pm_matrixDet::setMatDet Interface Reference

Return the determinant of the input square matrix. More...

Detailed Description

Return the determinant of the input 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., setMatDetSqrt).

Parameters

[in,out]	mat	: The input/output contiguous square matrix of shape (1:ndim, 1:ndim) of, type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128), type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), On input, it represents the general matrix whose determinant must be computed. On output, it is completely overwritten by its LUP factorization.
[out]	det	: The output scalar of the same type and kind as the input mat representing its determinant.
[out]	info	: The output scalar of type integer of default kind IK that is non-zero if and only if the Pivoted LU-factorization of the input mat fails. See the corresponding info argument of setMatLUP for possible meanings of the output non-zero error code.

Possible calling interfaces ⛓

use pm_matrixDet, only: setMatDet
 
call setMatDet(mat, det, info)

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 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.

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_matrixDet, only: setMatDet
    use pm_matrixInv, only: getMatInv
    use pm_distUnif, only: getUnifRand
    use pm_io, only: display_type
 
    implicit none
 
    integer(IK) :: info, 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(:,:), lup(:,:)
        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, 2._TKG, ndim, ndim)")
                            mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
            call disp%show("lup = mat")
                            lup = mat
            call disp%show("lup ! matrix.")
            call disp%show( lup )
            call disp%show("call setMatDet(lup, det, info)")
                            call setMatDet(lup, det, info)
            call disp%show("lup ! lup factorization.")
            call disp%show( lup )
            call disp%show("if (info /= 0) error stop 'determinant computation failed.'")
                            if (info /= 0) error stop 'determinant computation failed.'
            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(:,:), lup(:,:)
        complex(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("lup = mat")
                            lup = mat
            call disp%show("lup ! matrix.")
            call disp%show( lup )
            call disp%show("call setMatDet(lup, det, info)")
                            call setMatDet(lup, det, info)
            call disp%show("if (info /= 0) error stop 'determinant computation failed.'")
                            if (info /= 0) error stop 'determinant computation failed.'
            call disp%show("lup ! lup factorization.")
            call disp%show( lup )
            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)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.82299531713424301723195946926271165, +1.25321359533214518020879419361294697, +1.74664806330286039405155787971819054, +1.85092089587151419375318511960539098, +1.97304504441604288044541025634464131, +1.70438743841965354746378087194404323
+1.48015964585839319113065472979799770, +1.46197525775722790645881584724207164, +1.56099240257506532728168600404322505, +1.48115057841515096641031197402216012, +1.17962357142164361124198693664341453, +1.92213944162410819368237235081887701
+1.07631084888959809475495463388513969, +1.61365710012812191644911208377303408, +1.48091409853663104545557821040536327, +1.66377190811311366808857287098573701, +1.70681083994788720469562424423524551, +1.49791008614169995714566060753543323
+1.04006373907321772291959637574092673, +1.69733234688794108808706195534382468, +1.99931443588935724203245963724172312, +1.27250972935002679402220929662395781, +1.83585430447435341686522542846878832, +1.30062658669927680093125137971344807
+1.89420948049867318591824543988521537, +1.59462898995340308055620845753323980, +1.51401227646931917189833312898835209, +1.61481228712768320332372224433214529, +1.62659792230123095434726153415496181, +1.77231928738111713447585078846198602
+1.22810230777795443966271817221461107, +1.53401800297850415453661149311295577, +1.01101593950302453786429807725762819, +1.57725887708295201962658801193797264, +1.25213605711632087831373301802872628, +1.95235242703978976324172116277985774
