pm_matrixDet::getMatDet Interface Reference

Generate and return the determinant of the input general square matrix.
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Detailed Description

Generate and return the determinant of the input general square matrix.

This generic interface uses the pivoted LU (LUP) factorization to compute the determinant.
If the matrix is already known to be positive-definite, use the other more appropriate faster generic interfaces of this module (e.g., getMatDetSqrt).

Parameters

[in]

mat

: The input contiguous square matrix of shape (ndim,ndim) of type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128).

Returns

det : The output scalar of the same type and kind as the input mat containing the determinant of the input square matrix.

Possible calling interfaces ⛓

use pm_matrixDet, only: getMatDet
 
det = getMatDet(mat)

Warning

The condition size(mat, 1) == size(mat, 2) must hold for the corresponding input arguments.
This condition is verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The procedures under this generic interface call error stop if the Pivoted LU factorization of mat fails.
See setMatDet for the fault-tolerant potentially faster subroutine version of this interface.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks

The procedures under this generic interface are computationally demanding since the LU factorization requires creating a copy of the input mat to avoid the direct manipulation of the input intent(in) :: mat.
See setMatDet for the performant subroutine versions of these procedures where mat has intent(inout).

See also

getMatDet
setMatDet
getMatDetSqrtLog
setMatDetSqrtLog
getMatDetSqrt
setMatDetSqrt

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_matrixDet, only: getMatDet
    use pm_matrixInv, only: getMatInv
    use pm_distUnif, only: getUnifRand
    use pm_io, only: display_type
 
    implicit none
 
    integer(IK) :: ndim, itry, ntry = 10
    type(display_type) :: disp
 
    disp = display_type(file = "main.out.F90")
 
    call disp%skip()
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute the determinant of the square matrix.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip()
 
    block
        use pm_kind, only: TKG => RKH
        real(TKG), allocatable :: mat(:,:)
        real(TKG) :: det
        do itry = 1, ntry
            call disp%skip()
            call disp%show("ndim = getUnifRand(1, 9)")
                            ndim = getUnifRand(1, 9)
            call disp%show("ndim")
            call disp%show( ndim )
            call disp%show("mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)")
                            mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
            call disp%show("mat")
            call disp%show( mat )
            call disp%show("det = getMatDet(mat)")
                            det = getMatDet(mat)
            call disp%show("det")
            call disp%show( det )
            call disp%show("det * getMatDet(getMatInv(mat)) ! must be one.")
            call disp%show( det * getMatDet(getMatInv(mat)) )
            call disp%skip()
        end do
    end block
 
    block
        use pm_kind, only: TKG => CKH
        complex(TKG), allocatable :: mat(:,:)
        real(TKG) :: det
        do itry = 1, ntry
            call disp%skip()
            call disp%show("ndim = getUnifRand(1, 9)")
                            ndim = getUnifRand(1, 9)
            call disp%show("mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)")
                            mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
            call disp%show("mat")
            call disp%show( mat )
            call disp%show("det = getMatDet(mat)")
                            det = getMatDet(mat)
            call disp%show("det")
            call disp%show( det )
            call disp%show("det * getMatDet(getMatInv(mat)) ! must be one.")
            call disp%show( det * getMatDet(getMatInv(mat)) )
            call disp%skip()
        end do
    end block
 
end program example

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

Example output ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute the determinant of the square matrix.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
ndim = getUnifRand(1, 9)
ndim
+3
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.03818374981776673736094400497708881, +1.51443508969459627594765773885545598, +1.76395287978696041188370468956598599
+1.33986704838099138207727961780863919, +1.08669920190966101363841719416164429, +1.18471588025012920003867478790705223
+1.09137451016806959314705004379813157, +1.16466934584182435775611024022486425, +1.18094610201682720663697004571324081
det = getMatDet(mat)
det
+0.122269018411462711928600352682297466
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999904
 
 
ndim = getUnifRand(1, 9)
ndim
+2
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.53481343684725860608675029369531411, +1.17854468421189646471883581358238533
+1.34131649939303132800369303518838649, +1.53962607423823684609433956431343927
det = getMatDet(mat)
det
+0.782237356255874295335119982348538517
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999904
 
 
ndim = getUnifRand(1, 9)
ndim
+5
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.08658030501303681951640826019088467, +1.82477653611124365030413997905141321, +1.53135559340899395622570997793417565, +1.21252418859692266826474715176466005, +1.72321539676562773468204974025683360
+1.05154889658931812694511657351971031, +1.99893012594914990102886634028050645, +1.35471720022827533631647947554357728, +1.54544912824956940344002584767990417, +1.21844955896590050457772445454395153
+1.29016275259538510108764792761002772, +1.19989534724165180475607777230349376, +1.70407745386214472119086068010508277, +1.57186514551943393930284628091432345, +1.85381123311950372034689608575059401
+1.81522329627959193285637095911739136, +1.88556723254430344908598530380275411, +1.42222157402041377382988448586963551, +1.83072241671037239116900680268840235, +1.11980425639629985942108883580847744
+1.83008488712124136335724549627817640, +1.40336429150198902080735150607333623, +1.11703195028304035965218964569690149, +1.68116955760947679070638774774575977, +1.91386301263779410141546392870635460
det = getMatDet(mat)
det
+0.576994053023537675460068953582414633
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999422
 
