OREAnnotatedSource/qle/stabilisedglls_8cpp_source.html

/*

 Copyright (C) 2017 Quaternion Risk Management Ltd

 All rights reserved.


 This file is part of ORE, a free-software/open-source library

 for transparent pricing and risk analysis - http://opensourcerisk.org


 ORE is free software: you can redistribute it and/or modify it

 under the terms of the Modified BSD License.  You should have received a

 copy of the license along with this program.

 The license is also available online at <http://opensourcerisk.org>


 This program is distributed on the basis that it will form a useful

 contribution to risk analytics and model standardisation, but WITHOUT

 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.

*/


#include "toplevelfixture.hpp"

#include <boost/test/unit_test.hpp>

#include <ql/math/functional.hpp>

#include <ql/math/randomnumbers/mt19937uniformrng.hpp>

#include <ql/methods/montecarlo/lsmbasissystem.hpp>

#include <ql/types.hpp>

#include <qle/math/stabilisedglls.hpp>


using namespace boost::unit_test_framework;

using namespace QuantLib;

using namespace QuantExt;


BOOST_FIXTURE_TEST_SUITE(QuantExtTestSuite, qle::test::TopLevelFixture)


BOOST_AUTO_TEST_SUITE(StabilisedGLLSTest)


BOOST_AUTO_TEST_CASE(testBigInputNumbers) {


    BOOST_TEST_MESSAGE("Testing QuantExt::StablizedGLLS with big input numbers (1D)");


    std::vector<Real> x, y;


    std::vector<ext::function<Real(Real)> > v;

    v.push_back([](Real x) { return 1.0; });

    v.push_back([](Real x) { return x; });

    v.push_back([](Real x) { return x * x; });


    // the following test data is taken from a real use case, where GeneralLinearLeastSquares

    // fails to produce decent regression coefficient estimates


    // clang-format off

    x.push_back(-3785510); y.push_back(6647590000);

    x.push_back(-3705810); y.push_back(7956560000);

    x.push_back(-3471430); y.push_back(21228600000);

    x.push_back(-3314710); y.push_back(13044900000);

    x.push_back(-3255810); y.push_back(33468500000);

    x.push_back(-3248300); y.push_back(17334700000);

    x.push_back(-3114480); y.push_back(10151300000);

    x.push_back(-3113260); y.push_back(36295400);

    x.push_back(-3098690); y.push_back(4971880);

    x.push_back(-3057130); y.push_back(4898680000);

    x.push_back(-3051020); y.push_back(3176250000);

    x.push_back(-3046080); y.push_back(4372520000);

    x.push_back(-3036630); y.push_back(52151500000);

    x.push_back(-2993930); y.push_back(24165200000);

    x.push_back(-2960970); y.push_back(330354000);

    x.push_back(-2953400); y.push_back(5444900000);

    x.push_back(-2919570); y.push_back(13833100000);

    x.push_back(-2914280); y.push_back(219816000);

    x.push_back(-2887750); y.push_back(20394800000);

    x.push_back(-2859600); y.push_back(1236390000);

    x.push_back(-2847340); y.push_back(27781900000);

    x.push_back(-2845470); y.push_back(5648840000);

    x.push_back(-2829940); y.push_back(16720800000);

    x.push_back(-2809910); y.push_back(130198000000);

    x.push_back(-2795220); y.push_back(4639700000);

    x.push_back(-2789400); y.push_back(1451330000);

    x.push_back(-2778810); y.push_back(709615000);

    x.push_back(-2775750); y.push_back(27378800000);

    x.push_back(-2735680); y.push_back(14926200000);

    x.push_back(-2708270); y.push_back(32262700000);

    x.push_back(-2676490); y.push_back(59605300000);

    x.push_back(-2676470); y.push_back(2358130000);

    x.push_back(-2669310); y.push_back(108703000000);

    x.push_back(-2662420); y.push_back(25204900000);

    x.push_back(-2648670); y.push_back(47167500000);

    x.push_back(-2590840); y.push_back(1976380000);

    x.push_back(-2587530); y.push_back(8121390000);

    x.push_back(-2563420); y.push_back(171882000);

    x.push_back(-2561190); y.push_back(7222640000);

    x.push_back(-2545970); y.push_back(97811000);

