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1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2003 RiskMap srl
5 Copyright (C) 2015 Peter Caspers
6
7 This file is part of QuantLib, a free-software/open-source library
8 for financial quantitative analysts and developers - http://quantlib.org/
9
10 QuantLib is free software: you can redistribute it and/or modify it
11 under the terms of the QuantLib license. You should have received a
12 copy of the license along with this program; if not, please email
13 <quantlib-dev@lists.sf.net>. The license is also available online at
14 <http://quantlib.org/license.shtml>.
15
16 This program is distributed in the hope that it will be useful, but WITHOUT
17 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
18 FOR A PARTICULAR PURPOSE. See the license for more details.
19*/
20
21#include "integrals.hpp"
22#include "utilities.hpp"
23#include <ql/math/integrals/exponentialintegrals.hpp>
24#include <ql/math/integrals/filonintegral.hpp>
25#include <ql/math/integrals/segmentintegral.hpp>
26#include <ql/math/integrals/simpsonintegral.hpp>
27#include <ql/math/integrals/trapezoidintegral.hpp>
28#include <ql/math/integrals/kronrodintegral.hpp>
29#include <ql/math/integrals/gausslobattointegral.hpp>
30#include <ql/math/integrals/discreteintegrals.hpp>
31#include <ql/math/integrals/tanhsinhintegral.hpp>
32#include <ql/math/integrals/gaussianquadratures.hpp>
33#include <ql/math/interpolations/bilinearinterpolation.hpp>
34#include <ql/math/distributions/normaldistribution.hpp>
35#include <ql/termstructures/volatility/abcd.hpp>
36#include <ql/math/integrals/twodimensionalintegral.hpp>
37#include <ql/experimental/math/piecewisefunction.hpp>
38#include <ql/experimental/math/piecewiseintegral.hpp>
39
40using namespace QuantLib;
41using boost::unit_test_framework::test_suite;
42
43namespace integrals_test {
44
45 Real tolerance = 1.0e-6;
46
47 template <class T>
48 void testSingle(const T& I, const std::string& tag,
49 const ext::function<Real (Real)>& f,
50 Real xMin, Real xMax, Real expected) {
51 Real calculated = I(f,xMin,xMax);
52 if (std::fabs(x: calculated-expected) > integrals_test::tolerance) {
53 BOOST_FAIL(std::setprecision(10)
54 << "integrating " << tag
55 << " calculated: " << calculated
56 << " expected: " << expected);
57 }
58 }
59
60 template <class T>
61 void testSeveral(const T& I) {
62 testSingle(I, "f(x) = 0", [](Real x) -> Real { return 0.0; }, 0.0, 1.0, 0.0);
63 testSingle(I, "f(x) = 1", [](Real x) -> Real { return 1.0; }, 0.0, 1.0, 1.0);
64 testSingle(I, "f(x) = x", [](Real x) -> Real { return x; }, 0.0, 1.0, 0.5);
65 testSingle(I, "f(x) = x^2",
66 [](Real x) -> Real { return x * x; }, 0.0, 1.0, 1.0/3.0);
67 testSingle(I, "f(x) = sin(x)",
68 [](Real x) -> Real { return std::sin(x: x); }, 0.0, M_PI, 2.0);
69 testSingle(I, "f(x) = cos(x)",
70 [](Real x) -> Real { return std::cos(x: x); }, 0.0, M_PI, 0.0);
71
72 testSingle(I, "f(x) = Gaussian(x)",
73 NormalDistribution(), -10.0, 10.0, 1.0);
74 testSingle(I, "f(x) = Abcd2(x)",
75 AbcdSquared(0.07, 0.07, 0.5, 0.1, 8.0, 10.0), 5.0, 6.0,
76 AbcdFunction(0.07, 0.07, 0.5, 0.1).covariance(t1: 5.0, t2: 6.0, T: 8.0, S: 10.0));
77 }
78
79 template <class T>
80 void testDegeneratedDomain(const T& I) {
81 testSingle(I, "f(x) = 0 over [1, 1 + macheps]", [](Real x) -> Real { return 0.0; }, 1.0,
