SphericalBessel.testdata.hpp

#include <vector>
 
namespace UnitTest {
 
struct BesselTestData {
  int k;
  double x;
  double value;
};
 
// Spherical Bessel j_k(x) data from Mathematica
const std::vector<BesselTestData> jk_DATA{
  {0, 1.0 / 1000000, 0.999999999999833},
  {0, 1.0 / 100000, 0.999999999983333},
  {0, 1.0 / 10000, 0.999999998333333},
  {0, 1.0 / 1000, 0.999999833333342},
  {0, 1.0 / 100, 0.999983333416666},
  {0, 1.0 / 10, 0.998334166468282},
  {0, 1, 0.841470984807897},
  {0, 10, -0.0544021110889370},
  {1, 1.0 / 1000000, 3.33333333333300e-7},
  {1, 1.0 / 100000, 3.33333333330000e-6},
  {1, 1.0 / 10000, 0.0000333333333000000},
  {1, 1.0 / 1000, 0.000333333300000001},
  {1, 1.0 / 100, 0.00333330000011905},
  {1, 1.0 / 10, 0.0333000119025576},
  {1, 1, 0.301168678939757},
  {1, 10, 0.0784669417987515},
  {2, 1.0 / 1000000, 6.66666666666619e-14},
  {2, 1.0 / 100000, 6.66666666661905e-12},
  {2, 1.0 / 10000, 6.66666666190476e-10},
  {2, 1.0 / 1000, 6.66666619047620e-8},
  {2, 1.0 / 100, 6.66661904775132e-6},
  {2, 1.0 / 10, 0.000666190608445569},
  {2, 1, 0.0620350520113739},
  {2, 10, 0.0779421936285624},
  {3, 1.0 / 1000000, 9.52380952380899e-21},
  {3, 1.0 / 100000, 9.52380952375661e-18},
  {3, 1.0 / 10000, 9.52380951851852e-15},
  {3, 1.0 / 1000, 9.52380899470901e-12},
  {3, 1.0 / 100, 9.52375661387686e-9},
  {3, 1.0 / 10, 9.51851972086557e-6},
  {3, 1, 0.00900658111711252},
  {3, 10, -0.0394958449844703},
  {4, 1.0 / 1000000, 1.05820105820101e-27},
  {4, 1.0 / 100000, 1.05820105819625e-23},
  {4, 1.0 / 10000, 1.05820105772006e-19},
  {4, 1.0 / 1000, 1.05820101010101e-15},
  {4, 1.0 / 100, 1.05819624820550e-11},
  {4, 1.0 / 10, 1.05772015020987e-7},
  {4, 1, 0.00101101580841375},
  {4, 10, -0.105589285117692},
  {5, 1.0 / 1000000, 9.62000962000925e-35},
  {5, 1.0 / 100000, 9.62000961997262e-30},
  {5, 1.0 / 10000, 9.62000961630962e-25},
  {5, 1.0 / 1000, 9.62000925000926e-20},
  {5, 1.0 / 100, 9.61997262003429e-15},
  {5, 1.0 / 10, 9.61631023291645e-10},
  {5, 1, 0.0000925611586112582},
  {5, 10, -0.0555345116214522},
  {6, 1.0 / 1000000, 7.40000740000715e-42},
  {6, 1.0 / 100000, 7.40000739998273e-36},
  {6, 1.0 / 10000, 7.40000739754073e-30},
  {6, 1.0 / 1000, 7.40000715334049e-24},
  {6, 1.0 / 100, 7.39998273335234e-18},
  {6, 1.0 / 10, 7.39754109358771e-12},
  {6, 1, 7.15693631008709e-6},
  {6, 10, 0.0445013223340943},
  {7, 1.0 / 1000000, 4.93333826667145e-49},
  {7, 1.0 / 100000, 4.93333826665709e-42},
  {7, 1.0 / 10000, 4.93333826522062e-35},
  {7, 1.0 / 1000, 4.93333812157342e-28},
  {7, 1.0 / 100, 4.93332375687226e-21},
  {7, 1.0 / 10, 4.93188747573197e-14},
  {7, 1, 4.79013419873949e-7},
  {7, 10, 0.113386230655775},
  {8, 1.0 / 1000000, 2.90196368627734e-56},
  {8, 1.0 / 100000, 2.90196368626978e-48},
  {8, 1.0 / 10000, 2.90196368551374e-40},
  {8, 1.0 / 1000, 2.90196360990995e-32},
