rint 0.1.1

A pure Rust library for the numerical integration of real or complex valued functions of real variables in multiple dimensions.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272

// Test the basic Gauss-Kronrod integration rules with a smooth positive function.
// Ported from gsl-2.6/integration/test.c

use rint::quadrature::Basic;
use rint::quadrature::Rule;
use rint::Limits;

mod util;

basic_test! {
        name: basic_gauss_kronrod_smooth_function_15_point,
        function: util::Function1,
        alpha: f64 => 2.6,
        rule: gk15,
        lower: 0.0,
        upper: 1.0,
        exp_result: 7.716049357767090777E-02,
        exp_error: 2.990224871000550874E-06,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 Basic 15-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_function_21_point,
        function: util::Function1,
        alpha: f64 => 2.6,
        rule: gk21,
        lower: 0.0,
        upper: 1.0,
        exp_result: 7.716049379303084599E-02,
        exp_error: 9.424302194248481445E-08,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 Basic 21-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_function_31_point,
        function: util::Function1,
        alpha: f64 => 2.6,
        rule: gk31,
        lower: 0.0,
        upper: 1.0,
        exp_result: 7.716049382494900855E-02,
        exp_error: 1.713503193600029893E-09,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 Basic 31-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_function_41_point,
        function: util::Function1,
        alpha: f64 => 2.6,
        rule: gk41,
        lower: 0.0,
        upper: 1.0,
        exp_result: 7.716049382681375302E-02,
        exp_error: 9.576386660975511224E-11,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 Basic 41-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_function_51_point,
        function: util::Function1,
        alpha: f64 => 2.6,
        rule: gk51,
        lower: 0.0,
        upper: 1.0,
        exp_result: 7.716049382708510540E-02,
        exp_error: 1.002079980317363772E-11,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-5,
        "Function1 Basic 51-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_function_61_point,
        function: util::Function1,
        alpha: f64 => 2.6,
        rule: gk61,
        lower: 0.0,
        upper: 1.0,
        exp_result: 7.716049382713800753E-02,
        exp_error: 1.566060362296155616E-12,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-5,
        "Function1 Basic 61-point"
}

// Test the basic Gauss-Kronrod integration rules with a smooth oscillating
// function over an unsymmetric range. This should find any discrepancies in
// the abscissae.
//
// Ported from gsl-2.6/integration/test.c

basic_test! {
        name: basic_gauss_kronrod_smooth_oscillating_function_unsymmetric_range_15_point,
        function: util::Function3,
        alpha: f64 => 1.3,
        rule: gk15,
        lower: 0.3,
        upper: 2.71,
        exp_result: -7.238969575483799046E-01,
        exp_error:  8.760080200939757174E-06,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function3 Basic 15-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_oscillating_function_unsymmetric_range_21_point,
        function: util::Function3,
        alpha: f64 => 1.3,
        rule: gk21,
        lower: 0.3,
        upper: 2.71,
        exp_result: -7.238969575482959717E-01,
        exp_error:  7.999213141433641888E-11,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function3 Basic 21-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_oscillating_function_unsymmetric_range_31_point,
        function: util::Function3,
        alpha: f64 => 1.3,
        rule: gk31,
        lower: 0.3,
        upper: 2.71,
        exp_result: -7.238969575482959717E-01,
        exp_error:  1.285805464427459261E-14,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function3 Basic 31-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_oscillating_function_unsymmetric_range_41_point,
        function: util::Function3,
        alpha: f64 => 1.3,
        rule: gk41,
        lower: 0.3,
        upper: 2.71,
        exp_result: -7.238969575482959717E-01,
        exp_error:  1.286535726271015626E-14,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function3 Basic 41-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_oscillating_function_unsymmetric_range_51_point,
        function: util::Function3,
        alpha: f64 => 1.3,
        rule: gk51,
        lower: 0.3,
        upper: 2.71,
        exp_result: -7.238969575482961938E-01,
        exp_error:  1.285290995039385778E-14,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function3 Basic 51-point"
}

basic_test! {
        name: basic_gauss_kronrod_smooth_oscillating_function_unsymmetric_range_61_point,
        function: util::Function3,
        alpha: f64 => 1.3,
        rule: gk61,
        lower: 0.3,
        upper: 2.71,
        exp_result: -7.238969575482959717E-01,
        exp_error:  1.286438572027470736E-14,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function3 Basic 61-point"
}

// Test the basic Gauss-Kronrod integration rules with a positive function that
// has a singularity. This should give large values of the absolute error which
// would find discrepancies in the absolute error calculation.
//
// Ported from gsl-2.6/integration/test.c

basic_test! {
        name: basic_gauss_kronrod_positive_function_with_singularity_15_point,
        function: util::Function1,
        alpha: f64 => -0.9,
        rule: gk15,
        lower: 0.0,
        upper: 1.0,
        exp_result:     1.555688196612745777E+01,
        exp_error:      2.350164577239293706E+01,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 with singularity Basic 15-point"
}

basic_test! {
        name: basic_gauss_kronrod_positive_function_with_singularity_21_point,
        function: util::Function1,
        alpha: f64 => -0.9,
        rule: gk21,
        lower: 0.0,
        upper: 1.0,
        exp_result:     1.799045317938126232E+01,
        exp_error:      2.782360287710622515E+01,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 with singularity Basic 21-point"
}

basic_test! {
        name: basic_gauss_kronrod_positive_function_with_singularity_31_point,
        function: util::Function1,
        alpha: f64 => -0.9,
        rule: gk31,
        lower: 0.0,
        upper: 1.0,
        exp_result:     2.081873305159121657E+01,
        exp_error:      3.296500137482590276E+01,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 with singularity Basic 31-point"
}

basic_test! {
        name: basic_gauss_kronrod_positive_function_with_singularity_41_point,
        function: util::Function1,
        alpha: f64 => -0.9,
        rule: gk41,
        lower: 0.0,
        upper: 1.0,
        exp_result:     2.288677623903126701E+01,
        exp_error:      3.671538820274916048E+01,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 with singularity Basic 41-point"
}

basic_test! {
        name: basic_gauss_kronrod_positive_function_with_singularity_51_point,
        function: util::Function1,
        alpha: f64 => -0.9,
        rule: gk51,
        lower: 0.0,
        upper: 1.0,
        exp_result:     2.449953612016972215E+01,
        exp_error:      3.967771249391228849E+01,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 with singularity Basic 51-point"
}

basic_test! {
        name: basic_gauss_kronrod_positive_function_with_singularity_61_point,
        function: util::Function1,
        alpha: f64 => -0.9,
        rule: gk61,
        lower: 0.0,
        upper: 1.0,
        exp_result:     2.583030240976628988E+01,
        exp_error:      4.213750493076978643E+01,
        abs_tolerance: 1.0e-15,
        rel_tolerance: 1.0e-7,
        "Function1 with singularity Basic 61-point"
}