82 1.0 + QL_EPSILON, 0.0);
83 }
84
85}
86
87
88void IntegralTest::testSegment() {
89 BOOST_TEST_MESSAGE("Testing segment integration...");
90
91 using namespace integrals_test;
92
93 testSeveral(I: SegmentIntegral(10000));
94 testDegeneratedDomain(I: SegmentIntegral(10000));
95}
96
97void IntegralTest::testTrapezoid() {
98 BOOST_TEST_MESSAGE("Testing trapezoid integration...");
99
100 using namespace integrals_test;
101
102 testSeveral(I: TrapezoidIntegral<Default>(integrals_test::tolerance, 10000));
103 testDegeneratedDomain(I: TrapezoidIntegral<Default>(integrals_test::tolerance, 10000));
104}
105
106void IntegralTest::testMidPointTrapezoid() {
107 BOOST_TEST_MESSAGE("Testing mid-point trapezoid integration...");
108
109 using namespace integrals_test;
110
111 testSeveral(I: TrapezoidIntegral<MidPoint>(integrals_test::tolerance, 10000));
112 testDegeneratedDomain(I: TrapezoidIntegral<MidPoint>(integrals_test::tolerance, 10000));
113}
114
115void IntegralTest::testSimpson() {
116 BOOST_TEST_MESSAGE("Testing Simpson integration...");
117
118 using namespace integrals_test;
119
120 testSeveral(I: SimpsonIntegral(integrals_test::tolerance, 10000));
121 testDegeneratedDomain(I: SimpsonIntegral(integrals_test::tolerance, 10000));
122}
123
124void IntegralTest::testGaussKronrodAdaptive() {
125 BOOST_TEST_MESSAGE("Testing adaptive Gauss-Kronrod integration...");
126
127 using namespace integrals_test;
128
129 Size maxEvaluations = 1000;
130 testSeveral(I: GaussKronrodAdaptive(integrals_test::tolerance, maxEvaluations));
131 testDegeneratedDomain(I: GaussKronrodAdaptive(integrals_test::tolerance, maxEvaluations));
132}
133
134void IntegralTest::testGaussLobatto() {
135 BOOST_TEST_MESSAGE("Testing adaptive Gauss-Lobatto integration...");
136
137 using namespace integrals_test;
138
139 Size maxEvaluations = 1000;
140 testSeveral(I: GaussLobattoIntegral(maxEvaluations, integrals_test::tolerance));
141 // on degenerated domain [1,1+macheps] an exception is thrown
142 // which is also ok, but not tested here
143}
144
145void IntegralTest::testTanhSinh() {
146 BOOST_TEST_MESSAGE("Testing tanh-sinh integration...");
147
148 using namespace integrals_test;
149 testSeveral(I: TanhSinhIntegral());
150}
151
152void IntegralTest::testGaussLegendreIntegrator() {
153 BOOST_TEST_MESSAGE("Testing Gauss-Legendre integrator...");
154
155 using namespace integrals_test;
156
157 const GaussLegendreIntegrator integrator(64);
158 testSeveral(I: integrator);
159 testDegeneratedDomain(I: integrator);
160}
161
162void IntegralTest::testGaussChebyshevIntegrator() {
163 BOOST_TEST_MESSAGE("Testing Gauss-Chebyshev integrator...");
164
165 using namespace integrals_test;
166
167 const GaussChebyshevIntegrator integrator(64);
168 testSingle(I: integrator, tag: "f(x) = Gaussian(x)",
169 f: NormalDistribution(), xMin: -10.0, xMax: 10.0, expected: 1.0);
170 testDegeneratedDomain(I: integrator);
171}
172
173void IntegralTest::testGaussChebyshev2ndIntegrator() {
174 BOOST_TEST_MESSAGE("Testing Gauss-Chebyshev 2nd integrator...");
175
176 using namespace integrals_test;
177
178 const GaussChebyshev2ndIntegrator integrator(64);
179 testSingle(I: integrator, tag: "f(x) = Gaussian(x)",
180 f: NormalDistribution(), xMin: -10.0, xMax: 10.0, expected: 1.0);
