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
+2
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.40554047594670722562059272609521101, +1.60060475648769804822800545255684951
+1.95515656379963798142954812862514136, +1.11184348217265581099271543638285185
det = getMatDet(mat)
det
-1.56669187858464508537340627011563869
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000000
 
 
ndim = getUnifRand(1, 9)
ndim
+8
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.21173396395534330032783873530504978, +1.31128173374868112696701104272931404, +1.29416026047214541109957107632946689, +1.78200346315868836850662535636236535, +1.86997862837913857334200667290348974, +1.51518219932052646297224458290767655, +1.63687688148007061388898841448572967, +1.92779268807229144908877900335028965
+1.48169468513071338798774539516632006, +1.36329367765646211209477034346175107, +1.53964304819085283720087616211802242, +1.82314230055107470328581788259759937, +1.08747199226062232696367004053001916, +1.92477526071705017203151135553808612, +1.65241132541106950516711012487576627, +1.19044942400913044980236181971692390
+1.18201130570430964321517401038261846, +1.48257261890009171849941907946609839, +1.97016397420284270933819197352068162, +1.71657297319407958767872658340422515, +1.27502262549527435927340521048274753, +1.36406169730580904394832227262047767, +1.96350287332988796429056141187907416, +1.42079462315719012555849367789437159
+1.58611860598208610781624517055351169, +1.77626792266646391076005321242519886, +1.81700886728091705139525504741807283, +1.24409632193257568170078021614335355, +1.35245458152547999340870066066849616, +1.35890211243076236756197110819215361, +1.22620021978089248523741908853181517, +1.41083574385586248426148547709719638
+1.87171217414560586815794500429192151, +1.27348803206104805790506961462093758, +1.27511811618088442707844250102477953, +1.27994882000672783142478154502671460, +1.84742646611482810741856964023940652, +1.68214395137431262333125356222804041, +1.20560658017098547396606695742583397, +1.41029394163351391842224202151827898
+1.48597838692766856608668019727935670, +1.98511809502417452851035681403484870, +1.97416100401800569869252748087849614, +1.03145561380317223790291770725425441, +1.73024768237526407278227771446470537, +1.55382624391763965057699146114133782, +1.68774845519163674346014229610098684, +1.81315827101461865934755192576497551
+1.47239945186951858509665687649498753, +1.15047868172781800960780803199030271, +1.70225151228590357910758870871058640, +1.67052461496329102378031584726329335, +1.54533916665828440897241546170882880, +1.97416319921375190951919690437604248, +1.12114767218119441934550540093502583, +1.65357196706898701852955119068494658
+1.95846102039307004552704903625515341, +1.78371971444741256698791267562020572, +1.81795917720485185727938022342134133, +1.13165102824681485607011658124655162, +1.41616104524065579674808465869400500, +1.02065550140008529380146564804735269, +1.60461856863333759760805617622838940, +1.31279043227158367268556471314206412
det = getMatDet(mat)
det
-0.121911716195875301855180264145392307
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000000
 
 
ndim = getUnifRand(1, 9)
ndim
+3
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.03958022738714803351069965204964158, +1.34858688067629373587672055708913005, +1.22778109319801807718973247932769512
+1.01681046941890715030350084272593245, +1.04493572238961255799881521136238672, +1.40730198365155735165966404863495370
+1.54050771283349594700466016829334077, +1.96929514150309075942425358934304072, +1.87990594860127422989726822271504895
det = getMatDet(mat)
det
-0.109958484208580053740407658866379481E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000559
 
 
ndim = getUnifRand(1, 9)
ndim
+6
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.44044759890686133824388877135052015, +1.89414663693399018143085807465976492, +1.82934650132743367634984125641501210, +1.76006657320935445892730520666057611, +1.98774016754164858810291583034386077, +1.47045792104435428747253432202070825
+1.41654710271179381330297979614170426, +1.66401369156674264337663147092129980, +1.66291614605615012825979322098716536, +1.49590951729693275241164846944402004, +1.86701800006543002063515866763428734, +1.05402201793366247680345254778515907
+1.61888736706022759831409447031310843, +1.30503340658280938570938667390655155, +1.94807102330453681076713787184598719, +1.56496771572031849850631265738133372, +1.35945596792995730493477779436619246, +1.26247052467745220089955199432348136
+1.31575584141917026893845736653606992, +1.73654658607994855286362657498908007, +1.88153093361815985066109887132383626, +1.05076821711888320735252692652359448, +1.01504017841902515643151960718146756, +1.30091187567410641159868234976023643
+1.73539111236887078885676879741607032, +1.77323722368910869640504174849346643, +1.14213354521175655694466524008734794, +1.69441264822062217465276117587415148, +1.71752394316638643501176354897714278, +1.22210971107075260372745374635727108
+1.65207700042882863465089227295278581, +1.72778072997801933222481593793810365, +1.12171676906939275095606841523059933, +1.16836758266979165616403111294849354, +1.74243267806113781678769202882319661, +1.14196639627281925833226500275415789
det = getMatDet(mat)
det
-0.130772459435393803263506710908144782
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000019
 
