ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_optimization.F90
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54! <li> [getMinSimplex](@ref pm_optimization::getMinSimplex) and [setMinSimplex](@ref pm_optimization::setMinSimplex) perform unconstrained derivative-free minimization of **multivariate** functions.<br>
55! The **Nelder–Mead method** (also **downhill simplex method**, **amoeba method**, or **polytope method**)
56! is a numerical method used to find the minimum or maximum of an objective function in a **multidimensional** space.<br>
57! It is a direct search method (based on function comparison) and is often applied to **nonlinear optimization problems** for which **derivatives are unknown**.<br>
58! The Nelder–Mead technique is a **heuristic search method** that can converge to **non-stationary points**.<br>
59! The Nelder–Mead technique was proposed by [John Nelder](https://en.wikipedia.org/wiki/John_Nelder) and [Roger Mead](https://en.wikipedia.org/wiki/Roger_Mead) in 1965.<br>
60! According to Numerical Recipes by Press et al. (1992):<br>
61! > The Nelder–Mead method crawls downhill in a straightforward fashion that makes almost no special assumptions about the target function.<br>
62! > This can be extremely slow, but it can also, in some cases, be extremely robust.<br>
63! > The storage requirement for this method is of order \f$\ms{ndim}^2\f$, where \f$\ms{ndim}\f$ is the number of dimensions of the function support.<br>
64! > As such, the Nedler-Mead Simplex method is most useful when the minimization tasks are minimal and isolated.<br>
78
79!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
80
81module pm_optimization
82
83 use pm_kind, only: SK, IK, LK
84
85 implicit none
86
87 character(*, SK), parameter :: MODULE_NAME = "@pm_optimization"
88
89!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
90
151 interface isBracketMax
152
153 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
154
155#if RK5_ENABLED
156 pure elemental module function isBracketMax_RK5(xmax, xlow, xupp, fmax, flow, fupp) result(bracketed)
157#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
158 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMax_RK5
159#endif
160 use pm_kind, only: RKG => RK5
161 real(RKG) , intent(in) :: xmax, xlow, xupp, fmax, flow, fupp
162 logical(LK) :: bracketed
163 end function
164#endif
165
166#if RK4_ENABLED
167 pure elemental module function isBracketMax_RK4(xmax, xlow, xupp, fmax, flow, fupp) result(bracketed)
168#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
169 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMax_RK4
170#endif
171 use pm_kind, only: RKG => RK4
172 real(RKG) , intent(in) :: xmax, xlow, xupp, fmax, flow, fupp
173 logical(LK) :: bracketed
174 end function
175#endif
176
177#if RK3_ENABLED
178 pure elemental module function isBracketMax_RK3(xmax, xlow, xupp, fmax, flow, fupp) result(bracketed)
179#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
180 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMax_RK3
181#endif
182 use pm_kind, only: RKG => RK3
183 real(RKG) , intent(in) :: xmax, xlow, xupp, fmax, flow, fupp
184 logical(LK) :: bracketed
185 end function
186#endif
187
188#if RK2_ENABLED
189 pure elemental module function isBracketMax_RK2(xmax, xlow, xupp, fmax, flow, fupp) result(bracketed)
190#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
191 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMax_RK2
192#endif
193 use pm_kind, only: RKG => RK2
194 real(RKG) , intent(in) :: xmax, xlow, xupp, fmax, flow, fupp
195 logical(LK) :: bracketed
196 end function
197#endif
198
