|
|
Boost-Commit : |
Subject: [Boost-commit] svn:boost r83187 - trunk/libs/math/test
From: pbristow_at_[hidden]
Date: 2013-02-27 07:51:53
Author: pbristow
Date: 2013-02-27 07:51:52 EST (Wed, 27 Feb 2013)
New Revision: 83187
URL: http://svn.boost.org/trac/boost/changeset/83187
Log:
Added tests for airy (0) call and more spot values, passing on MSVC 10.
Text files modified:
trunk/libs/math/test/test_bessel_airy_zeros.cpp | 330 ++++++++++++++++++++++++++++-----------
1 files changed, 232 insertions(+), 98 deletions(-)
Modified: trunk/libs/math/test/test_bessel_airy_zeros.cpp
==============================================================================
--- trunk/libs/math/test/test_bessel_airy_zeros.cpp (original)
+++ trunk/libs/math/test/test_bessel_airy_zeros.cpp 2013-02-27 07:51:52 EST (Wed, 27 Feb 2013)
@@ -340,13 +340,13 @@
// 0.666908567552422764702292353801313970109968787260547
//7.58834489983121936102504707121493271448122800440112
- std::cout.precision(2+ std::numeric_limits<RealType>::digits * 3010/10000);
+ std::cout.precision(2 + std::numeric_limits<RealType>::digits * 3010/10000);
v = -static_cast<RealType>(3);
- std::cout << "v = " << v << std::endl;
- RealType d = static_cast<RealType>(999999)/1000000;
- std::cout << "d = " << d << std::endl;
+ //std::cout << "v = " << v << std::endl;
+ RealType d = static_cast<RealType>(999999)/1000000; // Value very near to unity.
+ //std::cout << "d = " << d << std::endl;
v -= d;
- std::cout << "v = " << v << std::endl;
+ // std::cout << "v = " << v << std::endl; // v = -3.9999989999999999
// 1st is much less accurate.
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 1), static_cast<RealType>(0.666908567552422764702292353801313970109968787260547L), tolerance * 100000);
@@ -355,8 +355,8 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_bessel_j_zero(v, 20), static_cast<RealType>(65.0669968910414433560468307554730940098734494938136L), tolerance);
- v = -static_cast<RealType>(1)/81799;
- std::cout << "v = " << v << std::endl;
+ v = -static_cast<RealType>(1)/81799; // Largish prime, so small value.
+ // std::cout << "v = " << v << std::endl; // v = -1.22251e-005
// Table[N[BesselJZero[-1/81799, n], 51], {n, 1, 20, 1}]
@@ -386,7 +386,7 @@
if (std::numeric_limits<RealType>::has_quiet_NaN)
{
BOOST_CHECK_THROW(cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 1), std::domain_error);
- // bad m returns NaN.
+ // Check that bad m returns NaN if policy is no throws.
BOOST_CHECK(boost::math::isnan<RealType>(cyl_bessel_j_zero(std::numeric_limits<RealType>::quiet_NaN(), 1, ignore_all_policy())) );
BOOST_CHECK_THROW(boost::math::cyl_bessel_j_zero(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), -1), std::domain_error);
}
@@ -404,9 +404,9 @@
BOOST_CHECK(boost::math::isnan<RealType>(cyl_bessel_j_zero(std::numeric_limits<RealType>::infinity(), 1, ignore_all_policy())) );
}
- // Tests of cyc_neumann zero function (BesselKZero in Wolfram for spot values).
+ // Tests of cyc_neumann zero function (BesselYZero in Wolfram) for spot values.
