This module contains classes and procedures for computing various statistical quantities related to the univariate Normal distribution. More...

Data Types
type	distNorm_type
	This is the derived type for signifying distributions that are of type Univariate Normal as defined in the description of pm_distNorm. More...

interface	getNormCDF
	Generate and return the Cumulative Distribution Function (CDF) of the univariate Normal distribution. More...

interface	getNormEntropy
	Generate and return the entropy of the Normal distribution with the input natural logarithm of the variance. More...

interface	getNormFisher
	Generate the Fisher Information of the Normal distribution. More...

interface	getNormKLD
	Generate and return the Kullback-Leibler Divergence (KLD) \(D_{KL}(P \parallel Q)\) of a given univariate Normal distribution \(Q\) from a reference Normal distribution \(P\). More...

interface	getNormLogPDF
	Generate the natural logarithm of probability density function (PDF) of the univariate Normal distribution. More...

interface	getNormQuan
	Generate and return the Normal Quantile corresponding to the input CDF of the univariate Normal distribution. More...

interface	getNormRand
	Generate and return a scalar or array of arbitrary rank of random values from the univariate Normal distribution with the specified input `mean` and optionally, with the specified input standard deviation `std` of the Normal distribution. More...

interface	getZigNorm
	Generate and return the lower right edges of the rectangles of a Ziggurat partitioning of the Normal density function (and the corresponding density function values) to be used for Normal random number generation using the Ziggurat algorithm. More...

interface	setNormCDF
	Generate and return the Cumulative Distribution Function (CDF) of the univariate Normal distribution. More...

interface	setNormLogPDF
	Generate the natural logarithm of probability density function (PDF) of the univariate Normal distribution. More...

interface	setNormQuan
	Generate and return the quantile of the univariate Normal distribution at the specified input CDF. More...

interface	setNormRand
	Return a scalar or array of arbitrary rank of random values from the standard univariate Normal distribution. More...

interface	setNormRandBox
	Return a scalar or array of arbitrary rank of random values from the univariate Normal distribution, using the Box-Muller algorithm. More...

Variables
character(*, SK), parameter	MODULE_NAME = "@pm_distNorm"

integer(IK), parameter	ZIG_PRECISION = 33_IK
	The scalar `integer` of default kind IK containing the output of Fortran intrinsic `precision()` for the `real` kind used to generate the constant array ZIG_RKB. More...