199#if RK1_ENABLED
200 pure elemental module function isBracketMax_RK1(xmax, xlow, xupp, fmax, flow, fupp) result(bracketed)
201#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
202 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMax_RK1
203#endif
204 use pm_kind, only: RKG => RK1
205 real(RKG) , intent(in) :: xmax, xlow, xupp, fmax, flow, fupp
206 logical(LK) :: bracketed
207 end function
208#endif
209
210 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
211
212 end interface
213
214!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
215
276 interface isBracketMin
277
278 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
279
280#if RK5_ENABLED
281 pure elemental module function isBracketMin_RK5(xmin, xlow, xupp, fmin, flow, fupp) result(bracketed)
282#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
283 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMin_RK5
284#endif
285 use pm_kind, only: RKG => RK5
286 real(RKG) , intent(in) :: xmin, xlow, xupp, fmin, flow, fupp
287 logical(LK) :: bracketed
288 end function
289#endif
290
291#if RK4_ENABLED
292 pure elemental module function isBracketMin_RK4(xmin, xlow, xupp, fmin, flow, fupp) result(bracketed)
293#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
294 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMin_RK4
295#endif
296 use pm_kind, only: RKG => RK4
297 real(RKG) , intent(in) :: xmin, xlow, xupp, fmin, flow, fupp
298 logical(LK) :: bracketed
299 end function
300#endif
301
302#if RK3_ENABLED
303 pure elemental module function isBracketMin_RK3(xmin, xlow, xupp, fmin, flow, fupp) result(bracketed)
304#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
305 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMin_RK3
306#endif
307 use pm_kind, only: RKG => RK3
308 real(RKG) , intent(in) :: xmin, xlow, xupp, fmin, flow, fupp
309 logical(LK) :: bracketed
310 end function
311#endif
312
313#if RK2_ENABLED
314 pure elemental module function isBracketMin_RK2(xmin, xlow, xupp, fmin, flow, fupp) result(bracketed)
315#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
316 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMin_RK2
317#endif
318 use pm_kind, only: RKG => RK2
319 real(RKG) , intent(in) :: xmin, xlow, xupp, fmin, flow, fupp
320 logical(LK) :: bracketed
321 end function
322#endif
323
324#if RK1_ENABLED
325 pure elemental module function isBracketMin_RK1(xmin, xlow, xupp, fmin, flow, fupp) result(bracketed)
326#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
327 !DEC$ ATTRIBUTES DLLEXPORT :: isBracketMin_RK1
328#endif
329 use pm_kind, only: RKG => RK1
330 real(RKG) , intent(in) :: xmin, xlow, xupp, fmin, flow, fupp
331 logical(LK) :: bracketed
332 end function
333#endif
334
335 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
336
337 end interface
338
339!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
340
433 interface setBracketMax
434
435 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
436
437#if RK5_ENABLED
438 recursive module subroutine setBracketMax_RK5(getFunc, niter, xmax, xlow, xupp, fmax, flow, fupp)
439#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
440 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMax_RK5
441#endif
442 use pm_kind, only: RKG => RK5
443 procedure(real(RKG)) :: getFunc
444 integer(IK) , intent(inout) :: niter
445 real(RKG) , intent(inout) :: xlow, xupp
446 real(RKG) , intent(out) :: xmax, fmax
447 real(RKG) , intent(out) , optional :: flow, fupp
448 end subroutine
449#endif
450
451#if RK4_ENABLED
452 recursive module subroutine setBracketMax_RK4(getFunc, niter, xmax, xlow, xupp, fmax, flow, fupp)