 
ndim = getUnifRand(1, 9)
ndim
+6
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.46207011445920540884683429418206241, +1.41733623523443685303039685738087454, +1.15226358820132256718412530472002987, +1.94582625039011957321565900792074742, +1.46357031878164323367068235021906865, +1.33601234474882187679578019155299907
+1.45349213264976708407667898890412420, +1.77066659439542923971146419889934813, +1.34556546400070068880123450702864120, +1.73582609453282281013451131203137174, +1.05276802504596500748929065336645702, +1.02386176934827640929610077516739318
+1.01309596607816362710360309518733968, +1.43333414629903015172423863872463969, +1.77184104179704964185225300152162823, +1.43168311064981778567328825155130566, +1.21347277961277223560444644182374088, +1.23539579109004129899731452876543447
+1.99548613486040017145923780429060934, +1.26175320386568893181129084572087233, +1.06323090283292246490379700329628304, +1.14311405689621816332353803559566236, +1.23573098514992439337623400233609448, +1.62211576672292700534102349202933030
+1.12782835245605655400440447853736059, +1.11160919092572230710862765074838342, +1.87989340858409270053025974602769574, +1.26242187375885968516741313720001661, +1.07568886181096335050272737272264539, +1.50337244906636047162481705102629627
+1.59631532525524179950286633103229227, +1.41280414187892883125181777241388585, +1.68828793784850176561813385774933898, +1.45410977063809847905243685949592128, +1.68715491134711298061281610700039825, +1.86343371150005022057984195743045674
det = getMatDet(mat)
det
+0.223466795658657367836759676922781845E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999998459
 
 
ndim = getUnifRand(1, 9)
ndim
+1
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.44920653809491297165314869499228904
det = getMatDet(mat)
det
+1.44920653809491297165314869499228904
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000000
 
 
ndim = getUnifRand(1, 9)
ndim
+9
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.87818006051502843778364463926571288, +1.40116882991386070423306420546588759, +1.57036452468509207575331473003551046, +1.07247479560715600454871126893830548, +1.70825450119300767327563105833103169, +1.68311621204433099567059646819123093, +1.02466418137331816026282515892645085, +1.46185400998213287271749294386761453, +1.84848004884270016170713966503936895
+1.58550001357588006196448784783163359, +1.01061787520553169461105094824005642, +1.46721668741625964957509243280059650, +1.74563769967717500655384494547213944, +1.31339491572829372476228901775346816, +1.92455029168020051752654326025481342, +1.74115254436995273370693398730531320, +1.74456830818873821228856533013970046, +1.25931231169215446451643580542119442
+1.23023324755756068190287761257875847, +1.20968600888650659347971391988576574, +1.62445685002467600280847530365809897, +1.30832196351870487196234374114270465, +1.52953198639079452145379404351730767, +1.09861582916926503289064772884471925, +1.40609746362991690384607935577874060, +1.27686776423012497450026729535026968, +1.86155525476639052360055620378629509
+1.66440580443747657651822702909998599, +1.71871614006584680627719249754110756, +1.59398707643677936383354388370106336, +1.90898370009137991967688217132060844, +1.36808644607230136808962755303082536, +1.61632013440191555055766064331439751, +1.51699850800705697662747102979546612, +1.41828835198426097300808391486731777, +1.24318124112065238390156564839105837
+1.28630404139978738148644970094481747, +1.94923658396195107336363750995677803, +1.61351212197075814925692514893348973, +1.82588053518142969312087401670050261, +1.52459901896618391940171776133199702, +1.38920339428380843529736162092698024, +1.89697646340191453860159206243745870, +1.58641948310304038811517447097582393, +1.37160210461167744795133249633107406
+1.85992114547571858735359881879952502, +1.13039206083353352958034290543892346, +1.06035921259073862687020258052922410, +1.86120963030955462787121219009009061, +1.49335425187656631316434866872453754, +1.43102716525174771404605645203607145, +1.76180750243130119706460791777822587, +1.92086095179256533649729917036163632, +1.39999795234161470235493434102726431
+1.88097099422279153186261994741718969, +1.18803684028012321173188853662056304, +1.15108922485309156214352419231089032, +1.20592766511542274439130173501343725, +1.20533437758437406859868067719370519, +1.83996906785788446054100264690413191, +1.50148141410604550396546544994896332, +1.70092063390250784036571793673833455, +1.16533264156270300069198089762024556
+1.84406608900022992617928559168424279, +1.62733003280728302235802139632742458, +1.08740739222451872313309719296872154, +1.38264520963571405811175241307289116, +1.97394893551038607666685293662739517, +1.10267953150687134789020490311993068, +1.94491499767220442973371685813107251, +1.73528168777940503302206010653263439, +1.62985551972552157638517128746072227
+1.93694060555946033529926965051305342, +1.27732469127421445841359366701126411, +1.81867433450878598182328884686282557, +1.16999218903411672073571373695013110, +1.44072497508982255101837465262990527, +1.72854483565220753600703879991110393, +1.71353898515438380877726255027526932, +1.97417021769004466927692545515271249, +1.96667043117337164108567528425403019
det = getMatDet(mat)
det
+0.238894772398963280949792614231387820E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000308
 
 
ndim = getUnifRand(1, 9)
ndim
+5
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.62002290006321517746107164702438589, +1.43477164808990149604749221199698137, +1.04861067736363366255616452960226375, +1.89199966216704523212831579733633331, +1.41619875301459723036767107608215488
+1.44577067767092207884436967882391943, +1.17793039935451250504995012292094192, +1.80606732291841482365175707270164514, +1.13393992294973597832799327100361921, +1.01299151487393084209019323272996939
+1.26619308316360011808041674232038992, +1.82736912448878762905405543053115226, +1.42444195459004362171035388925132857, +1.73706305655754606422806044746737333, +1.54986151896173441793267528166705377
+1.98181138315158508527169878369469423, +1.31327440637079140452613770722375766, +1.13250464334923588487301960365575427, +1.62648534657092992738981261718837346, +1.20434270172593940306287333211790906
+1.17847528461617458196581403503861751, +1.04379782364631528787167487112116338, +1.42733231604874608095131812818366072, +1.65042257860284362454769603973779021, +1.40690156836767412359660711788539070
det = getMatDet(mat)
det
+0.804588465932224025804629107377340811E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999995089
 
