pm_mathFisher::getFisherInv Interface Reference

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

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

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

Parameters

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

Returns

val : The output scalar (or array of the same shape as other array-like arguments) of the same type and kind as fisherz, containing the result of the inverse Fisher transformation of the input fisherz.

Possible calling interfaces ⛓

use pm_mathFisher, only: getFisherInv
 
val = getFisherInv(fisherz)
val = getFisherInv(fisherz, lb, ub)

Warning

The condition lb < 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. The procedures of this generic interface are always pure when both optional arguments lb and ub are missing.

See also

getFisher
getFisherInv

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK, RKG => RKD
    use pm_arraySpace, only: getLinSpace
    use pm_mathFisher, only: getFisherInv
    use pm_mathFisher, only: getFisher
    use pm_distUnif, only: getUnifRand
    use pm_io, only: display_type
 
    implicit none
 
    type(display_type) :: disp
    real(RKG) :: redshift = 5.5_RKG
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!Compute the Inverse Fisher z transformation of a random bounded variable.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    block
        use pm_kind, only: RKG => RKS
        real(RKG), allocatable :: rand(:)
        call disp%skip()
        call disp%show("rand = getUnifRand(-9, 9, 5_IK)")
                        rand = getUnifRand(-9, 9, 5_IK)
        call disp%show("rand")
        call disp%show( rand )
        call disp%show("getFisherInv(rand)")
        call disp%show( getFisherInv(rand) )
        call disp%show("getFisherInv(rand, lb = -1._RKG, ub = 1._RKG)")
        call disp%show( getFisherInv(rand, lb = -1._RKG, ub = 1._RKG) )
        call disp%show("getFisherInv(rand, lb = 0._RKG, ub = 1._RKG)")
        call disp%show( getFisherInv(rand, lb = 0._RKG, ub = 1._RKG) )
        call disp%skip()
    end block
 
    ! Generate both the cosmic rate and the rate density.
 
    block
        use pm_io, only: getErrTableWrite
        real(RKG), allocatable :: fish(:)
        fish = getFisher(getLinSpace(-.99, +.99, 500_IK))
        if (0 /= getErrTableWrite("getFisherInv.csv", reshape([fish, getFisherInv(fish)], [size(fish), 2]), header = "Fisher Transformation,Correlation Coefficient")) error stop "Table writing failed."
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!Compute the Inverse Fisher z transformation of a random bounded variable.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
rand = getUnifRand(-9, 9, 5_IK)
rand
+5.00000000, -9.00000000, -6.00000000, -1.00000000, -1.00000000
getFisherInv(rand)
+0.999909222, -0.999999940, -0.999987721, -0.761594176, -0.761594176
getFisherInv(rand, lb = -1._RKG, ub = 1._RKG)
+0.999909163, -0.999999940, -0.999987721, -0.761594176, -0.761594176
getFisherInv(rand, lb = 0._RKG, ub = 1._RKG)
+0.999954581, +0.298023224E-7, +0.613927841E-5, +0.119202912, +0.119202912
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
#pip install paramonte
 
import os
examname = os.path.basename(os.getcwd())
 
 
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
 
fontsize = 17
 
df = pd.read_csv(examname + ".csv", delimiter = ",")
 
fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
ax = plt.subplot()
 
plt.plot( df.values[:, 1]
        , df.values[:, 1]
        , linestyle = "-"
        , linewidth = 2
        )
for colname in df.columns[1:]:
    plt.plot( df.values[:, 0]
            , df[colname].values
            , linestyle = "-"
            , linewidth = 2
            )
 
labels = ["Equality"]
for colname in list(df.columns[1:]): labels.append(colname)
ax.legend   ( labels
            , fontsize = fontsize
           #, loc = "center left"
           #, bbox_to_anchor = (1, 0.5)
            )
 
ax.set_xlabel(df.columns[1], fontsize = fontsize)
ax.set_ylabel(df.columns[0], fontsize = fontsize)
 
plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
ax.tick_params(axis = "y", which = "minor")
ax.tick_params(axis = "x", which = "minor")
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
 
plt.tight_layout()
plt.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.

Copyright

Computational Data Science Lab

Author:

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

Definition at line 335 of file pm_mathFisher.F90.

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

• src/fortran/main/pm_mathFisher.F90