453#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
454 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMax_RK4
455#endif
456 use pm_kind, only: RKG => RK4
457 procedure(real(RKG)) :: getFunc
458 integer(IK) , intent(inout) :: niter
459 real(RKG) , intent(inout) :: xlow, xupp
460 real(RKG) , intent(out) :: xmax, fmax
461 real(RKG) , intent(out) , optional :: flow, fupp
462 end subroutine
463#endif
464
465#if RK3_ENABLED
466 recursive module subroutine setBracketMax_RK3(getFunc, niter, xmax, xlow, xupp, fmax, flow, fupp)
467#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
468 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMax_RK3
469#endif
470 use pm_kind, only: RKG => RK3
471 procedure(real(RKG)) :: getFunc
472 integer(IK) , intent(inout) :: niter
473 real(RKG) , intent(inout) :: xlow, xupp
474 real(RKG) , intent(out) :: xmax, fmax
475 real(RKG) , intent(out) , optional :: flow, fupp
476 end subroutine
477#endif
478
479#if RK2_ENABLED
480 recursive module subroutine setBracketMax_RK2(getFunc, niter, xmax, xlow, xupp, fmax, flow, fupp)
481#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
482 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMax_RK2
483#endif
484 use pm_kind, only: RKG => RK2
485 procedure(real(RKG)) :: getFunc
486 integer(IK) , intent(inout) :: niter
487 real(RKG) , intent(inout) :: xlow, xupp
488 real(RKG) , intent(out) :: xmax, fmax
489 real(RKG) , intent(out) , optional :: flow, fupp
490 end subroutine
491#endif
492
493#if RK1_ENABLED
494 recursive module subroutine setBracketMax_RK1(getFunc, niter, xmax, xlow, xupp, fmax, flow, fupp)
495#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
496 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMax_RK1
497#endif
498 use pm_kind, only: RKG => RK1
499 procedure(real(RKG)) :: getFunc
500 integer(IK) , intent(inout) :: niter
501 real(RKG) , intent(inout) :: xlow, xupp
502 real(RKG) , intent(out) :: xmax, fmax
503 real(RKG) , intent(out) , optional :: flow, fupp
504 end subroutine
505#endif
506
507 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
508
509 end interface
510
511!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
512
605 interface setBracketMin
606
607 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
608
609#if RK5_ENABLED
610 recursive module subroutine setBracketMin_RK5(getFunc, niter, xmin, xlow, xupp, fmin, flow, fupp)
611#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
612 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMin_RK5
613#endif
614 use pm_kind, only: RKG => RK5
615 procedure(real(RKG)) :: getFunc
616 integer(IK) , intent(inout) :: niter
617 real(RKG) , intent(inout) :: xlow, xupp
618 real(RKG) , intent(out) :: xmin, fmin
619 real(RKG) , intent(out) , optional :: flow, fupp
620 end subroutine
621#endif
622
623#if RK4_ENABLED
624 recursive module subroutine setBracketMin_RK4(getFunc, niter, xmin, xlow, xupp, fmin, flow, fupp)
625#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
626 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMin_RK4
627#endif
628 use pm_kind, only: RKG => RK4
629 procedure(real(RKG)) :: getFunc
630 integer(IK) , intent(inout) :: niter
631 real(RKG) , intent(inout) :: xlow, xupp
632 real(RKG) , intent(out) :: xmin, fmin
633 real(RKG) , intent(out) , optional :: flow, fupp
634 end subroutine
635#endif
636
637#if RK3_ENABLED
638 recursive module subroutine setBracketMin_RK3(getFunc, niter, xmin, xlow, xupp, fmin, flow, fupp)
639#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
640 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMin_RK3
641#endif
642 use pm_kind, only: RKG => RK3
643 procedure(real(RKG)) :: getFunc
