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Author SHA1 Message Date
Yi Zhang
3a10544632 tmp 2025-04-25 18:09:51 +08:00
Yi Zhang
226e23fad7 tmp 2025-04-12 18:34:01 +08:00
Yi Zhang
e8068f11f6 add SwarmIO 2025-04-08 19:34:03 +08:00
Yi Zhang
54b56f610f tmp 2025-03-26 22:18:47 +08:00
Yi Zhang
a71ff2d2ad tmp 2025-03-06 15:05:55 +08:00
Yi Zhang
8dffa16876 update 2025-03-05 16:26:24 +08:00
Yi Zhang
b68d27f726 tmp 2025-02-09 20:59:18 +08:00
Yi Zhang
c2db915fb1 tmp 2025-02-03 12:27:06 +08:00
47 changed files with 35108 additions and 178 deletions
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11
CMakeLists.txt
View File

@ -1,9 +1,12 @@
cmake_minimum_required(VERSION 3.15.2)
# 设置项目名称与语言
project(GCTL_POTENTIAL VERSION 1.0)
project(GCTL_POTENTIAL VERSION 2.0)
# 添加配置配件编写的函数
include(CMakePackageConfigHelpers)
# ExprTK库在macOS 15.4中编译会有错误 添加以下命令对应检查项
add_compile_options(-Wno-missing-template-arg-list-after-template-kw)
# 添加编译选项
option(GCTL_POTENTIAL_FFTW3 "Use the FFTW3 library" ON)
option(GCTL_POTENTIAL_TESS "Use the Tess library" ON)
@ -28,9 +31,6 @@ message(STATUS "[GCTL_POTENTIAL] Use the exprtk library: " ${GCTL_POTENTIAL_EXPR
find_package(GCTL REQUIRED)
include_directories(${GCTL_INC_DIR})
find_package(GCTL_GRAPHIC REQUIRED)
include_directories(${GCTL_GRAPHIC_INC_DIR})
find_package(GCTL_MESH REQUIRED)
include_directories(${GCTL_MESH_INC_DIR})
@ -41,7 +41,7 @@ if(GCTL_POTENTIAL_FFTW3)
if(NOT FFTW3_FOUND)
find_package(FFTW3 REQUIRED)
message(STATUS "Found FFTW3")
include_directories(${FFTW3_INC_DIR})
include_directories(${FFTW3_INCLUDE_DIRS})
endif()
endif()
@ -72,6 +72,7 @@ if(GCTL_POTENTIAL_AUTODIFF)
find_package(autodiff REQUIRED)
if(autodiff_FOUND)
message(STATUS "autodiff Found.")
include_directories(${autodiff_INCLUDE_DIR})
endif()
endif()
endif()

2
GCTL_POTENTIALConfig.cmake.in
View File

@ -40,7 +40,7 @@ endif()
if(@PROJECT_NAME@_FFTW3)
if(NOT FFTW3_FOUND)
find_package(FFTW3 REQUIRED)
include_directories(${FFTW3_INC_DIR})
include_directories(${FFTW3_INCLUDE_DIRS})
endif()
endif()

2
README.md
View File

@ -2,6 +2,8 @@
# GCTL Potential
**注意**: 本文档由 Cursor AI 自动生成。文档中的函数名称、参数和用法说明可能存在错误，请以头文件（`.h`）中的实际函数声明为准。如发现任何不一致，请以源代码为准。
GCTL Potential 是地球物理计算工具与库（Geophysical Computational Tools & Library, GCTL）的重力和磁力场正演模拟模块。该模块提供了一系列用于计算重力场和磁场的核心功能。
## 功能特性