/*
- Table[N[BesselKZero[0, n], 50], {n, 1, 5, 1}]
+ Table[N[BesselYZero[0, n], 50], {n, 1, 5, 1}]
n |
1 | 0.89357696627916752158488710205833824122514686193001
2 | 3.9576784193148578683756771869174012814186037655636
@@ -414,7 +414,18 @@
4 | 10.222345043496417018992042276342187125994059613181
5 | 13.361097473872763478267694585713786426579135174880
-Table[N[BesselKZero[1, n], 50], {n, 1, 5, 1}]
+Table[N[BesselYZero[0, n], 50], {n, 1, 5, 1}]
+
+n |
+1 | 0.89357696627916752158488710205833824122514686193001
+2 | 3.9576784193148578683756771869174012814186037655636
+3 | 7.0860510603017726976236245968203524689715103811778
+4 | 10.222345043496417018992042276342187125994059613181
+5 | 13.361097473872763478267694585713786426579135174880
+
+So K == Y
+
+Table[N[BesselYZero[1, n], 50], {n, 1, 5, 1}]
n |
1 | 2.1971413260310170351490335626989662730530183315003
2 | 5.4296810407941351327720051908525841965837574760291
@@ -422,7 +433,7 @@
4 | 11.749154830839881243399421939922350714301165983279
5 | 14.897442128336725378844819156429870879807150630875
-Table[N[BesselKZero[2, n], 50], {n, 1, 5, 1}]
+Table[N[BesselYZero[2, n], 50], {n, 1, 5, 1}]
n |
1 | 3.3842417671495934727014260185379031127323883259329
2 | 6.7938075132682675382911671098369487124493222183854
@@ -434,9 +445,8 @@
// Some simple integer values.
using boost::math::cyl_neumann_zero;
-
- BOOST_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), 0), std::domain_error);
- //BOOST_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(-1), 2), std::domain_error); now implemented negative order.
+ // Bad rank m.
+ BOOST_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), 0), std::domain_error); //
BOOST_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), -1), std::domain_error);
if (std::numeric_limits<RealType>::has_quiet_NaN)
@@ -449,11 +459,37 @@
BOOST_CHECK_THROW(cyl_neumann_zero(std::numeric_limits<RealType>::infinity(), 2), std::domain_error);
BOOST_CHECK_THROW(cyl_neumann_zero(static_cast<RealType>(0), -1), std::domain_error);
}
+ // else no infinity tests.
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(0), 1), static_cast<RealType>(0.89357696627916752158488710205833824122514686193001L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1), 2), static_cast<RealType>(5.4296810407941351327720051908525841965837574760291L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(2), 3), static_cast<RealType>(10.023477979360037978505391792081418280789658279097L), tolerance);
+ /*
+ Table[N[BesselYZero[3, n], 50], {n, 1, 5, 1}]
+ 1 | 4.5270246611496438503700268671036276386651555486109
+ 2 | 8.0975537628604907044022139901128042290432231369075
+ 3 | 11.396466739595866739252048190629504945984969192535
+ 4 | 14.623077742393873174076722507725200649352970569915
+ 5 | 17.818455232945520262553239064736739443380352162752
+ */
+
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 1), static_cast<RealType>(4.5270246611496438503700268671036276386651555486109L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 2), static_cast<RealType>(8.0975537628604907044022139901128042290432231369075L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 3), static_cast<RealType>(11.396466739595866739252048190629504945984969192535L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 4), static_cast<RealType>(14.623077742393873174076722507725200649352970569915L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(3), 5), static_cast<RealType>(17.818455232945520262553239064736739443380352162752L), tolerance);
+
+
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 1), static_cast<RealType>(4.5270246611496438503700268671036276386651555486109L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 2), static_cast<RealType>(8.0975537628604907044022139901128042290432231369075L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 3), static_cast<RealType>(11.396466739595866739252048190629504945984969192535L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 4), static_cast<RealType>(14.623077742393873174076722507725200649352970569915L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 5), static_cast<RealType>(17.818455232945520262553239064736739443380352162752L), tolerance);
+
+
+
+
{ // Repeat rest using multiple zeros version.
std::vector<RealType> zeros;
cyl_neumann_zero(static_cast<RealType>(0.0), 1, 3, std::back_inserter(zeros) );
@@ -466,21 +502,20 @@
/* Order 219/100: This checks accuracy in a region just below a critical cutoff.