644 integer(IK) , intent(inout) :: niter
645 real(RKG) , intent(inout) :: xlow, xupp
646 real(RKG) , intent(out) :: xmin, fmin
647 real(RKG) , intent(out) , optional :: flow, fupp
648 end subroutine
649#endif
650
651#if RK2_ENABLED
652 recursive module subroutine setBracketMin_RK2(getFunc, niter, xmin, xlow, xupp, fmin, flow, fupp)
653#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
654 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMin_RK2
655#endif
656 use pm_kind, only: RKG => RK2
657 procedure(real(RKG)) :: getFunc
658 integer(IK) , intent(inout) :: niter
659 real(RKG) , intent(inout) :: xlow, xupp
660 real(RKG) , intent(out) :: xmin, fmin
661 real(RKG) , intent(out) , optional :: flow, fupp
662 end subroutine
663#endif
664
665#if RK1_ENABLED
666 recursive module subroutine setBracketMin_RK1(getFunc, niter, xmin, xlow, xupp, fmin, flow, fupp)
667#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
668 !DEC$ ATTRIBUTES DLLEXPORT :: setBracketMin_RK1
669#endif
670 use pm_kind, only: RKG => RK1
671 procedure(real(RKG)) :: getFunc
672 integer(IK) , intent(inout) :: niter
673 real(RKG) , intent(inout) :: xlow, xupp
674 real(RKG) , intent(out) :: xmin, fmin
675 real(RKG) , intent(out) , optional :: flow, fupp
676 end subroutine
677#endif
678
679 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
680
681 end interface
682
683!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
684
768 interface getMinBrent
769
770 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
771
772#if RK5_ENABLED
773 recursive module function getMinBrent_RK5(getFunc, xlow, xupp, fmin, tol, niter) result(xmin)
774#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
775 !DEC$ ATTRIBUTES DLLEXPORT :: getMinBrent_RK5
776#endif
777 use pm_kind, only: RKG => RK5
778 procedure(real(RKG)) :: getFunc
779 integer(IK) , intent(inout) , optional :: niter
780 real(RKG) , intent(in) , optional :: xlow, xupp, tol
781 real(RKG) , intent(out) , optional :: fmin
782 real(RKG) :: xmin
783 end function
784#endif
785
786#if RK4_ENABLED
787 recursive module function getMinBrent_RK4(getFunc, xlow, xupp, fmin, tol, niter) result(xmin)
788#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
789 !DEC$ ATTRIBUTES DLLEXPORT :: getMinBrent_RK4
790#endif
791 use pm_kind, only: RKG => RK4
792 procedure(real(RKG)) :: getFunc
793 integer(IK) , intent(inout) , optional :: niter
794 real(RKG) , intent(in) , optional :: xlow, xupp, tol
795 real(RKG) , intent(out) , optional :: fmin
796 real(RKG) :: xmin
797 end function
798#endif
799
800#if RK3_ENABLED
801 recursive module function getMinBrent_RK3(getFunc, xlow, xupp, fmin, tol, niter) result(xmin)
802#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
803 !DEC$ ATTRIBUTES DLLEXPORT :: getMinBrent_RK3
804#endif
805 use pm_kind, only: RKG => RK3
806 procedure(real(RKG)) :: getFunc
807 integer(IK) , intent(inout) , optional :: niter
808 real(RKG) , intent(in) , optional :: xlow, xupp, tol
809 real(RKG) , intent(out) , optional :: fmin
810 real(RKG) :: xmin
811 end function
812#endif
813
814#if RK2_ENABLED
815 recursive module function getMinBrent_RK2(getFunc, xlow, xupp, fmin, tol, niter) result(xmin)
816#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
817 !DEC$ ATTRIBUTES DLLEXPORT :: getMinBrent_RK2
818#endif
819 use pm_kind, only: RKG => RK2
820 procedure(real(RKG)) :: getFunc
821 integer(IK) , intent(inout) , optional :: niter
822 real(RKG) , intent(in) , optional :: xlow, xupp, tol
823 real(RKG) , intent(out) , optional :: fmin
824 real(RKG) :: xmin
825 end function
826#endif
827
828#if RK1_ENABLED