 
ndim = getUnifRand(1, 9)
ndim
+7
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.60686169096038220212128409388625830, +1.48125019948683727522024341527763741, +1.15260185058156621829094866736912450, +1.96956513122528575982157803388737003, +1.08692507970497059895141927687898233, +1.24800952620174473344723665308840425, +1.22197241632610717627055436061812161
+1.28144799052917194359284938011712398, +1.68872186405707918473921666896593713, +1.55987903477425651806246711067233283, +1.27203030241198515944097362573862018, +1.15791584739449204006381452273839429, +1.25760258646586037099937854372595988, +1.11681659053510538154146735243312597
+1.20708503942846517215957386823143016, +1.60635061696171361374753629917133783, +1.03960130066403945144144861767669497, +1.78933896167417841404549916193917299, +1.42351239050009027483909246970088307, +1.78373972944138746871706261722967111, +1.72671697429881582230601789465748230
+1.08215786171655365192889846372258068, +1.69427059603431658640747233227579020, +1.71344963342694463795497934959715807, +1.98583341594127501995922475912258264, +1.22489255081794029742199648406281702, +1.63874967815254657367744672932587558, +1.85417221448084671418830842557908490
+1.12531397427031110071168130345502113, +1.71327947093406233829018582232088224, +1.78432112467838221327858657479318865, +1.76422285935596928738122557105814372, +1.49016596532031802432191912513841155, +1.78549604485171654344920465699038397, +1.81123847525283594375781005709890093
+1.84120518043801898623016230866436105, +1.49940034451094410985347318594948685, +1.20917183290452412230080383381727745, +1.98762816484764396550221184680444156, +1.07980588296893768080550745824511375, +1.28562536191695485452937027305180976, +1.18399321515429933599698947904077559
+1.04230677172059236931519715227519611, +1.19866336827533237561109829363401517, +1.72030965964330838467537807730140324, +1.68120998750477219957623489885302289, +1.70638302307524184307737925687363210, +1.23049899082798672767983694492324640, +1.09041240527005856115457163232576865
det = getMatDet(mat)
det
+0.887663401223694015752391325911238512E-3
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999958785
 
 
ndim = getUnifRand(1, 9)
ndim
+7
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.85841779797975176225756703242417910, +1.74482074885409772257142207931769902, +1.51595152508778765877536900698056898, +1.88847443028454893145434230832896154, +1.56127018209317766636412587838662779, +1.36581310892871882122540626702917444, +1.63149048725648522962632956445552783
+1.51700381278748030738876309956120828, +1.64977773313533577849949136411726459, +1.03600866472339095338191859780703313, +1.74559727831526834742792995942353190, +1.26186570155699031456882615809409569, +1.15571260276759465465559680483841821, +1.67217256871265622036122965051495874
+1.64477649465239149534082323329261251, +1.05998822192374139620633233586146545, +1.91740887145785226794971410782574490, +1.86924098543506851452156305541264030, +1.96849046317562786962440387449129506, +1.02762764666354643714334857360311824, +1.30664514522568617541432831091501550
+1.73793549345537166270182669717105649, +1.28952967473251651663620889161737398, +1.16711492746260653082540871610757437, +1.18714137354389213457725795900071278, +1.23382271600662049576036982324063533, +1.38274063373600723026704441719186306, +1.97063800519364229411608732302527471
+1.63961174039989040455757725332375030, +1.04183325585123704423215194424210649, +1.30374896455960796725885491102208353, +1.60656440738544515277149792174100393, +1.95911480354909571065156330242535283, +1.00865614379686304974307669419753660, +1.93040750943168960796081991238286796
+1.31519275840446643190153817322884639, +1.66777882852487563420600113829621051, +1.12341126974115886231862087312494711, +1.66085511050885322094701298924798371, +1.37328425959997095413407035500151779, +1.73964641763175206326611884669857934, +1.32956675017655478850139209053375316
+1.89666574015570957873971118865198186, +1.34874173414006757064954008441224617, +1.26544029188793955369254333852342397, +1.78556974848605253578222849915297132, +1.67477911287348340805288146805359285, +1.61953814091429543133451024936834163, +1.52606659478058275155545681186766091
det = getMatDet(mat)
det
-0.599004407659199397865907453815306098E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999615
 
 
ndim = getUnifRand(1, 9)
ndim
+4
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.78810290230754296306062667431373065, +1.84427156896816747611872406195943395, +1.65829226068628617419331165490703055, +1.02735607587283880338373467837802975
+1.90095875412407432238036568024450467, +1.66658918426464406584251192072201694, +1.06309730219586929111521841709477207, +1.35495714558652518701075827945591067
+1.17237392494304816122167303473895090, +1.90967366305725933059591363637317039, +1.64527768304792883510459903450423623, +1.83685391898751799868603763643127364
+1.06411889462513802139399862107940682, +1.89194664778761853705990214838961292, +1.40517612132820423438506814179554338, +1.99264299675123407304980634876308145
det = getMatDet(mat)
det
-0.165678402124728461614917488788420642
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999996919
 
 
ndim = getUnifRand(1, 9)
ndim
+1
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.67773362148595881627767096177913723
det = getMatDet(mat)
det
+1.67773362148595881627767096177913723
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000000
 