  {8, 1.0 / 100, 2.90195604953996e-24},
  {8, 1.0 / 10, 2.90120010253019e-16},
  {8, 1, 2.82649880221473e-8},
  {8, 10, 0.125578023649568},
  {9, 1.0 / 1000000, 1.52734930856702e-63},
  {9, 1.0 / 100000, 1.52734930856342e-54},
  {9, 1.0 / 10000, 1.52734930820340e-45},
  {9, 1.0 / 1000, 1.52734927220160e-36},
  {9, 1.0 / 100, 1.52734567202504e-27},
  {9, 1.0 / 10, 1.52698569349482e-18},
  {9, 1, 1.49137650255515e-9},
  {9, 10, 0.100096409548491},
  {10, 1.0 / 1000000, 7.27309194555726e-71},
  {10, 1.0 / 100000, 7.27309194554161e-61},
  {10, 1.0 / 10000, 7.27309194397632e-51},
  {10, 1.0 / 1000, 7.27309178744673e-41},
  {10, 1.0 / 100, 7.27307613450379e-31},
  {10, 1.0 / 10, 7.27151099671367e-21},
  {10, 1, 7.11655264004731e-11},
  {10, 10, 0.0646051544925643}};
 
// phi^tilde = (1-phi) , where phi(x) = [(2k+1)!! / x^k ] * j_k(x)
const std::vector<BesselTestData> PhikTilde_DATA{
  {0, 1.0 / 1000000, 1.66666666666658e-13},
  {0, 1.0 / 100000, 1.66666666665833e-11},
  {0, 1.0 / 10000, 1.66666666583333e-9},
  {0, 1.0 / 1000, 1.66666658333334e-7},
  {0, 1.0 / 100, 0.0000166665833335317},
  {0, 1.0 / 10, 0.00166583353171848},
  {0, 1, 0.158529015192103},
  {0, 10, 1.05440211108894},
  {1, 1.0 / 1000000, 9.99999999999964e-14},
  {1, 1.0 / 100000, 9.99999999996429e-12},
  {1, 1.0 / 10000, 9.99999999642857e-10},
  {1, 1.0 / 1000, 9.99999964285715e-8},
  {1, 1.0 / 100, 9.99996428578042e-6},
  {1, 1.0 / 10, 0.000999642923272908},
  {1, 1, 0.0964939631807296},
  {1, 10, 0.976459917460375},
  {2, 1.0 / 1000000, 7.14285714285694e-14},
  {2, 1.0 / 100000, 7.14285714283730e-12},
  {2, 1.0 / 10000, 7.14285714087302e-10},
  {2, 1.0 / 1000, 7.14285694444445e-8},
  {2, 1.0 / 100, 7.14283730161736e-6},
  {2, 1.0 / 10, 0.000714087331646941},
  {2, 1, 0.0694742198293921},
  {2, 10, 0.988308670955716},
  {3, 1.0 / 1000000, 5.55555555555543e-14},
  {3, 1.0 / 100000, 5.55555555554293e-12},
  {3, 1.0 / 10000, 5.55555555429293e-10},
  {3, 1.0 / 1000, 5.55555542929293e-8},
  {3, 1.0 / 100, 5.55554292930912e-6},
  {3, 1.0 / 10, 0.000555429309115460},
  {3, 1, 0.0543089827031858},
  {3, 10, 1.00414706372337},
  {4, 1.0 / 1000000, 4.54545454545446e-14},
  {4, 1.0 / 100000, 4.54545454544580e-12},
  {4, 1.0 / 10000, 4.54545454458042e-10},
  {4, 1.0 / 1000, 4.54545445804196e-8},
  {4, 1.0 / 100, 4.54544580420552e-6},
  {4, 1.0 / 10, 0.000454458051669838},
  {4, 1, 0.0445900610490037},
  {4, 10, 1.00997818744362},
  {5, 1.0 / 1000000, 3.84615384615378e-14},
  {5, 1.0 / 100000, 3.84615384614744e-12},
  {5, 1.0 / 10000, 3.84615384551282e-10},
  {5, 1.0 / 1000, 3.84615378205128e-8},
  {5, 1.0 / 100, 3.84614743590372e-6},
  {5, 1.0 / 10, 0.000384551288335434},
  {5, 1, 0.0378267562359714},
  {5, 10, 1.00577281248305},
  {6, 1.0 / 1000000, 3.33333333333328e-14},
  {6, 1.0 / 100000, 3.33333333332843e-12},