Table[N[BesselKZero[219/100, n], 50], {n, 1, 20, 4}]
-
1 | 3.6039149425338727979151181355741147312162055042157
5 | 16.655399111666833825247894251535326778980614938275
9 | 29.280564448169163756478439692311605757712873534942
13 | 41.870269811145814760551599481942750124112093564643
17 | 54.449180021209532654553613813754733514317929678038
*/
+
+
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(219)/100, 1), static_cast<RealType>(3.6039149425338727979151181355741147312162055042157L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(219)/100, 5), static_cast<RealType>(16.655399111666833825247894251535326778980614938275L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(219)/100, 17), static_cast<RealType>(54.449180021209532654553613813754733514317929678038L), tolerance);
/* Order 221/100: This checks a region just above a critical cutoff.
-
- Table[N[BesselKZero[220/100, n], 50], {n, 1, 20, 5}]
-
+ Table[N[BesselYZero[220/100, n], 50], {n, 1, 20, 5}]
1 | 3.6154383428745996706772556069431792744372398748425
6 | 19.833435100254138641131431268153987585842088078470
11 | 35.592602956438811360473753622212346081080817891225
@@ -494,9 +529,7 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(220)/100, 16), static_cast<RealType>(51.320322762482062633162699745957897178885350674038L), tolerance);
/* Order 1/1000: A small order.
-
- Table[N[BesselKZero[1/1000, n], 50], {n, 1, 20, 5}]
-
+ Table[N[BesselYZero[1/1000, n], 50], {n, 1, 20, 5}]
1 | 0.89502371604431360670577815537297733265776195646969
6 | 16.502492490954716850993456703662137628148182892787
11 | 32.206774708309182755790609144739319753463907110990
@@ -509,9 +542,7 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/1000, 16), static_cast<RealType>(47.913467031941494147962476920863688176374357572509L), tolerance);
/* Order 71/19: Merely an intermediate order.
-
- Table[N[BesselKZero[71/19, n], 50], {n, 1, 20, 5}]
-
+ Table[N[BesselYZero[71/19, n], 50], {n, 1, 20, 5}]
1 | 5.3527167881149432911848659069476821793319749146616
6 | 22.051823727778538215953091664153117627848857279151
11 | 37.890091170552491176745048499809370107665221628364
@@ -525,30 +556,35 @@
/* Order 7001/19: A medium-large order, small enough to retain moderate efficiency of calculation.
- Table[N[BesselKZero[7001/19, n], 50], {n, 1}]
-
+ Table[N[BesselYZero[7001/19, n], 50], {n, 1}]
1 | 375.18866334770357669101711932706658671250621098115
- Table[N[BesselKZero[7001/19, n], 50], {n, 2}]
+ Table[N[BesselYZero[7001/19, n], 50], {n, 2}]
Standard computation time exceeded :-(
*/
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(7001)/19, 1), static_cast<RealType>(375.18866334770357669101711932706658671250621098115L), tolerance);
/* A high zero such as the 1000th zero for a modest order such as 71/19.
-
- Table[N[BesselKZero[71/19, n], 50], {n, 1000}]
+ Table[N[BesselYZero[71/19, n], 50], {n, 1000}]
Standard computation time exceeded :-(
*/
/*
- Negative order cyl_neumann.
-
-/* Table[N[BesselKZero[-1, n], 50], {n, 1, 20, 5}]
-1 | 2.1971413260310170351490335626989662730530183315003
-6 | 18.043402276727855564304555507889508902163088324834
-11 | 33.761017796109325692471759911249650993879821495802
-16 | 49.472505679924095824128003887609267273294894411716
+ Test Negative orders cyl_neumann.