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.82299531713424301723195946926271165, +1.25321359533214518020879419361294697, +1.74664806330286039405155787971819054, +1.85092089587151419375318511960539098, +1.97304504441604288044541025634464131, +1.70438743841965354746378087194404323
+0.570524635635489553167471989818848892, +0.982343117037627107660404422662379668, +1.00280868599005932397107332462233132, +0.216513759642817258668128570323404964, +0.710183499416482250699513088828845435, +0.328231564413198572272464807000578518
+0.673672771528857731117072216420348890, +0.702160085341172389822588551529444223, -0.869785534723374167849595607762751414, +0.178316547332174114494567592106196488, -0.575713172864882560653051229255864939, +0.573681914360613391559988865454415059
+1.03906436988350532872315597191074424, +0.297716134126446184414906573608130842, +0.689158182294596452146552556745644783, -0.495761614383796470985426297345177497, -0.238198525758746515222408162129994213, -0.491726390129179680470265582132437807
+0.811938260041836492165037901189338101, +0.452431725732189426800209488065132040, +0.357421960724015212783353789806465495, +0.369885146067096459889167802267654511, -0.449798107599959423469167894343281001, +0.366615470284552893485310905985949171
+0.590407906577381490869952736106014408, +0.889454885629629506857957517356899373, +0.508486052589729615858502966436189544, -0.580365380878054955440381621098431705, -0.143916130182513637334634272168991587, -0.324649247979674166368304098313860357
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999326
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.62631656185463933066161956323415397
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.62631656185463933066161956323415397
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999904
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.51318039756212837586956702395873538, +1.74513282977157416700079251410662266, +1.53615707394468235760579128354080123, +1.95473560182083794176431966242454527, +1.72190348750911580572487990258278686, +1.75421920595746935034736186940510874
+1.89634008235264062135726610750347931, +1.18518997693450672469928891318366263, +1.43714833498189294670786868823086041, +1.70619102570533003350540483943103273, +1.03763293661867942670326427330398514, +1.56386102758758330346676272850139627
+1.08122593012998118138358916657312243, +1.27869373448045005982224949911330038, +1.85749796487349780236067328170223909, +1.44460918529443934385383824947716149, +1.19686086539618223142892371922438984, +1.08972449845231813863284326438465728
+1.61766922404171618973454146585830296, +1.57952979445034803006790531112219261, +1.59017650012281248610547541478988297, +1.36618766820308461056275923330757890, +1.22022302826642786149103555342142506, +1.57271088713410074295177914458655651
+1.72067751829694784293047386239940264, +1.11022864382393229817506041452677824, +1.23075739794156790742172125916934900, +1.31241124421393341579103376233955941, +1.37252664412972992312654458865447501, +1.22626399532836499035755160055158218
+1.80026067332114664321179221647907138, +1.80225351572383128355251683583898218, +1.86257048339382051318146276810726140, +1.64473783202437876938474666623749599, +1.06253395805359937929824195441991021, +1.11712296179557481730201218699720991
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.89634008235264062135726610750347931, +1.18518997693450672469928891318366263, +1.43714833498189294670786868823086041, +1.70619102570533003350540483943103273, +1.03763293661867942670326427330398514, +1.56386102758758330346676272850139627
+0.797947800420293793968697464257914873, +0.799413094596505789962312395039103824, +0.389387721168193314739393900326859104, +0.593284225762424893825719002452031748, +0.893926568090590434603403157448084287, +0.506339738830936861504754938882037491
+0.570164571319184927019695050491192592, +0.754228825403616043891593754261237296, +0.744399456973189228508766287225750984, +0.243274458072319259389601624457347064E-1, -0.689858585457257296212115782597038259E-1, -0.183829680418567553428498984358397584
+0.949334294030058268783284045968642215, +0.847011426577862732403505311516084444, +0.226250076637015816798903996604699490, -0.483030425751455081139415933140498818, -0.664084535205054022739970072155803630, -0.754788008027800290554107293524850036