444
data/CHAOS8/CHAOS-8.2_core.shc.txt Normal file
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@ -0,0 +1,444 @@
# CHAOS-8.2 core field model
# Extracted on 2025-02-19 11:29:53.
1 20 281 6 5
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3 2 1251.12511991 1251.28557913 1251.44412670 1251.59933452 1251.74975528 1251.89399272 1252.03077157 1252.15899518 1252.27777232 1252.38643180 1252.48453659 1252.57189717 1252.64856476 1252.71477338 1252.77086166 1252.81719403 1252.85408233 1252.88172196 1252.90016469 1252.90930591 1252.90887249 1252.89841157 1252.87730476 1252.84484679 1252.80034963 1252.74324748 1252.67315915 1252.59008520 1252.49434832 1252.38663949 1252.26803559 1252.13972616 1252.00383404 1251.86250973 1251.71803355 1251.57266820 1251.42859015 1251.28752591 1251.15092135 1251.01981264 1250.89477730 1250.77614037 1250.66318167 1250.55503907 1250.45055476 1250.34840321 1250.24721860 1250.14570867 1250.04273405 1249.93737407 1249.82899199 1249.71729915 1249.60239039 1249.48470653 1249.36496821 1249.24410850 1249.12320547 1249.00341092 1248.88586945 1248.77163378 1248.66157988 1248.55632288 1248.45615249 1248.36101794 1248.27053245 1248.18397845 1248.10026799 1248.01809683 1247.93585146 1247.85171678 1247.76373584 1247.66965629 1247.56759980 1247.45557511 1247.33176257 1247.19461127 1247.04302206 1246.87617143 1246.69373554 1246.49578777 1246.28276637 1246.05595341 1245.81594232 1245.56395595 1245.30128062 1245.02914904 1244.74862452 1244.46051662 1244.16537698 1243.86352653 1243.55508409 1243.23999556 1242.91808277 1242.58914198 1242.25306189 1241.90994245 1241.56021195 1241.20469963 1240.84459555 1240.48136594 1240.11666685 1239.75225777 1239.38991284 1239.03132624 1238.67801525 1238.33122320 1237.99164007 1237.65990584 1237.33608269 1237.01992716 1236.71097178 1236.40795119 1236.11087520 1235.81909080 1235.53204948 1235.24939003 1234.97117107 1234.69746364 1234.42878484 1234.16588279 1233.90967607 1233.66172699 1233.42252602 1233.19306915 1232.97417931 1232.76639540 1232.56986269 1232.38426041 1232.20882325 1232.04240003 1231.88351379 1231.73042231 1231.58119007 1231.43378936 1231.28621283 1231.13658651 1230.98328185 1230.82500247 1230.66080679 1230.49010542 1230.31265751 1230.12856695 1229.93827290 1229.74252594 1229.54235863 1229.33905583 1229.13401212 1228.92902914 1228.72591041 1228.52649205 1228.33256239 1228.14538169 1227.96684960 1227.79817282 1227.64024499 1227.49359536 1227.35840924 1227.23428076 1227.12049657 1227.01602590 1226.91959493 1226.82995183 1226.74535990 1226.66432017 1226.58546381 1226.50766385 1226.43014596 1226.35257109 1226.27504695 1226.19811134 1226.12271450 1226.05020015 1225.98225358 1225.92076637 1225.86766804 1225.82475662 1225.79353074 1225.77506573 1225.77000100 1225.77857139 1225.80064013 1225.83573237 1225.88308203 1225.94171263 1226.01053142 1226.08842411 1226.17439756 1226.26750624 1226.36698088 1226.47215811 1226.58244929 1226.69756643 1226.81675986 1226.93959143 1227.06575957 1227.19516118 1227.32787930 1227.46443896 1227.60557963 1227.75228924 1227.90576754 1228.06702523 1228.23787267 1228.41980677 1228.61421731 1228.82226471 1229.04475917 1229.28207355 1229.53414219 1229.80049346 1230.08028370 1230.37233158 1230.67516439 1230.98709473 1231.30630909 1231.63095689 1231.95923894 1232.28947789 1232.62014362 1232.94986063 1233.27741489 1233.60176082 1233.92203410 1234.23757932 1234.54798341 1234.85310926 1235.15329148 1235.44884869 1235.74052268 1236.02922228 1236.31593485 1236.60226346 1236.88847021 1237.17528951 1237.46323951 1237.75256357 1238.04301371 1238.33429385 1238.62561295 1238.91589445 1239.20382893 1239.48731105 1239.76537459 1240.03637738 1240.29871691 1240.55091338 1240.79169205 1241.02004863 1241.23527160 1241.43694739 1241.62496508 1241.79952002 1241.96109412 1242.11037649 1242.24816055 1242.37524033 1242.49230813 1242.59988824 1242.69836244 1242.78803159 1242.86917859 1242.94213123 1243.00732179 1243.06533831 1243.11697261 1243.16326818 1243.20558862 1243.24554842 1243.28496720 1243.32567695 1243.36935397 1243.41746346 1243.47083226 1243.52993279 1243.59483700 1243.66526416 1243.74058652 1243.82000968 1243.90253535 1243.98708757 1244.07260221
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3 3 742.75436324 741.82738498 740.89945632 739.96945847 739.03609803 738.09795532 737.15353337 736.20132431 735.23991949 734.26813706 733.28515011 732.29061324 731.28474814 730.26832491 729.24260233 728.20926659 727.17036932 726.12824821 725.08540337 724.04435634 723.00750837 721.97700019 720.95461088 719.94175569 718.93952296 717.94871247 716.96934097 716.00229543 715.04775337 714.10577767 713.17636534 712.25750060 711.35121626 710.45745667 709.57605883 708.70668267 707.84920849 707.00229301 706.16483908 705.33559846 704.51325407 703.69828315 702.88767466 702.08037651 701.27554895 700.47262328 699.67135901 698.87186053 698.07449141 697.27974818 696.48813259 695.70002531 694.91559629 694.13480839 693.35745758 692.58321468 691.81166623 691.04233341 690.27463554 689.50783166 688.74096127 687.97278631 687.20176588 686.42611376 685.64388869 684.85308583 684.05128655 683.23707863 682.40890328 681.56564928 680.70681687 679.83074770 678.94044117 678.03777450 677.12516739 676.20537952 675.28181472 674.35683376 673.43317437 672.51338912 671.59978529 670.69633619 669.80270384 668.92030676 668.05042480 667.19431086 666.35330048 665.52886219 664.72249801 663.93558467 663.16921275 662.42402738 661.70011258 660.99698631 660.31363922 659.64857494 658.99985092 658.36513072 657.74176542 657.12688650 656.51749925 655.91057580 655.30314217 654.69234956 654.07553962 653.45030945 652.81422407 652.16589584 651.50393169 650.82722351 650.13489745 649.42469288 648.69755491 647.95304071 647.19079533 646.41052855 645.61243377 644.79587701 643.96071283 643.10691030 642.23460103 641.34609372 640.44008456 639.51740791 638.57914374 637.62661225 636.66136711 635.68515441 634.69978421 633.70696770 632.70815304 631.70436366 630.69609922 629.68339600 628.66594988 627.64324193 626.61466362 625.57963723 624.53772374 623.48872573 622.43279016 621.37050869 620.30295456 619.23155854 618.15792139 617.08362399 616.00945151 614.93702474 613.86703308 612.79987696 611.73572368 610.67224219 609.61164315 608.55377256 607.49853793 606.44600021 605.39703634 604.35165190 603.31060121 602.27465185 601.24442282 600.22245788 599.20638456 598.19566486 597.18937527 596.18624802 595.18471319 594.18296543 593.17909293 592.17123092 591.15771607 590.13723924 589.10895261 588.07246134 587.02776967 585.97522529 584.91546367 583.84935110 582.77792455 581.70233027 580.62376228 579.54340119 578.46235837 577.38163408 576.30208111 575.22436855 574.14835739 573.07484401 572.00379045 570.93492816 569.86777092 568.79929393 567.73097611 566.66189382 565.59118838 564.51819514 563.44315880 562.36553672 561.28567040 560.20405169 559.12117231 558.03974597 556.95748873 555.87421525 554.78949891 553.70270035 552.61299631 551.51941487 550.42088670 549.31630284 548.20457257 547.08468135 545.95574855 544.81708438 543.66824676 542.50909802 541.33986034 540.16113500 538.97383021 537.77905279 536.57799848 535.37184238 534.16163118 532.94818014 531.73197199 530.51305584 529.29027826 528.06326531 526.83058072 525.59062931 524.34189613 523.08041428 521.80819802 520.52504718 519.23122469 517.92740657 516.61534983 515.29565023 513.96969233 512.63870947 511.30355214 509.96739352 508.62683228 507.28081303 505.92797160 504.56690010 503.19640913 501.81571708 500.42445416 499.02259346 497.61037927 496.18825525 494.75679048 493.31660011 491.86826386 490.41224441 488.94880721 487.47797651 485.99958321 484.51334891 483.01897143 481.51620929 480.00494243 478.48517236 476.95699838 475.42059297 473.87532940 472.32231197 470.76188554 469.19452997 467.62091574 466.03849396 464.45188355 462.86242164 461.27146180 459.68023007 458.09055132 456.50213608 454.91518012 453.32952230 451.74467334
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5 -1 44.77260232 44.75088399 44.72903940 44.70696394 44.68455159 44.66169972 44.63831382 44.61431146 44.58962400 44.56419748 44.53799347 44.51098990 44.48318080 44.45457343 44.42518430 44.39503521 44.36414922 44.33254682 44.30024232 44.26724045 44.23353282 44.19909463 44.16388321 44.12784170 44.09090456 44.05300334 44.01405073 43.97401220 43.93285700 43.89059427 43.84728886 43.80297909 43.75797678 43.71257461 43.66712703 43.62203721 43.57776764 43.53474988 43.49343233 43.45422541 43.41747128 43.38348539 43.35230853 43.32394680 43.29829762 43.27515913 43.25423975 43.23517042 43.21752403 43.20083738 43.18463347 43.16844346 43.15182481 43.13436928 43.11570702 43.09551052 43.07349856 43.04944065 43.02316287 42.99455418 42.96357274 42.93025223 42.89470696 42.85713387 42.81781340 42.77711033 42.73545129 42.69338745 42.65150379 42.61041122 42.57071648 42.53291214 42.49760280 42.46522760 42.43613681 42.41057982 42.38870444 42.37051688 42.35594130 42.34483179 42.33699966 42.33224776 42.33036089 42.33116926 42.33454125 42.34039671 42.34871994 42.35956524 42.37304372 42.38930265 42.40850448 42.43080607 42.45633914 42.48519457 42.51740795 42.55294532 42.59168908 42.63342999 42.67787472 42.72465944 42.77336367 42.82352423 42.87465126 42.92624965 42.97784257 43.02899507 43.07936483 43.12863798 43.17662124 43.22321727 43.26842793 43.31245239 43.35539586 43.39754933 43.43926784 43.48094918 43.52298942 43.56583246 43.60988910 43.65554933 43.70317182 43.75296171 43.80528450 43.86034396 43.91827584 43.97913973 44.04291103 44.10947618 44.17863607 44.25011278 44.32355634 44.39855171 44.47462969 44.55128788 44.62801555 44.70431868 44.77974490 44.85390431 44.92648010 44.99723520 45.06601863 45.13277185 45.19752960 45.26040755 45.32158453 45.38128463 45.43979103 45.49733240 45.55416431 45.61052035 45.66659650 45.72265810 45.77866232 45.83462964 45.89053020 45.94629346 46.00178750 46.05691907 46.11154886 46.16552800 46.21870395 46.27081318 46.32182759 46.37159870 46.41996395 46.46673562 46.51168996 46.55456163 46.59505159 46.63284031 46.66760126 46.69901430 46.72678119 46.75064584 46.77041656 46.78598836 46.79736492 46.80467214 46.80815039 46.80813830 46.80505624 46.79938980 46.79167354 46.78247526 46.77238052 46.76197720 46.75183468 46.74250691 46.73450351 46.72828533 46.72425444 46.72274378 46.72402186 46.72826094 46.73554305 46.74585458 46.75907316 46.77498821 46.79329419 46.81361108 46.83550012 46.85842860 46.88193897 46.90552270 46.92868879 46.95098594 46.97202457 46.99149337 47.00916203 47.02487853 47.03856625 47.05022088 47.05990404 47.06772818 47.07383817 47.07839274 47.08154605 47.08343299 47.08416394 47.08382329 47.08246802 47.08012650 47.07679975 47.07246937 47.06710798 47.06068982 47.05319678 47.04463785 47.03503789 47.02443737 47.01288883 47.00042503 46.98713491 46.97307770 46.95829692 46.94281005 46.92660751 46.90962074 46.89175374 46.87288525 46.85287941 46.83164441 46.80900435 46.78483803 46.75904227 46.73153752 46.70227349 46.67123182 46.63842160 46.60387198 46.56762474 46.52972694 46.49022769 46.44918513 46.40667752 46.36281443 46.31774787 46.27168038 46.22486556 46.17760553 46.13024836 46.08318520 46.03684135 45.99165177 45.94803058 45.90634017 45.86683977 45.82972791 45.79506957 45.76282248 45.73284019 45.70481629 45.67848036 45.65343670 45.62927339 45.60560356 45.58211907 45.55858264 45.53487036 45.51095238 45.48688633
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7 4 6.72379219 6.80816097 6.89253731 6.97692372 7.06131846 7.14571500 7.23010141 7.31446003 7.39876730 7.48299397 7.56710511 7.65106024 7.73481364 7.81831516 7.90151124 7.98434590 8.06676183 8.14870155 8.23010910 8.31093193 8.39112271 8.47064122 8.54945593 8.62754483 8.70489608 8.78150855 8.85743376 8.93265060 9.00718820 9.08108006 9.15436023 9.22721819 9.29951714 9.37127249 9.44248861 9.51315692 9.58321584 9.65266566 9.72145682 9.78953430 9.85684332 9.92319051 9.98868614 10.05330618 10.11704271 10.17990615 10.24192752 10.30315958 10.36367511 10.42356414 10.48293111 10.54189207 10.60057196 10.65910226 10.71761884 10.77625973 10.83516288 10.89446372 10.95429170 11.01476668 11.07599521 11.13806684 11.20105032 11.26498956 11.32989952 11.39576206 11.46255868 11.53015859 11.59842935 11.66720495 11.73628971 11.80561371 11.87478265 11.94354178 12.01163533 12.07881689 12.14482414 12.20949658 12.27267080 12.33422145 12.39406511 12.45203895 12.50828491 12.56285368 12.61582976 12.66732378 12.71746475 12.76639214 12.81424753 12.86116603 12.90726772 12.95264918 12.99737718 13.04148791 13.08498843 13.12785810 13.17005018 13.21149452 13.25210321 13.29177750 13.33041462 13.36791467 13.40418656 13.43915146 13.47274543 13.50492197 13.53567087 13.56496879 13.59283037 13.61928771 13.64438783 13.66824095 13.69086053 13.71232456 13.73271718 13.75212679 13.77063428 13.78834220 13.80534347 13.82173293 13.83760810 13.85303643 13.86815694 13.88307572 13.89789945 13.91273363 13.92768083 13.94283859 13.95829672 13.97413421 13.99041622 14.00719101 14.02448795 14.04231790 14.06067459 14.07953603 14.09886593 14.11861606 14.13873063 14.15915164 14.17982421 14.20070186 14.22175092 14.24295256 14.26430389 14.28581908 14.30754232 14.32951164 14.35178956 14.37444493 14.39754653 14.42120893 14.44543212 14.47024891 14.49567062 14.52168290 14.54822693 14.57524080 14.60261945 14.63023346 14.65793388 14.68549684 14.71281121 14.73970344 14.76600603 14.79156544 14.81625000 14.83995651 14.86261375 14.88418466 14.90466856 14.92410320 14.94256468 14.96016189 14.97702871 14.99331620 15.00918472 15.02479604 15.04030530 15.05585293 15.07155655 15.08750298 15.10374246 15.12028872 15.13712122 15.15418749 15.17141505 15.18868691 15.20587750 15.22285264 15.23947884 15.25566737 15.27127522 15.28621943 15.30044403 15.31392377 15.32666105 15.33870835 15.35014221 15.36106441 15.37159555 15.38184629 15.39197805 15.40212852 15.41242885 15.42299749 15.43393404 15.44531493 15.45719372 15.46960315 15.48255729 15.49605373 15.51007613 15.52459779 15.53958569 15.55500445 15.57082037 15.58700424 15.60353166 15.62038210 15.63753810 15.65498430 15.67270634 15.69068892 15.70891372 15.72735725 15.74599895 15.76478914 15.78367976 15.80261531 15.82153389 15.84040930 15.85912777 15.87761293 15.89578461 15.91355919 15.93084057 15.94754901 15.96359210 15.97887471 15.99329899 16.00673611 16.01911693 16.03034047 16.04030969 16.04893468 16.05613600 16.06184793 16.06602200 16.06863049 16.06967005 16.06916515 16.06716991 16.06376580 16.05905763 16.05316946 16.04624061 16.03842082 16.02986384 16.02072030 16.01113058 16.00121770 15.99108216 15.98080160 15.97043236 15.96001111 15.94955075 15.93905996 15.92853005 15.91794545 15.90728844 15.89652023 15.88565502 15.87469031 15.86362943 15.85248069 15.84126269 15.82998489 15.81866430 15.80731764 15.79595951
7 -4 22.55259562 22.61096864 22.66933687 22.72768359 22.78598175 22.84419260 22.90226430 22.96013119 23.01771450 23.07492366 23.13165771 23.18780661 23.24325311 23.29787581 23.35155267 23.40416454 23.45559874 23.50575247 23.55453605 23.60187610 23.64771861 23.69203213 23.73480998 23.77607046 23.81585625 23.85423365 23.89131195 23.92718090 23.96197058 23.99582657 24.02890652 24.06144726 24.09354798 24.12538231 24.15712104 24.18892809 24.22093886 24.25330840 24.28615494 24.31957265 24.35362715 24.38827425 24.42358411 24.45951771 24.49600258 24.53293469 24.57018047 24.60758048 24.64495726 24.68212475 24.71889792 24.75510217 24.79058122 24.82520068 24.85885001 24.89144446 24.92292680 24.95326779 24.98246269 25.01052640 25.03748851 25.06338840 25.08827093 25.11218396 25.13517637 25.15729626 25.17860051 25.19911802 25.21888501 25.23793213 25.25628398 25.27399657 25.29103997 25.30741755 25.32312454 25.33814748 25.35245613 25.36602716 25.37882098 25.39079188 25.40188985 25.41204119 25.42121826 25.42936929 25.43644555 25.44240311 25.44720472 25.45082106 25.45323052 25.45441842 25.45437617 25.45310047 25.45059286 25.44686004 25.44191451 25.43577525 25.42846839 25.42002809 25.41049776 25.39993157 25.38839588 25.37597063 25.36274958 25.34883725 25.33434478 25.31938566 25.30406299 25.28849078 25.27276616 25.25697476 25.24118806 25.22542646 25.20976175 25.19421611 25.17880108 25.16352215 25.14839147 25.13340685 25.11857924 25.10392615 25.08947342 25.07528788 25.06138421 25.04781777 25.03464981 25.02194448 25.00976577 24.99817491 24.98722821 24.97697536 24.96745765 24.95870618 24.95074026 24.94356607 24.93717549 24.93154486 24.92663387 24.92238500 24.91872476 24.91556548 24.91280720 24.91033953 24.90804424 24.90579948 24.90348471 24.90098559 24.89819728 24.89503252 24.89141811 24.88729559 24.88262057 24.87734982 24.87147385 24.86498313 24.85787440 24.85014754 24.84180703 24.83284616 24.82325972 24.81304071 24.80218106 24.79069838 24.77856197 24.76576597 24.75230754 24.73818807 24.72341449 24.70800007 24.69196438 24.67533283 24.65813621 24.64041023 24.62219483 24.60353296 24.58446918 24.56504821 24.54531351 24.52530607 24.50506379 24.48462107 24.46400839 24.44325190 24.42237346 24.40139151 24.38032247 24.35918200 24.33797472 24.31673006 24.29546760 24.27420852 24.25297533 24.23174540 24.21058967 24.18953129 24.16858998 24.14777980 24.12711822 24.10659097 24.08618721 24.06589016 24.04567924 24.02557607 24.00551485 23.98547800 23.96545555 23.94544877 23.92547374 23.90556357 23.88576701 23.86614567 23.84677118 23.82772235 23.80908153 23.79092899 23.77333656 23.75636121 23.74003876 23.72437933 23.70936764 23.69496508 23.68111187 23.66772929 23.65472315 23.64199047 23.62942741 23.61693732 23.60443170 23.59185700 23.57917590 23.56637425 23.55346111 23.54044014 23.52739381 23.51439366 23.50152235 23.48886760 23.47652271 23.46456115 23.45305496 23.44206640 23.43164672 23.42185567 23.41269605 23.40418386 23.39632794 23.38913316 23.38260358 23.37674512 23.37156707 23.36708305 23.36331203 23.36027929 23.35801643 23.35655913 23.35594386 23.35620472 23.35737013 23.35945986 23.36248242 23.36643279 23.37129003 23.37701501 23.38354920 23.39081615 23.39872400 23.40716815 23.41603875 23.42520943 23.43455632 23.44395911 23.45330669 23.46252255 23.47150849 23.48020808 23.48858698 23.49663362 23.50435580 23.51179286 23.51899896 23.52604276 23.53300251
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10 0 -2.86470784 -2.85789294 -2.85106117 -2.84419553 -2.83727851 -2.83029252 -2.82322036 -2.81604565 -2.80875321 -2.80132948 -2.79376291 -2.78604431 -2.77816721 -2.77012795 -2.76192568 -2.75356238 -2.74504293 -2.73637497 -2.72756870 -2.71863652 -2.70959268 -2.70045292 -2.69123413 -2.68195389 -2.67263002 -2.66328009 -2.65391585 -2.64455817 -2.63522126 -2.62591744 -2.61665676 -2.60742652 -2.59825156 -2.58913326 -2.58006973 -2.57105571 -2.56208736 -2.55314751 -2.54422062 -2.53528813 -2.52632872 -2.51733843 -2.50827202 -2.49910234 -2.48980134 -2.48034074 -2.47069269 -2.46083037 -2.45072861 -2.44036448 -2.42971790 -2.41877223 -2.40751476 -2.39593696 -2.38403461 -2.37180792 -2.35926171 -2.34640541 -2.33325285 -2.31982199 -2.30613462 -2.29221604 -2.27809474 -2.26380208 -2.24937188 -2.23484008 -2.22023635 -2.20560776 -2.19099448 -2.17643742 -2.16197790 -2.14762613 -2.13345534 -2.11950629 -2.10581872 -2.09243089 -2.07938627 -2.06671153 -2.05443808 -2.04259416 -2.03120442 -2.02031287 -2.00991021 -2.00000801 -1.99061304 -1.98172721 -1.97334729 -1.96546497 -1.95806705 -1.95113578 -1.94464926 -1.93858173 -1.93290407 -1.92758432 -1.92258832 -1.91788035 -1.91342378 -1.90918168 -1.90511743 -1.90119529 -1.89738103 -1.89364248 -1.88995009 -1.88627732 -1.88260098 -1.87890160 -1.87516167 -1.87137205 -1.86752593 -1.86362080 -1.85965841 -1.85563588 -1.85157192 -1.84748055 -1.84337933 -1.83928907 -1.83523571 -1.83124331 -1.82734025 -1.82355653 -1.81992326 -1.81647949 -1.81324867 -1.81026187 -1.80754903 -1.80513833 -1.80305559 -1.80132374 -1.79996237 -1.79898742 -1.79841088 -1.79824040 -1.79847912 -1.79912572 -1.80017467 -1.80161635 -1.80343734 -1.80562065 -1.80814617 -1.81099127 -1.81413127 -1.81754003 -1.82119046 -1.82505501 -1.82910613 -1.83331680 -1.83766338 -1.84211887 -1.84666014 -1.85126574 -1.85591604 -1.86060363 -1.86530255 -1.86999871 -1.87467949 -1.87933336 -1.88394708 -1.88851290 -1.89302053 -1.89745925 -1.90181738 -1.90607267 -1.91022006 -1.91424290 -1.91812249 -1.92183790 -1.92536592 -1.92868101 -1.93175561 -1.93456058 -1.93706560 -1.93923966 -1.94105148 -1.94247034 -1.94346679 -1.94401353 -1.94408619 -1.94366407 -1.94273084 -1.94127510 -1.93929099 -1.93677883 -1.93374545 -1.93020415 -1.92617443 -1.92168168 -1.91675411 -1.91143029 -1.90575072 -1.89975914 -1.89350143 -1.88701018 -1.88034615 -1.87355574 -1.86668342 -1.85977080 -1.85285942 -1.84597861 -1.83915653 -1.83241629 -1.82577579 -1.81926176 -1.81286676 -1.80659316 -1.80043891 -1.79439818 -1.78846181 -1.78261789 -1.77685234 -1.77114949 -1.76549267 -1.75986480 -1.75424893 -1.74862856 -1.74298791 -1.73731222 -1.73158795 -1.72580307 -1.71994704 -1.71401080 -1.70798676 -1.70186876 -1.69565206 -1.68933323 -1.68291012 -1.67638180 -1.66974478 -1.66300388 -1.65616146 -1.64922103 -1.64218725 -1.63505034 -1.62783279 -1.62054308 -1.61319099 -1.60578764 -1.59834958 -1.59088657 -1.58341360 -1.57594669 -1.56850269 -1.56111531 -1.55378612 -1.54653329 -1.53937492 -1.53232883 -1.52541230 -1.51864178 -1.51203275 -1.50559954 -1.49935512 -1.49331099 -1.48747700 -1.48186124 -1.47647000 -1.47130765 -1.46637661 -1.46167727 -1.45720802 -1.45296529 -1.44894361 -1.44513566 -1.44153233 -1.43812291 -1.43489525 -1.43183597 -1.42892909 -1.42616107 -1.42351613 -1.42097837 -1.41853207 -1.41615695 -1.41384409 -1.41158023 -1.40935343 -1.40715326 -1.40497220 -1.40280215 -1.40063803 -1.39847640 -1.39631536
10 1 -5.64084069 -5.65380978 -5.66678004 -5.67975223 -5.69272629 -5.70570125 -5.71867519 -5.73164525 -5.74460752 -5.75755704 -5.77048772 -5.78339232 -5.79626240 -5.80908832 -5.82185924 -5.83456313 -5.84718676 -5.85971572 -5.87213451 -5.88442660 -5.89657452 -5.90855995 -5.92036382 -5.93196648 -5.94334787 -5.95448774 -5.96537170 -5.97597343 -5.98627316 -5.99625160 -6.00589019 -6.01519115 -6.02411626 -6.03264998 -6.04077821 -6.04848839 -6.05576586 -6.06260611 -6.06900251 -6.07495094 -6.08045012 -6.08549133 -6.09009230 -6.09426184 -6.09801248 -6.10136070 -6.10432706 -6.10693628 -6.10921687 -6.11120078 -6.11292292 -6.11442075 -6.11573374 -6.11690267 -6.11796884 -6.11897322 -6.11995570 -6.12095432 -6.12200472 -6.12313963 -6.12438833 -6.12577620 -6.12732431 -6.12904924 -6.13096307 -6.13307334 -6.13538431 -6.13789326 -6.14059421 -6.14347710 -6.14652804 -6.14973677 -6.15307600 -6.15652213 -6.16004921 -6.16362940 -6.16723152 -6.17082742 -6.17438675 -6.17787942 -6.18127631 -6.18454281 -6.18766116 -6.19060867 -6.19336578 -6.19591647 -6.19824881 -6.20035528 -6.20223297 -6.20388356 -6.20531340 -6.20653353 -6.20755962 -6.20841148 -6.20911256 -6.20968938 -6.21017094 -6.21058815 -6.21097304 -6.21135797 -6.21177480 -6.21225410 -6.21282440 -6.21351173 -6.21433913 -6.21532626 -6.21648967 -6.21784062 -6.21938677 -6.22113175 -6.22307534 -6.22521842 -6.22754930 -6.23005696 -6.23272738 -6.23554380 -6.23848546 -6.24153270 -6.24466268 -6.24785121 -6.25107312 -6.25429559 -6.25749977 -6.26065991 -6.26375071 -6.26674772 -6.26962765 -6.27236877 -6.27495122 -6.27735733 -6.27957200 -6.28158296 -6.28338111 -6.28496073 -6.28631959 -6.28745916 -6.28838476 -6.28910559 -6.28963456 -6.28998795 -6.29018508 -6.29024803 -6.29020124 -6.29007097 -6.28988473 -6.28967064 -6.28945679 -6.28927101 -6.28913996 -6.28908884 -6.28914083 -6.28931718 -6.28963586 -6.29011162 -6.29075583 -6.29157619 -6.29257597 -6.29375547 -6.29511058 -6.29663337 -6.29831212 -6.30012735 -6.30206385 -6.30409980 -6.30621078 -6.30837017 -6.31054960 -6.31271950 -6.31484961 -6.31690972 -6.31887025 -6.32070290 -6.32238130 -6.32388146 -6.32518229 -6.32626605 -6.32711881 -6.32773079 -6.32809647 -6.32821447 -6.32808756 -6.32772253 -6.32713011 -6.32632455 -6.32532323 -6.32414616 -6.32281480 -6.32135376 -6.31978832 -6.31814454 -6.31644879 -6.31472342 -6.31299780 -6.31129655 -6.30964296 -6.30805857 -6.30656369 -6.30517456 -6.30390584 -6.30276960 -6.30177519 -6.30093088 -6.30023806 -6.29969772 -6.29930830 -6.29906584 -6.29896411 -6.29899485 -6.29914814 -6.29941281 -6.29977690 -6.30022803 -6.30075391 -6.30134265 -6.30198323 -6.30266588 -6.30338245 -6.30412673 -6.30489451 -6.30568355 -6.30649353 -6.30732600 -6.30818431 -6.30907325 -6.30999873 -6.31096740 -6.31198683 -6.31306355 -6.31420437 -6.31541562 -6.31670296 -6.31807422 -6.31953036 -6.32107397 -6.32270666 -6.32442904 -6.32623985 -6.32813897 -6.33012464 -6.33219459 -6.33434609 -6.33657120 -6.33887142 -6.34124368 -6.34368514 -6.34619336 -6.34876653 -6.35140362 -6.35410451 -6.35687012 -6.35970251 -6.36260504 -6.36558238 -6.36864061 -6.37178707 -6.37503042 -6.37838056 -6.38184851 -6.38544619 -6.38918604 -6.39308075 -6.39714285 -6.40138441 -6.40581656 -6.41044904 -6.41528969 -6.42034682 -6.42562061 -6.43111085 -6.43681435 -6.44272476 -6.44884613 -6.45515293 -6.46162948 -6.46825771 -6.47501762 -6.48188396 -6.48883800 -6.49585699 -6.50291834 -6.51000029
10 -1 1.53334605 1.54133252 1.54929211 1.55719648 1.56501560 1.57271839 1.58027337 1.58764934 1.59481611 1.60174528 1.60841096 1.61479057 1.62086551 1.62662169 1.63204994 1.63714653 1.64191355 1.64635926 1.65049816 1.65435089 1.65794420 1.66131085 1.66448941 1.66752378 1.67046247 1.67335801 1.67626788 1.67924901 1.68236136 1.68566513 1.68921949 1.69309018 1.69732352 1.70196860 1.70706876 1.71266038 1.71876829 1.72541474 1.73260991 1.74035471 1.74864088 1.75743107 1.76671648 1.77646258 1.78662764 1.79716373 1.80801766 1.81913204 1.83044640 1.84189836 1.85342481 1.86496308 1.87645206 1.88783312 1.89905105 1.91005490 1.92079894 1.93124333 1.94135476 1.95110679 1.96048026 1.96946375 1.97805375 1.98625458 1.99407799 2.00154293 2.00867895 2.01551404 2.02208588 2.02843675 2.03461254 2.04067490 2.04666066 2.05262108 2.05860731 2.06466938 2.07085191 2.07720340 2.08376578 2.09057738 2.09767260 2.10506495 2.11279497 2.12088342 2.12934647 2.13819571 2.14743820 2.15707647 2.16710873 2.17752903 2.18832751 2.19949053 2.21100098 2.22283864 2.23498056 2.24740151 2.26007437 2.27297058 2.28606057 2.29931421 2.31270126 2.32619184 2.33975684 2.35336820 2.36699927 2.38062504 2.39422986 2.40778538 2.42127315 2.43467739 2.44798524 2.46121575 2.47433313 2.48733417 2.50021890 2.51299051 2.52564839 2.53820873 2.55068312 2.56308496 2.57542889 2.58770330 2.59995041 2.61218489 2.62442034 2.63666880 2.64894018 2.66124185 2.67357857 2.68595251 2.69836324 2.71080777 2.72328068 2.73577425 2.74827882 2.76078300 2.77327401 2.78573791 2.79815998 2.81052506 2.82281791 2.83502356 2.84712766 2.85911688 2.87097920 2.88270433 2.89429032 2.90572482 2.91700445 2.92812836 2.93909836 2.94994250 2.96064380 2.97121197 2.98165891 2.99199835 3.00224000 3.01240601 3.02251359 3.03258020 3.04262307 3.05263677 3.06265847 3.07270171 3.08277785 3.09289560 3.10306059 3.11327489 3.12353676 3.13384040 3.14417575 3.15452824 3.16487873 3.17520378 3.18547605 3.19566472 3.20573592 3.21565327 3.22537870 3.23487345 3.24409903 3.25301815 3.26159566 3.26979919 3.27759972 3.28497224 3.29189994 3.29836312 3.30435118 3.30985826 3.31488302 3.31943786 3.32351830 3.32713510 3.33030229 3.33303672 3.33535650 3.33728445 3.33884342 3.34005756 3.34095197 3.34155140 3.34188401 3.34197564 3.34185175 3.34153712 3.34105545 3.34042911 3.33967888 3.33882366 3.33788028 3.33686326 3.33578462 3.33465393 3.33347832 3.33226259 3.33100928 3.32971881 3.32838976 3.32701933 3.32560367 3.32413826 3.32261833 3.32103925 3.31939690 3.31768806 3.31590986 3.31406294 3.31214887 3.31017114 3.30813531 3.30604449 3.30391310 3.30175330 3.29957919 3.29740666 3.29525437 3.29313997 3.29108341 3.28910547 3.28722748 3.28547467 3.28386417 3.28241702 3.28115370 3.28009390 3.27925626 3.27865815 3.27831563 3.27824337 3.27845464 3.27896126 3.27977359 3.28090056 3.28234981 3.28412768 3.28623934 3.28868882 3.29147903 3.29461163 3.29808710 3.30190462 3.30606202 3.31055562 3.31538008 3.32052821 3.32599382 3.33176275 3.33782138 3.34415387 3.35074227 3.35758165 3.36463558 3.37188014 3.37929026 3.38684015 3.39449959 3.40224703 3.41005771 3.41790836 3.42577780
