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1 : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2 : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3 : !!!! !!!!
4 : !!!! ParaMonte: Parallel Monte Carlo and Machine Learning Library. !!!!
5 : !!!! !!!!
6 : !!!! Copyright (C) 2012-present, The Computational Data Science Lab !!!!
7 : !!!! !!!!
8 : !!!! This file is part of the ParaMonte library. !!!!
9 : !!!! !!!!
10 : !!!! LICENSE !!!!
11 : !!!! !!!!
12 : !!!! https://github.com/cdslaborg/paramonte/blob/main/LICENSE.md !!!!
13 : !!!! !!!!
14 : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
15 : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
16 :
17 : !> \brief
18 : !> This module contains a collection of example functions
19 : !> for testing or examining the root-finding routines of the ParaMonte library.
20 : !>
21 : !> \see
22 : !> [pm_mathRoot](@ref pm_mathRoot)<br>
23 : !> [pm_mathRoot](@ref pm_mathRoot)<br>
24 : !> [pm_mathRoot](@ref pm_mathRoot)<br>
25 : !>
26 : !> \todo
27 : !> \pvhigh
28 : !> Unfortunately, gfortran 12 and older versions do not properly support the parameterized derived types (PDTs).<br>
29 : !> As such, the example generic-real-kind PDT types could not be used here.<br>
30 : !> This creates significant complexities when using the examples of these modules,<br>
31 : !> because all `real` kinds in this module are set to the highest precision available.<br>
32 : !> The onus is then on the end user to write wrappers that convert the relevant components and function-returns to the desired `real` kinds.<br>
33 : !> In addition to being ugly, error-prone and verbose, this usage of the highest-precision `real` kind is also highly inefficient computationally.<br>
34 : !> Fortunately, once PDTs are supported in gfortran, the conversion of the example types of this module to PDTs is straightforward and non-breaking.<br>
35 : !> The migration to PDTs must be done as soon as gfortran supports for PDTs is complete.<br>
36 : !> Note that other compilers have full support of PDTs.<br>
37 : !>
38 : !> \finmain
39 : !>
40 : !> \author
41 : !> \AmirShahmoradi, Oct 16, 2009, 11:14 AM, Michigan
42 :
43 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
44 :
45 : module pm_mathRootTest
46 :
47 : use pm_val2str, only: getStr
48 : use pm_option, only: getOption
49 : use pm_kind, only: SK, IK, LK, RKH
50 : use pm_str, only: getTTZ => getTrimmedTZ
51 :
52 : implicit none
53 :
54 : character(*, SK), parameter :: MODULE_NAME = "@pm_mathRootTest"
55 :
56 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
57 :
58 : !> \brief
59 : !> This is the base type `func_type` standing `abstract` function type to generate a variety of function test functions.<br>
60 : !>
61 : !> \details
62 : !> The abstract type minimally contains the function limits and deferred type-bound procedure `get()`.<br>
63 : !> It is primarily meant to be used internally within the ParaMonte library for testing and illustration purposes.<br>
64 : !> In particular, the implementations may not be ideal for benchmarks and performance tests of the library integrators.<br>
65 : !> Nevertheless, all relevant types and function test objects are `public` in this repository and available to the end user.<br>
66 : !>
67 : !> \interface{func_type}
68 : !> \code{.F90}
69 : !>
70 : !> use pm_mathRootTest, only: func_type
71 : !>
72 : !> type, extends(func_type) :: Func_type
73 : !> ...
74 : !> end type
75 : !>
76 : !> \endcode
77 : !>
78 : !> \see
79 : !> [getQuadErr](@ref pm_quadPack::getQuadErr)<br>
80 : !>
81 : !> \finmain{func_type}
82 : !>
83 : !> \author
84 : !> \AmirShahmoradi, September 1, 2017, 12:00 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin
85 : type, abstract :: func_type
86 : real(RKH) :: lb !< \public The scalar of type `real` of the highest kind supported by the processor \RKH, containing the lower limit of function.
87 : real(RKH) :: ub !< \public The scalar of type `real` of the highest kind supported by the processor \RKH, containing the upper limit of function.
88 : real(RKH) , allocatable :: root(:) !< \public The scalar of type `real` of the highest kind supported by the processor \RKH, containing the true roots of function.