 
ndim = getUnifRand(1, 9)
ndim
+8
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.80595550881079682219903056828191222, +1.61453680019968564506377313715318942, +1.78975359070300021130855895320109775, +1.15169073131877444211875258562116260, +1.80119650403322294996455253217411189, +1.28211034576866789424755166393886290, +1.44131012370478204625046010574839224, +1.91445963232776977943979346749726758
+1.60331992338161566497711828148350093, +1.08836764028289959462891731161028688, +1.73175566757633010203422713458584582, +1.24013822443922237611200019836524841, +1.73243018150146896406535379817756669, +1.07711591211049843795225576959608304, +1.19912513634348772178477768488046510, +1.08941301664075454804440484277343706
+1.64591814518532439392478046536813216, +1.07231923673516650648809369542699946, +1.73231890393045130722678344351702119, +1.84117304046507683577264413452134879, +1.53358430111712203146412232664206976, +1.19274212243308280289237661587310672, +1.23996093725610650992632398568063795, +1.97658160850293207853949197085167033
+1.60910296274761693906639594372072038, +1.34013889354741594112760918970175318, +1.14262692753662297939170858930214396, +1.67472277965204432509160974019162721, +1.15735221490290982940264741590379867, +1.38088315952415125569828267290780382, +1.09850925964091946095077131155469525, +1.99399867359052435739439323797142318
+1.66112953752523572823792008021374561, +1.24758846378702363033802745951486798, +1.15244283523549039185690619134179496, +1.82577377095118532224096022295642239, +1.57671057625090578270405504920371350, +1.18279910965425137521647227315273717, +1.35122316706010543555474462580167418, +1.55024444871948068946664874687093243
+1.98633647102108096457246531484449792, +1.31490580863938624840921320729398140, +1.68614306314385236721745995207741755, +1.64893693829715330057842113224529645, +1.05752453743478484397932944431664924, +1.08787582560271043071050541111896357, +1.11073881192278620419287556038275942, +1.22960862962567139181529032569690036
+1.09787942163085489452929074757876925, +1.47737988064601416317535005292692329, +1.18458668049246565896096432690551661, +1.08233986340691729639510472304402139, +1.79989163352565375987605452725604476, +1.41533747396180534580621342704329641, +1.19004447015029230919374878368170712, +1.12263506649412703334961983615018592
+1.00457088002973131737789442919289605, +1.79232300295032130667478326671989068, +1.14154129198760735303557068428255680, +1.67023070710808487381508198169279443, +1.37339718958972078968463640345509381, +1.60925186217101974157741996886160581, +1.98281117746149052730170208757403569, +1.14196161328993922662269410678247290
det = getMatDet(mat)
det
+0.955387367420770758680857044163911259E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000058
 
 
ndim = getUnifRand(1, 9)
ndim
+5
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.25414070055572094208828247195251966, +1.99205750199933765710696499135934687, +1.94471040006282313930426613127719127, +1.31157120329619582139347468227164895, +1.48490019520954406235423099996071593
+1.82262760565049060335052842197262830, +1.66338115287820782914685502914059150, +1.52360678849321061116070254752989793, +1.82924514293332692229136201876640135, +1.24178567737814949803435839555639554
+1.92622615164155232850241180708458076, +1.13327406451991976251100588462926415, +1.19935271033799605584180852590955731, +1.83717826056466279430219501409677768, +1.47703256820876010932481875297884638
+1.87592426213879771211546238112743035, +1.09379618415962405871346682131296009, +1.57537480606462015279261549006397397, +1.42434070373873120179870277211024041, +1.77334383622015527264190517401217761
+1.02412809279785576541373568385645661, +1.67533260417405014188815799355660172, +1.80835871197046653548501075071781893, +1.00094338103486044663739308974490286, +1.64876468371167098513698569544185654
det = getMatDet(mat)
det
+0.682256406926023150460221558226814498E-2
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000944
 
