ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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pm_mathGamma.F90
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4!!!! ParaMonte: Parallel Monte Carlo and Machine Learning Library. !!!!
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6!!!! Copyright (C) 2012-present, The Computational Data Science Lab !!!!
7!!!! !!!!
8!!!! This file is part of the ParaMonte library. !!!!
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10!!!! LICENSE !!!!
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14!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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16
36
37module pm_mathGamma
38
39 use pm_kind, only: SK, IK, LK
40
41 implicit none
42
43 character(*, SK), parameter :: MODULE_NAME = "@pm_mathGamma"
44
45!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
46
124 interface getGammaIncLow
125
126 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
127
128#if RK5_ENABLED
129 impure elemental module function getGammaIncLow_RK5(x, kappa) result(gammaIncLow)
130#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
131 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLow_RK5
132#endif
133 use pm_kind, only: RKG => RK5
134 real(RKG) , intent(in) :: x, kappa
135 real(RKG) :: gammaIncLow
136 end function
137#endif
138
139#if RK4_ENABLED
140 impure elemental module function getGammaIncLow_RK4(x, kappa) result(gammaIncLow)
141#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
142 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLow_RK4
143#endif
144 use pm_kind, only: RKG => RK4
145 real(RKG) , intent(in) :: x, kappa
146 real(RKG) :: gammaIncLow
147 end function
148#endif
149
150#if RK3_ENABLED
151 impure elemental module function getGammaIncLow_RK3(x, kappa) result(gammaIncLow)
152#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
153 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLow_RK3
154#endif
155 use pm_kind, only: RKG => RK3
156 real(RKG) , intent(in) :: x, kappa
157 real(RKG) :: gammaIncLow
158 end function
159#endif
160
161#if RK2_ENABLED
162 impure elemental module function getGammaIncLow_RK2(x, kappa) result(gammaIncLow)
163#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
164 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLow_RK2
165#endif
166 use pm_kind, only: RKG => RK2
167 real(RKG) , intent(in) :: x, kappa
168 real(RKG) :: gammaIncLow
169 end function
170#endif
171
172#if RK1_ENABLED
173 impure elemental module function getGammaIncLow_RK1(x, kappa) result(gammaIncLow)
174#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
175 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncLow_RK1
176#endif
177 use pm_kind, only: RKG => RK1
178 real(RKG) , intent(in) :: x, kappa
179 real(RKG) :: gammaIncLow
180 end function
181#endif
182
183 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
184
185 end interface
186
187!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
188
264 interface getGammaIncUpp
265
266 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
267
268#if RK5_ENABLED
269 impure elemental module function getGammaIncUpp_RK5(x, kappa) result(gammaIncUpp)
270#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
271 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUpp_RK5
272#endif
273 use pm_kind, only: RKG => RK5
274 real(RKG) , intent(in) :: x, kappa
275 real(RKG) :: gammaIncUpp
276 end function
277#endif
278
279#if RK4_ENABLED
280 impure elemental module function getGammaIncUpp_RK4(x, kappa) result(gammaIncUpp)
281#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
282 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUpp_RK4
283#endif
284 use pm_kind, only: RKG => RK4
285 real(RKG) , intent(in) :: x, kappa
286 real(RKG) :: gammaIncUpp
287 end function
288#endif
289
290#if RK3_ENABLED
291 impure elemental module function getGammaIncUpp_RK3(x, kappa) result(gammaIncUpp)
292#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
293 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUpp_RK3
294#endif
295 use pm_kind, only: RKG => RK3
296 real(RKG) , intent(in) :: x, kappa
297 real(RKG) :: gammaIncUpp
298 end function
299#endif
300
301#if RK2_ENABLED
302 impure elemental module function getGammaIncUpp_RK2(x, kappa) result(gammaIncUpp)
303#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
304 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUpp_RK2
305#endif
306 use pm_kind, only: RKG => RK2
307 real(RKG) , intent(in) :: x, kappa
308 real(RKG) :: gammaIncUpp
309 end function
310#endif
311
312#if RK1_ENABLED
313 impure elemental module function getGammaIncUpp_RK1(x, kappa) result(gammaIncUpp)
314#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
315 !DEC$ ATTRIBUTES DLLEXPORT :: getGammaIncUpp_RK1
316#endif
317 use pm_kind, only: RKG => RK1
318 real(RKG) , intent(in) :: x, kappa
319 real(RKG) :: gammaIncUpp
320 end function
321#endif
322
323 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
324
325 end interface
326
327!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
328
416 interface setGammaInc
417
418 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
419
420#if RK5_ENABLED
421 PURE elemental module subroutine setGammaInc_RK5(gammaIncLow, gammaIncUpp, x, kappa, info)
422#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
423 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaInc_RK5
424#endif
425 use pm_kind, only: RKG => RK5