    x.push_back(-2544910); y.push_back(1341230000);

    x.push_back(-2531030); y.push_back(5892440000);

    x.push_back(-2514290); y.push_back(296502000);

    x.push_back(-2512150); y.push_back(9890050000);

    x.push_back(-2499340); y.push_back(19302600000);

    x.push_back(-2492530); y.push_back(15483100000);

    x.push_back(-2486520); y.push_back(5123850000);

    x.push_back(-2475260); y.push_back(113184000);

    x.push_back(-2470970); y.push_back(2232020000);

    x.push_back(-2468900); y.push_back(25951800000);

    x.push_back(-2465320); y.push_back(12108600000);

    x.push_back(-2451530); y.push_back(10054400000);

    x.push_back(-2449550); y.push_back(789513000);

    x.push_back(-2438270); y.push_back(18344000000);

    x.push_back(-2438020); y.push_back(14633000000);

    x.push_back(-2436170); y.push_back(886414000);

    x.push_back(-2426210); y.push_back(663629000);

    x.push_back(-2415360); y.push_back(6439610000);

    x.push_back(-2412350); y.push_back(10155300000);

    x.push_back(-2407210); y.push_back(91927000000);

    x.push_back(-2401500); y.push_back(12008300000);

    x.push_back(-2381040); y.push_back(5631130000);

    x.push_back(-2369550); y.push_back(19146200000);

    x.push_back(-2351520); y.push_back(53207900000);

    x.push_back(-2321990); y.push_back(5529370000);

    x.push_back(-2319310); y.push_back(55292800000);

    x.push_back(-2316600); y.push_back(8031610000);

    x.push_back(-2311910); y.push_back(67915800000);

    x.push_back(-2305900); y.push_back(3414250000);

    x.push_back(-2297880); y.push_back(464327000);

    x.push_back(-2297830); y.push_back(5487780000);

    x.push_back(-2288690); y.push_back(438278);

    x.push_back(-2281220); y.push_back(42339500000);

    x.push_back(-2279540); y.push_back(35275200000);

    x.push_back(-2269110); y.push_back(370882000);

    x.push_back(-2267970); y.push_back(7833390000);

    x.push_back(-2260480); y.push_back(48407500000);

    x.push_back(-2259980); y.push_back(19963300000);

    x.push_back(-2252110); y.push_back(1055560000);

    x.push_back(-2249890); y.push_back(13131700000);

    x.push_back(-2238670); y.push_back(9621520000);

    x.push_back(-2234450); y.push_back(8279900000);

    x.push_back(-2228910); y.push_back(40985800);

    x.push_back(-2210330); y.push_back(6994520000);

    x.push_back(-2201120); y.push_back(2561510000);

    x.push_back(-2199540); y.push_back(58612700000);

    x.push_back(-2188400); y.push_back(23132000000);

    x.push_back(-2187090); y.push_back(79443300000);

    x.push_back(-2185380); y.push_back(98445700000);

    x.push_back(-2180480); y.push_back(10242800000);

    x.push_back(-2176810); y.push_back(895524000);

    x.push_back(-2175280); y.push_back(64544700000);

    x.push_back(-2170620); y.push_back(25701100000);

    x.push_back(-2157020); y.push_back(75964600000);

    x.push_back(-2155940); y.push_back(41396100000);

    x.push_back(-2138670); y.push_back(68850000000);

    x.push_back(-2137090); y.push_back(13561700000);

    x.push_back(-2128460); y.push_back(10827800000);

    x.push_back(-2126760); y.push_back(3441740000);

    x.push_back(-2126040); y.push_back(57062200000);

    x.push_back(-2120070); y.push_back(3749230000);

    x.push_back(-2115370); y.push_back(22334500000);

    x.push_back(-2111680); y.push_back(8920670000);

    x.push_back(-2101200); y.push_back(2171960000);

    x.push_back(-2091580); y.push_back(1038880000);

    x.push_back(-2086060); y.push_back(8118830000);

    x.push_back(-2085460); y.push_back(37523500000);

    x.push_back(-2077480); y.push_back(23531200000);

    x.push_back(-2074070); y.push_back(39098600000);

    x.push_back(-2068810); y.push_back(357532000);

    x.push_back(-2063370); y.push_back(5125550000);