181 testDegeneratedDomain(I: integrator);
182}
183
184
185
186void IntegralTest::testGaussKronrodNonAdaptive() {
187 BOOST_TEST_MESSAGE("Testing non-adaptive Gauss-Kronrod integration...");
188
189 using namespace integrals_test;
190
191 Real precision = integrals_test::tolerance;
192 Size maxEvaluations = 100;
193 Real relativeAccuracy = integrals_test::tolerance;
194 GaussKronrodNonAdaptive gaussKronrodNonAdaptive(precision, maxEvaluations,
195 relativeAccuracy);
196 testSeveral(I: gaussKronrodNonAdaptive);
197 testDegeneratedDomain(I: gaussKronrodNonAdaptive);
198}
199
200void IntegralTest::testTwoDimensionalIntegration() {
201 BOOST_TEST_MESSAGE("Testing two dimensional adaptive "
202 "Gauss-Lobatto integration...");
203
204 using namespace integrals_test;
205
206 const Size maxEvaluations = 1000;
207 const Real calculated = TwoDimensionalIntegral(
208 ext::shared_ptr<Integrator>(
209 new TrapezoidIntegral<Default>(integrals_test::tolerance, maxEvaluations)),
210 ext::shared_ptr<Integrator>(
211 new TrapezoidIntegral<Default>(integrals_test::tolerance, maxEvaluations)))(
212 std::multiplies<>(),
213 std::make_pair(x: 0.0, y: 0.0), std::make_pair(x: 1.0, y: 2.0));
214
215 const Real expected = 1.0;
216 if (std::fabs(x: calculated-expected) > integrals_test::tolerance) {
217 BOOST_FAIL(std::setprecision(10)
218 << "two dimensional integration: "
219 << "\n calculated: " << calculated
220 << "\n expected: " << expected);
221 }
222}
223
224namespace integrals_test {
225
226 class sineF {
227 public:
228 Real operator()(Real x) const {
229 return std::exp(x: -0.5*(x - M_PI_2/100));
230 }
231 };
232
233 class cosineF {
234 public:
235 Real operator()(Real x) const {
236 return std::exp(x: -0.5*x);
237 }
238 };
239
240}
241
242void IntegralTest::testFolinIntegration() {
243 BOOST_TEST_MESSAGE("Testing Folin's integral formulae...");
244
245 using namespace integrals_test;
246
247 // Examples taken from
248 // http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/Num_Methods_files/Comp_Phys5.pdf
249 const Size nr[] = { 4, 8, 16, 128, 256, 1024, 2048 };
250 const Real expected[] = { 4.55229440e-5,4.72338540e-5, 4.72338540e-5,
251 4.78308678e-5,4.78404787e-5, 4.78381120e-5,
252 4.78381084e-5};
253
254 const Real t = 100;
255 const Real o = M_PI_2/t;
256
257 const Real tol = 1e-12;
258
259 for (Size i=0; i < LENGTH(nr); ++i) {
260 const Size n = nr[i];
261 const Real calculatedCosine
262 = FilonIntegral(FilonIntegral::Cosine, t, n)(cosineF(),0,2*M_PI);
263 const Real calculatedSine
264 = FilonIntegral(FilonIntegral::Sine, t, n)
265 (sineF(), o,2*M_PI + o);
266
267 if (std::fabs(x: calculatedCosine-expected[i]) > tol) {
268 BOOST_FAIL(std::setprecision(10)
269 << "Filon Cosine integration failed: "
270 << "\n calculated: " << calculatedCosine
271 << "\n expected: " << expected[i]);
272 }
273 if (std::fabs(x: calculatedSine-expected[i]) > tol) {
274 BOOST_FAIL(std::setprecision(10)
275 << "Filon Sine integration failed: "
276 << "\n calculated: " << calculatedCosine
277 << "\n expected: " << expected[i]);
278 }
279 }
280}
281
282namespace integrals_test {
283
284 Real f1(Real x) {
285 return 1.2*x*x+3.2*x+3.1;
286 }
287
288 Real f2(Real x) {
289 return 4.3*(x-2.34)*(x-2.34)-6.2*(x-2.34) + f1(x: 2.34);
290 }
291
292}
293
294void IntegralTest::testDiscreteIntegrals() {
