ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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pm_mathFisher::getFisher Interface Reference

Generate and return the Fisher transformation of the input Fisher z value.
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Detailed Description

Generate and return the Fisher transformation of the input Fisher z value.

See the documentation of pm_mathFisher for information about the Fisher transformation.

Parameters
[in]val: The input scalar (or array of the same shape as other array-like arguments) of,
  1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the bounded value to be Fisher-transformed.
[in]lb: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as val, containing the lower bound of the range of the input val. (optional, default = -1. It must be present if and only if the optional input argument ub is also present.)
[in]ub: The input scalar (or array of the same shape as other array-like arguments) of the same type and kind as val, containing the upper bound of the range of the input val. (optional, default = +1. It must be present if and only if the optional input argument lb is also present.)
Returns
fisherz : The output scalar (or array of the same shape as other array-like arguments) of the same type and kind as val, containing the result of the Fisher transformation of the input val.


Possible calling interfaces

fisherz = getFisher(val)
fisherz = getFisher(val, lb, ub)
Generate and return the Fisher transformation of the input Fisher z value.
This module contains procedures and generic interfaces for evaluating the Fisher transformation and i...
Warning
The condition lb < ub must hold for the corresponding input arguments.
The condition lb < val .and. val < ub must hold for the corresponding input arguments.
This condition is 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
getFisher
getFisherInv


Example usage

1program example
2
3 use pm_kind, only: SK, IK, LK, RKG => RKD
5 use pm_mathFisher, only: getFisher
6 use pm_distUnif, only: getUnifRand
7 use pm_io, only: display_type
8
9 implicit none
10
11 type(display_type) :: disp
12 real(RKG) :: redshift = 5.5_RKG
13 disp = display_type(file = "main.out.F90")
14
15 call disp%skip()
16 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
17 call disp%show("!Compute the Fisher z transformation of a random bounded variable.")
18 call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
19 call disp%skip()
20
21 block
22 use pm_kind, only: RKG => RKS
23 real(RKG), allocatable :: rand(:)
24 call disp%skip()
25 call disp%show("rand = getUnifRand(0._RKG, 1._RKG, 5_IK)")
26 rand = getUnifRand(0._RKG, 1._RKG, 5_IK)
27 call disp%show("rand")
28 call disp%show( rand )
29 call disp%show("getFisher(rand)")
30 call disp%show( getFisher(rand) )
31 call disp%show("getFisher(rand, lb = -1._RKG, ub = 1._RKG)")
32 call disp%show( getFisher(rand, lb = -1._RKG, ub = 1._RKG) )
33 call disp%show("getFisher(rand, lb = 0._RKG, ub = 1._RKG)")
34 call disp%show( getFisher(rand, lb = 0._RKG, ub = 1._RKG) )
35 call disp%skip()
36 end block
37
38 ! Generate both the cosmic rate and the rate density.
39
40 block
41 use pm_io, only: getErrTableWrite
42 real(RKG), allocatable :: rho(:)
43 rho = getLinSpace(-.99, +.99, 500_IK)
44 if (0 /= getErrTableWrite("getFisher.csv", reshape([rho, getFisher(rho)], [size(rho), 2]), header = "Correlation Coefficient,Fisher Transformation")) error stop "Table writing failed."
45 end block
46
47end program example
Generate count evenly spaced points over the interval [x1, x2] if x1 < x2, or [x2,...
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Generate and return the iostat code resulting from writing the input table of rank 1 or 2 to the spec...
Definition: pm_io.F90:5940
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
This module contains procedures and generic interfaces for generating arrays with linear or logarithm...
This module contains classes and procedures for computing various statistical quantities related to t...
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 RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568
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
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!Compute the Fisher z transformation of a random bounded variable.
4!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5
6
7rand = getUnifRand(0._RKG, 1._RKG, 5_IK)
8rand
9+0.969238281, +0.808126211, +0.185186863E-1, +0.627437592, +0.332009792E-2
10getFisher(rand)
11+2.07956553, +1.12160420, +0.185208023E-1, +0.737178743, +0.332011003E-2
12getFisher(rand, lb = -1._RKG, ub = 1._RKG)
13+2.07956553, +1.12160420, +0.185208023E-1, +0.737178743, +0.332011003E-2
14getFisher(rand, lb = 0._RKG, ub = 1._RKG)
15+1.72511971, +0.718940198, -1.98514140, +0.260619819, -2.85221767
16
17

Postprocessing of the example output
1#!/usr/bin/env python
2#pip install paramonte
3
4import os
5examname = os.path.basename(os.getcwd())
6
7
8
9import matplotlib.pyplot as plt
10import pandas as pd
11import numpy as np
12
13fontsize = 17
14
15df = pd.read_csv(examname + ".csv", delimiter = ",")
16
17fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
18ax = plt.subplot()
19
20plt.plot( df.values[:, 0]
21 , df.values[:, 0]
22 , linestyle = "-"
23 , linewidth = 2
24 )
25for colname in df.columns[1:]:
26 plt.plot( df.values[:, 0]
27 , df[colname].values
28 , linestyle = "-"
29 , linewidth = 2
30 )
31
32labels = ["Equality"]
33for colname in list(df.columns[1:]): labels.append(colname)
34ax.legend ( labels
35 , fontsize = fontsize
36 #, loc = "center left"
37 #, bbox_to_anchor = (1, 0.5)
38 )
39
40ax.set_xlabel(df.columns[0], fontsize = fontsize)
41ax.set_ylabel(df.columns[1], fontsize = fontsize)
42
43plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
44ax.tick_params(axis = "y", which = "minor")
45ax.tick_params(axis = "x", which = "minor")
46plt.xticks(fontsize = fontsize)
47plt.yticks(fontsize = fontsize)
48
49plt.tight_layout()
50plt.savefig(examname + ".png")

Visualization of the example output
Test:
test_pm_mathFisher


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, April 23, 2017, 1:36 AM, Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin

Definition at line 153 of file pm_mathFisher.F90.


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