    x.push_back(-2061570); y.push_back(554719000);

    x.push_back(-2048470); y.push_back(4556820000);

    x.push_back(-2043840); y.push_back(2789040000);

    x.push_back(-2040270); y.push_back(50977700000);

    x.push_back(-2040100); y.push_back(4580650000);

    x.push_back(-2037580); y.push_back(358515000);

    x.push_back(-2037210); y.push_back(60210700);

    x.push_back(-2032200); y.push_back(56995300000);

    x.push_back(-2010490); y.push_back(11028500000);

    x.push_back(-2007580); y.push_back(21341300000);

    x.push_back(-2007370); y.push_back(2769080000);

    x.push_back(-1999220); y.push_back(18404800000);

    x.push_back(-1993890); y.push_back(33280900000);

    x.push_back(-1992740); y.push_back(39607100000);

    x.push_back(-1983530); y.push_back(17512800000);

    x.push_back(-1981280); y.push_back(75433800000);

    x.push_back(-1974760); y.push_back(67683800);

    x.push_back(-1967500); y.push_back(25633500000);

    x.push_back(-1963860); y.push_back(15472500000);

    x.push_back(-1963710); y.push_back(8035400000);

    x.push_back(-1963670); y.push_back(56209300000);

    x.push_back(-1963660); y.push_back(40213100000);

    x.push_back(-1963330); y.push_back(6937200000);

    x.push_back(-1962190); y.push_back(554226000);

    x.push_back(-1957650); y.push_back(3276860000);

    x.push_back(-1955200); y.push_back(313041000);

    x.push_back(-1954620); y.push_back(23962700000);

    x.push_back(-1948270); y.push_back(17393500000);

    x.push_back(-1934970); y.push_back(7285600000);

    x.push_back(-1934330); y.push_back(439341000);

    x.push_back(-1930610); y.push_back(32918300000);

    x.push_back(-1928480); y.push_back(652619000);

    x.push_back(-1919910); y.push_back(17619600000);

    x.push_back(-1914650); y.push_back(1817170000);

    x.push_back(-1910250); y.push_back(41127100000);

    x.push_back(-1909970); y.push_back(38804100000);

    x.push_back(-1896280); y.push_back(16247700000);

    x.push_back(-1895790); y.push_back(1805770000);

    x.push_back(-1894120); y.push_back(9988020000);

    x.push_back(-1892200); y.push_back(2857270000);

    x.push_back(-1890260); y.push_back(14383700000);

    x.push_back(-1889660); y.push_back(4420730000);

    x.push_back(-1880740); y.push_back(84390400000);

    x.push_back(-1877200); y.push_back(65460800000);

    x.push_back(-1876620); y.push_back(25201800000);

    x.push_back(-1875840); y.push_back(29691800000);

    x.push_back(-1874290); y.push_back(36662700000);

    x.push_back(-1864660); y.push_back(74300100000);

    x.push_back(-1861630); y.push_back(69185000000);

    x.push_back(-1861270); y.push_back(13635600000);

    x.push_back(-1860050); y.push_back(8666950000);

    x.push_back(-1856210); y.push_back(77616600);

    x.push_back(-1852170); y.push_back(35845300000);

    x.push_back(-1851760); y.push_back(73509600000);

    x.push_back(-1839340); y.push_back(233971000000);

    x.push_back(-1823400); y.push_back(1003360000);

    x.push_back(-1820530); y.push_back(2663990000);

    x.push_back(-1820410); y.push_back(4699760000);

    x.push_back(-1814910); y.push_back(38534300000);

    x.push_back(-1813220); y.push_back(111583000);

    x.push_back(-1780030); y.push_back(55287800000);

    x.push_back(-1778780); y.push_back(4155900000);

    x.push_back(-1754210); y.push_back(58371000000);

    x.push_back(-1751880); y.push_back(1793200000);

    x.push_back(-1750810); y.push_back(44557300000);

    x.push_back(-1748620); y.push_back(3059980000);

    x.push_back(-1744860); y.push_back(159269000);

    x.push_back(-1740270); y.push_back(4575270000);

    x.push_back(-1734860); y.push_back(35236500000);

    x.push_back(-1719490); y.push_back(2360650000);