  {6, 1.0 / 10000, 3.33333333284314e-10},
  {6, 1.0 / 1000, 3.33333328431373e-8},
  {6, 1.0 / 100, 3.33332843137685e-6},
  {6, 1.0 / 10, 0.000333284318025200},
  {6, 1, 0.0328474117363817},
  {6, 10, 0.993986313806382},
  {7, 1.0 / 1000000, 2.94117647058820e-14},
  {7, 1.0 / 100000, 2.94117647058437e-12},
  {7, 1.0 / 10000, 2.94117647020124e-10},
  {7, 1.0 / 1000, 2.94117643188855e-8},
  {7, 1.0 / 100, 2.94117260062227e-6},
  {7, 1.0 / 10, 0.000294078950439658},
  {7, 1, 0.0290278225800088},
  {7, 10, 0.977016327580498},
  {8, 1.0 / 1000000, 2.63157894736839e-14},
  {8, 1.0 / 100000, 2.63157894736529e-12},
  {8, 1.0 / 10000, 2.63157894705514e-10},
  {8, 1.0 / 1000, 2.63157891604010e-8},
  {8, 1.0 / 100, 2.63157581453861e-6},
  {8, 1.0 / 10, 0.000263126568686095},
  {8, 1, 0.0260047651249170},
  {8, 10, 0.956726535123995},
  {9, 1.0 / 1000000, 2.38095238095236e-14},
  {9, 1.0 / 100000, 2.38095238094979e-12},
  {9, 1.0 / 10000, 2.38095238069358e-10},
  {9, 1.0 / 1000, 2.38095235507246e-8},
  {9, 1.0 / 100, 2.38094979296239e-6},
  {9, 1.0 / 10, 0.000238069359903302},
  {9, 1, 0.0235524420053343},
  {9, 10, 0.934463970365496},
  {10, 1.0 / 1000000, 2.17391304347824e-14},
  {10, 1.0 / 100000, 2.17391304347609e-12},
  {10, 1.0 / 10000, 2.17391304326087e-10},
  {10, 1.0 / 1000, 2.17391302173913e-8},
  {10, 1.0 / 100, 2.17391086956656e-6},
  {10, 1.0 / 10, 0.000217369566559255},
  {10, 1, 0.0215230752865331},
  {10, 10, 0.911172366613588}};
 
// Spherical Bessel (2nd kind) y_k(x) data from Mathematica
const std::vector<BesselTestData> yk_DATA{
  {0, 1.0 / 1000000, -999999.999999500},
  {0, 1.0 / 100000, -99999.9999950000},
  {0, 1.0 / 10000, -9999.99995000000},
  {0, 1.0 / 1000, -999.999500000042},
  {0, 1.0 / 100, -99.9950000416665},
  {0, 1.0 / 10, -9.95004165278026},
  {0, 1, -0.540302305868140},
  {0, 10, 0.0839071529076452},
  {1, 1.0 / 1000000, -1.00000000000050e12},
  {1, 1.0 / 100000, -1.00000000005000e10},
  {1, 1.0 / 10000, -1.00000000500000e8},
  {1, 1.0 / 1000, -1.00000049999988e6},
  {1, 1.0 / 100, -10000.4999875001},
  {1, 1.0 / 10, -100.498750694271},
  {1, 1, -1.38177329067604},
  {1, 10, 0.0627928263797015},
  {2, 1.0 / 1000000, -3.00000000000050e18},
  {2, 1.0 / 100000, -3.00000000005000e15},
  {2, 1.0 / 10000, -3.00000000500000e12},
  {2, 1.0 / 1000, -3.00000050000012e9},
  {2, 1.0 / 100, -3.00005000124998e6},
  {2, 1.0 / 10, -3005.01247917535},
  {2, 1, -3.60501756615997},
  {2, 10, -0.0650693049937348},
  {3, 1.0 / 1000000, -1.50000000000015e25},
  {3, 1.0 / 100000, -1.50000000001500e21},
  {3, 1.0 / 10000, -1.50000000150000e17},
  {3, 1.0 / 1000, -1.50000015000001e13},
  {3, 1.0 / 100, -1.50001500012500e9},
  {3, 1.0 / 10, -150150.125208073},
  {3, 1, -16.6433145401238},
  {3, 10, -0.0953274788765689},
  {4, 1.0 / 1000000, -1.05000000000008e32},
  {4, 1.0 / 100000, -1.05000000000750e27},
