Fortran中随机数据的半高全宽答案

【问题标题】：Full width at half maximum of random data in FortranFortran中随机数据的半高全宽
【发布时间】：2021-03-18 16:18:20
【问题描述】：

我有一组高斯随机生成的数据。我获取这些数据的方式并不重要，但它是通过带有扩散的粒子代码。

我知道 python 中有可以做到这一点的函数，但是我不能在每个时间步将这些数据写入文件，然后再分析它，因为我需要它进行诊断。因此我需要在代码中计算它。

我的代码是用 Fortran 95 编写的。

我需要找到半最大值全宽的数据示例是这样的（完整数据在下面）

但是如你所见，它有点吵。

我手动计算出这个长度是0.00235（因为这是起始数据，我知道这个长度是0.0023548200450309495，所以它真的很接近）。但是我不得不用我的光标估计一个最大值（33.6），然后用我的光标找到长度。

有没有办法用 Fortran 中的代码来做到这一点？如果您不了解 Fortran，也可以使用它（我可以自己将其翻译成 Fortran）

不要犹豫，问任何问题。

编辑：我忘了说我已经计算了西格玛槽：

Sigma = Sum( (x - Av(x))**2 )/N

问题是这给了我一个答案，但由于某些物理特性，至少在模拟开始时它没有给我正确的值，它适用于后面的时间步，但不是在开始时。

   1.89624932667106                0
   1.89626438944774                0
   1.89627945222442                0
   1.89629451500110                0
   1.89630957777777                0
   1.89632464055445                0
   1.89633970333113                0
   1.89635476610781                0
   1.89636982888449                0
   1.89638489166117                0
   1.89639995443785                0
   1.89641501721453                0
   1.89643007999121                0
   1.89644514276789                0
   1.89646020554457                0
   1.89647526832125                0
   1.89649033109793                0
   1.89650539387460                0
   1.89652045665128                0
   1.89653551942796                0
   1.89655058220464                0
   1.89656564498132                0
   1.89658070775800                0
   1.89659577053468                0
   1.89661083331136                0
   1.89662589608804                1
   1.89664095886472                1
   1.89665602164140                0
   1.89667108441808                0
   1.89668614719475                0
   1.89670120997143                0
   1.89671627274811                0
   1.89673133552479                1
   1.89674639830147                0
   1.89676146107815                0
   1.89677652385483                0
   1.89679158663151                1
   1.89680664940819                0
   1.89682171218487                1
   1.89683677496155                0
   1.89685183773823                0
   1.89686690051490                0
   1.89688196329158                0
   1.89689702606826                0
   1.89691208884494                0
   1.89692715162162                1
   1.89694221439830                3
   1.89695727717498                1
   1.89697233995166                0
   1.89698740272834                0
   1.89700246550502                0
   1.89701752828170                1
   1.89703259105838                1
   1.89704765383505                0
   1.89706271661173                1
   1.89707777938841                3
   1.89709284216509                0
   1.89710790494177                1
   1.89712296771845                1
   1.89713803049513                1
   1.89715309327181                1
   1.89716815604849                1
   1.89718321882517                3
   1.89719828160185                1
   1.89721334437853                2
   1.89722840715520                2
   1.89724346993188                0
   1.89725853270856                2
   1.89727359548524                1
   1.89728865826192                1
   1.89730372103860                1
   1.89731878381528                1
   1.89733384659196                1
   1.89734890936864                2
   1.89736397214532                2
   1.89737903492200                3
   1.89739409769868                2
   1.89740916047535                2
   1.89742422325203                2
   1.89743928602871                1
   1.89745434880539                4
   1.89746941158207                2
   1.89748447435875                2
   1.89749953713543                3
   1.89751459991211                9
   1.89752966268879                3
   1.89754472546547                1
   1.89755978824215                2
   1.89757485101883                3
   1.89758991379551                4
   1.89760497657218                3
   1.89762003934886                2
   1.89763510212554                5
   1.89765016490222                4
   1.89766522767890                4
   1.89768029045558                4
   1.89769535323226                3
   1.89771041600894                6
   1.89772547878562                9
   1.89774054156230                3
   1.89775560433898                5
   1.89777066711566                4
   1.89778572989233                5
   1.89780079266901                5
   1.89781585544569                9
   1.89783091822237                5
   1.89784598099905                4
   1.89786104377573                7
   1.89787610655241                9
   1.89789116932909                3
   1.89790623210577                4
   1.89792129488245                8
   1.89793635765913                9
   1.89795142043581                6
   1.89796648321248                9
   1.89798154598916                5
   1.89799660876584                8
   1.89801167154252               11
   1.89802673431920                7
   1.89804179709588                7
   1.89805685987256                6
   1.89807192264924                9
   1.89808698542592               15
   1.89810204820260                9
   1.89811711097928                9
   1.89813217375596                7
   1.89814723653263                8
   1.89816229930931               15
   1.89817736208599                9
   1.89819242486267                6
   1.89820748763935               14
   1.89822255041603               10
   1.89823761319271               13
   1.89825267596939                8
   1.89826773874607               16
   1.89828280152275               13
   1.89829786429943               15
   1.89831292707611                8
   1.89832798985278               19
   1.89834305262946               16
   1.89835811540614               21
   1.89837317818282               19
   1.89838824095950               11
   1.89840330373618               11
   1.89841836651286               20
   1.89843342928954               25
   1.89844849206622               17
   1.89846355484290               19
   1.89847861761958               25
   1.89849368039626               13
   1.89850874317293               17
   1.89852380594961               21
   1.89853886872629               14
   1.89855393150297               24
   1.89856899427965               14