426 real(RKG) , intent(out) :: gammaIncLow, gammaIncUpp
427 real(RKG) , intent(in) :: x, kappa
428 integer(IK) , intent(out) :: info
429 end subroutine
430#endif
431
432#if RK4_ENABLED
433 PURE elemental module subroutine setGammaInc_RK4(gammaIncLow, gammaIncUpp, x, kappa, info)
434#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
435 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaInc_RK4
436#endif
437 use pm_kind, only: RKG => RK4
438 real(RKG) , intent(out) :: gammaIncLow, gammaIncUpp
439 real(RKG) , intent(in) :: x, kappa
440 integer(IK) , intent(out) :: info
441 end subroutine
442#endif
443
444#if RK3_ENABLED
445 PURE elemental module subroutine setGammaInc_RK3(gammaIncLow, gammaIncUpp, x, kappa, info)
446#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
447 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaInc_RK3
448#endif
449 use pm_kind, only: RKG => RK3
450 real(RKG) , intent(out) :: gammaIncLow, gammaIncUpp
451 real(RKG) , intent(in) :: x, kappa
452 integer(IK) , intent(out) :: info
453 end subroutine
454#endif
455
456#if RK2_ENABLED
457 PURE elemental module subroutine setGammaInc_RK2(gammaIncLow, gammaIncUpp, x, kappa, info)
458#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
459 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaInc_RK2
460#endif
461 use pm_kind, only: RKG => RK2
462 real(RKG) , intent(out) :: gammaIncLow, gammaIncUpp
463 real(RKG) , intent(in) :: x, kappa
464 integer(IK) , intent(out) :: info
465 end subroutine
466#endif
467
468#if RK1_ENABLED
469 PURE elemental module subroutine setGammaInc_RK1(gammaIncLow, gammaIncUpp, x, kappa, info)
470#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
471 !DEC$ ATTRIBUTES DLLEXPORT :: setGammaInc_RK1
472#endif
473 use pm_kind, only: RKG => RK1
474 real(RKG) , intent(out) :: gammaIncLow, gammaIncUpp
475 real(RKG) , intent(in) :: x, kappa
476 integer(IK) , intent(out) :: info
477 end subroutine
478#endif
479
480 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
481
482 end interface
483
484!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
485
486!contains
487
488!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
489
490! !> \brief
491! !> Return the Gamma function for a half-integer input as real of kind \RK.
492! !>
493! !> \param[in] positiveHalfInteger : The input half integer as a real number
494! !>
495! !> \return
496! !> `gammaHalfInt` : The Gamma function for a half integer input.
497! !>
498! !> \remark
499! !> The equation for half-integer Gamma-function is given as,
500! !> \f{equation}{
501! !> \Gamma \left( \frac{n}{2} \right) = \sqrt \pi \frac{ (n-2)!! }{ 2^\frac{n-1}{2} } ~,
502! !> \f}
503! pure function getGamHalfInt(positiveHalfInteger) result(gammaHalfInt)
504!#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
505! !DEC$ ATTRIBUTES DLLEXPORT :: getGamHalfInt
506!#endif
507! use pm_kind, only: IK, RK, SQRT_PI
508! implicit none
509! real(RK), intent(in) :: positiveHalfInteger
510! real(RKG) :: gammaHalfInt
511! integer(IK) :: i,k
512! gammaHalfInt = SQRT_PI
513! k = nint(positiveHalfInteger-0.5_RK,kind=IK) ! positiveHalfInteger = k + 1/2
514! do i = k+1, 2*k
515! gammaHalfInt = gammaHalfInt * 0.25_RK * i
516! end do
517! end function getGamHalfInt
518!
519!!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
520!
521! !> \brief
522! !> Return the natural logarithm of the Gamma function for a half-integer input as real of kind \RK.
523! !>
524! !> \param[in] positiveHalfInteger : The input half integer as a real number
525! !>
526! !> \return
527! !> `gammaHalfInt` : The Gamma function for a half integer input.
528! !>
529! !> \remark
530! !> The equation for half-integer Gamma-function is given as,
531! !> \f{equation}{
532! !> \Gamma \left( \frac{n}{2} \right) = \sqrt \pi \frac{ (n-2)!! }{ 2^\frac{n-1}{2} } ~,
533! !> \f}
534! pure function getLogGammaHalfInt(positiveHalfInteger) result(logGammaHalfInt)
535!#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
536! !DEC$ ATTRIBUTES DLLEXPORT :: getLogGammaHalfInt
537!#endif
538! use pm_kind, only: IK, RK, SQRT_PI
539! implicit none
540! real(RK), intent(in) :: positiveHalfInteger
541! real(RK), parameter :: COEF = log(0.25_RK)
542! real(RK), parameter :: LOG_SQRTPI = log(SQRT_PI)
543! real(RKG) :: logGammaHalfInt
544! integer(IK) :: i, k
545! k = nint(positiveHalfInteger-0.5_RK,kind=IK) ! positiveHalfInteger = k + 1/2
546! logGammaHalfInt = LOG_SQRTPI
547! do i = k+1, 2*k
548! logGammaHalfInt = logGammaHalfInt + COEF + log(real(i,kind=RK))
549! end do
550! end function getLogGammaHalfInt
551
552!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
553
554end module pm_mathGamma ! LCOV_EXCL_LINE
pm_mathGamma::getGammaIncLow
Generate and return the regularized Lower Incomplete Gamma function for the specified shape parameter...
Definition: pm_mathGamma.F90:124
pm_mathGamma::getGammaIncUpp
Generate and return the regularized Upper Incomplete Gamma function for the specified shape parameter...
Definition: pm_mathGamma.F90:264
pm_mathGamma::setGammaInc
Return the regularized Lower Incomplete Gamma function for the specified shape parameter ( ) and uppe...
Definition: pm_mathGamma.F90:416
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_mathGamma
This module contains procedures and generic interfaces for the Lower and Upper Incomplete Gamma funct...
Definition: pm_mathGamma.F90:37
pm_mathGamma::MODULE_NAME
character(*, SK), parameter MODULE_NAME
Definition: pm_mathGamma.F90:43