    x.push_back(-1719300); y.push_back(55787500000);

    x.push_back(-1717030); y.push_back(870937000);

    x.push_back(-1710070); y.push_back(6165510000);

    x.push_back(-1707140); y.push_back(1071020000);

    x.push_back(-1703700); y.push_back(33099900000);

    x.push_back(-1666250); y.push_back(18262100000);

    x.push_back(-1666010); y.push_back(486805000);

    x.push_back(-1663120); y.push_back(20967100000);

    x.push_back(-1654990); y.push_back(470454000);

    x.push_back(-1653580); y.push_back(2998690000);

    x.push_back(-1639660); y.push_back(44373200000);

    x.push_back(-1639000); y.push_back(1267830000);

    x.push_back(-1634390); y.push_back(15732900000);

    x.push_back(-1633300); y.push_back(65058700);

    x.push_back(-1626460); y.push_back(2020740000);

    x.push_back(-1623240); y.push_back(12074700000);

    x.push_back(-1619910); y.push_back(21753100000);

    x.push_back(-1608060); y.push_back(17984900000);

    x.push_back(-1606680); y.push_back(22051100000);

    x.push_back(-1606170); y.push_back(37747300000);

    x.push_back(-1602990); y.push_back(475291000);

    x.push_back(-1600340); y.push_back(29972900000);

    x.push_back(-1596460); y.push_back(1940680000);

    x.push_back(-1588470); y.push_back(87234700000);

    x.push_back(-1586120); y.push_back(50444500000);

    x.push_back(-1584800); y.push_back(2321190000);

    x.push_back(-1579740); y.push_back(3085400000);

    x.push_back(-1574780); y.push_back(3186990000);

    x.push_back(-1574380); y.push_back(961264000);

    x.push_back(-1568050); y.push_back(173244000);

    x.push_back(-1565350); y.push_back(810019000);

    x.push_back(-1563200); y.push_back(11511900000);

    x.push_back(-1548860); y.push_back(154903000);

    x.push_back(-1544360); y.push_back(2607070000);

    x.push_back(-1542580); y.push_back(468262000);

    x.push_back(-1529820); y.push_back(548601000);

    x.push_back(-1529560); y.push_back(34995000000);

    x.push_back(-1518810); y.push_back(37212000000);

    x.push_back(-1518750); y.push_back(25748000000);

    x.push_back(-1516600); y.push_back(1237850000);

    x.push_back(-1511430); y.push_back(109024000000);

    x.push_back(-1505770); y.push_back(16061000000);

    x.push_back(-1501360); y.push_back(6813310000);

    x.push_back(-1496150); y.push_back(4001070000);

    x.push_back(-1493520); y.push_back(18352200000);

    x.push_back(-1487860); y.push_back(17579700000);

    x.push_back(-1485790); y.push_back(4482060000);

    x.push_back(-1483540); y.push_back(27163100000);

    x.push_back(-1479260); y.push_back(11395800000);

    x.push_back(-1474260); y.push_back(6867880000);

    x.push_back(-1467990); y.push_back(13878100000);

    x.push_back(-1463870); y.push_back(62355100000);

    x.push_back(-1458340); y.push_back(13743400000);

    x.push_back(-1450910); y.push_back(7176080000);

    x.push_back(-1444330); y.push_back(63445600000);

    x.push_back(-1438760); y.push_back(19276800000);

    x.push_back(-1433670); y.push_back(41227900000);

    x.push_back(-1433110); y.push_back(118382000000);

    x.push_back(-1430240); y.push_back(6801420000);

    x.push_back(-1429350); y.push_back(20656100000);

    x.push_back(-1427450); y.push_back(56217400000);

    x.push_back(-1420470); y.push_back(20045000000);

    x.push_back(-1419650); y.push_back(343972000);

    x.push_back(-1418440); y.push_back(72124700000);

    x.push_back(-1408830); y.push_back(217039000000);

    x.push_back(-1408530); y.push_back(269983000000);

    x.push_back(-1406940); y.push_back(33940900000);

    x.push_back(-1389990); y.push_back(7653740000);

    x.push_back(-1385820); y.push_back(29413900000);

    x.push_back(-1382460); y.push_back(81026800000);

    x.push_back(-1380870); y.push_back(12674900000);