   1.89858405705633               21
   1.89859911983301               22
   1.89861418260969               17
   1.89862924538637               18
   1.89864430816305               27
   1.89865937093973               22
   1.89867443371641               20
   1.89868949649308               30
   1.89870455926976               27
   1.89871962204644               30
   1.89873468482312               31
   1.89874974759980               23
   1.89876481037648               24
   1.89877987315316               41
   1.89879493592984               21
   1.89880999870652               32
   1.89882506148320               31
   1.89884012425988               46
   1.89885518703656               20
   1.89887024981324               28
   1.89888531258991               35
   1.89890037536659               32
   1.89891543814327               32
   1.89893050091995               24
   1.89894556369663               36
   1.89896062647331               47
   1.89897568924999               31
   1.89899075202667               38
   1.89900581480335               32
   1.89902087758003               34
   1.89903594035671               47
   1.89905100313339               29
   1.89906606591006               36
   1.89908112868674               43
   1.89909619146342               32
   1.89911125424010               41
   1.89912631701678               39
   1.89914137979346               45
   1.89915644257014               37
   1.89917150534682               46
   1.89918656812350               46
   1.89920163090018               31
   1.89921669367686               54
   1.89923175645354               33
   1.89924681923021               43
   1.89926188200689               39
   1.89927694478357               50
   1.89929200756025               46
   1.89930707033693               45
   1.89932213311361               54
   1.89933719589029               65
   1.89935225866697               42
   1.89936732144365               59
   1.89938238422033               46
   1.89939744699701               48
   1.89941250977369               56
   1.89942757255036               50
   1.89944263532704               36
   1.89945769810372               55
   1.89947276088040               57
   1.89948782365708               38
   1.89950288643376               48
   1.89951794921044               69
   1.89953301198712               56
   1.89954807476380               62
   1.89956313754048               52
   1.89957820031716               58
   1.89959326309384               55
   1.89960832587051               49
   1.89962338864719               60
   1.89963845142387               49
   1.89965351420055               59
   1.89966857697723               56
   1.89968363975391               47
   1.89969870253059               48
   1.89971376530727               67
   1.89972882808395               62
   1.89974389086063               61
   1.89975895363731               62
   1.89977401641399               52
   1.89978907919066               42
   1.89980414196734               68
   1.89981920474402               49
   1.89983426752070               63
   1.89984933029738               53
   1.89986439307406               64
   1.89987945585074               66
   1.89989451862742               60
   1.89990958140410               57
   1.89992464418078               79
   1.89993970695746               54
   1.89995476973414               55
   1.89996983251081               64
   1.89998489528749               70
   1.89999995806417               65
   1.90001502084085               60
   1.90003008361753               61
   1.90004514639421               67
   1.90006020917089               63
   1.90007527194757               65
   1.90009033472425               41
   1.90010539750093               59
   1.90012046027761               73
   1.90013552305429               51
   1.90015058583097               55
   1.90016564860764               56
   1.90018071138432               51
   1.90019577416100               57
   1.90021083693768               50
   1.90022589971436               60
   1.90024096249104               81
   1.90025602526772               52
   1.90027108804440               62
   1.90028615082108               45
   1.90030121359776               63
   1.90031627637444               46
   1.90033133915112               64
   1.90034640192779               58
   1.90036146470447               61
   1.90037652748115               60
   1.90039159025783               58
   1.90040665303451               58
   1.90042171581119               59
   1.90043677858787               44
   1.90045184136455               62
   1.90046690414123               47
   1.90048196691791               52
   1.90049702969459               49
   1.90051209247127               45
   1.90052715524794               48
   1.90054221802462               54
   1.90055728080130               65
   1.90057234357798               57
   1.90058740635466               51
   1.90060246913134               57
   1.90061753190802               42
   1.90063259468470               47
   1.90064765746138               54
   1.90066272023806               48
   1.90067778301474               46
   1.90069284579142               45
   1.90070790856809               53
   1.90072297134477               55
   1.90073803412145               49
   1.90075309689813               57
   1.90076815967481               50
   1.90078322245149               37
   1.90079828522817               35
   1.90081334800485               52
   1.90082841078153               55
   1.90084347355821               43
   1.90085853633489               36
   1.90087359911157               45
   1.90088866188824               48
   1.90090372466492               37
   1.90091878744160               52
   1.90093385021828               47
   1.90094891299496               39
   1.90096397577164               35
   1.90097903854832               42
   1.90099410132500               35
   1.90100916410168               25
   1.90102422687836               23
   1.90103928965504               36
   1.90105435243172               23
   1.90106941520839               34
   1.90108447798507               32
   1.90109954076175               23
   1.90111460353843               40
   1.90112966631511               37
   1.90114472909179               29
   1.90115979186847               25
   1.90117485464515               30
