ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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pm_mathGammaAM.F90
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16
56
57module pm_mathGammaAM
58
59 use pm_kind, only: SK, IK, LK
60
61 implicit none
62
63 character(*, SK), parameter :: MODULE_NAME = "@pm_mathGammaAM"
64
65!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
66
142 interface getGammaIncLowAM
143
144 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
145
146#if RK5_ENABLED
147 impure elemental module function getGammaIncLowAM_RK5(x, kappa) result(gammaIncLow)
148#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
149 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLowAM_RK5
150#endif
151 use pm_kind, only: RKG => RK5
152 real(RKG) , intent(in) :: x, kappa
153 real(RKG) :: gammaIncLow
154 end function
155#endif
156
157#if RK4_ENABLED
158 impure elemental module function getGammaIncLowAM_RK4(x, kappa) result(gammaIncLow)
159#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
160 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLowAM_RK4
161#endif
162 use pm_kind, only: RKG => RK4
163 real(RKG) , intent(in) :: x, kappa
164 real(RKG) :: gammaIncLow
165 end function
166#endif
167
168#if RK3_ENABLED
169 impure elemental module function getGammaIncLowAM_RK3(x, kappa) result(gammaIncLow)
170#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
171 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLowAM_RK3
172#endif
173 use pm_kind, only: RKG => RK3
174 real(RKG) , intent(in) :: x, kappa
175 real(RKG) :: gammaIncLow
176 end function
177#endif
178
179#if RK2_ENABLED
180 impure elemental module function getGammaIncLowAM_RK2(x, kappa) result(gammaIncLow)
181#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
182 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLowAM_RK2
183#endif
184 use pm_kind, only: RKG => RK2
185 real(RKG) , intent(in) :: x, kappa
186 real(RKG) :: gammaIncLow
187 end function
188#endif
189
190#if RK1_ENABLED
191 impure elemental module function getGammaIncLowAM_RK1(x, kappa) result(gammaIncLow)
192#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
193 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLowAM_RK1
194#endif
195 use pm_kind, only: RKG => RK1
196 real(RKG) , intent(in) :: x, kappa
197 real(RKG) :: gammaIncLow
198 end function
199#endif
200
201 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
202
203 end interface
204
205!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
206
279 interface getGammaIncUppAM
280
281 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
282
283#if RK5_ENABLED
284 impure elemental module function getGammaIncUppAM_RK5(x, kappa) result(gammaIncUpp)
285#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
286 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUppAM_RK5
287#endif
288 use pm_kind, only: RKG => RK5
289 real(RKG) , intent(in) :: x, kappa
290 real(RKG) :: gammaIncUpp
291 end function
292#endif
293
294#if RK4_ENABLED
295 impure elemental module function getGammaIncUppAM_RK4(x, kappa) result(gammaIncUpp)
296#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
297 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUppAM_RK4
298#endif
299 use pm_kind, only: RKG => RK4
300 real(RKG) , intent(in) :: x, kappa
301 real(RKG) :: gammaIncUpp
302 end function
303#endif
304
305#if RK3_ENABLED
306 impure elemental module function getGammaIncUppAM_RK3(x, kappa) result(gammaIncUpp)
307#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
308 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUppAM_RK3
309#endif
310 use pm_kind, only: RKG => RK3
311 real(RKG) , intent(in) :: x, kappa
312 real(RKG) :: gammaIncUpp
313 end function
314#endif
315
316#if RK2_ENABLED
317 impure elemental module function getGammaIncUppAM_RK2(x, kappa) result(gammaIncUpp)
318#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
319 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUppAM_RK2
320#endif
321 use pm_kind, only: RKG => RK2
322 real(RKG) , intent(in) :: x, kappa
323 real(RKG) :: gammaIncUpp
324 end function