 
ndim = getUnifRand(1, 9)
ndim
+3
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.29310586413265213184815585960119259, +1.92830575736374148475020229895674605, +1.48007325345494641909568376528576050
+1.77460473119297617099957097601270798, +1.09206149080866740625903839917448080, +1.18206575802520322457103705898546169
+1.79744810845637888909336890420013124, +1.01537781752432391184553040759937200, +1.55090531993455533824458612915451764
det = getMatDet(mat)
det
-0.810357572582312406776382280884544448
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000000
 
 
ndim = getUnifRand(1, 9)
ndim
+2
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.22563179089741654578507813579380008, +1.96802699463824654565337654927601629
+1.13352781356085534005527222393895265, +1.38660532349169597708119482651018598
det = getMatDet(mat)
det
-0.531345770362013832064123295152485324
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000019
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.60386173050316749823809398670720240, +1.86028112537483729673253928986370842), (+1.36904505314319914472586663758701210, +1.59089723977262188128257091679040863), (+1.59615641024770142436817363851908100, +1.04931937093446008239200422579422065), (+1.83689011640161967190855413190342991, +1.38724081991067007324088627857752770), (+1.21284412707886333093010605886176948, +1.27347663822873242524388838658224289), (+1.14085766852410593018221973040263457, +1.27158358914273964316100290094602933), (+1.94632822951723870831717057177279330, +1.69250328448747105114355535351899430), (+1.10597911885734352267806362427673122, +1.83954632915142490837921563061066363), (+1.09046715977162294904917000083364603, +1.91381231297206298434458836259728618)
(+1.07099156105955468073168696616109666, +1.80512830022648605458990837699669011), (+1.34895165866727504194594260624937976, +1.65544083689202629702917757843538843), (+1.23140259003053821328240697887392283, +1.73541009915948699128346733693659197), (+1.76376978473060216806934487713638147, +1.65104706430155967231511792793178024), (+1.93755376569797125713255184591304727, +1.30558737669925713341576797672590731), (+1.74241724021260429906755842206386638, +1.62424853708076640986912620969786814), (+1.95996878020411562922940922087502746, +1.75561541017476439953548493175147356), (+1.71940352151837880767697854248807149, +1.66761947577419531981992076915737297), (+1.67276244853863026974976500621739180, +1.04866277625268723884682431542417678)
(+1.84775627228324662234272371830245048, +1.76168063068742955636401180591429048), (+1.26849773680274525473847257616039432, +1.63731640077296304981099062171783661), (+1.26845150398216272154615418335024607, +1.45387163382603500420637598973161692), (+1.30070337444594504079686873686135813, +1.08540658189379190638679912180376765), (+1.03231392427892948887066741396013385, +1.69001486953487138594294168781382438), (+1.68003358404053313009862676101755189, +1.02350262445620336395377332034190800), (+1.23003866115307340590868654314927886, +1.81817727077379142335753536381209633), (+1.78007731475863584785873851365043163, +1.13816786748862491369431572650953391), (+1.57142510343822087493309605713755085, +1.93940487645595865926195113613514210)
(+1.10306915586204449817509694955223745, +1.20208249306472381830564699308348682), (+1.26249897362301123469742821892826778, +1.92854338489147026489489622755725714), (+1.71455723312502749211954340359034542, +1.97706289240786083307030425406445597), (+1.24410716988052373188584484381589598, +1.19761127353496395638751516247510730), (+1.64922062739747100544391213902334421, +1.07062030225624652002649860758777783), (+1.27016008310883237421073997898516494, +1.08150395064072759797557867236429912), (+1.43631155274083602390838733728602312, +1.71006302548025645874500718686806378), (+1.56040770460216540362566278661943206, +1.53967308717881037568350038734489492), (+1.26012677273822966092444517113268290, +1.16749404765930545982259365748994923)
(+1.55704832398902056410102956351890623, +1.57132490016408497305925571460996914), (+1.87635826287509134912121818632776757, +1.71533511361142406099229945643501425), (+1.99759033169594386794925397081675161, +1.10114775272237499194699904569383030), (+1.92552058713890509489054956662625304, +1.63959534202517880032168288498836434), (+1.36777401744780657052811744646473087, +1.69907794733720620909075250910767308), (+1.67815454920769117477143899487933567, +1.07429992433352258152236569573363325), (+1.52483429020416274837164716152105091, +1.87573795238389381609988416890789141), (+1.07503955637694580950365956165313530, +1.31400419007909185080132524220436893), (+1.50758855458558439800764519895812867, +1.73439133772333295879828709742529352)
(+1.89514409434283311772513964256401546, +1.34557722013793105803010920258236473), (+1.94693574058097953870905497421158527, +1.20417935618526942275004621169729903), (+1.20777981590529090222742913640037702, +1.08705388068984592318490119257492339), (+1.71938525117599156704319419865722577, +1.71258534012120034450097558205533748), (+1.19994223900717044013281031536807598, +1.80064454495812458064541269077710926), (+1.90594828882612166772838231589324592, +1.17699709678855389578411917742099704), (+1.02060289254348763768137309295508707, +1.68053380842266808864151648781361559), (+1.72806584766187387528334943808306437, +1.66455403280733962448430696458197276), (+1.71011619382606621248818282751972959, +1.17764705686112905665384260768449501)
