample, dim))
41sample
42-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000
43-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000
44getMean(sample, dim)
45+0.00000000, +0.00000000
46
47sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))
48sample
49(+1.00000000, -1.00000000), (+3.00000000, -3.00000000), (+5.00000000, -5.00000000), (+7.00000000, -7.00000000), (+9.00000000, -9.00000000)
50(+2.00000000, -2.00000000), (+4.00000000, -4.00000000), (+6.00000000, -6.00000000), (+8.00000000, -8.00000000), (+10.0000000, -10.0000000)
51dim = 2
52getMean(sample, dim)
53(+5.00000000, -5.00000000), (+6.00000000, -6.00000000)
54sample = getShifted(sample, dim, -getMean(sample, dim))
55sample
56(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)
57(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)
58getMean(sample, dim)
59(+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
60
61
62!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
63!Shift a 2D sample to have a zero mean along the second dimension, and transpose the result upon return.
64!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
65
66sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
67sample
68+1.00000000, +3.00000000, +5.00000000, +7.00000000, +9.00000000
69+2.00000000, +4.00000000, +6.00000000, +8.00000000, +10.0000000
70dim = 2
71getMean(sample, dim)
72+5.00000000, +6.00000000
73sample = getShifted(sample, dim, -getMean(sample, dim), transHerm)
74sample
75-4.00000000, -4.00000000
76-2.00000000, -2.00000000
77+0.00000000, +0.00000000
78+2.00000000, +2.00000000
79+4.00000000, +4.00000000
80getMean(sample, 3_IK - dim)
81+0.00000000, +0.00000000
82
83sample = cmplx(reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]), -reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5]))
84sample
85(+1.00000000, -1.00000000), (+3.00000000, -3.00000000), (+5.00000000, -5.00000000), (+7.00000000, -7.00000000), (+9.00000000, -9.00000000)
86(+2.00000000, -2.00000000), (+4.00000000, -4.00000000), (+6.00000000, -6.00000000), (+8.00000000, -8.00000000), (+10.0000000, -10.0000000)
87dim = 2
88getMean(sample, dim)
89(+5.00000000, -5.00000000), (+6.00000000, -6.00000000)
90sample = getShifted(sample, dim, -getMean(sample, dim), transHerm)
91sample
92(-4.00000000, -4.00000000), (-4.00000000, -4.00000000)
93(-2.00000000, -2.00000000), (-2.00000000, -2.00000000)
94(+0.00000000, -0.00000000), (+0.00000000, -0.00000000)
95(+2.00000000, +2.00000000), (+2.00000000, +2.00000000)
96(+4.00000000, +4.00000000), (+4.00000000, +4.00000000)
97getMean(sample, 3_IK - dim)
98(+0.00000000, +0.00000000), (+0.00000000, +0.00000000)
99
100
Test:
test_pm_sampleShift
Todo:
Very Low Priority: The functionality of this interface can be expanded to include shifting of higher dimensional input sample and whole sample input arrays of arbitrary shape, although the latter is trivial using the Fortran array syntax.


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.

  1. 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.
  2. 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:
Amir Shahmoradi, Saturday 2:48 AM, August 22, 2021, Dallas, TX

Definition at line 197 of file pm_sampleShift.F90.

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