Class: Distribution::MathExtension::ChebyshevSeries

Inherits:
Object
  • Object
show all
Defined in:
lib/distribution/math_extension/chebyshev_series.rb

Overview

Adapted from GSL-1.9.

Constant Summary collapse

DATA = 
{:lopx => [  2.16647910664395270521272590407,
                   -0.28565398551049742084877469679,
                    0.01517767255690553732382488171,
                   -0.00200215904941415466274422081,
                    0.00019211375164056698287947962,
                   -0.00002553258886105542567601400,
                    2.9004512660400621301999384544e-06,
                   -3.8873813517057343800270917900e-07,
                    4.7743678729400456026672697926e-08,
                   -6.4501969776090319441714445454e-09,
                    8.2751976628812389601561347296e-10,
                   -1.1260499376492049411710290413e-10,
                    1.4844576692270934446023686322e-11,
                   -2.0328515972462118942821556033e-12,
                    2.7291231220549214896095654769e-13,
                   -3.7581977830387938294437434651e-14,
                    5.1107345870861673561462339876e-15,
                   -7.0722150011433276578323272272e-16,
                    9.7089758328248469219003866867e-17,
                   -1.3492637457521938883731579510e-17,
                    1.8657327910677296608121390705e-18  ],
  :lopxmx => [ -1.12100231323744103373737274541,
                0.19553462773379386241549597019,
               -0.01467470453808083971825344956,
                0.00166678250474365477643629067,
               -0.00018543356147700369785746902,
                0.00002280154021771635036301071,
               -2.8031253116633521699214134172e-06,
                3.5936568872522162983669541401e-07,
               -4.6241857041062060284381167925e-08,
                6.0822637459403991012451054971e-09,
               -8.0339824424815790302621320732e-10,
                1.0751718277499375044851551587e-10,
               -1.4445310914224613448759230882e-11,
                1.9573912180610336168921438426e-12,
               -2.6614436796793061741564104510e-13,
                3.6402634315269586532158344584e-14,
               -4.9937495922755006545809120531e-15,
                6.8802890218846809524646902703e-16,
               -9.5034129794804273611403251480e-17,
                1.3170135013050997157326965813e-17],
  :gstar_a => [   2.16786447866463034423060819465,
                 -0.05533249018745584258035832802,
                  0.01800392431460719960888319748,
                 -0.00580919269468937714480019814,
                  0.00186523689488400339978881560,
                 -0.00059746524113955531852595159,
                  0.00019125169907783353925426722,
                 -0.00006124996546944685735909697,
                  0.00001963889633130842586440945,
                 -6.3067741254637180272515795142e-06,
                  2.0288698405861392526872789863e-06,
                 -6.5384896660838465981983750582e-07,
                  2.1108698058908865476480734911e-07,
                 -6.8260714912274941677892994580e-08,
                  2.2108560875880560555583978510e-08,
                 -7.1710331930255456643627187187e-09,
                  2.3290892983985406754602564745e-09,
                 -7.5740371598505586754890405359e-10,
                  2.4658267222594334398525312084e-10,
                 -8.0362243171659883803428749516e-11,
                  2.6215616826341594653521346229e-11,
                 -8.5596155025948750540420068109e-12,
                  2.7970831499487963614315315444e-12,
                 -9.1471771211886202805502562414e-13,
                  2.9934720198063397094916415927e-13,
                 -9.8026575909753445931073620469e-14,
                  3.2116773667767153777571410671e-14,
                 -1.0518035333878147029650507254e-14,
                  3.4144405720185253938994854173e-15,
                 -1.0115153943081187052322643819e-15 ],
    :gstar_b => [ 0.0057502277273114339831606096782,
                  0.0004496689534965685038254147807,
                 -0.0001672763153188717308905047405,
                  0.0000615137014913154794776670946,
                 -0.0000223726551711525016380862195,
                  8.0507405356647954540694800545e-06,
                 -2.8671077107583395569766746448e-06,
                  1.0106727053742747568362254106e-06,
                 -3.5265558477595061262310873482e-07,
                  1.2179216046419401193247254591e-07,
                 -4.1619640180795366971160162267e-08,
                  1.4066283500795206892487241294e-08,
                 -4.6982570380537099016106141654e-09,
                  1.5491248664620612686423108936e-09,
                 -5.0340936319394885789686867772e-10,
                  1.6084448673736032249959475006e-10,
                 -5.0349733196835456497619787559e-11,
                  1.5357154939762136997591808461e-11,
                 -4.5233809655775649997667176224e-12,
                  1.2664429179254447281068538964e-12,
                 -3.2648287937449326771785041692e-13,
                  7.1528272726086133795579071407e-14,
                 -9.4831735252566034505739531258e-15,
                 -2.3124001991413207293120906691e-15,
                  2.8406613277170391482590129474e-15,
                 -1.7245370321618816421281770927e-15,