(+1.28307954460998100903852731034424102, +1.02538357331300900136769362129191925), (+1.52097312450859717646591084093701806, +1.03605198297295831262295237014029180), (+1.24978122905666095236634122255423943, +1.35077237726146242908360315898893619), (+1.21655911973842863293654219438285261, +1.97378135701018893936915362258991485), (+1.82588907736220276222168970478076260, +1.95982082783163850075420815626492184), (+1.16097206078846878503986303832285687, +1.55962333645274785684230961054489086), (+1.61082979250535785984345017818691287, +1.88641444207224145494640299972575314), (+1.40503563323352510128967455024313701, +1.71137927778536280509350347189989195), (+1.35251310887830013761024312933038310, +1.27286578456604997109029878992674881)
(+1.79445620040758622809067585017767977, +1.18776370596625104813448822985220450), (+1.90392874090618359549016838893995034, +1.97321053768330777884007660637969374), (+1.18455537541775845039395444571290883, +1.70739104211034192732394895097228747), (+1.44684798999706799317894895811926087, +1.92950292164959122366180515104177825), (+1.89156716944785511309608923100324407, +1.52149213318055048508969831164786376), (+1.29787903650890613202882532664708630, +1.96909698681248389144988909165433735), (+1.01737986881447605019489628546044975, +1.80024763229188062004611664008325819), (+1.45794316970309842880723172987439737, +1.24423309408008158019716900863917548), (+1.73316063887667313081055467140963453, +1.73549954176949993851490235094305052)
(+1.49119094710864638808311661153404531, +1.95690520848694310441919972492782406), (+1.68213833207239370573198915622995231, +1.97674547140528194721012016841510642), (+1.82509713426442160615676848181798525, +1.05112341381939536062602965553921933), (+1.90357610577610536700792810695336774, +1.33497814978821971964436957712601758), (+1.50671304205800318990427115952221338, +1.49337131872613642657854604718960363), (+1.97881534721427617394260674786819652, +1.80001768325876292175314940963379473), (+1.84892181133233694139790202500048109, +1.40168562437723724756495939275308040), (+1.56775094507593927377539021712062352, +1.10196960872925888091907810267301664), (+1.21874619074209720009255741709819370, +1.81195929223756051736172792628503237)
det = getMatDet(mat)
det
+1.37843830885890967468157356892923626
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.139425615310034134588087405850367720, -0.346390116928085160574775839580526880)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.75920481866356893419757249696319988, +1.05087464878500068396054280443796416), (+1.32220695243676929157127743214345549, +1.33950093811234952772675064864483858), (+1.86886510440104674701228484631130712, +1.73038220970996301000738210707894233), (+1.71157615946707668977738213886071593, +1.60407895640813143232514339728107913), (+1.13740555488747251080772146490994822, +1.42224927806292103190260498200121809)
(+1.22538175635385353453768813484298683, +1.44570597341568206871920066559997500), (+1.21981190521817298442033530584685470, +1.49221693093324970479214220493733736), (+1.65658749859414131671706413072851062, +1.54567044985998757720557154090834948), (+1.40472559473916777971392288253180408, +1.19000550453873194962755732617394859), (+1.52694462609582725298022119546078041, +1.35349074576827520883448515901687077)
(+1.81594562060481344860727558413017498, +1.28153284216571599886918560882859633), (+1.35473251854657430321532524679268454, +1.97338809160670705951124715915947659), (+1.49191071263073752156842558806227145, +1.18174715186240977203869665803198736), (+1.88771123800497297864565955531090825, +1.09038150162872766607517677546021714), (+1.68453106856922256856056525829606295, +1.91591416886739160418673855840228721)
(+1.43105349685407241849590409036990055, +1.59054422806665812458664883049434320), (+1.70183143219204400730773819448065765, +1.67135491728564409401572110835142325), (+1.11124339446142825371211035037665040, +1.27155751183194372064488808128257599), (+1.46329270127207282332217893689373063, +1.69537019577000686852814436738266950), (+1.16186689161378584771865583432327928, +1.98739420526024248109952646064417159)
(+1.67420473130369608829521053244702136, +1.22084651782187734178337514752548394), (+1.53156585966857310590366008912314331, +1.10178564743826310176373513335573474), (+1.38172682504854424973033905735308299, +1.52971429537760704204941148693135041), (+1.22481320049569496216963387845269253, +1.38876169940925511395408744786001785), (+1.07591985473472430292805321373525379, +1.74557421855427769077362433145696831)
det = getMatDet(mat)
det
+0.440154961508526636254664537111098749
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.949550388779854370443461125388704274E-1, -0.293152826132830776770097867003010934)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.53353712039320428047945095696031701, +1.26557592158149904431689127351210720), (+1.34915316154439891679848228832562207, +1.23873395035182750182634811273673028), (+1.18413470702281853905363909636890233, +1.42532173485642021630041443726684868), (+1.51997333362202446457698738301188971, +1.98708423304565445666539938393482397), (+1.96075197448681744442986156837967821, +1.02098721600363616816938465757867357), (+1.92912484927431858097389966645744628, +1.03929422265520955945992365183231118), (+1.99583637256180202585063792540471031, +1.80099444813835960838320012565997355)
(+1.33648100896664050696795799515594733, +1.89937943495823235929168342935487623), (+1.55851354411142488852642217131574089, +1.58353230928310373594479108276554991), (+1.65005926592611448362941785902739147, +1.91944983075184473203926318804879108), (+1.81859775241049972352276118830435768, +1.04644161888315929537320448562184827), (+1.43780087067516146816809032036733552, +1.26296855195994893323392840711320510), (+1.36509719123254101469976536443842536, +1.47514218781140801899557537093762640), (+1.41554177746542976386583418448077209, +1.80385135339712335043961529721805858)