real(RKB), dimension(2, 0:128), parameter	ZIGSET1 = reshape([ +3.910757959524915869549621434510571640_RKB, +0.000000000000000000000000000000000000E+0_RKB , +3.654152885361008771645429720399515670_RKB, +0.502781343070952005087938400241541891E-3_RKB , +3.449278298561431270627228213833611250_RKB, +0.104086943106322506013635915064907845E-2_RKB , +3.320244733839825517532232984442230700_RKB, +0.161091799459473453538408742342021986E-2_RKB , +3.224575052047801587144019828764775500_RKB, +0.220312016549958827311372671027399889E-2_RKB , +3.147889289518000685451855194084413580_RKB, +0.281289233937616172611348633870502865E-2_RKB , +3.083526132002143251877768947617198840_RKB, +0.343751917929162224416229759239016324E-2_RKB , +3.027837791769593524571714584215607150_RKB, +0.407518400039001087464038448139061472E-2_RKB , +2.978603279881843165536974212294808030_RKB, +0.472457682607575925888895096351016103E-2_RKB , +2.934366867208887589959928979567677640_RKB, +0.538470372266379748395288853907771468E-2_RKB , +2.894121053613412181388100356210103800_RKB, +0.605478221942164063991037466747021604E-2_RKB , +2.857138730873224588561645268053226920_RKB, +0.673417886624137640800598237565554838E-2_RKB , +2.822877396826442907534115515646593530_RKB, +0.742236950888280249329920345563351449E-2_RKB , +2.790921174001927318997779045468293070_RKB, +0.811891273868296054077142626445965006E-2_RKB , +2.760944005279986201244382392492695240_RKB, +0.882343143223528339445647449425005264E-2_RKB , +2.732685359044011420043182513046678140_RKB, +0.953559949343287212693559957627379651E-2_RKB , +2.705933656123062221333700225998574460_RKB, +0.102551320707227866483396053794922990E-1_RKB , +2.680514643285745101098374611431323380_RKB, +0.109817781711791129427823736030159900E-1_RKB , +2.656283037576743296802124304559512000_RKB, +0.117153149732408013682731286377880085E-1_RKB , +2.633116393631582759976309292516893140_RKB, +0.124555433719091587849084452906815838E-1_RKB , +2.610910518488823671930263694478955450_RKB, +0.132022844366303809959357880408105012E-1_RKB , +2.589575986708286649808805574507900700_RKB, +0.139553765573260408177619288977468218E-1_RKB , +2.569035452681843781314262921528081910_RKB, +0.147146731176153334234423656007745630E-1_RKB , +2.549221550324783104422671371241746650_RKB, +0.154800405777112059806768992081788185E-1_RKB , +2.530075232159854187716539084126876370_RKB, +0.162513568797661774124156785927309438E-1_RKB , +2.511544441626694343254607344580084390_RKB, +0.170285101099635321775373808069033731E-1_RKB , +2.493583041271046768170053296506813290_RKB, +0.178113973671931254109163549358583312E-1_RKB , +2.476149939670523163756216268162166500_RKB, +0.185999237995485118944697972790344771E-1_RKB , +2.459208374334705035673859596487019180_RKB, +0.193940017783549904963609637793049119E-1_RKB , +2.442725318200364223794234919225453500_RKB, +0.201935501858165129428739457647187713E-1_RKB , +2.426670984937146719863529851633726960_RKB, +0.209984937972267218821328887239805004E-1_RKB , +2.411018413901119491690349211725038630_RKB, +0.218087627424279111659346610629834973E-1_RKB , +2.395743119781927356168686681412574760_RKB, +0.226242920341075527766680294896069533E-1_RKB , +2.380822795172085556506619691319380400_RKB, +0.234450211528013514383037474818822027E-1_RKB , +2.366237056717290911362148128140186000_RKB, +0.242708936802748765008871090362921378E-1_RKB , +2.351967227379144761902530751453964640_RKB, +0.251018569743934986305835005740321359E-1_RKB , +2.337996148796528635433480327093713940_RKB, +0.259378618797451777000075273655017443E-1_RKB , +2.324308018871132508266119157050790040_RKB, +0.267788624692146997471273278024758566E-1_RKB , +2.310888250601371758550614355860895420_RKB, +0.276248158124683715174543699462393572E-1_RKB , +2.297723348902863520079790814230529130_RKB, +0.284756817679310236840265332909329685E-1_RKB , +2.284800802724492127387834486937223350_RKB, +0.293314227953502809501556980682789090E-1_RKB , +2.272108990228381861937683717373910900_RKB, +0.301920037864680654091842729977054983E-1_RKB , +2.259637095173787624597566531167311770_RKB, +0.310573919116731481152577086508924965E-1_RKB , +2.247375032947389262297952392515659590_RKB, +0.319275564808046037696524061552362067E-1_RKB , +2.235313384929921110748362199673550240_RKB, +0.328024688165248443463852626030938600E-1_RKB , +2.223443340092510611365346409716922540_RKB, +0.336821021388909593274737975695380343E-1_RKB , +2.211756642884160997470500709266731210_RKB, +0.345664314599311541791934500133628777E-1_RKB , +2.200245546611276427712165173291835590_RKB, +0.354554334871846263278378901217329216E-1_RKB , +2.188902771626360742839576505604305880_RKB, +0.363490865352926868627480678085691155E-1_RKB , +2.177721467740293002579164079152503390_RKB, +0.372473704448399433976210004282028638E-1_RKB , +2.166695180354308542353137142121026540_RKB, +0.381502665077398667348211240367435477E-1_RKB , +2.155817819876737469119503677197502650_RKB, +0.390577573985415074098963321878992358E-1_RKB , +2.145083634047888982767999729572053870_RKB, +0.399698271111055203479683284323823695E-1_RKB , +2.134487182846016909178836604796243250_RKB, +0.408864609001596660576863760104051322E-1_RKB , +2.124023315689523545420714787478384860_RKB, +0.418076452272979751244992871255722388E-1_RKB , +2.113687150686653177781935198589005610_RKB, +0.427333677110349512002228670090424488E-1_RKB , +2.103474055714877305933714304045440450_RKB, +0.436636170805675209921984193602696278E-1_RKB , +2.093379631138791930166361585961667970_RKB, +0.445983831329337385181389634688869380E-1_RKB , +2.083399693998304613670792088175897210_RKB, +0.455376566932892082093887264381438529E-1_RKB , +2.073530263518743034646393248416971800_RKB, +0.464814295780503946152953311870656232E-1_RKB , +2.063767547811732114341853749078149630_RKB, +0.474296945606789346776298063351001244E-1_RKB , +2.054107931650652130219475666313816510_RKB, +0.483824453399031873773625284851490337E-1_RKB , +2.044547965217531455282628792749082960_RKB, +0.493396765101929088581344120097015200E-1_RKB , +2.035084353729618971413871948694988270_RKB, +0.503013835343204408492863489427518069E-1_RKB , +2.025713947863854245252399025955272060_RKB, +0.512675627178574145127079248497036520E-1_RKB , +2.016433734906204123873988577023278720_RKB, +0.522382111854699318500836298767666937E-1_RKB , +2.007240830560528758913239738198299090_RKB, +0.532133268588876922360496499106520185E-1_RKB , +1.998132471358419680392214769162858870_RKB, +0.541929084364337554633405727268610055E-1_RKB , +1.989106007617438123201023091217180910_RKB, +0.551769553740117250736639942272910314E-1_RKB , +1.980158896900476605540416694815765850_RKB, +0.561654678674562273820736142229565223E-1_RKB , +1.971288697933659294606356474434686550_RKB, +0.571584468361607664497222499802473837E-1_RKB , +1.962493064944363052826024381256974850_RKB, +0.581558939079044529261453899150298019E-1_RKB , +1.953769742384646776692572811817963060_RKB, +0.591578114048058224055549195846209505E-1_RKB , +1.945116560008678301234686281875394240_RKB, +0.601642023303380532839147151743642514E-1_RKB , +1.936531428275694700380702197135648770_RKB, +0.611750703573454323914419246868044098E-1_RKB , +1.928012334052665710328808957510011910_RKB, +0.621904198170059582295143354352838012E-1_RKB , +1.919557336593188113064282063465457130_RKB, +0.632102556886895688287062083850491706E-1_RKB , +1.911164563771253338349016119398665420_RKB, +0.642345835906656803805852580678544053E-1_RKB , +1.902832208550429269452784399230803680_RKB, +0.652634097716175649174146849378032930E-1_RKB , +1.894558525670704732040885690575958130_RKB, +0.662967411029246168483446165075442866E-1_RKB , +1.886341828536782820037856553309563160_RKB, +0.673345850716767915010299444811729445E-1_RKB , +1.878180486292995844684467996043645020_RKB, +0.683769497743884728203642791575539760E-1_RKB , +1.870072921071266778496337776290841830_RKB, +0.694238439113817677925134633773045847E-1_RKB , +1.862017605399674118665348784397922740_RKB, +0.704752767818117550133248257276187773E-1_RKB , +1.854013059760201906750898441184461490_RKB, +0.715312582793085547211649297744966411E-1_RKB , +1.846057850285185505570580952991448920_RKB, +0.725917988882132560598516526262197654E-1_RKB , +1.838150586582806633764931304898561700_RKB, +0.736569096803867509488343563799016629E-1_RKB , +1.830289919682756933756055676984081970_RKB, +0.747266023125723976798301015314803279E-1_RKB , +1.822474540093885838871898571617810260_RKB, +0.758008890242951847298446370142010715E-1_RKB , +1.814703175966282671680772343522476780_RKB, +0.768797826362816984781690401687711081E-1_RKB , +1.806974591350820938703420428388107530_RKB, +0.779632965493867285846698800079747914E-1_RKB , +1.799287584549720199341728680984235510_RKB, +0.790514447440137817496961412302243116E-1_RKB , +1.791640986552162594624382322132709310_RKB, +0.801442417800181275436054931177368005E-1_RKB , +1.784033659549441512971864077807943680_RKB, +0.812417027970822772687529532474258376E-1_RKB , +1.776464495524522868996124119276484200_RKB, +0.823438435155550059817881401744955979E-1_RKB , +1.768932414911268589029665159840958690_RKB, +0.834506802377461758021915029242417507E-1_RKB , +1.761436365318910280539794251593908460_RKB, +0.845622298496707118376316534786168010E-1_RKB , +1.753975320317671535176286495650271100_RKB, +0.856785098232361263350014624915617177E-1_RKB , +1.746548278281722412853610819915111290_RKB, +0.867995382188689874348253633476266673E-1_RKB , +1.739154261285911657262420055628115450_RKB, +0.879253336885766911833903717911534395E-1_RKB , +1.731792314052963154137933505808925000_RKB, +0.890559154794418239043567001488716945E-1_RKB , +1.724461502948044912052862397775662270_RKB, +0.901913034375473009991491331657262247E-1_RKB , +1.717160915017823089741659119609676780_RKB, +0.913315180123313418058911041645338441E-1_RKB , +1.709889657071301820241745482016102880_RKB, +0.924765802613721921296195811766027943E-1_RKB , +1.702646854799923151653900407051805770_RKB, +0.936265118556033400788781021199070560E-1_RKB , +1.695431651934561568299588089192625460_RKB, +0.947813350849607903374772538857282822E-1_RKB , +1.688243209437195389093695018261921410_RKB, +0.959410728644647702377950152378611650E-1_RKB , +1.681080704725173871909617303396002540_RKB, +0.971057487407390411201725488177809241E-1_RKB , +1.673943330926124999231911729230294350_RKB, +0.982753868989717834844303967803275557E-1_RKB , +1.666830296161665512280717200364773540_RKB, +0.994500121703228172933039137854161328E-1_RKB , +1.659740822858182552384789747414556960_RKB, +0.100629650039782712328127609576129162E+0_RKB , +1.652674147083055944977076666279072050_RKB, +0.101814326654490140522320621972065562E+0_RKB , +1.645629517904782346099997435068184430_RKB, +0.103004068832514625466733060901486566E+0_RKB , +1.638606196775547730191205373889528150_RKB, +0.104198904072112656528428960098709859E+0_RKB , +1.631603456934873546471532683464361160_RKB, +0.105398860561465958979782511482284346E+0_RKB , +1.624620582833034778354059455865975410_RKB, +0.106603967188911549935198869215607602E+0_RKB , +1.617656869573015532637880619762087450_RKB, +0.107814253553674065499513686193278908E+0_RKB , +1.610711622369830051160545249046193620_RKB, +0.109029749977111720145296612324748632E+0_RKB , +1.603784156026094530393066805218239570_RKB, +0.110250487514488157810061008578271138E+0_RKB , +1.596873794422788175563087978818873180_RKB, +0.111476497967283378462230486935475436E+0_RKB , +1.589979870024190797461111747861209560_RKB, +0.112707813896057876934855393386708534E+0_RKB , +1.583101723396029247521107058058590910_RKB, +0.113944468633885115777321981289805190E+0_RKB , +1.576238702735906320876658002975291310_RKB, +0.115186496300368473953376646626857215E+0_RKB , +1.569390163415123656042832370955675890_RKB, +0.116433931816259871778263682344311485E+0_RKB , +1.562555467531044820930627254229273630_RKB, +0.117686810918698373049736317381864947E+0_RKB , +1.555733983469176375991038619565492320_RKB, +0.118945170177088211568318678970235501E+0_RKB , +1.548925085474173406375274133330557850_RKB, +0.120209047009636885032310150781360772E+0_RKB , +1.542128153229001959318075945656599760_RKB, +0.121478479700575208713903649777558606E+0_RKB , +1.535342571441514138082707130216935300_RKB, +0.122753507418082528688239173356532507E+0_RKB ], shape = [2, 129])

