pm_distBand::setBandUCDF Interface Reference

Generate and return the unnormalized cumulative distribution function (UCDF) of the Band spectral model/distribution.
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Detailed Description

Generate and return the unnormalized cumulative distribution function (UCDF) of the Band spectral model/distribution.

See the documentation of pm_distBand for more information on the Band distribution.
The UCDF of the Band model is the integral of its UDF over a range \((\ms{lb}, \ms{ub})\) written as,

\begin{equation} \large \ms{UCDF}_\ms{BAND} = \int_{\ms{lb}}^{\ms{ub}} f_{\ms{BAND}}(E | \alpha, \beta, \ebreak) dE ~. \end{equation}

where \(f_{\ms{BAND}}\) is the UDF of the Band distribution.

While the integration domain should be ideally \([0, +\infty)\), the arbitrary values of \(\alpha\) and \(\beta\) require finite bounds for the integral to be specified by user to ensure convergence.

Parameters

[out]	ucdf	: The output scalar or array of the same shape as any input array-like argument, of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128) as the input argument ucdf, containing the distribution UCDF.
[in]	lb	: The input positive scalar or array of the same shape as any input array-like argument, of the same type and kind as the input argument ucdf, representing the lower bound of the Band distribution.
[in]	ub	: The input positive scalar or array of the same shape as any input array-like argument, of the same type and kind as the input argument ucdf, representing the upper bound of the Band distribution.
[in]	alpha	: The input scalar or array of the same shape as other array-like arguments of the same type and kind as ucdf, containing the first shape parameter of the distribution.
[in]	beta	: The input scalar or array of the same shape as other array-like arguments of the same type and kind as ucdf, containing the second shape parameter of the distribution.
[in]	ebreak	: The input scalar or array of the same shape as other array-like arguments of the same type and kind as ucdf, containing the normalized spectral break energy values: \(\ebreak = \frac{\ebreak}{100\kev}\).
[out]	info	: The output scalar of type integer of default kind IK. On output, it is set to positive the number of iterations taken for the series representation of the Gamma function to converge. If the algorithm fails to converge, then info is set to the negative of the number of iterations taken by the algorithm or, to the output error returned by brute force integrator getQuadErr. An negative output value signifies the lack of convergence and failure to compute the UCDF. This is likely to happen if the input value for alpha or beta are too extreme.

Possible calling interfaces ⛓

use pm_distBand, only: setBandUCDF
 
call setBandUCDF(ucdf, lb, ub, alpha, beta, ebreak, info)

Warning

The condition 0 < lb must hold for the corresponding input arguments.
The condition 0 < ub must hold for the corresponding input arguments.
The condition alpha /= -2 must hold for the corresponding input arguments.
The condition 0 < ebreak must hold for the corresponding input arguments.
The condition 0 < invEfold must hold for the corresponding input arguments.
The condition beta < alpha must hold for the corresponding input arguments.
The condition ebreak = (alpha - beta) * invEfold must hold for the corresponding input arguments.
The condition zeta = getZeta(alpha, beta, ebreak) 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.

The procedures under discussion are elemental.

Note

The normalization (and the physical units) of the input energy is irrelevant as long as the input values ebreak and zeta are computed in the same physical dimensions and with the same normalizations.

See also

getBandUDF
setBandUCDF
setBandMean
getBandZeta
getBandEpeak
getBandEbreak
setBandPhoton
setBandEnergy

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_kind, only: RKG => RKH ! all processor kinds are supported.
    use pm_io, only: display_type
    use pm_distBand, only: setBandUCDF
 
    implicit none
 
    real(RKG) :: ucdf(4)
    integer(IK) :: info(4)
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("call setBandUCDF(ucdf(1), lb = .01_RKG, ub = 10._RKG, alpha = +2._RKG, beta = -3._RKG, ebreak = 1._RKG, info = info(1))")
                    call setBandUCDF(ucdf(1), lb = .01_RKG, ub = 10._RKG, alpha = +2._RKG, beta = -3._RKG, ebreak = 1._RKG, info = info(1))
    call disp%show("if (info(1) < 0) error stop")
                    if (info(1) < 0) error stop
    call disp%show("ucdf(1)")
    call disp%show( ucdf(1) )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example array for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
 
        use pm_arraySpace, only: setLinSpace
        integer(IK) , parameter :: NP = 1000_IK
        real(RKG) :: ucdf(4), ub(NP)
        integer :: fileUnit, i
 
        call setLinSpace(ub, 0.01_RKG, 10._RKG)
        open(newunit = fileUnit, file = "setBandUCDF.RK.txt")
        do i = 1, NP
            call setBandUCDF(ucdf, 0.01_RKG, ub(i), [.5_RKG, 1.5_RKG, -.5_RKG, -1.1_RKG], -[.5_RKG, 1._RKG, 2._RKG, 3._RKG], [.5_RKG, 1.0_RKG, 2.0_RKG, 5._RKG], info = info)
            if (any(info < 0)) error stop
            write(fileUnit, "(*(g0,:,' '))") ub(i), ucdf
        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 ⛓

 
call setBandUCDF(ucdf(1), lb = .01_RKG, ub = 10._RKG, alpha = +2._RKG, beta = -3._RKG, ebreak = 1._RKG, info = info(1))
if (info(1) < 0) error stop
ucdf(1)
+0.173405303729200175851483190089853506E-1
 
 

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
 
fontsize = 17
 
kind = "RK"
label = [ r"$\alpha, \beta = +0.5, -0.5, x_b = 0.5, \mathrm{lb} = .01$"
        , r"$\alpha, \beta = +1.5, -1.0, x_b = 1.5, \mathrm{lb} = .01$"
        , r"$\alpha, \beta = -0.5, -2.0, x_b = 2.0, \mathrm{lb} = .01$"
        , r"$\alpha, \beta = -1.1, -3.0, x_b = 5.0, \mathrm{lb} = .01$"
        ]
 
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()
 
    for i in range(1,len(df.values[0,:]+1)):
 
        plt.plot( df.values[:, 0]
                , df.values[:,i] / df.values[-1,i]
                , linewidth = 2
                )
 
    plt.xticks(fontsize = fontsize - 2)
    plt.yticks(fontsize = fontsize - 2)
    ax.set_xlabel(r"$\mathrm{ub}$", fontsize = fontsize)
    ax.set_ylabel("Normalized Band UCDF", 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")
 
    ax.legend   ( label
                , fontsize = fontsize
               #, loc = "center left"
               #, bbox_to_anchor = (1, 0.5)
                )
 
    plt.savefig(fileList[0].replace(".txt",".png"))
 
else:
 
    sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_distBand

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.
   
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Copyright

Computational Data Science Lab

Author:

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

Definition at line 815 of file pm_distBand.F90.

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

• src/fortran/main/pm_distBand.F90