295 BOOST_TEST_MESSAGE("Testing discrete integral formulae...");
296
297 using namespace integrals_test;
298
299 Array x(6), f(6);
300 x[0] = 1.0; x[1] = 2.02; x[2] = 2.34; x[3] = 3.3; x[4] = 4.2; x[5] = 4.6;
301
302 std::transform(first: x.begin(), last: x.begin()+3, result: f.begin(), unary_op: f1);
303 std::transform(first: x.begin()+3, last: x.end(), result: f.begin()+3, unary_op: f2);
304
305 const Real expectedSimpson =
306 16.0401216 + 30.4137528 + 0.2*f2(x: 4.2) + 0.2*f2(x: 4.6);
307 const Real expectedTrapezoid =
308 0.5*(f1(x: 1.0) + f1(x: 2.02))*1.02
309 + 0.5*(f1(x: 2.02) + f1(x: 2.34))*0.32
310 + 0.5*(f2(x: 2.34) + f2(x: 3.3) )*0.96
311 + 0.5*(f2(x: 3.3) + f2(x: 4.2) )*0.9
312 + 0.5*(f2(x: 4.2) + f2(x: 4.6) )*0.4;
313
314 const Real calculatedSimpson = DiscreteSimpsonIntegral()(x, f);
315 const Real calculatedTrapezoid = DiscreteTrapezoidIntegral()(x, f);
316
317 const Real tol = 1e-12;
318 if (std::fabs(x: calculatedSimpson-expectedSimpson) > tol) {
319 BOOST_FAIL(std::setprecision(16)
320 << "discrete Simpson integration failed: "
321 << "\n calculated: " << calculatedSimpson
322 << "\n expected: " << expectedSimpson);
323 }
324
325 if (std::fabs(x: calculatedTrapezoid-expectedTrapezoid) > tol) {
326 BOOST_FAIL(std::setprecision(16)
327 << "discrete Trapezoid integration failed: "
328 << "\n calculated: " << calculatedTrapezoid
329 << "\n expected: " << expectedTrapezoid);
330 }
331}
332
333void IntegralTest::testDiscreteIntegrator() {
334 BOOST_TEST_MESSAGE("Testing discrete integrator formulae...");
335
336 using namespace integrals_test;
337
338 testSeveral(I: DiscreteSimpsonIntegrator(300));
339 testSeveral(I: DiscreteTrapezoidIntegrator(3000));
340}
341
342namespace integrals_test{
343
344std::vector<Real> x, y;
345
346Real pw_fct(const Real t) { return QL_PIECEWISE_FUNCTION(x, y, t); }
347
348void pw_check(const Integrator &in, const Real a, const Real b,
349 const Real expected) {
350 Real calculated = in(pw_fct, a, b);
351 if (!close(x: calculated, y: expected))
352 BOOST_FAIL(std::setprecision(16)
353 << "piecewise integration over [" << a << "," << b
354 << "] failed: "
355 << "\n calculated: " << calculated
356 << "\n expected: " << expected
357 << "\n difference: " << (calculated - expected));
358}
359} // empty namespace
360
361void IntegralTest::testPiecewiseIntegral() {
362 BOOST_TEST_MESSAGE("Testing piecewise integral...");
363
364 using namespace integrals_test;
365
366 x = { 1.0, 2.0, 3.0, 4.0, 5.0 };
367 y = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
368 ext::shared_ptr<Integrator> segment =
369 ext::make_shared<SegmentIntegral>(args: 1);
370 ext::shared_ptr<Integrator> piecewise =
371 ext::make_shared<PiecewiseIntegral>(args&: segment, args&: x);
372 pw_check(in: *piecewise, a: -1.0, b: 0.0, expected: 1.0);
373 pw_check(in: *piecewise, a: 0.0, b: 1.0, expected: 1.0);
374 pw_check(in: *piecewise, a: 0.0, b: 1.5, expected: 2.0);
375 pw_check(in: *piecewise, a: 0.0, b: 2.0, expected: 3.0);
376 pw_check(in: *piecewise, a: 0.0, b: 2.5, expected: 4.5);
377 pw_check(in: *piecewise, a: 0.0, b: 3.0, expected: 6.0);
378 pw_check(in: *piecewise, a: 0.0, b: 4.0, expected: 10.0);
379 pw_check(in: *piecewise, a: 0.0, b: 5.0, expected: 15.0);
380 pw_check(in: *piecewise, a: 0.0, b: 6.0, expected: 21.0);