    x.push_back(-1379210); y.push_back(5360790000);

    x.push_back(-1378790); y.push_back(154367000000);

    x.push_back(-1363090); y.push_back(12466100000);

    x.push_back(-1358890); y.push_back(2547120000);

    x.push_back(-1355810); y.push_back(58044300000);

    x.push_back(-1352120); y.push_back(98736100000);

    x.push_back(-1343170); y.push_back(9317640000);

    x.push_back(-1340560); y.push_back(1045490000);

    x.push_back(-1340550); y.push_back(20136400000);

    x.push_back(-1333100); y.push_back(6108130000);

    x.push_back(-1321540); y.push_back(10709000000);

    x.push_back(-1305340); y.push_back(57110700000);

    x.push_back(-1303310); y.push_back(30371600);

    x.push_back(-1298780); y.push_back(586226000);

    x.push_back(-1298120); y.push_back(96072500000);

    x.push_back(-1289750); y.push_back(3009440000);

    x.push_back(-1279520); y.push_back(30911700);

    x.push_back(-1279180); y.push_back(6184920000);

    x.push_back(-1270940); y.push_back(7996100000);

    x.push_back(-1265140); y.push_back(17123900000);

    x.push_back(-1263700); y.push_back(10639900000);

    x.push_back(-1258810); y.push_back(17014700000);

    x.push_back(-1258350); y.push_back(227967000000);

    x.push_back(-1251800); y.push_back(81266700000);

    x.push_back(-1249700); y.push_back(63571200000);

    x.push_back(-1247970); y.push_back(8079130000);

    x.push_back(-1246780); y.push_back(43539400000);

    x.push_back(-1243090); y.push_back(179318000000);

    x.push_back(-1240820); y.push_back(1059750000);

    x.push_back(-1239260); y.push_back(151087000000);

    x.push_back(-1232500); y.push_back(49744700000);

    x.push_back(-1219900); y.push_back(17484200000);

    x.push_back(-1217290); y.push_back(26273100000);

    x.push_back(-1216700); y.push_back(3952690000);

    x.push_back(-1212470); y.push_back(49007000000);

    x.push_back(-1200970); y.push_back(26281000000);

    x.push_back(-1199880); y.push_back(40463800000);

    x.push_back(-1188570); y.push_back(27455100000);

    x.push_back(-1187470); y.push_back(612916000);

    x.push_back(-1178840); y.push_back(12828400000);

    x.push_back(-1178140); y.push_back(36469400000);

    x.push_back(-1175400); y.push_back(12088900000);

    x.push_back(-1173550); y.push_back(6231780000);

    x.push_back(-1171510); y.push_back(36856000000);

    x.push_back(-1169290); y.push_back(22897300);

    x.push_back(-1169110); y.push_back(154804000);

    x.push_back(-1168500); y.push_back(57566400000);

    x.push_back(-1166450); y.push_back(42294600000);

    x.push_back(-1165490); y.push_back(8246510000);

    x.push_back(-1163580); y.push_back(2731020000);

    x.push_back(-1163140); y.push_back(41714800000);

    x.push_back(-1162760); y.push_back(1515270000);

    x.push_back(-1162030); y.push_back(41843700000);

    x.push_back(-1159160); y.push_back(913801000);

    x.push_back(-1143400); y.push_back(62628100000);

    x.push_back(-1129490); y.push_back(37251700000);

    x.push_back(-1125790); y.push_back(5636130000);

    x.push_back(-1125530); y.push_back(8557710000);

    x.push_back(-1123620); y.push_back(18241800000);

    x.push_back(-1121100); y.push_back(2736250000);

    x.push_back(-1117690); y.push_back(34174500000);

    x.push_back(-1116830); y.push_back(10687100000);

    x.push_back(-1113660); y.push_back(109939000000);

    x.push_back(-1107590); y.push_back(2504280000);

    x.push_back(-1097840); y.push_back(781542000);

    x.push_back(-1092910); y.push_back(9956610000);

    x.push_back(-1085620); y.push_back(50411400000);

    x.push_back(-1081180); y.push_back(22804100000);

    x.push_back(-1080430); y.push_back(77770000000);

    x.push_back(-1077380); y.push_back(93696700);