(+1.14718678779696835001078438676913790, +1.90717836986391484918881100231926283), (+1.75250891732216751471786966700722933, +1.95115387731310382642586969593065036), (+1.71742146025153215372088400492309899, +1.13223940913003102849974426551833209), (+1.10184759031842577006868554960139713, +1.34779038232747915224859667447101745), (+1.14634801979514734910374698529530290, +1.43492614094197058461207720131640554), (+1.81376766947931789588951819713216203, +1.71604794151499043281465573669995351), (+1.73615699464699099561449961821674376, +1.26401895297009570737565637015105766)
(+1.89433608992596355274880355591086548, +1.76320568556076608752363780881280174), (+1.91125588589814539230840382288282027, +1.65104268162093267692105096077095204), (+1.91035700025433128720548961541294612, +1.93669713773947765591772013547793997), (+1.97741187151079901854774079848688089, +1.14310345893745692809017377900629197), (+1.54938454283633331012706947289689627, +1.18489928661016169106421658566117389), (+1.88556398462893023809523305422283971, +1.66591217018874716092925039665926792), (+1.07221386535284895397117494054192725, +1.78651177814584392210767009341307548)
(+1.52485407873876547004908291867389155, +1.24055882777317440768258349905986184), (+1.24618049868012923607172046024428145, +1.08034496867495250163313669465271345), (+1.78138635213612394682312668868061780, +1.47536572565076853226450732729600534), (+1.53130151268852930161983984783919253, +1.84854042934214888048254961921251812), (+1.34550988386829807907773989183748422, +1.45831940787915835834363479621060070), (+1.25329818440472579854763794794195508, +1.25204402553568695956910083868748358), (+1.25459763594242056316636297686752013, +1.70394364910622822106802089449469828)
(+1.92379677880648394619552665688743295, +1.54931742808901241078526730675719056), (+1.50417088127588810039079438643370689, +1.43906071730631200480387522309478651), (+1.52236815170703465946736939237387455, +1.81103373134794765392749284510984414), (+1.72123312378899115199324987287655709, +1.16941777529035879696176526736155193), (+1.93460158032589418382732984070069452, +1.69936007100840504993713993394225753), (+1.71207557321856365858818555148037727, +1.68991808420589277917575813189865353), (+1.44123962391166342713245559634755089, +1.30167053891745394221646088494025446)
(+1.02727614427368131101298146405768624, +1.57807926352296231472295696247638802), (+1.23297569640490766865298324538379022, +1.22036679538829934704321582767261018), (+1.72514241449515895949329016677766161, +1.59662815612489004993787115794443861), (+1.67757657655265801277457403810458798, +1.00831061535035985001395957732382915), (+1.15917644040841540928499782403414379, +1.97567719098186113195337195169531064), (+1.78072493849893447680098173008036725, +1.97467513036796288015146917382516858), (+1.22705927215456681671656579978032294, +1.99825856368724371836406032984300960)
det = getMatDet(mat)
det
-1.74959485184795801832738646236589040
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.305845181953906298385038757080811991, +0.460764480650894191190924602253721764)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.44799417564451705507267663627180535, +1.39897399870532255771363933734214532), (+1.31507673644239886764648820098382355, +1.65539284182697678843282520668952439), (+1.36349867129471492246032094569338279, +1.13653967213653715373670846246573726)
(+1.93365633168709862066600839721991349, +1.99119999619626430550397561568211227), (+1.42909118760864105963802672464614965, +1.12444254045031316486766381918149622), (+1.67978285555197275426271797629660745, +1.49230465627734875080343799978208210)
(+1.05104122127073187335355090193416134, +1.47500951099756577689612969029513071), (+1.97298537122222989658918419011063330, +1.12154053970425058150877731752865654), (+1.61625551192265011426956195285475572, +1.79191841696306324724396553145527372)
det = getMatDet(mat)
det
+2.23533423313216952914091909697984358
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.993087931755405424873489222472455614, +0.828510202542892189535515813577925099E-1)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.15564870828890111245197031175367860, +1.61642664054857035754968646070594759), (+1.97785919068399834006359661460567635, +1.35594245379356825848673023029035518), (+1.02702186064953507307778189334579278, +1.14881734473368164296900245951697045), (+1.04047411342640950743231765111884424, +1.54009025477522846420418752475301141), (+1.39924508371244294248518513706450894, +1.43418175668237030435857587035543153), (+1.81045230179298914175934175898496043, +1.95342197008339023059695694948251932), (+1.24101841224548742424556379850375160, +1.67331917534702512385340805398323559)
(+1.90971706869393433874378566255658519, +1.28439952218088299662178739752354077), (+1.87548616054677268019280213675093007, +1.42151358357558632415674988914519526), (+1.26481562640328428321550668932607083, +1.34775109311525006202534215012699673), (+1.27737916058733163159904068537097523, +1.94609410149549452917551454188221339), (+1.68432123428501273531419638225272326, +1.96124329284255883340267809869658405), (+1.66671763198513969787940982083996095, +1.80775055011668600582184340635804691), (+1.04039365535428056301277318518697443, +1.40440064219433090053237770760558823)
(+1.63663434189337923974627645706652302, +1.47279462434616397419924665616029065), (+1.64624232066469038393276674618994783, +1.45027661299625536496398473059367506), (+1.31658411833971926975945908525513582, +1.51964474318629260774840828976518751), (+1.08946755164756444282854789763096358, +1.36856871072463662374052294356397418), (+1.85662076549702368766108925323407097, +1.13474986193092476620550723706810460), (+1.25939761143641347627790100299593498, +1.71027076755189914310939657907432540), (+1.13984872824111939049166239987738271, +1.74454923117250289686236823119837989)