381 pw_check(in: *piecewise, a: 0.0, b: 7.0, expected: 27.0);
382 pw_check(in: *piecewise, a: 3.5, b: 4.5, expected: 4.5);
383 pw_check(in: *piecewise, a: 5.0, b: 10.0, expected: 30.0);
384 pw_check(in: *piecewise, a: 9.0, b: 10.0, expected: 6.0);
385}
386
387namespace integrals_test {
388 template <class T>
389 void reportSiCiFail(
390 const std::string& name, T z, T c, T e, Real diff, Real tol) {
391 BOOST_FAIL(std::setprecision(16)
392 << name << " calculation failed for " << z
393 << "\n calculated: " << c
394 << "\n expected: " << e
395 << "\n difference: " << diff
396 << "\n tolerance: " << tol);
397 }
398}
399
400void IntegralTest::testExponentialIntegral() {
401 BOOST_TEST_MESSAGE("Testing exponential integrals...");
402
403 using namespace ExponentialIntegral;
404
405 // reference values are calculated with Mathematica or Python/mpmath
406 const Real data[][10] = {
407 {0.0010000000000000000208, 0.0, 0.00099999994444444613193, 0.0, -6.330539864080593754, 0.0, -6.3295393640250381967, 0.0, 6.3315393641361493112, 0.0},
408 {0.00070710678118654756077, 0.00070710678118654751747, 0.00070710682047025644818, 0.00070710674190283627304, -6.3305396140806145873, 0.785397913397448279, -6.329832507338711751, 0.7861055202179185354, 6.3312467208225174236, -0.78469130657697802259},
409 {6.1232339957367660136e-20, 0.0010000000000000000208, 6.1232350162201617204e-20, 0.001000000055555557243, -6.330539364080593754, 1.570796326794896558, -6.3305398640805937539, 1.5717963267393410041, 6.330539864080593754, -1.5697963268504521119},
410 {-0.00070710678118654747417, 0.00070710678118654760407, -0.00070710682047025636158, 0.00070710674190283635964, -6.3305396140806145873, 2.356194740192344837, -6.3312467208225174235, 2.3569013470128150935, 6.3298325073387117511, -2.3554871333718745805},
411 {-0.0010000000000000000208, 1.2246467991473532027e-19, -0.00099999994444444613193, 1.2246465950321797194e-19, -6.330539864080593754, 3.141592653589793116, -6.3315393641361493112, 3.1415926535897931161, 6.3295393640250381967, -3.1415926535897931159},
412 {-0.00070710678118654764736, -0.00070710678118654743088, -0.00070710682047025653477, -0.00070710674190283618645, -6.3305396140806145873, -2.3561947401923450819, -6.3312467208225174237, -2.3569013470128153382, 6.3298325073387117509, 2.3554871333718748256},
413 {-1.8369701987210298041e-19, -0.0010000000000000000208, -1.8369705049015472569e-19, -0.001000000055555557243, -6.330539364080593754, -1.5707963267948968029, -6.3305398640805937541, -1.5717963267393412491, 6.3305398640805937538, 1.5697963268504523568},
414 {0.00070710678118654738758, -0.00070710678118654769066, 0.00070710682047025627499, -0.00070710674190283644623, -6.3305396140806145873, -0.78539791339744852393, -6.3298325073387117512, -0.78610552021791878051, 6.3312467208225174234, 0.78469130657697826735},
415 {0.10000000000000000555, 0.0, 0.099944461108276955702, 0.0, -1.7278683866572965838, 0.0, -1.6228128139692766136, 0.0, 1.8229239584193906159, 0.0},
416 {0.07071067811865475853, 0.0707106781186547542, 0.070749950041603603669, 0.070671382625480302524, -1.7253704697591484327, 0.78289816362892975745, -1.6546990871336681256, 0.8586481132075703999, 1.7960418523846287393, -0.7171482131243632012},