   1.90118991742183               35
   1.90120498019851               27
   1.90122004297519               36
   1.90123510575187               27
   1.90125016852855               23
   1.90126523130522               30
   1.90128029408190               26
   1.90129535685858               19
   1.90131041963526               35
   1.90132548241194               30
   1.90134054518862               23
   1.90135560796530               30
   1.90137067074198               24
   1.90138573351866               26
   1.90140079629534               22
   1.90141585907202               24
   1.90143092184870               17
   1.90144598462537               21
   1.90146104740205               20
   1.90147611017873               16
   1.90149117295541               19
   1.90150623573209               17
   1.90152129850877               14
   1.90153636128545               15
   1.90155142406213               17
   1.90156648683881               22
   1.90158154961549               11
   1.90159661239217                8
   1.90161167516885               19
   1.90162673794552               18
   1.90164180072220               15
   1.90165686349888               17
   1.90167192627556               17
   1.90168698905224               17
   1.90170205182892               16
   1.90171711460560               11
   1.90173217738228               12
   1.90174724015896               15
   1.90176230293564               16
   1.90177736571232               12
   1.90179242848900               16
   1.90180749126567               10
   1.90182255404235               10
   1.90183761681903               11
   1.90185267959571               13
   1.90186774237239               16
   1.90188280514907               13
   1.90189786792575               14
   1.90191293070243               12
   1.90192799347911                8
   1.90194305625579               14
   1.90195811903247                6
   1.90197318180915               10
   1.90198824458582                5
   1.90200330736250                9
   1.90201837013918               12
   1.90203343291586                5
   1.90204849569254                5
   1.90206355846922                9
   1.90207862124590                8
   1.90209368402258                4
   1.90210874679926                3
   1.90212380957594                6
   1.90213887235262                7
   1.90215393512930                6
   1.90216899790597                5
   1.90218406068265               10
   1.90219912345933                5
   1.90221418623601                4
   1.90222924901269                8
   1.90224431178937                6
   1.90225937456605                9
   1.90227443734273                8
   1.90228950011941                2
   1.90230456289609                4
   1.90231962567277                3
   1.90233468844945                3
   1.90234975122612                5
   1.90236481400280                3
   1.90237987677948                4
   1.90239493955616                5
   1.90241000233284                3
   1.90242506510952                2
   1.90244012788620                1
   1.90245519066288                3
   1.90247025343956                2
   1.90248531621624                1
   1.90250037899292                2
   1.90251544176960                4
   1.90253050454628                1
   1.90254556732295                1
   1.90256063009963                3
   1.90257569287631                0
   1.90259075565299                0
   1.90260581842967                3
   1.90262088120635                0
   1.90263594398303                1
   1.90265100675971                1
   1.90266606953639                1
   1.90268113231307                1
   1.90269619508975                5
   1.90271125786643                2
   1.90272632064310                1
   1.90274138341978                0
   1.90275644619646                3
   1.90277150897314                0
   1.90278657174982                2
   1.90280163452650                1
   1.90281669730318                0
   1.90283176007986                0
   1.90284682285654                0
   1.90286188563322                1
   1.90287694840990                1
   1.90289201118658                0
   1.90290707396325                0
   1.90292213673993                3
   1.90293719951661                1
   1.90295226229329                1
   1.90296732506997                1
   1.90298238784665                0
   1.90299745062333                2
   1.90301251340001                0
   1.90302757617669                1
   1.90304263895337                0
   1.90305770173005                0
   1.90307276450673                0
   1.90308782728340                1
   1.90310289006008                1
   1.90311795283676                0
   1.90313301561344                0
   1.90314807839012                0
   1.90316314116680                0
   1.90317820394348                0
   1.90319326672016                0
   1.90320832949684                0
   1.90322339227352                0
   1.90323845505020                0
   1.90325351782688                1
   1.90326858060355                0
   1.90328364338023                0
   1.90329870615691                0
   1.90331376893359                0
   1.90332883171027                2
   1.90334389448695                0
   1.90335895726363                0
   1.90337402004031                0
   1.90338908281699                0
   1.90340414559367                0
   1.90341920837035                1
   1.90343427114703                0
   1.90344933392370                0
   1.90346439670038                0
   1.90347945947706                0
   1.90349452225374                0
   1.90350958503042                0
   1.90352464780710                0
   1.90353971058378                0
   1.90355477336046                0
   1.90356983613714                0
   1.90358489891382                0
   1.90359996169050                0
   1.90361502446718                1
   1.90363008724385                0
   1.90364515002053                0
   1.90366021279721                0
   1.90367527557389                0
   1.90369033835057                0
   1.90370540112725                0
   1.90372046390393                0
   1.90373552668061                0
   1.90375058945729                0
   1.90376565223397                0

