pm_distNorm::getNormRand Interface Reference

Generate and return a scalar or array of arbitrary rank of random values from the univariate Normal distribution with the specified input mean and optionally, with the specified input standard deviation std of the Normal distribution. More...

Detailed Description

Generate and return a scalar or array of arbitrary rank of random values from the univariate Normal distribution with the specified input mean and optionally, with the specified input standard deviation std of the Normal distribution.

The procedures of this generic interface are merely convenient wrappers around the procedures of setNormRand.

Parameters

[in]	mean	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand, representing the mean of the Normal distribution.
[in]	std	: The input scalar or array of the same shape as other array-like arguments, of the same type and kind as rand, representing the standard deviation of the Normal distribution. (optional, default = 1., can be present only if mean is also present.)

Returns

rand : The output scalar or array of arbitrary rank, of

1. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the Normal-distributed random output value.

Possible calling interfaces ⛓

use pm_distNorm, only: getNormRand
 
rand = getNormRand(mean, std = std)
rand = getNormRand(rng, mean, std = std)

Warning

The condition 0. < std must hold for the corresponding input arguments.
All warnings and notes for setNormRand also apply to the procedures of this generic interface.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

Remarks

The procedures under discussion are impure.

The procedures under discussion are elemental.

On input, the procedures of this generic interface minimally require the argument mean to allow compile-time resolution of the procedure calls.

The procedures of this generic interface internally use the intrinsic Fortran RNG for uniform random number generation.

See also

getNormRand
setNormRand
setNormRandBox
getNormLogPDF
getNormCDF

Example usage ⛓

program example
 
    use pm_kind, only: SK
    use pm_kind, only: IK, RK ! all real kinds are supported.
    use pm_distNorm, only: getNormRand
    use pm_arraySpace, only: setLinSpace
    use pm_arraySpace, only: setLogSpace
    use pm_io, only: display_type
 
    implicit none
 
    integer(IK), parameter  :: NP = 1000_IK
    real(RK), dimension(NP) :: mean, std, rand
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call setLinSpace(mean, x1 = -5._RK, x2 = +5._RK)
    call setLogSpace(std, logx1 = log(0.1_RK), logx2 = log(10._RK))
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Generate random numbers from the Normal distribution.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Normal random number with a particular mean and default unity standard deviation.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("mean(1)")
    call disp%show( mean(1) )
    call disp%show("rand(1:3) = getNormRand(mean(1))")
                    rand(1:3) = getNormRand(mean(1))
    call disp%show("rand(1:3)")
    call disp%show( rand(1:3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Normal random number with given mean and standard deviation.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("mean(1)")
    call disp%show( mean(1) )
    call disp%show("std(1)")
    call disp%show( std(1) )
    call disp%show("rand(1:2) = getNormRand(mean(1), std(1))")
                    rand(1:2) = getNormRand(mean(1), std(1))
    call disp%show("rand(1)")
    call disp%show( rand(1) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Normal random numbers with a fixed set of mean and standard deviation.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("mean(1:NP:NP/3)")
    call disp%show( mean(1:NP:NP/3) )
    call disp%show("std(1:NP:NP/3)")
    call disp%show( std(1:NP:NP/3) )
    call disp%show("rand(1:NP:NP/3) = getNormRand(mean(1), std(1))")
                    rand(1:NP:NP/3) = getNormRand(mean(1), std(1))
    call disp%show("rand(1:NP:NP/3)")
    call disp%show( rand(1:NP:NP/3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Normal random number with a range of means and standard deviations.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%skip()
    call disp%show("mean(1:NP:NP/3)")
    call disp%show( mean(1:NP:NP/3) )
    call disp%show("std(1:NP:NP/3)")
    call disp%show( std(1:NP:NP/3) )
    call disp%show("rand(1:NP:NP/3) = getNormRand(mean(1:NP:NP/3), std(1:NP:NP/3))")
                    rand(1:NP:NP/3) = getNormRand(mean(1:NP:NP/3), std(1:NP:NP/3))
    call disp%show("rand(1:NP:NP/3)")
    call disp%show( rand(1:NP:NP/3) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example rand array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        integer(IK) :: fileUnit, i
        integer(IK), parameter :: NP = 5000_IK
        open(newunit = fileUnit, file = "getNormRand.RK.txt")
        write(fileUnit,"(3(g0,:,' '))") ( getNormRand(+2._RK, std = 3.0_RK) &
                                        , getNormRand(+0._RK, std = 1.0_RK) &
                                        , getNormRand(-5._RK) &
                                        , i = 1, NP &
                                        )
        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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Generate random numbers from the Normal distribution.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Normal random number with a particular mean and default unity standard deviation.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
mean(1)
-5.0000000000000000
rand(1:3) = getNormRand(mean(1))
rand(1:3)
-5.3683824624367800, -5.3683824624367800, -5.3683824624367800
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Normal random number with given mean and standard deviation.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
mean(1)
-5.0000000000000000
std(1)
+0.10000000000000003
rand(1:2) = getNormRand(mean(1), std(1))
rand(1)
-4.8176936429469901
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Normal random numbers with a fixed set of mean and standard deviation.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
mean(1:NP:NP/3)
-5.0000000000000000, -1.6666666666666665, +1.6666666666666670, +5.0000000000000000
std(1:NP:NP/3)
+0.10000000000000003, +0.46415888336127803, +2.1544346900318851, +10.000000000000004
rand(1:NP:NP/3) = getNormRand(mean(1), std(1))
rand(1:NP:NP/3)
-4.9825134267578610, -4.9825134267578610, -4.9825134267578610, -4.9825134267578610
 
 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Normal random number with a range of means and standard deviations.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
mean(1:NP:NP/3)
-5.0000000000000000, -1.6666666666666665, +1.6666666666666670, +5.0000000000000000
std(1:NP:NP/3)
+0.10000000000000003, +0.46415888336127803, +2.1544346900318851, +10.000000000000004
rand(1:NP:NP/3) = getNormRand(mean(1:NP:NP/3), std(1:NP:NP/3))
rand(1:NP:NP/3)
-5.0890111408403875, -1.7740432547419096, +1.5570261651935300, -11.862232629955805
 
 

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" : "Normal Random Number ( real/imaginary components )"
        , "IK" : "Normal Random Number ( integer-valued )"
        , "RK" : "Normal Random Number ( real-valued )"
        }
legends =   [ r"$\mu = -5.,~\sigma = 1.0$"
            , r"$\mu = 0.0,~\sigma = 1.0$"
            , r"$\mu = 2.0,~\sigma = 3.0$"
            ]
 
for kind in ["IK", "CK", "RK"]:
 
    pattern = "*." + kind + ".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = " ", header = None)
 
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
        ax = plt.subplot()
 
        if kind == "CK":
            plt.hist( df.values[:,0:3]
                    , histtype = "stepfilled"
                    , alpha = 0.5
                    , bins = 75
                    )
        else:
            plt.hist( df.values[:,0:3]
                    , histtype = "stepfilled"
                    , alpha = 0.5
                    , bins = 75
                    )
            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("Count", fontsize = 17)
        ax.set_title("Histograms of {} Normal random numbers".format(len(df.values[:, 0])), 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 1849 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