real(RKB), dimension(2, 1:128), parameter	ZIGSET2 = reshape([ +1.528567729437712402628199461442167180_RKB, +0.124034170232941664267186768442998377E+0_RKB , +1.521803020760998008679228498636570410_RKB, +0.125320509137949586535569901372920916E+0_RKB , +1.515047842776714566947194255734634790_RKB, +0.126612566068111349659514010876108850E+0_RKB , +1.508301596281311496171425183785073880_RKB, +0.127910383921646379432792471520964754E+0_RKB , +1.501563685115463738688173273682448190_RKB, +0.129214006581837895215365859576747957E+0_RKB , +1.494833515780493555035890159317754310_RKB, +0.130523478939758003270817270840923056E+0_RKB , +1.488110497057447553013103271226758760_RKB, +0.131838846917902858239534927650542548E+0_RKB , +1.481394039628187363902263028944763970_RKB, +0.133160157494774252287691074366070633E+0_RKB , +1.474683555697855570628865196528769660_RKB, +0.134487458730446066069814161355648980E+0_RKB , +1.467978458618079624962505551018572310_RKB, +0.135820799793156210330787895235534157E+0_RKB , +1.461278162510275558141634572902431380_RKB, +0.137160230986967010673991854114446593E+0_RKB , +1.454582081888410275202473614895370850_RKB, +0.138505803780539450342898439610712141E+0_RKB , +1.447889631280576100338960603208179050_RKB, +0.139857570837069297157912765350925466E+0_RKB , +1.441200224848723969896483905460819290_RKB, +0.141215586045435912189035654183361969E+0_RKB , +1.434513276005892200373197821347744230_RKB, +0.142579904552617481390538701477587025E+0_RKB , +1.427828197030256028046923580264626420_RKB, +0.143950582797429540314021584008091148E+0_RKB , +1.421144398675309048678328840045534000_RKB, +0.145327678545646990255525094264574683E+0_RKB , +1.414461289775471190729091975769526810_RKB, +0.146711250926573347052911625905291106E+0_RKB , +1.407778276846398829890729544114189010_RKB, +0.148101360471124737782233265331001140E+0_RKB , +1.401094763679250977372468027391928780_RKB, +0.149498069151500183758164830605819877E+0_RKB , +1.394410150928141013910818209046742880_RKB, +0.150901440422514000012107606564276651E+0_RKB , +1.387723835689976042816457610158740000_RKB, +0.152311539264670722976597120096621794E+0_RKB , +1.381035211075855426557023886048995030_RKB, +0.153728432229067872471998597962422358E+0_RKB , +1.374343665773166259809330405021183000_RKB, +0.155152187484217086331763054685730862E+0_RKB , +1.367648583597476202662733878746826080_RKB, +0.156582874864879763414378129073938725E+0_RKB , +1.360949343033283011396528844287145660_RKB, +0.158020565923019343095774015163019653E+0_RKB , +1.354245316762634995007843766072061330_RKB, +0.159465333980978769091659649295558937E+0_RKB , +1.347535871180587198226303191916842980_RKB, +0.160917254186998568094181273666041719E+0_RKB , +1.340820365896404038797740514363138740_RKB, +0.162376403573198357993539454690214112E+0_RKB , +1.334098153219360045667959181721837720_RKB, +0.163842861116152528813630294472766962E+0_RKB , +1.327368577627925853644432080219569470_RKB, +0.165316707800199358376684187822216740E+0_RKB , +1.320630975221056264316363281880977050_RKB, +0.166798026683631985045755192821871952E+0_RKB , +1.313884673150220489854736808952840970_RKB, +0.168286902967929517543098016930008494E+0_RKB , +1.307128989030731110178131195502915220_RKB, +0.169783424070197178160245257400787177E+0_RKB , +1.300363230330837190351929439655934200_RKB, +0.171287679698995818105358886788417999E+0_RKB , +1.293586693736947753945601406359300470_RKB, +0.172799761933753486486498659023686530E+0_RKB , +1.286798664493243646316660896517199420_RKB, +0.174319765307965059246455246546117697E+0_RKB , +1.279998415713817924797308907917922830_RKB, +0.175847786896400331371952020571991623E+0_RKB , +1.273185207665356364764060323720764170_RKB, +0.177383926406556544373322976411406151E+0_RKB , +1.266358287018229453775313848849852450_RKB, +0.178928286274608171283092549748417432E+0_RKB , +1.259516886063714228190559472001646690_RKB, +0.180480971766125034830178787412733260E+0_RKB , +1.252660221894897227354473865616388090_RKB, +0.182042091081849625639024292847696263E+0_RKB , +1.245787495548627294596662055366290760_RKB, +0.183611755468845965529740751119222664E+0_RKB , +1.238897891105687374493975672708951630_RKB, +0.185190079337355691907687938603429913E+0_RKB , +1.231990574746136091354596183983300960_RKB, +0.186777180383722406901836668848789685E+0_RKB , +1.225064693756530787096859391988721310_RKB, +0.188373179719772944131913560975705614E+0_RKB , +1.218119375485481656036492926236470550_RKB, +0.189978202009074284878057268848586717E+0_RKB , +1.211153726243699183035927701680494030_RKB, +0.191592375610517658429468812562799404E+0_RKB , +1.204166830144381512972585409228431810_RKB, +0.193215832729717172651871738633649002E+0_RKB , +1.197157747879441555149951169947666830_RKB, +0.194848709578749458096518050299059063E+0_RKB , +1.190125515426692069320479795685490130_RKB, +0.196491146544803628100426175257282935E+0_RKB , +1.183069142682686761029921497512774320_RKB, +0.198143288368357757303338740744073695E+0_RKB , +1.175987612015452098437940687032687740_RKB, +0.199805284331549509895377775340098004E+0_RKB , +1.168879876730833138384076802216189500_RKB, +0.201477288457465010601480272621186237E+0_RKB , +1.161744859445611442407678658730303350_RKB, +0.203159459721132113428367115004471988E+0_RKB , +1.154581450359927740740669252500180290_RKB, +0.204851962273072525723359017960643915E+0_RKB , +1.147388505420849058458757243582079270_RKB, +0.206554965676342511391397805599266881E+0_RKB , +1.140164844368151242664448937938463130_RKB, +0.208268645158074945659692042041697417E+0_RKB , +1.132909248652533753115898715892141530_RKB, +0.209993181876627252316799052585710853E+0_RKB , +1.125620459215533391227475593856507500_RKB, +0.211728763205541276296151308493989896E+0_RKB , +1.118297174119344981546693309349106980_RKB, +0.213475583035633628019879947303927958E+0_RKB , +1.110938046013575721417560779257849040_RKB, +0.215233842096659846410648766825208954E+0_RKB , +1.103541679424639718350709546845052450_RKB, +0.217003748300134423613077654918982009E+0_RKB , +1.096106627852021437094938365415991340_RKB, +0.218785517105043099072370007214575357E+0_RKB , +1.088631390653979821403993213445028160_RKB, +0.220579371908355906900178024260990122E+0_RKB , +1.081114409703403838077538136757234410_RKB, +0.222385544462441594762945169415386684E+0_RKB , +1.073554065792436288292686500464555760_RKB, +0.224204275321698924941276382479365999E+0_RKB , +1.065948674762122501754284026538321330_RKB, +0.226035814320961132564753113117134625E+0_RKB , +1.058296483330675084513966896229645790_RKB, +0.227880421088500051269826182271994471E+0_RKB , +1.050595664590929901514279329073961990_RKB, +0.229738365596760291802256320937473869E+0_RKB , +1.042844313144148970939980229020163640_RKB, +0.231609928754296215469589885980076311E+0_RKB , +1.035040439833440875887862746039381010_RKB, +0.233495403042770916853974440099008843E+0_RKB , +1.027181966035645772350639887939364020_RKB, +0.235395093203313594481836509609421923E+0_RKB , +1.019266717465484244962537467525869270_RKB, +0.237309316977027237519675921574483765E+0_RKB , +1.011292417439995739530489041191619980_RKB, +0.239238405905001516168070540916910782E+0_RKB , +1.003256679544672977063838476902952280_RKB, +0.241182706193826750302150947619295807E+0_RKB , +0.995156999635090923837912834290083799_RKB, +0.243142579653336370820347935962210089E+0_RKB , +0.986990747099062472368807733566367723_RKB, +0.245118404714142202924320107980890993E+0_RKB , +0.978755155294224603880824209605885949_RKB, +0.247110577533486783260721039414118216E+0_RKB , +0.970447311064224450680967868251783851_RKB, +0.249119513199040723215271175059742679E+0_RKB , +0.962064143223040583869351754884239000_RKB, +0.251145647041545878684196026994747375E+0_RKB , +0.953602409881086036147944393710646946_RKB, +0.253189436068676791163884011564958290E+0_RKB , +0.945058684468165463037907528952905452_RKB, +0.255251360534199633721355034811644515E+0_RKB , +0.936429340286575141234349646203595494_RKB, +0.257331925658493337610224432667231202E+0_RKB , +0.927710533402000123870677193352685174_RKB, +0.259431663518814566212074318832185428E+0_RKB , +0.918898183649590612180034442455129809_RKB, +0.261551135130401113878336401593219032E+0_RKB , +0.909987953496718494483529567690366580_RKB, +0.263690932742695838070411741690697980E+0_RKB , +0.900975224461221833746547856386022859_RKB, +0.265851682378732029260877257163356597E+0_RKB , +0.891855070732941566850586789359498648_RKB, +0.268034046650170417793435080776528378E+0_RKB , +0.882622229585165554772936671621819385_RKB, +0.270238727885765625479222906930855857E+0_RKB , +0.873271068088860754125762716220304264_RKB, +0.272466471617349972495381721975295691E+0_RKB , +0.863795545553308854813178505394360638_RKB, +0.274718070474985863152207934163143218E+0_RKB , +0.854189171008163807454180162989399104_RKB, +0.276994368552045124993231875042116081E+0_RKB , +0.844444954909153918889582440732428571_RKB, +0.279296266311992916126496729438627603E+0_RKB , +0.834555354086382178924726895193815695_RKB, +0.281624726122054644081592741705012005E+0_RKB , +0.824512208752292130518310689451625822_RKB, +0.283980778515329245279710753274268026E+0_RKB , +0.814306670135215230392694899997583155_RKB, +0.286365529303059635938328101021065686E+0_RKB , +0.803929116989971220407539518038181495_RKB, +0.288780167683694362995818015176624321E+0_RKB , +0.793369058840623296211094246674767659_RKB, +0.291225975526402318340687192537257840E+0_RKB , +0.782615023307233120893558043746138323_RKB, +0.293704338045591948359518681668325255E+0_RKB , +0.771654424224568084749572873233895398_RKB, +0.296216756132081268041022602880704688E+0_RKB , +0.760473406430108029348112105521972518_RKB, +0.298764860669019852359816171738518807E+0_RKB , +0.749056662017815292302576863549466866_RKB, +0.301350429240767224099410447613497339E+0_RKB , +0.737387211434295591278302895320305406_RKB, +0.303975405746574722328106158035369533E+0_RKB , +0.725446140909999639160421404681071701_RKB, +0.306641923566284096197801960631070354E+0_RKB , +0.713212285190975958395437234225351400_RKB, +0.309352333103853461802712328689370145E+0_RKB , +0.700661841106815072627797458756938969_RKB, +0.312109234772742761743862339129657007E+0_RKB , +0.687767892795788534294858623414951669_RKB, +0.314915518808718397997156048518493503E+0_RKB , +0.674499822837293822822291441953147501_RKB, +0.317774413735206587646816278462680542E+0_RKB , +0.660822574244419738417074112845703024_RKB, +0.320689545915737438541580666581786760E+0_RKB , +0.646695714894993817513389454402005337_RKB, +0.323665013485929872609853214812546138E+0_RKB , +0.632072236386061170945000136838048409_RKB, +0.326705479185682685503639905197287285E+0_RKB , +0.616896990007751449983468424580333684_RKB, +0.329816288403562001297942710464242773E+0_RKB , +0.601104617755992621533900682881952269_RKB, +0.333003621412417574590814956444079152E+0_RKB , +0.584616766106379321441587601292714165_RKB, +0.336274692838645610198728629890296241E+0_RKB , +0.567338257053818748196811566000406618_RKB, +0.339638017760732372141674530066184563E+0_RKB , +0.549151702327165120668100504067842453_RKB, +0.343103774061966311836681659618112095E+0_RKB , +0.529909720661558116786810165407173123_RKB, +0.346684307694080825876172229626686798E+0_RKB , +0.509423329602091814469823299066412422_RKB, +0.350394856987006815154163453112784578E+0_RKB , +0.487443966139236039301073245095571196_RKB, +0.354254625523424624005573055746854654E+0_RKB , +0.463634336790882217507922976793371502_RKB, +0.358288435101351989902170775658332694E+0_RKB , +0.437518402207871681933515025173607280_RKB, +0.362529398255472763687561092414814622E+0_RKB , +0.408389134611991145290558016416221589_RKB, +0.367023508970343116977068094647372845E+0_RKB , +0.375121332878380591495093443929722987_RKB, +0.371838172174307847618293715165674310E+0_RKB , +0.335737519214425235638195399148542308_RKB, +0.377079825919318504715611620323180171E+0_RKB , +0.286174591792072510002201653739714122_RKB, +0.382936353792390580381634933484297406E+0_RKB , +0.215241895984881699325976137068393403_RKB, +0.389807180887844207493515693365586429E+0_RKB , +0.000000000000000000000000000000000000_RKB, +0.398942280401432677939946059934381874E+0_RKB ], shape = [2, 128])