829 recursive module function getMinBrent_RK1(getFunc, xlow, xupp, fmin, tol, niter) result(xmin)
830#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
831 !DEC$ ATTRIBUTES DLLEXPORT :: getMinBrent_RK1
832#endif
833 use pm_kind, only: RKG => RK1
834 procedure(real(RKG)) :: getFunc
835 integer(IK) , intent(inout) , optional :: niter
836 real(RKG) , intent(in) , optional :: xlow, xupp, tol
837 real(RKG) , intent(out) , optional :: fmin
838 real(RKG) :: xmin
839 end function
840#endif
841
842 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
843
844 end interface
845
846!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
847
935 interface setMinBrent
936
937 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
938
939#if RK5_ENABLED
940 recursive module subroutine setMinBrent_RK5(getFunc, xmin, xlow, xupp, fmin, tol, niter)
941#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
942 !DEC$ ATTRIBUTES DLLEXPORT :: setMinBrent_RK5
943#endif
944 use pm_kind, only: RKG => RK5
945 procedure(real(RKG)) :: getFunc
946 real(RKG) , value :: xlow, xupp, tol
947 real(RKG) , intent(inout) :: fmin, xmin
948 integer(IK) , intent(inout) :: niter
949 end subroutine
950#endif
951
952#if RK4_ENABLED
953 recursive module subroutine setMinBrent_RK4(getFunc, xmin, xlow, xupp, fmin, tol, niter)
954#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
955 !DEC$ ATTRIBUTES DLLEXPORT :: setMinBrent_RK4
956#endif
957 use pm_kind, only: RKG => RK4
958 procedure(real(RKG)) :: getFunc
959 real(RKG) , value :: xlow, xupp, tol
960 real(RKG) , intent(inout) :: fmin, xmin
961 integer(IK) , intent(inout) :: niter
962 end subroutine
963#endif
964
965#if RK3_ENABLED
966 recursive module subroutine setMinBrent_RK3(getFunc, xmin, xlow, xupp, fmin, tol, niter)
967#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
968 !DEC$ ATTRIBUTES DLLEXPORT :: setMinBrent_RK3
969#endif
970 use pm_kind, only: RKG => RK3
971 procedure(real(RKG)) :: getFunc
972 real(RKG) , value :: xlow, xupp, tol
973 real(RKG) , intent(inout) :: fmin, xmin
974 integer(IK) , intent(inout) :: niter
975 end subroutine
976#endif
977
978#if RK2_ENABLED
979 recursive module subroutine setMinBrent_RK2(getFunc, xmin, xlow, xupp, fmin, tol, niter)
980#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
981 !DEC$ ATTRIBUTES DLLEXPORT :: setMinBrent_RK2
982#endif
983 use pm_kind, only: RKG => RK2
984 procedure(real(RKG)) :: getFunc
985 real(RKG) , value :: xlow, xupp, tol
986 real(RKG) , intent(inout) :: fmin, xmin
987 integer(IK) , intent(inout) :: niter
988 end subroutine
989#endif
990
991#if RK1_ENABLED
992 recursive module subroutine setMinBrent_RK1(getFunc, xmin, xlow, xupp, fmin, tol, niter)
993#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
994 !DEC$ ATTRIBUTES DLLEXPORT :: setMinBrent_RK1
995#endif
996 use pm_kind, only: RKG => RK1
997 procedure(real(RKG)) :: getFunc
998 real(RKG) , value :: xlow, xupp, tol
999 real(RKG) , intent(inout) :: fmin, xmin
1000 integer(IK) , intent(inout) :: niter
1001 end subroutine
1002#endif
1003
1004 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1005
1006 end interface
1007
1008!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1009
1089 interface isFailedMinPowell
1090
1091 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1092
1093#if RK5_ENABLED
1094 recursive module function isFailedMinPowell_RK5(getFunc, xmin, fmin, tol, niter) result(failed)
1095#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1096 !DEC$ ATTRIBUTES DLLEXPORT :: isFailedMinPowell_RK5
1097#endif
1098 use pm_kind, only: RKG => RK5
1099 procedure(real(RKG)) :: getFunc
1100 real(RKG) , intent(inout) , contiguous :: xmin(:)
