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

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

Detailed Description

Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is scaled 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 square-root of the inverse of the variance of the (zero-mean) sample, then the returned sample will have a variance of one.

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 scaled.
[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,
  1. the same type and kind as sample,
  2. type real of the same kind as that of sample if sample is of type complex,
representing the amount by which the input sample must be scaled.
  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 scaled to have a unit variance, then the input amount corresponds to the square-root of the inverse of the variance of the sample that is returned by procedures collectively represented by the generic interface getVar.
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 getScaled(sample, dim, transHerm) and transpose(conjg(getScaled(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
sampleScaled : The output object of the same type and kind and rank as sample, containing the scaled sample.
  1. If the input sample is a vector, then sampleScaled has the same shape and size as that of sample.
  2. If the input sample is a matrix of shape (nrow, ncol), then
    1. sampleScaled has the shape (nrow, ncol) if operation is missing.
    2. sampleScaled has the shape (ncol, nrow) if operation = transHerm.


Possible calling interfaces

sampleScaled(:) = getScaled(sample(:), amount)
sampleScaled(:,:) = getScaled(sample(:,:), dim, amount(:))
sampleScaled(:,:) = getScaled(sample(:,:), dim, amount(:), operation)
Generate a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is scaled by the specified in...
This module contains classes and procedures for scaling (i.e., multiplying) univariate or multivariat...
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
getVar
setVar
getScaled
setScaled