real(RKB), dimension(2, 0:256), parameter	ZIG_RKB = reshape([ZIGSET1, ZIGSET2], shape = [2, 257])
	The constant array of type `real` of kind RKB of shape `(1 : 2, 0 : 256)` containing the default 256-layers Ziggurat set information that is used within setNormRand to generate standard Normal random numbers. More...

Detailed Description

This module contains classes and procedures for computing various statistical quantities related to the univariate Normal distribution.

Specifically, this module contains routines for computing the following quantities of the univariate Normal distribution:

the Probability Density Function (PDF)
the Cumulative Distribution Function (CDF)
the Random Number Generation from the distribution (RNG)
the Inverse Cumulative Distribution Function (ICDF) or the Quantile Function

The PDF of the Normal distribution is defined with the two location and scale parameters \((\mu \in (-\infty, +\infty), \sigma > 0)\) as,

\begin{equation} \large \pi(x | \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\exp\bigg( -\frac{\big(x - \mu\big)^2}{2\sigma^2} \bigg) ~,~ x \in (-\infty, +\infty) ~. \end{equation}

The CDF of the Normal distribution is defined with the two location and scale parameters \((\mu \in (-\infty, +\infty), \sigma > 0)\) as,

\begin{equation} \large \mathrm{CDF}(x | \mu, \sigma) = \frac{1}{2} \bigg[ 1 + \mathrm{erf} \bigg( \frac{x - \mu}{\sigma\sqrt{2}} \bigg) \bigg] ~,~ x \in (-\infty, +\infty) ~. \end{equation}

Quantile Function

In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value.
Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution.
It is also called the percentile function, percent-point function or inverse cumulative distribution function (ICDF).

See the documentation of pm_distNorm for information on the CDF of the Normal distribution.

The quantile function of the standard normal distribution is called the probit function, and can be expressed in terms of the inverse error function:

\begin{equation} \Phi^{-1}(p) = {\sqrt{2}}\ms{erf}^{-1}(2p - 1), \quad p \in (0,1) ~. \end{equation}

For a normal random variable with mean \(\mu\) and variance \(\sigma^{2}\), the quantile function is,

\begin{equation} F^{-1}(p) = \mu + \sigma \Phi^{-1}(p) = \mu + \sigma \sqrt{2} \ms{erf}^{-1}(2p - 1), \quad p \in (0,1) ~. \end{equation}

The quantile \(\Phi^{-1}(p)\) of the standard normal distribution is commonly denoted as \(z_{p}\).
These values are used in hypothesis testing, construction of confidence intervals and Q–Q plots.
A normal random variable \(X\) will exceed \(\mu + z_{p}\sigma\) with probability \(1 − p\), and will lie outside the interval \(\mu \pm z_{p} \sigma\) with probability \(2(1 - p)\).
In particular, the quantile \(z_{0.975}\) is \(1.96\).
Therefore a normal random variable will lie outside the interval \(\mu \pm 1.96\sigma\) in only \(5\%\) of cases.

The following table gives the quantile \(z_{p}\) such that \(X\) will lie in the range \(\mu \pm z_{p}\sigma\) with a specified probability \(p\).
These values are useful to determine tolerance interval for sample averages and other statistical estimators with normal (or asymptotically normal) distributions.
Note that the following table shows \(\sqrt{2} \ms{erf}^{-1}(p) = \Phi^{-1}\left(\frac{p + 1}{2}\right)\), not \(\Phi^{-1}(p)\) as defined above.

\(p\)	\(z_{p}\)
0.80	1.281551565545
0.90	1.644853626951
0.95	1.959963984540
0.98	2.326347874041
0.99	2.575829303549
0.995	2.807033768344
0.998	3.090232306168
0.999	3.290526731492
0.9999	3.890591886413
0.99999	4.417173413469
0.999999	4.891638475699
0.9999999	5.326723886384
0.99999999	5.730728868236
0.999999999	6.109410204869

For small \(p\), the quantile function has the useful asymptotic expansion \(\Phi^{-1}(p) = -\sqrt{\ln{\frac{1}{p^{2}}} - \ln\ln{\frac{1}{p^{2}}} - \ln(2\pi)} + \mathcal{o}(1)\).

Random Number Generation

The current implementations of the RNG generic interfaces of this module use the Box-Muller trigonometric and rejection methods for Normal random number generation.

Note: The real32 Standard Normal random numbers generated by the Box-Muller algorithm are known to be limited to the range \([-6.66, +6.66]\).
The real64 Standard Normal random numbers generated by the Box-Muller algorithm are known to be limited to the range \([-9.419, +9.419]\).
Entropy

The entropy of the Normal distribution is defined by the following equation,

\begin{equation} \large \mathcal{H}(\sigma^2) = \frac{1}{2} \log(2\pi\sigma^2) + \frac{1}{2} \end{equation}

Fisher Information

The Fisher information for the Normal distribution is defined by the following equation,

\begin{equation} \large \mathcal{I}(\mu,\sigma) = \begin{pmatrix} \frac{1}{\sigma^2} & 0 \\ 0 & \frac{2}{\sigma^2} \\ \end{pmatrix} \end{equation}

Kullback-Leibler Divergence (KLD)

The Kullback-Leibler Divergence, also known as the relative entropy, of a univariate Normal distribution \(Q\) from a reference univariate Normal distribution \(P\) is defined as,

\begin{equation} \large D_{KL}(P \parallel Q) = \frac{(\mu_P - \mu_Q)^2}{2\sigma_Q^2} + \frac{1}{2}\bigg( \frac{\sigma_P}{\sigma_Q} - \ln\big(\frac{\sigma_P}{\sigma_Q}\big) - 1 \bigg) ~, \end{equation}

See also: pm_distNorm
pm_distNorm
pm_distNorm
pm_distNorm
pm_distNorm
pm_distNorm

Benchmarks:

Benchmark :: The runtime performance of setNormRand and setNormRandBox. ⛓

module zig_mod
    use pm_distNorm, only: xoshiro256ssw_type
    use pm_distNorm, only: getZigNorm
    use pm_kind, only: RKC => RK
    implicit none
    real(RKC) :: abserr
    real(RKC), allocatable :: zig(:,:)
end module zig_mod
 
