This module contains the procedures and interfaces for computing the cumulative sum of the exponential of an array without undue numerical overflow.
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This module contains the procedures and interfaces for computing the cumulative sum of the exponential of an array without undue numerical overflow.
- Benchmarks:
Benchmark :: The runtime performance of getCumPropExp vs. setCumPropExp ⛓
4 use iso_fortran_env,
only:
error_unit
12 integer(IK) :: fileUnit
13 integer(IK) ,
parameter :: NARR
= 11_IK
14 integer(IK) :: arraySize(NARR)
15 real(RK) :: dummySum
= 0._RK
17 real(RK) ,
allocatable :: array(:)
18 real(RK) ,
allocatable :: cumPropExp(:)
19 type(bench_type),
allocatable :: bench(:)
21 bench
= [
bench_type(name
= SK_
"setCumPropExp", exec
= setCumPropExp , overhead
= setOverhead)
&
22 ,
bench_type(name
= SK_
"getCumPropExp", exec
= getCumPropExp , overhead
= setOverhead)
&
25 arraySize
= [(
2_IK**iarr, iarr
= 1_IK, NARR )]
27 write(
*,
"(*(g0,:,' '))")
28 write(
*,
"(*(g0,:,' '))")
"getCumPropExp() vs. setCumPropExp()"
29 write(
*,
"(*(g0,:,' '))")
31 open(newunit
= fileUnit, file
= "main.out", status
= "replace")
33 write(fileUnit,
"(*(g0,:,','))")
"arraySize", (bench(i)
%name, i
= 1,
size(bench))
35 loopOverArraySize:
do iarr
= 1, NARR
37 allocate(array(arraySize(iarr)))
38 allocate(cumPropExp(arraySize(iarr)),
source = 0._RK)
39 write(
*,
"(*(g0,:,' '))")
"Benchmarking with array size", arraySize(iarr)
42 bench(i)
%timing
= bench(i)
%getTiming(minsec
= 0.1_RK)
44 write(fileUnit,
"(*(g0,:,','))") arraySize(iarr), (bench(i)
%timing
%mean, i
= 1,
size(bench))
46 deallocate(array, cumPropExp)
48 end do loopOverArraySize
49 write(
*,
"(*(g0,:,' '))") dummySum
50 write(
*,
"(*(g0,:,' '))")
60 subroutine setOverhead()
66 call random_number(array)
67 maxArray
= maxval(array)
71 dummySum
= dummySum
+ cumPropExp(
1)
74 subroutine getCumPropExp()
83 subroutine setCumPropExp()
Generate and return an object of type timing_type containing the benchmark timing information and sta...
Generate and return the cumulative sum of the proportions of the exponential of the input array,...
Return the cumulative sum of the proportions of the exponential of the input array,...
This module contains abstract interfaces and types that facilitate benchmarking of different procedur...
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 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...
This module contains the procedures and interfaces for computing the cumulative sum of the exponentia...
This is the class for creating benchmark and performance-profiling objects.
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
Postprocessing of the benchmark output ⛓
3import matplotlib.pyplot
as plt
8dirname = os.path.basename(os.getcwd())
12df = pd.read_csv(
"main.out", delimiter =
",")
13colnames = list(df.columns.values)
19ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
22for colname
in colnames[1:]:
23 plt.plot( df[colnames[0]].values
28plt.xticks(fontsize = fontsize)
29plt.yticks(fontsize = fontsize)
30ax.set_xlabel(colnames[0], fontsize = fontsize)
31ax.set_ylabel(
"Runtime [ seconds ]", fontsize = fontsize)
32ax.set_title(
" vs. ".join(colnames[1:])+
"\nLower is better.", fontsize = fontsize)
36plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"-")
37ax.tick_params(axis =
"y", which =
"minor")
38ax.tick_params(axis =
"x", which =
"minor")
39ax.legend ( colnames[1:]
46plt.savefig(
"benchmark." + dirname +
".runtime.png")
52ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
55plt.plot( df[colnames[0]].values
56 , np.ones(len(df[colnames[0]].values))
61for colname
in colnames[2:]:
62 plt.plot( df[colnames[0]].values
63 , df[colname].values / df[colnames[1]].values
67plt.xticks(fontsize = fontsize)
68plt.yticks(fontsize = fontsize)
69ax.set_xlabel(colnames[0], fontsize = fontsize)
70ax.set_ylabel(
"Runtime compared to {}".format(colnames[1]), fontsize = fontsize)
71ax.set_title(
"Runtime Ratio Comparison. Lower means faster.\nLower than 1 means faster than {}().".format(colnames[1]), fontsize = fontsize)
75plt.grid(visible =
True, which =
"both", axis =
"both", color =
"0.85", linestyle =
"-")
76ax.tick_params(axis =
"y", which =
"minor")
77ax.tick_params(axis =
"x", which =
"minor")
78ax.legend ( colnames[1:]
85plt.savefig(
"benchmark." + dirname +
".runtime.ratio.png")
Visualization of the benchmark output ⛓
Benchmark moral ⛓
- The procedures under the generic interface getCumPropExp are functions while the procedures under the generic interface setCumPropExp are subroutines.
From the benchmark results, it appears that the functional interface performs significantly worse than the procedural interface.
However, the difference appears to diminish toward larger array sizes.
- Test:
- test_pm_mathCumPropExp
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, April 25, 2015, 2:21 PM, National Institute for Fusion Studies, The University of Texas Austin
pure real(RKG) function, dimension(lenArray) pm_mathCumPropExp::getCumPropExp_RK |
( |
real(RKG), dimension(lenArray), intent(in) |
array, |
|
|
real(RKG) |
maxArray, |
|
|
integer(IK) |
lenArray |
|
) |
| |
[LEGACY code]
Generate and return the normalized cumulative sum (i.e., Cumulative Density Function (CDF)) of the exponentials of the input real vector robustly (without overflow or underflow). The last element of the returned vector is one.
- Parameters
-
[in] | array | : The input contiguous vector of log-values whose log-sum-exp must be computed. |
[in] | maxArray | : The maximum of the input array argument (maxArray = maxval(array) ). |
[in] | lenArray | : The length of the input array. |
- Returns
cumPropExp
: A real vector of the same length as the input array array
.
- Warning
- This routine is only kept for backward compatibility and should not be used in production code. Instead, use the procedures under the generic interface setCumPropExp.
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
- Test:
- test_pm_mathCumPropExp
- Author:
- Amir Shahmoradi, April 25, 2015, 2:21 PM, National Institute for Fusion Studies, The University of Texas Austin
Definition at line 2128 of file pm_mathCumPropExp.F90.
References pm_kind::RK.