  {4, 1.0 / 10000, -1.05000000075000e22},
  {4, 1.0 / 1000, -1.05000007500000e17},
  {4, 1.0 / 100, -1.05000750003750e12},
  {4, 1.0 / 10, -1.05075037520859e7},
  {4, 1, -112.898184214707},
  {4, 10, -0.00165993021986344},
  {5, 1.0 / 1000000, -9.45000000000053e38},
  {5, 1.0 / 100000, -9.45000000005250e32},
  {5, 1.0 / 10000, -9.45000000525000e26},
  {5, 1.0 / 1000, -9.45000052500002e20},
  {5, 1.0 / 100, -9.45005250018750e14},
  {5, 1.0 / 10, -9.45525187562526e8},
  {5, 1, -999.440343392236},
  {5, 10, 0.0938335416786918},
  {6, 1.0 / 1000000, -1.03950000000005e46},
  {6, 1.0 / 100000, -1.03950000000473e39},
  {6, 1.0 / 10000, -1.03950000047250e32},
  {6, 1.0 / 1000, -1.03950004725000e25},
  {6, 1.0 / 100, -1.03950472501313e18},
  {6, 1.0 / 10, -1.03997263128126e11},
  {6, 1, -10880.9455930999},
  {6, 10, 0.104876826066424},
  {7, 1.0 / 1000000, -1.35135000000005e53},
  {7, 1.0 / 100000, -1.35135000000520e45},
  {7, 1.0 / 10000, -1.35135000051975e37},
  {7, 1.0 / 1000, -1.35135005197500e29},
  {7, 1.0 / 100, -1.35135519751181e21},
  {7, 1.0 / 10, -1.35186986814688e13},
  {7, 1, -140452.852366906},
  {7, 10, 0.0425063322076599},
  {8, 1.0 / 1000000, -2.02702500000007e60},
  {8, 1.0 / 100000, -2.02702500000676e51},
  {8, 1.0 / 10000, -2.02702500067568e42},
  {8, 1.0 / 1000, -2.02702506756750e33},
  {8, 1.0 / 100, -2.02703175676299e24},
  {8, 1.0 / 10, -2.02770080495719e15},
  {8, 1, -2.09591183991050e6},
  {8, 10, -0.0411173277549345},
  {9, 1.0 / 1000000, -3.44594250000010e67},
  {9, 1.0 / 100000, -3.44594250001014e57},
  {9, 1.0 / 10000, -3.44594250101351e47},
  {9, 1.0 / 1000, -3.44594260135125e37},
  {9, 1.0 / 100, -3.44595263514189e27},
  {9, 1.0 / 10, -3.44695618144041e17},
  {9, 1, -3.54900484261115e7},
  {9, 10, -0.112405789391049},
  {10, 1.0 / 1000000, -6.54729075000017e74},
  {10, 1.0 / 100000, -6.54729075001723e63},
  {10, 1.0 / 10000, -6.54729075172297e52},
  {10, 1.0 / 1000, -6.54729092229713e41},
  {10, 1.0 / 100, -6.54730797973784e30},
  {10, 1.0 / 10, -6.54901397465628e19},
  {10, 1, -6.72215008256208e8},
  {10, 10, -0.172453672088058}};
 
// psi^tilde = (1-psi) , where psi(x) = [ x^{k+1} / (2k-1)!! ] * y_k(x)
const std::vector<BesselTestData> PsikTilde_DATA{
  {0, 1.0 / 1000000, 4.99999999999958e-13},
  {0, 1.0 / 100000, 4.99999999995833e-11},
  {0, 1.0 / 10000, 4.99999999583333e-9},
  {0, 1.0 / 1000, 4.99999958333335e-7},
  {0, 1.0 / 100, 0.0000499995833347222},
  {0, 1.0 / 10, 0.00499583472197423},
  {0, 1, 0.459697694131860},
  {0, 10, 1.83907152907645},
  {1, 1.0 / 1000000, -4.99999999999875e-13},
  {1, 1.0 / 100000, -4.99999999987500e-11},
  {1, 1.0 / 10000, -4.99999998750000e-9},
  {1, 1.0 / 1000, -4.99999875000007e-7},
  {1, 1.0 / 100, -0.0000499987500069444},
  {1, 1.0 / 10, -0.00498750694270858},
  {1, 1, -0.381773290676036},
  {1, 10, 7.27928263797015},