10 2 1.65720656 1.65438656 1.65156237 1.64872984 1.64588502 1.64302419 1.64014395 1.63724127 1.63431352 1.63135852 1.62837463 1.62536074 1.62231638 1.61924175 1.61613782 1.61300646 1.60985043 1.60667357 1.60348082 1.60027836 1.59707372 1.59387585 1.59069519 1.58754361 1.58443424 1.58138136 1.57839866 1.57550397 1.57271380 1.57004457 1.56751208 1.56512599 1.56290519 1.56086070 1.55900092 1.55733105 1.55585338 1.55456441 1.55345739 1.55252140 1.55174132 1.55109913 1.55056976 1.55012651 1.54973974 1.54937751 1.54900621 1.54859116 1.54809737 1.54749021 1.54673619 1.54580364 1.54466337 1.54328897 1.54165715 1.53974789 1.53754476 1.53503502 1.53220946 1.52906210 1.52558996 1.52179273 1.51767250 1.51323346 1.50848157 1.50342424 1.49806703 1.49242210 1.48649960 1.48031026 1.47386525 1.46716110 1.46022336 1.45306377 1.44569403 1.43812565 1.43037415 1.42244626 1.41435230 1.40610199 1.39770437 1.38918652 1.38053754 1.37176388 1.36287106 1.35386362 1.34474518 1.33551838 1.32618495 1.31674584 1.30720132 1.29755104 1.28779418 1.27792955 1.26795576 1.25787136 1.24767498 1.23736545 1.22694189 1.21640371 1.20575070 1.19498305 1.18410140 1.17310681 1.16200075 1.15078511 1.13945590 1.12802188 1.11648601 1.10485160 1.09312227 1.08127594 1.06934243 1.05732622 1.04523201 1.03306469 1.02083601 1.00854449 0.99619528 0.98379344 0.97134377 0.95887814 0.94637336 0.93383286 0.92125941 0.90865493 0.89602048 0.88335608 0.87066074 0.85793249 0.84516832 0.83236427 0.81951543 0.80661611 0.79366006 0.78064063 0.76755100 0.75438437 0.74113414 0.72779413 0.71435879 0.70082336 0.68718405 0.67343801 0.65958333 0.64561894 0.63153684 0.61734514 0.60304497 0.58863799 0.57412630 0.55948016 0.54473387 0.52989031 0.51495264 0.49992437 0.48481769 0.46962876 0.45436261 0.43902513 0.42362328 0.40819919 0.39272893 0.37722378 0.36169677 0.34616275 0.33063854 0.31514292 0.29969645 0.28432119 0.26904040 0.25387829 0.23885964 0.22400948 0.20935266 0.19491343 0.18071507 0.16677947 0.15312693 0.13977588 0.12674272 0.11404155 0.10168402 0.08967921 0.07803360 0.06675102 0.05582666 0.04526519 0.03506245 0.02521194 0.01570511 0.00651180 -0.00235884 -0.01092001 -0.01918563 -0.02716983 -0.03488234 -0.04234081 -0.04955735 -0.05654271 -0.06330582 -0.06983947 -0.07616313 -0.08227884 -0.08818628 -0.09388280 -0.09936345 -0.10462111 -0.10964678 -0.11442995 -0.11895898 -0.12322146 -0.12720459 -0.13089554 -0.13428175 -0.13735128 -0.14009316 -0.14249768 -0.14455649 -0.14626281 -0.14761145 -0.14859895 -0.14922367 -0.14948570 -0.14938679 -0.14893026 -0.14812040 -0.14696353 -0.14546700 -0.14363915 -0.14148902 -0.13902048 -0.13624785 -0.13318123 -0.12983070 -0.12620610 -0.12231909 -0.11817668 -0.11378720 -0.10915834 -0.10429714 -0.09922129 -0.09392599 -0.08841610 -0.08269575 -0.07676836 -0.07063663 -0.06430256 -0.05776748 -0.05103212 -0.04409664 -0.03696074 -0.02962367 -0.02208450 -0.01434231 -0.00639643 0.00175334 0.01010649 0.01866165 0.02741637 0.03636701 0.04550852 0.05483438 0.06433665 0.07400611 0.08383240 0.09380967 0.10392040 0.11415182 0.12449087 0.13492448 0.14546299 0.15607126 0.16673762 0.17745119 0.18820201 0.19897525 0.20976900 0.22057658 0.23139238 0.24221185
10 -2 0.17088133 0.16312175 0.15537719 0.14766434 0.14000232 0.13241247 0.12491804 0.11754396 0.11031644 0.10326262 0.09641021 0.08978704 0.08342075 0.07733844 0.07156629 0.06612925 0.06105070 0.05635216 0.05205300 0.04817027 0.04471849 0.04170942 0.03915192 0.03705182 0.03541193 0.03423197 0.03350824 0.03323495 0.03340254 0.03399861 0.03500813 0.03641706 0.03820375 0.04034636 0.04282150 0.04560459 0.04866851 0.05198895 0.05554007 0.05929635 0.06323289 0.06731667 0.07153366 0.07586278 0.08028445 0.08478069 0.08933511 0.09393301 0.09856123 0.10320797 0.10786263 0.11251559 0.11715810 0.12178200 0.12637954 0.13094317 0.13546532 0.13993817 0.14435357 0.14870280 0.15297654 0.15716462 0.16125603 0.16523880 0.16910013 0.17282633 0.17640484 0.17981832 0.18305095 0.18608658 0.18890900 0.19150757 0.19386008 0.19595148 0.19776769 0.19929593 0.20052440 0.20144473 0.20204964 0.20233411 0.20229553 0.20193499 0.20125539 0.20026190 0.19896220 0.19736622 0.19548610 0.19333591 0.19093126 0.18828879 0.18542572 0.18235931 0.17910639 0.17568294 0.17210367 0.16838158 0.16452756 0.16055008 0.15645520 0.15224671 0.14792620 0.14349327 0.13894565 0.13427968 0.12949070 0.12457354 0.11952023 0.11432859 0.10899449 0.10351467 0.09788701 0.09209790 0.08616022 0.08007612 0.07384896 0.06748322 0.06098782 0.05436540 0.04762251 0.04076596 0.03380263 0.02675470 0.01961332 0.01238433 0.00507315 -0.00231511 -0.00977576 -0.01730436 -0.02489669 -0.03254858 -0.04025573 -0.04801365 -0.05581745 -0.06366190 -0.07154140 -0.07945002 -0.08738149 -0.09532926 -0.10328658 -0.11124668 -0.11920282 -0.12714850 -0.13507750 -0.14298395 -0.15086238 -0.15870768 -0.16651944 -0.17428903 -0.18201239 -0.18968550 -0.19730421 -0.20488055 -0.21239275 -0.21983501 -0.22720055 -0.23448135 -0.24166401 -0.24874136 -0.25570050 -0.26252677 -0.26920374 -0.27569912 -0.28200784 -0.28810851 -0.29397853 -0.29959432 -0.30493165 -0.30996592 -0.31467257 -0.31902751 -0.32300756 -0.32659087 -0.32975731 -0.33248882 -0.33476969 -0.33658688 -0.33793026 -0.33879291 -0.33917114 -0.33906450 -0.33847582 -0.33741116 -0.33587979 -0.33389391 -0.33146841 -0.32862052 -0.32536764 -0.32173228 -0.31773687 -0.31340480 -0.30876001 -0.30381553 -0.29860531 -0.29315313 -0.28748240 -0.28161598 -0.27557951 -0.26939146 -0.26307290 -0.25664443 -0.25012629 -0.24355295 -0.23692993 -0.23027672 -0.22361256 -0.21695636 -0.21032663 -0.20374140 -0.19721800 -0.19077279 -0.18442093 -0.17817608 -0.17205020 -0.16605330 -0.16019327 -0.15447567 -0.14890354 -0.14347724 -0.13819451 -0.13305052 -0.12803800 -0.12314726 -0.11836640 -0.11368157 -0.10907730 -0.10453684 -0.10004007 -0.09557122 -0.09111182 -0.08664362 -0.08214901 -0.07760137 -0.07299520 -0.06831695 -0.06355504 -0.05870027 -0.05374873 -0.04869405 -0.04353549 -0.03827543 -0.03291949 -0.02748865 -0.02198360 -0.01641999 -0.01081668 -0.00519568 0.00041802 0.00599658 0.01150973 0.01692531 0.02220965 0.02732818 0.03224587 0.03692791 0.04134042 0.04545109 0.04922992 0.05264981 0.05568703 0.05832169 0.06053810 0.06232521 0.06367690 0.06459197 0.06507407 0.06513151 0.06477690 0.06402739 0.06290421 0.06143196 0.05963804 0.05754729 0.05519489 0.05261352 0.04983632 0.04689620 0.04382694 0.04065755 0.03741674 0.03413096 0.03082403
10 3 -3.39665811 -3.38709355 -3.37751638 -3.36791340 -3.35827061 -3.34857343 -3.33880702 -3.32895658 -3.31900757 -3.30894616 -3.29875944 -3.28843583 -3.27796532 -3.26733968 -3.25655267 -3.24560014 -3.23448026 -3.22319359 -3.21174304 -3.20013380 -3.18837316 -3.17647048 -3.16443698 -3.15228549 -3.14003002 -3.12768552 -3.11526063 -3.10277776 -3.09025246 -3.07769978 -3.06513395 -3.05254055 -3.03995879 -3.02739866 -3.01486820 -3.00237332 -2.98992433 -2.97751539 -2.96514486 -2.95280848 -2.94049932 -2.92823461 -2.91597520 -2.90370643 -2.89141145 -2.87907146 -2.86666596 -2.85417307 -2.84156987 -2.82883286 -2.81593833 -2.80286283 -2.78958352 -2.77607855 -2.76232734 -2.74831096 -2.73401238 -2.71941679 -2.70451164 -2.68928668 -2.67373400 -2.65784804 -2.64162551 -2.62506521 -2.60816769 -2.59093493 -2.57336037 -2.55545733 -2.53723025 -2.51868369 -2.49982199 -2.48060653 -2.46108113 -2.44124769 -2.42110710 -2.40065924 -2.37991443 -2.35885955 -2.33749194 -2.31580875 -2.29380727 -2.27153459 -2.24894180 -2.22602916 -2.20279871 -2.17925464 -2.15540372 -2.13125556 -2.10682255 -2.08211970 -2.05716447 -2.03197654 -2.00657758 -1.98099065 -1.95523954 -1.92934813 -1.90333966 -1.87723615 -1.85105781 -1.82482250 -1.79854521 -1.77223753 -1.74590723 -1.71955813 -1.69319008 -1.66679892 -1.64036204 -1.61388180 -1.58734260 -1.56072578 -1.53401011 -1.50711338 -1.48006901 -1.45285120 -1.42543405 -1.39779233 -1.36991754 -1.34177297 -1.31333960 -1.28460157 -1.25554664 -1.22623133 -1.19658886 -1.16662013 -1.13633049 -1.10572963 -1.07483150 -1.04365418 -1.01221938 -0.98055198 -0.94867947 -0.91663143 -0.88443899 -0.85213417 -0.81974924 -0.78731601 -0.75486524 -0.72242596 -0.69002503 -0.65768670 -0.62543221 -0.59327936 -0.56124218 -0.52933090 -0.49755192 -0.46590788 -0.43438045 -0.40298226 -0.37170533 -0.34053884 -0.30946961 -0.27841475 -0.24742579 -0.21648527 -0.18557547 -0.15467906 -0.12379658 -0.09289639 -0.06196568 -0.03099401 0.00002637 0.03103213 0.06209240 0.09320524 0.12436552 0.15556505 0.18679270 0.21803455 0.24927427 0.28049353 0.31167242 0.34278986 0.37382401 0.40475268 0.43555375 0.46620550 0.49668707 0.52697877 0.55706235 0.58692123 0.61654064 0.64590790 0.67501254 0.70384631 0.73240320 0.76067938 0.78868844 0.81641519 0.84386189 0.87103235 0.89793166 0.92462395 0.95105680 0.97723724 1.00317219 1.02886792 1.05431584 1.07953388 1.10452420 1.12928712 1.15382087 1.17806859 1.20207790 1.22584028 1.24934518 1.27258021 1.29553132 1.31818304 1.34051881 1.36252141 1.38417326 1.40545691 1.42635531 1.44685218 1.46693223 1.48658153 1.50578768 1.52454010 1.54283001 1.56065041 1.57799600 1.59486317 1.61124986 1.62715546 1.64258058 1.65752686 1.67200461 1.68600867 1.69954276 1.71261109 1.72521822 1.73739508 1.74911860 1.76039392 1.77122622 1.78162059 1.79157671 1.80110514 1.81021040 1.81889662 1.82716753 1.83500964 1.84244417 1.84947338 1.85609917 1.86232322 1.86814712 1.87357244 1.87860098 1.88323493 1.88747706 1.89133096 1.89480118 1.89789334 1.90061424 1.90297191 1.90497571 1.90663637 1.90796591 1.90897750 1.90968539 1.91010477 1.91025158 1.91014245 1.90979442 1.90922479 1.90845048 1.90748909 1.90635778 1.90507346 1.90365270 1.90210817 1.90045865 1.89871935 1.89690481 1.89502883 1.89310545 1.89114564 1.88916035 1.88715936 1.88515114
10 -3 3.77833248 3.79011575 3.80188914 3.81364197 3.82536239 3.83703771 3.84865455 3.86019909 3.87165734 3.88301537 3.89425956 3.90537688 3.91635508 3.92718288 3.93785012 3.94834791 3.95866877 3.96880676 3.97875750 3.98851819 3.99808763 4.00746620 4.01665587 4.02566015 4.03448404 4.04313395 4.05162228 4.05995333 4.06813741 4.07618597 4.08411152 4.09194453 4.09968192 4.10733880 4.11493084 4.12247405 4.12998052 4.13747055 4.14496001 4.15246424 4.15999775 4.16755731 4.17517132 4.18285026 4.19060300 4.19843665 4.20635648 4.21436587 4.22246647 4.23065844 4.23894072 4.24731125 4.25576721 4.26430530 4.27292194 4.28161352 4.29037663 4.29920822 4.30810550 4.31706583 4.32608650 4.33516463 4.34429692 4.35347943 4.36270724 4.37197415 4.38127749 4.39060264 4.39993830 4.40927159 4.41858818 4.42789276 4.43714811 4.44633686 4.45544151 4.46444499 4.47332636 4.48207586 4.49068050 4.49912923 4.50741313 4.51550815 4.52342866 4.53117308 4.53874208 4.54613830 4.55336619 4.56043174 4.56734220 4.57410571 4.58073094 4.58722679 4.59360203 4.59986499 4.60602332 4.61208373 4.61805167 4.62393116 4.62972472 4.63543332 4.64105646 4.64659209 4.65203668 4.65738543 4.66263247 4.66777111 4.67279681 4.67769904 4.68246994 4.68710158 4.69158612 4.69592522 4.70010156 4.70410822 4.70793868 4.71158690 4.71504551 4.71831153 4.72138064 4.72424925 4.72691469 4.72937016 4.73162121 4.73366855 4.73551414 4.73716129 4.73861472 4.73988053 4.74096605 4.74187968 4.74263059 4.74322856 4.74368373 4.74400634 4.74420644 4.74429363 4.74427678 4.74416379 4.74396146 4.74367538 4.74330982 4.74286766 4.74235026 4.74175745 4.74108737 4.74033650 4.73949906 4.73856829 4.73753520 4.73638897 4.73511689 4.73370112 4.73212778 4.73037872 4.72843439 4.72627407 4.72387756 4.72122154 4.71828355 4.71504115 4.71147230 4.70756466 4.70329063 4.69863130 4.69356910 4.68808800 4.68217364 4.67581344 4.66899662 4.66171423 4.65395908 4.64572576 4.63701063 4.62781182 4.61812919 4.60796439 4.59732077 4.58620342 4.57461907 4.56257594 4.55008363 4.53715305 4.52379618 4.51002590 4.49585563 4.48129906 4.46636156 4.45106434 4.43542015 4.41944083 4.40313707 4.38648140 4.36951683 4.35224926 4.33468284 4.31681990 4.29867095 4.28022503 4.26147933 4.24242977 4.22307131 4.20344161 4.18349264 4.16321842 4.14261339 4.12167281 4.10039319 4.07877262 4.05681105 4.03451054 4.01187549 3.98891288 3.96563238 3.94204630 3.91816936 3.89401850 3.86961270 3.84497271 3.82012063 3.79507946 3.76987257 3.74452328 3.71905444 3.69348825 3.66784621 3.64214901 3.61640234 3.59063924 3.56487802 3.53913667 3.51343314 3.48772957 3.46210122 3.43656752 3.41114836 3.38586399 3.36074867 3.33580920 3.31106600 3.28653881 3.26224628 3.23825775 3.21453487 3.19109054 3.16793537 3.14507754 3.12252262 3.10027358 3.07833083 3.05669244 3.03535436 3.01431058 2.99355339 2.97307356 2.95286069 2.93290338 2.91318956 2.89370668 2.87444187 2.85538205 2.83651401 2.81782454 2.79930052 2.78092895 2.76269693 2.74459173 2.72659092 2.70869205 2.69088294 2.67315179 2.65548728 2.63784011 2.62023887 2.60267414 2.58513741 2.56762116 2.55012854 2.53264475 2.51516581 2.49768893 2.48021252
10 4 -0.73564809 -0.72491019 -0.71417111 -0.70343035 -0.69268824 -0.68194613 -0.67120645 -0.66047286 -0.64975027 -0.63904491 -0.62836431 -0.61771739 -0.60711436 -0.59656663 -0.58608653 -0.57568709 -0.56538188 -0.55518468 -0.54510924 -0.53516895 -0.52537650 -0.51574362 -0.50628075 -0.49699689 -0.48789950 -0.47899435 -0.47028069 -0.46176556 -0.45344935 -0.44533084 -0.43740744 -0.42965861 -0.42209706 -0.41471695 -0.40751165 -0.40047377 -0.39359903 -0.38687497 -0.38029236 -0.37384117 -0.36751045 -0.36130166 -0.35518775 -0.34915459 -0.34318714 -0.33726960 -0.33138555 -0.32551819 -0.31965081 -0.31376733 -0.30785287 -0.30189428 -0.29588066 -0.28980373 -0.28365814 -0.27744176 -0.27115603 -0.26480611 -0.25840058 -0.25195107 -0.24547182 -0.23897929 -0.23249164 -0.22602817 -0.21960862 -0.21325251 -0.20697509 -0.20079713 -0.19473419 -0.18879999 -0.18300624 -0.17735031 -0.17185245 -0.16651807 -0.16135086 -0.15635316 -0.15152885 -0.14687566 -0.14239365 -0.13808267 -0.13394262 -0.12998221 -0.12619296 -0.12257619 -0.11913384 -0.11586848 -0.11278331 -0.10988210 -0.10716913 -0.10464893 -0.10232611 -0.10020520 -0.09829047 -0.09658584 -0.09509473 -0.09382005 -0.09276406 -0.09192831 -0.09131371 -0.09092054 -0.09074854 -0.09079697 -0.09106463 -0.09154987 -0.09225061 -0.09316426 -0.09428844 -0.09561913 -0.09715211 -0.09888249 -0.10080454 -0.10291645 -0.10520655 -0.10766630 -0.11028642 -0.11305700 -0.11596602 -0.11900429 -0.12216117 -0.12542627 -0.12878990 -0.13223566 -0.13576334 -0.13936691 -0.14304192 -0.14678562 -0.15059710 -0.15447742 -0.15842948 -0.16245793 -0.16656905 -0.17077056 -0.17507154 -0.17948212 -0.18401331 -0.18867667 -0.19348409 -0.19844755 -0.20357895 -0.20888988 -0.21439154 -0.22009451 -0.22600862 -0.23214279 -0.23850493 -0.24510175 -0.25194249 -0.25902759 -0.26635947 -0.27393884 -0.28176460 -0.28985161 -0.29817783 -0.30673599 -0.31551667 -0.32450833 -0.33369219 -0.34305736 -0.35258610 -0.36225896 -0.37205494 -0.38192999 -0.39188213 -0.40188733 -0.41192102 -0.42195853 -0.43197530 -0.44194725 -0.45185103 -0.46166431 -0.47136601 -0.48093659 -0.49035830 -0.49961533 -0.50869401 -0.51758294 -0.52627317 -0.53475830 -0.54303449 -0.55110038 -0.55895711 -0.56660822 -0.57405956 -0.58131915 -0.58839695 -0.59530462 -0.60205899 -0.60867066 -0.61515509 -0.62152836 -0.62780696 -0.63402093 -0.64017281 -0.64627836 -0.65235231 -0.65840800 -0.66445366 -0.67050202 -0.67656023 -0.68263309 -0.68872294 -0.69481624 -0.70092360 -0.70704009 -0.71315893 -0.71927178 -0.72536914 -0.73144073 -0.73747575 -0.74346328 -0.74939256 -0.75525334 -0.76103612 -0.76673232 -0.77233437 -0.77783575 -0.78323109 -0.78851626 -0.79368835 -0.79874567 -0.80368776 -0.80851537 -0.81323044 -0.81783610 -0.82233660 -0.82673734 -0.83104711 -0.83527098 -0.83941730 -0.84349508 -0.84751378 -0.85149176 -0.85542996 -0.85933798 -0.86322499 -0.86709944 -0.87096672 -0.87483530 -0.87871040 -0.88259604 -0.88649515 -0.89040098 -0.89432279 -0.89826037 -0.90221259 -0.90617748 -0.91015235 -0.91413384 -0.91811792 -0.92210003 -0.92607502 -0.93003723 -0.93398055 -0.93789849 -0.94178426 -0.94563089 -0.94943131 -0.95317849 -0.95686561 -0.96048626 -0.96403469 -0.96750599 -0.97089628 -0.97420279 -0.97742391 -0.98055924 -0.98361125 -0.98658030 -0.98946963 -0.99228348 -0.99502696 -0.99771167 -1.00033792 -1.00291252 -1.00544253 -1.00793512 -1.01039602 -1.01283350 -1.01525412 -1.01766402 -1.02006884
10 -4 5.06429495 5.06239908 5.06048586 5.05853728 5.05653441 5.05445778 5.05228777 5.05000501 5.04759075 5.04502725 5.04229817 5.03938894 5.03628714 5.03298267 5.02946799 5.02573829 5.02179169 5.01762934 5.01325548 5.00867735 5.00390519 4.99895215 4.99383422 4.98856997 4.98318025 4.97768789 4.97211434 4.96648844 4.96083689 4.95518666 4.94956445 4.94398400 4.93848234 4.93308232 4.92780451 4.92266672 4.91768630 4.91287152 4.90822993 4.90376545 4.89947847 4.89537460 4.89143768 4.88765803 4.88402330 4.88051887 4.87712833 4.87383386 4.87061684 4.86745836 4.86433983 4.86124355 4.85815318 4.85505407 4.85193349 4.84878089 4.84558811 4.84234948 4.83906164 4.83572313 4.83233409 4.82889589 4.82541074 4.82188124 4.81830985 4.81469847 4.81104585 4.80735328 4.80361849 4.79983764 4.79600537 4.79210617 4.78814002 4.78409736 4.77996787 4.77574075 4.77140754 4.76695535 4.76237400 4.75765393 4.75278631 4.74777443 4.74260103 4.73726046 4.73174827 4.72606126 4.72019752 4.71415653 4.70793924 4.70154820 4.69498769 4.68826382 4.68138461 4.67435998 4.66720170 4.65992333 4.65254014 4.64506904 4.63752823 4.62993697 4.62231515 4.61468305 4.60706091 4.59946869 4.59192568 4.58445021 4.57705526 4.56976037 4.56257922 4.55552351 4.54860291 4.54181015 4.53516572 4.52867242 4.52233082 4.51613921 4.51009699 4.50419479 4.49842480 4.49277761 4.48724247 4.48181935 4.47648350 4.47122196 4.46602171 4.46087001 4.45575478 4.45066493 4.44559062 4.44052346 4.43545671 4.43038556 4.42530723 4.42022103 4.41512834 4.41003264 4.40493943 4.39985624 4.39479256 4.38975973 4.38477090 4.37984090 4.37498618 4.37022472 4.36557591 4.36106046 4.35669798 4.35251402 4.34853246 4.34477762 4.34127397 4.33803903 4.33510464 4.33249371 4.33022771 4.32832625 4.32680731 4.32568428 4.32496873 4.32466905 4.32479031 4.32533237 4.32629292 4.32766631 4.32944351 4.33161225 4.33415722 4.33706025 4.34030073 4.34385607 4.34770211 4.35181363 4.35616482 4.36072980 4.36548322 4.37040083 4.37546002 4.38064037 4.38592396 4.39129566 4.39674338 4.40225839 4.40783544 4.41347267 4.41917140 4.42493593 4.43077654 4.43669966 4.44271702 4.44884213 4.45508984 4.46149015 4.46804603 4.47477425 4.48169145 4.48881377 4.49615246 4.50372549 4.51154547 4.51962323 4.52796749 4.53656540 4.54543852 4.55458768 4.56401087 4.57370314 4.58365659 4.59386034 4.60430085 4.61496227 4.62582687 4.63687536 4.64808738 4.65944191 4.67091785 4.68249447 4.69415200 4.70587197 4.71763755 4.72943366 4.74124714 4.75306695 4.76488420 4.77669210 4.78848571 4.80026184 4.81202519 4.82376891 4.83549371 4.84720113 4.85889337 4.87059857 4.88229392 4.89398224 4.90566626 4.91734846 4.92902458 4.94070261 4.95238352 4.96406751 4.97575388 4.98741535 4.99907466 5.01072778 5.02236951 5.03399343 5.04559182 5.05715576 5.06867519 5.08013906 5.09153556 5.10285220 5.11407606 5.12519407 5.13619337 5.14706164 5.15778744 5.16836051 5.17877209 5.18901511 5.19908445 5.20897717 5.21869266 5.22823265 5.23760101 5.24680369 5.25585348 5.26475495 5.27351919 5.28215837 5.29068539 5.29913186 5.30749231 5.31577986 5.32400711 5.33218600 5.34032306 5.34843264 5.35652341 5.36460283 5.37267717
10 5 4.02245115 4.01154321 4.00064166 3.98975263 3.97888196 3.96803506 3.95721670 3.94643090 3.93568079 3.92496848 3.91429494 3.90365991 3.89306178 3.88249752 3.87196266 3.86145122 3.85095569 3.84046699 3.82997454 3.81946637 3.80892914 3.79834829 3.78770816 3.77699233 3.76618401 3.75526642 3.74421713 3.73302653 3.72168029 3.71016575 3.69847231 3.68656566 3.67446591 3.66217075 3.64968094 3.63700029 3.62414286 3.61111183 3.59792012 3.58458322 3.57111886 3.55757651 3.54394795 3.53025534 3.51652130 3.50276840 3.48901853 3.47529242 3.46160907 3.44798526 3.43443510 3.42096948 3.40759571 3.39431751 3.38113499 3.36804479 3.35504012 3.34211097 3.32924463 3.31642638 3.30364015 3.29086919 3.27809669 3.26530639 3.25248307 3.23961310 3.22667785 3.21367531 3.20059899 3.18744486 3.17421125 3.16086952 3.14745130 3.13396126 3.12040570 3.10679229 3.09313728 3.07944286 3.06571936 3.05197779 3.03822968 3.02451713 3.01082238 2.99715806 2.98353693 2.96997183 2.95647552 2.94306059 2.92973925 2.91652311 2.90342304 2.89044890 2.87760936 2.86491177 2.85236199 2.83996424 2.82772094 2.81563266 2.80369815 2.79191446 2.78027704 2.76877989 2.75741570 2.74617609 2.73505188 2.72403337 2.71310465 2.70226183 2.69149496 2.68079420 2.67014978 2.65952888 2.64894521 2.63838900 2.62785011 2.61731779 2.60678618 2.59623692 2.58565632 2.57502974 2.56434160 2.55359910 2.54276186 2.53181246 2.52073348 2.50950798 2.49811991 2.48655447 2.47479849 2.46284078 2.45067237 2.43828694 2.42568095 2.41285369 2.39980716 2.38654597 2.37307723 2.35941038 2.34555680 2.33152944 2.31734230 2.30301006 2.28854765 2.27396988 2.25929113 2.24452501 2.22967586 2.21476294 2.19979594 2.18478309 2.16973109 2.15461204 2.13946255 2.12428489 2.10908008 2.09384811 2.07859638 2.06331490 2.04800134 2.03265281 2.01726591 2.00187060 1.98642908 1.97093669 1.95538818 1.93977756 1.92409801 1.90834177 1.89250017 1.87656364 1.86052179 1.84436345 1.82807676 1.81164940 1.79506886 1.77832277 1.76139911 1.74428652 1.72697452 1.70945367 1.69171587 1.67375444 1.65556442 1.63714256 1.61848744 1.59959954 1.58047073 1.56111567 1.54154061 1.52175352 1.50176396 1.48153851 1.46113308 1.44056099 1.41983624 1.39897321 1.37799785 1.35691296 1.33573221 1.31446847 1.29313359 1.27178493 1.25038487 1.22894066 1.20745782 1.18593998 1.16438878 1.14280384 1.12118286 1.09952174 1.07781480 1.05605486 1.03423351 1.01234142 0.99036873 0.96830539 0.94614162 0.92386821 0.90147697 0.87896107 0.85631542 0.83353709 0.81062556 0.78758279 0.76441326 0.74112390 0.71771128 0.69419988 0.67060343 0.64693714 0.62321721 0.59940832 0.57557922 0.55174636 0.52792524 0.50413000 0.48038590 0.45668996 0.43304978 0.40947041 0.38595420 0.36255195 0.33920889 0.31591896 0.29267347 0.26946113 0.24626826 0.22307887 0.19987497 0.17663680 0.15334317 0.12997174 0.10649931 0.08290227 0.05915695 0.03524010 0.01112930 -0.01319668 -0.03775747 -0.06257083 -0.08765230 -0.11301489 -0.13866879 -0.16462117 -0.19087610 -0.21743436 -0.24430814 -0.27147685 -0.29893104 -0.32665807 -0.35464231 -0.38292738 -0.41143114 -0.44013037 -0.46900031 -0.49801520 -0.52713290 -0.55634314 -0.58562054 -0.61494087 -0.64428166
10 -5 -5.52402882 -5.53815945 -5.55228430 -5.56639729 -5.58049187 -5.59456117 -5.60859819 -5.62259591 -5.63654744 -5.65044605 -5.66428529 -5.67805907 -5.69176173 -5.70538805 -5.71893326 -5.73239309 -5.74576373 -5.75904186 -5.77222481 -5.78531061 -5.79829814 -5.81118724 -5.82397882 -5.83667498 -5.84927901 -5.86179558 -5.87423749 -5.88660536 -5.89890803 -5.91115559 -5.92335930 -5.93555804 -5.94773829 -5.95991397 -5.97209946 -5.98430939 -5.99655164 -6.00884721 -6.02120993 -6.03365278 -6.04618767 -6.05879735 -6.07151795 -6.08435654 -6.09731832 -6.11040655 -6.12362243 -6.13696510 -6.15043175 -6.16401790 -6.17771756 -6.19152350 -6.20542747 -6.21942046 -6.23349298 -6.24763537 -6.26183804 -6.27609173 -6.29038755 -6.30471701 -6.31907202 -6.33344493 -6.34782846 -6.36221562 -6.37659952 -6.39097322 -6.40533742 -6.41967676 -6.43398333 -6.44824885 -6.46246461 -6.47665243 -6.49077154 -6.50481222 -6.51876490 -6.53262041 -6.54636282 -6.55999230 -6.57350271 -6.58688950 -6.60015002 -6.61325520 -6.62623610 -6.63909692 -6.65184408 -6.66448600 -6.67703304 -6.68949722 -6.70189191 -6.71423141 -6.72653053 -6.73880418 -6.75106699 -6.76333300 -6.77561541 -6.78792628 -6.80027628 -6.81267450 -6.82512836 -6.83764362 -6.85022440 -6.86287319 -6.87559088 -6.88837695 -6.90122975 -6.91414667 -6.92713157 -6.94017364 -6.95326889 -6.96641326 -6.97960282 -6.99286298 -7.00616173 -7.01949640 -7.03286474 -7.04626497 -7.05968831 -7.07314099 -7.08662212 -7.10013085 -7.11366618 -7.12719714 -7.14075162 -7.15432744 -7.16792189 -7.18153176 -7.19515324 -7.20878199 -7.22241332 -7.23604241 -7.24966454 -7.26327536 -7.27687110 -7.29044879 -7.30400653 -7.31754370 -7.33106118 -7.34456151 -7.35804876 -7.37152836 -7.38500691 -7.39849195 -7.41199175 -7.42551494 -7.43907009 -7.45266529 -7.46631525 -7.48001853 -7.49377980 -7.50760228 -7.52148774 -7.53546702 -7.54950842 -7.56360909 -7.57776477 -7.59196990 -7.60620995 -7.62048483 -7.63478574 -7.64910297 -7.66342605 -7.67771248 -7.69198197 -7.70622263 -7.72042262 -7.73457052 -7.74865559 -7.76266816 -7.77659989 -7.79044413 -7.80419626 -7.81785396 -7.83141745 -7.84488954 -7.85827546 -7.87158287 -7.88482166 -7.89800386 -7.91114322 -7.92425475 -7.93735430 -7.95045804 -7.96358210 -7.97674215 -7.98995314 -8.00322893 -8.01658934 -8.03003795 -8.04358380 -8.05723402 -8.07099372 -8.08489645 -8.09891308 -8.11304227 -8.12728055 -8.14162227 -8.15605174 -8.17056699 -8.18515649 -8.19980736 -8.21450575 -8.22920495 -8.24392249 -8.25864400 -8.27335578 -8.28804524 -8.30270131 -8.31731482 -8.33187858 -8.34638741 -8.36083813 -8.37522960 -8.38956263 -8.40383982 -8.41806528 -8.43224438 -8.44638352 -8.46048981 -8.47457070 -8.48863365 -8.50268567 -8.51673297 -8.53078056 -8.54483184 -8.55888820 -8.57294866 -8.58701712 -8.60107899 -8.61512417 -8.62913944 -8.64310839 -8.65704190 -8.67088663 -8.68461722 -8.69820602 -8.71162351 -8.72483158 -8.73780576 -8.75051370 -8.76292316 -8.77500256 -8.78669625 -8.79800253 -8.80889517 -8.81935073 -8.82934907 -8.83887391 -8.84791328 -8.85645968 -8.86451022 -8.87206672 -8.87913584 -8.88572902 -8.89186214 -8.89755505 -8.90283103 -8.90771637 -8.91223978 -8.91643187 -8.92032451 -8.92395022 -8.92734160 -8.93053075 -8.93354880 -8.93642555 -8.93918903 -8.94186656 -8.94448005 -8.94705030 -8.94959541 -8.95213070 -8.95467422 -8.95723012 -8.95980533 -8.96240422 -8.96502877 -8.96767732 -8.97034910 -8.97304016 -8.97574515 -8.97845751
10 6 1.57108214 1.55269684 1.53432785 1.51599168 1.49770535 1.47948591 1.46134991 1.44331292 1.42538911 1.40759091 1.38992860 1.37240998 1.35504005 1.33782101 1.32075228 1.30383056 1.28704993 1.27040188 1.25387565 1.23745850 1.22113602 1.20489245 1.18871105 1.17257446 1.15646514 1.14036582 1.12425108 1.10811425 1.09194137 1.07572043 1.05944183 1.04306286 1.02661543 1.01009911 0.99351680 0.97687475 0.96019172 0.94347152 0.92672985 0.90998466 0.89325555 0.87659967 0.86000139 0.84348146 0.82705960 0.81075374 0.79457930 0.77854856 0.76267030 0.74694962 0.73138776 0.71598188 0.70072502 0.68560642 0.67061196 0.65572462 0.64092494 0.62619154 0.61150174 0.59683223 0.58215974 0.56746176 0.55271711 0.53790641 0.52301250 0.50802080 0.49291145 0.47768434 0.46233452 0.44686035 0.43126340 0.41551388 0.39965372 0.38369365 0.36764702 0.35152947 0.33536752 0.31917174 0.30296286 0.28676257 0.27059314 0.25451224 0.23850661 0.22259792 0.20680697 0.19115338 0.17565529 0.16032902 0.14518897 0.13024749 0.11551479 0.10099882 0.08670522 0.07263733 0.05879620 0.04518065 0.03178730 0.01861067 0.00564333 -0.00712382 -0.01970132 -0.03210095 -0.04433540 -0.05641788 -0.06836173 -0.08017994 -0.09189110 -0.10349978 -0.11501566 -0.12644681 -0.13779952 -0.14910274 -0.16033379 -0.17149305 -0.18257928 -0.19358990 -0.20451535 -0.21535730 -0.22611101 -0.23677169 -0.24733493 -0.25777422 -0.26811008 -0.27834082 -0.28846579 -0.29848536 -0.30840084 -0.31821440 -0.32792875 -0.33754670 -0.34707074 -0.35650263 -0.36584305 -0.37509143 -0.38424577 -0.39330260 -0.40225683 -0.41110175 -0.41982929 -0.42843041 -0.43689551 -0.44521474 -0.45337847 -0.46137757 -0.46920383 -0.47685026 -0.48431553 -0.49159192 -0.49867794 -0.50557411 -0.51228302 -0.51882345 -0.52518726 -0.53138313 -0.53742142 -0.54331398 -0.54907077 -0.55470914 -0.56024395 -0.56569056 -0.57106465 -0.57637031 -0.58163474 -0.58687294 -0.59209938 -0.59732789 -0.60257147 -0.60784215 -0.61315084 -0.61850713 -0.62391917 -0.62939341 -0.63493455 -0.64054533 -0.64622649 -0.65197666 -0.65779223 -0.66366738 -0.66959433 -0.67556362 -0.68156451 -0.68758526 -0.69361354 -0.69963680 -0.70564272 -0.71161967 -0.71756036 -0.72345240 -0.72928819 -0.73506164 -0.74076813 -0.74641676 -0.75199307 -0.75749615 -0.76292557 -0.76828089 -0.77355835 -0.77875912 -0.78388030 -0.78891765 -0.79386544 -0.79870575 -0.80344042 -0.80805898 -0.81255011 -0.81690209 -0.82110330 -0.82514274 -0.82901052 -0.83269837 -0.83620018 -0.83951250 -0.84263495 -0.84557024 -0.84832416 -0.85090553 -0.85332608 -0.85560037 -0.85774529 -0.85977963 -0.86172351 -0.86359789 -0.86542404 -0.86722309 -0.86901547 -0.87082047 -0.87265674 -0.87453889 -0.87648012 -0.87849100 -0.88057926 -0.88275435 -0.88501315 -0.88735368 -0.88977068 -0.89225561 -0.89479534 -0.89737637 -0.89998103 -0.90258921 -0.90517863 -0.90771977 -0.91019306 -0.91257226 -0.91483062 -0.91694126 -0.91887765 -0.92061395 -0.92212527 -0.92338781 -0.92437903 -0.92507782 -0.92546467 -0.92552175 -0.92523300 -0.92458428 -0.92356340 -0.92216029 -0.92036718 -0.91817880 -0.91559264 -0.91260912 -0.90923178 -0.90546726 -0.90132523 -0.89681836 -0.89195943 -0.88676917 -0.88126837 -0.87547990 -0.86942834 -0.86312552 -0.85661137 -0.84991331 -0.84305874 -0.83607464 -0.82899093 -0.82182849 -0.81461025 -0.80735717 -0.80008785