! Test the performance of `setNormRandZiggurat()` vs. `setNormRandBoxBasic()`.
program benchmark
 
    use iso_fortran_env, only: error_unit
    use pm_bench, only: bench_type, benchMulti_type
    use pm_io, only: display_type
    use pm_kind, only: SK, IK, LK, RK
    use zig_mod
 
    implicit none
 
    integer(IK)                         :: isim
    integer(IK)                         :: itime
    integer(IK)                         :: ibench
    integer(IK)         , parameter     :: NSIM = 10000_IK ! must be even number.
    real(RKC)                           :: rand(NSIM) = 0._RKC
    real(RKC)                           :: dummy = 0._RKC
    type(benchMulti_type)               :: bench
    type(display_type)                  :: disp
    integer(IK)                         :: miniter = 10_IK
    type(xoshiro256ssw_type)            :: rng
 
    zig = getZigNorm(256_IK, abserr)
    rng = xoshiro256ssw_type()
    bench = benchMulti_type([ bench_type(name = SK_"setNormRandZiggurat", exec = setNormRandZiggurat, overhead = setOverhead, minsec = 0._RK, miniter = miniter) &
                            , bench_type(name = SK_"setNormRandZigX256S", exec = setNormRandZigX256S, overhead = setOverhead, minsec = 0._RK, miniter = miniter) &
                            , bench_type(name = SK_"setNormRandBoxBasic", exec = setNormRandBoxBasic, overhead = setOverhead, minsec = 0._RK, miniter = miniter) &
                            ], sorted = .true._LK, repeat = 1_IK)
 
    disp = display_type()
    call disp%show(bench%name, tmsize = 1_IK, bmsize = 1_IK)
    disp = display_type(file = "main.out")
 
    write(disp%unit, "(*(g0,:,','))") (bench%case(ibench)%name, ibench = 1, size(bench%case))
    do itime = 1, size(bench%case(1)%timing%values)
        call disp%show([(bench%case(ibench)%timing%values(itime) / NSIM, ibench = 1, size(bench%case))])
    end do
 
    write(*,"(*(g0,:,' '))") dummy
    write(*,"(*(g0,:,' '))")
 
contains
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! procedure wrappers.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    subroutine setOverhead()
        call finalize()
    end subroutine
 
    subroutine finalize()
        dummy = dummy + sum(rand)
    end subroutine
 
    subroutine setNormRandZiggurat()
        use pm_distNorm, only: setNormRand
        call setNormRand(rand)!, zig)
        call finalize()
    end subroutine
 
    subroutine setNormRandZigX256S()
        use pm_distNorm, only: setNormRand
        call setNormRand(rng, rand)!, zig)
        call finalize()
    end subroutine
 
    subroutine setNormRandBoxBasic()
        use pm_distNorm, only: setNormRandBox
        call random_number(rand)
        call setNormRandBox(rand(1:NSIM-1:2), rand(2:NSIM:2))
        call finalize()
    end subroutine
 
end program benchmark

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Postprocessing of the benchmark output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
 
import os
dirname = os.path.basename(os.getcwd()) 
 
fontsize = 14
 
df = pd.read_csv("main.out", delimiter = ",")
colnames = list(df.columns.values)
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
for colname in colnames[:]:
    plt.hist( np.log10(df[colname].values)
            , histtype = "step"
            , linewidth = 2
            , alpha = .5
            , bins = 50
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Log10( Runtime [ seconds ] )", fontsize = fontsize)
ax.set_ylabel("Count", fontsize = fontsize)
ax.set_title(" vs. ".join(colnames[:])+"\nLower is better.", fontsize = fontsize)
#ax.set_xscale("log")
#ax.set_yscale("log")
plt.minorticks_on()
plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
ax.tick_params(axis = "y", which = "minor")
ax.tick_params(axis = "x", which = "minor")
ax.legend   ( colnames[:]
           #, loc='center left'
           #, bbox_to_anchor=(1, 0.5)
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark." + dirname + ".runtime.png")
 
 
 
ax = plt.figure(figsize = 1.25 * np.array([6.4,4.6]), dpi = 200)
ax = plt.subplot()
 
for colname in colnames[1:]:
    plt.hist( np.log10(df[colname].values / df[colnames[0]].values)
            , histtype = "step"
            , linewidth = 2
            , alpha = .5
            , bins = 50
            )
 
plt.xticks(fontsize = fontsize)
plt.yticks(fontsize = fontsize)
ax.set_xlabel("Log10( Runtime Ratio compared to {} )".format(colnames[0]), fontsize = fontsize)
ax.set_ylabel("Count", fontsize = fontsize)
ax.set_title("Runtime Ratio Comparison. Lower means faster.\nLower than 0 means faster than {}().".format(colnames[0]), fontsize = fontsize)
#ax.set_xscale("log")
#ax.set_yscale("log")
plt.minorticks_on()
plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
ax.tick_params(axis = "y", which = "minor")
ax.tick_params(axis = "x", which = "minor")
ax.legend   ( colnames[1:]
           #, bbox_to_anchor = (1, 0.5)
           #, loc = "center left"
            , fontsize = fontsize
            )
 
plt.tight_layout()
plt.savefig("benchmark." + dirname + ".runtime.ratio.png")

Visualization of the benchmark output ⛓

Benchmark moral ⛓

The benchmark procedures named setNormRandZiggurat and setNormRandBoxBasic call the generic interfaces setNormRand (ziggurat method) and setNormRandBox (basic trigonometric Box-Muller method) respectively.
The benchmark procedure named setNormRandZigX256S calls the generic interface setNormRand with the xoshiro256ssw_type RNG instead of the default intrinsic Fortran RNG.
While setNormRandBox are pure subroutines, setNormRand is impure when the default intrinsic Fortran RNG is used.
The benchmark results confirm the widespread community observation that the Ziggurat method for Normal RNG can slightly faster than the Box-Muller method.
The difference, however, appears to be marginal, compiler and hardware dependent.

See also: pm_distLogNorm
pm_distMultiNorm
pm_distNormShell

Test:: test_pm_distNorm

Todo:: Very Low Priority: The performance of the current implementation of the Ziggurat RNG algorithm can be slightly improved for single-precision Normal RNG in the procedures that rely on xoshiro256ssw_type for uniform RNG.
This requires a customized implementation of the Ziggurat method for this real kind.

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Variable Documentation

◆ MODULE_NAME

character(*, SK), parameter pm_distNorm::MODULE_NAME = "@pm_distNorm"

Definition at line 187 of file pm_distNorm.F90.

◆ ZIG_PRECISION

integer(IK), parameter pm_distNorm::ZIG_PRECISION = 33_IK

The scalar integer of default kind IK containing the output of Fortran intrinsic precision() for the real kind used to generate the constant array ZIG_RKB.

See also: setZig ZIG_RKB setNormRand ZIG_PRECISION

Test:: test_pm_distNorm

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1487 of file pm_distNorm.F90.

◆ ZIG_RKB

real(RKB), dimension(2, 0:256), parameter pm_distNorm::ZIG_RKB = reshape([ZIGSET1, ZIGSET2], shape = [2, 257])

The constant array of type real of kind RKB of shape (1 : 2, 0 : 256) containing the default 256-layers Ziggurat set information that is used within setNormRand to generate standard Normal random numbers.

The subset ZIG_RKB(1, :) corresponding to the lower right corners of the 256 Ziggurat rectangles are computed via getZigNorm yielding a maximum absolute error abserr = +0.562732655625645475814793555099033451E-33 in the rectangle areas.

Warning: This constant vector was generated on an amd64 processor with the highest machine precision available for real type, yielding a maximum of ZIG_PRECISION digits of precision.
As such, care must be taken to not use this default Ziggurat set on processors with higher precision than used to generate this set.

See also: setZig ZIG_RKB setNormRand ZIG_PRECISION

Test:: test_pm_distNorm

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Amir Shahmoradi, Oct 16, 2009, 11:14 AM, Michigan

Definition at line 1774 of file pm_distNorm.F90.