325#endif
326
327#if RK1_ENABLED
328 impure elemental module function getGammaIncUppAM_RK1(x, kappa) result(gammaIncUpp)
329#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
330 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUppAM_RK1
331#endif
332 use pm_kind, only: RKG => RK1
333 real(RKG) , intent(in) :: x, kappa
334 real(RKG) :: gammaIncUpp
335 end function
336#endif
337
338 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
339
340 end interface
341
342!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
343
416 interface setGammaIncLowAM
417
418 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
419
420#if RK5_ENABLED
421 PURE elemental module subroutine setGammaIncLowAM_RK5(gammaIncLow, x, logGammaKappa, kappa, info)
422#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
423 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncLowAM_RK5
424#endif
425 use pm_kind, only: RKG => RK5
426 real(RKG) , intent(out) :: gammaIncLow
427 real(RKG) , intent(in) :: x, logGammaKappa, kappa
428 integer(IK) , intent(out) :: info
429 end subroutine
430#endif
431
432#if RK4_ENABLED
433 PURE elemental module subroutine setGammaIncLowAM_RK4(gammaIncLow, x, logGammaKappa, kappa, info)
434#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
435 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncLowAM_RK4
436#endif
437 use pm_kind, only: RKG => RK4
438 real(RKG) , intent(out) :: gammaIncLow
439 real(RKG) , intent(in) :: x, logGammaKappa, kappa
440 integer(IK) , intent(out) :: info
441 end subroutine
442#endif
443
444#if RK3_ENABLED
445 PURE elemental module subroutine setGammaIncLowAM_RK3(gammaIncLow, x, logGammaKappa, kappa, info)
446#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
447 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncLowAM_RK3
448#endif
449 use pm_kind, only: RKG => RK3
450 real(RKG) , intent(out) :: gammaIncLow
451 real(RKG) , intent(in) :: x, logGammaKappa, kappa
452 integer(IK) , intent(out) :: info
453 end subroutine
454#endif
455
456#if RK2_ENABLED
457 PURE elemental module subroutine setGammaIncLowAM_RK2(gammaIncLow, x, logGammaKappa, kappa, info)
458#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
459 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncLowAM_RK2
460#endif
461 use pm_kind, only: RKG => RK2
462 real(RKG) , intent(out) :: gammaIncLow
463 real(RKG) , intent(in) :: x, logGammaKappa, kappa
464 integer(IK) , intent(out) :: info
465 end subroutine
466#endif
467
468#if RK1_ENABLED
469 PURE elemental module subroutine setGammaIncLowAM_RK1(gammaIncLow, x, logGammaKappa, kappa, info)
470#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
471 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncLowAM_RK1
472#endif
473 use pm_kind, only: RKG => RK1
474 real(RKG) , intent(out) :: gammaIncLow
475 real(RKG) , intent(in) :: x, logGammaKappa, kappa
476 integer(IK) , intent(out) :: info
477 end subroutine
478#endif
479
480 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
481
482 end interface
483
484!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
485
564 interface setGammaIncUppAM
565
566 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
567
568#if RK5_ENABLED
569 PURE elemental module subroutine setGammaIncUppAM_RK5(gammaIncUpp, x, logGammaKappa, kappa, info)
570#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
571 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncUppAM_RK5
572#endif
573 use pm_kind, only: RKG => RK5
574 real(RKG) , intent(out) :: gammaIncUpp
575 real(RKG) , intent(in) :: x, logGammaKappa, kappa
576 integer(IK) , intent(out) :: info
577 end subroutine
578#endif
579
580#if RK4_ENABLED
581 PURE elemental module subroutine setGammaIncUppAM_RK4(gammaIncUpp, x, logGammaKappa, kappa, info)
582#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
583 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncUppAM_RK4
584#endif
585 use pm_kind, only: RKG => RK4
586 real(RKG) , intent(out) :: gammaIncUpp
587 real(RKG) , intent(in) :: x, logGammaKappa, kappa
588 integer(IK) , intent(out) :: info
589 end subroutine