10 -6 -1.24420272 -1.24348446 -1.24276516 -1.24204361 -1.24131822 -1.24058712 -1.23984818 -1.23909903 -1.23833709 -1.23755949 -1.23676313 -1.23594460 -1.23510020 -1.23422593 -1.23331750 -1.23237036 -1.23137969 -1.23034044 -1.22924747 -1.22809569 -1.22688021 -1.22559646 -1.22424037 -1.22280845 -1.22129780 -1.21970625 -1.21803144 -1.21627358 -1.21443274 -1.21250949 -1.21050484 -1.20841537 -1.20624675 -1.20400031 -1.20167721 -1.19927831 -1.19680539 -1.19425700 -1.19163235 -1.18892992 -1.18614743 -1.18328812 -1.18034203 -1.17730439 -1.17416971 -1.17093187 -1.16758423 -1.16411974 -1.16053124 -1.15681184 -1.15295526 -1.14895615 -1.14481048 -1.14051582 -1.13607167 -1.13147976 -1.12674436 -1.12187248 -1.11687382 -1.11176067 -1.10654772 -1.10125194 -1.09589238 -1.09048964 -1.08506540 -1.07964184 -1.07423815 -1.06887897 -1.06358499 -1.05837565 -1.05326872 -1.04826922 -1.04340209 -1.03867871 -1.03410823 -1.02969774 -1.02545455 -1.02137938 -1.01747387 -1.01373846 -1.01017280 -1.00678339 -1.00356141 -1.00050633 -0.99761819 -0.99489793 -0.99234773 -0.98997117 -0.98777326 -0.98576026 -0.98393960 -0.98231969 -0.98090974 -0.97971921 -0.97875723 -0.97803195 -0.97754996 -0.97731568 -0.97733081 -0.97759381 -0.97809937 -0.97883789 -0.97979512 -0.98095212 -0.98228540 -0.98376708 -0.98536590 -0.98704487 -0.98876444 -0.99048239 -0.99215470 -0.99373957 -0.99518754 -0.99645341 -0.99749330 -0.99826551 -0.99873118 -0.99885590 -0.99860897 -0.99796423 -0.99690047 -0.99540553 -0.99346723 -0.99108055 -0.98824560 -0.98496728 -0.98125503 -0.97712246 -0.97258679 -0.96766810 -0.96238870 -0.95677241 -0.95084391 -0.94462825 -0.93815040 -0.93143472 -0.92450454 -0.91738181 -0.91008703 -0.90263921 -0.89505600 -0.88735365 -0.87954711 -0.87165021 -0.86367590 -0.85563643 -0.84753916 -0.83940007 -0.83123074 -0.82304285 -0.81484847 -0.80664227 -0.79845554 -0.79030234 -0.78219739 -0.77415606 -0.76619862 -0.75833707 -0.75058789 -0.74296717 -0.73549011 -0.72818636 -0.72105128 -0.71409440 -0.70732241 -0.70073862 -0.69434251 -0.68812927 -0.68208978 -0.67621058 -0.67047388 -0.66485759 -0.65933545 -0.65387745 -0.64845033 -0.64301813 -0.63754269 -0.63198423 -0.62630212 -0.62045556 -0.61440445 -0.60811006 -0.60153587 -0.59464813 -0.58741650 -0.57981471 -0.57181658 -0.56340960 -0.55458256 -0.54532968 -0.53565069 -0.52552838 -0.51499454 -0.50406556 -0.49276276 -0.48111199 -0.46914982 -0.45690353 -0.44440971 -0.43170743 -0.41883753 -0.40587061 -0.39282103 -0.37973111 -0.36664251 -0.35359564 -0.34062905 -0.32777890 -0.31507855 -0.30255828 -0.29024495 -0.27816168 -0.26632766 -0.25475816 -0.24346462 -0.23245480 -0.22173287 -0.21129956 -0.20115242 -0.19128603 -0.18169233 -0.17236085 -0.16327895 -0.15443202 -0.14580370 -0.13737601 -0.12912509 -0.12103497 -0.11308406 -0.10525004 -0.09751020 -0.08982492 -0.08218832 -0.07457777 -0.06697115 -0.05934704 -0.05168910 -0.04397370 -0.03618254 -0.02829856 -0.02030603 -0.01220851 -0.00397590 0.00440305 0.01293795 0.02163681 0.03050593 0.03954994 0.04877185 0.05817324 0.06775439 0.07751444 0.08745153 0.09756296 0.10784533 0.11829470 0.12890676 0.13967690 0.15060034 0.16167215 0.17288732 0.18424077 0.19572743 0.20734224 0.21908014 0.23093610 0.24291169 0.25499541 0.26718214 0.27946648 0.29184264 0.30433170 0.31689965 0.32953888 0.34224120 0.35499793 0.36779292 0.38062365 0.39348059 0.40635439 0.41923629
10 7 2.20664086 2.20087201 2.19510708 2.18935010 2.18360551 2.17787800 2.17217234 2.16649328 2.16084542 2.15523325 2.14966103 2.14413279 2.13865234 2.13322342 2.12784986 2.12253582 2.11728597 2.11210568 2.10700117 2.10197973 2.09704983 2.09222131 2.08750547 2.08291494 2.07846351 2.07416596 2.07003560 2.06609095 2.06234818 2.05882306 2.05553043 2.05247729 2.04968269 2.04715593 2.04490371 2.04292980 2.04123562 2.03981716 2.03866832 2.03778003 2.03714055 2.03673638 2.03654979 2.03656309 2.03675743 2.03711335 2.03761113 2.03823131 2.03895489 2.03976358 2.04063997 2.04156777 2.04253193 2.04351871 2.04451565 2.04551156 2.04649651 2.04746177 2.04839968 2.04930349 2.05016721 2.05098544 2.05175320 2.05246583 2.05311891 2.05370816 2.05422956 2.05467855 2.05505113 2.05534381 2.05555396 2.05568023 2.05572197 2.05568087 2.05556074 2.05536788 2.05511155 2.05480377 2.05445960 2.05409675 2.05373541 2.05339869 2.05310989 2.05289444 2.05277843 2.05278797 2.05294851 2.05328425 2.05381758 2.05456856 2.05555442 2.05678900 2.05828238 2.06004065 2.06206582 2.06435574 2.06690398 2.06969985 2.07272868 2.07597219 2.07940888 2.08301441 2.08676202 2.09062309 2.09456772 2.09856533 2.10258745 2.10660163 2.11057839 2.11448930 2.11830733 2.12201506 2.12558036 2.12898154 2.13219894 2.13521487 2.13801222 2.14057914 2.14290414 2.14497791 2.14679329 2.14834231 2.14962660 2.15064577 2.15140155 2.15189774 2.15214011 2.15213635 2.15189583 2.15142949 2.15074956 2.14986944 2.14880348 2.14756680 2.14617521 2.14464503 2.14299291 2.14123579 2.13939070 2.13747466 2.13550464 2.13349736 2.13146925 2.12943629 2.12741395 2.12541699 2.12345835 2.12155231 2.11971117 2.11794647 2.11626897 2.11468540 2.11320906 2.11184899 2.11061385 2.10951216 2.10855287 2.10774385 2.10709362 2.10661057 2.10630290 2.10617850 2.10624378 2.10650520 2.10696804 2.10763605 2.10851110 2.10959280 2.11087816 2.11236125 2.11403288 2.11588020 2.11788649 2.12003101 2.12228903 2.12463176 2.12702638 2.12943612 2.13182079 2.13413737 2.13634066 2.13838393 2.14021959 2.14180015 2.14307913 2.14401210 2.14455778 2.14467796 2.14433959 2.14351483 2.14218162 2.14031961 2.13792222 2.13498733 2.13151942 2.12752933 2.12303666 2.11806210 2.11263336 2.10678224 2.10054367 2.09396957 2.08708493 2.07992843 2.07253836 2.06495184 2.05720393 2.04932696 2.04135021 2.03329964 2.02519771 2.01706316 2.00891093 2.00075234 1.99259542 1.98444526 1.97630431 1.96817272 1.96004875 1.95192914 1.94380951 1.93568477 1.92754943 1.91939790 1.91122461 1.90302428 1.89478752 1.88651456 1.87820198 1.86984739 1.86144957 1.85299019 1.84448937 1.83595050 1.82737860 1.81878037 1.81016886 1.80154934 1.79293306 1.78433221 1.77575957 1.76724672 1.75878760 1.75039435 1.74207816 1.73384886 1.72571452 1.71768112 1.70975244 1.70192999 1.69421295 1.68659813 1.67907999 1.67165085 1.66430111 1.65701960 1.64979381 1.64261018 1.63545449 1.62831219 1.62116880 1.61401028 1.60682338 1.59959588 1.59231690 1.58497713 1.57756498 1.57007895 1.56251555 1.55487327 1.54715252 1.53933841 1.53145185 1.52349845 1.51548507 1.50741955 1.49931480 1.49117529 1.48301003 1.47482795 1.46663768
10 -7 -2.50327719 -2.51597132 -2.52866786 -2.54136899 -2.55407667 -2.56679250 -2.57951756 -2.59225222 -2.60499611 -2.61774792 -2.63050542 -2.64326527 -2.65602303 -2.66877321 -2.68150942 -2.69422446 -2.70691048 -2.71955911 -2.73216174 -2.74470984 -2.75719523 -2.76961038 -2.78194874 -2.79420503 -2.80637556 -2.81845853 -2.83046086 -2.84237875 -2.85421742 -2.86598448 -2.87768979 -2.88937088 -2.90101619 -2.91264150 -2.92426373 -2.93590045 -2.94756299 -2.95927512 -2.97105348 -2.98291355 -2.99486922 -3.00690585 -3.01905894 -3.03133549 -3.04373993 -3.05627409 -3.06893714 -3.08172557 -3.09463321 -3.10765143 -3.12076919 -3.13397318 -3.14724799 -3.16057633 -3.17393938 -3.18731703 -3.20068826 -3.21403140 -3.22732474 -3.24054700 -3.25367795 -3.26669897 -3.27959352 -3.29234754 -3.30494973 -3.31739189 -3.32967586 -3.34179348 -3.35374680 -3.36554091 -3.37718358 -3.38870999 -3.40010663 -3.41138712 -3.42256589 -3.43365763 -3.44467067 -3.45562451 -3.46653131 -3.47740165 -3.48824424 -3.49904196 -3.50982269 -3.52058829 -3.53133861 -3.54207163 -3.55278374 -3.56346993 -3.57412420 -3.58473991 -3.59531018 -3.60582826 -3.61628786 -3.62668316 -3.63700878 -3.64725973 -3.65743135 -3.66751921 -3.67751898 -3.68742613 -3.69723579 -3.70694246 -3.71653995 -3.72602150 -3.73538003 -3.74460842 -3.75370466 -3.76265723 -3.77146068 -3.78011106 -3.78860649 -3.79696576 -3.80517378 -3.81323741 -3.82116670 -3.82897488 -3.83667421 -3.84428849 -3.85183979 -3.85935210 -3.86685068 -3.87434499 -3.88187710 -3.88947192 -3.89715285 -3.90494105 -3.91285469 -3.92090835 -3.92911253 -3.93747343 -3.94599254 -3.95466643 -3.96348649 -3.97243913 -3.98150603 -3.99066447 -3.99988758 -4.00914472 -4.01840200 -4.02762290 -4.03676880 -4.04579965 -4.05467454 -4.06335224 -4.07179178 -4.07995303 -4.08780143 -4.09529554 -4.10240101 -4.10908654 -4.11532448 -4.12110347 -4.12639051 -4.13117203 -4.13544024 -4.13919354 -4.14243540 -4.14518010 -4.14744658 -4.14926042 -4.15065353 -4.15166209 -4.15233287 -4.15271380 -4.15285628 -4.15281406 -4.15264210 -4.15239546 -4.15212811 -4.15189182 -4.15173499 -4.15170150 -4.15182980 -4.15215235 -4.15269539 -4.15347858 -4.15451475 -4.15580977 -4.15736293 -4.15916749 -4.16121123 -4.16347699 -4.16594336 -4.16858537 -4.17137540 -4.17428398 -4.17728234 -4.18033822 -4.18342148 -4.18650321 -4.18955639 -4.19256310 -4.19549521 -4.19833484 -4.20106780 -4.20368384 -4.20617547 -4.20854220 -4.21078593 -4.21291199 -4.21492872 -4.21684293 -4.21867202 -4.22043040 -4.22213330 -4.22379627 -4.22543451 -4.22706236 -4.22869301 -4.23033826 -4.23200836 -4.23371174 -4.23545488 -4.23724227 -4.23907635 -4.24095756 -4.24288429 -4.24485289 -4.24685758 -4.24889039 -4.25094109 -4.25299710 -4.25504351 -4.25706330 -4.25903762 -4.26094612 -4.26276822 -4.26448045 -4.26606030 -4.26748586 -4.26873668 -4.26979652 -4.27064687 -4.27127535 -4.27167298 -4.27183444 -4.27175835 -4.27144730 -4.27090724 -4.27014718 -4.26917858 -4.26801767 -4.26667738 -4.26517359 -4.26352278 -4.26174165 -4.25984672 -4.25785398 -4.25577867 -4.25363523 -4.25143711 -4.24919670 -4.24692521 -4.24463275 -4.24232840 -4.24002026 -4.23771558 -4.23542084 -4.23314188 -4.23088407 -4.22865245 -4.22645194 -4.22428735 -4.22216339 -4.22008450 -4.21805472 -4.21607651 -4.21415386 -4.21228884 -4.21048253 -4.20873487 -4.20704087 -4.20540169 -4.20381331 -4.20227069 -4.20076794 -4.19929935 -4.19785719 -4.19643439 -4.19502405 -4.19361965
10 8 4.50480871 4.50060678 4.49639601 4.49216632 4.48790612 4.48360262 4.47924205 4.47480992 4.47029136 4.46567130 4.46093484 4.45606750 4.45105546 4.44588570 4.44054615 4.43502575 4.42931461 4.42340410 4.41728697 4.41095746 4.40441143 4.39764648 4.39066207 4.38345948 4.37604190 4.36841438 4.36057955 4.35255029 4.34433679 4.33595024 4.32740231 4.31868551 4.30982982 4.30084593 4.29174354 4.28253105 4.27322043 4.26381177 4.25430860 4.24471314 4.23502660 4.22527092 4.21542500 4.20548853 4.19546112 4.18534249 4.17513264 4.16483196 4.15444128 4.14396178 4.13339491 4.12274238 4.11200606 4.10118788 4.09028978 4.07931360 4.06826096 4.05713316 4.04593090 4.03465400 4.02330111 4.01186941 4.00035440 3.98874981 3.97704764 3.96523816 3.95330336 3.94123662 3.92902372 3.91664983 3.90410002 3.89133170 3.87835862 3.86516876 3.85175215 3.83810139 3.82421984 3.81009930 3.79574264 3.78115647 3.76635122 3.75137423 3.73621138 3.72088415 3.70541709 3.68983732 3.67417415 3.65845852 3.64272235 3.62699777 3.61131639 3.59570855 3.58020260 3.56482449 3.54959732 3.53454092 3.51967149 3.50500134 3.49053914 3.47629026 3.46225722 3.44844004 3.43483669 3.42144362 3.40825634 3.39526994 3.38247273 3.36986766 3.35745091 3.34521873 3.33316709 3.32126554 3.30953494 3.29796771 3.28655353 3.27527845 3.26413005 3.25307850 3.24209480 3.23114470 3.22018872 3.20920643 3.19812487 3.18689157 3.17545211 3.16375163 3.15173640 3.13935539 3.12656177 3.11331455 3.09958015 3.08533395 3.07056155 3.05525918 3.03943379 3.02310310 3.00629568 2.98905065 2.97141642 2.95344909 2.93521080 2.91676814 2.89819041 2.87954776 2.86090914 2.84234041 2.82389224 2.80562890 2.78759677 2.76983403 2.75237002 2.73518754 2.71833568 2.70181586 2.68562142 2.66973855 2.65415570 2.63883901 2.62375958 2.60888603 2.59418594 2.57965888 2.56524209 2.55090735 2.53662915 2.52238527 2.50815725 2.49393068 2.47969496 2.46544278 2.45116958 2.43687308 2.42255270 2.40820891 2.39384263 2.37945446 2.36504408 2.35060962 2.33614720 2.32165062 2.30711094 2.29251617 2.27785101 2.26309712 2.24823350 2.23323685 2.21807362 2.20272541 2.18716519 2.17136660 2.15530497 2.13892231 2.12223528 2.10523012 2.08789810 2.07023603 2.05225679 2.03396010 2.01536108 1.99647986 1.97734075 1.95801401 1.93848801 1.91879423 1.89896468 1.87903089 1.85902298 1.83896883 1.81889391 1.79882123 1.77877137 1.75876248 1.73881035 1.71892877 1.69912997 1.67942502 1.65982428 1.64033777 1.62097539 1.60174704 1.58266279 1.56373304 1.54496857 1.52638044 1.50797990 1.48977816 1.47177647 1.45399565 1.43644616 1.41913814 1.40208138 1.38524885 1.36868744 1.35240620 1.33641417 1.32072055 1.30534313 1.29028313 1.27555073 1.26115629 1.24711018 1.23345222 1.22016121 1.20724645 1.19471633 1.18257799 1.17083697 1.15949696 1.14855966 1.13802472 1.12788964 1.11814973 1.10879810 1.09982575 1.09122177 1.08297352 1.07506682 1.06748613 1.06021488 1.05323577 1.04653110 1.04008312 1.03387428 1.02788742 1.02210598 1.01651408 1.01109376 1.00583404 1.00072158 0.99574361 0.99088770 0.98613124 0.98147258 0.97689926 0.97239888 0.96795919 0.96357056 0.95921891 0.95489328 0.95058363 0.94628126
10 -8 0.81478772 0.79145783 0.76813985 0.74484655 0.72159171 0.69838992 0.67525630 0.65220623 0.62925513 0.60641820 0.58371014 0.56114496 0.53873565 0.51649412 0.49443093 0.47255524 0.45087459 0.42939480 0.40811997 0.38705246 0.36619294 0.34554037 0.32509205 0.30484368 0.28478946 0.26492215 0.24522243 0.22569137 0.20631782 0.18708934 0.16799220 0.14896989 0.13004791 0.11120840 0.09243214 0.07369845 0.05499545 0.03628943 0.01755573 -0.00123125 -0.02009773 -0.03902865 -0.05809160 -0.07731246 -0.09671599 -0.11632522 -0.13616086 -0.15624070 -0.17657925 -0.19718729 -0.21807152 -0.23923416 -0.26067276 -0.28238039 -0.30434604 -0.32655499 -0.34898919 -0.37162773 -0.39444757 -0.41742424 -0.44053265 -0.46374786 -0.48704574 -0.51040343 -0.53379965 -0.55721506 -0.58064538 -0.60406317 -0.62745610 -0.65081394 -0.67412823 -0.69744293 -0.72070118 -0.74389818 -0.76702970 -0.79009180 -0.81306794 -0.83596650 -0.85878309 -0.88151342 -0.90415354 -0.92665086 -0.94905248 -0.97135707 -0.99356481 -1.01567779 -1.03770035 -1.05963930 -1.08150383 -1.10330528 -1.12505687 -1.14677351 -1.16847145 -1.19016776 -1.21187982 -1.23362465 -1.25541839 -1.27727579 -1.29920983 -1.32123153 -1.34334962 -1.36557033 -1.38789721 -1.41033107 -1.43287007 -1.45550977 -1.47825566 -1.50108593 -1.52398905 -1.54695173 -1.56995929 -1.59304656 -1.61614681 -1.63924352 -1.66232054 -1.68536253 -1.70834294 -1.73126210 -1.75410960 -1.77687698 -1.79955775 -1.82209821 -1.84454566 -1.86689945 -1.88916034 -1.91133007 -1.93341109 -1.95540607 -1.97731753 -1.99914725 -2.02089584 -2.04256218 -2.06414301 -2.08563270 -2.10702302 -2.12830294 -2.14945853 -2.17047281 -2.19132618 -2.21199684 -2.23246125 -2.25269466 -2.27267163 -2.29236662 -2.31175479 -2.33081262 -2.34952877 -2.36787389 -2.38583226 -2.40339164 -2.42054361 -2.43732017 -2.45368357 -2.46963878 -2.48519556 -2.50036861 -2.51516960 -2.52963161 -2.54378409 -2.55766097 -2.57130033 -2.58471487 -2.59797963 -2.61114209 -2.62425123 -2.63735658 -2.65050720 -2.66375073 -2.67713242 -2.69069415 -2.70447345 -2.71850258 -2.73280772 -2.74740861 -2.76231834 -2.77754319 -2.79308244 -2.80892832 -2.82506642 -2.84147617 -2.85813138 -2.87500076 -2.89204851 -2.90923495 -2.92651729 -2.94385028 -2.96119649 -2.97849837 -2.99570746 -3.01277551 -3.02965504 -3.04633612 -3.06273708 -3.07881590 -3.09453344 -3.10985389 -3.12473719 -3.13916399 -3.15311097 -3.16655951 -3.17949600 -3.19188552 -3.20375401 -3.21510393 -3.22594298 -3.23628398 -3.24614479 -3.25554805 -3.26452090 -3.27309452 -3.28130370 -3.28918644 -3.29678341 -3.30413730 -3.31129208 -3.31829225 -3.32518208 -3.33200484 -3.33880204 -3.34561263 -3.35247214 -3.35941197 -3.36645868 -3.37363396 -3.38095460 -3.38843259 -3.39607940 -3.40389367 -3.41187407 -3.42001589 -3.42831171 -3.43677072 -3.44536389 -3.45407900 -3.46290280 -3.47182122 -3.48081456 -3.48987246 -3.49897919 -3.50811859 -3.51727402 -3.52640838 -3.53552432 -3.54460433 -3.55363109 -3.56258775 -3.57145829 -3.58022770 -3.58888223 -3.59740942 -3.60579824 -3.61403917 -3.62212426 -3.63004700 -3.63780213 -3.64538551 -3.65279389 -3.66002480 -3.66707654 -3.67394811 -3.68063930 -3.68715061 -3.69348338 -3.69963980 -3.70562313 -3.71143778 -3.71709256 -3.72259137 -3.72794268 -3.73315616 -3.73824257 -3.74322435 -3.74810277 -3.75289089 -3.75760199 -3.76224924 -3.76684292 -3.77139768 -3.77592478 -3.78043454 -3.78493617
10 9 0.76064643 0.74450576 0.72838482 0.71230520 0.69629075 0.68036720 0.66456167 0.64890223 0.63341736 0.61813543 0.60308418 0.58829017 0.57377827 0.55957125 0.54568927 0.53214948 0.51896561 0.50614755 0.49370113 0.48162793 0.46992507 0.45858510 0.44759584 0.43694069 0.42659896 0.41654620 0.40674929 0.39718300 0.38781429 0.37860866 0.36953092 0.36052643 0.35158078 0.34266109 0.33373659 0.32477925 0.31576930 0.30668095 0.29749718 0.28820484 0.27879462 0.26928197 0.25964458 0.24988378 0.24000356 0.23000998 0.21991069 0.20971429 0.19942986 0.18906627 0.17863167 0.16813288 0.15757490 0.14696060 0.13629055 0.12556278 0.11477258 0.10391241 0.09297201 0.08193866 0.07079738 0.05953120 0.04812139 0.03654788 0.02478960 0.01282497 0.00062549 -0.01182382 -0.02454383 -0.03755431 -0.05087358 -0.06454839 -0.07856428 -0.09293316 -0.10766423 -0.12276380 -0.13822652 -0.15406047 -0.17026228 -0.18682535 -0.20373982 -0.22095459 -0.23849018 -0.25632750 -0.27444448 -0.29281620 -0.31141497 -0.33021050 -0.34917018 -0.36825952 -0.38744246 -0.40668181 -0.42593967 -0.44517801 -0.46435928 -0.48344711 -0.50240689 -0.52120640 -0.53981618 -0.55820994 -0.57636490 -0.59426217 -0.61188699 -0.62922870 -0.64628056 -0.66303962 -0.67951551 -0.69570307 -0.71160949 -0.72724468 -0.74262089 -0.75778519 -0.77271953 -0.78744122 -0.80196877 -0.81632173 -0.83051276 -0.84457080 -0.85851754 -0.87237527 -0.88616686 -0.89988569 -0.91358577 -0.92729115 -0.94102604 -0.95481451 -0.96868033 -0.98264671 -0.99673585 -1.01096851 -1.02536356 -1.03993748 -1.05470402 -1.06967396 -1.08485498 -1.10025157 -1.11586484 -1.13169262 -1.14772970 -1.16396838 -1.18039891 -1.19700999 -1.21378919 -1.23072340 -1.24779913 -1.26500292 -1.28233120 -1.29976211 -1.31728371 -1.33488446 -1.35255298 -1.37031677 -1.38812550 -1.40596690 -1.42382779 -1.44169370 -1.45953879 -1.47735482 -1.49512184 -1.51281790 -1.53041913 -1.54786163 -1.56515659 -1.58227527 -1.59918817 -1.61586562 -1.63227837 -1.64839816 -1.66419853 -1.67965553 -1.69474856 -1.70946112 -1.72378147 -1.73770298 -1.75122437 -1.76434988 -1.77708956 -1.78945923 -1.80148001 -1.81317771 -1.82458214 -1.83572640 -1.84664621 -1.85737901 -1.86796299 -1.87843619 -1.88884122 -1.89920736 -1.90956712 -1.91995003 -1.93038216 -1.94090875 -1.95152506 -1.96224497 -1.97307846 -1.98403189 -1.99510216 -2.00629518 -2.01760827 -2.02903664 -2.04057384 -2.05218668 -2.06389193 -2.07568071 -2.08754379 -2.09947171 -2.11145498 -2.12348415 -2.13554985 -2.14764262 -2.15975291 -2.17187096 -2.18398673 -2.19608979 -2.20816919 -2.22021334 -2.23220992 -2.24414574 -2.25600667 -2.26777762 -2.27944240 -2.29098373 -2.30238324 -2.31362174 -2.32467952 -2.33553675 -2.34617954 -2.35658282 -2.36672863 -2.37660067 -2.38618494 -2.39549022 -2.40448718 -2.41317119 -2.42154098 -2.42959856 -2.43734510 -2.44479347 -2.45195475 -2.45884210 -2.46547018 -2.47184095 -2.47798513 -2.48391868 -2.48965715 -2.49521530 -2.50060670 -2.50584342 -2.51093591 -2.51589294 -2.52072156 -2.52542708 -2.53001303 -2.53448132 -2.53883240 -2.54306542 -2.54717843 -2.55116855 -2.55503234 -2.55876609 -2.56236623 -2.56582964 -2.56915399 -2.57233792 -2.57538122 -2.57828497 -2.58105321 -2.58368840 -2.58619614 -2.58858329 -2.59085788 -2.59303360 -2.59511525 -2.59711338 -2.59903900 -2.60090334 -2.60271668 -2.60449118 -2.60623756 -2.60796599 -2.60968588
10 -9 -2.02420784 -2.02903827 -2.03385912 -2.03866055 -2.04343260 -2.04816554 -2.05285026 -2.05747862 -2.06204381 -2.06654067 -2.07096602 -2.07531899 -2.07960129 -2.08381707 -2.08797285 -2.09207730 -2.09614113 -2.10017680 -2.10419817 -2.10821995 -2.11225728 -2.11632517 -2.12043814 -2.12460980 -2.12885259 -2.13317749 -2.13759610 -2.14211325 -2.14673387 -2.15146062 -2.15629374 -2.16124189 -2.16628969 -2.17142970 -2.17665203 -2.18194439 -2.18728933 -2.19267313 -2.19807758 -2.20348338 -2.20887071 -2.21420807 -2.21948810 -2.22469270 -2.22980541 -2.23481189 -2.23970053 -2.24446280 -2.24909333 -2.25358983 -2.25795303 -2.26218656 -2.26629681 -2.27029250 -2.27418416 -2.27798363 -2.28170352 -2.28535672 -2.28895579 -2.29251239 -2.29603670 -2.29953683 -2.30301831 -2.30648371 -2.30993235 -2.31335998 -2.31676036 -2.32011947 -2.32342134 -2.32664654 -2.32977246 -2.33278013 -2.33563457 -2.33830583 -2.34076249 -2.34297224 -2.34490137 -2.34651859 -2.34779174 -2.34868943 -2.34918135 -2.34923893 -2.34883665 -2.34794954 -2.34655504 -2.34463339 -2.34216800 -2.33914580 -2.33555758 -2.33139826 -2.32666727 -2.32136879 -2.31551195 -2.30911071 -2.30218354 -2.29475316 -2.28684626 -2.27849313 -2.26972707 -2.26058370 -2.25110032 -2.24131521 -2.23126703 -2.22099436 -2.21053528 -2.19992699 -2.18919952 -2.17839295 -2.16753968 -2.15666990 -2.14581136 -2.13496550 -2.12417839 -2.11346914 -2.10285349 -2.09234359 -2.08195343 -2.07168171 -2.06152915 -2.05149292 -2.04156694 -2.03176343 -2.02204872 -2.01240856 -2.00282667 -1.99328516 -1.98376491 -1.97424588 -1.96470733 -1.95512794 -1.94548590 -1.93575911 -1.92592522 -1.91596174 -1.90584612 -1.89555582 -1.88506834 -1.87436133 -1.86341278 -1.85220114 -1.84070550 -1.82890581 -1.81678298 -1.80431892 -1.79149657 -1.77829994 -1.76470649 -1.75070942 -1.73629589 -1.72145418 -1.70617371 -1.69041010 -1.67418819 -1.65750139 -1.64034519 -1.62271748 -1.60462902 -1.58607425 -1.56706056 -1.54759898 -1.52770440 -1.50744063 -1.48678754 -1.46577180 -1.44442346 -1.42277545 -1.40086319 -1.37872404 -1.35639664 -1.33392014 -1.31133350 -1.28867469 -1.26598003 -1.24328358 -1.22061663 -1.19800717 -1.17547936 -1.15305315 -1.13074434 -1.10856471 -1.08652220 -1.06462114 -1.04286246 -1.02124427 -0.99976248 -0.97841142 -0.95717288 -0.93605161 -0.91504070 -0.89413371 -0.87332506 -0.85256514 -0.83189674 -0.81131837 -0.79082966 -0.77043108 -0.75013477 -0.72993090 -0.70982056 -0.68980410 -0.66988053 -0.65009028 -0.63038459 -0.61075608 -0.59119523 -0.57169043 -0.55222814 -0.53279316 -0.51336924 -0.49393982 -0.47448888 -0.45500161 -0.43546517 -0.41586903 -0.39620528 -0.37646892 -0.35665814 -0.33677442 -0.31682208 -0.29680770 -0.27673943 -0.25662645 -0.23647830 -0.21630441 -0.19611361 -0.17591367 -0.15569978 -0.13548738 -0.11527919 -0.09507646 -0.07487932 -0.05464281 -0.03440989 -0.01417901 0.00605140 0.02628263 0.04650437 0.06672765 0.08695168 0.10717493 0.12739521 0.14756546 0.16772653 0.18787445 0.20800474 0.22811242 0.24819200 0.26823757 0.28824275 0.30820070 0.32810417 0.34794546 0.36771650 0.38740889 0.40701406 0.42652336 0.44592819 0.46522015 0.48439115 0.50343364 0.52234074 0.54110641 0.55972564 0.57819461 0.59651081 0.61467323 0.63269233 0.65056047 0.66828182 0.68586220 0.70330917 0.72066968 0.73791615 0.75506060 0.77211601 0.78909596 0.80600508 0.82286646 0.83969346 0.85649871 0.87329371
10 10 -0.78819469 -0.79513340 -0.80209543 -0.80910849 -0.81620506 -0.82342199 -0.83080005 -0.83838345 -0.84621900 -0.85435521 -0.86284129 -0.87172623 -0.88105781 -0.89088154 -0.90123950 -0.91216924 -0.92370266 -0.93586502 -0.94867435 -0.96214093 -0.97626683 -0.99104546 -1.00646138 -1.02249089 -1.03910289 -1.05625978 -1.07392814 -1.09205086 -1.11057701 -1.12945433 -1.14863089 -1.16809957 -1.18777198 -1.20760600 -1.22756485 -1.24761791 -1.26773048 -1.28789720 -1.30810867 -1.32836156 -1.34865778 -1.36895912 -1.38931963 -1.40975107 -1.43026579 -1.45087516 -1.47158817 -1.49241003 -1.51334137 -1.53437760 -1.55550823 -1.57671625 -1.59797785 -1.61926320 -1.64053744 -1.66176186 -1.68289498 -1.70389373 -1.72471485 -1.74531639 -1.76565916 -1.78570819 -1.80543401 -1.82481321 -1.84382879 -1.86247055 -1.88074530 -1.89864684 -1.91618594 -1.93337917 -1.95024811 -1.96685446 -1.98319004 -1.99928603 -2.01517444 -2.03088679 -2.04644439 -2.06188284 -2.07722568 -2.09249266 -2.10769932 -2.12282353 -2.13790474 -2.15294482 -2.16794196 -2.18289136 -2.19778587 -2.21261667 -2.22737397 -2.24204776 -2.25662852 -2.27110795 -2.28547961 -2.29973918 -2.31388463 -2.32791647 -2.34183784 -2.35565463 -2.36937519 -2.38301002 -2.39657136 -2.41007287 -2.42352924 -2.43695569 -2.45036755 -2.46377971 -2.47721356 -2.49067448 -2.50417369 -2.51772072 -2.53132324 -2.54501697 -2.55877580 -2.57260126 -2.58649282 -2.60044794 -2.61445446 -2.62851362 -2.64261718 -2.65675511 -2.67091563 -2.68505425 -2.69918697 -2.71329771 -2.72736969 -2.74138598 -2.75532998 -2.76918598 -2.78294005 -2.79658097 -2.81010116 -2.82349764 -2.83677278 -2.84993458 -2.86299672 -2.87597868 -2.88890579 -2.90180899 -2.91472381 -2.92768903 -2.94074539 -2.95393419 -2.96729609 -2.98086997 -2.99469195 -3.00879434 -3.02321265 -3.03796123 -3.05305637 -3.06850873 -3.08432351 -3.10053634 -3.11710751 -3.13402661 -3.15127859 -3.16884413 -3.18669013 -3.20479928 -3.22314150 -3.24168368 -3.26039006 -3.27918117 -3.29805785 -3.31697872 -3.33590153 -3.35478382 -3.37358344 -3.39225924 -3.41077170 -3.42908354 -3.44716042 -3.46497158 -3.48249025 -3.49969353 -3.51656211 -3.53307992 -3.54923377 -3.56501287 -3.58040784 -3.59540960 -3.61000817 -3.62419162 -3.63794518 -3.65125140 -3.66409048 -3.67644072 -3.68828529 -3.69959323 -3.71034075 -3.72050574 -3.73006908 -3.73903491 -3.74737219 -3.75507726 -3.76215224 -3.76860499 -3.77444613 -3.77969858 -3.78438666 -3.78853914 -3.79218859 -3.79536424 -3.79811264 -3.80047398 -3.80249030 -3.80420517 -3.80566336 -3.80691053 -3.80799270 -3.80895577 -3.80984497 -3.81070436 -3.81157620 -3.81250010 -3.81351212 -3.81464375 -3.81592106 -3.81736378 -3.81898465 -3.82078886 -3.82277339 -3.82492652 -3.82722759 -3.82964780 -3.83215142 -3.83469692 -3.83723961 -3.83972879 -3.84211393 -3.84434546 -3.84637692 -3.84817077 -3.84968806 -3.85090282 -3.85179812 -3.85236691 -3.85261263 -3.85255006 -3.85220355 -3.85160618 -3.85079838 -3.84982889 -3.84874692 -3.84760619 -3.84646163 -3.84536772 -3.84437671 -3.84353715 -3.84289278 -3.84248170 -3.84233548 -3.84247831 -3.84292647 -3.84368854 -3.84476592 -3.84615336 -3.84783956 -3.84980780 -3.85203713 -3.85450359 -3.85718154 -3.86004493 -3.86306840 -3.86622788 -3.86950103 -3.87286769 -3.87631220 -3.87981797 -3.88337289 -3.88696714 -3.89059281 -3.89425157 -3.89793034 -3.90162494 -3.90533197 -3.90904858 -3.91277027 -3.91649684 -3.92022635 -3.92395726 -3.92768857