 
ndim = getUnifRand(1, 9)
ndim
+3
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.28642802637370043130623284343300920, +1.41362085735484921011029388884949487, +1.12508251543143409831687848662073960
+1.15846428641461055239852238781529982, +1.91501932860220726951385210843738434, +1.39527892587650100315346940145719096
+1.25534041866394527931398217735576050, +1.69959021024674501340898088584307117, +1.84554813569882208904220149700798094
det = getMatDet(mat)
det
+0.460128719195369007111896393097860746
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000039
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.06918805017235393276222190822004033, +1.60591859235904204926330836199589633), (+1.58245578350599552597839849600557723, +1.61118517322108627428777329195906600), (+1.56166703930374201059380904256524189, +1.28041546453820511402154829731460742), (+1.10003171639440290262354763457974972, +1.45344450863333017946221589547523170), (+1.59726792401258381265505731442791408, +1.11293232347305214097601443635667912)
(+1.62757467429813518226422136927188510, +1.46468194954563530066284299163017356), (+1.38700389237190824863161261527941493, +1.37197172991366503572051886565408975), (+1.31785640184711396472334087378907568, +1.70580503433960081536536444419940370), (+1.02197343038039459177509344445859432, +1.81845355518691051714334759380097385), (+1.65441355651784658388644167079830780, +1.20763885335465555181701524370990232)
(+1.46941548966770894062226811178494429, +1.07607558830242101666425583926988540), (+1.00386321062849473222275545530213211, +1.40924125888792111471541437196507032), (+1.83360033006161105063992889454370751, +1.20547331713015911684417917007180461), (+1.83144579303672507595644127779747804, +1.98945930366405556720628692290442231), (+1.21368823567357120638027162232975231, +1.65922997490750130404690214890777631)
(+1.09525611726917403817286539561386460, +1.28455907858572785610935466854606199), (+1.04371707109928843015280224734011821, +1.13263973093258104487104715097711442), (+1.09836538052149605956527874090623165, +1.01012168162974455850490126999907397), (+1.60559187101268426887519926376723934, +1.94223035519608841074210738552452366), (+1.38280696139735126296662541047243483, +1.41445010689066985166288185685381247)
(+1.82807348804934894724605273037444209, +1.37644611691195959211106574617474530), (+1.40422140441248544684338232017965801, +1.58021324508641239998418492865358267), (+1.99503977665148775062924571271126166, +1.27354134090708393899890982442095637), (+1.12988130652906012537210568352806623, +1.20456698897029585486605786418753413), (+1.14252575726091432020720019572594479, +1.27222892992215626145417807414254558)
det = getMatDet(mat)
det
-0.870558734687966660759265777043505028E-1
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.173975398414437234237905853937177712, +0.379088326331707376833070894563022723)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.39386871263957367420459628961378335, +1.08626388178586213903541770748102018), (+1.94429636122855482516659270393471028, +1.30190007445382079015061295548870182)
(+1.39474351429786945929415007149045328, +1.93110768117600459991983868118933961), (+1.73875927958424828883136349057441192, +1.23433125649464532496864002251045542)
det = getMatDet(mat)
det
+0.885107190739625820492461753759483920
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.169212095130343230842685335948522826, +0.374939144384715989213666609750016473)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.50008370251646839088409936157395209, +1.37626377577665458205390755411380424)
det = getMatDet(mat)
det
+1.50008370251646839088409936157395209
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.542968000779677967240994103359208210, -0.498150329628514442077433410901919710)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.02188161717910252780863870915620257, +1.00885231139824438990492326145893831)
det = getMatDet(mat)
det
+1.02188161717910252780863870915620257
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.506415793451748849833506293298982741, -0.499958835899901359648000617784639075)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.26659887463017817983500108570981687, +1.77859524989490341888939187634884946), (+1.29556365068452968171345779551864727, +1.40224750441721014210495495309804678), (+1.71040533101092611479269542621613478, +1.33198371139234316658160037000705902), (+1.23080195505026669233560802620287449, +1.50257711252365829473537102609872634), (+1.64914178566664030223824139129887617, +1.40758851264786509409138129479771910), (+1.85424847433574882982105904435936186, +1.68284294018222349375581859351930732), (+1.68452146355534366190033862275875914, +1.86550294165569480580299167898734081), (+1.44096563844624372486584846668230950, +1.41829120660645701055354606551464084), (+1.78299369758706830269527609175565378, +1.61779895331496543070686922985124942)
(+1.78209973870792688901487402866142235, +1.71682369502704603800398122613919417), (+1.44349055331647145376424080794606814, +1.61559471185881195527851377350506699), (+1.39253901610470659846200439869612223, +1.54816184558977104372298404718999823), (+1.54003058914718631291953885740873680, +1.91074436799143074881830202769305903), (+1.22228291831232024563272879026412899, +1.17490099716216177720044628268115359), (+1.53440910919251623915764978030812277, +1.37071411241934481634423517472672470), (+1.41856014921122379363538999655359343, +1.33777814890079427295851405266978767), (+1.90118727144768608646946687202106857, +1.29039260483713726636521691231311522), (+1.28856505546384512301922094399901502, +1.91206701859184760805584659876155210)
(+1.71775182057312305298171200604520480, +1.68647117831114463113399784617812982), (+1.13868723617124018650609367422142543, +1.00791220030363669202874713824986088), (+1.80309261607631566369904472966670868, +1.82021811022603561134388612437810726), (+1.80870932678148377999586518456360943, +1.10848518727703885516085620232065532), (+1.47603261413284455513536679844663614, +1.99183223795580979378562775247230475), (+1.37065725803056915370690781581614785, +1.26601201512853517821232231324799704), (+1.14504548337413632646075843044165256, +1.69997826793844737184296448182217516), (+1.60485516029975741140190636453907817, +1.20862533040970855991653277749374453), (+1.74927391935840187487742935275259935, +1.53647012007903034794770696811446764)
(+1.60914249449035311131176201789739917, +1.91054483490493209217980341990921806), (+1.34633773171893036416958191747030873, +1.69522854115547099870609436162585461), (+1.23150534918005364782403166237277930, +1.82155685515182506279068118655020930), (+1.70749907889858883007042495981169228, +1.09435284311424579165557313753885037), (+1.79772517223750687002337480736400182, +1.74636550584219639762822676478502789), (+1.19071234473010837724179815528423026, +1.45777422479008473547530768345041082), (+1.36622559519785977428785882183753864, +1.57417244437099677614467288455474767), (+1.95667135714972411127739056852652108, +1.11315619170802540365194680227765452), (+1.71439922274698044842248342329682646, +1.77048840735058456190101714349865985)