590#endif
591
592#if RK3_ENABLED
593 PURE elemental module subroutine setGammaIncUppAM_RK3(gammaIncUpp, x, logGammaKappa, kappa, info)
594#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
595 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncUppAM_RK3
596#endif
597 use pm_kind, only: RKG => RK3
598 real(RKG) , intent(out) :: gammaIncUpp
599 real(RKG) , intent(in) :: x, logGammaKappa, kappa
600 integer(IK) , intent(out) :: info
601 end subroutine
602#endif
603
604#if RK2_ENABLED
605 PURE elemental module subroutine setGammaIncUppAM_RK2(gammaIncUpp, x, logGammaKappa, kappa, info)
606#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
607 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncUppAM_RK2
608#endif
609 use pm_kind, only: RKG => RK2
610 real(RKG) , intent(out) :: gammaIncUpp
611 real(RKG) , intent(in) :: x, logGammaKappa, kappa
612 integer(IK) , intent(out) :: info
613 end subroutine
614#endif
615
616#if RK1_ENABLED
617 PURE elemental module subroutine setGammaIncUppAM_RK1(gammaIncUpp, x, logGammaKappa, kappa, info)
618#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
619 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncUppAM_RK1
620#endif
621 use pm_kind, only: RKG => RK1
622 real(RKG) , intent(out) :: gammaIncUpp
623 real(RKG) , intent(in) :: x, logGammaKappa, kappa
624 integer(IK) , intent(out) :: info
625 end subroutine
626#endif
627
628 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
629
630 end interface
631
632!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
633
635 ! This algorithm is taken from Abergel and Moisan, 2020, Algorithm 1006: Fast and Accurate Evaluation of a Generalized Incomplete Gamma Function
636 ! It claims superb performance and accuracy. However, I could not substantiate their claims regarding accuracy, particularly,
637 ! for very large `kappa` and `x` values `(kappa, x) > 1e7`.
638 interface setGammaIncAM
639
640 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
641
642#if RK5_ENABLED
643 PURE elemental module subroutine setGammaIncAMDef_RK5(gammaInc, x, kappa, info)
644#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
645 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMDef_RK5
646#endif
647 use pm_kind, only: RKG => RK5
648 real(RKG) , intent(out) :: gammaInc
649 real(RKG) , intent(in) :: x, kappa
650 integer(IK) , intent(out) :: info
651 end subroutine
652#endif
653
654#if RK4_ENABLED
655 PURE elemental module subroutine setGammaIncAMDef_RK4(gammaInc, x, kappa, info)
656#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
657 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMDef_RK4
658#endif
659 use pm_kind, only: RKG => RK4
660 real(RKG) , intent(out) :: gammaInc
661 real(RKG) , intent(in) :: x, kappa
662 integer(IK) , intent(out) :: info
663 end subroutine
664#endif
665
666#if RK3_ENABLED
667 PURE elemental module subroutine setGammaIncAMDef_RK3(gammaInc, x, kappa, info)
668#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
669 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMDef_RK3
670#endif
671 use pm_kind, only: RKG => RK3
672 real(RKG) , intent(out) :: gammaInc
673 real(RKG) , intent(in) :: x, kappa
674 integer(IK) , intent(out) :: info
675 end subroutine
676#endif
677
678#if RK2_ENABLED
679 PURE elemental module subroutine setGammaIncAMDef_RK2(gammaInc, x, kappa, info)
680#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
681 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMDef_RK2
682#endif
683 use pm_kind, only: RKG => RK2
684 real(RKG) , intent(out) :: gammaInc
685 real(RKG) , intent(in) :: x, kappa
686 integer(IK) , intent(out) :: info
687 end subroutine
688#endif
689
690#if RK1_ENABLED
691 PURE elemental module subroutine setGammaIncAMDef_RK1(gammaInc, x, kappa, info)
692#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
693 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMDef_RK1
694#endif
695 use pm_kind, only: RKG => RK1
696 real(RKG) , intent(out) :: gammaInc
697 real(RKG) , intent(in) :: x, kappa
698 integer(IK) , intent(out) :: info
699 end subroutine
700#endif
701