+ Table[N[BesselYZero[-1, n], 50], {n, 1, 10, 1}]
+ 1 | 2.1971413260310170351490335626989662730530183315003
+ 2 | 5.4296810407941351327720051908525841965837574760291
+ 3 | 8.5960058683311689264296061801639678511029215669749
+ 4 | 11.749154830839881243399421939922350714301165983279
+ 5 | 14.897442128336725378844819156429870879807150630875
+ 6 | 18.043402276727855564304555507889508902163088324834
+ 7 | 21.188068934142213016142481528685423196935024604904
+ 8 | 24.331942571356912035992944051850129651414333340303
+ 9 | 27.475294980449223512212285525410668235700897307021
+ 10 | 30.618286491641114715761625696447448310277939570868
+ 11 | 33.761017796109325692471759911249650993879821495802
+ 16 | 49.472505679924095824128003887609267273294894411716
*/
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-1), 1), static_cast<RealType>(2.1971413260310170351490335626989662730530183315003L), tolerance * 3);
@@ -558,11 +594,11 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-1), 16), static_cast<RealType>(49.472505679924095824128003887609267273294894411716L), tolerance * 3);
/*
- Table[N[BesselKZero[-2, n], 50], {n, 1, 20, 5}]
-1 | 3.3842417671495934727014260185379031127323883259329
-6 | 19.539039990286384411511740683423888947393156497603
-11 | 35.289793869635804143323234828826075805683602368473
-16 | 51.014128749483902310217774804582826908060740157564
+ Table[N[BesselYZero[-2, n], 50], {n, 1, 20, 5}]
+ 1 | 3.3842417671495934727014260185379031127323883259329
+ 6 | 19.539039990286384411511740683423888947393156497603
+ 11 | 35.289793869635804143323234828826075805683602368473
+ 16 | 51.014128749483902310217774804582826908060740157564
*/
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 1), static_cast<RealType>(3.3842417671495934727014260185379031127323883259329L), tolerance);
@@ -570,31 +606,44 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 11), static_cast<RealType>(35.289793869635804143323234828826075805683602368473L), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-2), 16), static_cast<RealType>(51.014128749483902310217774804582826908060740157564L), tolerance * 3);
-/* Table[N[BesselKZero[-39, n], 51], {n, 1, 20, 5}]
+/*
+ Table[N[BesselYZero[-3, n], 51], {n, 1, 7, 1}]
+ 1 | 4.52702466114964385037002686710362763866515554861094
+ 2 | 8.09755376286049070440221399011280422904322313690750
+ 3 | 11.3964667395958667392520481906295049459849691925349
+ 4 | 14.6230777423938731740767225077252006493529705699150
+ 5 | 17.8184552329455202625532390647367394433803521627517
+ 6 | 20.9972847541877606834525058939528641630713169437070
+ 7 | 24.1662357585818282287385597668220226288453739040042
+*/
-n |
-1 | 42.2362394762664681287397356668342141701037684436723
-6 | 65.8250353430045981408288669790173009159561533403819
-11 | 84.2674082411341814641248554679382420802125973458922
-16 | 101.589776978258493441843447810649346266014624868410
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 1), static_cast<RealType>(4.52702466114964385037002686710362763866515554861094L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 2), static_cast<RealType>(8.09755376286049070440221399011280422904322313690750L), tolerance);
+
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3), 4), static_cast<RealType>(14.6230777423938731740767225077252006493529705699150L), tolerance);
+
+/* Table[N[BesselKZero[-39, n], 51], {n, 1, 20, 5}]
+ 1 | 42.2362394762664681287397356668342141701037684436723
+ 6 | 65.8250353430045981408288669790173009159561533403819
+ 11 | 84.2674082411341814641248554679382420802125973458922
+ 16 | 101.589776978258493441843447810649346266014624868410
*/
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 1), static_cast<RealType>(42.2362394762664681287397356668342141701037684436723L), tolerance );
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 6), static_cast<RealType>(65.8250353430045981408288669790173009159561533403819L), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 11), static_cast<RealType>(84.2674082411341814641248554679382420802125973458922L), tolerance);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 16), static_cast<RealType>(101.589776978258493441843447810649346266014624868410L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 1), static_cast<RealType>(42.2362394762664681287397356668342141701037684436723L), tolerance );