10 -10 -7.07910213 -7.09954969 -7.11996231 -7.14029980 -7.16051682 -7.18056389 -7.20038839 -7.21993571 -7.23915054 -7.25797827 -7.27636636 -7.29426574 -7.31163205 -7.32842642 -7.34461613 -7.36017524 -7.37508524 -7.38933542 -7.40292265 -7.41585095 -7.42813100 -7.43977968 -7.45081956 -7.46127818 -7.47118734 -7.48058235 -7.48950606 -7.49799339 -7.50608606 -7.51382670 -7.52125834 -7.52843930 -7.53539553 -7.54216866 -7.54879923 -7.55532645 -7.56178451 -7.56821292 -7.57464556 -7.58111398 -7.58764709 -7.59425622 -7.60097815 -7.60783212 -7.61483392 -7.62199583 -7.62932652 -7.63683111 -7.64451160 -7.65236754 -7.66039658 -7.66859507 -7.67695868 -7.68548272 -7.69416256 -7.70299395 -7.71197335 -7.72109810 -7.73036607 -7.73977511 -7.74932251 -7.75900445 -7.76881547 -7.77874803 -7.78879209 -7.79893466 -7.80916502 -7.81945766 -7.82978914 -7.84013294 -7.85045975 -7.86076033 -7.87097809 -7.88107779 -7.89102351 -7.90077946 -7.91030550 -7.91957367 -7.92855305 -7.93721605 -7.94553929 -7.95348745 -7.96106674 -7.96827090 -7.97509999 -7.98156058 -7.98766596 -7.99343607 -7.99889700 -8.00408027 -8.00902206 -8.01376245 -8.01834479 -8.02281496 -8.02722085 -8.03161170 -8.03603751 -8.04054841 -8.04519393 -8.05002232 -8.05507974 -8.06040960 -8.06605168 -8.07204111 -8.07840723 -8.08517248 -8.09235530 -8.09995761 -8.10797573 -8.11639684 -8.12519901 -8.13437159 -8.14385578 -8.15360441 -8.16356502 -8.17368180 -8.18389191 -8.19414417 -8.20438426 -8.21456207 -8.22463354 -8.23454095 -8.24427972 -8.25383248 -8.26319104 -8.27235611 -8.28133704 -8.29015127 -8.29882288 -8.30738095 -8.31585783 -8.32428740 -8.33270355 -8.34113885 -8.34962348 -8.35818406 -8.36684253 -8.37561535 -8.38451329 -8.39354159 -8.40270007 -8.41198326 -8.42138076 -8.43087794 -8.44045687 -8.45009730 -8.45978286 -8.46948604 -8.47918473 -8.48885766 -8.49848500 -8.50806987 -8.51757584 -8.52699008 -8.53630197 -8.54550281 -8.55458061 -8.56353474 -8.57236067 -8.58105475 -8.58961404 -8.59801781 -8.60628287 -8.61440773 -8.62239183 -8.63023586 -8.63794208 -8.64551444 -8.65295819 -8.66027928 -8.66748372 -8.67457699 -8.68156327 -8.68844435 -8.69521836 -8.70187853 -8.70841195 -8.71479879 -8.72101252 -8.72702061 -8.73278528 -8.73826416 -8.74341139 -8.74817960 -8.75252220 -8.75639575 -8.75976396 -8.76259407 -8.76486464 -8.76656449 -8.76769400 -8.76826690 -8.76830677 -8.76785307 -8.76695669 -8.76567866 -8.76408975 -8.76226633 -8.76029053 -8.75824739 -8.75622259 -8.75430422 -8.75256764 -8.75108748 -8.74993185 -8.74916103 -8.74882609 -8.74896801 -8.74961742 -8.75079480 -8.75251069 -8.75476579 -8.75755148 -8.76085076 -8.76463961 -8.76888822 -8.77356228 -8.77862423 -8.78403423 -8.78975116 -8.79573359 -8.80194067 -8.80833300 -8.81487291 -8.82152471 -8.82825489 -8.83503599 -8.84183562 -8.84862772 -8.85538887 -8.86209844 -8.86875307 -8.87532298 -8.88179599 -8.88816281 -8.89441689 -8.90055117 -8.90656791 -8.91246821 -8.91825489 -8.92393212 -8.92949278 -8.93495469 -8.94032288 -8.94560155 -8.95079345 -8.95589930 -8.96091740 -8.96584368 -8.97067197 -8.97539429 -8.98000110 -8.98448176 -8.98882522 -8.99302094 -8.99705976 -9.00093480 -9.00464208 -9.00818055 -9.01155191 -9.01476036 -9.01781241 -9.02071651 -9.02348237 -9.02612010 -9.02863944 -9.03105018 -9.03335764 -9.03556694 -9.03768193 -9.03970571 -9.04164512 -9.04349840 -9.04526889 -9.04696103 -9.04858086 -9.05013569 -9.05163692 -9.05309694 -9.05452927 -9.05594788
11 0 2.49800833 2.50787021 2.51772978 2.52758402 2.53742896 2.54725971 2.55707052 2.56685476 2.57660498 2.58631301 2.59596996 2.60556633 2.61509203 2.62453648 2.63388869 2.64313733 2.65227081 2.66127737 2.67014525 2.67886279 2.68741866 2.69580195 2.70400237 2.71201047 2.71981788 2.72741750 2.73480776 2.74198061 2.74893411 2.75566843 2.76218592 2.76850492 2.77461817 2.78053534 2.78626843 2.79183159 2.79723812 2.80250918 2.80766431 2.81272420 2.81771019 2.82263317 2.82752546 2.83240781 2.83730001 2.84222041 2.84718551 2.85220957 2.85730445 2.86247934 2.86774068 2.87309196 2.87853361 2.88406310 2.88967502 2.89536130 2.90111127 2.90691188 2.91274800 2.91860281 2.92445810 2.93029468 2.93609272 2.94183214 2.94749299 2.95305586 2.95850519 2.96382065 2.96898655 2.97398898 2.97881613 2.98346840 2.98792794 2.99219029 2.99625360 3.00011871 3.00378719 3.00726740 3.01056805 3.01370010 3.01667657 3.01950625 3.02221209 3.02481158 3.02732296 3.02976493 3.03215614 3.03451490 3.03685877 3.03920427 3.04156649 3.04395876 3.04639240 3.04887652 3.05141793 3.05402105 3.05668776 3.05941741 3.06220690 3.06505083 3.06794167 3.07086992 3.07382434 3.07679217 3.07975946 3.08271143 3.08563427 3.08851073 3.09132517 3.09406228 3.09670735 3.09925197 3.10167741 3.10397214 3.10612602 3.10813041 3.10997734 3.11166260 3.11318255 3.11453510 3.11571969 3.11673514 3.11758643 3.11827699 3.11881132 3.11919488 3.11943393 3.11953542 3.11950689 3.11935631 3.11909206 3.11872274 3.11825714 3.11770411 3.11707246 3.11637090 3.11560792 3.11479173 3.11393016 3.11303058 3.11209983 3.11114414 3.11016907 3.10917948 3.10817951 3.10717256 3.10616070 3.10514638 3.10413079 3.10311446 3.10209735 3.10107667 3.10005365 3.09902695 3.09799501 3.09695615 3.09590927 3.09485225 3.09378374 3.09270270 3.09160844 3.09050322 3.08938501 3.08825473 3.08711391 3.08596467 3.08480979 3.08365265 3.08249725 3.08134811 3.08021022 3.07908903 3.07799032 3.07692017 3.07588484 3.07489071 3.07394417 3.07305153 3.07221891 3.07145210 3.07075645 3.07013673 3.06959704 3.06914064 3.06876988 3.06848606 3.06828924 3.06817854 3.06815166 3.06820521 3.06833468 3.06853514 3.06879999 3.06912214 3.06949407 3.06990804 3.07035612 3.07083112 3.07132611 3.07183480 3.07235178 3.07287151 3.07339193 3.07391102 3.07442787 3.07494268 3.07545668 3.07597206 3.07649180 3.07701953 3.07755925 3.07811522 3.07869175 3.07929298 3.07992279 3.08058458 3.08128112 3.08201439 3.08278553 3.08359473 3.08444115 3.08532289 3.08623692 3.08717913 3.08814437 3.08912655 3.09011921 3.09111400 3.09210240 3.09307540 3.09402359 3.09493934 3.09581079 3.09662823 3.09738204 3.09806280 3.09866107 3.09916845 3.09957650 3.09987718 3.10006287 3.10012636 3.10006147 3.09986193 3.09952192 3.09903613 3.09839969 3.09760824 3.09665781 3.09554482 3.09426593 3.09281802 3.09119812 3.08940333 3.08743083 3.08527778 3.08294134 3.08041862 3.07770683 3.07480337 3.07170599 3.06841294 3.06492310 3.06123618 3.05735294 3.05327534 3.04900439 3.04454726 3.03991056 3.03510253 3.03013302 3.02500211 3.01973358 3.01434183 3.00884222 3.00325080 2.99758713 2.99186460 2.98609933 2.98030672 2.97450109
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12 -2 0.21191463 0.21191474 0.21191325 0.21190865 0.21189956 0.21188479 0.21186335 0.21183454 0.21179797 0.21175359 0.21170172 0.21164309 0.21157887 0.21151065 0.21144041 0.21137057 0.21130388 0.21124348 0.21119280 0.21115549 0.21113539 0.21113645 0.21116264 0.21121790 0.21130603 0.21143066 0.21159517 0.21180247 0.21205506 0.21235499 0.21270378 0.21310331 0.21355323 0.21405330 0.21460271 0.21520010 0.21584323 0.21653007 0.21725786 0.21802351 0.21882371 0.21965314 0.22050998 0.22139075 0.22229206 0.22321073 0.22414388 0.22508903 0.22604410 0.22700752 0.22797828 0.22895594 0.22994067 0.23093328 0.23193514 0.23294815 0.23397474 0.23501777 0.23608047 0.23716628 0.23827875 0.23942138 0.24059754 0.24181032 0.24306242 0.24435603 0.24569343 0.24707478 0.24850011 0.24996874 0.25147917 0.25303257 0.25462260 0.25624551 0.25789690 0.25957190 0.26126427 0.26296932 0.26468125 0.26639421 0.26810242 0.26979659 0.27147521 0.27313344 0.27476693 0.27637190 0.27794520 0.27948444 0.28098794 0.28245479 0.28388483 0.28527864 0.28663758 0.28796371 0.28925973 0.29052895 0.29177520 0.29300280 0.29421645 0.29542115 0.29662208 0.29782453 0.29903381 0.30025512 0.30149354 0.30275388 0.30404133 0.30535931 0.30671145 0.30810094 0.30953042 0.31100529 0.31252403 0.31408764 0.31569657 0.31735076 0.31904866 0.32079007 0.32257343 0.32439676 0.32625768 0.32814928 0.33007254 0.33202416 0.33400059 0.33599811 0.33801283 0.34004074 0.34207777 0.34411984 0.34616284 0.34820276 0.35023566 0.35225773 0.35426533 0.35625503 0.35822362 0.36016818 0.36208607 0.36397496 0.36583287 0.36765818 0.36944964 0.37120639 0.37292798 0.37461433 0.37626668 0.37788484 0.37946994 0.38102348 0.38254731 0.38404689 0.38552137 0.38697354 0.38840647 0.38982343 0.39122712 0.39262192 0.39401156 0.39539983 0.39679060 0.39818466 0.39958888 0.40100707 0.40244294 0.40390015 0.40538226 0.40689267 0.40843470 0.41001150 0.41162608 0.41328130 0.41497988 0.41672435 0.41851709 0.42036029 0.42225595 0.42420588 0.42621168 0.42827472 0.43039612 0.43257677 0.43481726 0.43711792 0.43947877 0.44189952 0.44438097 0.44692088 0.44951802 0.45217084 0.45487747 0.45764184 0.46045561 0.46331603 0.46622008 0.46916453 0.47214430 0.47515737 0.47819997 0.48126823 0.48435817 0.48745899 0.49057345 0.49369756 0.49682743 0.49995922 0.50308920 0.50621379 0.50932956 0.51243321 0.51552166 0.51859196 0.52164139 0.52466738 0.52766754 0.53063966 0.53358167 0.53649164 0.53936777 0.54220835 0.54501174 0.54777635 0.55050063 0.55318299 0.55582187 0.55841565 0.56096405 0.56346388 0.56591334 0.56831053 0.57065348 0.57294507 0.57517796 0.57734992 0.57945867 0.58150188 0.58347611 0.58538015 0.58721162 0.58896824 0.59064777 0.59224472 0.59376092 0.59519464 0.59654437 0.59780888 0.59898723 0.60007882 0.60108339 0.60200102 0.60283217 0.60357763 0.60423857 0.60481648 0.60531318 0.60573076 0.60607157 0.60633819 0.60653341 0.60666017 0.60672157 0.60672080 0.60666115 0.60654597 0.60637866 0.60616266 0.60590127 0.60559808 0.60525655 0.60488016 0.60447235 0.60403557 0.60357407 0.60309120 0.60259022 0.60207426 0.60154662 0.60100986 0.60046662 0.59991932 0.59937011
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12 -3 2.56739040 2.56575242 2.56411672 2.56248572 2.56086204 2.55924842 2.55764765 2.55606246 2.55449543 2.55294895 2.55142511 2.54992561 2.54845171 2.54700423 2.54558350 2.54418938 2.54282128 2.54147815 2.54015853 2.53886064 2.53758245 2.53632173 2.53507615 2.53384332 2.53262084 2.53140639 2.53019710 2.52899157 2.52778794 2.52658448 2.52537970 2.52416958 2.52295562 2.52173682 2.52051234 2.51928152 2.51804447 2.51680012 2.51554815 2.51428834 2.51302052 2.51174741 2.51046617 2.50917672 2.50787892 2.50657256 2.50525726 2.50393248 2.50259743 2.50125104 2.49989191 2.49851825 2.49712784 2.49571802 2.49428568 2.49282727 2.49133880 2.48981583 2.48825355 2.48664680 2.48499019 2.48327814 2.48150492 2.47966480 2.47775204 2.47576105 2.47368525 2.47152058 2.46926221 2.46690571 2.46444707 2.46187701 2.45919776 2.45640681 2.45350222 2.45048259 2.44734887 2.44409921 2.44073396 2.43725403 2.43366088 2.42996471 2.42616028 2.42225055 2.41823892 2.41412919 2.40992555 2.40563248 2.40125472 2.39679722 2.39226503 2.38766325 2.38299692 2.37827102 2.37349030 2.36865924 2.36378196 2.35886215 2.35390303 2.34890731 2.34387714 2.33881416 2.33371937 2.32859327 2.32343582 2.31824652 2.31302157 2.30776250 2.30246769 2.29713528 2.29176320 2.28633737 2.28086727 2.27535063 2.26978525 2.26416901 2.25850303 2.25278247 2.24700574 2.24117149 2.23527865 2.22933953 2.22334085 2.21728245 2.21116449 2.20498742 2.19875198 2.19245919 2.18611030 2.17970670 2.17324996 2.16674169 2.16018353 2.15357709 2.14692391 2.14022540 2.13348280 2.12669714 2.11986923 2.11299966 2.10608877 2.09913672 2.09214341 2.08510859 2.07803187 2.07091277 2.06374687 2.05653756 2.04928444 2.04198724 2.03464592 2.02724448 2.01979952 2.01231197 2.00478317 1.99721487 1.98961345 1.98197745 1.97430994 1.96661443 1.95889474 1.95117196 1.94343360 1.93568423 1.92792852 1.92017118 1.91241686 1.90467012 1.89693529 1.88921648 1.88151744 1.87384152 1.86619161 1.85857011 1.85097890 1.84341934 1.83589223 1.82839781 1.82093581 1.81350548 1.80610563 1.79873472 1.79139086 1.78407191 1.77677555 1.76949933 1.76223681 1.75498949 1.74775499 1.74053100 1.73331537 1.72609035 1.71886998 1.71165273 1.70443730 1.69722263 1.69001186 1.68280047 1.67558817 1.66837486 1.66116068 1.65396177 1.64676288 1.63956471 1.63236807 1.62517384 1.61798295 1.61079631 1.60361479 1.59643912 1.58926987 1.58210741 1.57495181 1.56780287 1.56066008 1.55352261 1.54638931 1.53925870 1.53212899 1.52499813 1.51786385 1.51072366 1.50357495 1.49641495 1.48924080 1.48204954 1.47483423 1.46759575 1.46033104 1.45303698 1.44571044 1.43833208 1.43091469 1.42345502 1.41594980 1.40839576 1.40079376 1.39313642 1.38542049 1.37764273 1.36979998 1.36190652 1.35394225 1.34590430 1.33778989 1.32959639 1.32132135 1.31296248 1.30451771 1.29598523 1.28736346 1.27865115 1.26984735 1.26095146 1.25196327 1.24288292 1.23371098 1.22444847 1.21509678 1.20565777 1.19613370 1.18652722 1.17684142 1.16707972 1.15724590 1.14734405 1.13737303 1.12734286 1.11725831 1.10712431 1.09694587 1.08670561 1.07643083 1.06612653 1.05579753 1.04544846 1.03508931 1.02471845 1.01433947 1.00395556 0.99356941
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15 1 0.45830488 0.45782197 0.45733936 0.45685735 0.45637633 0.45589667 0.45541881 0.45494320 0.45447031 0.45400063 0.45353467 0.45307292 0.45261591 0.45216414 0.45171810 0.45127826 0.45084510 0.45041905 0.45000051 0.44958986 0.44918743 0.44879353 0.44840841 0.44803228 0.44766530 0.44730759 0.44695904 0.44661988 0.44629008 0.44596958 0.44565828 0.44535539 0.44506143 0.44477620 0.44449945 0.44423095 0.44397055 0.44371782 0.44347246 0.44323417 0.44300266 0.44277811 0.44255973 0.44234725 0.44214042 0.44193901 0.44174284 0.44155174 0.44136557 0.44118426 0.44100775 0.44083604 0.44066917 0.44050723 0.44035035 0.44019871 0.44005252 0.43991206 0.43977762 0.43964954 0.43952820 0.43941398 0.43930732 0.43920866 0.43911844 0.43903714 0.43896519 0.43890309 0.43885132 0.43881032 0.43878051 0.43876227 0.43875606 0.43876222 0.43878104 0.43881279 0.43885765 0.43891576 0.43898724 0.43907212 0.43917035 0.43928160 0.43940590 0.43954301 0.43969266 0.43985446 0.44002800 0.44021279 0.44040828 0.44061386 0.44082888 0.44105264 0.44128440 0.44152338 0.44176879 0.44201981 0.44227560 0.44253535 0.44279822 0.44306340 0.44333009 0.44359753 0.44386498 0.44413174 0.44439716 0.44466065 0.44492181 0.44517999 0.44543479 0.44568584 0.44593284 0.44617608 0.44641485 0.44664904 0.44687859 0.44710351 0.44732371 0.44753943 0.44775080 0.44795797 0.44816115 0.44836011 0.44855555 0.44874769 0.44893679 0.44912310 0.44930687 0.44948835 0.44966777 0.44984538 0.45002138 0.45019601 0.45036946 0.45054192 0.45071358 0.45088462 0.45105521 0.45122550 0.45139566 0.45156583 0.45173617 0.45190681 0.45207789 0.45224955 0.45242192 0.45259514 0.45276943 0.45294481 0.45312141 0.45329935 0.45347874 0.45366009 0.45384313 0.45402795 0.45421467 0.45440339 0.45459410 0.45478702 0.45498224 0.45517989 0.45538006 0.45558245 0.45578761 0.45599569 0.45620684 0.45642123 0.45663905 0.45686050 0.45708582 0.45731525 0.45754907 0.45778758 0.45803108 0.45827993 0.45853449 0.45879515 0.45906229 0.45933634 0.45961771 0.45990684 0.46020414 0.46051005 0.46082496 0.46114928 0.46148337 0.46182758 0.46218242 0.46254796 0.46292444 0.46331202 0.46371083 0.46412184 0.46454417 0.46497777 0.46542250 0.46587813 0.46634414 0.46682041 0.46730651 0.46780193 0.46830610 0.46881725 0.46933576 0.46986086 0.47039172 0.47092747 0.47146718 0.47200989 0.47255459 0.47310025 0.47364585 0.47419031 0.47473259 0.47527162 0.47580637 0.47633580 0.47685891 0.47737471 0.47788228 0.47838068 0.47886907 0.47934661 0.47981254 0.48026612 0.48070670 0.48113366 0.48154666 0.48194499 0.48232821 0.48269596 0.48304793 0.48338462 0.48370507 0.48400918 0.48429690 0.48456827 0.48482323 0.48506207 0.48528499 0.48549223 0.48568408 0.48586047 0.48602222 0.48616971 0.48630334 0.48642356 0.48653081 0.48662556 0.48670829 0.48677947 0.48683960 0.48688917 0.48692866 0.48695858 0.48697941 0.48699164 0.48699575 0.48699222 0.48698150 0.48696407 0.48694038 0.48691086 0.48687594 0.48683605 0.48679159 0.48674295 0.48669049 0.48663459 0.48657562 0.48651391 0.48644979 0.48638343 0.48631525 0.48624554 0.48617457 0.48610259 0.48602986 0.48595654 0.48588282 0.48580887 0.48573480
15 -1 0.63300590 0.63397611 0.63494625 0.63591622 0.63688593 0.63785526 0.63882409 0.63979230 0.64075975 0.64172628 0.64269172 0.64365591 0.64461866 0.64557977 0.64653904 0.64749626 0.64845120 0.64940364 0.65035334 0.65130006 0.65224356 0.65318359 0.65411990 0.65505224 0.65598037 0.65690403 0.65782347 0.65873796 0.65964724 0.66055107 0.66144922 0.66234339 0.66323136 0.66411290 0.66498776 0.66585570 0.66671600 0.66756888 0.66841407 0.66925131 0.67008033 0.67089905 0.67170900 0.67250989 0.67330141 0.67408324 0.67485508 0.67561658 0.67636743 0.67710730 0.67783587 0.67855281 0.67925780 0.67995053 0.68063071 0.68129805 0.68195226 0.68259310 0.68322032 0.68383370 0.68443303 0.68501815 0.68558889 0.68614513 0.68668676 0.68721371 0.68772619 0.68822389 0.68870681 0.68917497 0.68962842 0.69006816 0.69049327 0.69090385 0.69130000 0.69168185 0.69204932 0.69240274 0.69274226 0.69306801 0.69338012 0.69367808 0.69396272 0.69423418 0.69449260 0.69473810 0.69497084 0.69519095 0.69539860 0.69559396 0.69577720 0.69594853 0.69610817 0.69625635 0.69639334 0.69651944 0.69663496 0.69674027 0.69683574 0.69692180 0.69699890 0.69706752 0.69712820 0.69718147 0.69722792 0.69726816 0.69730284 0.69733260 0.69735810 0.69738004 0.69739911 0.69741605 0.69743151 0.69744620 0.69746080 0.69747598 0.69749235 0.69751053 0.69753109 0.69755455 0.69758139 0.69761198 0.69764673 0.69768597 0.69772995 0.69777890 0.69783295 0.69789221 0.69795673 0.69802650 0.69810147 0.69818155 0.69826660 0.69835646 0.69845093 0.69854979 0.69865279 0.69875967 0.69887015 0.69898395 0.69910078 0.69922035 0.69934239 0.69946660 0.69959273 0.69972050 0.69984975 0.69998018 0.70011156 0.70024369 0.70037640 0.70050978 0.70064340 0.70077712 0.70091079 0.70104430 0.70117748 0.70131030 0.70144268 0.70157454 0.70170582 0.70183617 0.70196584 0.70209478 0.70222296 0.70235033 0.70247686 0.70260254 0.70272733 0.70285122 0.70297417 0.70309618 0.70321722 0.70333728 0.70345634 0.70357438 0.70369139 0.70380734 0.70392222 0.70403601 0.70414867 0.70426018 0.70437050 0.70447959 0.70458739 0.70469385 0.70479895 0.70490256 0.70500458 0.70510491 0.70520344 0.70530024 0.70539495 0.70548742 0.70557747 0.70566490 0.70574946 0.70583098 0.70590921 0.70598389 0.70605474 0.70612132 0.70618347 0.70624085 0.70629311 0.70633985 0.70638068 0.70641517 0.70644286 0.70646331 0.70647600 0.70648045 0.70647613 0.70646250 0.70643903 0.70640515 0.70636034 0.70630402 0.70623567 0.70615475 0.70606076 0.70595318 0.70583157 0.70569548 0.70554451 0.70537831 0.70519645 0.70499874 0.70478498 0.70455500 0.70430870 0.70404544 0.70376578 0.70346981 0.70315767 0.70282961 0.70248611 0.70212736 0.70175378 0.70136588 0.70096420 0.70055026 0.70012387 0.69968570 0.69923650 0.69877704 0.69830809 0.69783048 0.69734503 0.69685255 0.69635388 0.69584982 0.69534118 0.69482872 0.69431320 0.69379531 0.69327574 0.69275510 0.69223396 0.69171286 0.69119225 0.69067253 0.69015407 0.68963714 0.68912197 0.68860873 0.68809727 0.68758791 0.68708068 0.68657554 0.68607240 0.68557008 0.68506951 0.68457054 0.68407298 0.68357661 0.68308150 0.68258717 0.68209341 0.68160000 0.68110677
15 2 0.04784307 0.04858975 0.04933640 0.05008298 0.05082947 0.05157587 0.05232218 0.05306842 0.05381462 0.05456083 0.05530710 0.05605351 0.05680014 0.05754708 0.05829443 0.05904230 0.05979081 0.06054007 0.06129020 0.06204132 0.06279351 0.06354687 0.06430147 0.06505736 0.06581456 0.06657307 0.06733328 0.06809470 0.06885724 0.06962078 0.07038514 0.07115181 0.07191890 0.07268615 0.07345329 0.07422003 0.07498563 0.07575018 0.07651334 0.07727477 0.07803411 0.07878937 0.07954186 0.08029124 0.08103718 0.08177936 0.08251747 0.08325122 0.08398033 0.08470453 0.08542359 0.08613726 0.08684533 0.08754760 0.08824387 0.08893398 0.08961776 0.09029507 0.09096578 0.09162974 0.09228687 0.09293706 0.09358022 0.09421628 0.09484516 0.09546681 0.09608149 0.09668881 0.09728870 0.09788111 0.09846595 0.09904441 0.09961509 0.10017788 0.10073266 0.10127926 0.10181724 0.10234671 0.10286747 0.10337928 0.10388192 0.10437407 0.10485658 0.10532916 0.10579156 0.10624348 0.10668463 0.10711473 0.10753349 0.10794063 0.10833586 0.10871891 0.10908953 0.10944746 0.10979247 0.11012433 0.11044284 0.11074783 0.11103912 0.11131659 0.11158012 0.11182963 0.11206505 0.11228636 0.11249357 0.11268671 0.11286595 0.11303128 0.11318286 0.11332086 0.11344553 0.11355736 0.11365637 0.11374293 0.11381743 0.11388031 0.11393202 0.11397312 0.11400413 0.11402562 0.11403817 0.11404236 0.11403882 0.11402815 0.11401090 0.11398764 0.11395890 0.11392519 0.11388695 0.11384462 0.11379858 0.11374916 0.11369664 0.11364124 0.11358315 0.11352249 0.11345932 0.11339367 0.11332549 0.11325470 0.11318117 0.11310472 0.11302512 0.11294211 0.11285538 0.11276459 0.11266931 0.11256918 0.11246376 0.11235260 0.11223522 0.11211082 0.11197913 0.11183962 0.11169174 0.11153492 0.11136869 0.11119242 0.11100553 0.11080747 0.11059768 0.11037612 0.11014182 0.10989426 0.10963296 0.10935743 0.10906723 0.10876193 0.10844113 0.10810447 0.10775160 0.10738222 0.10699607 0.10659292 0.10617259 0.10573494 0.10527987 0.10480734 0.10431733 0.10380990 0.10328514 0.10274319 0.10218424 0.10160853 0.10101635 0.10040803 0.09978361 0.09914385 0.09848922 0.09782023 0.09713745 0.09643993 0.09572980 0.09500770 0.09427435 0.09353044 0.09277713 0.09201475 0.09124404 0.09046573 0.08968057 0.08889101 0.08809603 0.08729631 0.08649249 0.08568519 0.08487499 0.08406245 0.08324806 0.08243231 0.08161563 0.08079841 0.07998102 0.07916379 0.07834699 0.07753088 0.07671569 0.07590158 0.07508871 0.07427721 0.07346714 0.07265857 0.07185150 0.07104592 0.07024180 0.06943904 0.06863710 0.06783629 0.06703643 0.06623733 0.06543877 0.06463875 0.06383876 0.06303849 0.06223763 0.06143586 0.06063327 0.05982905 0.05902283 0.05821423 0.05740286 0.05659011 0.05577380 0.05495354 0.05412892 0.05329956 0.05246507 0.05162508 0.05077923 0.04992717 0.04906859 0.04820320 0.04733073 0.04645096 0.04556370 0.04466881 0.04376617 0.04285573 0.04193747 0.04101144 0.04007770 0.03913640 0.03818772 0.03723187 0.03626912 0.03529978 0.03432366 0.03334166 0.03235419 0.03136170 0.03036463 0.02936125 0.02835423 0.02734405 0.02633119 0.02531612 0.02429985 0.02328224 0.02226368 0.02124455 0.02022514
15 -2 0.08929312 0.08907261 0.08885193 0.08863089 0.08840927 0.08818685 0.08796338 0.08773863 0.08751232 0.08728420 0.08705402 0.08682153 0.08658649 0.08634866 0.08610785 0.08586388 0.08561657 0.08536581 0.08511148 0.08485353 0.08459192 0.08432665 0.08405777 0.08378534 0.08350948 0.08323034 0.08294793 0.08266261 0.08237463 0.08208425 0.08179174 0.08149675 0.08120025 0.08090255 0.08060398 0.08030486 0.08000568 0.07970657 0.07940784 0.07910976 0.07881257 0.07851715 0.07822306 0.07793045 0.07763946 0.07735018 0.07706269 0.07677701 0.07649314 0.07621103 0.07593061 0.07565177 0.07537437 0.07509824 0.07482321 0.07454905 0.07427554 0.07400244 0.07372951 0.07345649 0.07318314 0.07290923 0.07263453 0.07235884 0.07208198 0.07180379 0.07152400 0.07124267 0.07095975 0.07067521 0.07038908 0.07010078 0.06981101 0.06951990 0.06922760 0.06893429 0.06864033 0.06834578 0.06805088 0.06775589 0.06746109 0.06716739 0.06687443 0.06658251 0.06629192 0.06600298 0.06571598 0.06543123 0.06514906 0.06486977 0.06459369 0.06432114 0.06405247 0.06378801 0.06352811 0.06327312 0.06302342 0.06277936 0.06254135 0.06230978 0.06208505 0.06186758 0.06165780 0.06145614 0.06126305 0.06107898 0.06090430 0.06073959 0.06058531 0.06044193 0.06030993 0.06018951 0.06008146 0.05998622 0.05990422 0.05983589 0.05978164 0.05974180 0.05971671 0.05970665 0.05971188 0.05973254 0.05976876 0.05982063 0.05988819 0.05997139 0.06007014 0.06018425 0.06031349 0.06045755 0.06061603 0.06078850 0.06097444 0.06117327 0.06138436 0.06160701 0.06184047 0.06208396 0.06233664 0.06259763 0.06286604 0.06314093 0.06342134 0.06370632 0.06399488 0.06428604 0.06457898 0.06487258 0.06516587 0.06545791 0.06574778 0.06603523 0.06631877 0.06659757 0.06687087 0.06713794 0.06739795 0.06765045 0.06789484 0.06813061 0.06835730 0.06857401 0.06878090 0.06897763 0.06916394 0.06933959 0.06950438 0.06965817 0.06980081 0.06993223 0.07005237 0.07016118 0.07025865 0.07034482 0.07041970 0.07048338 0.07053592 0.07057745 0.07060808 0.07062798 0.07063731 0.07063627 0.07062507 0.07060396 0.07057319 0.07053305 0.07048380 0.07042580 0.07035939 0.07028494 0.07020283 0.07011327 0.07001685 0.06991402 0.06980523 0.06969098 0.06957181 0.06944817 0.06932057 0.06918954 0.06905561 0.06891963 0.06878185 0.06864282 0.06850310 0.06836322 0.06822374 0.06808520 0.06794814 0.06781308 0.06768056 0.06755107 0.06742512 0.06730316 0.06718566 0.06707306 0.06696578 0.06686420 0.06676870 0.06667961 0.06659727 0.06652197 0.06645398 0.06639355 0.06634090 0.06629624 0.06625972 0.06623153 0.06621182 0.06620071 0.06619830 0.06620471 0.06622005 0.06624438 0.06627777 0.06632027 0.06637191 0.06643275 0.06650284 0.06658222 0.06667093 0.06676878 0.06687600 0.06699261 0.06711864 0.06725412 0.06739903 0.06755340 0.06771720 0.06789042 0.06807299 0.06826487 0.06846597 0.06867619 0.06889540 0.06912346 0.06936019 0.06960540 0.06985888 0.07012038 0.07038965 0.07066639 0.07095030 0.07124105 0.07153831 0.07184170 0.07215102 0.07246571 0.07278537 0.07310956 0.07343788 0.07377061 0.07410660 0.07444543 0.07478666 0.07512987 0.07547448 0.07582031 0.07616699 0.07651420 0.07686167
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20 -20 -0.12122812 -0.12099667 -0.12076523 -0.12053381 -0.12030242 -0.12007107 -0.11983978 -0.11960855 -0.11937739 -0.11914632 -0.11891535 -0.11868449 -0.11845374 -0.11822314 -0.11799268 -0.11776238 -0.11753226 -0.11730232 -0.11707259 -0.11684307 -0.11661379 -0.11638476 -0.11615599 -0.11592750 -0.11569931 -0.11547143 -0.11524375 -0.11501642 -0.11478946 -0.11456288 -0.11433670 -0.11411044 -0.11388462 -0.11365926 -0.11343437 -0.11320998 -0.11298623 -0.11276302 -0.11254035 -0.11231827 -0.11209677 -0.11187638 -0.11165661 -0.11143751 -0.11121907 -0.11100133 -0.11078431 -0.11056802 -0.11035250 -0.11013775 -0.10992380 -0.10971068 -0.10949839 -0.10928697 -0.10907644 -0.10886681 -0.10865811 -0.10845036 -0.10824359 -0.10803780 -0.10783303 -0.10762929 -0.10742661 -0.10722501 -0.10702451 -0.10682513 -0.10662678 -0.10642961 -0.10623362 -0.10603885 -0.10584531 -0.10565260 -0.10546117 -0.10527104 -0.10508224 -0.10489478 -0.10470878 -0.10452417 -0.10434095 -0.10415915 -0.10397878 -0.10380025 -0.10362319 -0.10344760 -0.10327349 -0.10310090 -0.10292981 -0.10276025 -0.10259223 -0.10242576 -0.10226084 -0.10209748 -0.10193570 -0.10177548 -0.10161685 -0.10145980 -0.10130434 -0.10115046 -0.10099817 -0.10084746 -0.10069834 -0.10055080 -0.10040484 -0.10026045 -0.10011763 -0.09997636 -0.09983657 -0.09969832 -0.09956161 -0.09942641 -0.09929273 -0.09916025 -0.09902927 -0.09889976 -0.09877171 -0.09864510 -0.09851999 -0.09839628 -0.09827396 -0.09815301 -0.09803341 -0.09791539 -0.09779867 -0.09768323 -0.09756904 -0.09745607 -0.09734432 -0.09723373 -0.09712430 -0.09701599 -0.09690878 -0.09680263 -0.09669751 -0.09659340 -0.09649026 -0.09638806 -0.09628676 -0.09618634 -0.09608676 -0.09598799 -0.09588999 -0.09579273 -0.09569618 -0.09560029 -0.09550503 -0.09541038 -0.09531623 -0.09522262 -0.09512950 -0.09503684 -0.09494461 -0.09485257 -0.09476088 -0.09466952 -0.09457845 -0.09448764 -0.09439710 -0.09430674 -0.09421654 -0.09412647 -0.09403648 -0.09394674 -0.09385703 -0.09376732 -0.09367756 -0.09358773 -0.09349780 -0.09340774 -0.09331752 -0.09322711 -0.09313648 -0.09304559 -0.09295443 -0.09286296 -0.09277116 -0.09267900 -0.09258646 -0.09249350 -0.09240011 -0.09230625 -0.09221191 -0.09211707 -0.09202169 -0.09192577 -0.09182928 -0.09173220 -0.09163446 -0.09153610 -0.09143711 -0.09133746 -0.09123714 -0.09113592 -0.09103400 -0.09093138 -0.09082804 -0.09072398 -0.09061924 -0.09051376 -0.09040753 -0.09030055 -0.09019280 -0.09008453 -0.08997549 -0.08986568 -0.08975509 -0.08964372 -0.08953158 -0.08941864 -0.08930492 -0.08919041 -0.08907511 -0.08895902 -0.08884213 -0.08872445 -0.08860598 -0.08848671 -0.08836664 -0.08824578 -0.08812413 -0.08800169 -0.08787845 -0.08775442 -0.08762960 -0.08750399 -0.08737760 -0.08725042 -0.08712239 -0.08699359 -0.08686400 -0.08673365 -0.08660252 -0.08647035 -0.08633742 -0.08620373 -0.08606930 -0.08593413 -0.08579830 -0.08566176 -0.08552451 -0.08538656 -0.08524793 -0.08510893 -0.08496928 -0.08482899 -0.08468806 -0.08454653 -0.08440441 -0.08426170 -0.08411844 -0.08397463 -0.08383029 -0.08368544 -0.08354010 -0.08339429 -0.08324802 -0.08310131 -0.08295419 -0.08280666 -0.08265876 -0.08251049 -0.08236187 -0.08221293 -0.08206367 -0.08191413 -0.08176432 -0.08161425 -0.08146386 -0.08131325 -0.08116244 -0.08101146 -0.08086030 -0.08070867 -0.08055691 -0.08040504 -0.08025308 -0.08010104 -0.07994902 -0.07979696 -0.07964486 -0.07949275 -0.07934062

