pm_distEggBox::getEggBoxLogUDF Interface Reference

Generate and return the natural logarithm of the EggBox density function at the specified input point X. More...

Detailed Description

Generate and return the natural logarithm of the EggBox density function at the specified input point X.

See the documentation of pm_distEggBox for details of the EggBox density function.

Parameters

[in]	X	: The input contiguous vector of size (1:ndim) of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the ndim-dimensional point at which the function must be evaluated.
[in]	mu	: The input contiguous vector of the same type, kind, rank, and size as the input X, representing the location parameter ( \(\mu\)) of the density function. (optional, default = 0.. It must be present if and only if the input argument sigma is also present.)
[in]	sigma	: The input contiguous vector of the same type, kind, rank, and size as the input X, representing the scale parameter ( \(\sigma\)) of the density function. (optional, default = 1. It must be present if and only if the input argument mu is also present.)
[in]	alpha	: The input scalar of the same type and kind as the input X, representing the shape parameter ( \(\alpha\)) of the density function. (optional, default = 5.)
[in]	zeta	: The input scalar of the same type and kind as the input X, representing the intercept parameter ( \(\zeta\)) of the density function. (optional, default = 2.)

Returns

logUDF : The output scalar of the same type and kind as the output argument x representing the value of the density function at the specified location.

Possible calling interfaces ⛓

use pm_distEggBox, only: getEggBoxLogUDF
 
logUDF = getEggBoxLogUDF(X(1:ndim), alpha = alpha, zeta = zeta)
logUDF = getEggBoxLogUDF(X(1:ndim), mu(1:ndim), sigma(1:ndim), alpha = alpha, zeta = zeta)

Warning

The condition size(X) == size(mu) must hold for the corresponding input arguments.
The condition size(X) == size(sigma) must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

Remarks

The procedures under discussion are impure.

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK
    use pm_kind, only: RKG => RK ! all real kinds are supported.
    use pm_distEggBox, only: getEggBoxLogUDF
    use pm_arraySpace, only: getLinSpace
    use pm_arraySpace, only: setLinSpace
    use pm_arraySpace, only: setLogSpace
    use pm_io, only: display_type
 
    implicit none
 
    integer(IK), parameter  :: NP = 5_IK
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("getEggBoxLogUDF([0._RKG]) ! 1D eggbox")
    call disp%show( getEggBoxLogUDF([0._RKG]) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getEggBoxLogUDF([0._RKG], [0._RKG], [1._RKG], 5._RKG, 2._RKG) ! 1D eggbox")
    call disp%show( getEggBoxLogUDF([0._RKG], [0._RKG], [1._RKG], 5._RKG, 2._RKG) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getEggBoxLogUDF([real(RKG) :: 0, 1], mu = [-1._RKG, 1._RKG], sigma = [2._RKG, .5_RKG]) ! 2D EggBox")
    call disp%show( getEggBoxLogUDF([real(RKG) :: 0, 1], mu = [-1._RKG, 1._RKG], sigma = [2._RKG, .5_RKG]) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example density array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        use pm_mathSubAdd, only: operator(.subadd.)
        use pm_arrayMembership, only: operator(.inrange.)
        integer(IK) :: fileUnit, i, j
        real(RKG) , parameter :: signif = 2
        real(RKG) :: point(1000), density(4), mu(4), sigma(4)
        mu = [+0._RKG, +0._RKG, +0._RKG, -2._RKG]
        sigma = [+3._RKG, +1._RKG, +.3_RKG, 1._RKG]
        call setLinSpace( point &
                        , x1 = minval(mu) - signif * sigma(minloc(mu, 1)) &
                        , x2 = maxval(mu) + signif * sigma(maxloc(mu, 1)) &
                        )
        open(newunit = fileUnit, file = "getEggBoxLogUDF.D1.RK.txt")
        do i = 1, size(point)
            do j = 1, size(density)
                density(j) = getEggBoxLogUDF(point(i:i), mu(j:j), sigma(j:j))
            end do
            write(fileUnit,"(5(g0,:,','))") point(i), density
        end do
        close(fileUnit)
    end block
 
    block
        use pm_mathSubAdd, only: operator(.subadd.)
        use pm_arrayMembership, only: operator(.inrange.)
        integer(IK) :: fileUnit, i, j
        real(RKG)   , parameter :: signif = 2
        integer(IK) , parameter :: ndim = 2, npnt = 500
        real(RKG) :: grid(ndim, npnt, npnt), mu(ndim), sigma(ndim)
        mu = [+0._RKG, -2._RKG]
        sigma = [+3._RKG, +1._RKG]
        do i = 1, ndim
            grid(i, :, :) = spread  ( getLinSpace( x1 = mu(i) - signif * sigma(i) &
                                                    , x2 = mu(i) + signif * sigma(i) &
                                                    , count = npnt &
                                                    ) , 3 - i, npnt)
        end do
        open(newunit = fileUnit, file = "getEggBoxLogUDF.D2.RK.txt")
        do i = 1, size(grid, 2)
            do j = 1, size(grid, 3)
                write(fileUnit,"(5(g0,:,','))") grid(:, i, j), getEggBoxLogUDF(grid(:, i, j), mu, sigma)
            end do
        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 ⛓

 
getEggBoxLogUDF([0._RKG]) ! 1D eggbox
+243.00000000000000
 
 
getEggBoxLogUDF([0._RKG], [0._RKG], [1._RKG], 5._RKG, 2._RKG) ! 1D eggbox
+243.00000000000000
 
 
getEggBoxLogUDF([real(RKG) :: 0, 1], mu = [-1._RKG, 1._RKG], sigma = [2._RKG, .5_RKG]) ! 2D EggBox
+32.000000000000000
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import math
import glob
import sys
 
linewidth = 2
fontsize = 17
 
marker ={ "CK" : "-"
        , "IK" : "."
        , "RK" : "-"
        }
xlab =  { "CK" : "X ( real/imaginary components )"
        , "IK" : "X ( integer-valued )"
        , "RK" : "X ( 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"]:
 
        # Make 1d plot.
 
    pattern = "*.D1."+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 = 300)
        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("Probability Density Function (PDF)", 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.tight_layout()
            plt.savefig(fileList[0].replace(".txt",".png"))
 
    elif len(fileList) > 1:
 
        sys.exit("Ambiguous file list exists.")
    # Make 2d plot.
 
    pattern = "*.D2."+kind+".txt"
    fileList = glob.glob(pattern)
    if len(fileList) == 1:
 
        df = pd.read_csv(fileList[0], delimiter = ",", header = None)
        df = df.values
 
        npnt = math.isqrt(len(df[:, 0]))
        gridx = np.reshape(df[:, 0], newshape = (npnt, npnt), order = 'F')
        gridy = np.reshape(df[:,1], newshape = (npnt, npnt), order = 'F')
        gridz = np.reshape(df[:,2], newshape = (npnt, npnt), order = 'C')
 
        fig, ax = plt.subplots(subplot_kw = {"projection": "3d"})
        fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 300)
        ax = fig.add_subplot(1, 1, 1, projection = '3d')
        
        ax.plot_surface(gridx, gridy, gridz, cmap = 'viridis', linewidth = 0)
        ax.set_xlabel('X axis')
        ax.set_ylabel('Y axis')
        ax.set_zlabel("Log ( Density )", fontsize = 17)
        
        plt.xticks(fontsize = fontsize - 2)
        plt.yticks(fontsize = fontsize - 2)
        
        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.tight_layout()
        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_distEggBox

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 110 of file pm_distEggBox.F90.

---

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

• src/fortran/main/pm_distEggBox.F90