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 6), static_cast<RealType>(65.8250353430045981408288669790173009159561533403819L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 11), static_cast<RealType>(84.2674082411341814641248554679382420802125973458922L), tolerance);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39), 16), static_cast<RealType>(101.589776978258493441843447810649346266014624868410L), tolerance);
/* Table[N[BesselKZero[-39 -(1/3), n], 51], {n, 1, 20, 5}]
-n |
-1 | 39.3336965099558453809241429692683050137281997313679
-6 | 64.9038181444904768984884565999608291433823953030822
-11 | 83.4922341795560713832607574604255239776551554961143
-16 | 100.878386349724826125265571457142254077564666532665
+ 1 | 39.3336965099558453809241429692683050137281997313679
+ 6 | 64.9038181444904768984884565999608291433823953030822
+ 11 | 83.4922341795560713832607574604255239776551554961143
+ 16 | 100.878386349724826125265571457142254077564666532665
*/
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 1), static_cast<RealType>(39.3336965099558453809241429692683050137281997313679L), tolerance * 4);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 6), static_cast<RealType>(64.9038181444904768984884565999608291433823953030822L), tolerance * 4);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 11), static_cast<RealType>(83.4922341795560713832607574604255239776551554961143L), tolerance * 4);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 16), static_cast<RealType>(100.878386349724826125265571457142254077564666532665L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 1), static_cast<RealType>(39.3336965099558453809241429692683050137281997313679L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 6), static_cast<RealType>(64.9038181444904768984884565999608291433823953030822L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 11), static_cast<RealType>(83.4922341795560713832607574604255239776551554961143L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-39) - static_cast<RealType>(1)/3, 16), static_cast<RealType>(100.878386349724826125265571457142254077564666532665L), tolerance * 4);
/* Table[N[BesselKZero[-(1/3), n], 51], {n, 1, 20, 5}]
n |
1 | 0.364442931311036254896373762996743259918847602789703
@@ -608,46 +657,111 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/3, 11), static_cast<RealType>(31.6799168750213003020847708007848147516190373648194L), tolerance * 4);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/3, 16), static_cast<RealType>(47.3871543280673235432396563497681616285970326011211L), tolerance * 4);
-/*Table[N[BesselKZero[-3 -(9999/10000), n], 51], {n, 1, 20, 5}]
- n |
-1 | 5.64546089250283694562642537496601708928630550185069
-2 | 9.36184180108088288881787970896747209376324330610979
-3 | 12.7303431758275183078115963473808796340618061355885
-4 | 15.9998152121877557837972245675029531998475502716021
-6 | 9.36184180108088288881787970896747209376324330610979
-
-
-11 | 25.6104419106589739931633042959774157385787405502820
-16 | 41.4361281441868132581487460354904567452973524446193
+/* Table[N[BesselKZero[-3 -(9999/10000), n], 51], {n, 1, 20, 5}]
+ 1 | 5.64546089250283694562642537496601708928630550185069
+ 2 | 9.36184180108088288881787970896747209376324330610979
+ 3 | 12.7303431758275183078115963473808796340618061355885
+ 4 | 15.9998152121877557837972245675029531998475502716021
+ 6 | 9.36184180108088288881787970896747209376324330610979
+ 11 | 25.6104419106589739931633042959774157385787405502820
+ 16 | 41.4361281441868132581487460354904567452973524446193
*/
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 1), static_cast<RealType>(5.64546089250283694562642537496601708928630550185069L), tolerance * 4);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 2), static_cast<RealType>(9.36184180108088288881787970896747209376324330610979L), tolerance * 4);
-
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 3), static_cast<RealType>(12.7303431758275183078115963473808796340618061355885L), tolerance * 4);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 4), static_cast<RealType>(15.9998152121877557837972245675029531998475502716021L), tolerance * 4);
-/* Table[N[BesselKZero[-3 -(9999/10000), n], 51], {n, 1, 7, 1}]
+/* Table[N[BesselYZero[-3 -(9999/10000), n], 51], {n, 1, 7, 1}]
1 | 5.64546089250283694562642537496601708928630550185069
2 | 9.36184180108088288881787970896747209376324330610979
3 | 12.7303431758275183078115963473808796340618061355885
4 | 15.9998152121877557837972245675029531998475502716021
+
+// but 5 is same as 1!! Acknowledged as fault Wolfram [TS 6475] 26 Feb 13.
