pm_distNorm::getNormFisher Interface Reference

Generate the Fisher Information of the Normal distribution. More...

Detailed Description

Generate the Fisher Information of the Normal distribution.

The Fisher information for the Normal distribution is defined by the following equation,

\begin{equation} \large \mathcal{I}(\mu,\sigma) = \begin{pmatrix} \frac{1}{\sigma^2} & 0 \\ 0 & \frac{2}{\sigma^2} \\ \end{pmatrix} \end{equation}

Parameters

[in]

varInv

: The input non-negative scalar of the same type and kind as the output Fisher representing the inverse of the variance of the Normal distribution.

Returns

Fisher : The output scalar of,

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

containing the Fisher Information matrix of the Normal distribution.

Possible calling interfaces ⛓

use pm_distNorm, only: getNormFisher
 
Fisher(1:2,1:2) = getNormFisher(varInv)

Warning

The condition 0. <= varInv must hold for the correspondddding input arguments.
This condition is 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.

Example usage ⛓

 
program example
 
    use pm_io, only: display_type
    use pm_kind, only: IK, RKS, RKD, RKH
    use pm_distNorm, only: getNormFisher
 
    implicit none
 
    type(display_type) :: disp
    disp = display_type(file = "main.out.F90")
 
    ! Inverse variance.
 
    call disp%skip()
    call disp%show("getNormFisher(varInv = 1. / 3.3)")
    call disp%show( getNormFisher(varInv = 1. / 3.3) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getNormFisher(varInv = 1._RKS / 3.3_RKS)")
    call disp%show( getNormFisher(varInv = 1._RKS / 3.3_RKS) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getNormFisher(varInv = 1._RKD / 3.3_RKD)")
    call disp%show( getNormFisher(varInv = 1._RKD / 3.3_RKD) )
    call disp%skip()
 
    call disp%skip()
    call disp%show("getNormFisher(varInv = 1._RKH / 3.3_RKH)")
    call disp%show( getNormFisher(varInv = 1._RKH / 3.3_RKH) )
    call disp%skip()
 
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 ⛓

 
getNormFisher(varInv = 1. / 3.3)
+0.303030312, +0.00000000
+0.00000000, +0.606060624
 
 
getNormFisher(varInv = 1._RKS / 3.3_RKS)
+0.303030312, +0.00000000
+0.00000000, +0.606060624
 
 
getNormFisher(varInv = 1._RKD / 3.3_RKD)
+0.30303030303030304, +0.0000000000000000
+0.0000000000000000, +0.60606060606060608
 
 
getNormFisher(varInv = 1._RKH / 3.3_RKH)
+0.303030303030303030303030303030303038, +0.00000000000000000000000000000000000
+0.00000000000000000000000000000000000, +0.606060606060606060606060606060606075
 
 

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.

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Copyright

Computational Data Science Lab

Author:

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

Definition at line 3805 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