89 : character(:, SK), allocatable :: desc !< \public The scalar `allocatable` character of default kind \SK containing a description of the function and function limits and difficulties.
90 : contains
91 : procedure(get_proc) , deferred :: get
92 : end type
93 :
94 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
95 :
96 : !> \brief
97 : !> This is the abstract interface of the `get()` type-bound procedure of [func_type](@ref pm_mathRootTest::func_type)
98 : !> class whose arguments of type `real` are of the highest precision kind \RKH, made available by the processor.
99 : !>
100 : !> \see
101 : !> [func_type](@ref pm_mathRootTest::func_type)<br>
102 : !>
103 : !> \finmain{get_proc}
104 : !>
105 : !> \author
106 : !> \AmirShahmoradi, Oct 16, 2009, 11:14 AM, Michigan
107 : abstract interface
108 : PURE function get_proc(self, x) result(func)
109 : use pm_kind, only: RKC => RKH
110 : import :: func_type
111 : class(func_type) , intent(in) :: self
112 : real(RKC) , intent(in) :: x
113 : real(RKC) :: func
114 : end function
115 : end interface
116 :
117 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
118 :
119 : !> \brief
120 : !> This is the derived type for generating test function objects of the algebraic form as described below.
121 : !>
122 : !> \details
123 : !> The full function is defined as,<br>
124 : !> \f{equation}{
125 : !>
126 : !> f(x) = x (x^2 - 1)(x^2 - 4) ~,~ x \in (\ms{lb}, \ms{ub})
127 : !>
128 : !> \f}
129 : !> where the function bounds could be infinities.<br>
130 : !> The real roots of the function are `-2, -1, 0, 1, 2`.<br>
131 : !>
132 : !> \param[in] lb : The input scalar of type `real` of kind \RKH, containing the lower limit of the root search bracket.<br>
133 : !> (**optional**, default = `-3.`)<br>
134 : !> \param[in] ub : The input scalar of the same type and kind as `lb`, containing the upper limit of the root search bracket.<br>
135 : !> (**optional**, default = `+3.`)<br>
136 : !>
137 : !> \interface{func1_type}
138 : !> \code{.F90}
139 : !>
140 : !> use pm_mathRootTest, only: func1_type
141 : !> type(func1_type) :: Func
142 : !>
143 : !> Func = func1_type(lb = lb, ub = ub)
144 : !> print *, "description: ", Func%desc
145 : !> print *, "lower search limit: ", Func%lb
146 : !> print *, "upper search limit: ", Func%ub
147 : !> print *, "Example function value: ", Func%get(x)
148 : !>
149 : !> \endcode
150 : !>
151 : !> \see
152 : !> [func_type](@ref pm_mathRootTest::func_type)<br>
153 : !>
154 : !> \test
155 : !> [test_pm_quadPack](@ref test_pm_quadPack)
156 : !>
157 : !> \finmain{func1_type}
158 : !>
159 : !> \author
160 : !> \AmirShahmoradi, Oct 16, 2009, 11:14 AM, Michigan
161 : type, extends(func_type) :: func1_type
162 : contains
163 : procedure :: get => getFunc1
164 : end type
165 :
166 : !> \cond excluded
167 : interface func1_type
168 : PURE module function constructFunc1(lb, ub) result(self)
169 : #if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
170 : !DEC$ ATTRIBUTES DLLEXPORT :: constructFunc1
171 : #endif
172 : use pm_kind, only: RKC => RKH
173 : real(RKC), intent(in), optional :: lb, ub
174 : type(func1_type) :: self
175 : end function
176 : end interface
177 : !> \endcond excluded
178 :
179 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
180 :
181 : interface
182 : PURE module function getFunc1(self, x) result(func)
183 : #if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
184 : !DEC$ ATTRIBUTES DLLEXPORT :: getFunc1
185 : #endif
186 : use pm_kind, only: RKC => RKH
187 : class(func1_type) , intent(in) :: self
188 : real(RKC) , intent(in) :: x
189 : real(RKC) :: func
190 : end function
191 : end interface
192 :
193 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
194 :
195 0 : end module pm_mathRootTest
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