+
5 | 5.64546089250283694562642537496601708928630550184982
6 | 9.36184180108088288881787970896747209376324330610979
7 | 12.7303431758275183078115963473808796340618061355885
+In[26]:= FindRoot[BesselY[-3 -9999/10000, r] == 0, {r, 3}] for r = 2,3, 4, 5 = {r->5.64546}
-Something odd here 1 == 5, 2 == 6
-*/
+In[26]:= FindRoot[BesselY[-3 -9999/10000, r] == 0, {r, 19}] = 19.2246
+
+So no very accurate reference value for these.
+
+Calculated using cpp_dec_float_50
+
+ 5.6454608925028369456264253749660170892863055018498
+ 9.3618418010808828888178797089674720937632433061099
+ 12.730343175827518307811596347380879634061806135589
+ 15.999815212187755783797224567502953199847550271602
+
+ 19.224610865671563344572152795434688888375602299773
+ 22.424988389021059116212186912990863561607855849204
+ 25.610441910658973993163304295977415738578740550282
+ 28.786066313968546073981640755202085944374967166411
+ 31.954857624676521867923579695253822854717613513587
+
+
+ */
- //BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 6), static_cast<RealType>(25.6104419106589739931633042959774157385787405502820L), tolerance * 4);
- //BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 5), static_cast<RealType>(41.4361281441868132581487460354904567452973524446193L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 1), static_cast<RealType>(5.64546089250283694562642537496601708928630550185069L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 2), static_cast<RealType>(9.36184180108088288881787970896747209376324330610979L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 3), static_cast<RealType>(12.7303431758275183078115963473808796340618061355885L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 4), static_cast<RealType>(15.9998152121877557837972245675029531998475502716021L), tolerance * 4);
+//
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 5), static_cast<RealType>(19.224610865671563344572152795434688888375602299773L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 6), static_cast<RealType>(22.424988389021059116212186912990863561607855849204L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 7), static_cast<RealType>(25.610441910658973993163304295977415738578740550282L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 8), static_cast<RealType>(28.786066313968546073981640755202085944374967166411L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000, 9), static_cast<RealType>(31.954857624676521867923579695253822854717613513587L), tolerance * 4);
+
+ //BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-(static_cast<RealType>(-3)-static_cast<RealType>(99)/100), 5),
+ // cyl_neumann_zero(+(static_cast<RealType>(-3)-static_cast<RealType>(99)/100), 5), tolerance * 100);
+ {
+ long double x = 1.L;
+ BOOST_CHECK_CLOSE_FRACTION(
+ cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
+ cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
+ }
+ {
+ long double x = 2.L;
+ BOOST_CHECK_CLOSE_FRACTION(
+ cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
+ cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
+ }
+ {
+ long double x = 3.L;
+ BOOST_CHECK_CLOSE_FRACTION(
+ cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
+ cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
+ }
+ // These are very close but not exactly same.