702 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
703
704#if RK5_ENABLED
705 PURE elemental module subroutine setGammaIncAMNXIK_RK5(gammaInc, x, logGammaKappa, kappa, info)
706#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
707 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMNXIK_RK5
708#endif
709 use pm_kind, only: RKG => RK5
710 real(RKG) , intent(out) :: gammaInc
711 real(RKG) , intent(in) :: x, logGammaKappa
712 integer(IK) , intent(in) :: kappa
713 integer(IK) , intent(out) :: info
714 end subroutine
715#endif
716
717#if RK4_ENABLED
718 PURE elemental module subroutine setGammaIncAMNXIK_RK4(gammaInc, x, logGammaKappa, kappa, info)
719#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
720 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMNXIK_RK4
721#endif
722 use pm_kind, only: RKG => RK4
723 real(RKG) , intent(out) :: gammaInc
724 real(RKG) , intent(in) :: x, logGammaKappa
725 integer(IK) , intent(in) :: kappa
726 integer(IK) , intent(out) :: info
727 end subroutine
728#endif
729
730#if RK3_ENABLED
731 PURE elemental module subroutine setGammaIncAMNXIK_RK3(gammaInc, x, logGammaKappa, kappa, info)
732#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
733 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMNXIK_RK3
734#endif
735 use pm_kind, only: RKG => RK3
736 real(RKG) , intent(out) :: gammaInc
737 real(RKG) , intent(in) :: x, logGammaKappa
738 integer(IK) , intent(in) :: kappa
739 integer(IK) , intent(out) :: info
740 end subroutine
741#endif
742
743#if RK2_ENABLED
744 PURE elemental module subroutine setGammaIncAMNXIK_RK2(gammaInc, x, logGammaKappa, kappa, info)
745#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
746 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMNXIK_RK2
747#endif
748 use pm_kind, only: RKG => RK2
749 real(RKG) , intent(out) :: gammaInc
750 real(RKG) , intent(in) :: x, logGammaKappa
751 integer(IK) , intent(in) :: kappa
752 integer(IK) , intent(out) :: info
753 end subroutine
754#endif
755
756#if RK1_ENABLED
757 PURE elemental module subroutine setGammaIncAMNXIK_RK1(gammaInc, x, logGammaKappa, kappa, info)
758#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
759 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaIncAMNXIK_RK1
760#endif
761 use pm_kind, only: RKG => RK1
762 real(RKG) , intent(out) :: gammaInc
763 real(RKG) , intent(in) :: x, logGammaKappa
764 integer(IK) , intent(in) :: kappa
765 integer(IK) , intent(out) :: info
766 end subroutine
767#endif
768
769 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
770
771 end interface
773
774!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
775
776end module pm_mathGammaAM ! LCOV_EXCL_LINE
pm_mathGammaAM::getGammaIncLowAM
Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter...
Definition: pm_mathGammaAM.F90:142
pm_mathGammaAM::getGammaIncUppAM
Generate and return the regularized Upper Incomplete Gamma function for the specified shape parameter...
Definition: pm_mathGammaAM.F90:279
pm_mathGammaAM::setGammaIncLowAM
Return the regularized Lower Incomplete Gamma function for the specified shape parameter ( ) and uppe...
Definition: pm_mathGammaAM.F90:416
pm_mathGammaAM::setGammaIncUppAM
Return the regularized Upper Incomplete Gamma function for the specified shape parameter ( ) and lowe...
Definition: pm_mathGammaAM.F90:564
pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
pm_kind::RK5
integer, parameter RK5
Definition: pm_kind.F90:478
pm_kind::RK4
integer, parameter RK4
Definition: pm_kind.F90:489
pm_kind::RK2
integer, parameter RK2
Definition: pm_kind.F90:511
pm_kind::RK3
integer, parameter RK3
Definition: pm_kind.F90:500
pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
pm_kind::IK
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
pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
pm_kind::RK1
integer, parameter RK1
Definition: pm_kind.F90:522
pm_mathGammaAM
This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma funct...
Definition: pm_mathGammaAM.F90:57
pm_mathGammaAM::MODULE_NAME
character(*, SK), parameter MODULE_NAME
Definition: pm_mathGammaAM.F90:63