417 {6.123233995736766226e-18, 0.10000000000000000555, 6.1334444895968712791e-18, 0.10005557222505700112, -1.7228683861943336147, 1.5707963267948965577, -1.7278683866572965777, 1.670740787903173514, 1.7278683866572965899, -1.4708518656866196026},
418 {-0.070710678118654749871, 0.07071067811865476286, -0.070749950041603595024, 0.070671382625480311198, -1.7253704697591484321, 2.3586944899608633586, -1.7960418523846287312, 2.4244444404654299234, 1.6546990871336681349, -2.2829445403822227075},
419 {-0.10000000000000000555, 1.2246467991473532452e-17, -0.099944461108276955702, 1.2226067414369268591e-17, -1.7278683866572965838, 3.1415926535897931166, -1.8229239584193906159, 3.1415926535897931277, 1.6228128139692766136, -3.1415926535897931031},
420 {-0.07071067811865476719, -0.070710678118654745541, -0.070749950041603612314, -0.07067138262548029385, -1.7253704697591484333, -2.3586944899608636035, -1.7960418523846287474, -2.4244444404654301511, 1.6546990871336681163, 2.2829445403822229697},
421 {-1.8369701987210298678e-17, -0.10000000000000000555, -1.8400333469093536425e-17, -0.10005557222505700112, -1.7228683861943336147, -1.5707963267948968038, -1.7278683866572966021, -1.6707407879031737577, 1.7278683866572965654, 1.4708518656866198463},
422 {0.070710678118654741211, -0.07071067811865477152, 0.070749950041603586379, -0.070671382625480319872, -1.7253704697591484315, -0.78289816362893000238, -1.6546990871336681441, -0.85864811320757066212, 1.7960418523846287232, 0.71714821312436342884},
423 {0.25, 0.0, 0.2491335703197571641, 0.0, -0.82466306258094565309, 0.0, -0.54254326466191372953, 0.0, 1.0442826344437381945, 0.0},
424 {0.17677669529663688651, 0.17677669529663687569, 0.17738935115398995617, 0.17616173766104897661, -0.80911938627521916259, 0.76977321991145556311, -0.63295764861417017313, 0.97841245803743094036, 0.98528112393626814822, -0.62363375572945104943},
425 {1.5308084989341914715e-17, 0.25, 1.5468043259937507815e-17, 0.2508696848909122325, -0.79341294955282596203, 1.5707963267948965561, -0.82466306258094563794, 1.819929897114653724, 0.82466306258094566823, -1.3216627564751393958},
426 {-0.17677669529663686486, 0.17677669529663689734, -0.17738935115398993475, 0.17616173766104899848, -0.80911938627521915876, 2.3718194336783375529, -0.98528112393626813018, 2.517958897860342088, 0.63295764861417019883, -2.1631801955523621542},
427 {-0.25, 3.0616169978683829431e-17, -0.2491335703197571641, 3.0298246679137807606e-17, -0.82466306258094565309, 3.1415926535897931198, -1.0442826344437381945, 3.1415926535897931431, 0.54254326466191372953, -3.1415926535897930812},
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495 {24.989999999999998437, 0.0, 1.5315374843262580141, 0.0, -0.0072448862399538447391, 0.0, 2977286754.0962403117, 0.0, 5.4047414055481939457e-13, 0.0},
496 {17.67059846185182207, 17.670598461851820988, -885673.16331345207799, -400248.00540652140574, -400248.00540652215797, 885674.7341097792085, -800496.01081304623667, -1771346.3266269055961, 7.5223231588352466724e-10, 3.3560562518531656391e-10},
497 {1.5301961755346176992e-15, 24.989999999999998437, 2.1825789542468514196e-6, 1488643377.0481201559, 1488643377.0481201559, 1.5707941442159423724, -0.0072448862399538534498, 3.1023338111211545727, 0.0072448862399538360284, -0.039258842468638544566},
498 {-17.670598461851819906, 17.670598461851823152, 885673.16331345318248, -400248.0054065240787, -400248.00540652483093, -885671.59251712672318, -7.5223231588352706351e-10, 3.1415926539253988636, 800496.01081304089075, -1771349.4682195569769},