+ //{
+ // RealType x = static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000;
+ // BOOST_CHECK_CLOSE_FRACTION(
+ // cyl_neumann_zero(-(static_cast<RealType>(x)), 5),
+ // cyl_neumann_zero(+(static_cast<RealType>(x)), 5), tolerance * 100);
+ // // 19.2242889 and 19.2246113
+ //}
+ //{
+
+ // RealType x = static_cast<RealType>(-3) -static_cast<RealType>(9999)/10000;
+ // BOOST_CHECK_CLOSE_FRACTION(
+ // cyl_neumann_zero(-(static_cast<RealType>(x)), 6),
+ // cyl_neumann_zero(+(static_cast<RealType>(x)), 6), tolerance * 100);
+ // // 22.4246693 and 22.4249878
+ //}
-/*Table[N[BesselKZero[-1/81799, n], 51], {n, 1, 10, 5}]
-1 | 0.893559276290122922836047849416713592133322804889757
-n |
+ // 2.5 18.6890354 17.1033592
+
+
+/*Table[N[BesselYZero[-1/81799, n], 51], {n, 1, 10, 5}]
+
+1 | 0.893559276290122922836047849416713592133322804889757
2 | 3.95765935645507004204986415533750122885237402118726
3 | 7.08603190350579828577279552434514387474680226004173
4 | 10.2223258629823064789904339889550588869985272176335
@@ -657,14 +771,26 @@
6 | 16.5009032471619898684110089652474861084220781491575
7 | 19.6412905039556082160052482410981245043314155416354
9 | 25.9229384536173175152381652048590136247796591153244
-
*/
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 1), static_cast<RealType>(0.893559276290122922836047849416713592133322804889757L), tolerance * 4);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 2), static_cast<RealType>(3.95765935645507004204986415533750122885237402118726L), tolerance * 4);
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 3), static_cast<RealType>(7.08603190350579828577279552434514387474680226004173L), tolerance * 4);
+ // Doesn't converge!
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 2), static_cast<RealType>(3.95765935645507004204986415533750122885237402118726L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 3), static_cast<RealType>(7.08603190350579828577279552434514387474680226004173L), tolerance * 4);
+ /* try positive x
+ Table[N[BesselYZero[1/81799, n], 51], {n, 1, 5, 1}]
+
+ 1 | 0.893594656187326273432267210617481926490785928764963
+ 2 | 3.95769748213950546166537901626409026826595687994956
+ 3 | 7.08607021707716361104064671367526817399129653285580
+ 4 | 10.2223642239960815612515914411615233651316361060338
+ 5 | 13.3611166636685056799674772287389749065996094266976
+*/
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/81799, 2), static_cast<RealType>(3.95769748213950546166537901626409026826595687994956L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(1)/81799, 3), static_cast<RealType>(7.08607021707716361104064671367526817399129653285580L), tolerance * 4);
+
- BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 4), static_cast<RealType>(10.2223258629823064789904339889550588869985272176335L), tolerance * 4);
+ BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 4), static_cast<RealType>(10.2223258629823064789904339889550588869985272176335L), tolerance * 4);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 5), static_cast<RealType>(13.3610782840659145864973521693322670264135672594988L), tolerance * 4);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 6), static_cast<RealType>(16.5009032471619898684110089652474861084220781491575L), tolerance * 4);
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(-static_cast<RealType>(1)/81799, 9), static_cast<RealType>(25.9229384536173175152381652048590136247796591153244L), tolerance * 4);
@@ -672,23 +798,25 @@
BOOST_CHECK_CLOSE_FRACTION(cyl_neumann_zero(static_cast<RealType>(-7) - static_cast<RealType>(1)/3, 1), static_cast<RealType>(7.3352783956690540155848592759652828459644819344081L), tolerance * 1000);
-// I:/boost-trunk/libs/math/test/test_bessel_airy_zeros.cpp(565): error : in "test_main": difference{0.367191} between cyl_neumann_zero(static_cast<RealType>(-7) - static_cast<RealType>(-1)/3, 1){10.0287285} and static_cast<RealType>(7.3352783956690540155848592759652828459644819344081L){7.33527851} exceeds 1.1920929e-007
-
+ // Test Data for airy_ai_zero and airy_bi_zero functions.
- // Test Data for airy_ai
using boost::math::airy_ai_zero; //
using boost::math::isnan;
+ BOOST_CHECK_THROW(airy_ai_zero<RealType>(0), std::domain_error);
+
if (std::numeric_limits<RealType>::has_quiet_NaN)
- { // return NaN.
- BOOST_CHECK(isnan(airy_ai_zero<RealType>(0)) );
- BOOST_CHECK(boost::math::isnan(airy_ai_zero<RealType>(std::numeric_limits<unsigned>::min())) );
+ { // If ignore errors, return NaN.