  {2, 1.0 / 1000000, -1.66666666666708e-13},
  {2, 1.0 / 100000, -1.66666666670833e-11},
  {2, 1.0 / 10000, -1.66666667083333e-9},
  {2, 1.0 / 1000, -1.66666708333326e-7},
  {2, 1.0 / 100, -0.0000166670833263889},
  {2, 1.0 / 10, -0.00167082639178183},
  {2, 1, -0.201672522053323},
  {2, 10, -20.6897683312449},
  {3, 1.0 / 1000000, -1.00000000000008e-13},
  {3, 1.0 / 100000, -1.00000000000833e-11},
  {3, 1.0 / 10000, -1.00000000083333e-9},
  {3, 1.0 / 1000, -1.00000008333335e-7},
  {3, 1.0 / 100, -0.0000100000833347222},
  {3, 1.0 / 10, -0.00100083472048669},
  {3, 1, -0.109554302674921},
  {3, 10, -62.5516525843793},
  {4, 1.0 / 1000000, -7.14285714285750e-14},
  {4, 1.0 / 100000, -7.14285714289286e-12},
  {4, 1.0 / 10000, -7.14285714642857e-10},
  {4, 1.0 / 1000, -7.14285750000002e-8},
  {4, 1.0 / 100, -7.14289285734127e-6},
  {4, 1.0 / 10, -0.000714643055803323},
  {4, 1, -0.0752208020448256},
  {4, 10, -0.580885923679465},
  {5, 1.0 / 1000000, -5.55555555555575e-14},
  {5, 1.0 / 100000, -5.55555555557540e-12},
  {5, 1.0 / 10000, -5.55555555753968e-10},
  {5, 1.0 / 1000, -5.55555575396826e-8},
  {5, 1.0 / 100, -5.55557539689153e-6},
  {5, 1.0 / 10, -0.000555754034419119},
  {5, 1, -0.0576088289864936},
  {5, 10, 100.294753099145},
  {6, 1.0 / 1000000, -4.54545454545467e-14},
  {6, 1.0 / 100000, -4.54545454546717e-12},
  {6, 1.0 / 10000, -4.54545454671717e-10},
  {6, 1.0 / 1000, -4.54545467171717e-8},
  {6, 1.0 / 100, -4.54546717174723e-6},
  {6, 1.0 / 10, -0.000454671747241765},
  {6, 1, -0.0467480128042226},
  {6, 10, 101.891607567508},
  {7, 1.0 / 1000000, -3.84615384615393e-14},
  {7, 1.0 / 100000, -3.84615384616259e-12},
  {7, 1.0 / 10000, -3.84615384702797e-10},
  {7, 1.0 / 1000, -3.84615393356644e-8},
  {7, 1.0 / 100, -3.84616258742877e-6},
  {7, 1.0 / 10, -0.000384702813393205},
  {7, 1, -0.0393521468672541},
  {7, 10, 32.4547172883856},
  {8, 1.0 / 1000000, -3.33333333333340e-14},
  {8, 1.0 / 100000, -3.33333333333974e-12},
  {8, 1.0 / 10000, -3.33333333397436e-10},
  {8, 1.0 / 1000, -3.33333339743590e-8},
  {8, 1.0 / 100, -3.33333974359946e-6},
  {8, 1.0 / 10, -0.000333397445611295},
  {8, 1, -0.0339842083400530},
  {8, 10, -19.2845686436697},
  {9, 1.0 / 1000000, -2.94117647058828e-14},
  {9, 1.0 / 100000, -2.94117647059314e-12},
  {9, 1.0 / 10000, -2.94117647107843e-10},
  {9, 1.0 / 1000, -2.94117651960784e-8},
  {9, 1.0 / 100, -2.94118137255530e-6},
  {9, 1.0 / 10, -0.000294166672951946},
  {9, 1, -0.0299083175680245},
  {9, 10, -31.6197518940170},
  {10, 1.0 / 1000000, -2.63157894736846e-14},
  {10, 1.0 / 100000, -2.63157894737229e-12},
  {10, 1.0 / 10000, -2.63157894775542e-10},
  {10, 1.0 / 1000, -2.63157898606811e-8},
  {10, 1.0 / 100, -2.63158281734176e-6},
  {10, 1.0 / 10, -0.000263196598727624},
  {10, 1, -0.0267071280685197},
  {10, 10, -25.3396996823545}};
 
} // namespace UnitTest