Return the natural logarithm of the Probability Mass Function (PMF) of the Poisson distribution for an input count
within the discrete integer support of the distribution \([0, +\infty)\).
- Parameters
-
[out] | logPMF | : The output scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as lambda , containing the natural logarithm of the PMF of the distribution at the specified count .
|
[in] | count | : The input scalar (or array of the same rank, shape, and size as other array-like arguments), of
type integer of default kind IK, containing the values at which the PMF must be computed.
|
[in] | lambda | : The input scalar (or array of the same rank, shape, and size as other array-like arguments), of
-
type
real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the location parameter of the distribution.
|
[in] | logLambda | : The input scalar (or array of the same rank, shape, and size as other array-like arguments), of the same type and kind as lambda containing the natural logarithm of the location parameter of the PMF lambda .
Specifying this argument leads to significantly faster computations of the PMF.
(optional, default = log(lambda) .) |
Possible calling interfaces ⛓
Return the natural logarithm of the Probability Mass Function (PMF) of the Poisson distribution for a...
This module contains classes and procedures for computing various statistical quantities related to t...
- Warning
- The condition
0 <= count
must hold for the corresponding input arguments.
The condition 0 < lambda
must hold for the corresponding input arguments.
The condition logLambda = log(lambda)
must hold for the corresponding input arguments.
These conditions are 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.
- See also
- getPoisLogPMF
Example usage ⛓
10 real(RKG) :: logPMF(
3)
11 type(display_type) :: disp
15 call disp%show(
"call setPoisLogPMF(logPMF(1), 0_IK, lambda = 2._RKG)")
22 call disp%show(
"call setPoisLogPMF(logPMF(1), 0_IK, lambda = 2._RKG, logLambda = log(2._RKG))")
23 call setPoisLogPMF(logPMF(
1),
0_IK, lambda
= 2._RKG, logLambda
= log(
2._RKG))
29 call disp%show(
"call setPoisLogPMF(logPMF(1), 1_IK, lambda = 2._RKG)")
36 call disp%show(
"call setPoisLogPMF(logPMF(1), 2_IK, lambda = 2._RKG)")
43 call disp%show(
"call setPoisLogPMF(logPMF(1:3), [integer(IK) :: 0, 1, 2], lambda = 2._RKG)")
44 call setPoisLogPMF(logPMF(
1:
3), [
integer(IK) ::
0,
1,
2], lambda
= 2._RKG)
50 call disp%show(
"call setPoisLogPMF(logPMF(1:3), [integer(IK) :: 0, 1, 2], lambda = [0.1_RKG, 1._RKG, 10._RKG])")
51 call setPoisLogPMF(logPMF(
1:
3), [
integer(IK) ::
0,
1,
2], lambda
= [
0.1_RKG,
1._RKG,
10._RKG])
63 integer(IK),
allocatable ::
count(:)
64 real(RKG) :: logPMF(
4)
65 integer :: fileUnit, i
68 open(newunit
= fileUnit, file
= "setPoisLogPMF.IK.txt")
70 call setPoisLogPMF(logPMF,
count(i), [.
1_RKG,
1._RKG,
4._RKG,
10._RKG])
71 write(fileUnit,
"(*(g0,:,' '))")
count(i),
exp(logPMF)
Generate minimally-spaced character, integer, real sequences or sequences at fixed intervals of size ...
This is a generic method of the derived type display_type with pass attribute.
This is a generic method of the derived type display_type with pass attribute.
This module contains procedures and generic interfaces for generating ranges of discrete character,...
This module contains classes and procedures for input/output (IO) or generic display operations on st...
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
integer, parameter RK
The default real kind in the ParaMonte library: real64 in Fortran, c_double in C-Fortran Interoperati...
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Generate and return an object of type display_type.
Example Unix compile command via Intel ifort
compiler ⛓
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example Windows Batch compile command via Intel ifort
compiler ⛓
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
Example Unix / MinGW compile command via GNU gfortran
compiler ⛓
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
Example output ⛓
7call setPoisLogPMF(logPMF(
1),
0_IK, lambda
= 2._RKG, logLambda
= log(
2._RKG))
22call setPoisLogPMF(logPMF(
1:
3), [
integer(IK) ::
0,
1,
2], lambda
= 2._RKG)
24-2.0000000000000000,
-1.3068528194400546,
-1.3068528194400546
27call setPoisLogPMF(logPMF(
1:
3), [
integer(IK) ::
0,
1,
2], lambda
= [
0.1_RKG,
1._RKG,
10._RKG])
29-0.10000000000000001,
-1.0000000000000000,
-6.0879769945718536
Postprocessing of the example output ⛓
3import matplotlib.pyplot
as plt
12label = [
r"$\lambda = 0.1$"
18pattern =
"*." + kind +
".txt"
19fileList = glob.glob(pattern)
22 df = pd.read_csv(fileList[0], delimiter =
" ", header =
None)
24 fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
27 for i
in range(1,len(df.values[0,:]+1)):
29 plt.plot( df.values[:, 0]
34 plt.xticks(fontsize = fontsize - 2)
35 plt.yticks(fontsize = fontsize - 2)
36 ax.set_xlim([0,
None])
37 ax.set_xlabel(
"Count", fontsize = fontsize)
38 ax.set_ylabel(
"PMF", fontsize = fontsize)
40 plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"-")
41 ax.tick_params(axis =
"y", which =
"minor")
42 ax.tick_params(axis =
"x", which =
"minor")
50 plt.savefig(fileList[0].replace(
".txt",
".png"))
54 sys.exit(
"Ambiguous file list exists.")
Visualization of the example output ⛓
- Test:
- test_pm_distPois
- Todo:
- Normal Priority: This generic interface can be extended to
complex
arguments.
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.
-
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.
-
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 358 of file pm_distPois.F90.