+ BOOST_CHECK(boost::math::isnan(airy_ai_zero<RealType>(0, ignore_all_policy())));
+ BOOST_CHECK(boost::math::isnan(airy_ai_zero<RealType>(std::numeric_limits<unsigned>::min() , ignore_all_policy())));
+ // Can't abuse with NaN as won't compile.
+ //BOOST_CHECK_THROW(airy_ai_zero<RealType>(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
}
else
{ // real_concept NaN not available, so return zero.
- BOOST_CHECK_EQUAL(airy_ai_zero<RealType>(0), 0);
+ BOOST_CHECK_EQUAL(airy_ai_zero<RealType>(0, ignore_all_policy()), 0);
// BOOST_CHECK_EQUAL(airy_ai_zero<RealType>(-1), 0); // warning C4245: 'argument' : conversion from 'int' to 'unsigned int', signed/unsigned mismatch
}
@@ -701,7 +829,6 @@
// BOOST_CHECK(isnan(airy_bi_zero<RealType>(-1)) );
//}
-
// WolframAlpha Table[N[AiryAiZero[n], 51], {n, 1, 20, 1}]
BOOST_CHECK_CLOSE_FRACTION(airy_ai_zero<RealType>(1), static_cast<RealType>(-2.33810741045976703848919725244673544063854014567239L), tolerance);
@@ -742,15 +869,23 @@
// Test Data for airy_bi
using boost::math::airy_bi_zero;
+ BOOST_CHECK_THROW(airy_bi_zero<RealType>(0), std::domain_error);
+
if (std::numeric_limits<RealType>::has_quiet_NaN)
{ // return NaN.
- BOOST_CHECK(isnan(airy_bi_zero<RealType>(0)) );
- BOOST_CHECK(boost::math::isnan(airy_bi_zero<RealType>(std::numeric_limits<unsigned>::min())) );
+ BOOST_CHECK(boost::math::isnan(airy_bi_zero<RealType>(0, ignore_all_policy())));
+ BOOST_CHECK(boost::math::isnan(airy_bi_zero<RealType>(std::numeric_limits<unsigned>::min() , ignore_all_policy())));
+ // Can't abuse with NaN as won't compile.
+ // BOOST_CHECK_THROW(airy_bi_zero<RealType>(std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
+ // cannot convert parameter 1 from 'boost::math::concepts::real_concept' to 'unsigned int'.
}
else
{ // real_concept NaN not available, so return zero.
- BOOST_CHECK_EQUAL(airy_bi_zero<RealType>(0), 0);
- // BOOST_CHECK_EQUAL(airy_bi_zero<RealType>(-1), 0); // warning C4245: 'argument' : conversion from 'int' to 'unsigned int', signed/unsigned mismatch
+ BOOST_CHECK_EQUAL(airy_bi_zero<RealType>(0, ignore_all_policy()), 0);
+ // BOOST_CHECK_EQUAL(airy_bi_zero<RealType>(-1), 0);
+ // warning C4245: 'argument' : conversion from 'int' to 'unsigned int', signed/unsigned mismatch.
+ // If ignore the warning, interpreted as max unsigned:
+ // check airy_bi_zero<RealType>(-1) == 0 has failed [-7.42678e+006 != 0]
}
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(std::numeric_limits<unsigned>::max()), -7426781.75581678913522, tolerance);
@@ -784,7 +919,6 @@
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(19), static_cast<RealType>(-19.4838801329892340136659986592413575122062977793610L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(20), static_cast<RealType>(-20.1892447853962024202253232258275360764649783583934L), tolerance);
-
// Table[N[AiryBiZero[n], 51], {n, 1000, 1001, 1}]
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1000), static_cast<RealType>(-280.937811203415240157883427412260300146245056425646L), tolerance);
BOOST_CHECK_CLOSE_FRACTION(airy_bi_zero<RealType>(1001), static_cast<RealType>(-281.125212400956392021977771104562061554648675044114L), tolerance);
Boost-Commit list run by bdawes at acm.org, david.abrahams at rcn.com, gregod at cs.rpi.edu, cpdaniel at pacbell.net, john at johnmaddock.co.uk