+0.907367583646830903421158759882518426, +0.435640578392120580474603501854726161E-1, -0.121208744142217249382181806706927404, +0.535428700561860516807200934020041952, +0.739277315471535839121944665862482662, +0.167062377536447639853853128560609360
+0.853048057727494045875421704897173926, +0.711153958361440283265418485533380220, +0.117282843554317231035312209125005965, +1.06420809660646122234582639779591548, +0.560233403422059545513188291531534907, +0.609794418112264825301125881695208450
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999904
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.98395374918827855182464581644920442, +1.78192902656938163062153436785297200, +1.89445515180564721262672592485973631, +1.80516557169643592044290313752871430, +1.04511660584533490670956244913858339, +1.87365022559349701861348469715117995, +1.50556466700572241738392655506373046, +1.66393342227335409633793837456232874, +1.82625838015754998221396387553567467
+1.13342951105956080957578821271399431, +1.73230684218117623305013389446047569, +1.69995460232573061262725805474288727, +1.70513824139563447313214153340494057, +1.48375800782859402617704765455420771, +1.91618014130210247321350638238086225, +1.42291098309360332999796573581561813, +1.25432647881096362264181509121791361, +1.84332120167376244639875323207641962
+1.31934468525570130813787191921043055, +1.84548766185368138288986550884098462, +1.20195046930140760965438964183788555, +1.90339304807960555407772114802550629, +1.18521333611828462761892461878630273, +1.96893843916773816062697066106895653, +1.71279306143197737510627909069839707, +1.37958021801340597290192357746018233, +1.64782878388633557344611115543765789
+1.18229291136425642807006827026830530, +1.35820703816733492830498373047208378, +1.63563688087603904505856441219347877, +1.66602326883513994631127593458302650, +1.03910734964381141970522844063318084, +1.43613089411668580820922775244257454, +1.28779506352458044124861561482137339, +1.82678761506776166792583453211508250, +1.54146657886741755811794848046558066
+1.17525148922328162032111956964983702, +1.26172930220332678488080662540217570, +1.70546786431856489678890992380767515, +1.54934529769978696818583683412719862, +1.91520739174960620435913734405836409, +1.53297403101085392334584185691210107, +1.45881951661131585224544301848138501, +1.90568973324901644481945813583919707, +1.05860980991883279078663933537557322
+1.41576532890606520050313658463626765, +1.91149671476474451388516203282973095, +1.32508234392554486568473796133269171, +1.25175263207236994249045384413931760, +1.59072527156836568044511840117296602, +1.93006031967469479075209373026300315, +1.30192769002430161559575098953919705, +1.58951597347209032832849586404166839, +1.70966377218886461840098586984425698
+1.08347204288852898252419997805990403, +1.02846367034785273976508304726700924, +1.31039205338259909019650157940044654, +1.85043881376347159195521846090504521, +1.83113604388642059308484470834065408, +1.09602038878795888340627961659701724, +1.34910375701719708583440312034571009, +1.03158747146219933296977182476000902, +1.37371762327489445995161137119149255
+1.39188175863405669519120644982169225, +1.35323336303486563832599702010738488, +1.67854186775877959555781992473678177, +1.41939529831844675039312093500532572, +1.47420199032463429353082302323002662, +1.92463579418729648080943668590360603, +1.30317006312996096554022895609918545, +1.13033788357099476196906629793751263, +1.79447619929433596153652747455895137
+1.46032252806053936897855318645411950, +1.54687249563548640147644969871492047, +1.38842356522673296373545461509015639, +1.97729888788716093347857184965413443, +1.63535467412029463360143415775576236, +1.71864860205814397656161536456926742, +1.44904764883550334063558125087161144, +1.03375890437648955846040196981456524, +1.96340873227005400567050505518822309
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.98395374918827855182464581644920442, +1.78192902656938163062153436785297200, +1.89445515180564721262672592485973631, +1.80516557169643592044290313752871430, +1.04511660584533490670956244913858339, +1.87365022559349701861348469715117995, +1.50556466700572241738392655506373046, +1.66393342227335409633793837456232874, +1.82625838015754998221396387553567467
+0.571298353867017281384165047298323663, +0.714293722594232007011880075766065181, +0.617655492624274028531810790353296064, +0.673850121828047469392535994031048659, +0.886684611310069862910997730344138719, +0.845766851697972054110310907412178873, +0.562784367192890086835992742962847688, +0.303724053721883879434454197188922118, +0.799982795353908685175488402188457259