1101 real(RKG) , intent(inout) , optional :: fmin
1102 real(RKG) , intent(in) , optional :: tol
1103 integer(IK) , intent(in) , optional :: niter
1104 logical(LK) :: failed
1105 end function
1106#endif
1107
1108#if RK4_ENABLED
1109 recursive module function isFailedMinPowell_RK4(getFunc, xmin, fmin, tol, niter) result(failed)
1110#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1111 !DEC$ ATTRIBUTES DLLEXPORT :: isFailedMinPowell_RK4
1112#endif
1113 use pm_kind, only: RKG => RK4
1114 procedure(real(RKG)) :: getFunc
1115 real(RKG) , intent(inout) , contiguous :: xmin(:)
1116 real(RKG) , intent(inout) , optional :: fmin
1117 real(RKG) , intent(in) , optional :: tol
1118 integer(IK) , intent(in) , optional :: niter
1119 logical(LK) :: failed
1120 end function
1121#endif
1122
1123#if RK3_ENABLED
1124 recursive module function isFailedMinPowell_RK3(getFunc, xmin, fmin, tol, niter) result(failed)
1125#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1126 !DEC$ ATTRIBUTES DLLEXPORT :: isFailedMinPowell_RK3
1127#endif
1128 use pm_kind, only: RKG => RK3
1129 procedure(real(RKG)) :: getFunc
1130 real(RKG) , intent(inout) , contiguous :: xmin(:)
1131 real(RKG) , intent(inout) , optional :: fmin
1132 real(RKG) , intent(in) , optional :: tol
1133 integer(IK) , intent(in) , optional :: niter
1134 logical(LK) :: failed
1135 end function
1136#endif
1137
1138#if RK2_ENABLED
1139 recursive module function isFailedMinPowell_RK2(getFunc, xmin, fmin, tol, niter) result(failed)
1140#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1141 !DEC$ ATTRIBUTES DLLEXPORT :: isFailedMinPowell_RK2
1142#endif
1143 use pm_kind, only: RKG => RK2
1144 procedure(real(RKG)) :: getFunc
1145 real(RKG) , intent(inout) , contiguous :: xmin(:)
1146 real(RKG) , intent(inout) , optional :: fmin
1147 real(RKG) , intent(in) , optional :: tol
1148 integer(IK) , intent(in) , optional :: niter
1149 logical(LK) :: failed
1150 end function
1151#endif
1152
1153#if RK1_ENABLED
1154 recursive module function isFailedMinPowell_RK1(getFunc, xmin, fmin, tol, niter) result(failed)
1155#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1156 !DEC$ ATTRIBUTES DLLEXPORT :: isFailedMinPowell_RK1
1157#endif
1158 use pm_kind, only: RKG => RK1
1159 procedure(real(RKG)) :: getFunc
1160 real(RKG) , intent(inout) , contiguous :: xmin(:)
1161 real(RKG) , intent(inout) , optional :: fmin
1162 real(RKG) , intent(in) , optional :: tol
1163 integer(IK) , intent(in) , optional :: niter
1164 logical(LK) :: failed
1165 end function
1166#endif
1167
1168 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1169
1170 end interface
1171
1172!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1173
1257 interface setMinPowell
1258
1259 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1260
1261#if RK5_ENABLED
1262 recursive module subroutine setMinPowell_RK5(getFunc, xmin, fmin, dirset, tol, niter)
1263#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1264 !DEC$ ATTRIBUTES DLLEXPORT :: setMinPowell_RK5
1265#endif
1266 use pm_kind, only: RKG => RK5
1267 procedure(real(RKG)) :: getFunc
1268 real(RKG) , intent(inout) , contiguous :: xmin(:), dirset(:,:)
1269 real(RKG) , intent(inout) :: fmin
1270 real(RKG) , intent(in) :: tol
1271 integer(IK) , intent(inout) :: niter
1272 end subroutine
1273#endif
1274
1275#if RK4_ENABLED
1276 recursive module subroutine setMinPowell_RK4(getFunc, xmin, fmin, dirset, tol, niter)
1277#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1278 !DEC$ ATTRIBUTES DLLEXPORT :: setMinPowell_RK4
1279#endif
1280 use pm_kind, only: RKG => RK4
1281 procedure(real(RKG)) :: getFunc
1282 real(RKG) , intent(inout) , contiguous :: xmin(:), dirset(:,:)