(+1.81261962062714548247126796426640376, +1.17422847232980246376644581997089939), (+1.40757544408498253410609485600996168, +1.38002620304524143701997211471766961), (+1.99514148009328424891255317453372329, +1.44480944056597894713645233457530011), (+1.18350149801218747173047106146310133, +1.72254175796681600639215977175320845), (+1.16751926442476052011582910472056484, +1.33592284304596434027745961552432907), (+1.84280086792912343107732462808236918, +1.79827998233676646543872882326174637), (+1.28761292971320234908484630999738562, +1.45820698611633632201776341829125123)
(+1.25750640165154513953976560475823892, +1.37965064085625491303672395066504081), (+1.91778789726397691502810363400211495, +1.80201857380780849770261550608469113), (+1.30059730920373898733271651839833855, +1.02209763444692016989601545090148202), (+1.88488587205164382736147367230579904, +1.90309471046610305981383619272084208), (+1.37071604076136044220885598285066221, +1.44362646750803686218737811662864634), (+1.80437320813138291553310619281394688, +1.23571370618379503723514037626898926), (+1.41005359823288927836087480553539449, +1.71023447246566879993404722712612502)
(+1.79821535995284823687232844928255965, +1.39663637979293518074522511612704579), (+1.70916348083688381636170779183890481, +1.96135982074380507640843982653202632), (+1.68404948333467675798355361537540285, +1.96712442867733624984475147117413019), (+1.87833344003554478118505049711965633, +1.05622579129622965478850990711987877), (+1.13302472942164285933648636621058431, +1.65457917737237906567239556977333657), (+1.45031850694568663617628054062977187, +1.83752132942136162866099076898028013), (+1.79883345700716295899894729161157342, +1.18568775441495039959451277681287126)
(+1.78841360810490864986895439822902538, +1.57218237600199424720581417168879640), (+1.96110912327869721168272999673489355, +1.25459391736407269376718319544811627), (+1.42559466660753496797076320077024203, +1.13295946913701848368699447691251460), (+1.87169603078770048592857008457806085, +1.70844264664038197067621055227636419), (+1.51883699449801612068277353204658735, +1.07517622946478485137335435190972403), (+1.62485388971959506486126190967786212, +1.16424782351610086210590306103582476), (+1.52904674073322852089134552766098445, +1.20913612894343115504304614918764618)
det = getMatDet(mat)
det
+0.551262630642563455247406188086985255
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.210211948725243554184766737667089317, -0.407459059708308767234747478442639184)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.03136363800801494615083914070082377, +1.76569770403458288804419362485669933), (+1.46490848965987277617808456518926420, +1.96806519747601603472116709456596707), (+1.89466319513708573621849739179771006, +1.71775175234668997135617907442870004), (+1.60826787342848119081609910836902887, +1.89628903724584131702429227283783839)
(+1.16772049239664859957407624510598271, +1.48191300227265609488239510213282914), (+1.76467054332263586459414691177289974, +1.27187607870654104556319674088133495), (+1.76721990853165746993483500547983264, +1.31518852474506043831651955498230059), (+1.64668413222236492881594088021943847, +1.55053404277282941259193959896762615)
(+1.10532204190517936175301081801245878, +1.46632444809633198810427043110378292), (+1.14425406737536132386466741787221299, +1.44936606282994409247244251846018634), (+1.39729236209824617461224569343866067, +1.35424931690502733672812277538207645), (+1.23295758701197866300293484747896192, +1.41702796816344011612199821585381032)
(+1.80057351810408762811344309332332488, +1.94354798650994622517846665388574392), (+1.05142835537857802877946625170941374, +1.77667338753634078835860358711867860), (+1.61616314662424718008606323015061017, +1.22722588729672502452292152337968889), (+1.86309622784351271632673915360085679, +1.20377993397333352655389166609171157)
det = getMatDet(mat)
det
-0.140318746757826976960590170300624995
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.795112870816902372664194833357064296, -0.403619119316969785094249340862570623)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.84741137579747795994386022158797394, +1.63393715276326646341803435469249105)
det = getMatDet(mat)
det
+1.84741137579747795994386022158797394
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.561089704230503928363392345364508962, -0.496254015638190630085347493915937407)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.65276521154042640253122333240470165, +1.66336756648162406550203009987552161), (+1.14024337185145195983651000744146819, +1.30339470130685353631590336099141238), (+1.13586261534104775021878542148202108, +1.68928910439079035175303277193078047), (+1.44969361215633856432182216728246844, +1.13754528390610008681812171773368507), (+1.88683421855394259396683276229455231, +1.60704706446702907431757519681514513), (+1.89854986848570020003874182642208806, +1.49199607449676667490196684154321870), (+1.45436961860373203976157132441752201, +1.71998514788799441796637581710245883)
(+1.73112142908031869899149323187351779, +1.85266618814819420344551117694742389), (+1.55409503073788918233216686853589260, +1.92673579613978271135872349981067441), (+1.27237739791845860377458982667873389, +1.61309523200174161791962603291510400), (+1.36182162927107613639832591797982683, +1.59683952101150601999918317604594441), (+1.94763702119646788782013923331098962, +1.70669432307905933274210653811904583), (+1.74764281507519905684129849129419884, +1.31735393185705223801032090759514620), (+1.41812986335209074530946525257262979, +1.62295631294320348594031242101809475)