+0.665007783470508014203675386445292791, +0.924677018291845270997554419672707645, -0.629008791336545159314337389824070860, +0.798501710209306709977112543123915489E-1, -0.329694223954601303297445903539776230, -0.591147149513726895711572250188227983E-1, +0.191187068757803827826450178949803071, -0.779511135415788070336033495323591589E-2, -0.306372959439304868164250145016191558
+0.546117591366141647536874677007152205, +0.774483669987321002200505272507876240E-1, -0.362412040651122383134715503746426447, +0.841356211620087571241257891662842554, +1.07222204872226343047548861297339576, -0.141401054794927906737985158605020947E-1, +0.552590172949182822323116868990959661, +0.965361845046959472904336909075802592E-1, +0.203375184933058669408660457394036587
+0.713608031177801470926600427936292280, +0.895846946676161424333613511811732739, +0.922309611987511070029139281632200424, -0.848322223152051753211034550665070317, +1.26425791026779477272636819810101731, -0.122142476526877255658972432817877058, +0.158168480098474006745722167187305519E-1, +0.219112750615897775329100756615180543, +0.144867394851717618520674520961784654
+0.701569660685656526095358529939525312, +0.144318810648742449276609783306127636, -0.413842075375418508404899559729706368, +0.105474960347318749516459917455437612, +0.287505180987803085100112507946497657, +0.500223440615092695270221457888111524, +0.181980601023271339835307427453634013, -0.157264563411263037226116143429984150, +0.207885024122146038879019255040913007
+0.592378471375216247341306568490277520, +0.288610837284564009726574293987248603, -0.643824623917942540903322362154330677, +0.400464309370857938885130777025314635, +0.315239557590649072366832281982256245, +0.369982129896483220278394146334739356, +0.234012387317940540226780219258733300, +0.777787433113013787458207338675788414, -0.655386677863096924378446574451568092
+0.595927658015205087135684366403018862, +0.414824094405280826990865476490088377, -0.398182477117941272888109419885519720, +0.407129400100364499365536517419510079, -0.410783480632200310584733262135445618, -0.198369887635598700734557565624086896, +0.217421517356493878290873775425647936, +0.556508637158807486754927006445150037, +0.159746627398170499275838104969557612
+0.736066820437734798211954117899877325, +0.329351435356928207666200441272873424, +0.332980620877472284274892472254714938, +0.475487475193578223892928889545846526, +0.137631569326386757736468236543595695, +0.208267868150432915725217766929149841, -0.901624459135585263655080307074197212, +0.664002523629486548511766509557453700, -0.399219964146273286926098612149499947
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000366
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.93755934933566481263238822502608758, +1.27416225603746712925406382741112088, +1.05031099801386669276982404233280809, +1.15508509225545970677727102806190888, +1.14086933967119172129708079401574946
+1.12200594368181933792159252183346492, +1.01940472282080860472359636388500901, +1.38552118396591161709056920206232268, +1.27890867829765404579766129037221745, +1.03870202186504269240607488223777080
+1.64292687937941293106294281381441014, +1.68042886743488005019723482641557024, +1.41451249110768093412212693735737965, +1.32305599663651070575088541812403793, +1.04635841066255455666243717365317293
+1.45222938104091209860580316486098689, +1.48417047566369466856882768118448090, +1.62152550749755129279699265905887304, +1.87810140252261207933289473679854967, +1.19203814790606603342269627393302880
+1.16287961890121512039739698409883501, +1.53751046311629783701781486158450105, +1.37543337364993062467167473941740139, +1.47393007245150931177096151795105940, +1.66320706606108463366752748420706731
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.64292687937941293106294281381441014, +1.68042886743488005019723482641557024, +1.41451249110768093412212693735737965, +1.32305599663651070575088541812403793, +1.04635841066255455666243717365317293
+1.17933389102961427922135606500060158, -0.707624458792997839155160111613140698, -0.617871522034147331128697389048651615, -0.405239684307940726208959907606975550, -0.931365961870417821503864573899590039E-1
+0.682931150353835332468047449241118137, +0.181187203340851206609258473312768010, +0.531456954325196084578140181999033473, +0.448776769614626905322080687425224488, +0.340986428180669757511130085809073054