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_sampleVar, only: getVar
5 use pm_sampleMean, only: getMean
6 use pm_sampleScale, only: transHerm
10 use pm_io, only: display_type
11
12 implicit none
13
14 integer(IK) :: dim
15 type(display_type) :: disp
16 disp = display_type(file = "main.out.F90")
17
18 call disp%skip()
19 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
20 call disp%show("!Scale a 1D zero-mean sample to have a unit variance.")
21 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
22 call disp%skip()
23
24 block
25 use pm_kind, only: TKG => RKS ! All kinds are supported.
26 real(TKG), allocatable :: sample(:)
27 call disp%show("sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)")
28 sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)
29 call disp%show("call setShifted(sample, -getMean(sample))")
30 call setShifted(sample, -getMean(sample))
31 call disp%show("sample")
32 call disp%show( sample )
33 call disp%show("getVar(sample)")
34 call disp%show( getVar(sample) )
35 call disp%show("sample = getScaled(sample, 1._TKG / sqrt(getVar(sample)))")
36 sample = getScaled(sample, 1._TKG / sqrt(getVar(sample)))
37 call disp%show("sample")
38 call disp%show( sample )
39 call disp%show("getVar(sample)")
40 call disp%show( getVar(sample) )
41 call disp%skip()
42 end block
43
44 block
45 use pm_kind, only: TKG => RKS ! All kinds are supported.
46 complex(TKG), allocatable :: sample(:)
47 call disp%show("sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)")
48 sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)
49 call disp%show("call setShifted(sample, -getMean(sample))")
50 call setShifted(sample, -getMean(sample))
51 call disp%show("sample")
52 call disp%show( sample )
53 call disp%show("getVar(sample)")
54 call disp%show( getVar(sample) )
55 call disp%show("sample = getScaled(sample, 1._TKG / sqrt(getVar(sample)))")
56 sample = getScaled(sample, 1._TKG / sqrt(getVar(sample)))
57 call disp%show("sample")
58 call disp%show( sample )
59 call disp%show("getVar(sample)")
60 call disp%show( getVar(sample) )
61 call disp%skip()
62 end block
63
64 call disp%skip()
65 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
66 call disp%show("!Scale a 2D zero-mean sample to have a unit variance.")
67 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
68 call disp%skip()
69
70 block
71 use pm_kind, only: TKG => RKS ! All kinds are supported.
72 real(TKG), allocatable :: sample(:,:)
73 call disp%show("sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")
74 sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
75 call disp%show("dim = 2")
76 dim = 2
77 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")
78 call setShifted(sample, dim, -getMean(sample, dim))
79 call disp%show("sample")
80 call disp%show( sample )
81 call disp%show("getVar(sample, dim)")
82 call disp%show( getVar(sample, dim) )
83 call disp%show("sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)))")
84 sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)))
85 call disp%show("sample")
86 call disp%show( sample )
87 call disp%show("getVar(sample, dim)")
88 call disp%show( getVar(sample, dim) )
89 call disp%skip()
90 end block
91
92 block
93 use pm_kind, only: TKG => RKS ! All kinds are supported.
94 complex(TKG), allocatable :: sample(:,:)
95 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]))")
96 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]))
97 call disp%show("dim = 2")
98 dim = 2
99 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")
100 call setShifted(sample, dim, -getMean(sample, dim))
101 call disp%show("sample")
102 call disp%show( sample )
103 call disp%show("getVar(sample, dim)")
104 call disp%show( getVar(sample, dim) )
105 call disp%show("sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)))")
106 sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)))
107 call disp%show("sample")
108 call disp%show( sample )
109 call disp%show("getVar(sample, dim)")
110 call disp%show( getVar(sample, dim) )
111 call disp%skip()
112 end block
113
114 call disp%skip()
115 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
116 call disp%show("!Scale a 2D zero-mean sample to have a unit variance and transpose the result upon return.")
117 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
118 call disp%skip()
119
120 block
121 use pm_kind, only: TKG => RKS ! All kinds are supported.
122 real(TKG), allocatable :: sample(:,:)
123 call disp%show("sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")
124 sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
125 call disp%show("dim = 2")
126 dim = 2
127 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")
128 call setShifted(sample, dim, -getMean(sample, dim))
129 call disp%show("sample")
130 call disp%show( sample )
131 call disp%show("getVar(sample, dim)")
132 call disp%show( getVar(sample, dim) )
133 call disp%show("sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)), transHerm)")
134 sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)), transHerm)
135 call disp%show("sample")
136 call disp%show( sample )
137 call disp%show("getVar(sample, 3_IK - dim)")
138 call disp%show( getVar(sample, 3_IK - dim) )
139 call disp%skip()
140 end block
141
142 block
143 use pm_kind, only: TKG => RKS ! All kinds are supported.
144 complex(TKG), allocatable :: sample(:,:)
145 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]))")
146 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]))
147 call disp%show("dim = 2")
148 dim = 2
149 call disp%show("call setShifted(sample, dim, -getMean(sample, dim))")
150 call setShifted(sample, dim, -getMean(sample, dim))
151 call disp%show("sample")
152 call disp%show( sample )
153 call disp%show("getVar(sample, dim)")
154 call disp%show( getVar(sample, dim) )
155 call disp%show("sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)), transHerm)")
