Return a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is normalized by the specified input shift and scale 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 shift is the negative of the mean of the sample and scale is the square-root of the inverse of the variance of the sample, then the returned sample will be a standard score (i.e., z-score).
- Parameters
-
| [in,out] | sample | : The input/output contiguous array of shape (nsam), (ndim, nsam), or (nsam, ndim) of,
-
type
complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
-
type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the sample to be normalized.
|
| [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:
-
If
dim = 1, the input sample is assumed to have the shape (nsam, ndim).
-
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] | shift | : 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.
-
If the input
rank(sample) = 1, then shift must be a scalar.
-
If the input
rank(sample) = 2, then shift 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 shift 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 shift must be consistent with the size of the input sample:
-
If the input argument
dim = 1 then, size(shift) == size(sample, 2) == ndim must hold.
-
If the input argument
dim = 2 then, size(shift) == size(sample, 1) == ndim must hold.
|
| [in] | scale | : The input scalar or the contiguous vector of,
-
the same type and kind as
sample,
-
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.
-
If the input
rank(sample) = 1, then scale must be a scalar.
-
If the input
rank(sample) = 2, then scale must be a vector of size ndim.
If the sample is to be scaled to have a unit variance, then the input scale 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 scale must be consistent with the size of the input sample:
-
If the input argument
dim = 1 then, size(scale) == size(sample, 2) == ndim must hold.
-
If the input argument
dim = 2 then, size(scale) == size(sample, 1) == ndim must hold.
|
Possible calling interfaces ⛓
call setNormed(sample(:,:), dim, shift(:),
scale(:))
Return a sample of shape (nsam), or (ndim, nsam) or (nsam, ndim) that is normalized by the specified ...
This module contains classes and procedures for normalizing univariate or multivariate samples by arb...
- Warning
- The condition
1 <= dim .and. dim <= rank(sample) must hold for the corresponding input arguments.
The condition size(scale) == size(sample, 3 - dim) .or. rank(sample) /= 2 must hold for the corresponding input arguments.
The condition size(shift) == 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
getNormed
setNormed
Example usage ⛓
15 type(display_type) :: disp
19 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
20 call disp%show(
"!Normalize a 1D zero-mean sample to have a unit variance.")
21 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
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)
35 call disp%show(
"call setNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))")
48 complex(TKG),
allocatable :: sample(:)
49 call disp%show(
"sample = cmplx(getLinSpace(x1 = 0., x2 = 10., count = 11_IK), -getLinSpace(x1 = 0., x2 = 10., count = 11_IK), TKG)")
50 sample
= cmplx(
getLinSpace(x1
= 0., x2
= 10., count
= 11_IK),
-getLinSpace(x1
= 0., x2
= 10., count
= 11_IK), TKG)
57 call disp%show(
"call setNormed(sample, -getMean(sample), 1._TKG / sqrt(getVar(sample)))")
69 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
70 call disp%show(
"!Normalize a 2D zero-mean sample to have a unit variance.")
71 call disp%show(
"!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
76 real(TKG),
allocatable :: sample(:,:)
77 call disp%show(
"sample = reshape(getLinSpace(x1 = 1._TKG, x2 = 10._TKG, count = 10_IK), [2,5])")
78 sample
= reshape(
getLinSpace(x1
= 1._TKG, x2
= 10._TKG, count
= 10_IK), [
2,
5])
81 call disp%show(
"call setShifted(sample, dim, -getMean(sample, dim))")
85 call disp%show(
"getMean(sample, dim)")
87 call disp%show(
"getVar(sample, dim)")
89 call disp%show(
"call setNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))")
93 call disp%show(
"getMean(sample, dim)")
95 call disp%show(
"getVar(sample, dim)")
102 complex(TKG),
allocatable :: sample(:,:)
103 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]))")
104 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]))
107 call disp%show(
"call setShifted(sample, dim, -getMean(sample, dim))")
111 call disp%show(
"getMean(sample, dim)")
113 call disp%show(
"getVar(sample, dim)")
115 call disp%show(
"call setNormed(sample, dim, -getMean(sample, dim), 1._TKG / sqrt(getVar(sample, dim)))")
119 call disp%show(
"getMean(sample, dim)")
121 call disp%show(
"getVar(sample, dim)")
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.
This is a generic method of the derived type display_type with pass attribute.
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...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
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.
Example Unix compile command via Intel ifort compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
6sample
= getLinSpace(x1
= 0., x2
= 10., count
= 11_IK)
8+0.00000000,
+1.00000000,
+2.00000000,
+3.00000000,
+4.00000000,
+5.00000000,
+6.00000000,
+7.00000000,
+8.00000000,
+9.00000000,
+10.0000000
15-1.58113885,
-1.26491106,
-0.948683262,
-0.632455528,
-0.316227764,
+0.00000000,
+0.316227764,
+0.632455528,
+0.948683262,
+1.26491106,
+1.58113885
21sample
= cmplx(
getLinSpace(x1
= 0., x2
= 10., count
= 11_IK),
-getLinSpace(x1
= 0., x2
= 10., count
= 11_IK), TKG)
23(
+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)
25(
+5.00000000,
-5.00000000)
30(
-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)
32(
+0.00000000,
+0.00000000)
41sample
= reshape(
getLinSpace(x1
= 1._TKG, x2
= 10._TKG, count
= 10_IK), [
2,
5])
45-4.00000000,
-2.00000000,
+0.00000000,
+2.00000000,
+4.00000000
46-4.00000000,
-2.00000000,
+0.00000000,
+2.00000000,
+4.00000000
48+0.00000000,
+0.00000000
50+8.00000000,
+8.00000000
53-1.41421354,
-0.707106769,
+0.00000000,
+0.707106769,
+1.41421354
54-1.41421354,
-0.707106769,
+0.00000000,
+0.707106769,
+1.41421354
56+0.238418583E-7,
+0.238418583E-7
58+0.999999940,
+0.999999940
60sample
= 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]))
64(
-4.00000000,
+4.00000000), (
-2.00000000,
+2.00000000), (
+0.00000000,
+0.00000000), (
+2.00000000,
-2.00000000), (
+4.00000000,
-4.00000000)
65(
-4.00000000,
+4.00000000), (
-2.00000000,
+2.00000000), (
+0.00000000,
+0.00000000), (
+2.00000000,
-2.00000000), (
+4.00000000,
-4.00000000)
67(
+0.00000000,
+0.00000000), (
+0.00000000,
+0.00000000)
69+16.0000000,
+16.0000000
72(
-1.00000000,
+1.00000000), (
-0.500000000,
+0.500000000), (
+0.00000000,
+0.00000000), (
+0.500000000,
-0.500000000), (
+1.00000000,
-1.00000000)
73(
-1.00000000,
+1.00000000), (
-0.500000000,
+0.500000000), (
+0.00000000,
+0.00000000), (
+0.500000000,
-0.500000000), (
+1.00000000,
-1.00000000)
75(
+0.00000000,
+0.00000000), (
+0.00000000,
+0.00000000)
77+1.00000000,
+1.00000000
- Test:
- test_pm_sampleNorm
- Todo:
- Normal Priority: The functionality of this interface can be expanded to include normalizing 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.
-
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:
- Amir Shahmoradi, Wednesday 00:01 AM, August 25, 2021, Dallas, TX
Definition at line 1059 of file pm_sampleNorm.F90.
1.9.3