+0.883928188934048301971433754534761378, +0.170707745542492777612549339581785075E-2, +0.700438284839873547090916343456858737, +0.394966256301646121761227700560694623, +0.284514954682878744164300383458320556E-1
+0.707809722694702445655800348877302418, -0.491908622043360769879676340607602278, +0.132261606504725181533390368185751552, +0.705785212530467367924388869899359686, +0.811589657315196994573429844678509906
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999904
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.72543272247840724185606142331070522, +1.33014233702538371994126579747476886, +1.90370061916907070739700700475549019, +1.95299307819193901064642041236042684, +1.89320892015875130455598083340616555, +1.12794764138830721690945351309266056, +1.20681419904448926795765070714973447, +1.52061049100857373735999228080333079, +1.45226101868879497802899861270437719
+1.38635607790316270119448437737040803, +1.43273866421094246646540335605229413, +1.71375870761284069183666419924868212, +1.20887449565705608288659681010331187, +1.99326806164139588779531860389824172, +1.51668569628010628256964106309156473, +1.12124299058869072405660158714907940, +1.14555853751496088142454734765836528, +1.85649890190986044938734141525767749
+1.74264852198232103698330271574042538, +1.47630943160113971959125776798665167, +1.71735423711963773360239293151388767, +1.17471765819244638398963513644805284, +1.36577747785702277644670048404696767, +1.97895128778003789838509252796316139, +1.98903511283841769100354761806494706, +1.04718199806401412854451015259586519, +1.79471644922683385604397533909029572
+1.51779032007495523387337350772761769, +1.59351145203099994551042805033662579, +1.98054883630539739981480017333171933, +1.99534174686392756456794396296075222, +1.93790474199332686123708248678281578, +1.39079903288642281329544707925466928, +1.72275912860859334087023616905368782, +1.35884589803162758396514251850033700, +1.74192769955316806277921503745921135
+1.25115259903233012039999427703326490, +1.49993061743725788664763180830400525, +1.62141221418462863674684803245484006, +1.01886593667716158819777847267380688, +1.51465794522609603157856446020128326, +1.04309916688720849579184227656247608, +1.94679886933130496116027611455245936, +1.50570661978237680314302251713517429, +1.71241844501255340403577068550233607
+1.57900397819295475588154240927061390, +1.38391818236994934936140420440773022, +1.34800455119030354555566170235260892, +1.19684430452455470110590496426144706, +1.79420761291311257394885621315837322, +1.86723053334313237572170300695399088, +1.80816111217142134110173573977396893, +1.89130664821665827501413024941917225, +1.08911609444397686970049145526110363
+1.14455364270406910395826572312141949, +1.73053838709859284563041644932317488, +1.12127424111227944222635371505927466, +1.01354420695136400304098368070634050, +1.94969222007908915488758162886535517, +1.83562929791107621920340503401956257, +1.99813114175103854163584082663818097, +1.62192483230461399550837066318037761, +1.99209069201097629395918037222242448
+1.30074700738059272072831897900313641, +1.51092229529929978510958294398876521, +1.44833646223779747418938143517288282, +1.95306327517861359737174500702041617, +1.46056083479311375857903463184506916, +1.24069837851146310211806232922973422, +1.06536078537440332391722875430722674, +1.06935237039725652626693869846554495, +1.04929751109351271279326504297234855
+1.81592298262962610457858761464329227, +1.57105193398365582619663401170251117, +1.12997493915204996608650272440140545, +1.22823190023788015371860005446189517, +1.54112836483491172531382497839661653, +1.19535218222175590551601048401291932, +1.38438742090973349067766492419845205, +1.97895882065483507853073795743945413, +1.49085032447912368153283350315484237
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.72543272247840724185606142331070522, +1.33014233702538371994126579747476886, +1.90370061916907070739700700475549019, +1.95299307819193901064642041236042684, +1.89320892015875130455598083340616555, +1.12794764138830721690945351309266056, +1.20681419904448926795765070714973447, +1.52061049100857373735999228080333079, +1.45226101868879497802899861270437719
+0.663342956113661225626902570476916647, +0.848197837204240953525763428959596922, -0.141532155162739130192837847317886766, -0.281959994805995542561081260365076548, +0.693845418440230629021532629110836152, +1.08741317513112465473938598160011795, +1.19759944347692667415119132057753428, +0.613238574101540819114865145496507815, +1.02874357482531402184112688215514866