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    x.push_back(5177230); y.push_back(123157000000);

    x.push_back(5326160); y.push_back(55445200000);

    x.push_back(5338670); y.push_back(8993170000);

    x.push_back(5428300); y.push_back(8562550000);

    x.push_back(5452630); y.push_back(107327000000);

    x.push_back(5473440); y.push_back(1713490000);

    x.push_back(5564510); y.push_back(30016800000);

    x.push_back(5605190); y.push_back(101928000);

    x.push_back(5780430); y.push_back(265159000000);

    x.push_back(5873870); y.push_back(12441500000);

    x.push_back(5926190); y.push_back(3499210000);

    x.push_back(5987320); y.push_back(21360000000);

    x.push_back(6191300); y.push_back(43263700000);

    x.push_back(6345250); y.push_back(80164900000);

    x.push_back(6539470); y.push_back(2794630000);

    x.push_back(6575520); y.push_back(9829000000);

    x.push_back(6612570); y.push_back(65350400000);

    x.push_back(6929240); y.push_back(113606000000);

    x.push_back(7532910); y.push_back(12801500000);

    x.push_back(7946080); y.push_back(355173000000);

    // clang-format on


    // run stabilized GLLS

    StabilisedGLLS m(x, y, v, StabilisedGLLS::MaxAbs);


    // calculate effective parameters

    Real c0 = m.transformedCoefficients()[0] / m.yMultiplier();

    Real c1 = m.transformedCoefficients()[1] * m.xMultiplier()[0] / m.yMultiplier();

    Real c2 = m.transformedCoefficients()[2] * m.xMultiplier()[0] / m.yMultiplier() * m.xMultiplier()[0];


    // transform data manually and compute effective coefficients

    Real scaling = 1E-12;

    std::vector<Real> xt(x.size()), yt(y.size());

    std::transform(x.begin(), x.end(), xt.begin(), std::bind(std::multiplies<Real>(), std::placeholders::_1, scaling));

    std::transform(y.begin(), y.end(), yt.begin(), std::bind(std::multiplies<Real>(), std::placeholders::_1, scaling));

    GeneralLinearLeastSquares m2(xt, yt, v);

    Real d0 = m2.coefficients()[0] / scaling;

    Real d1 = m2.coefficients()[1];

    Real d2 = m2.coefficients()[2] * scaling;


    // check coefficients

    Real tol = 1E-8;

    if (std::abs((c0 - d0) / d0) > tol)

        BOOST_ERROR("could not verify c0 (" << c0 << ") against expected value (" << d0 << "), relative error ("

                                            << (c0 - d0) / d0 << ") exceeds tolerance (" << tol << ")");

    if (std::abs((c1 - d1) / d1) > tol)

        BOOST_ERROR("could not verify c1 (" << c1 << ") against expected value (" << d1 << "), relative error ("

                                            << (c1 - d1) / d1 << ") exceeds tolerance (" << tol << ")");

    if (std::abs((c2 - d2) / d2) > tol)

        BOOST_ERROR("could not verify c2 (" << c2 << ") against expected value (" << d2 << "), relative error ("

                                            << (c2 - d2) / d2 << ") exceeds tolerance (" << tol << ")");


    // check eval function

    Real x0 = -1E10;

    while (x0 < 1E10) {

        Real y = m.eval(x0, v);

        Real y2 = c0 + c1 * x0 + c2 * x0 * x0;

        if (std::abs((y - y2) / y2) > tol)

            BOOST_ERROR("could not verify eval(" << x0 << ") for MaxBas mode, got " << y << ", expected " << y2

                                                 << ", relative error " << (y - y2) / y2 << ", tolerance " << tol);

        x0 += 1E7;

    }


    // check alternative mode

    StabilisedGLLS mb(x, y, v, StabilisedGLLS::MeanStdDev);


    x0 = -1E10;

    while (x0 < 1E10) {

        Real y = mb.eval(x0, v);

        Real y2 = c0 + c1 * x0 + c2 * x0 * x0;

        if (std::abs((y - y2) / y2) > tol)

            BOOST_ERROR("could not verify eval(" << x0 << ") for MeanStdDev mode, got " << y << ", expected " << y2

                                                 << ", relative error " << (y - y2) / y2 << ", tolerance " << tol);

        x0 += 1E7;