1283 real(RKG) , intent(inout) :: fmin
1284 real(RKG) , intent(in) :: tol
1285 integer(IK) , intent(inout) :: niter
1286 end subroutine
1287#endif
1288
1289#if RK3_ENABLED
1290 recursive module subroutine setMinPowell_RK3(getFunc, xmin, fmin, dirset, tol, niter)
1291#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1292 !DEC$ ATTRIBUTES DLLEXPORT :: setMinPowell_RK3
1293#endif
1294 use pm_kind, only: RKG => RK3
1295 procedure(real(RKG)) :: getFunc
1296 real(RKG) , intent(inout) , contiguous :: xmin(:), dirset(:,:)
1297 real(RKG) , intent(inout) :: fmin
1298 real(RKG) , intent(in) :: tol
1299 integer(IK) , intent(inout) :: niter
1300 end subroutine
1301#endif
1302
1303#if RK2_ENABLED
1304 recursive module subroutine setMinPowell_RK2(getFunc, xmin, fmin, dirset, tol, niter)
1305#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1306 !DEC$ ATTRIBUTES DLLEXPORT :: setMinPowell_RK2
1307#endif
1308 use pm_kind, only: RKG => RK2
1309 procedure(real(RKG)) :: getFunc
1310 real(RKG) , intent(inout) , contiguous :: xmin(:), dirset(:,:)
1311 real(RKG) , intent(inout) :: fmin
1312 real(RKG) , intent(in) :: tol
1313 integer(IK) , intent(inout) :: niter
1314 end subroutine
1315#endif
1316
1317#if RK1_ENABLED
1318 recursive module subroutine setMinPowell_RK1(getFunc, xmin, fmin, dirset, tol, niter)
1319#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
1320 !DEC$ ATTRIBUTES DLLEXPORT :: setMinPowell_RK1
1321#endif
1322 use pm_kind, only: RKG => RK1
1323 procedure(real(RKG)) :: getFunc
1324 real(RKG) , intent(inout) , contiguous :: xmin(:), dirset(:,:)
1325 real(RKG) , intent(inout) :: fmin
1326 real(RKG) , intent(in) :: tol
1327 integer(IK) , intent(inout) :: niter
1328 end subroutine
1329#endif
1330
1331 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1332
1333 end interface
1334
1335!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1336
1337end module pm_optimization ! LCOV_EXCL_LINE
pm_optimization::getMinBrent
Generate and return the minimum value and the corresponding abscissa xmin of the input 1-dimensional ...
Definition: pm_optimization.F90:768
pm_optimization::isBracketMax
Generate and return .true. if and only if a concave quadratic curve can fit the specified input tripl...
Definition: pm_optimization.F90:151
pm_optimization::isBracketMin
Generate and return .true. if and only if a convex quadratic curve can fit the specified input triple...
Definition: pm_optimization.F90:276
pm_optimization::isFailedMinPowell
Generate and return .true. if and only if the algorithm fails to find the minimum value and the corre...
Definition: pm_optimization.F90:1089
pm_optimization::setBracketMax
Refine an initial input interval such that the final returned interval is guaranteed to contain the m...
Definition: pm_optimization.F90:433
pm_optimization::setBracketMin
Refine an initial input interval such that the final returned interval is guaranteed to contain the m...
Definition: pm_optimization.F90:605
pm_optimization::setMinBrent
Compute and return the minimum value and the corresponding abscissa xmin of the input 1-dimensional f...
Definition: pm_optimization.F90:935
pm_optimization::setMinPowell
Compute and return the minimum value and the corresponding abscissa xmin(1:ndim) of the input arbitra...
Definition: pm_optimization.F90:1257
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_optimization
This module contains procedures, generic interfaces, and types for numerical optimizations of mathema...
Definition: pm_optimization.F90:81
pm_optimization::MODULE_NAME
character(*, SK), parameter MODULE_NAME
Definition: pm_optimization.F90:87