◆ ZIGSET1

real(RKB), dimension(2, 0:128), parameter pm_distNorm::ZIGSET1 = reshape([ +3.910757959524915869549621434510571640_RKB, +0.000000000000000000000000000000000000E+0_RKB , +3.654152885361008771645429720399515670_RKB, +0.502781343070952005087938400241541891E-3_RKB , +3.449278298561431270627228213833611250_RKB, +0.104086943106322506013635915064907845E-2_RKB , +3.320244733839825517532232984442230700_RKB, +0.161091799459473453538408742342021986E-2_RKB , +3.224575052047801587144019828764775500_RKB, +0.220312016549958827311372671027399889E-2_RKB , +3.147889289518000685451855194084413580_RKB, +0.281289233937616172611348633870502865E-2_RKB , +3.083526132002143251877768947617198840_RKB, +0.343751917929162224416229759239016324E-2_RKB , +3.027837791769593524571714584215607150_RKB, +0.407518400039001087464038448139061472E-2_RKB , +2.978603279881843165536974212294808030_RKB, +0.472457682607575925888895096351016103E-2_RKB , +2.934366867208887589959928979567677640_RKB, +0.538470372266379748395288853907771468E-2_RKB , +2.894121053613412181388100356210103800_RKB, +0.605478221942164063991037466747021604E-2_RKB , +2.857138730873224588561645268053226920_RKB, +0.673417886624137640800598237565554838E-2_RKB , +2.822877396826442907534115515646593530_RKB, +0.742236950888280249329920345563351449E-2_RKB , +2.790921174001927318997779045468293070_RKB, +0.811891273868296054077142626445965006E-2_RKB , +2.760944005279986201244382392492695240_RKB, +0.882343143223528339445647449425005264E-2_RKB , +2.732685359044011420043182513046678140_RKB, +0.953559949343287212693559957627379651E-2_RKB , +2.705933656123062221333700225998574460_RKB, +0.102551320707227866483396053794922990E-1_RKB , +2.680514643285745101098374611431323380_RKB, +0.109817781711791129427823736030159900E-1_RKB , +2.656283037576743296802124304559512000_RKB, +0.117153149732408013682731286377880085E-1_RKB , +2.633116393631582759976309292516893140_RKB, +0.124555433719091587849084452906815838E-1_RKB , +2.610910518488823671930263694478955450_RKB, +0.132022844366303809959357880408105012E-1_RKB , +2.589575986708286649808805574507900700_RKB, +0.139553765573260408177619288977468218E-1_RKB , +2.569035452681843781314262921528081910_RKB, +0.147146731176153334234423656007745630E-1_RKB , +2.549221550324783104422671371241746650_RKB, +0.154800405777112059806768992081788185E-1_RKB , +2.530075232159854187716539084126876370_RKB, +0.162513568797661774124156785927309438E-1_RKB , +2.511544441626694343254607344580084390_RKB, +0.170285101099635321775373808069033731E-1_RKB , +2.493583041271046768170053296506813290_RKB, +0.178113973671931254109163549358583312E-1_RKB , +2.476149939670523163756216268162166500_RKB, +0.185999237995485118944697972790344771E-1_RKB , +2.459208374334705035673859596487019180_RKB, +0.193940017783549904963609637793049119E-1_RKB , +2.442725318200364223794234919225453500_RKB, +0.201935501858165129428739457647187713E-1_RKB , +2.426670984937146719863529851633726960_RKB, +0.209984937972267218821328887239805004E-1_RKB , +2.411018413901119491690349211725038630_RKB, +0.218087627424279111659346610629834973E-1_RKB , +2.395743119781927356168686681412574760_RKB, +0.226242920341075527766680294896069533E-1_RKB , +2.380822795172085556506619691319380400_RKB, +0.234450211528013514383037474818822027E-1_RKB , +2.366237056717290911362148128140186000_RKB, +0.242708936802748765008871090362921378E-1_RKB , +2.351967227379144761902530751453964640_RKB, +0.251018569743934986305835005740321359E-1_RKB , +2.337996148796528635433480327093713940_RKB, +0.259378618797451777000075273655017443E-1_RKB , +2.324308018871132508266119157050790040_RKB, +0.267788624692146997471273278024758566E-1_RKB , +2.310888250601371758550614355860895420_RKB, +0.276248158124683715174543699462393572E-1_RKB , +2.297723348902863520079790814230529130_RKB, +0.284756817679310236840265332909329685E-1_RKB , +2.284800802724492127387834486937223350_RKB, +0.293314227953502809501556980682789090E-1_RKB , +2.272108990228381861937683717373910900_RKB, +0.301920037864680654091842729977054983E-1_RKB , +2.259637095173787624597566531167311770_RKB, +0.310573919116731481152577086508924965E-1_RKB , +2.247375032947389262297952392515659590_RKB, +0.319275564808046037696524061552362067E-1_RKB , +2.235313384929921110748362199673550240_RKB, +0.328024688165248443463852626030938600E-1_RKB , +2.223443340092510611365346409716922540_RKB, +0.336821021388909593274737975695380343E-1_RKB , +2.211756642884160997470500709266731210_RKB, +0.345664314599311541791934500133628777E-1_RKB , +2.200245546611276427712165173291835590_RKB, +0.354554334871846263278378901217329216E-1_RKB , +2.188902771626360742839576505604305880_RKB, +0.363490865352926868627480678085691155E-1_RKB , +2.177721467740293002579164079152503390_RKB, +0.372473704448399433976210004282028638E-1_RKB , +2.166695180354308542353137142121026540_RKB, +0.381502665077398667348211240367435477E-1_RKB , +2.155817819876737469119503677197502650_RKB, +0.390577573985415074098963321878992358E-1_RKB , +2.145083634047888982767999729572053870_RKB, +0.399698271111055203479683284323823695E-1_RKB , +2.134487182846016909178836604796243250_RKB, +0.408864609001596660576863760104051322E-1_RKB , +2.124023315689523545420714787478384860_RKB, +0.418076452272979751244992871255722388E-1_RKB , +2.113687150686653177781935198589005610_RKB, +0.427333677110349512002228670090424488E-1_RKB , +2.103474055714877305933714304045440450_RKB, +0.436636170805675209921984193602696278E-1_RKB , +2.093379631138791930166361585961667970_RKB, +0.445983831329337385181389634688869380E-1_RKB , +2.083399693998304613670792088175897210_RKB, +0.455376566932892082093887264381438529E-1_RKB , +2.073530263518743034646393248416971800_RKB, +0.464814295780503946152953311870656232E-1_RKB , +2.063767547811732114341853749078149630_RKB, +0.474296945606789346776298063351001244E-1_RKB , +2.054107931650652130219475666313816510_RKB, +0.483824453399031873773625284851490337E-1_RKB , +2.044547965217531455282628792749082960_RKB, +0.493396765101929088581344120097015200E-1_RKB , +2.035084353729618971413871948694988270_RKB, +0.503013835343204408492863489427518069E-1_RKB , +2.025713947863854245252399025955272060_RKB, +0.512675627178574145127079248497036520E-1_RKB , +2.016433734906204123873988577023278720_RKB, +0.522382111854699318500836298767666937E-1_RKB , +2.007240830560528758913239738198299090_RKB, +0.532133268588876922360496499106520185E-1_RKB , +1.998132471358419680392214769162858870_RKB, +0.541929084364337554633405727268610055E-1_RKB , +1.989106007617438123201023091217180910_RKB, +0.551769553740117250736639942272910314E-1_RKB , +1.980158896900476605540416694815765850_RKB, +0.561654678674562273820736142229565223E-1_RKB , +1.971288697933659294606356474434686550_RKB, +0.571584468361607664497222499802473837E-1_RKB , +1.962493064944363052826024381256974850_RKB, +0.581558939079044529261453899150298019E-1_RKB , +1.953769742384646776692572811817963060_RKB, +0.591578114048058224055549195846209505E-1_RKB , +1.945116560008678301234686281875394240_RKB, +0.601642023303380532839147151743642514E-1_RKB , +1.936531428275694700380702197135648770_RKB, +0.611750703573454323914419246868044098E-1_RKB , +1.928012334052665710328808957510011910_RKB, +0.621904198170059582295143354352838012E-1_RKB , +1.919557336593188113064282063465457130_RKB, +0.632102556886895688287062083850491706E-1_RKB , +1.911164563771253338349016119398665420_RKB, +0.642345835906656803805852580678544053E-1_RKB , +1.902832208550429269452784399230803680_RKB, +0.652634097716175649174146849378032930E-1_RKB , +1.894558525670704732040885690575958130_RKB, +0.662967411029246168483446165075442866E-1_RKB , +1.886341828536782820037856553309563160_RKB, +0.673345850716767915010299444811729445E-1_RKB , +1.878180486292995844684467996043645020_RKB, +0.683769497743884728203642791575539760E-1_RKB , +1.870072921071266778496337776290841830_RKB, +0.694238439113817677925134633773045847E-1_RKB , +1.862017605399674118665348784397922740_RKB, +0.704752767818117550133248257276187773E-1_RKB , +1.854013059760201906750898441184461490_RKB, +0.715312582793085547211649297744966411E-1_RKB , +1.846057850285185505570580952991448920_RKB, +0.725917988882132560598516526262197654E-1_RKB , +1.838150586582806633764931304898561700_RKB, +0.736569096803867509488343563799016629E-1_RKB , +1.830289919682756933756055676984081970_RKB, +0.747266023125723976798301015314803279E-1_RKB , +1.822474540093885838871898571617810260_RKB, +0.758008890242951847298446370142010715E-1_RKB , +1.814703175966282671680772343522476780_RKB, +0.768797826362816984781690401687711081E-1_RKB , +1.806974591350820938703420428388107530_RKB, +0.779632965493867285846698800079747914E-1_RKB , +1.799287584549720199341728680984235510_RKB, +0.790514447440137817496961412302243116E-1_RKB , +1.791640986552162594624382322132709310_RKB, +0.801442417800181275436054931177368005E-1_RKB , +1.784033659549441512971864077807943680_RKB, +0.812417027970822772687529532474258376E-1_RKB , +1.776464495524522868996124119276484200_RKB, +0.823438435155550059817881401744955979E-1_RKB , +1.768932414911268589029665159840958690_RKB, +0.834506802377461758021915029242417507E-1_RKB , +1.761436365318910280539794251593908460_RKB, +0.845622298496707118376316534786168010E-1_RKB , +1.753975320317671535176286495650271100_RKB, +0.856785098232361263350014624915617177E-1_RKB , +1.746548278281722412853610819915111290_RKB, +0.867995382188689874348253633476266673E-1_RKB , +1.739154261285911657262420055628115450_RKB, +0.879253336885766911833903717911534395E-1_RKB , +1.731792314052963154137933505808925000_RKB, +0.890559154794418239043567001488716945E-1_RKB , +1.724461502948044912052862397775662270_RKB, +0.901913034375473009991491331657262247E-1_RKB , +1.717160915017823089741659119609676780_RKB, +0.913315180123313418058911041645338441E-1_RKB , +1.709889657071301820241745482016102880_RKB, +0.924765802613721921296195811766027943E-1_RKB , +1.702646854799923151653900407051805770_RKB, +0.936265118556033400788781021199070560E-1_RKB , +1.695431651934561568299588089192625460_RKB, +0.947813350849607903374772538857282822E-1_RKB , +1.688243209437195389093695018261921410_RKB, +0.959410728644647702377950152378611650E-1_RKB , +1.681080704725173871909617303396002540_RKB, +0.971057487407390411201725488177809241E-1_RKB , +1.673943330926124999231911729230294350_RKB, +0.982753868989717834844303967803275557E-1_RKB , +1.666830296161665512280717200364773540_RKB, +0.994500121703228172933039137854161328E-1_RKB , +1.659740822858182552384789747414556960_RKB, +0.100629650039782712328127609576129162E+0_RKB , +1.652674147083055944977076666279072050_RKB, +0.101814326654490140522320621972065562E+0_RKB , +1.645629517904782346099997435068184430_RKB, +0.103004068832514625466733060901486566E+0_RKB , +1.638606196775547730191205373889528150_RKB, +0.104198904072112656528428960098709859E+0_RKB , +1.631603456934873546471532683464361160_RKB, +0.105398860561465958979782511482284346E+0_RKB , +1.624620582833034778354059455865975410_RKB, +0.106603967188911549935198869215607602E+0_RKB , +1.617656869573015532637880619762087450_RKB, +0.107814253553674065499513686193278908E+0_RKB , +1.610711622369830051160545249046193620_RKB, +0.109029749977111720145296612324748632E+0_RKB , +1.603784156026094530393066805218239570_RKB, +0.110250487514488157810061008578271138E+0_RKB , +1.596873794422788175563087978818873180_RKB, +0.111476497967283378462230486935475436E+0_RKB , +1.589979870024190797461111747861209560_RKB, +0.112707813896057876934855393386708534E+0_RKB , +1.583101723396029247521107058058590910_RKB, +0.113944468633885115777321981289805190E+0_RKB , +1.576238702735906320876658002975291310_RKB, +0.115186496300368473953376646626857215E+0_RKB , +1.569390163415123656042832370955675890_RKB, +0.116433931816259871778263682344311485E+0_RKB , +1.562555467531044820930627254229273630_RKB, +0.117686810918698373049736317381864947E+0_RKB , +1.555733983469176375991038619565492320_RKB, +0.118945170177088211568318678970235501E+0_RKB , +1.548925085474173406375274133330557850_RKB, +0.120209047009636885032310150781360772E+0_RKB , +1.542128153229001959318075945656599760_RKB, +0.121478479700575208713903649777558606E+0_RKB , +1.535342571441514138082707130216935300_RKB, +0.122753507418082528688239173356532507E+0_RKB ], shape = [2, 129])

