pm_distBern::isHead Interface Reference

Generate and return a scalar (or a vector of length size or an array of the same shape as the input p) containing the odds of getting a head in a single (or a series) of coin-flipping experiment(s).
More...

Detailed Description

Generate and return a scalar (or a vector of length size or an array of the same shape as the input p) containing the odds of getting a head in a single (or a series) of coin-flipping experiment(s).

The coin can be optionally biased toward getting a head (.true.) with the input user-specified probability p.

Parameters

[in]	p	: The input scalar or array of arbitrary rank of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128) within the range [0, 1], representing the probability of success/yes/true (or getting head in a coin-flip). A value other than p = 0.5 corresponds to a biased coin-flip experiment. If the input argument size is present, then p must be a scalar. If the input argument size is missing, then p can be a scalar or array of arbitrary rank and shape. (optional, default = 0.5)
[in]	size	: The input scalar of type integer of default kind IK, representing the size of the output rand vector. (optional, if present, then p must be a scalar and the output will be a vector.)

Returns

rand : The output scalar or vector of length size, or array of the same shape as the input p of type logical of default kind LK, containing the Bernoulli-distributed random output value.

Possible calling interfaces ⛓

use pm_distBern, only: isHead
 
rand = isHead() ! single fair-coin flipping.
rand = isHead(p) ! elemental coin-flipping with `p` as the odds of success.
rand(1:size) = isHead(p, size) ! non-elemental coin-flipping of `size` times with `p` as the odds of success.
!

Warning

The input value for p must be a number between 0 and 1.
This condition is verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

Keep in mind that the interface isHead() uses a default single-precision value p = .5.
On the current hardware technology, this corresponds to a 32-bit real precision.
This implies a repeat cycle of \(\sim10^6\) for the generated random numbers.
If more random numbers are needed, specify the value p = .5_RKG, where RKG refers to a higher real precision kind capable of generating the desired number of random coin-flipping.

Remarks

The procedures under discussion are impure.

The procedures under this generic interface are elemental when p is present and the size argument is missing.

Note

The procedure isHead() without any input arguments is equivalent to getUnifRand() without any input arguments.

See also

getBernRand
setBernRand
getUnifRand
setUnifRand

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_kind, only: RK, RKS, RKD, RKH
    use pm_io, only: display_type
    use pm_distBern, only: isHead
 
    implicit none
 
    type(display_type) :: disp
 
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Flip a potentially biased coin (as determined by the success rate `p`).")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    call disp%show("isHead() ! flip a fair coin.")
    call disp%show( isHead() )
    call disp%skip()
 
    call disp%show("isHead(size = 5_IK) ! flip a fair coin 5 times.")
    call disp%show( isHead(size = 5_IK) )
    call disp%skip()
 
    call disp%show("isHead(p = 0.5_RKS) ! flip a fair coin with real-32bit precision.")
    call disp%show( isHead(p = 0.5_RKS) )
    call disp%skip()
 
    call disp%show("isHead(p = 0.5_RKD) ! flip a fair coin with real-64bit precision.")
    call disp%show( isHead(p = 0.5_RKD) )
    call disp%skip()
 
    call disp%show("isHead(p = 0.5_RKH) ! flip a fair coin with real-128bit precision.")
    call disp%show( isHead(p = 0.5_RKH) )
    call disp%skip()
 
    call disp%show("isHead(0.25) ! flip an unfair coin with 0.25 odds of success.")
    call disp%show( isHead(0.25) )
    call disp%skip()
 
    call disp%show("isHead(0.25, size = 5_IK) ! flip an unfair coin with 0.25 odds of success 5 times.")
    call disp%show( isHead(0.25, size = 5_IK) )
    call disp%skip()
 
    call disp%show("isHead(p = [0.05, 0.25, 0.75, 0.95]) ! flip four different unfair coins.")
    call disp%show( isHead(p = [0.05, 0.25, 0.75, 0.95]) )
    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 ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Flip a potentially biased coin (as determined by the success rate `p`).
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
isHead() ! flip a fair coin.
F
 
isHead(size = 5_IK) ! flip a fair coin 5 times.
F, F, T, T, T
 
isHead(p = 0.5_RKS) ! flip a fair coin with real-32bit precision.
T
 
isHead(p = 0.5_RKD) ! flip a fair coin with real-64bit precision.
F
 
isHead(p = 0.5_RKH) ! flip a fair coin with real-128bit precision.
F
 
isHead(0.25) ! flip an unfair coin with 0.25 odds of success.
F
 
isHead(0.25, size = 5_IK) ! flip an unfair coin with 0.25 odds of success 5 times.
F, T, F, F, F
 
isHead(p = [0.05, 0.25, 0.75, 0.95]) ! flip four different unfair coins.
F, F, T, T
 
 

Test:

test_pm_distBern

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.
   
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 160 of file pm_distBern.F90.

---

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

• src/fortran/main/pm_distBern.F90