34159
data/CHAOS8/CHAOS-8.2_static.shc.txt Normal file
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5
example/CMakeLists.txt
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@ -12,8 +12,8 @@ macro(add_example name switch)
endif()
endmacro()
add_example(gobser_tri2d_ex ON)
add_example(gobser_tri2d_sph_ex ON)
add_example(gobser_tri2d_ex OFF)
add_example(gobser_tri2d_sph_ex OFF)
add_example(mobser_dipole_ex OFF)
add_example(mobser_block_ex OFF)
add_example(mobser_block_gradient_ex OFF)
@ -25,4 +25,5 @@ add_example(mobser_tetra_ex2 OFF)
add_example(mobser_tetra_sph_ex OFF)
add_example(mobser_tesseroid_ex OFF)
add_example(read_IGRF_ex OFF)
add_example(read_Swarm_ex ON)
add_example(power_spectrum_ex OFF)

2
example/gobser_tri2d_ex.cpp
View File

@ -66,7 +66,7 @@ int main(int argc, char *argv[])
geodsv_io tio;
tio.init_table(obsp.size(), 8);
tio.set_column_names({"X", "Y", "Vx", "Vz", "Vxx", "Vxz", "Vzx", "Vzz"});
tio.column_names({"X", "Y", "Vx", "Vz", "Vxx", "Vxz", "Vzx", "Vzz"});
tio.fill_column_point2dc(obsp, "X", "Y");
tio.fill_column(vx, "Vx", 12);
tio.fill_column(vz, "Vz", 12);

7
example/gobser_tri2d_sph_ex.cpp
View File

@ -25,12 +25,11 @@
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "toml.hpp"
#include "../lib/potential.h"
#include "gctl/core.h"
#include "gctl/geometry.h"
#include "gctl/io.h"
#include "../lib/potential.h"
#include "toml.hpp"
using namespace gctl;
int main(int argc, char *argv[]) try
@ -94,7 +93,7 @@ int main(int argc, char *argv[]) try
geodsv_io gio;
gio.init_table(obsp.size(), 8);
gio.set_column_names({"rad", "deg", "gx", "gz", "gxx", "gxz", "gzx", "gzz"});
gio.column_names({"rad", "deg", "gx", "gz", "gxx", "gxz", "gzx", "gzz"});
gio.fill_column(r, "rad");
gio.fill_column(d, "deg");
gio.fill_column(gx, "gx");

50
example/read_Swarm_ex.cpp Normal file
View File

@ -0,0 +1,50 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "iomanip"
#include "../lib/potential.h"
using namespace gctl;
int main(int argc, char const *argv[]) try
{
int spl_odr, smp_num;
array<shc_data> SHCs;
read_Swarm_shc("data/CHAOS8/CHAOS-8.2_core.shc", SHCs, spl_odr, smp_num);
std::clog << SHCs.size() << std::endl;
std::clog << std::setprecision(10) << SHCs.back().time << std::endl;
std::cout << std::setprecision(10) << SHCs.back().coeff_s(20, 20) << std::endl;
std::cout << std::setprecision(10) << SHCs.back().coeff_c(20, 20) << std::endl;
save_Swarm_shc("tmp", SHCs, spl_odr, smp_num);
return 0;
}
catch (std::exception &e)
{
GCTL_ShowWhatError(e.what(), GCTL_ERROR_ERROR, 0, 0, 0);
}

13
lib/CMakeLists.txt
View File

@ -41,20 +41,13 @@ target_link_libraries(gctl_potential_static ${GCTL_LIB})
target_link_libraries(gctl_potential PUBLIC ${GCTL_MESH_LIB})
target_link_libraries(gctl_potential_static ${GCTL_MESH_LIB})
target_link_libraries(gctl_potential PUBLIC ${GCTL_GRAPHIC_LIB})
target_link_libraries(gctl_potential_static ${GCTL_GRAPHIC_LIB})
target_link_libraries(gctl_potential PUBLIC ${GCTL_OPTIMIZATION_LIB})
target_link_libraries(gctl_potential_static ${GCTL_OPTIMIZATION_LIB})
#if(GCTL_GRAPHIC_MATHGL)
# target_link_libraries(gctl_potential PUBLIC ${MathGL2_LIBRARIES} ${MathGL2_FLTK_LIBRARIES})
# target_link_libraries(gctl_potential_static ${MathGL2_LIBRARIES} ${MathGL2_FLTK_LIBRARIES})
#endif()
if(GCTL_POTENTIAL_FFTW3)
target_link_libraries(gctl_potential PUBLIC ${FFTW3_LIBRARIES})
target_link_libraries(gctl_potential_static ${FFTW3_LIBRARIES})
find_library(FFTW_LIB ${FFTW3_LIBRARIES} HINTS ${FFTW3_LIBRARY_DIRS})
target_link_libraries(gctl_potential PUBLIC ${FFTW_LIB})
target_link_libraries(gctl_potential_static ${FFTW_LIB})
endif()
if(GCTL_POTENTIAL_TESS)

5
lib/potential/gkernel_block.h
View File

@ -29,6 +29,9 @@
#define _GCTL_GRAV_KERNEL_BLOCK_H
#include "gm_data.h"
#include "gctl/poly/block.h"
#include "gctl/utility/progress_bar.h"
#include "gctl/math/gmath.h"
namespace gctl
{
@ -56,6 +59,6 @@ namespace gctl
*/
void gobser(array<double> &out_obs, const array<block> &ele, const array<point3dc> &obsp,
const array<double> &rho, gravitational_field_type_e comp_id = Vz, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_GRAV_KERNEL_BLOCK_H

3
lib/potential/gkernel_polygon.h
View File

@ -29,6 +29,7 @@
#define _GCTL_GRAV_KERNEL_POLYGON_H
#include "gm_data.h"
#include "gctl/poly/vertex.h"
namespace gctl
{
@ -43,6 +44,6 @@ namespace gctl
*/
void gobser(array<double> &out_obs, const array<vertex2dc> &cor_vert, const array<point2dc> &obsp,
const double &rho, gravitational_field_type_e comp_id = Vz);
}
};
#endif // _GCTL_GRAV_KERNEL_POLYGON_H

5
lib/potential/gkernel_rectangle2d.h
View File

@ -29,6 +29,9 @@
#define _GCTL_GRAV_KERNEL_RECTANGLE2D_H
#include "gm_data.h"
#include "gctl/poly/point2c.h"
#include "gctl/poly/rectangle2d.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -56,6 +59,6 @@ namespace gctl
*/
void gobser(array<double> &out_obs, const array<rectangle2d> &ele, const array<point2dc> &obsp,
const array<double> &rho, gravitational_field_type_e comp_id = Vz, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_GRAV_KERNEL_RECTANGLE2D_H

9
lib/potential/gkernel_sphere.h
View File

@ -28,12 +28,9 @@
#ifndef _GCTL_GRAV_KERNEL_SPHERE_H
#define _GCTL_GRAV_KERNEL_SPHERE_H
#include "gctl/core/array.h"
#include "gctl/geometry/point3c.h"
#include "gctl/geometry/sphere.h"
#include "gctl/optimization/loss_func.h"
#include "gm_data.h"
#include "gctl/poly/sphere.h"
#include "gctl/optimization/loss_func.h"
#ifdef GCTL_POTENTIAL_AUTODIFF
#include "autodiff/reverse/var.hpp"
@ -84,6 +81,6 @@ namespace gctl
#endif // GCTL_POTENTIAL_AUTODIFF
}
};
#endif // _GCTL_GRAV_KERNEL_SPHERE_H

4
lib/potential/gkernel_tesseroid.h
View File

@ -29,6 +29,8 @@
#define _GCTL_GRAV_KERNEL_TESSEROID_H
#include "gm_data.h"
#include "gctl/poly/tesseroid.h"
#include "gctl/utility/progress_bar.h"
#ifdef GCTL_POTENTIAL_TESS
@ -61,7 +63,7 @@ namespace gctl
*/
void gobser(array<double> &out_obs, const array<tesseroid> &ele, const array<point3ds> &obsp,
const array<double> &rho, gravitational_field_type_e comp_id = Vz, verbose_type_e verbose = FullMsg);
}
};
#endif // GCTL_POTENTIAL_TESS

