ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
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

Fisher(1:2,1:2) = getNormFisher(varInv)
Generate the Fisher Information of the Normal distribution.
This module contains classes and procedures for computing various statistical quantities related to t...
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

1
2program example
3
4 use pm_io, only: display_type
5 use pm_kind, only: IK, RKS, RKD, RKH
7
8 implicit none
9
10 type(display_type) :: disp
11 disp = display_type(file = "main.out.F90")
12
13 ! Inverse variance.
14
15 call disp%skip()
16 call disp%show("getNormFisher(varInv = 1. / 3.3)")
17 call disp%show( getNormFisher(varInv = 1. / 3.3) )
18 call disp%skip()
19
20 call disp%skip()
21 call disp%show("getNormFisher(varInv = 1._RKS / 3.3_RKS)")
22 call disp%show( getNormFisher(varInv = 1._RKS / 3.3_RKS) )
23 call disp%skip()
24
25 call disp%skip()
26 call disp%show("getNormFisher(varInv = 1._RKD / 3.3_RKD)")
27 call disp%show( getNormFisher(varInv = 1._RKD / 3.3_RKD) )
28 call disp%skip()
29
30 call disp%skip()
31 call disp%show("getNormFisher(varInv = 1._RKH / 3.3_RKH)")
32 call disp%show( getNormFisher(varInv = 1._RKH / 3.3_RKH) )
33 call disp%skip()
34
35end program example
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11726
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output
1
2getNormFisher(varInv = 1. / 3.3)
3+0.303030312, +0.00000000
4+0.00000000, +0.606060624
5
6
7getNormFisher(varInv = 1._RKS / 3.3_RKS)
8+0.303030312, +0.00000000
9+0.00000000, +0.606060624
10
11
12getNormFisher(varInv = 1._RKD / 3.3_RKD)
13+0.30303030303030304, +0.0000000000000000
14+0.0000000000000000, +0.60606060606060608
15
16
17getNormFisher(varInv = 1._RKH / 3.3_RKH)
18+0.303030303030303030303030303030303038, +0.00000000000000000000000000000000000
19+0.00000000000000000000000000000000000, +0.606060606060606060606060606060606075
20
21
Test:
test_pm_distNorm


Final Remarks


If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
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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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

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

Definition at line 3805 of file pm_distNorm.F90.


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