(+1.83558104173954719385653734527278512, +1.75464204860800886176291587596864360), (+1.11162414246104814347983246640698282, +1.34758699316245737605647277533279597), (+1.13928588939969321248840327144002400, +1.05116800335558815911520048014624315), (+1.99634573401194895384930272725153533, +1.75736355496756360684808101845192792), (+1.97246412733664226979462140741590932, +1.45721945991228518794817293621772239), (+1.81904225900977033473592959394385969, +1.36120803382656701381904101346550937), (+1.21857848216282148239949789135226169, +1.69562270547886665831236190219149759), (+1.68062158192801497659699398127681116, +1.61505558678717816386310304418728539), (+1.70454223833834656637430410879857354, +1.51493290513343582531229836572521553)
(+1.48187973126698602410738873702740882, +1.07978298800921897369740260184809972), (+1.08367760776961707091812784535568460, +1.32970566432495394781439712954455039), (+1.42139649382543382419481224535599271, +1.02871208421026238877253109137524912), (+1.09137151056855522652969219949848644, +1.33608871390841978150692946896866946), (+1.65574660890946305689741852585535366, +1.87896379960356994183969285845907141), (+1.15439499396469262516859471363780585, +1.82147727231090129764965463062832701), (+1.47209527857495669908666907286972070, +1.94772500278356954379676068780702358), (+1.50734908585284820014547220422492830, +1.80867389751919347059103723311083393), (+1.27951500190056407472185127235726978, +1.61979401952628643717489943134828753)
(+1.42735421656122800363806646841839568, +1.28824101944439401268895635149952519), (+1.36274924013678889601275647236767123, +1.19605577834921726147757260378857686), (+1.27395987258680654376568172422531820, +1.39966046749419323996220645010228656), (+1.10944569256831878846886694235231319, +1.52583583643094018841079123788597120), (+1.10357809500945845708418411049793408, +1.50805709338350761339943714096511982), (+1.75092873972583324483186857341080961, +1.91586610764788575016342958904034367), (+1.04912845880474868889840540402194046, +1.11873406478779141921392551567272835), (+1.68886092910560925219710684404969726, +1.83560256555546301430578268667663655), (+1.88490722168630710671616694777320741, +1.71694585660367513437299856460225043)
(+1.42090346342527645975480030374289100, +1.35656247145232650895417319603048326), (+1.85751023452516048332366417937569063, +1.73139155135771286157223105829761098), (+1.91272918322139704935124152947334873, +1.06767718639058162195027453669650607), (+1.22469928887637075011460722318565462, +1.27009262143001805930867317274868693), (+1.84845465171041895657433312431126412, +1.34687106786317860427213498742033623), (+1.78274375548191463381829525046294155, +1.71780949758567152765602635263325480), (+1.28616396332435176806863474146696239, +1.25924506561584144168657316656286198), (+1.96089675102213669767632724990564238, +1.70897937977606501609340078024354993), (+1.14210045502248252990352026687100001, +1.07133899814139164648493727974565335)
(+1.85829237151128903292157137287697416, +1.97412637632907450969638635857901479), (+1.25658966952486886790325587980112671, +1.99745465332625057804346364462152929), (+1.04011131324731687222578785465195985, +1.10609763533151888308619027352949788), (+1.33801135983398698869975342225376841, +1.16098371526532143474013403323147999), (+1.77822926430973899794975574466536961, +1.67015946636220163311116541948228238), (+1.79880585027093069773284515143566837, +1.95784109267649927644701587070243078), (+1.07449753506816560164217174900800349, +1.17185242984256948412866277196902509), (+1.23058780041786757245185464398382816, +1.05179949403587302035906349228463152), (+1.13235443803520096914737665935651085, +1.25157192258008360400158684111666049)
det = getMatDet(mat)
det
+5.85247243559673290735288633567624314
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.909765921938221120597693346592060456, +0.286516821876342323344836867178641180)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.12740725428723536552164306370967339, +1.93015379397052460596911563487114867), (+1.86580686598189593698361883686237037, +1.18266717348419830671025190401204365), (+1.25725939042363274865586322222332570, +1.43352697013695979241701492032245033), (+1.46093816936747450822192669216112649, +1.79514596575470582809178392600087270), (+1.70125953879783329414480733769399175, +1.73047618962831206732365264762858677)
(+1.42656577757750863282332677609701104, +1.48160620053351211502607209633701881), (+1.69256959950691168196172818068839466, +1.24404591457723885053688126826041096), (+1.11077391048136541285946469208393669, +1.79201632994877147829494992409363294), (+1.05369171696851649399479757211225399, +1.71591471184232987162457906866596322), (+1.76874665490444951231370218398514176, +1.81743340762027557315001371838507891)
(+1.34965827811579053249606591139647564, +1.35205215940372972730623219878674438), (+1.98022528968134848768191327662561960, +1.55063221784136785477379710874408324), (+1.06867566332225784453270325561281970, +1.57749139449948450281580507650381953), (+1.59729218381436053523647527593050929, +1.40032590445521184068895226085660548), (+1.41647454355504250629168987386933711, +1.22689902622742419436495148628102018)
(+1.30544475600569573821208800370143177, +1.85019333216005155886328522432768628), (+1.45685228220260320382376848435752630, +1.03032507575209975899401160757700823), (+1.19585856986122416716307399714380997, +1.52589285399100381284672393920913743), (+1.28699785183578180556102264466632366, +1.24219683491965213944723758834135166), (+1.59226195007907287432077262390762581, +1.94211146456415448308923026253976567)
(+1.04652979338786980910512929896987921, +1.03272782420836673697114895522400125), (+1.97356458259984646409170170313572189, +1.89605214460719404316996868623162550), (+1.54338892296442221694659529053408709, +1.69171745587188552376510443780557598), (+1.44004409433669314373510813491821844, +1.78919070202361597724932808112452553), (+1.29638825174170720738242218002297234, +1.58656567559970736320073253854455452)
det = getMatDet(mat)
det
-0.123192567587612445945374292128210911
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.510271146165212084466575716942776510E-1, +0.220053057671175330780412945869549921)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.18874459940030130467523214837259424, +1.17445669947621797135907599116312494), (+1.22990495124410483151779714057103708, +1.09876953772731438885163705082968992), (+1.97956724567507022325281670822673500, +1.95143171679083308002917931778574532), (+1.69549182979404536888547635598439773, +1.55162655722113032244804794298343207), (+1.55627538093400524279254771584367321, +1.83126385095125413579759960867596615), (+1.93607445056416217439388048444501828, +1.88797767068709932459499329277381394)
(+1.64610049609076566420889969885040373, +1.64580523847712368154266117455347221), (+1.25403373629781767914104390230271600, +1.36247710919554372284854559610980762), (+1.23229286537374105404427819006279751, +1.99355127982912067752487081366117617), (+1.84886997343043556809635545003398287, +1.10727202730442246279761107701574955), (+1.90990516036448226024091631503292033, +1.68949631704497328343395055301520025), (+1.27902219989925582935939700930811473, +1.66684219731146900600081876890885792)
(+1.59525564444822504136430355227581128, +1.68161798423774965298620371986926794), (+1.30500426829074187987097683621333244, +1.16232245764832633354604300532630725), (+1.89738396561802251714193688984562731, +1.90811881341964120026322904609228591), (+1.96378643934917852720090672138930075, +1.27845199148232387325407606050804494), (+1.72885886180642635689027273856641607, +1.59816780446770950431669395405494914), (+1.04920861703615321023837909443136844, +1.10127003614675468538829148928431087)