【问题讨论】：

这能回答你的问题吗？ Finding the full width half maximum of a peak
看起来很有希望。我完全忘记了使用插值，也许它会起作用，我会试试的。
@Gundro 插值对噪声数据不利，您需要曲线拟合，就像那里的最后一个答案一样。
您所说的“它适用于后面的时间步但不适用于开始时”究竟是什么意思？您的系统是否显示瞬态行为，或者您的意思是对于少数样本量而言误差太大？

标签： fortran gfortran

【解决方案1】：

假设一个高斯分布，您可以使用平均值和标准差计算FWHM。

一个示例实现

program main
  implicit none
  integer           :: n
  real              :: mu, sigma, FWHM
  real, allocatable :: x(:)

  ! read data from file. here we just set some values as an easy example
  x = [-2, 0, 5, -10, 3]

  ! estimator for mean value
  n  = size(x)
  mu = sum(x) / n

  ! estimator for standard deviation (biased estimator -> divide by (n-1) )
  sigma = sqrt(sum((x-mu)**2)/(n-1))

  ! full-width half maximum is simple scaling of standard deviation
  ! for Gaussian distribution
  FWHM = 2*sqrt(2*log(2.0)) * sigma
end program

【讨论】：

在维基百科中，他们在离散点计算的标准差中除以 n 而不是 n-1。
@JAlex 请发布您所指的维基百科文章（部分）。我指的是Bessel's correction。还提到了here。
我忘了说我已经做了那个计算。但是需要另一种计算方式。
@Gundro 为什么？在哪方面不同？您需要具体才能获得适合您的答案。
@JAlex 我也链接到那个页面。见我之前的评论。在“更正样本标准偏差”小节中，它解释了n-1 的划分。