pm_distNorm::setNormQuan Interface Reference

Generate and return the quantile of the univariate Normal distribution at the specified input CDF. More...

Detailed Description

Generate and return the quantile of the univariate Normal distribution at the specified input CDF.

Parameters

[out]	quantile	: The output scalar or array of the same shape as the input array-like arguments, of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the quantile of the distribution at the specified input cdf.
[in]	cdf	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as the output quantile, representing the point(s) (probabilities) at which the quantile must be computed. The cdf must be in the range \([0, 1]\).
[in]	mu	: The input scalar or array of the same shape as other array-like arguments of the same type and kind as the output quantile representing the location parameter of the distribution. (optional, default = 0)
[in]	sigma	: The input scalar of the same type and kind as the output quantile, representing the scale parameter of the distribution. (optional, default = 1.)

Possible calling interfaces ⛓

use pm_distNorm, only: setNormQuan
 
call setNormQuan(quantile, cdf)
call setNormQuan(quantile, cdf, mu)
call setNormQuan(quantile, cdf, mu, sigma)

Warning

The condition 0. < sigma must hold for the corresponding procedure argument.
The condition 0. <= cdf .and. cdf <= 1. must hold for the corresponding procedure 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.

Remarks

The procedures under discussion are elemental.

Note

The procedures of this generic interface are merely wrappers around the procedures of setErfInv.
See the documentation of setErfInv about the accuracy of the computed quantile.

See also

getNormQuan

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_arrayResize, only: setResized
    use pm_distNorm, only: setNormQuan
    use pm_arraySpace, only: getLinSpace
    use pm_io, only: display_type
 
    implicit none
 
    real, allocatable :: cdf(:), quantile(:), mu(:), sigma(:) ! all real kinds are supported.
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
                    cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
    call disp%show("call setResized(quantile, size(cdf, 1, IK))")
                    call setResized(quantile, size(cdf, 1, IK))
    call disp%show("call setNormQuan(quantile, cdf)")
                    call setNormQuan(quantile, cdf)
    call disp%show("quantile")
    call disp%show( quantile )
    call disp%skip()
 
    call disp%skip()
    call disp%show("cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
                    cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
    call disp%show("call setResized(quantile, size(cdf, 1, IK))")
                    call setResized(quantile, size(cdf, 1, IK))
    call disp%show("call setNormQuan(quantile, cdf, mu = 1.)")
                    call setNormQuan(quantile, cdf, mu = 1.)
    call disp%show("quantile")
    call disp%show( quantile )
    call disp%skip()
 
    call disp%skip()
    call disp%show("cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]")
                    cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
    call disp%show("call setResized(quantile, size(cdf, 1, IK))")
                    call setResized(quantile, size(cdf, 1, IK))
    call disp%show("call setNormQuan(quantile, cdf, mu = 1., sigma = 10.)")
                    call setNormQuan(quantile, cdf, mu = 1., sigma = 10.)
    call disp%show("quantile")
    call disp%show( quantile )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example quantile array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        integer(IK) :: fileUnit, i
        open(newunit = fileUnit, file = "setNormQuan.RK.txt")
        cdf = getLinSpace(0., 1., count = 1000_IK, lopen = .true._LK, fopen = .true._LK)
        call setResized(quantile, 4_IK)
        do i = 1, size(cdf)
            call setNormQuan(quantile, cdf(i), [0., 0., 0., -2.], sigma = [3., 1., 0.3, 1.])
            write(fileUnit, "(5(g0,:,','))") cdf(i), quantile
        end do
        close(fileUnit)
    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 ⛓

 
cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
call setResized(quantile, size(cdf, 1, IK))
call setNormQuan(quantile, cdf)
quantile
-0.340282347E+39, -1.64485335, -1.00000107, +0.00000000, +0.408795118, +1.64485335, +0.340282347E+39
 
 
cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
call setResized(quantile, size(cdf, 1, IK))
call setNormQuan(quantile, cdf, mu = 1.)
quantile
-0.340282347E+39, -0.644853354, -0.107288361E-5, +1.00000000, +1.40879512, +2.64485335, +0.340282347E+39
 
 
cdf = [0., 0.05, 0.158655, 0.5, 0.658655, 0.95, 1.]
call setResized(quantile, size(cdf, 1, IK))
call setNormQuan(quantile, cdf, mu = 1., sigma = 10.)
quantile
-0.340282347E+39, -15.4485340, -9.00001049, +1.00000000, +5.08795118, +17.4485340, +0.340282347E+39
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
 
linewidth = 2
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "CDF ( real/imaginary components )"
        , "IK" : "CDF ( integer-valued )"
        , "RK" : "CDF ( real-valued )"
        }
legends =   [ r"$\mu = 0.0,~\sigma = 3.0$"
            , r"$\mu = 0.0,~\sigma = 1.0$"
            , r"$\mu = 0.0,~\sigma = 0.3$"
            , r"$\mu = -2.,~\sigma = 1.0$"
            ]
 
for kind in ["IK", "CK", "RK"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = ",")
 
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
        ax = plt.subplot()
 
        if kind == "CK":
            plt.plot( df.values[:, 0]
                    , df.values[:,1:5]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            plt.plot( df.values[:, 1]
                    , df.values[:,1:5]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "blue"
                    )
        else:
            plt.plot( df.values[:, 0]
                    , df.values[:,1:5]
                    , marker[kind]
                    , linewidth = linewidth
                   #, color = "r"
                    )
            ax.legend   ( legends
                        , fontsize = fontsize
                        )
 
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        ax.set_xlabel(xlab[kind], fontsize = 17)
        ax.set_ylabel("Quantile Function (ICDF)", fontsize = 17)
 
        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.savefig(fileList[0].replace(".txt",".png"))
 
    elif len(fileList) > 1:
 
        sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_distNorm

Final Remarks ⛓

---

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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, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1276 of file pm_distNorm.F90.

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

• src/fortran/main/pm_distNorm.F90