+1.05244496581775664926587488924674824, +0.201781141206816045789237302827689857, -0.845006674130387160121091305691779805, -0.770291623655528731869574421206311226, -0.591374752781427811220484158846374739, -0.211170106104665969028838458357301059, -0.127371089965449438900854302279900651, +0.254859985108945003489090695503249334, -0.245155526230697016800324122543850569
+1.00997767069073841594383363249586112, +0.156679687846347478446170790382184515, +0.216762389739273194893558442474207470, -0.586614084683904927388339531161267057, -0.526844936386300520231317816361532630, +0.715147536270756127962332867290569108, +0.610149474006637713872654440427957585, -0.639926731459424348865692252635349721, +0.219922523882554921919776990781794960
+0.753867125872171345266661288155153581, +0.599119323812559987328638007334533039, -0.115968074623101689104734895311629906, -0.955252279209232988010727083717624676, -0.954213748182506786758912294065738340, +0.397542809144930248455986063106828888, +0.615396054202952077609052394165659488E-2, -1.02612481686391496982312615215158326, -0.480203206179388390402615836683788476
+0.725123954549313090690473968107972651, +0.631235452880578751430289715148315802, -0.390924021204974203512851685606083894, +0.887190565282129770439739275168568076, +0.627781356825014882471111283943461692E-1, -1.20319704584604970322526750230981984, -0.275755851753773220934996603942210965, +0.747763649992166463511682184838135075, -0.250834334633382459570281987960213155
+0.803483126199093003471908520033781054, +0.429135426904386873732763143630701762, -0.289824745886441740830672235809142965, +0.788547448270761090996164341612088827, -0.438476372454718813968065705720519486, +0.255208136819843928878826364499157334, -0.807317804374205655436166823051620276, -0.401678264510006813479030100757766762, -0.142852914412853873731933591981051230
+0.915135060105315144157082700581601029, +0.196485168338704626031127674674090519, +0.433522800751859344110214289850451789, +0.342760597801119040802819480421842578, -0.379675460851940911279630121428546663, -0.514217891548307478405969850366276261, -0.216858326079792962437507651336520695, +0.395916203823309026796629568744970175, -0.753415720250930876852238010375767861
+0.879657781089722825509864269987290982, +0.499224799612157563010458277517194871, -0.445677113704886382473911096997422829, -0.127573247107023869477218199244240832, +0.424044999142370831419427772963541974, +0.262408008939881244408742850338548510, -0.190913222479347145977139381381594703, -0.229212367687554193538057389853150783, -0.608592924052657890466492363987659499E-1
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000001156
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.60476827967593728145552944005214016, +1.06048748730125780058570628390591285, +1.73526368579969704001374553245755158, +1.41501916278473860906018342991685116, +1.52221734235347425547528984556700080
+1.73280435069198637359375316314701136, +1.20971561852932800218682327647118343, +1.73741340286653573780055077269114270, +1.83949054483122083944163407929806484, +1.64103149378193932241137585013182985
+1.62344567062704541899429925616919459, +1.82303888151305134171404463109459155, +1.98691450514829363538511730278490570, +1.63742698775732615776526141565814068, +1.25074832934503461208574280689502239
+1.80879632875357253819146277542661359, +1.58893323528745059045118278353184767, +1.26998143450183585095770438187528197, +1.29132651878870021014696402255538274, +1.13089635355546001323812163189145539
+1.79415169419286167309306701263448971, +1.74881519936513332193583480971090492, +1.59134226131378125238795397372853783, +1.60776603479187140348328519932346378, +1.83138597701722818997464666353072502
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.80879632875357253819146277542661359, +1.58893323528745059045118278353184767, +1.26998143450183585095770438187528197, +1.29132651878870021014696402255538274, +1.13089635355546001323812163189145539
+0.897528176511586125313113792219567999, +0.396926532246850780354334510766206055, +0.847070384036292554127256824390330230, +0.478425052067849598480057126968991019, +0.235736987314800587917028638323370313