499 {-24.989999999999998437, 3.0603923510692353985e-15, -1.5315374843262580141, -1.7421457417638512695e-17, -0.0072448862399538447391, 3.1415926535897931172, -5.4047414055481939457e-13, 3.1415926535897932385, -2977286754.0962403117, -3.1415839232739762511},
500 {-17.670598461851824234, -17.670598461851818824, 885673.16331345097349, 400248.00540651873277, -400248.005406519485, 885671.5925171245142, -7.5223231588352227096e-10, -3.1415926539253988636, 800496.01081305158263, 1771349.4682195613948},
501 {-4.5905885266038530977e-15, -24.989999999999998437, -6.5477368627405542588e-6, -1488643377.0481201559, 1488643377.0481201559, -1.5708028745317593598, -0.0072448862399538186069, -3.1023338111211548151, 0.0072448862399538708713, 0.039258842468638787005},
502 {17.670598461851817742, -17.670598461851825316, -885673.16331345428695, 400248.00540652675168, -400248.00540652750391, -885674.73410978141745, -800496.01081303554482, 1771346.3266269011781, 7.5223231588352945979e-10, -3.3560562518531458362e-10}
503 };
504
505 const Real tol = 1e-10;
506
507 for (const auto& i : data) {
508 const Real x = i[0];
509 const Real y = (std::abs(x: i[1]) < 1e-12) ? 0.0 : i[1];
510 const std::complex<Real> z(x, y);
511
512
513 const std::complex<Real> si = Si(z);
514 std::complex<Real> ref(i[2], i[3]);
515 Real diff = std::abs(z: si-ref)/std::abs(z: ref);
516 if (diff > tol
517 || (std::abs(x: ref.real()) < tol && std::abs(x: si.real()) > tol)
518 || (std::abs(x: ref.imag()) < tol && std::abs(x: si.imag()) > tol)) {
519 integrals_test::reportSiCiFail(name: "Si", z, c: si, e: ref, diff, tol);
520 }
521
522 const std::complex<Real> ci = Ci(z);
523 ref = std::complex<Real>(i[4], i[5]);
524 diff = std::min(a: std::abs(z: ci-ref), b: std::abs(z: ci-ref)/std::abs(z: ref));
525 if (diff > tol
526 || (std::abs(x: ref.real()) < tol && std::abs(x: ci.real()) > tol)
527 || (std::abs(x: ref.imag()) < tol && std::abs(x: ci.imag()) > tol)) {
528 integrals_test::reportSiCiFail(name: "Ci", z, c: ci, e: ref, diff, tol);
529 }
530
531 const std::complex<Real> ei = Ei(z);
532 ref = std::complex<Real>(i[6], i[7]);
533 diff = std::abs(z: ei-ref)/std::abs(z: ref);
534 if (diff > tol
535 || (std::abs(x: ref.real()) < tol && std::abs(x: ei.real()) > tol)
536 || (std::abs(x: ref.imag()) < tol && std::abs(x: ei.imag()) > tol)) {
537 integrals_test::reportSiCiFail(name: "Ei", z, c: ei, e: ref, diff, tol);
538 }
539
540 const std::complex<Real> e1 = E1(z);
541 ref = std::complex<Real>(i[8], i[9]);
542 diff = std::min(a: std::abs(z: e1-ref), b: std::abs(z: e1-ref)/std::abs(z: ref));
543 if (std::abs(z: z) < 10.0)
544 if (diff > tol
545 || (std::abs(x: ref.real()) < tol && std::abs(x: e1.real()) > tol)
546 || (std::abs(x: ref.imag()) < tol && std::abs(x: e1.imag()) > tol)) {
547 integrals_test::reportSiCiFail(name: "E1", z, c: e1, e: ref, diff, tol);
548 }
549 }
550}
551
552
553
554void IntegralTest::testRealSiCiIntegrals() {
555 BOOST_TEST_MESSAGE("Testing real Ci and Si...");
556
557 using namespace ExponentialIntegral;
558
559 // reference values are calculated with Mathematica or Python/mpmath
560 const Real data[][3] = {
561 {1e-12, 1e-12, -27.0538054510270153677},