(+1.54968205365634722143759542131878297, +1.78158576638218610094440533267392084), (+1.26391247490282038380769899514372062, +1.04801944152758372315162894714366934), (+1.78809878193513852769026155738220336, +1.18099722071148317433823764562337906), (+1.14621244033955942926207675003107962, +1.99518751216771485554357826842791950), (+1.39074061359274984588058316440780867, +1.41871526681906405811201489712058589), (+1.16198303517295664346206624531236812, +1.35383327671877567814392170888699483), (+1.29809214879891268258478440226093059, +1.44321234414559124625385417013269510)
(+1.63945645565750492278717247809940491, +1.87154570434738603681192828138050507), (+1.60498686057670431727037037417080415, +1.47221355072759968277089260286377559), (+1.74847259950727316900144685932064164, +1.20335178106433987248730167222255478), (+1.71729601667692641784146434364402177, +1.66567845457074114897327309548588778), (+1.81098964011795871867179571080247977, +1.19854164667621928485346939089758050), (+1.50735556860217762998389560956369949, +1.18948182942101624466445741139864216), (+1.84749147360934502021901292571209916, +1.90182197870569438846984345741944915)
(+1.26927897898111387191169326787200289, +1.95563139417592972910652088455000054), (+1.64456094575588689222565856548288865, +1.30665945319937183661424220205405457), (+1.66703631890329353247002047980551489, +1.77397455867632593550166387597977076), (+1.54922632318594793764916633054128566, +1.54688442963452042062983217609551007), (+1.67479858567741579148091242800633328, +1.16976716771054054312435577451790622), (+1.07192593196540222259561982295659806, +1.08120966876740634173293268145439562), (+1.22048803001962326696059046985122382, +1.55676251830154369864584715601181297)
(+1.84543556958350400811130767735580858, +1.86265589054650096177430862904189697), (+1.29096728828367786941747836887792977, +1.20233888432211506631532573369343089), (+1.75218139096773023020372330905128613, +1.14704178229443942506267231731242062), (+1.89980205825184118066252069237128349, +1.31255502207068183458203458623395012), (+1.16285837001449956369668240415463785, +1.89984542966146261928053093423485294), (+1.35765999090003907411617416340113016, +1.52427894328718720050385665129201830), (+1.83893514994817966640421318069350442, +1.19640509049528669225948587039316981)
(+1.20466266561825622731754347458128877, +1.96944966672375903827904583989645226), (+1.31238046012858663980279716683963119, +1.22470051141560455245450418374069849), (+1.45593306094105042046141565661066038, +1.29330133539150909806577149058734138), (+1.19509326342724138530269520682161307, +1.98650949701076124494354464849319810), (+1.62762996949640448708557385085771063, +1.30410262683324313260126610152780237), (+1.33621937122277171543678678744030975, +1.24404637963847910280050669346943909), (+1.57936917179610044853559278100194062, +1.09860630075951403638195855687356550)
det = getMatDet(mat)
det
+0.158587922984065083571070702986403078
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.296239782842427768671073670717277611, -0.456598044130610580167749704375590089)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.48852621176386047291554176047072602, +1.70669526217034456296390176470140310), (+1.83413861344829387638316589135409978, +1.56350657573338088332115265107827018), (+1.77335177887348542865036961891357834, +1.50366980894752438214151565978532633), (+1.80432125785704701171522258960147258, +1.91900003969158223672995994437204040), (+1.59471613525117148461687000850560619, +1.97749118449928333709376579465600817)
(+1.64256515596712982218289132328633888, +1.11229075832369172892452493026847579), (+1.57496103156062597662943668517704041, +1.25651440375097312177691026843147555), (+1.33578507441435305626591109018563961, +1.54349582931855257490498453810937457), (+1.92763744826228426793919279930536910, +1.51235971072918208175121605935600855), (+1.74465216096237343834340344659670691, +1.91639390993945486812083005315809769)
(+1.39050398549005182197054776840549850, +1.24031609296945111949223342525790483), (+1.61605274006429036648689080651582027, +1.91630841446893057641412225577811990), (+1.82385022804139176136593291108892579, +1.84092490724342110662825766621911822), (+1.71600910988529801494648230166891998, +1.36406984025538356684878150935248453), (+1.64365422945917649712903314923287498, +1.19768423881144171741323060163189747)
(+1.01840053103765694383451819772078524, +1.99084293752923771544031411210127661), (+1.89455680330739006705060028637633774, +1.35306069287977926998208286398218132), (+1.03605061093813949601210330818983876, +1.19032315839759356806696292231613068), (+1.00998469610135685482451076896337165, +1.00053434061579240085734217317678554), (+1.87202155072982045119132953124187299, +1.68714168266789366102844650093765310)
(+1.64550979501595078107740571966625744, +1.36162074863826232983220871065616487), (+1.47121145355319135029078257576823372, +1.91364094244618610992885359165702256), (+1.18769425437510803332707791648461121, +1.20690329417612310362624235987513094), (+1.77765380910989260851228309734145843, +1.91060845213669006365437336766715928), (+1.98131030199014413371867562278364335, +1.72446513397208983539494565445933562)
det = getMatDet(mat)
det
+1.90483427916365516641374265230248996