+0.887202309163116559273639139106658836, -0.879804497257969990109490143235348858, +1.35378955788454694528841124578519455, +0.690271805842007692677866709341009847, +0.726285947664528430279871979201385755
+0.957987542956839344762294740714220037, -0.787205193105700658761467009439113267, +0.877245068962195476199428910939697048, +0.373496973522970278525223682516493101, +0.106089489076556063862557498962142717
+0.991903657516375893625241938621075917, +0.435210291326030117195656312668383609, -0.273386043946181172503482909671136463E-1, +0.368276342366572090832836637707414979, +0.587835979927958195157343314078764029
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999998844
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.62100312177514916612737687755625300, +1.83039382460829618872113653010522513, +1.35157983462935950552312635301274387
+1.52572507856163849927447393358707238, +1.35868011175782343206959511177513499, +1.05688169462558309075004500983725946
+1.31108126293116527942086953300331455, +1.73615784165169142601614168132285272, +1.23673575365649311210355205142642629
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.62100312177514916612737687755625300, +1.83039382460829618872113653010522513, +1.35157983462935950552312635301274387
+0.941222788572317893503030070882997779, -0.364128268025547252589061928004474870, -0.215256046302374933548982142779822228
+0.808808598403813911479508332479915387, -0.702278840447832799567124815130177102, -0.760340461755461431228919551328273988E-2
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000270
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.74698728895208266312261604925696337, +1.40319187695940318971990629255242181, +1.81157005182672375044595742194544968, +1.44037404364962039326209966375052821
+1.02334745468312127880417485774571407, +1.49215031895014581653782371264298324, +1.30555212437683603058367093178239157, +1.75637424887941544424010325896899944
+1.40328179202745387824259686343453143, +1.91104694393883752833373359814218611, +1.70845681475974438953758174995316499, +1.31611863838307513738989404268514428
+1.58512941800119766670468245791968614, +1.89610658013585778533090582746707259, +1.77326241152229671260736463430684837, +1.92682282848498168531235054208885676
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.74698728895208266312261604925696337, +1.40319187695940318971990629255242181, +1.81157005182672375044595742194544968, +1.44037404364962039326209966375052821
+0.803258158145616519139978312326282902, +0.783921621327536764571676106042682789, +0.253298391577651209454272690424727583, +0.159126437040327208403111350481580071
+0.907350286991513122607640106803620632, +0.794620292291078385255461415947506302, -0.717422368602046152509023564734509453E-1, +0.493453930692149683490545027622993377
+0.585778420458324365468682150877746878, +0.854920669913372927742776377281661735, -0.387825240337065758217475699292322188, +0.967967625831679300824076902158667516
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000077
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
lup = mat
lup ! matrix.
+1.92216679920895940138965355611312149, +1.89301069874196279661415361105776717, +1.27819207590545740095677755966312053, +1.57512607369892512904540597273869899
+1.28657407984223427367679074783301983, +1.01181728907189235914611066754427196, +1.69890211982557602852574555167225329, +1.20322823344071738105899061994870741
+1.62606085574204662114087888233691304, +1.67178529756860968192942921017095313, +1.01918536658970146849756311300510451, +1.76853742824109641776638123109474545
+1.57989335956319171686628288905997444, +1.05343614581264833547701140705189087, +1.09125588301405334567596790899938453, +1.36799052371636020132547064815676267
call setMatDet(lup, det, info)
lup ! lup factorization.
+1.92216679920895940138965355611312149, +1.89301069874196279661415361105776717, +1.27819207590545740095677755966312053, +1.57512607369892512904540597273869899
+0.821933538865292291734621655891834531, -0.502492836914192860801024751610103162, +0.406669467155064399620124310801855689E-1, +0.733415758020094731301740606890340529E-1
+0.669335294091910059723374456865964520, +0.507950690913584627839151197242612622, +0.822706247111960245558862064411052430, +0.111686855568289979322659253482659982
+0.845952003963042645805466156262917905, -0.140079814623081861523171728581132537, -0.685629449308539443510880545316764601E-1, +0.453987623771390601877243339373395643
if (info /= 0) error stop 'determinant computation failed.'