                  8.6507923128671112154695006592e-16,
                 -3.9506563665427555895391869919e-16,
                  1.6779342132074761078792361165e-16,
                 -6.0483153034414765129837716260e-17 ],
    :e11 => [  -16.11346165557149402600,
                7.79407277874268027690,
               -1.95540581886314195070,
                0.37337293866277945612,
               -0.05692503191092901938,
                0.00721107776966009185,
               -0.00078104901449841593,
                0.00007388093356262168,
               -0.00000620286187580820,
                0.00000046816002303176,
               -0.00000003209288853329,
                0.00000000201519974874,
               -0.00000000011673686816,
                0.00000000000627627066,
               -0.00000000000031481541,
                0.00000000000001479904,
               -0.00000000000000065457,
                0.00000000000000002733,
               -0.00000000000000000108],
    :e12 => [  -0.03739021479220279500,
                 0.04272398606220957700,
                -0.13031820798497005440,
                 0.01441912402469889073,
                -0.00134617078051068022,
                 0.00010731029253063780,
                -0.00000742999951611943,
                 0.00000045377325690753,
                -0.00000002476417211390,
                 0.00000000122076581374,
                -0.00000000005485141480,
                 0.00000000000226362142,
                -0.00000000000008635897,
                 0.00000000000000306291,
                -0.00000000000000010148,
                 0.00000000000000000315 ],
    :ae11 => [   0.121503239716065790,
                -0.065088778513550150,
                 0.004897651357459670,
                -0.000649237843027216,
                 0.000093840434587471,
                 0.000000420236380882,
                -0.000008113374735904,
                 0.000002804247688663,
                 0.000000056487164441,
                -0.000000344809174450,
                 0.000000058209273578,
                 0.000000038711426349,
                -0.000000012453235014,
                -0.000000005118504888,
                 0.000000002148771527,
                 0.000000000868459898,
                -0.000000000343650105,
                -0.000000000179796603,
                 0.000000000047442060,
                 0.000000000040423282,
                -0.000000000003543928,
                -0.000000000008853444,
                -0.000000000000960151,
                 0.000000000001692921,
                 0.000000000000607990,
                -0.000000000000224338,
                -0.000000000000200327,
                -0.000000000000006246,
                 0.000000000000045571,
                 0.000000000000016383,
                -0.000000000000005561,
                -0.000000000000006074,
                -0.000000000000000862,
                 0.000000000000001223,
                 0.000000000000000716,
                -0.000000000000000024,
                -0.000000000000000201,
                -0.000000000000000082,
                 0.000000000000000017],
    :ae12 => [   0.582417495134726740,
                -0.158348850905782750,
                -0.006764275590323141,
                 0.005125843950185725,
                 0.000435232492169391,
                -0.000143613366305483,
                -0.000041801320556301,
                -0.000002713395758640,
                 0.000001151381913647,
                 0.000000420650022012,
                 0.000000066581901391,
                 0.000000000662143777,
                -0.000000002844104870,
                -0.000000000940724197,
                -0.000000000177476602,
                -0.000000000015830222,
                 0.000000000002905732,
                 0.000000000001769356,
                 0.000000000000492735,
                 0.000000000000093709,
                 0.000000000000010707,
                -0.000000000000000537,
                -0.000000000000000716,
                -0.000000000000000244,
                -0.000000000000000058],
    :ae13 => [  -0.605773246640603460,
                -0.112535243483660900,
                 0.013432266247902779,
                -0.001926845187381145,
                 0.000309118337720603,
                -0.000053564132129618,
                 0.000009827812880247,
                -0.000001885368984916,
                 0.000000374943193568,
                -0.000000076823455870,
                 0.000000016143270567,
                -0.000000003466802211,
                 0.000000000758754209,
                -0.000000000168864333,
                 0.000000000038145706,
                -0.000000000008733026,
                 0.000000000002023672,
                -0.000000000000474132,
                 0.000000000000112211,
                -0.000000000000026804,
                 0.000000000000006457,
                -0.000000000000001568,
                 0.000000000000000383,
                -0.000000000000000094,
                 0.000000000000000023],
    :ae14 => [  -0.18929180007530170,
                -0.08648117855259871,
                 0.00722410154374659,
                -0.00080975594575573,
                 0.00010999134432661,
                -0.00001717332998937,