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.937904355978757632347237283596148710, -0.241329183926912400797749232340325976)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.39334229806664610833836637196361277, +1.83969358688483621212035680122816340), (+1.24980095004147769080266976809686085, +1.78560298587163040738718810696611207), (+1.71890513964215280667666976231270087, +1.70317240864250215357586315516612045), (+1.94184873700276080608071707480380774, +1.08792144300824788144464409825204305), (+1.23026565945414043768883185061913655, +1.76859050421060863957982029532300812), (+1.56013825065511404285683680609019940, +1.15135426636388622090009540317114312), (+1.08363006045468478628955422268567446, +1.29969566964214095171636789052824185), (+1.60739416624037752305414983608885382, +1.57666677877960818046749733614151115)
(+1.61393159893036133948984607157621533, +1.83768186412223931004578037297933544), (+1.80789397997661962451302887844657969, +1.08782615718722927261577189232816339), (+1.50514693106604719251845033260796911, +1.43930927598819294320586366255867430), (+1.66653748468150119941915923241825049, +1.90105105727004987793077845870555178), (+1.16983581445545657884964801823782583, +1.79147187994130989409645931090157789), (+1.01537033534066793837303370995309798, +1.59402096615070049840283009899422994), (+1.44206905765616984131776135407763780, +1.86224782763931053551888205414976223), (+1.48595732185533181282750501060235629, +1.22178516817426130320994453333352022)
(+1.71556400242274042675794705814507356, +1.40905160144650112379531711885554399), (+1.23231836536738033915740890633554587, +1.60439065091872353394715353870632740), (+1.74946387416048405108607096718056641, +1.38073974198564295766758931523587143), (+1.03729604821176989617189544506786080, +1.09376918143973654598790320828548001), (+1.95417562046934541597194792585743323, +1.87721612542494525194952284602019216), (+1.18678856092590258936612067860328510, +1.00203158208665898232970733053347753), (+1.18080994621192478447961092474234134, +1.08731341603056182686748066394414549), (+1.89005395778557501984930961685866998, +1.74693151745886832488801240469856072)
(+1.56256733777651912885932286051610972, +1.67067720521040305969466725344904015), (+1.76600367483295445205768178468246142, +1.58381872400393237041125679358845870), (+1.43232835177336803660026307730394178, +1.39723511140434836936163619252677396), (+1.81119147833047318485100559217985646, +1.91433544822738644722444998802036534), (+1.51637544192531295177461552811340060, +1.20158939883487935247218945484780939), (+1.75208071718688052988548332503754749, +1.10084555974861522602269065131081961), (+1.22240973994758706430696202221634319, +1.39571338665342141493277855695727724), (+1.86602273557582808789980104799911659, +1.13515588023514444613702866791232358)
(+1.01873567095689284693403832315315820, +1.50236392922218320387094882563676884), (+1.01554976078364106678318281496967128, +1.52477092918412871901443138678550126), (+1.07934995484835852723097854745966718, +1.25686927185175800835099015895500927), (+1.77634801116048731917089224330526503, +1.83339500476781940815517769349378153), (+1.16517891310529284899282675555370706, +1.45803080705679064011798520494588425), (+1.50147985673521272843096062133994057, +1.46153680293657930657628967059096374), (+1.64887060402265608505948123702943718, +1.61092265485558134297268224448502677), (+1.18715872784485237105508870877534905, +1.81876262446546276427937011328489096)
(+1.61831144946587759988580581426138683, +1.30340834261413534900764537591365906), (+1.44780811939711951434489787223831183, +1.06708629458260610969694749880606407), (+1.20674886161391224588547038165595482, +1.56726646179403246922711732687082985), (+1.11519327009368583400010242646129172, +1.56557851670378636686264511773061942), (+1.40420610236404233430827347792576505, +1.23761901457222071766771142960003070), (+1.24673295847558720009697187995300475, +1.77765750525033349935768952383002750), (+1.48886897855879202834009259641872589, +1.25412547329698455949811510627955402), (+1.14828765209072077236990947852538429, +1.99389372023347593971761774970297884)
(+1.18542666553495492645981904116910383, +1.23335968117392599475656811348871389), (+1.65525484071952292689194817601851326, +1.68928315987614487048264671889879422), (+1.28455394938710925818840310357494555, +1.86054528779586194384137732538846051), (+1.60327122938974662159169439130468288, +1.68394012484782847915722556058990733), (+1.73451829295131966472873640760090637, +1.46133269493529217308348253528725316), (+1.61740592968025840634101413185904315, +1.40623681347909176189700131357839652), (+1.73351462518469564973947834417509538, +1.03369847851842240070195782740087489), (+1.79071001139320749132130198871291357, +1.29737001546946771999918582197661521)
(+1.66917220015199587557939576803778261, +1.76245352265440100665774548500897688), (+1.14961313606640749541339428819726577, +1.59890009858032059968366829133294297), (+1.59655240006885942733618551940859011, +1.24630866157279304099656023446569747), (+1.50383439631163996644397790303335149, +1.15079079551300826044722778854606890), (+1.55810914722593112067620847361013870, +1.58922248522335447805446123347267150), (+1.49594172991231131518749196486939651, +1.29366501592661940625782143229243431), (+1.37157897659461204991941871265587528, +1.96679236608978392348484841157978788), (+1.05005222963004540899581143078128024, +1.82420367597624409045258546179882024)
det = getMatDet(mat)
det
-0.148936654552746562808271435126465157
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.220052951387771655869883169149614173E-1, +0.146700586654016062362495107033605308)
 
 

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 ⛓

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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 at Austin

Definition at line 216 of file pm_matrixDet.F90.

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

• src/fortran/main/pm_matrixDet.F90