562 {0.1, 0.09994446110827695570, -1.7278683866572965838},
563 {1.0, 0.9460830703671830149, 0.3374039229009681347},
564 {1.9999, 1.6053675097543679041, 0.4230016343635392},
565 {3.9999, 1.758222058430840841, -0.140965355646150101},
566 {4.0001, 1.758184218306157867, -0.140998037827177150},
567 {5.0, 1.5499312449446741373, -0.19002974965664387862},
568 {7.0, 1.4545966142480935906, 0.076695278482184518383,},
569 {10.0, 1.6583475942188740493, -0.045456433004455372635},
570 {15.0, 1.6181944437083687391, 0.046278677674360439604},
571 {20.0, 1.5482417010434398402, 0.04441982084535331654},
572 {24.9, 1.532210740207620024, -0.010788215638781789846},
573 {25.1, 1.5311526281483412938, -0.0028719014454227088097},
574 {30.0, 1.566756540030351111, -0.033032417282071143779},
575 {40.0, 1.5869851193547845068, 0.019020007896208766962},
576 {400.0, 1.5721148692738117518, -0.00212398883084634893},
577 {4000.0, 1.5709788562309441985, -0.00017083030544201591130}
578 };
579
580
581 const Real tol = 1e-12;
582
583 for (const auto& i : data) {
584 Real x = i[0];
585 Real si = Si(x);
586
587 Real diff = std::fabs(x: si - i[1]);
588 if (diff > tol) {
589 integrals_test::reportSiCiFail(name: "SineIntegral", z: x, c: si, e: i[1], diff, tol);
590 }
591
592 const Real ci = Ci(x);
593 diff = std::fabs(x: ci - i[2]);
594 if (diff > tol) {
595 integrals_test::reportSiCiFail(name: "CosineIntegral", z: x, c: ci, e: i[2], diff, tol);
596 }
597
598 x = -i[0];
599 si = Si(x);
600 diff = std::fabs(x: si + i[1]);
601 if (diff > tol) {
602 integrals_test::reportSiCiFail(name: "SineIntegral", z: x, c: si, e: Real(-i[1]), diff, tol);
603 }
604 }
605}
606
607test_suite* IntegralTest::suite() {
608 auto* suite = BOOST_TEST_SUITE("Integration tests");
609 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testSegment));
610 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testTrapezoid));
611 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testMidPointTrapezoid));
612 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testSimpson));
613 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testGaussKronrodAdaptive));
614 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testGaussKronrodNonAdaptive));
615 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testGaussLobatto));
616 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testGaussLegendreIntegrator));
617 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testGaussChebyshevIntegrator));
618 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testGaussChebyshev2ndIntegrator));
619 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testTwoDimensionalIntegration));
620 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testFolinIntegration));
621 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testDiscreteIntegrals));
622 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testDiscreteIntegrator));
623 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testPiecewiseIntegral));
624 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testExponentialIntegral));
625 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testRealSiCiIntegrals));
626
627#ifdef QL_BOOST_HAS_TANH_SINH
628 suite->add(QUANTLIB_TEST_CASE(&IntegralTest::testTanhSinh));
629#endif
630
631 return suite;
632}
633
634

source code of quantlib/test-suite/integrals.cpp