(+1.24038558793611485395429180626947373, +1.04251414710649923743139591342720465), (+1.03963543605090512765121989279104597, +1.51454442552088053748855789941920484), (+1.68972783527776771786051714296282009, +1.11445528316578158028004219916434941), (+1.47338533079833312003954722918918037, +1.84072494148992508850417763995263661), (+1.45446900386123510750607610877934889, +1.18893737301091198454922973535168431), (+1.85131642701150504997504505716436215, +1.23146429848508214596917445352400110)
(+1.41023953176607630310106093042028628, +1.38456341493456337681305470091964149), (+1.75221048970956373574959072212875954, +1.60399324795253389465643502650656776), (+1.14114143989537771656206893422024401, +1.50239173000172925811169998650922027), (+1.00183131721270420051998952109819575, +1.13917608070962110890755185795777117), (+1.26048129881833829274470852951566575, +1.67737958740395229689864538231291510), (+1.55806209970919209002716181509246230, +1.39224355060785759570646409695104367)
(+1.30278815363113006467143598934063379, +1.87483519739493793700824032825860103), (+1.92855065047306124404830430687177495, +1.17825729739872792549250013457006955), (+1.96340966811636560073839122931560325, +1.86747514764269199249859960716433507), (+1.85345335055106402337909780168662293, +1.64891063688774678982511945101007003), (+1.53543608928363093652209700663683538, +1.11828723510749073897314654411073362), (+1.20152314101367690400911956073028279, +1.43022996820637392169263582678727609)
det = getMatDet(mat)
det
+4.09265467595062400304020996452573478
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.668888113082723318645378829131547543, +0.470613222571739117321314594336435660)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.09799628011914875451499721158744022, +1.55650943368838392832180219601370342), (+1.75081702425262213167865003784022687, +1.75685378481822720235322816045173914), (+1.47056976802279057863039628812777968, +1.87310678849352201273546515948864401), (+1.97265676478348729210845427554647723, +1.48521356612901325684342651148252194), (+1.79308591311194829629625340343709544, +1.05095661018563281872863565744895460), (+1.21435127562479661005926833423079311, +1.84090570358451354447090175478334189), (+1.18029617363733920535014532944377800, +1.54889318652554338058007327479282540), (+1.71861584339021420124129750321478618, +1.73531619338933212480724246413045432)
(+1.64143067294960939974798794044128228, +1.30468929694550213946614287145843808), (+1.48170165078933712768303485804282098, +1.00138418108348304796641555056034974), (+1.40628045292244588910670434582591747, +1.16671639314494718620048665166618263), (+1.62570403202784443666155261448533837, +1.63046581509154632573169601447637849), (+1.87602544279555480283702307746120248, +1.92098309586754305038421533424930271), (+1.96281004624448872176596178398184115, +1.18810580729035536868765432268193150), (+1.40988830337889664668897112309233799, +1.39492388652117097968804289389381690), (+1.30996164700406397809134615696503928, +1.03113989688067562465155526487109101)
(+1.46008326790714672912671680336587704, +1.73592112897547623154889469385903184), (+1.74202609431541596034408757239553572, +1.58522318769316014423378839282449909), (+1.91605417352558820599405639366545345, +1.04140418151217668877571074758031604), (+1.45567071752516775415027150828666360, +1.51283821850753568741947432745108117), (+1.87412724393613082635224855898447673, +1.23650062875363018538808147651784062), (+1.30411761677792405596232543433185107, +1.71187459862281425539943251353705115), (+1.47278317307908355253656466244017564, +1.66695277434102618063915144292171665), (+1.14498132288476134414412139285327578, +1.10138989496965556552798565177233931)
(+1.19791991933130869667904777587446419, +1.54663149010047324970268300118497078), (+1.09084071422915181449107770891353726, +1.74848736737360470579420004294197452), (+1.61828041118753533820398263091453950, +1.54922929609403269601497274911083358), (+1.14435931060163412892732697547410875, +1.71013632126584372570958359470180333), (+1.50677033141616339628920120538967426, +1.83726291170414438804658579920783509), (+1.97306647398670905219833586735649980, +1.18457862192081828545939135062047733), (+1.81035959973593653638895078691865544, +1.73435405791561716228834832744025533), (+1.97834051289306390635451346183707993, +1.13661029396550194901997306291538269)
(+1.19883790543699923023253461402559718, +1.90761369130201083554274792829703111), (+1.30563552276761954432603515812684674, +1.85364089911765417661768220350971045), (+1.98042873803628693464611425968025639, +1.18731476981160633145318556052004116), (+1.32844500294621753951343761823732996, +1.89920941776643554505751558758125189), (+1.31234130341273528928672018586968594, +1.22864873535675551854999845568170370), (+1.12405434073736818446108575389912081, +1.50506961164763762867348245166583759), (+1.07695953929515806234402788104566196, +1.88583961295279708499899521381338893), (+1.45769713009975304899049027208600610, +1.34125158493130653209213579944895154)
(+1.98021271476811179400132286135890067, +1.74041409673522775024471585550449373), (+1.56288574911446556493847463898082650, +1.60976504618066850673296262441936339), (+1.65313570275484851123762614115679000, +1.84062778928889441862146744333759869), (+1.30056160977634155883516300066846664, +1.87172538701059071562888765349633223), (+1.02674223812931146853791987454603723, +1.84264052630244939631770331607635744), (+1.63434675060729166396328575685463550, +1.83342640248054096405302931395524358), (+1.60661567580220508367003532475480216, +1.59035772430688082042646259441303892), (+1.04215972779478678497783272930565016, +1.45659592925572892131099966371886909)
(+1.88849149123779490344163936420040580, +1.75114075515103634228750294368468638), (+1.27458896774580964262710211086320172, +1.26848674634984657990023032682703188), (+1.62031918372104467502969150616827285, +1.38320655656425281399402345774093104), (+1.25034171759550437907291293181010456, +1.68892735307123721194830056966962246), (+1.10695203200241120610732649137931861, +1.84332537276765442441373740006267372), (+1.21722876974907613400698836833601164, +1.58293986470235046049407703339491818), (+1.73355222740701890877358713778489885, +1.67096888458161720218604374495046362), (+1.97452226049237152631361401047540933, +1.85990178220450193215128383455458840)
(+1.55847943462929003851209208725020441, +1.86660698168504410152872299829077743), (+1.45633259909876732308464927109938398, +1.66274748777079589951060618767218518), (+1.63142631100942130872794768837455544, +1.59118561153529191734249703567212032), (+1.95106922843537912570133237584888468, +1.58981805187828513062688409592709944), (+1.42873186259901819583242447158568822, +1.85945165191289132476454559909791619), (+1.28905967725951472514382266419109220, +1.07585445001152905607540867314630853), (+1.50574575507393164731187406629962091, +1.97096187336895810996130991506047351), (+1.57578933488338521117241506219411208, +1.04752487485149134089682712573976908)
det = getMatDet(mat)
det
-0.198043419276223317821410019562115054