156 sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)), transHerm)
157 call disp%show("sample")
158 call disp%show( sample )
159 call disp%show("getVar(sample, 3_IK - dim)")
160 call disp%show( getVar(sample, 3_IK - dim) )
161 call disp%skip()
162 end block
163
164end program example
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
Generate and return the (weighted) mean of an input sample of nsam observations with ndim = 1 or 2 at...
Return a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is shifted by the specified inp...
Generate and return the variance of the input sample of type complex or real of shape (nsam) or (ndim...
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
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
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
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
This module contains classes and procedures for computing the first moment (i.e., the statistical mea...
This module contains classes and procedures for shifting univariate or multivariate samples by arbitr...
This module contains classes and procedures for computing the properties related to the covariance ma...
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!Scale a 1D zero-mean sample to have a unit variance.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6sample = getLinSpace(x1 = 0., x2 = 10., count = 11_IK)
7call setShifted(sample, -getMean(sample))
8sample
9-5.00000000, -4.00000000, -3.00000000, -2.00000000, -1.00000000, +0.00000000, +1.00000000, +2.00000000, +3.00000000, +4.00000000, +5.00000000
10getVar(sample)
11+10.0000000
12sample = getScaled(sample, 1._TKG / sqrt(getVar(sample)))
13sample
14-1.58113885, -1.26491106, -0.948683262, -0.632455528, -0.316227764, +0.00000000, +0.316227764, +0.632455528, +0.948683262, +1.26491106, +1.58113885
15getVar(sample)
16+1.00000000
17
18sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)
19call setShifted(sample, -getMean(sample))
20sample
21(-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)
22getVar(sample)
23+20.0000000
24sample = getScaled(sample, 1._TKG / sqrt(getVar(sample)))
25sample
26(-1.11803401, +1.11803401), (-0.894427180, +0.894427180), (-0.670820355, +0.670820355), (-0.447213590, +0.447213590), (-0.223606795, +0.223606795), (+0.00000000, +0.00000000), (+0.223606795, -0.223606795), (+0.447213590, -0.447213590), (+0.670820355, -0.670820355), (+0.894427180, -0.894427180), (+1.11803401, -1.11803401)
27getVar(sample)
28+1.00000000
29
30
31!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
32!Scale a 2D zero-mean sample to have a unit variance.
33!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
34
35sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
36dim = 2
37call setShifted(sample, dim, -getMean(sample, dim))
38sample
39-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000
40-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000
41getVar(sample, dim)
42+8.00000000, +8.00000000
43sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)))
44sample
45-1.41421354, -0.707106769, +0.00000000, +0.707106769, +1.41421354
46-1.41421354, -0.707106769, +0.00000000, +0.707106769, +1.41421354
47getVar(sample, dim)
48+0.999999940, +0.999999940
49
50sample = 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]))
51dim = 2
52call setShifted(sample, dim, -getMean(sample, dim))
53sample
54(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)
55(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)
56getVar(sample, dim)
57+16.0000000, +16.0000000
58sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)))
59sample
60(-1.00000000, +1.00000000), (-0.500000000, +0.500000000), (+0.00000000, +0.00000000), (+0.500000000, -0.500000000), (+1.00000000, -1.00000000)
61(-1.00000000, +1.00000000), (-0.500000000, +0.500000000), (+0.00000000, +0.00000000), (+0.500000000, -0.500000000), (+1.00000000, -1.00000000)
62getVar(sample, dim)
63+1.00000000, +1.00000000
64
65
66!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
67!Scale a 2D zero-mean sample to have a unit variance and transpose the result upon return.
68!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
69
70sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])
71dim = 2
72call setShifted(sample, dim, -getMean(sample, dim))
73sample
74-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000
75-4.00000000, -2.00000000, +0.00000000, +2.00000000, +4.00000000
76getVar(sample, dim)
77+8.00000000, +8.00000000
78sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)), transHerm)
79sample
80-1.41421354, -1.41421354
81-0.707106769, -0.707106769
82+0.00000000, +0.00000000
83+0.707106769, +0.707106769
84+1.41421354, +1.41421354
85getVar(sample, 3_IK - dim)
86+0.999999940, +0.999999940
87
88sample = 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]))
89dim = 2
90call setShifted(sample, dim, -getMean(sample, dim))
91sample
92(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)
93(-4.00000000, +4.00000000), (-2.00000000, +2.00000000), (+0.00000000, +0.00000000), (+2.00000000, -2.00000000), (+4.00000000, -4.00000000)
94getVar(sample, dim)
95+16.0000000, +16.0000000
96sample = getScaled(sample, dim, 1._TKG / sqrt(getVar(sample, dim)), transHerm)
97sample
98(-1.00000000, -1.00000000), (-1.00000000, -1.00000000)
99(-0.500000000, -0.500000000), (-0.500000000, -0.500000000)
100(+0.00000000, -0.00000000), (+0.00000000, -0.00000000)
101(+0.500000000, +0.500000000), (+0.500000000, +0.500000000)
102(+1.00000000, +1.00000000), (+1.00000000, +1.00000000)
103getVar(sample, 3_IK - dim)
104+1.00000000, +1.00000000
105
106
Test:
test_pm_sampleScale
Todo:
Very Low Priority: The functionality of this interface can be expanded to include scaling 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.

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

Definition at line 198 of file pm_sampleScale.F90.


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