Definition at line 1489 of file pm_distNorm.F90.

◆ ZIGSET2

real(RKB), dimension(2, 1:128), parameter pm_distNorm::ZIGSET2 = reshape([ +1.528567729437712402628199461442167180_RKB, +0.124034170232941664267186768442998377E+0_RKB , +1.521803020760998008679228498636570410_RKB, +0.125320509137949586535569901372920916E+0_RKB , +1.515047842776714566947194255734634790_RKB, +0.126612566068111349659514010876108850E+0_RKB , +1.508301596281311496171425183785073880_RKB, +0.127910383921646379432792471520964754E+0_RKB , +1.501563685115463738688173273682448190_RKB, +0.129214006581837895215365859576747957E+0_RKB , +1.494833515780493555035890159317754310_RKB, +0.130523478939758003270817270840923056E+0_RKB , +1.488110497057447553013103271226758760_RKB, +0.131838846917902858239534927650542548E+0_RKB , +1.481394039628187363902263028944763970_RKB, +0.133160157494774252287691074366070633E+0_RKB , +1.474683555697855570628865196528769660_RKB, +0.134487458730446066069814161355648980E+0_RKB , +1.467978458618079624962505551018572310_RKB, +0.135820799793156210330787895235534157E+0_RKB , +1.461278162510275558141634572902431380_RKB, +0.137160230986967010673991854114446593E+0_RKB , +1.454582081888410275202473614895370850_RKB, +0.138505803780539450342898439610712141E+0_RKB , +1.447889631280576100338960603208179050_RKB, +0.139857570837069297157912765350925466E+0_RKB , +1.441200224848723969896483905460819290_RKB, +0.141215586045435912189035654183361969E+0_RKB , +1.434513276005892200373197821347744230_RKB, +0.142579904552617481390538701477587025E+0_RKB , +1.427828197030256028046923580264626420_RKB, +0.143950582797429540314021584008091148E+0_RKB , +1.421144398675309048678328840045534000_RKB, +0.145327678545646990255525094264574683E+0_RKB , +1.414461289775471190729091975769526810_RKB, +0.146711250926573347052911625905291106E+0_RKB , +1.407778276846398829890729544114189010_RKB, +0.148101360471124737782233265331001140E+0_RKB , +1.401094763679250977372468027391928780_RKB, +0.149498069151500183758164830605819877E+0_RKB , +1.394410150928141013910818209046742880_RKB, +0.150901440422514000012107606564276651E+0_RKB , +1.387723835689976042816457610158740000_RKB, +0.152311539264670722976597120096621794E+0_RKB , +1.381035211075855426557023886048995030_RKB, +0.153728432229067872471998597962422358E+0_RKB , +1.374343665773166259809330405021183000_RKB, +0.155152187484217086331763054685730862E+0_RKB , +1.367648583597476202662733878746826080_RKB, +0.156582874864879763414378129073938725E+0_RKB , +1.360949343033283011396528844287145660_RKB, +0.158020565923019343095774015163019653E+0_RKB , +1.354245316762634995007843766072061330_RKB, +0.159465333980978769091659649295558937E+0_RKB , +1.347535871180587198226303191916842980_RKB, +0.160917254186998568094181273666041719E+0_RKB , +1.340820365896404038797740514363138740_RKB, +0.162376403573198357993539454690214112E+0_RKB , +1.334098153219360045667959181721837720_RKB, +0.163842861116152528813630294472766962E+0_RKB , +1.327368577627925853644432080219569470_RKB, +0.165316707800199358376684187822216740E+0_RKB , +1.320630975221056264316363281880977050_RKB, +0.166798026683631985045755192821871952E+0_RKB , +1.313884673150220489854736808952840970_RKB, +0.168286902967929517543098016930008494E+0_RKB , +1.307128989030731110178131195502915220_RKB, +0.169783424070197178160245257400787177E+0_RKB , +1.300363230330837190351929439655934200_RKB, +0.171287679698995818105358886788417999E+0_RKB , +1.293586693736947753945601406359300470_RKB, +0.172799761933753486486498659023686530E+0_RKB , +1.286798664493243646316660896517199420_RKB, +0.174319765307965059246455246546117697E+0_RKB , +1.279998415713817924797308907917922830_RKB, +0.175847786896400331371952020571991623E+0_RKB , +1.273185207665356364764060323720764170_RKB, +0.177383926406556544373322976411406151E+0_RKB , +1.266358287018229453775313848849852450_RKB, +0.178928286274608171283092549748417432E+0_RKB , +1.259516886063714228190559472001646690_RKB, +0.180480971766125034830178787412733260E+0_RKB , +1.252660221894897227354473865616388090_RKB, +0.182042091081849625639024292847696263E+0_RKB , +1.245787495548627294596662055366290760_RKB, +0.183611755468845965529740751119222664E+0_RKB , +1.238897891105687374493975672708951630_RKB, +0.185190079337355691907687938603429913E+0_RKB , +1.231990574746136091354596183983300960_RKB, +0.186777180383722406901836668848789685E+0_RKB , +1.225064693756530787096859391988721310_RKB, +0.188373179719772944131913560975705614E+0_RKB , +1.218119375485481656036492926236470550_RKB, +0.189978202009074284878057268848586717E+0_RKB , +1.211153726243699183035927701680494030_RKB, +0.191592375610517658429468812562799404E+0_RKB , +1.204166830144381512972585409228431810_RKB, +0.193215832729717172651871738633649002E+0_RKB , +1.197157747879441555149951169947666830_RKB, +0.194848709578749458096518050299059063E+0_RKB , +1.190125515426692069320479795685490130_RKB, +0.196491146544803628100426175257282935E+0_RKB , +1.183069142682686761029921497512774320_RKB, +0.198143288368357757303338740744073695E+0_RKB , +1.175987612015452098437940687032687740_RKB, +0.199805284331549509895377775340098004E+0_RKB , +1.168879876730833138384076802216189500_RKB, +0.201477288457465010601480272621186237E+0_RKB , +1.161744859445611442407678658730303350_RKB, +0.203159459721132113428367115004471988E+0_RKB , +1.154581450359927740740669252500180290_RKB, +0.204851962273072525723359017960643915E+0_RKB , +1.147388505420849058458757243582079270_RKB, +0.206554965676342511391397805599266881E+0_RKB , +1.140164844368151242664448937938463130_RKB, +0.208268645158074945659692042041697417E+0_RKB , +1.132909248652533753115898715892141530_RKB, +0.209993181876627252316799052585710853E+0_RKB , +1.125620459215533391227475593856507500_RKB, +0.211728763205541276296151308493989896E+0_RKB , +1.118297174119344981546693309349106980_RKB, +0.213475583035633628019879947303927958E+0_RKB , +1.110938046013575721417560779257849040_RKB, +0.215233842096659846410648766825208954E+0_RKB , +1.103541679424639718350709546845052450_RKB, +0.217003748300134423613077654918982009E+0_RKB , +1.096106627852021437094938365415991340_RKB, +0.218785517105043099072370007214575357E+0_RKB , +1.088631390653979821403993213445028160_RKB, +0.220579371908355906900178024260990122E+0_RKB , +1.081114409703403838077538136757234410_RKB, +0.222385544462441594762945169415386684E+0_RKB , +1.073554065792436288292686500464555760_RKB, +0.224204275321698924941276382479365999E+0_RKB , +1.065948674762122501754284026538321330_RKB, +0.226035814320961132564753113117134625E+0_RKB , +1.058296483330675084513966896229645790_RKB, +0.227880421088500051269826182271994471E+0_RKB , +1.050595664590929901514279329073961990_RKB, +0.229738365596760291802256320937473869E+0_RKB , +1.042844313144148970939980229020163640_RKB, +0.231609928754296215469589885980076311E+0_RKB , +1.035040439833440875887862746039381010_RKB, +0.233495403042770916853974440099008843E+0_RKB , +1.027181966035645772350639887939364020_RKB, +0.235395093203313594481836509609421923E+0_RKB , +1.019266717465484244962537467525869270_RKB, +0.237309316977027237519675921574483765E+0_RKB , +1.011292417439995739530489041191619980_RKB, +0.239238405905001516168070540916910782E+0_RKB , +1.003256679544672977063838476902952280_RKB, +0.241182706193826750302150947619295807E+0_RKB , +0.995156999635090923837912834290083799_RKB, +0.243142579653336370820347935962210089E+0_RKB , +0.986990747099062472368807733566367723_RKB, +0.245118404714142202924320107980890993E+0_RKB , +0.978755155294224603880824209605885949_RKB, +0.247110577533486783260721039414118216E+0_RKB , +0.970447311064224450680967868251783851_RKB, +0.249119513199040723215271175059742679E+0_RKB , +0.962064143223040583869351754884239000_RKB, +0.251145647041545878684196026994747375E+0_RKB , +0.953602409881086036147944393710646946_RKB, +0.253189436068676791163884011564958290E+0_RKB , +0.945058684468165463037907528952905452_RKB, +0.255251360534199633721355034811644515E+0_RKB , +0.936429340286575141234349646203595494_RKB, +0.257331925658493337610224432667231202E+0_RKB , +0.927710533402000123870677193352685174_RKB, +0.259431663518814566212074318832185428E+0_RKB , +0.918898183649590612180034442455129809_RKB, +0.261551135130401113878336401593219032E+0_RKB , +0.909987953496718494483529567690366580_RKB, +0.263690932742695838070411741690697980E+0_RKB , +0.900975224461221833746547856386022859_RKB, +0.265851682378732029260877257163356597E+0_RKB , +0.891855070732941566850586789359498648_RKB, +0.268034046650170417793435080776528378E+0_RKB , +0.882622229585165554772936671621819385_RKB, +0.270238727885765625479222906930855857E+0_RKB , +0.873271068088860754125762716220304264_RKB, +0.272466471617349972495381721975295691E+0_RKB , +0.863795545553308854813178505394360638_RKB, +0.274718070474985863152207934163143218E+0_RKB , +0.854189171008163807454180162989399104_RKB, +0.276994368552045124993231875042116081E+0_RKB , +0.844444954909153918889582440732428571_RKB, +0.279296266311992916126496729438627603E+0_RKB , +0.834555354086382178924726895193815695_RKB, +0.281624726122054644081592741705012005E+0_RKB , +0.824512208752292130518310689451625822_RKB, +0.283980778515329245279710753274268026E+0_RKB , +0.814306670135215230392694899997583155_RKB, +0.286365529303059635938328101021065686E+0_RKB , +0.803929116989971220407539518038181495_RKB, +0.288780167683694362995818015176624321E+0_RKB , +0.793369058840623296211094246674767659_RKB, +0.291225975526402318340687192537257840E+0_RKB , +0.782615023307233120893558043746138323_RKB, +0.293704338045591948359518681668325255E+0_RKB , +0.771654424224568084749572873233895398_RKB, +0.296216756132081268041022602880704688E+0_RKB , +0.760473406430108029348112105521972518_RKB, +0.298764860669019852359816171738518807E+0_RKB , +0.749056662017815292302576863549466866_RKB, +0.301350429240767224099410447613497339E+0_RKB , +0.737387211434295591278302895320305406_RKB, +0.303975405746574722328106158035369533E+0_RKB , +0.725446140909999639160421404681071701_RKB, +0.306641923566284096197801960631070354E+0_RKB , +0.713212285190975958395437234225351400_RKB, +0.309352333103853461802712328689370145E+0_RKB , +0.700661841106815072627797458756938969_RKB, +0.312109234772742761743862339129657007E+0_RKB , +0.687767892795788534294858623414951669_RKB, +0.314915518808718397997156048518493503E+0_RKB , +0.674499822837293822822291441953147501_RKB, +0.317774413735206587646816278462680542E+0_RKB , +0.660822574244419738417074112845703024_RKB, +0.320689545915737438541580666581786760E+0_RKB , +0.646695714894993817513389454402005337_RKB, +0.323665013485929872609853214812546138E+0_RKB , +0.632072236386061170945000136838048409_RKB, +0.326705479185682685503639905197287285E+0_RKB , +0.616896990007751449983468424580333684_RKB, +0.329816288403562001297942710464242773E+0_RKB , +0.601104617755992621533900682881952269_RKB, +0.333003621412417574590814956444079152E+0_RKB , +0.584616766106379321441587601292714165_RKB, +0.336274692838645610198728629890296241E+0_RKB , +0.567338257053818748196811566000406618_RKB, +0.339638017760732372141674530066184563E+0_RKB , +0.549151702327165120668100504067842453_RKB, +0.343103774061966311836681659618112095E+0_RKB , +0.529909720661558116786810165407173123_RKB, +0.346684307694080825876172229626686798E+0_RKB , +0.509423329602091814469823299066412422_RKB, +0.350394856987006815154163453112784578E+0_RKB , +0.487443966139236039301073245095571196_RKB, +0.354254625523424624005573055746854654E+0_RKB , +0.463634336790882217507922976793371502_RKB, +0.358288435101351989902170775658332694E+0_RKB , +0.437518402207871681933515025173607280_RKB, +0.362529398255472763687561092414814622E+0_RKB , +0.408389134611991145290558016416221589_RKB, +0.367023508970343116977068094647372845E+0_RKB , +0.375121332878380591495093443929722987_RKB, +0.371838172174307847618293715165674310E+0_RKB , +0.335737519214425235638195399148542308_RKB, +0.377079825919318504715611620323180171E+0_RKB , +0.286174591792072510002201653739714122_RKB, +0.382936353792390580381634933484297406E+0_RKB , +0.215241895984881699325976137068393403_RKB, +0.389807180887844207493515693365586429E+0_RKB , +0.000000000000000000000000000000000000_RKB, +0.398942280401432677939946059934381874E+0_RKB ], shape = [2, 128])

Definition at line 1618 of file pm_distNorm.F90.

Data Types

Variables

Detailed Description

Variable Documentation

◆ MODULE_NAME

◆ ZIG_PRECISION

◆ ZIG_RKB

◆ ZIGSET1

◆ ZIGSET2