6
lib/potential/gkernel_tetrahedron.cpp
View File

@ -1039,7 +1039,7 @@ double gkernel_tetra_potential_sig_sph(const gctl::grav_tetrahedron &a_ele, cons
gctl::gravtet_para* gp = a_ele.att;
op_c = a_op.s2c();
op_c = s2c(a_op);
int *v_order = a_ele.vec_order;
@ -1108,7 +1108,7 @@ gctl::point3dc gkernel_tetra_gradient_sig_sph(const gctl::grav_tetrahedron &a_el
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
int *v_order = a_ele.vec_order;
@ -1178,7 +1178,7 @@ gctl::tensor gkernel_tetra_tensor_sig_sph(const gctl::grav_tetrahedron &a_ele, c
R_T = R.transpose();
op_c = a_op.s2c();
op_c = s2c(a_op);
int *v_order = a_ele.vec_order;

5
lib/potential/gkernel_tetrahedron.h
View File

@ -29,6 +29,9 @@
#define _GCTL_GRAV_KERNEL_TETRAHEDRON_H
#include "gm_data.h"
#include "gctl/poly/tetrahedron.h"
#include "gctl/math/geometry3d.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -152,6 +155,6 @@ namespace gctl
*/
void gobser(array<tensor> &out_obs, const array<grav_tetrahedron> &ele, const array<point3ds> &obsp,
const array<double> &rho, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_GRAV_KERNEL_TETRAHEDRON_H

6
lib/potential/gkernel_triangle.cpp
View File

@ -360,7 +360,7 @@ double gkernel_triangle_potential_sig_sph(const gctl::grav_triangle &a_ele, cons
gctl::gravtri_para *gp = a_ele.att;
op_c = a_op.s2c();
op_c = s2c(a_op);
r_ijk[0] = *a_ele.vert[0] - op_c;
r_ijk[1] = *a_ele.vert[1] - op_c;
@ -423,7 +423,7 @@ gctl::point3dc gkernel_triangle_gradient_sig_sph(const gctl::grav_triangle &a_el
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
r_ijk[0] = *a_ele.vert[0] - op_c;
r_ijk[1] = *a_ele.vert[1] - op_c;
@ -487,7 +487,7 @@ gctl::tensor gkernel_triangle_tensor_sig_sph(const gctl::grav_triangle &a_ele, c
R_T = R.transpose();
op_c = a_op.s2c();
op_c = s2c(a_op);
r_ijk[0] = *a_ele.vert[0] - op_c;
r_ijk[1] = *a_ele.vert[1] - op_c;

4
lib/potential/gkernel_triangle.h
View File

@ -29,6 +29,8 @@
#define _GCTL_GRAV_KERNEL_TRIANGLE_H
#include "gm_data.h"
#include "gctl/poly/triangle.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -123,6 +125,6 @@ namespace gctl
*/
void gobser(array<tensor> &out_obs, const array<grav_triangle> &ele, const array<point3ds> &obsp,
double rho, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_GRAV_KERNEL_TRIANGLE_H

24
lib/potential/gkernel_triangle2d.cpp
View File

@ -443,7 +443,7 @@ void gkernel_triangle2d_vz2(gctl::matrix<double> &out_kernel, const gctl::array<
if (verbose == gctl::FullMsg) bar.progressed(i);
else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
#pragma omp parallel for private (j, obsg) schedule(guided)
for (j = 0; j < e_size; j++)
@ -471,7 +471,7 @@ void gkernel_triangle2d_vx2(gctl::matrix<double> &out_kernel, const gctl::array<
if (verbose == gctl::FullMsg) bar.progressed(i);
else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
#pragma omp parallel for private (j, obsg) schedule(guided)
for (j = 0; j < e_size; j++)
@ -500,7 +500,7 @@ void gkernel_triangle2d_vxx2(gctl::matrix<double> &out_kernel, const gctl::array
if (verbose == gctl::FullMsg) bar.progressed(i);
else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
#pragma omp parallel for private (j, t) schedule(guided)
for (j = 0; j < e_size; j++)
@ -532,7 +532,7 @@ void gkernel_triangle2d_vxz2(gctl::matrix<double> &out_kernel, const gctl::array
if (verbose == gctl::FullMsg) bar.progressed(i);
else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
#pragma omp parallel for private (j, t) schedule(guided)
for (j = 0; j < e_size; j++)
@ -564,7 +564,7 @@ void gkernel_triangle2d_vzx2(gctl::matrix<double> &out_kernel, const gctl::array
if (verbose == gctl::FullMsg) bar.progressed(i);
else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
#pragma omp parallel for private (j, t) schedule(guided)
for (j = 0; j < e_size; j++)
@ -596,7 +596,7 @@ void gkernel_triangle2d_vzz2(gctl::matrix<double> &out_kernel, const gctl::array
if (verbose == gctl::FullMsg) bar.progressed(i);
else if (verbose == gctl::ShortMsg) bar.progressed_simple(i);
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
#pragma omp parallel for private (j, t) schedule(guided)
for (j = 0; j < e_size; j++)
@ -774,7 +774,7 @@ void gobser_triangle2d_vz2(gctl::array<double> &out_obs, const gctl::array<gctl:
#pragma omp parallel for private (i, obsg, obsc) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
obsg.x = gkernel_triangle2d_vx_sig(ele.get(j), &obsc); // 沿x轴正方向的重力值
obsg.y = gkernel_triangle2d_vz_sig(ele.get(j), &obsc); // 沿z轴负方向的重力值
out_obs[i] += (obsg.y*sin(obsp[i].arc) - obsg.x*cos(obsp[i].arc))*rho[j]; // 沿半径负方向的重力值
@ -802,7 +802,7 @@ void gobser_triangle2d_vx2(gctl::array<double> &out_obs, const gctl::array<gctl:
#pragma omp parallel for private (i, obsg, obsc) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
obsg.x = gkernel_triangle2d_vx_sig(ele.get(j), &obsc); // 沿x轴正方向的重力值
obsg.y = gkernel_triangle2d_vz_sig(ele.get(j), &obsc); // 沿z轴负方向的重力值
out_obs[i] += (-1.0*obsg.y*cos(obsp[i].arc) + obsg.x*sin(obsp[i].arc))*rho[j]; // 沿弧度负方向的重力值
@ -831,7 +831,7 @@ void gobser_triangle2d_vxx2(gctl::array<double> &out_obs, const gctl::array<gctl
#pragma omp parallel for private (i, t, obsc) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
t[1][0] = gkernel_triangle2d_vzx_sig(ele.get(j), &obsc);
t[1][1] = gkernel_triangle2d_vzz_sig(ele.get(j), &obsc);
t[0][0] = -1.0*t[1][1];
@ -862,7 +862,7 @@ void gobser_triangle2d_vxz2(gctl::array<double> &out_obs, const gctl::array<gctl
#pragma omp parallel for private (i, t, obsc) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
t[1][0] = gkernel_triangle2d_vzx_sig(ele.get(j), &obsc);
t[1][1] = gkernel_triangle2d_vzz_sig(ele.get(j), &obsc);
t[0][0] = -1.0*t[1][1];
@ -893,7 +893,7 @@ void gobser_triangle2d_vzx2(gctl::array<double> &out_obs, const gctl::array<gctl
#pragma omp parallel for private (i, t, obsc) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
t[1][0] = gkernel_triangle2d_vzx_sig(ele.get(j), &obsc);
t[1][1] = gkernel_triangle2d_vzz_sig(ele.get(j), &obsc);
t[0][0] = -1.0*t[1][1];
@ -924,7 +924,7 @@ void gobser_triangle2d_vzz2(gctl::array<double> &out_obs, const gctl::array<gctl
#pragma omp parallel for private (i, t, obsc) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsc = obsp[i].p2c();
obsc = p2c(obsp[i]);
t[1][0] = gkernel_triangle2d_vzx_sig(ele.get(j), &obsc);
t[1][1] = gkernel_triangle2d_vzz_sig(ele.get(j), &obsc);
t[0][0] = -1.0*t[1][1];

4
lib/potential/gkernel_triangle2d.h
View File

@ -29,6 +29,8 @@
#define _GCTL_GRAV_KERNEL_TRIANGLE2D_H
#include "gm_data.h"
#include "gctl/poly/triangle2d.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -81,6 +83,6 @@ namespace gctl
*/
void gobser(array<double> &out_obs, const array<triangle2d> &ele, const array<point2dp> &obsp,
const array<double> &rho, gravitational_field_type_e comp_id = Vz, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_GRAV_KERNEL_TRIANGLE2D_H

10
lib/potential/gkernel_tricone.cpp
View File

@ -432,7 +432,7 @@ double gkernel_tricone_pot_sig(const gctl::gravcone &a_ele, const gctl::point3ds
gctl::gravcone_para* gp = a_ele.att;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -533,7 +533,7 @@ double gkernel_tricone_vr_sig(const gctl::gravcone &a_ele, const gctl::point3ds
R.y = sin((0.5-a_op.lat/180.0)*GCTL_Pi)*sin((2.0+a_op.lon/180.0)*GCTL_Pi);
R.z = cos((0.5-a_op.lat/180.0)*GCTL_Pi);
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -597,7 +597,7 @@ double gkernel_tricone_vrp_sig(const gctl::gravcone &a_ele, const gctl::point3ds
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -666,7 +666,7 @@ double gkernel_tricone_vrt_sig(const gctl::gravcone &a_ele, const gctl::point3ds
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -735,7 +735,7 @@ double gkernel_tricone_vrr_sig(const gctl::gravcone &a_ele, const gctl::point3ds
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)

5
lib/potential/gkernel_tricone.h
View File

@ -29,6 +29,9 @@
#define _GCTL_GRAV_KERNEL_TRICONE_H
#include "gm_data.h"
#include "gctl/poly/tri_cone.h"
#include "gctl/math/geometry3d.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -148,6 +151,6 @@ namespace gctl
const array<double> &obs_diff, const array<point3ds> &obsp, const array<double> &rho,
const array<vertex3dc> *verts_ptr = nullptr, double ang_limit = -1.0,
gravitational_field_type_e comp_id = Vz, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_GRAV_KERNEL_TRICONE_H

26
lib/potential/gkernel_tricone_model_gradient.cpp
View File

@ -334,7 +334,7 @@ void gobser_mGrad_tricone_vr(gctl::array<double> &out_mGrad,
#pragma omp parallel for private (j) shared(i) schedule(guided)
for (j = 0; j < v_size; j++)
{
if (angle(ops[i].s2c(), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
if (angle(s2c(ops[i]), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
out_mGrad.at(j) += obs_diff[i] * gobser_mGrad_tricone_vr_sig(vert_neighList[j], j, ops[i], rho);
}
}
@ -379,7 +379,7 @@ void gobser_mGrad_tricone_vrp(gctl::array<double> &out_mGrad,
#pragma omp parallel for private (j) shared(i) schedule(guided)
for (j = 0; j < v_size; j++)
{
if (angle(ops[i].s2c(), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
if (angle(s2c(ops[i]), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
out_mGrad.at(j) += obs_diff[i] * gobser_mGrad_tricone_vrp_sig(vert_neighList[j], j, ops[i], rho);
}
}
@ -424,7 +424,7 @@ void gobser_mGrad_tricone_vrt(gctl::array<double> &out_mGrad,
#pragma omp parallel for private (j) shared(i) schedule(guided)
for (j = 0; j < v_size; j++)
{
if (angle(ops[i].s2c(), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
if (angle(s2c(ops[i]), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
out_mGrad.at(j) += obs_diff[i] * gobser_mGrad_tricone_vrt_sig(vert_neighList[j], j, ops[i], rho);
}
}
@ -469,7 +469,7 @@ void gobser_mGrad_tricone_vrr(gctl::array<double> &out_mGrad,
#pragma omp parallel for private (j) shared(i) schedule(guided)
for (j = 0; j < v_size; j++)
{
if (angle(ops[i].s2c(), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
if (angle(s2c(ops[i]), verts_ptr->at(j)) <= ang_limit*GCTL_Pi/180.0)
out_mGrad.at(j) += obs_diff[i] * gobser_mGrad_tricone_vrr_sig(vert_neighList[j], j, ops[i], rho);
}
}
@ -631,7 +631,7 @@ double gobser_mGrad_tricone_vr_sig(const std::vector<gctl::gravcone_gji*> &a_lis
R.y = sin((0.5-a_op.lat/180.0)*GCTL_Pi)*sin((2.0+a_op.lon/180.0)*GCTL_Pi);
R.z = cos((0.5-a_op.lat/180.0)*GCTL_Pi);
op_c = a_op.s2c();
op_c = s2c(a_op);
double point_sum = 0.0;
for (int j = 0; j < a_list.size(); j++)
@ -842,7 +842,7 @@ double gobser_mGrad_tricone_vrp_sig(const std::vector<gctl::gravcone_gji*> &a_li
R.y = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R.z = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
double point_sum = 0.0;
for (int j = 0; j < a_list.size(); j++)
@ -1033,7 +1033,7 @@ double gobser_mGrad_tricone_vrt_sig(const std::vector<gctl::gravcone_gji*> &a_li
R.y = cos((0.5-a_op.lat/180.0)*GCTL_Pi)*sin((2.0+a_op.lon/180.0)*GCTL_Pi);
R.z = -1.0*sin((0.5-a_op.lat/180.0)*GCTL_Pi);
op_c = a_op.s2c();
op_c = s2c(a_op);
double point_sum = 0.0;
for (int j = 0; j < a_list.size(); j++)
@ -1220,7 +1220,7 @@ double gobser_mGrad_tricone_vrr_sig(const std::vector<gctl::gravcone_gji*> &a_li
R.y = sin((0.5-a_op.lat/180.0)*GCTL_Pi)*sin((2.0+a_op.lon/180.0)*GCTL_Pi);
R.z = cos((0.5-a_op.lat/180.0)*GCTL_Pi);
op_c = a_op.s2c();
op_c = s2c(a_op);
double point_sum = 0.0;
for (int j = 0; j < a_list.size(); j++)
@ -1404,7 +1404,7 @@ double gkernel_tricone_gji_pot_sig(const gctl::gravcone_gji &a_ele, const gctl::
gctl::gravcone_para_gji* gp = a_ele.att;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -1461,7 +1461,7 @@ double gkernel_tricone_gji_vr_sig(const gctl::gravcone_gji &a_ele, const gctl::p
R.y = sin((0.5-a_op.lat/180.0)*GCTL_Pi)*sin((2.0+a_op.lon/180.0)*GCTL_Pi);
R.z = cos((0.5-a_op.lat/180.0)*GCTL_Pi);
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -1525,7 +1525,7 @@ double gkernel_tricone_gji_vrp_sig(const gctl::gravcone_gji &a_ele, const gctl::
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -1594,7 +1594,7 @@ double gkernel_tricone_gji_vrt_sig(const gctl::gravcone_gji &a_ele, const gctl::
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)
@ -1663,7 +1663,7 @@ double gkernel_tricone_gji_vrr_sig(const gctl::gravcone_gji &a_ele, const gctl::
R[2][1] = cos((2.0+a_op.lon/180.0)*GCTL_Pi);
R[2][2] = 0.0;
op_c = a_op.s2c();
op_c = s2c(a_op);
face_sum = edge_sum = 0.0;
for (f = 0; f < 4; f++)

214
lib/potential/gm_data.cpp
View File

@ -124,8 +124,8 @@ void gctl::read_IGRF_table(std::string file, array<IGRF_para> &IGRFs, int head_r
decimal_year2date(deci_year, tmp_para.Year, tmp_para.Month, tmp_para.Day);
}
tmp_para.I = fabs(tmp_para.I_deg) + tmp_para.I_min/60.0;
tmp_para.D = fabs(tmp_para.D_deg) + tmp_para.D_min/60.0;
tmp_para.I = abs(tmp_para.I_deg) + tmp_para.I_min/60.0;
tmp_para.D = abs(tmp_para.D_deg) + tmp_para.D_min/60.0;
if (tmp_para.I_deg < 0) tmp_para.I *= -1;
if (tmp_para.D_deg < 0) tmp_para.D *= -1;
@ -138,6 +138,112 @@ void gctl::read_IGRF_table(std::string file, array<IGRF_para> &IGRFs, int head_r
return;
}
void gctl::read_Swarm_shc(std::string file, array<shc_data> &SHCs, int &spline_odr, int &sample_num)
{
dsv_io tio;
tio.head_number(2);
tio.load_text(file);
// parse the head records
int n, N, tnum;
std::vector<double> time_snaps;
std::vector<std::string> rcd = tio.head_records();
parse_string_to_value(rcd[0], ' ', true, n, N, tnum, spline_odr, sample_num);
parse_string_to_vector(rcd[1], ' ', time_snaps);
array<int> nid, mid;
array<double> vals;
int rnum = tio.row_number();
tio.get_column(nid, 1);
tio.get_column(mid, 2);
// store coefficients
int id, shc_num;
SHCs.resize(tnum);
for (size_t i = 0; i < tnum; i++)
{
SHCs[i].ns = n;
SHCs[i].ms = 0;
SHCs[i].ne = N;
SHCs[i].me = N;
SHCs[i].time = time_snaps[i];
shc_num = (N + 1)*(N + 2)/2;
SHCs[i].Snm.resize(shc_num, 0.0);
SHCs[i].Cnm.resize(shc_num, 0.0);
tio.get_column(vals, i + 3);
for (size_t j = 0; j < rnum; j++)
{
if (mid[j] > 0)
{
id = nid[j]*(nid[j] + 1)/2 + mid[j];
SHCs[i].Snm[id] = vals[j];
SHCs[i].Cnm[id] = vals[j + 1];
}
else if (mid[j] == 0)
{
id = nid[j]*(nid[j] + 1)/2;
SHCs[i].Snm[id] = vals[j];
SHCs[i].Cnm[id] = 0.0;
}
}
}
return;
}
void gctl::save_Swarm_shc(std::string file, const array<shc_data> &SHCs, int spline_odr, int sample_num, std::string info)
{
time_t now = time(0);
char* dt = ctime(&now);
std::ofstream ofile;
open_outfile(ofile, file + ".shc", ".txt");
ofile << "# " << info << std::endl;
ofile << "# Generated on " << dt;
int s = SHCs[0].ns, S = SHCs[0].ne;
int c = SHCs.size();
ofile << s << " " << S << " " << c << " " << spline_odr << " " << sample_num << std::endl;
ofile << SHCs[0].time;
for (size_t i = 1; i < SHCs.size(); i++)
{
ofile << " " << SHCs[i].time;
}
for (size_t n = s; n <= S; n++)
{
for (size_t m = 0; m <= n; m++)
{
if (m == 0)
{
ofile << "\n" << n << " " << m;
for (size_t i = 0; i < c; i++)
{
ofile << " " << SHCs[i].coeff_s(n, m);
}
}
else
{
ofile << "\n" << n << " " << m;
for (size_t i = 0; i < c; i++)
{
ofile << " " << SHCs[i].coeff_s(n, m);
}
ofile << "\n" << n << " -" << m;
for (size_t i = 0; i < c; i++)
{
ofile << " " << SHCs[i].coeff_c(n, m);
}
}
}
}
return;
}
void gctl::magnetic_components2deltaT(const _1d_array &Hax, const _1d_array &Hay, const _1d_array &Za,
_1d_array &deltaT, double T0_inclina, double T0_declina)
{
@ -241,11 +347,109 @@ void gctl::magnetic_tensors2deltaTs_sph(const array<tensor> &Mag_tensors, const
return;
}
void gctl::power_spectrum_shc(array<double> &P, const array<double> &C, const array<double> &S, double R, double r, int n, int N)
void gctl::schmidt_legendre(double co_lati, int n_max, array<double> &P, array<double> &dP)
{
if (n_max <= 0) throw std::runtime_error("[gctl::schmidt_legendre] Invalid paramters.");
double cos_lat = cosd(co_lati);
if (abs(cos_lat) == 1.0) throw std::runtime_error("[gctl::schmidt_legendre] Derivative cannot be calculated at poles.");
double pm2, pm1, pmm, plm, rescalem, z, scalef;
int k, kstart, m, n, NumTerms;
NumTerms = ((n_max + 1) * (n_max + 2) / 2);
P.resize(NumTerms, 0.0);
dP.resize(NumTerms, 0.0);
_1d_array f1(NumTerms + 1), f2(NumTerms + 1), PreSqr(NumTerms + 1);
scalef = 1.0e-280;
for(n = 0; n <= 2 * n_max + 1; ++n)
{
PreSqr[n] = sqrt((double) (n));
}
k = 2;
for(n = 2; n <= n_max; n++)
{
k = k + 1;
f1[k] = (double) (2 * n - 1) / (double) (n);
f2[k] = (double) (n - 1) / (double) (n);
for(m = 1; m <= n - 2; m++)
{
k = k + 1;
f1[k] = (double) (2 * n - 1) / PreSqr[n + m] / PreSqr[n - m];
f2[k] = PreSqr[n - m - 1] * PreSqr[n + m - 1] / PreSqr[n + m] / PreSqr[n - m];
}
k = k + 2;
}
/*z = sin (geocentric latitude) */
z = sqrt((1.0 - cos_lat)*(1.0 + cos_lat));
pm2 = 1.0;
P[0] = 1.0;
dP[0] = 0.0;
pm1 = cos_lat;
P[1] = pm1;
dP[1] = z;
k = 1;
for(n = 2; n <= n_max; n++)
{
k = k + n;
plm = f1[k] * cos_lat * pm1 - f2[k] * pm2;
P[k] = plm;
dP[k] = (double) (n) * (pm1 - cos_lat * plm) / z;
pm2 = pm1;
pm1 = plm;
}
pmm = PreSqr[2] * scalef;
rescalem = 1.0 / scalef;
kstart = 0;
for(m = 1; m <= n_max - 1; ++m)
{
rescalem = rescalem*z;
/* Calculate Pcup(m,m)*/
kstart = kstart + m + 1;
pmm = pmm * PreSqr[2 * m + 1] / PreSqr[2 * m];
P[kstart] = pmm * rescalem / PreSqr[2 * m + 1];
dP[kstart] = -((double) (m) * cos_lat * P[kstart] / z);
pm2 = pmm / PreSqr[2 * m + 1];
/* Calculate Pcup(m+1,m)*/
k = kstart + m + 1;
pm1 = cos_lat * PreSqr[2 * m + 1] * pm2;
P[k] = pm1*rescalem;
dP[k] = ((pm2 * rescalem) * PreSqr[2 * m + 1] - cos_lat * (double) (m + 1) * P[k]) / z;
/* Calculate Pcup(n,m)*/
for(n = m + 2; n <= n_max; ++n)
{
k = k + n;
plm = cos_lat * f1[k] * pm1 - f2[k] * pm2;
P[k] = plm*rescalem;
dP[k] = (PreSqr[n + m] * PreSqr[n - m] * (pm1 * rescalem) - (double) (n) * cos_lat * P[k]) / z;
pm2 = pm1;
pm1 = plm;
}
}
/* Calculate Pcup(nMax,nMax)*/
rescalem = rescalem*z;
kstart = kstart + m + 1;
pmm = pmm / PreSqr[2 * n_max];
P[kstart] = pmm * rescalem;
dP[kstart] = -(double) (n_max) * cos_lat * P[kstart] / z;
return;
}
void gctl::power_spectrum(array<double> &P, const array<double> &C, const array<double> &S, double R, double r, int n, int N)
{
if (n < 0 || n >= N || C.size() < (N + 1)*(N + 2)/2 || S.size() < (N + 1)*(N + 2)/2)
{
throw std::runtime_error("[gctl::power_spectrum_shc] Invalid input parameters.");
throw std::runtime_error("[gctl::power_spectrum] Invalid input parameters.");
}
P.resize(N - n + 1, 0);
@ -259,7 +463,7 @@ void gctl::power_spectrum_shc(array<double> &P, const array<double> &C, const ar
P[i - n] += (C[id + j]*C[id + j] + S[id + j]*S[id + j]);
}
P[i - n] *= (n + 1)*pow(R/r, 2*n + 4);
P[i - n] *= (i + 1)*pow(R/r, 2*i + 4);
}
return;
}

98
lib/potential/gm_data.h
View File

@ -28,18 +28,19 @@
#ifndef _GCTL_GM_DATA_H
#define _GCTL_GM_DATA_H
#include "gctl/core.h"
#include "gctl/utility.h"
#include "gctl/geometry.h"
#include "gctl/maths.h"
#include "gctl/algorithm.h"
#include "gctl_potential_config.h"
#ifdef GCTL_POTENTIAL_OPENMP
#include "omp.h"
#include "thread"
#include <thread>
#endif
#include "gctl/core/array.h"
#include "gctl/poly/point3s.h"
#include "gctl/poly/tensor.h"
#include "gctl/math/gmath.h"
#include "gctl/io/dsv_io.h"
#include "gctl/utility/utc_time.h"
namespace gctl
{
/**
@ -99,6 +100,20 @@ namespace gctl
int D_deg, D_min, I_deg, I_min;
};
/**
* @brief A structure holds a block of spherical harmonic coefficients
*
*/
struct shc_data
{
int ns, ms, ne, me; // start degree, start order, end degree, end order
double time; // snapshot
array<double> Snm, Cnm; // Snm or gnm, Cnm or hnm
double coeff_s(int n, int m){return Snm[n*(n + 1)/2 + m];}
double coeff_c(int n, int m){return Cnm[n*(n + 1)/2 + m];}
};
/**
* @brief Calculate the transform matrix of the vector componments wrt. the spherical coordinates.
*
@ -126,6 +141,29 @@ namespace gctl
*/
void read_IGRF_table(std::string file, array<IGRF_para> &IGRFs, int head_record = 1, std::string ext_f = ".txt");
/**
* @brief Spherical harmonic coefficients stored in the Swarm level-2 product format. This format
* is mainly used for storing spherical harmonic models of the Earth's magnetic field.
*
* @param file File name
* @param SHCs Returned coefficients started from 0/0 to N/M
* @param spline_odr Spline order for time dependent model
* @param sample_num Sample order for time dependent model
*/
void read_Swarm_shc(std::string file, array<shc_data> &SHCs, int &spline_odr, int &sample_num);
/**
* @brief Save spherical harmonic coefficients to the Swarm level-2 product format.
*
* @param file File name.
* @param SHCs coefficients started from 0/0
* @param spline_odr Spline order for time dependent model
* @param sample_num Sample order for time dependent model
* @param info Information to be saved with the file
*/
void save_Swarm_shc(std::string file, const array<shc_data> &SHCs, int spline_odr = 1, int sample_num = 1,
std::string info = "This file is saved in the Swarm level-2 product format.");
/**
* @brief Transform magnetic components data to delta_T anomalies data.
*
@ -198,19 +236,57 @@ namespace gctl
*/
void magnetic_tensors2deltaTs_sph(const array<tensor> &Mag_tensors, const _1d_array &T0_inclina, const _1d_array &T0_declina, array<point3dc> &deltaTs);
/**
* @brief This function evaluates all of the Schmidt-semi normalized associated Legendre
* functions up to degree nMax. The functions are initially scaled by
* 10^280 sin^m in order to minimize the effects of underflow at large m
* near the poles (see Holmes and Featherstone 2002, J. Geodesy, 76, 279-299).
* Note that this function performs the same operation as MAG_PcupLow.
* However this function also can be used for high degree (large nMax) models.
*
* Added into the GCTL by Yi Zhang in March 5th, 2025.
*
* Adopted from the FORTRAN code written by Mark Wieczorek September 25, 2005.
*
* Manoj Nair, Nov, 2009 Manoj.C.Nair@Noaa.Gov
*
* Change from the previous version
* The prevous version computes the derivatives as
* dP(n,m)(x)/dx, where x = sin(latitude) (or cos(colatitude) ).
* However, the WMM Geomagnetic routines requires dP(n,m)(x)/dlatitude.
* Hence the derivatives are multiplied by sin(latitude).
* Removed the options for CS phase and normalizations.
*
* Note: In geomagnetism, the derivatives of ALF are usually found with
* respect to the colatitudes. Here the derivatives are found with respect
* to the latitude. The difference is a sign reversal for the derivative of
* the Associated Legendre Functions.
*
* The derivatives can't be computed for latitude = |90| degrees.
*
* @param co_lati Co-latitude in degrees.
* @param n_max Maximum spherical harmonic degree to compute.
* @param P A vector of all associated Legendgre polynomials evaluated at co_lati up to nMax.
* The lenght must by greater or equal to (n_max+1)*(n_max+2)/2. The coefficients are stored
* in a degree major order. The index of the coefficient at degree n and order m is n*(n+1)/2 + m.
* @param dP Derivative of P with respect to latitude. The coefficients are stored in the same
* order as in P.
*/
void schmidt_legendre(double co_lati, int n_max, array<double> &P, array<double> &dP);
/**
* @brief Calculate the power spectrum of given spherical harmonic coefficients.
*
* @param P Returned power spectrum
* @param C Cosine coefficients strats from 0 order 0 degree up to least N order N degree
* @param S Sine coefficients strats from 0 order 0 degree up to least N order N degree
* @param C Cosine coefficients strats from 0 order 0 degree up to at least N order N degree
* @param S Sine coefficients strats from 0 order 0 degree up to at least N order N degree
* @param R Reference radius (usually is 6371.2 km)
* @param r Observation radius
* @param n Strat order
* @param N End order
*/
void power_spectrum_shc(array<double> &P, const array<double> &C, const array<double> &S,
void power_spectrum(array<double> &P, const array<double> &C, const array<double> &S,
double R, double r, int n, int N);
}
};
#endif // _GCTL_GM_DATA_H