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.321330982274580300482116440345866503, -0.466987560974629881225606518432541771)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.94611247216524540799051812282528088, +1.41070144841520962261063604098154417), (+1.29046090792709803788995152635390388, +1.22715707191285879000021266548378756), (+1.36229508649181691342799761097901688, +1.32442461824129217904464894283274907), (+1.88324979896422364759183001035619933, +1.69000997788352945123084232746253371), (+1.93960787407020340410549084768393952, +1.88433283109098871801454061759469949), (+1.32182503468916183692678689620197739, +1.71968352384668848002434373868053043), (+1.61636546010702679983819164862716444, +1.15074243744060720663805373828733923)
(+1.07237727946326655909677016808705136, +1.91487012724058812247067799639149246), (+1.52631238607057341703314665492758507, +1.27771788788350362174518153470131378), (+1.31964105266084061869342119727423754, +1.55103666408887139771346609305597853), (+1.08763157590645776060294801747495413, +1.73786798282690452001744499474132103), (+1.89429780940253873175652137149641947, +1.41533506731332490316110277781540478), (+1.39479811824978736014626670930919217, +1.59859023505105298338308631911888453), (+1.21145376242381054207845502797951579, +1.74196127372254939178716253029171062)
(+1.39114852558738109085027249653494596, +1.18426221444599202430498572177354641), (+1.13814888835077995432773933786006524, +1.33087958533353932421333195430408778), (+1.80808659280385730972501383628077892, +1.38606875811375631748642254882069280), (+1.46199742878298623095698497529640641, +1.46416951548005132751656697744551639), (+1.44139311372064582072806410495891436, +1.40078271834612377453231006069391083), (+1.14534384097867256139468257272515877, +1.66797360135237395331083621080041425), (+1.25314627757916286771856297919890173, +1.06616736748606883062520686360844090)
(+1.49011280806373643120223283965368395, +1.53196038054699554062213488531465788), (+1.66496513277365598940244433892173684, +1.76038313527605169235735792233701585), (+1.32542557565763024903125950081251608, +1.98878929743164369055469123231088048), (+1.11760719612927373251051209562538166, +1.75130403952720799151679968253086776), (+1.61794822451193079449967713630500385, +1.99788073308341820172135974457112346), (+1.09271910537714726138026629786702178, +1.93791682232181420901417745076252183), (+1.18244240094131732951438656865360228, +1.68150060544160861913914077473335320)
(+1.45608782690352393046454642924567887, +1.99546381781454405961516499764716278), (+1.46498249028001508303537132254540469, +1.01873014631031603294738021924480417), (+1.05065214316635256743565831331807512, +1.50954738240456439237223113862378791), (+1.41446875712121367749959909985317312, +1.66904308147204499287553217436432960), (+1.45846215053513591419047698538390136, +1.94094439957324610879286666751169755), (+1.12878185489008075178347656775062678, +1.45035264322977608948931405359080737), (+1.83844260461779434950985351329037857, +1.48717981736058715835103925444956965)
(+1.11045919691218828348737319373897150, +1.49362937733005868713771355973989031), (+1.04225264878533500702941319717269051, +1.16972063246656386634771347886414244), (+1.67965658642968982167942433592888058, +1.03030008379453370132688388450474104), (+1.01379134139256964535525561169581843, +1.82904158313500873765651351874412694), (+1.25715175697258152151027707931687384, +1.27613875272844258009930421684777804), (+1.51414085657887749504147323496742927, +1.50433227467237219739839274289209047), (+1.70871314936461890685142566409230432, +1.58455367470838276483742729985733605)
(+1.26624020308298681859934153983167472, +1.76765175039933398016487806543135889), (+1.70606746355803282773552700469842515, +1.57588916114945911409466421599071695), (+1.57612939795645251927188316306729212, +1.24213581299843437137705890934159363), (+1.56774770742145296933445791668254405, +1.33820212124428307728673344949831943), (+1.55825249936738847751928853894185571, +1.78906020688231459684233336554991462), (+1.56457752425272946231273838425300028, +1.11012834381650864004498131173835676), (+1.26278000429166143731267017803191838, +1.21778419103207899006010784969646835)
det = getMatDet(mat)
det
-0.171905759303339132808234333416621053
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.100468437846191031100541730969984635, +0.300623570005641907566148262437213549)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.03081779295877089258173717552280441, +1.01421718017170436019218667502836685), (+1.42408981564397399720498357359461641, +1.33895309724108641291794304611467678), (+1.44781358901813327192819607236573674, +1.06466768481706594840496305356465880), (+1.60929745479494474047325366165539173, +1.12707428170250946151519559054492816), (+1.49717105362466128239449799411488236, +1.48857333844127710341277284783348126), (+1.86147978874232407205215338848981196, +1.27219267230381530310377193041893717)
(+1.96632565433948860432264056607490056, +1.55836186695250914943072900988369258), (+1.91790492064091000474304963651687550, +1.83711288717441193437893752183849679), (+1.26954359443822818928618950560250207, +1.98719834321798479298087553815674379), (+1.30119980998947979039721519404560840, +1.03605176272168055345896658343724543), (+1.30059468866430908048153971208711531, +1.06807820864934915731782895734689428), (+1.04329025251136672799926760722513594, +1.62109021327839954159354827799416351)
(+1.18086787883962521775818163197599689, +1.07932698542207434113523349585557570), (+1.22790322086483400472153846816007636, +1.08806962429365541319217727115907319), (+1.41148158851394329605606534016334701, +1.87437685999713571795401039605095347), (+1.48519618723184219801557394612456220, +1.98516688968747459042101806466587294), (+1.43586162051262954948177621075479878, +1.95330650635849203954858360617120338), (+1.20766588608162096332692988370845062, +1.18068979651726024786572296761765016)
(+1.71859035690342656764732524086433100, +1.80897563216915077195247582172052331), (+1.31815414370243294127293545664026882, +1.67815071042390038308048704298051449), (+1.85096075435862438392302457668853983, +1.45349812938607611276389935012568048), (+1.33563915458484456154987687088174745, +1.46113590020950174133868727220632175), (+1.09030620433334587771049470046529611, +1.38252433966156712387018462679700785), (+1.10583850507172767971204623710401508, +1.28846756478658565516471487525798504)
(+1.55088602763263780672034535779047121, +1.53968893254439187098063553199069666), (+1.03967305574557924287906956403787407, +1.02233118138651734644126615349636906), (+1.04584029602706953877735223400503842, +1.59098918529978506576954230506337617), (+1.43757688280239012824032207176827612, +1.48495828555845839012427045385533011), (+1.91807094161947799559754698701050913, +1.46915693035909759743051946707031690), (+1.87189512747176150575134215487579200, +1.71542633984757864664801339859715538)
(+1.61914608987494867650522754749247272, +1.87623999169065363265698466767009306), (+1.10793615283056947256136732460474902, +1.68762084520002214732605586278651855), (+1.26088384628760322701871905159963269, +1.82926060325568804080337520797140538), (+1.72348144304813027697767251721866157, +1.23872801518517577857808505652398553), (+1.41316755191542814948828390395270436, +1.62538615816144198891162065293128128), (+1.79678471105866351653484087070151266, +1.95649159267912178920730555841544902)
det = getMatDet(mat)
det
-0.659810629878237708507509818988195186
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.261220751973845777766597046643291151E-1, +0.159498314676885420840482000532067665)
 