                 0.00000298562751447,
                -0.00000056596491457,
                 0.00000011526808397,
                -0.00000002495030440,
                 0.00000000569232420,
                -0.00000000135995766,
                 0.00000000033846628,
                -0.00000000008737853,
                 0.00000000002331588,
                -0.00000000000641148,
                 0.00000000000181224,
                -0.00000000000052538,
                 0.00000000000015592,
                -0.00000000000004729,
                 0.00000000000001463,
                -0.00000000000000461,
                 0.00000000000000148,
                -0.00000000000000048,
                 0.00000000000000016,
                -0.00000000000000005],
    :erfc_xlt1 => [   1.06073416421769980345174155056,
                     -0.42582445804381043569204735291,
                      0.04955262679620434040357683080,
                      0.00449293488768382749558001242,
                     -0.00129194104658496953494224761,
                     -0.00001836389292149396270416979,
                      0.00002211114704099526291538556,
                     -5.23337485234257134673693179020e-7,
                     -2.78184788833537885382530989578e-7,
                      1.41158092748813114560316684249e-8,
                      2.72571296330561699984539141865e-9,
                     -2.06343904872070629406401492476e-10,
                     -2.14273991996785367924201401812e-11,
                      2.22990255539358204580285098119e-12,
                      1.36250074650698280575807934155e-13,
                     -1.95144010922293091898995913038e-14,
                     -6.85627169231704599442806370690e-16,
                      1.44506492869699938239521607493e-16,
                      2.45935306460536488037576200030e-18,
                     -9.29599561220523396007359328540e-19 ],
    :erfc_x15 => [  0.44045832024338111077637466616,
                   -0.143958836762168335790826895326,
                    0.044786499817939267247056666937,
                   -0.013343124200271211203618353102,
                    0.003824682739750469767692372556,
                   -0.001058699227195126547306482530,
                    0.000283859419210073742736310108,
                   -0.000073906170662206760483959432,
                    0.000018725312521489179015872934,
                   -4.62530981164919445131297264430e-6,
                    1.11558657244432857487884006422e-6,
                   -2.63098662650834130067808832725e-7,
                    6.07462122724551777372119408710e-8,
                   -1.37460865539865444777251011793e-8,
                    3.05157051905475145520096717210e-9,
                   -6.65174789720310713757307724790e-10,
                    1.42483346273207784489792999706e-10,
                   -3.00141127395323902092018744545e-11,
                    6.22171792645348091472914001250e-12,
                   -1.26994639225668496876152836555e-12,
                    2.55385883033257575402681845385e-13,
                   -5.06258237507038698392265499770e-14,
                    9.89705409478327321641264227110e-15,
                   -1.90685978789192181051961024995e-15,
                    3.50826648032737849245113757340e-16 ],
    :erfc_x510 => [ 1.11684990123545698684297865808,
                    0.003736240359381998520654927536,
                   -0.000916623948045470238763619870,
                    0.000199094325044940833965078819,
                   -0.000040276384918650072591781859,
                    7.76515264697061049477127605790e-6,
                   -1.44464794206689070402099225301e-6,
                    2.61311930343463958393485241947e-7,
                   -4.61833026634844152345304095560e-8,
                    8.00253111512943601598732144340e-9,
                   -1.36291114862793031395712122089e-9,
                    2.28570483090160869607683087722e-10,
                   -3.78022521563251805044056974560e-11,
                    6.17253683874528285729910462130e-12,
                   -9.96019290955316888445830597430e-13,
                    1.58953143706980770269506726000e-13,
                   -2.51045971047162509999527428316e-14,
                    3.92607828989125810013581287560e-15,
                   -6.07970619384160374392535453420e-16,
                    9.12600607264794717315507477670e-17  ],
    :sin => [ -0.3295190160663511504173,
               0.0025374284671667991990,
               0.0006261928782647355874,
              -4.6495547521854042157541e-06,
              -5.6917531549379706526677e-07,
               3.7283335140973803627866e-09,
               3.0267376484747473727186e-10,
              -1.7400875016436622322022e-12,
              -1.0554678305790849834462e-13,
               5.3701981409132410797062e-16,
               2.5984137983099020336115e-17,
              -1.1821555255364833468288e-19],
}
PARAMS = 
{
  :lopx => [20, -1, 1, 10],
  :lopxmx => [19, -1, 1, 9],
  :gstar_a => [29, -1, 1, 17],
  :gstar_b => [29, -1, 1, 18],
  :e11 => [18, -1, 1, 13],
  :e12 => [15, -1, 1, 10],
  :ae11 => [38, -1, 1, 20],
  :ae12 => [24, -1, 1, 15],
  :ae13 => [24, -1, 1, 15],
  :ae14 => [25, -1, 1, 13],
  :erfc_xlt1 => [19, -1, 1, 12],
  :erfc_x15 => [24, -1, 1, 16],
  :erfc_x510 => [19, -1, 1, 12],
  :sin => [11, -1, 1, 11]
}

