pm_distBand::setBandMean Interface Reference

Generate and return the mean of the Band distribution for an input set of parameters.
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Detailed Description

Generate and return the mean of the Band distribution for an input set of parameters.

See the documentation of pm_distBand for more information on the Band distribution.
This generic interface performs one of the following quantities:

1. The mean of the Band distribution.
   The mean of the Band distribution with an unknown normalization (amplitude) over an arbitrary range \((\ms{lb}, \ms{ub})\) is defined by the following integral ratio,
   

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

   where \(\mu_E\) is the mean of the Band distribution.
   The mean of the Band distribution is particularly important for converting the photon fluence of a Band spectrum to the corresponding energy fluence.
   For example, the energy fluence \(\sergs\) of the Band distribution with the same physical unit as \(E\) can be computed from the corresponding the Band photon fluence \(\sphot\) as,

   \begin{equation} \large \sergs = \sphot \mu_E ~, \end{equation}

2. The generalized mean of the Band distribution.
   Optionally, this generic interface also computes the above integral with new support \((\ms{lbnew}, \ms{ubnew})\),

   \begin{equation} \large \mu_E = \frac{ \int_{\ms{lbnew}}^{\ms{ubnew}} E ~ f_{\ms{BAND}}(E | \alpha, \beta, \ebreak) dE }{ \int_{\ms{lb}}^{\ms{ub}} f_{\ms{BAND}}(E | \alpha, \beta, \ebreak) dE } ~, \end{equation}

   where \(\mu_E\) is not anymore the common definition of the distribution mean, but a generalization of the concept.
   This generalized mean facilitates the computation of the energy or photon fluence over a different range from the range of the original photon or energy fluence.
   

Warning

The input arguments lbnew, ubnew, lb, ub, ebreak must all be unit-less (without physical dimensions) or all have the same physical units (typically, \(\kev\)).

Note

The physical units of the input or output units can be changed via the facilities of module pm_physUnit.

Parameters

[out]	mean	: The output positive 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). If the input arguments lbnew and ubnew are missing, then mean will contain the mean of the Band distribution on return. If the input arguments lbnew and ubnew are present, then mean will contain the ratio of the UCDF of the Band distribution in the range \((\ms{lbnew}, \ms{ubnew})\) to the UCDF of the Band distribution in the \((\ms{lb}, \ms{ub})\) as defined above.
[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 output argument mean, 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 output argument mean, 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 mean, 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 mean, 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 mean, 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.
[in]	lbnew	: The input positive scalar or array of the same shape as any input array-like argument, of the same type and kind as the output argument mean, representing the new lower bound of the Band distribution. (optional, default = lb)
[in]	ubnew	: The input positive scalar or array of the same shape as any input array-like argument, of the same type and kind as the output argument mean, representing the new upper bound of the Band distribution. (optional, default = ub)

Possible calling interfaces ⛓

use pm_distBand, only: setBandMean
 
call setBandMean(mean, lb, ub, alpha, beta, ebreak, info)
call setBandMean(mean, lb, ub, alpha, beta, ebreak, info, lbnew, ubnew)

Warning

The condition 0 < lb must hold for the corresponding input arguments.
The condition lb < ub must hold for the corresponding input arguments.
The condition 0 < lbnew must hold for the corresponding input arguments.
The condition lbnew < ubnew must hold for the corresponding input arguments.
The condition 0 < fluence must hold for the corresponding input arguments.
The condition 0 < lbnew must hold for the corresponding input arguments.
The condition 0 < ubnew 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: setBandMean
    use pm_distBand, only: getBandEbreak
    use pm_physUnit, only: ERGS2KEV, KEV2ERGS
 
    implicit none
 
    integer(IK) :: info
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    block
 
        use pm_kind, only: RKG => RKD
        real(RKG) :: mean, fluence, lbnew, ubnew, lb, ub, alpha, beta, ebreak
 
        call disp%skip()
        call disp%show("fluence = 2.044544e-07_RKG; lbnew = 50._RKG; ubnew = 300._RKG; lb = 50._RKG; ub = 300._RKG; alpha = -9.469590e-01_RKG; beta = -3.722981_RKG; ebreak = getBandEbreak(alpha, beta, 1.928073e+02_RKG);")
                        fluence = 2.044544e-07_RKG; lbnew = 50._RKG; ubnew = 300._RKG; lb = 50._RKG; ub = 300._RKG; alpha = -9.469590e-01_RKG; beta = -3.722981_RKG; ebreak = getBandEbreak(alpha, beta, 1.928073e+02_RKG);
        call disp%show("call setBandMean(mean, lb, ub, alpha, beta, ebreak, info)")
                        call setBandMean(mean, lb, ub, alpha, beta, ebreak, info)
        call disp%show("if (info < 0) error stop")
                        if (info < 0) error stop
        call disp%show("real(ERGS2KEV * fluence / mean, RKG) ! photon fluence 1.084876")
        call disp%show( real(ERGS2KEV * fluence / mean, RKG) )
        call disp%skip()
 
    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 ⛓

 
fluence = 2.044544e-07_RKG; lbnew = 50._RKG; ubnew = 300._RKG; lb = 50._RKG; ub = 300._RKG; alpha = -9.469590e-01_RKG; beta = -3.722981_RKG; ebreak = getBandEbreak(alpha, beta, 1.928073e+02_RKG);
call setBandMean(mean, lb, ub, alpha, beta, ebreak, info)
if (info < 0) error stop
real(ERGS2KEV * fluence / mean, RKG) ! photon fluence 1.084876
+1.0860736204671377
 
 

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 1008 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