Extensions

IncreasePrecisionExt

This extension allows increasing the precision of tabulated embedded cubature. To use this extension you must add the package ForwardDiff.

using HAdaptiveIntegration
using ForwardDiff

For example if we want to increase the precision of the rule HAdaptiveIntegration.SQUARE_CH21, we do:

tec0 = HAdaptiveIntegration.SQUARE_CH21
tec0.nodes

21-element Vector{Vector{String}}:
 ["5.000000000000000000000000000000000000e-01", "5.000000000000000000000000000000000000e-01"]
 ["9.530899229693320005789205883895798105e-01", "5.000000000000000000000000000000000000e-01"]
 ["5.000000000000000000000000000000000000e-01", "9.530899229693320005789205883895798105e-01"]
 ["4.691007703066799942107941161042018947e-02", "5.000000000000000000000000000000000000e-01"]
 ["5.000000000000000000000000000000000000e-01", "4.691007703066799942107941161042018947e-02"]
 ["7.692346550528415200375282027103137048e-01", "7.692346550528415200375282027103137048e-01"]
 ["2.307653449471584799624717972896862952e-01", "7.692346550528415200375282027103137048e-01"]
 ["7.692346550528415200375282027103137048e-01", "2.307653449471584799624717972896862952e-01"]
 ["2.307653449471584799624717972896862952e-01", "2.307653449471584799624717972896862952e-01"]
 ["9.530899229693319571124065987079251159e-01", "9.530899229693319571124065987079251159e-01"]
 ⋮
 ["4.691007703066804288759340129207488409e-02", "4.691007703066804288759340129207488409e-02"]
 ["9.530899229693320081691800769275475942e-01", "7.692346550528415524068181972304942518e-01"]
 ["7.692346550528415524068181972304942518e-01", "9.530899229693320081691800769275475942e-01"]
 ["4.691007703066799183081992307245240580e-02", "7.692346550528415524068181972304942518e-01"]
 ["7.692346550528415524068181972304942518e-01", "4.691007703066799183081992307245240580e-02"]
 ["9.530899229693320081691800769275475942e-01", "2.307653449471584475931818027695057482e-01"]
 ["2.307653449471584475931818027695057482e-01", "9.530899229693320081691800769275475942e-01"]
 ["4.691007703066799183081992307245240580e-02", "2.307653449471584475931818027695057482e-01"]
 ["2.307653449471584475931818027695057482e-01", "4.691007703066799183081992307245240580e-02"]

tec1 = HAdaptiveIntegration.increase_precision(
    tec0, BigFloat; x_atol=big"1e-64", f_atol=big"1e-64"
)

[ Info: Increasing to target precision 64 from tabulated precision 35. This may take some time.
[ Info: iter   1: |xₙ - xₙ₋₁| = 3.96e-38, |f(xₙ)| = 1.16e-37
[ Info: iter   2: |xₙ - xₙ₋₁| = 6.73e-74, |f(xₙ)| = 2.26e-75
┌ Info: Newton convergence report:
│ 
│       iteration = 2 / 16
│     |xₙ - xₙ₋₁ | = 6.73e-74 ≤ 1.00e-64
└         |f(xₙ)| = 2.26e-75 ≤ 1.00e-64

tec1.nodes

21-element Vector{Vector{String}}:
 ["0.4999999999999999999999999999999999999982213851754709631884816406137113604246799", "0.4999999999999999999999999999999999999982213851754709631884816406137113604125072"]
 ["0.9530899229693320005789205883895798105223193134839831874164781263671271860711774", "0.4999999999999999999999999999999999999998459567123802915150035977327656154833857"]
 ["0.4999999999999999999999999999999999999998459567123802915150035977327656154694081", "0.9530899229693320005789205883895798105223193134839831874164781263671271861017235"]
 ["0.04691007703066799942107941161042018947733281333972961108762555909031749163802912", "0.4999999999999999999999999999999999999998459567123802915150035977327656154812439"]
 ["0.4999999999999999999999999999999999999998459567123802915150035977327656154693994", "0.04691007703066799942107941161042018947733281333972961108762555909031749166454486"]
 ["0.7692346550528415200375282027103137047931600686128846368644846829910603597064122", "0.7692346550528415200375282027103137047931600686128846368644846829910603597487639"]
 ["0.2307653449471584799624717972896862952049935849822725131053815342287701087238417", "0.769234655052841520037528202710313704794401227675805002754709965445986107609818"]
 ["0.7692346550528415200375282027103137047944012276758050027547099654459861076128321", "0.2307653449471584799624717972896862952049935849822725131053815342287701087101274"]
 ["0.2307653449471584799624717972896862952037524259193521472151562517738443608163941", "0.2307653449471584799624717972896862952037524259193521472151562517738443608553626"]
 ["0.9530899229693319571124065987079251159160657333910708523579591058987239102509191", "0.9530899229693319571124065987079251159160657333910708523579591058987239102386989"]
 ⋮
 ["0.04691007703066804288759340129207488408174916973089781735697912697081010531155385", "0.04691007703066804288759340129207488408174916973089781735697912697081010529524931"]
 ["0.9530899229693320081691800769275475941988675518635660699264550005155568815047789", "0.7692346550528415524068181972304942517999779453859381711369011772988930236526333"]
 ["0.7692346550528415524068181972304942517999779453859381711369011772988930236412594", "0.9530899229693320081691800769275475941988675518635660699264550005155568815529688"]
 ["0.04691007703066799183081992307245240580187761997364183391392548231637123942923074", "0.7692346550528415524068181972304942518001124903388710857150939722637942882597455"]
 ["0.7692346550528415524068181972304942518001124903388710857150939722637942881967015", "0.04691007703066799183081992307245240580187761997364183391392548231637123941484342"]
 ["0.95308992296933200816918007692754759419770207371160535296421219029425547823963", "0.2307653449471584475931818027695057482013229298900554866362689789172706768402058"]
 ["0.230765344947158447593181802769505748201322929890055486636268978917270676785405", "0.9530899229693320081691800769275475941977020737116053529642121902942554781883916"]
 ["0.04691007703066799183081992307245240580304309812560255087616829253767264269419991", "0.2307653449471584475931818027695057482011883849371225720580761839523694122342314"]
 ["0.2307653449471584475931818027695057482011883849371225720580761839523694122298356", "0.0469100770306679918308199230724524058030430981256025508761682925376726427769954"]