    }


    BOOST_CHECK(true);

}


BOOST_AUTO_TEST_CASE(test2DRegression) {


    BOOST_TEST_MESSAGE("Testing QuantExt::StablizedGLLS 2D Regression");


    std::vector<Array> x;

    std::vector<Real> y;


    // both GeneralLinearLeastSquares and StabilisedGLLS should work on this data

    MersenneTwisterUniformRng mt(42);

    for (Size n = 0; n < 1000; ++n) {

        Array xa(2);

        xa[0] = mt.nextReal() * 1000.0;

        xa[1] = mt.nextReal() * 2000.0;

        Real yt = -4982.0 + xa[0] * 43.0 + xa[1] * 142.0 + xa[0] * xa[1] * 0.8 - xa[0] * xa[0] * 0.02948 +

                  xa[1] * xa[1] * 1533.0;

        x.push_back(xa);

        y.push_back(yt);

    }


    std::vector<ext::function<Real(Array)> > basis =

        LsmBasisSystem::multiPathBasisSystem(2, 2, LsmBasisSystem::Monomial);


    StabilisedGLLS m(x, y, basis, StabilisedGLLS::MaxAbs);

    StabilisedGLLS mb(x, y, basis, StabilisedGLLS::MeanStdDev);

    GeneralLinearLeastSquares m2(x, y, basis);


    Real tol = 5E-4;


    Real x0 = -10.0;

    while (x0 < 10.0) {

        Real x1 = -10.0;

        while (x1 < 10.0) {

            Array p(2);

            p[0] = x0;

            p[1] = x1;

            Real yn = 0.0;

            for (Size i = 0; i < basis.size(); ++i) {

                yn += basis[i](p) * m2.coefficients()[i];

            }

            Real ys = m.eval(p, basis);

            if (std::abs((ys - yn) / yn) > tol)

                BOOST_ERROR("could not verify eval(" << p << ") for MaxAbs mode, got " << ys << ", expected " << yn

                                                     << ", relative error " << (ys - yn) / yn << ", tolerance " << tol);

            Real ysb = mb.eval(p, basis);

            if (std::abs((ysb - yn) / yn) > tol)

                BOOST_ERROR("could not verify eval(" << p << ") for MeanStdDev mode, got " << ysb << ", expected " << yn

                                                     << ", relative error " << (ysb - yn) / yn << ", tolerance "

                                                     << tol);

            x1 += 0.1;

        }

        x0 += 0.1;

    }

    BOOST_CHECK(true);

}


BOOST_AUTO_TEST_SUITE_END()


BOOST_AUTO_TEST_SUITE_END()

QuantExt::StabilisedGLLS
Numerically stabilised general linear least squares.
Definition: stabilisedglls.hpp:51

QuantExt::StabilisedGLLS::MaxAbs
@ MaxAbs
Definition: stabilisedglls.hpp:55

QuantExt::StabilisedGLLS::MeanStdDev
@ MeanStdDev
Definition: stabilisedglls.hpp:56

QuantExt::StabilisedGLLS::transformedCoefficients
const Array & transformedCoefficients() const
Definition: stabilisedglls.hpp:61

QuantExt::StabilisedGLLS::eval
Real eval(xType x, vContainer &v, typename boost::enable_if< typename boost::is_arithmetic< xType >::type >::type *=0)
evaluate regression function in terms of original x, y
Definition: stabilisedglls.hpp:248

QuantExt::StabilisedGLLS::yMultiplier
const Real yMultiplier() const
Definition: stabilisedglls.hpp:69

QuantExt::StabilisedGLLS::xMultiplier
const Array & xMultiplier() const
Transformation parameters (u => (u + shift) * multiplier for u = x, y)
Definition: stabilisedglls.hpp:67

qle::test::TopLevelFixture
Top level fixture.
Definition: toplevelfixture.hpp:35

QuantExt
Definition: namespaces.docs:19

QuantLib
Definition: colombia.cpp:21

BOOST_AUTO_TEST_CASE
BOOST_AUTO_TEST_CASE(testBigInputNumbers)
Definition: stabilisedglls.cpp:35

stabilisedglls.hpp
Numerically stabilised general linear least squares.

toplevelfixture.hpp
Fixture that can be used at top level.