 

Test:

test_pm_matrixDet

Bug:

Status: Unresolved
Source: GNU Fortran Compiler gfortran version 11.2
Description: The GNU Fortran Compiler gfortran version 11.2 cannot compile the following code,

interface
function test(mat) result(res)
    real, value :: mat(:,:)
    real :: res
end function
end interface
end

yielding the following error message,

Error: VALUE attribute conflicts with DIMENSION attribute at (1)

This error appears to conform with the Fortran 2003 standard but not with the newer standards.
The Intel Classic Fortran Compiler ifort has no problem compiling this code.

Remedy (as of ParaMonte Library version 2.0.0): Avoid such interfaces until the GNU Fortran Compiler gfortran bug is resolved.

Todo:

Critical Priority: As soon as the Gfortran bug described above is resolved, the mat argument of the procedures under this generic interface can be changed to have the value attribute instead of the intent(in).
This will obviate the need for creating an additional copy of the array inside the routine, which has to be also modified subsequently.

Todo:

Low Priority: This generic interface could be extended to accept different classes of matrices , for example,

1. posdefmat_type,
2. upperDiag_type,
3. lowerDiag_type,
4. upperUnit_type,
5. lowerUnit_type,

and other types to facilitate runtime dispatch to the appropriate routines.
However, class-specific routines were deemed unnecessary of this version of the library as the task of computing the determinant of such matrices is either trivially explained in the module documentation or already implemented by other generic interfaces of this module.

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.

1. 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.
   
2. 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, Apr 21, 2017, 1:43 PM, Institute for Computational Engineering and Sciences (ICES), The University of Texas Austin

Definition at line 216 of file pm_matrixDet.F90.

---

The documentation for this interface was generated from the following file:

• src/fortran/main/pm_matrixDet.F90