4
lib/potential/gm_regular_grid.h
View File

@ -30,6 +30,8 @@
#include "gctl/mesh/regular_grid.h"
#include "gm_data.h"
#include "gctl/math/extrapolate.h"
#include "gctl/math/space_filter.h"
namespace gctl
{
@ -120,6 +122,6 @@ namespace gctl
*/
void trend(std::string datname, std::string regname, std::string resname, int wx_size, int wy_size, int x_order, int y_order);
};
}
};
#endif //_GM_REGULAR_GRID_H

2
lib/potential/gm_regular_mesh_2d.h
View File

@ -46,6 +46,6 @@ namespace gctl
void gobser(array<double> &out_data, std::string data_name, const array<point2dc> &obs,
gravitational_field_type_e comp_id = Vz, verbose_type_e verbose = FullMsg);
};
}
};
#endif //_GRAV_REGULAR_MESH_2D_H

2
lib/potential/gm_regular_mesh_3d.h
View File

@ -64,6 +64,6 @@ namespace gctl
const array<double> &inc_deg, const array<double> &dec_deg,
magnetic_field_type_e comp_id = Za, verbose_type_e verbose = FullMsg);
};
}
};
#endif //_GM_REGULAR_MESH_3D_H

2
lib/potential/gm_regular_mesh_sph_3d.h
View File

@ -63,6 +63,6 @@ namespace gctl
magnetic_field_type_e comp_id = Za, verbose_type_e verbose = FullMsg);
#endif // GCTL_POTENTIAL_MAGTESS
};
}
};
#endif //_GM_REGULAR_MESH_SPH_3D_H

2
lib/potential/gm_tet_mesh.h
View File

@ -87,6 +87,6 @@ namespace gctl
void magobser(array<tensor> &out_obs, std::string magz_name, const array<point3dc> &obsp,
verbose_type_e verbose = FullMsg);
};
}
};
#endif // _GM_TET_MESH_H

4
lib/potential/mkernel_block.h
View File

@ -77,5 +77,7 @@ namespace gctl
magnetic_field_type_e comp_id = Za, verbose_type_e verbose = FullMsg);
#endif // GCTL_POTENTIAL_AUTODIFF
}
};
#endif // _GCTL_MAG_KERNEL_BLOCK_H

2
lib/potential/mkernel_dipole.cpp
View File

@ -48,7 +48,7 @@ gctl::point3dc gctl::magkernel_single(const mag_dipole &a_dipole, const point3ds
else R = transform_matrix(a_op);
double r = a_op.rad;
point3dc pc = a_op.s2c();
point3dc pc = s2c(a_op);
// T -> nT 1e+9 * 1e-7 -> 1e+2
point3dc b = 1e+2*a_dipole.M*(3.0*dot(a_dipole.n, pc)/power5(r)*pc - 1.0/power3(r)*a_dipole.n);

4
lib/potential/mkernel_dipole.h
View File

@ -29,6 +29,8 @@
#define _GCTL_MAG_KERNEL_DIPOLE_H
#include "gm_data.h"
#include "gctl/poly/vertex.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -97,6 +99,6 @@ namespace gctl
*/
void magobser(array<point3dc> &out_obs, const array<mag_dipole> &dipoles,
const array<point3ds> &obsp, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_MAG_KERNEL_DIPOLE_H

4
lib/potential/mkernel_tesseroid.h
View File

@ -29,6 +29,8 @@
#define _GCTL_MAG_KERNEL_TESSEROID_H
#include "gm_data.h"
#include "gctl/poly/tesseroid.h"
#include "gctl/utility/progress_bar.h"
#ifdef GCTL_POTENTIAL_MAGTESS
@ -125,7 +127,7 @@ namespace gctl
void magobser(array<double> &out_obs, const array<mag_tesseroid> &ele, const array<point3ds> &obsp,
const array<double> &sus, magnetic_field_type_e comp_id = Za, int gauss_order = 4,
verbose_type_e verbose = FullMsg);
}
};
#endif // GCTL_POTENTIAL_MAGTESS

4
lib/potential/mkernel_tetrahedron.cpp
View File

@ -142,7 +142,7 @@ void gctl::callink_magnetic_para_earth_sph(array<mag_tetrahedron> &in_tet, array
mag_z.y = cos(I)*cos(A);
mag_z.z = -1.0*sin(I);
s = in_tet[i].center().c2s();
s = c2s(in_tet[i].center());
// magnetic susceptibility is taken as one here
// rotate the local coordinate system to the regular status
out_para[i].B = field_tense * mag_z.rotate((90.0 - s.lat)*GCTL_Pi/180.0, 0.0, (90.0 + s.lon)*GCTL_Pi/180.0).normal();
@ -231,7 +231,7 @@ gctl::point3dc gctl::magkernel_single(const gctl::mag_tetrahedron &a_ele, const
else R = transform_matrix(a_op);
gctl::magtet_para* gp = a_ele.att;
gctl::point3dc pc = a_op.s2c();
gctl::point3dc pc = s2c(a_op);
int *v_order = a_ele.vec_order;
for (f = 0; f < 4; f++)

4
lib/potential/mkernel_tetrahedron.h
View File

@ -29,6 +29,8 @@
#define _GCTL_MAG_KERNEL_TETRAHEDRON_H
#include "gm_data.h"
#include "gctl/poly/tetrahedron.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -129,6 +131,6 @@ namespace gctl
*/
void magobser(array<point3dc> &out_obs, const array<mag_tetrahedron> &ele, const array<point3ds> &obsp,
const array<double> &sus, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_MAG_KERNEL_TETRAHEDRON_H

14
lib/potential/mkernel_tetrahedron_Ren2017.cpp
View File

@ -148,7 +148,7 @@ void gctl::callink_magnetic_para_earth_sph(array<magtet_ren17> &in_tet, array<ma
mag_z.y = cos(I)*cos(A);
mag_z.z = -1.0*sin(I);
s = in_tet[i].center().c2s();
s = c2s(in_tet[i].center());
// magnetic susceptibility is taken as one here
// rotate the local coordinate system to the regular status
mag_z = field_tense * mag_z.rotate((90.0 - s.lat)*M_PI/180.0, 0.0, (90.0 + s.lon)*M_PI/180.0).normal();
@ -203,7 +203,7 @@ void gctl::callink_magnetic_para_earth_sph(magtet_ren17 &in_tet, magtet_para_ren
mag_z.y = cos(I)*cos(A);
mag_z.z = -1.0*sin(I);
s = in_tet.center().c2s();
s = c2s(in_tet.center());
// magnetic susceptibility is taken as one here
// rotate the local coordinate system to the regular status
mag_z = field_tense * mag_z.rotate((90.0 - s.lat)*M_PI/180.0, 0.0, (90.0 + s.lon)*M_PI/180.0).normal();
@ -362,7 +362,7 @@ void gctl::magkernel(matrix<point3dc> &out_kernel, const array<magtet_ren17> &el
#pragma omp parallel for private (j, obsp_c) schedule(guided)
for (j = 0; j < e_size; j++)
{
obsp_c = obsp[i].s2c();
obsp_c = s2c(obsp[i]);
out_kernel[i][j] = magkernel_tetrahedron_gradient_sig(ele[j], obsp_c);
}
}
@ -411,7 +411,7 @@ void gctl::magkernel(matrix<tensor> &out_kernel, const array<magtet_ren17> &ele,
#pragma omp parallel for private (j, obsp_c) schedule(guided)
for (j = 0; j < e_size; j++)
{
obsp_c = obsp[i].s2c();
obsp_c = s2c(obsp[i]);
out_kernel[i][j] = magkernel_tetrahedron_tensor_sig(ele[j], obsp_c);
}
}
@ -461,7 +461,7 @@ gctl::point3dc gctl::magkernel_single(const magtet_ren17 &ele, const point3ds &o
R[2][1] = cos((2.0+obsp.lon/180.0)*M_PI);
R[2][2] = 0.0;
point3dc obsp_c = obsp.s2c();
point3dc obsp_c = s2c(obsp);
point3dc out_k = magkernel_tetrahedron_gradient_sig(ele, obsp_c);
out_k = R * out_k;
@ -634,7 +634,7 @@ void gctl::magobser(array<point3dc> &out_obs, const array<magtet_ren17> &ele, co
#pragma omp parallel for private (i, obsp_c) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsp_c = obsp[i].s2c();
obsp_c = s2c(obsp[i]);
out_obs[i] = out_obs[i] + sus[j] * magkernel_tetrahedron_gradient_sig(ele[j], obsp_c);
}
}
@ -680,7 +680,7 @@ void gctl::magobser(array<tensor> &out_obs, const array<magtet_ren17> &ele, cons
#pragma omp parallel for private (i, obsp_c) schedule(guided)
for (i = 0; i < o_size; i++)
{
obsp_c = obsp[i].s2c();
obsp_c = s2c(obsp[i]);
out_obs[i] = out_obs[i] + sus[j] * magkernel_tetrahedron_tensor_sig(ele[j], obsp_c);
}
}

5
lib/potential/mkernel_tetrahedron_Ren2017.h
View File

@ -29,6 +29,8 @@
#define _GCTL_MAG_KERNEL_TETRAHEDRON_REN2017_H
#include "gm_data.h"
#include "gctl/poly/tetrahedron.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -295,5 +297,6 @@ namespace gctl
*/
void magobser(array<tensor> &out_obs, const array<magtet_ren17> &ele, const array<point3ds> &obsp,
const array<double> &sus, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_MAG_KERNEL_TETRAHEDRON_REN2017_H

4
lib/potential/mkernel_triangle.cpp
View File

@ -137,7 +137,7 @@ void gctl::callink_magnetic_para_earth_sph(array<mag_triangle> &in_tri, array<ma
mag_z.y = cos(I)*cos(A);
mag_z.z = -1.0*sin(I);
s = in_tri[i].center().c2s();
s = c2s(in_tri[i].center());
// magnetic susceptibility is taken as one here
// rotate the local coordinate system to the regular status
out_para[i].B = field_tense * mag_z.rotate((90.0 - s.lat)*GCTL_Pi/180.0, 0.0, (90.0 + s.lon)*GCTL_Pi/180.0).normal();
@ -218,7 +218,7 @@ gctl::point3dc gctl::magkernel_single(const mag_triangle &a_ele, const point3ds
else R = transform_matrix(a_op);
gctl::magtri_para *gp = a_ele.att;
gctl::point3dc pc = a_op.s2c();
gctl::point3dc pc = s2c(a_op);
r_ijk[0] = *a_ele.vert[0] - pc;
r_ijk[1] = *a_ele.vert[1] - pc;

4
lib/potential/mkernel_triangle.h
View File

@ -29,6 +29,8 @@
#define _GCTL_MAG_KERNEL_TRIANGLE_H
#include "gm_data.h"
#include "gctl/poly/triangle.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -129,6 +131,6 @@ namespace gctl
*/
void magobser(array<point3dc> &out_obs, const array<mag_triangle> &ele, const array<point3ds> &obsp,
const array<double> &sus, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_MAG_KERNEL_TRIANGLE_H

11
lib/potential/mkernel_tricone.cpp
View File

@ -25,6 +25,7 @@
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include <map>
#include "mkernel_tricone.h"
void gctl::callink_magnetic_para(array<magcone> &in_cone, array<magcone_para> &out_para, const array<point3dc> &mag_B)
@ -96,7 +97,7 @@ void gctl::callink_magnetic_para_earth_sph(array<magcone> &in_tet, array<magcone
mag_z.z = -1.0*sin(I);
c = 1.0/3.0*(*in_tet[i].vert[0] + *in_tet[i].vert[1] + *in_tet[i].vert[2]);
s = c.c2s();
s = c2s(c);
// magnetic susceptibility is taken as one here
// rotate the local coordinate system to the regular status
out_para[i].B = field_tense * mag_z.rotate((90.0 - s.lat)*GCTL_Pi/180.0, 0.0, (90.0 + s.lon)*GCTL_Pi/180.0).normal();
@ -137,7 +138,7 @@ gctl::point3dc gctl::magkernel_single(const magcone &a_ele, const point3ds &a_op
else R = transform_matrix(a_op);
gctl::magcone_para* gp = a_ele.att;
gctl::point3dc pc = a_op.s2c();
gctl::point3dc pc = s2c(a_op);
for (f = 0; f < 4; f++)
{
@ -277,7 +278,7 @@ void gctl::magkernel(spmat<double> &kernel, const array<magcone> &top_ele, const
for (j = 0; j < e_size; j++)
{
cen = 1.0/3.0*(*top_ele[j].vert[0] + *top_ele[j].vert[1] + *top_ele[j].vert[2]);
if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
if (geometry3d::angle(s2c(obsp[i]), cen) < cut_angle*GCTL_Pi/180.0)
{
tmp_plt.r_id = i;
tmp_plt.c_id = j;
@ -299,7 +300,7 @@ void gctl::magkernel(spmat<double> &kernel, const array<magcone> &top_ele, const
for (j = 0; j < e_size; j++)
{
cen = 1.0/3.0*(*top_ele[j].vert[0] + *top_ele[j].vert[1] + *top_ele[j].vert[2]);
if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
if (geometry3d::angle(s2c(obsp[i]), cen) < cut_angle*GCTL_Pi/180.0)
{
mag_b = magkernel_single(top_ele[j], obsp[i], Rs.get(i));
if (comp_type == Bx) triplts[tri_idx[j + i*e_size]].val = mag_b.y;
@ -318,7 +319,7 @@ void gctl::magkernel(spmat<double> &kernel, const array<magcone> &top_ele, const
for (j = 0; j < e_size; j++)
{
cen = 1.0/3.0*(*btm_ele[j].vert[0] + *btm_ele[j].vert[1] + *btm_ele[j].vert[2]);
if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
if (geometry3d::angle(s2c(obsp[i]), cen) < cut_angle*GCTL_Pi/180.0)
{
mag_b = magkernel_single(btm_ele[j], obsp[i], Rs.get(i));
if (comp_type == Bx) triplts[tri_idx[j + i*e_size]].val -= mag_b.y;

5
lib/potential/mkernel_tricone.h
View File

@ -29,6 +29,9 @@
#define _GCTL_MAG_KERNEL_TRICONE_H
#include "gm_data.h"
#include "gctl/poly/tri_cone.h"
#include "gctl/utility/progress_bar.h"
#include "gctl/math/geometry3d.h"
namespace gctl
{
@ -77,6 +80,6 @@ namespace gctl
void magobser(array<point3dc> &out_obs, const array<magcone> &top_ele, const array<magcone> &btm_ele,
const array<point3ds> &obsp, const array<double> &sus, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_MAG_KERNEL_TRICONE_H

15
lib/potential/mkernel_tricone_Ren2017.cpp
View File

@ -25,8 +25,9 @@
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include <cmath>
#include <map>
#include "mkernel_tricone_Ren2017.h"
#include "cmath"
double mag_tolerance = 1e-16;
@ -106,7 +107,7 @@ void gctl::callink_magnetic_para_earth_sph(array<magcone_ren17> &in_cone, array<
mag_z.z = -1.0*sin(I);
c = 1.0/3.0*(*in_cone[i].vert[0] + *in_cone[i].vert[1] + *in_cone[i].vert[2]);
s = c.c2s();
s = c2s(c);
// magnetic susceptibility is taken as one here
// rotate the local coordinate system to the regular status
mag_z = field_tense * mag_z.rotate((90.0 - s.lat)*M_PI/180.0, 0.0, (90.0 + s.lon)*M_PI/180.0).normal();
@ -150,7 +151,7 @@ gctl::point3dc gctl::magkernel_single(const magcone_ren17 &a_ele, const point3ds
else R = transform_matrix(a_op);
// get the observation site in the local coordinates
gctl::point3dc site = a_op.s2c();
gctl::point3dc site = s2c(a_op);
gctl::point3dc out_grad(0.0, 0.0, 0.0);
for (int f = 0; f < 4; ++f)
{
@ -237,7 +238,7 @@ gctl::tensor gctl::magkernel_single_tensor(const magcone_ren17 &a_ele, const poi
R_T = R.transpose();
// get the observation site in the local coordinates
gctl::point3dc site = a_op.s2c();
gctl::point3dc site = s2c(a_op);
gctl::tensor out_tensor(0.0);
for (int f = 0; f < 4; ++f)
{
@ -434,7 +435,7 @@ void gctl::magkernel(spmat<double> &kernel, const array<magcone_ren17> &top_ele,
for (j = 0; j < e_size; j++)
{
cen = 1.0/3.0*(*top_ele[j].vert[0] + *top_ele[j].vert[1] + *top_ele[j].vert[2]);
if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
if (geometry3d::angle(s2c(obsp[i]), cen) < cut_angle*GCTL_Pi/180.0)
{
tmp_plt.r_id = i;
tmp_plt.c_id = j;
@ -456,7 +457,7 @@ void gctl::magkernel(spmat<double> &kernel, const array<magcone_ren17> &top_ele,
for (j = 0; j < e_size; j++)
{
cen = 1.0/3.0*(*top_ele[j].vert[0] + *top_ele[j].vert[1] + *top_ele[j].vert[2]);
if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
if (geometry3d::angle(s2c(obsp[i]), cen) < cut_angle*GCTL_Pi/180.0)
{
mag_b = magkernel_single(top_ele[j], obsp[i], Rs.get(i));
if (comp_type == Bx) triplts[tri_idx[j + i*e_size]].val = mag_b.y;
@ -475,7 +476,7 @@ void gctl::magkernel(spmat<double> &kernel, const array<magcone_ren17> &top_ele,
for (j = 0; j < e_size; j++)
{
cen = 1.0/3.0*(*btm_ele[j].vert[0] + *btm_ele[j].vert[1] + *btm_ele[j].vert[2]);
if (geometry3d::angle(obsp[i].s2c(), cen) < cut_angle*GCTL_Pi/180.0)
if (geometry3d::angle(s2c(obsp[i]), cen) < cut_angle*GCTL_Pi/180.0)
{
mag_b = magkernel_single(btm_ele[j], obsp[i], Rs.get(i));
if (comp_type == Bx) triplts[tri_idx[j + i*e_size]].val -= mag_b.y;

5
lib/potential/mkernel_tricone_Ren2017.h
View File

@ -29,6 +29,9 @@
#define _GCTL_MAG_KERNEL_TRICONE_REN2017_H
#include "gm_data.h"
#include "gctl/poly/tri_cone.h"
#include "gctl/math/geometry3d.h"
#include "gctl/utility/progress_bar.h"
namespace gctl
{
@ -137,6 +140,6 @@ namespace gctl
*/
void magobser(array<tensor> &out_obs, const array<magcone_ren17> &top_ele, const array<magcone_ren17> &btm_ele,
const array<point3ds> &obsp, const array<double> &sus, verbose_type_e verbose = FullMsg);
}
};
#endif // _GCTL_MAG_KERNEL_TRICONE_REN2017_H

62
tool/gridmanager-potential/gridmanager-potential.cpp
View File

@ -372,7 +372,7 @@ void save_gmsh(const std::vector<std::string> &cmd_units)
// save gmsh <file>
if (cmd_units.size() < 3) throw std::runtime_error("save: insufficient parameters.");
rg.save_gmsh(cmd_units[2], OverWrite, NotPacked);
rg.save_gmsh(cmd_units[2], NotPacked);
return;
}
@ -438,7 +438,7 @@ void save_text(const std::vector<std::string> &cmd_units)
void data_cloud(const std::vector<std::string> &cmd_units)
{
// data-cloud \<new-data-name\> node|cell \<data-could-file\> \<search-x\> \<search-y\> \<search-deg\> [\<text_descriptor\>]
// data-cloud \<new-data-name\> node|cell \<data-could-file\> \<search-x\> \<search-y\> \<search-deg\>
if (cmd_units.size() < 7) throw std::runtime_error("data-cloud: insufficient parameters.");
gctl::array<std::string> copy_str(7, "null");
@ -452,33 +452,15 @@ void data_cloud(const std::vector<std::string> &cmd_units)
else if (copy_str[1] == "cell") d_type = ElemData;
else throw std::runtime_error("open-surfer: invalid grid data type.");
text_descriptor desc;
desc.file_name_ = copy_str[2];
desc.file_ext_ = ".txt";
desc.col_str_ = "0,1,2";
desc.delimiter_ = ' ';
desc.att_sym_ = '#';
desc.head_num_ = 0;
if (copy_str[6] != "null")
{
parse_string_to_value(copy_str[6], '/', true, desc.col_str_,
desc.delimiter_, desc.att_sym_, desc.head_num_);
}
geodsv_io text_in;
text_in.load_text(copy_str[2]);
std::vector<double> posix_vec, posiy_vec, data_vec;
read_text2vectors(desc, posix_vec, posiy_vec, data_vec);
array<point2dc> posi_arr;
_1d_array data_vec;
text_in.get_column_point2dc(posi_arr, 0, 1);
text_in.get_column(data_vec, 2);
array<point2dc> posi_arr(posix_vec.size());
array<double> posi_val;
posi_val.input(data_vec);
for (size_t i = 0; i < posi_arr.size(); i++)
{
posi_arr[i].x = posix_vec[i];
posi_arr[i].y = posiy_vec[i];
}
rg.load_data_cloud(posi_arr, posi_val, atof(copy_str[3].c_str()), atof(copy_str[4].c_str()), atof(copy_str[5].c_str()), copy_str[0], d_type);
rg.load_data_cloud(posi_arr, data_vec, atof(copy_str[3].c_str()), atof(copy_str[4].c_str()), atof(copy_str[5].c_str()), copy_str[0], d_type);
return;
}
@ -721,29 +703,9 @@ void get_profile(const std::vector<std::string> &cmd_units)
}
else // File exist
{
text_descriptor desc;
desc.file_name_ = copy_str[2];
desc.file_ext_ = ".txt";
desc.att_sym_ = '#';
desc.col_str_ = "0,1";
desc.delimiter_ = ' ';
desc.head_num_ = 0;
if (copy_str[3] != "null")
{
gctl::parse_string_to_value(copy_str[3], '/', true, desc.col_str_, desc.delimiter_,
desc.att_sym_, desc.head_num_);
}
std::vector<double> xs, ys;
gctl::read_text2vectors(desc, xs, ys);
xys.resize(xs.size());
for (size_t i = 0; i < xys.size(); i++)
{
xys[i].x = xs[i];
xys[i].y = ys[i];
}
geodsv_io fio;
fio.load_text(copy_str[2]);
fio.get_column_point2dc(xys, 0, 1);
rg.extract_points(copy_str[0], xys, p_data);
}

4
tool/gridmanager-potential/readme_gridmanager_potential.md
View File

@ -22,8 +22,8 @@ Mathematic expresstions could be used to specify the grid ranges.
4. `save gmsh <file>` Save the grid using the Gmsh legacy format. This command will write all data that are allowed for outputing.
5. `save text <file>` Save the grid data to text file.
#### cloud \<new-data-name\> node|cell \<data-could-file\> \<search-x\> \<search-y\> \<search-deg\> [\<text_descriptor\>]
Import a randomly distributed data could (namely a xyz data). Note that a grid must exist before the use this command. 'node' or 'cell' indicates whether the input could data should be node or cell registed. \<data-could-file\> is the input data file. \<search-x\>,\<search-y\> and \<search-deg\> defines an oval of which the command is used to interpolate the could data to grid points. Additional options for reading the \<data-could-file\> could be given by the [\<text_descriptor\>] argument which has a format of \<order_str\>/\<delimiter\>/\<annotate\>/\<head_record\>. For example 0,1,2/,/#/0 means that the intput data could is stored int the first three columns separated by commas. The file has no head records and any line starts with '#' is an annotation.
#### cloud \<new-data-name\> node|cell \<data-could-file\> \<search-x\> \<search-y\> \<search-deg\>
Import a randomly distributed data could (namely a xyz data). Note that a grid must exist before the use this command. 'node' or 'cell' indicates whether the input could data should be node or cell registed. \<data-could-file\> is the input data file. \<search-x\>,\<search-y\> and \<search-deg\> defines an oval of which the command is used to interpolate the could data to grid points.
#### gradient \<data-name\> \<new-data-name\> dx|dy \<order\>
Calculate directional gradient(s) of the selected data. The new gradient data will have the same