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(coefficients, expansion_order, lower_interval_point, upper_interval_point, single_precision_order) ⇒ ChebyshevSeries

Returns a new instance of ChebyshevSeries.



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 355

def initialize(coefficients, expansion_order, lower_interval_point, upper_interval_point, single_precision_order)
  @c = coefficients.is_a?(Symbol) ? DATA[coefficients] : coefficients
  @order        = expansion_order
  @lower_interval_point = lower_interval_point
  @upper_interval_point = upper_interval_point
  @single_precision_order = single_precision_order
end

Instance Attribute Details

#c ⇒ Object (readonly)

double * c; /* coefficients */ int order; /* order of expansion */ double a; /* lower interval point */ double b; /* upper interval point */ int order_sp; /* effective single precision order */



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 368

def c
  @c
end

#lower_interval_point ⇒ Object (readonly)

double * c; /* coefficients */ int order; /* order of expansion */ double a; /* lower interval point */ double b; /* upper interval point */ int order_sp; /* effective single precision order */



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 368

def lower_interval_point
  @lower_interval_point
end

#order ⇒ Object (readonly)

double * c; /* coefficients */ int order; /* order of expansion */ double a; /* lower interval point */ double b; /* upper interval point */ int order_sp; /* effective single precision order */



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 368

def order
  @order
end

#single_precision_order ⇒ Object (readonly)

double * c; /* coefficients */ int order; /* order of expansion */ double a; /* lower interval point */ double b; /* upper interval point */ int order_sp; /* effective single precision order */



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 368

def single_precision_order
  @single_precision_order
end

#upper_interval_point ⇒ Object (readonly)

double * c; /* coefficients */ int order; /* order of expansion */ double a; /* lower interval point */ double b; /* upper interval point */ int order_sp; /* effective single precision order */



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 368

def upper_interval_point
  @upper_interval_point
end

Class Method Details

.evaluate(series, x, with_error = false) ⇒ Object

cheb_eval_e in specfunc/cheb_eval.c (gsl-1.9)

Raises:

  • (ArgumentError) 


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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 376

def evaluate series, x, with_error = false
  cs = Math.const_get "#{series.to_s.upcase}_CS"
  raise(ArgumentError, "Unrecognized series #{series.to_s}") if cs.nil?

  d  = 0.0
  dd = 0.0
  y  = (2*x - cs.a - cs.b).quo(cs.b - cs.a)
  y2 = 2*y

  e  = 0.0

  cs.order.downto(1) do |j|
    temp = d
    d    = y2*d - dd + cs.c[j]
    e   += (y2*temp).abs + dd.abs + cs.c[j].abs
    dd   = temp
  end

  begin
    temp = d
    d    = y*d - dd + 0.5 * cs.c[0]
    e   += (y*temp).abs + dd.abs + 0.5*cs.c[0].abs
  end

  with_error ? [d, Float::EPSILON*e + (cs.c[cs.order])] : d
end

Instance Method Details

#a ⇒ Object 



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 369

def a; @lower_interval_point; end

#b ⇒ Object 



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 370

def b; @upper_interval_point; end

#coefficients(idx) ⇒ Object 



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 372

def coefficients(idx); @c[idx]; end

#order_sp ⇒ Object 



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# File 'lib/distribution/math_extension/chebyshev_series.rb', line 371

def order_sp; @single_precision_order; end