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999615
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.44667612573842713296529775209054535, +1.02744185356788368660753559336499394), (+1.56033640112309318158402938205165697, +1.95817579066701228818718911555361172)
(+1.00220539256290981048925732617326789, +1.69795232274400110104072629383843017), (+1.73621852219973591224205316983696060, +1.24942509153775581210863147022571818)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.44667612573842713296529775209054535, +1.02744185356788368660753559336499394), (+1.56033640112309318158402938205165697, +1.95817579066701228818718911555361172)
(+1.01458002095768159708576537186682022, +0.453128612379426654036504140790894284), (+1.04043786246716447359132112986743433, -1.44433401148202192152856934755602229)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000019, +0.144444745829042688979198345693869549E-33)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.63619176447749491625449740764594985, +1.47093508246910799876694766239597456), (+1.29622860604855001211765966108510299, +1.31222299637626832208795354353277351), (+1.34718151708464202999165163549640741, +1.51756174714575553680585277501875765), (+1.64874191083467866990512616139908820, +1.88105591316994040557131413305793524)
(+1.38364756521420505686906469455949890, +1.24056196726769728647489600872860197), (+1.72453090222365613358560679959299563, +1.89660458315641559337871464798687840), (+1.76063180565896623237251236931492012, +1.90119688014987976006446431021174472), (+1.12798124211265022179386481291820123, +1.30001729042132122071878044965903678)
(+1.75501360700349038564112983251776346, +1.28574335258156616294059383688919664), (+1.54777997138422379279885978102861629, +1.56334769014992026221512793186174148), (+1.21668061582751086021051998305028801, +1.52534697577582655919971165509317109), (+1.10897121299153809672066378504332285, +1.84633274614353736073661033727430005)
(+1.08314704493370922494059351302579719, +1.29904512887688590350876985861391291), (+1.19734797722895967852853501845177953, +1.30834619500079709253970005860348364), (+1.53348904274746891383967115341607557, +1.90111745999876736093927656413529295), (+1.87764811351273800497278317488943513, +1.17924102376690508222105724401891080)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.63619176447749491625449740764594985, +1.47093508246910799876694766239597456), (+1.29622860604855001211765966108510299, +1.31222299637626832208795354353277351), (+1.34718151708464202999165163549640741, +1.51756174714575553680585277501875765), (+1.64874191083467866990512616139908820, +1.88105591316994040557131413305793524)
(+0.844637507802459509448863346443445369, -0.112760311368791248378559520894317932E-2), (+0.628207936131985996582396132108826526, +0.789713453228320149350395528413197173), (+0.621040559159762438355810832485728733, +0.620926394177710030673416063666821279), (-0.266729100968929168421769722688495620, -0.286933961603291973870233882021083485)
(+0.760838598026084332769674743631203081, +0.109951013597209370388280417392100477), (+0.349109086881913773555968958022842580, -0.172333864754937482135004272799754321), (+0.351541250535273972115956239014094865, +0.488629207816802648085800643173392496), (+0.972611625269129737467928995873372581, -0.379014967756311048888923081210059191)
(+0.983889001999131038026322894647488916, -0.987008376527586939587904687563772072E-1), (+0.398538639742837199693104437357573022, +0.136059152868187608131929295991416632), (-0.633922939669320592700723195745180590, +0.406764377804358090921010365844311271), (-0.169216720070924629744830567525552477, -0.326930110157317886464553984999345838)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000135, +0.361111864572606722447995864234673872E-32)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.13283943083750789149537969722193837, +1.37562176081485051682910972065380012), (+1.68289484812962915010220564382089114, +1.91676507747608959673533460979645552), (+1.50629038996816984037864341782498128, +1.98965776104216854192073793026525138), (+1.39141943339605013498122072498229038, +1.34038413446176275639914405175701247), (+1.56006177298771030929492963107390352, +1.14457372746945087830895343471017302)
(+1.19251605887964842802381014615059121, +1.84518102942507892974780463215049841), (+1.39411213946170351823244037021191844, +1.37146524516487150944112895787942563), (+1.39295088574103593467502448961526975, +1.46140303830342289612502484322602369), (+1.63517492453087443141130222455182379, +1.13294870537173616064909210722610056), (+1.68790932412556924802004790588061681, +1.01666857099386706808778708349608336)
(+1.20911984496308312460576961365236075, +1.42928718318820602207355792263392102), (+1.21430740599056174196687630411176997, +1.55825496235809957705485804846136714), (+1.72238182845220546327783453194702982, +1.47041649227010203895092270392360829), (+1.17525577729813710843887815649029743, +1.31840482124951945933689255511042863), (+1.95110765348686087292070828341924753, +1.77302425610870455690718453556362346)
(+1.86144427969400098946374129081941198, +1.92107880161162291257520072171525329), (+1.03660096654733344148346839174375724, +1.29566284611996914414156632733454495), (+1.24490505322019504558370834100550105, +1.79385713726835067578075187459478314), (+1.08156086314887426952004169639019549, +1.01450066915222533057194429435854061), (+1.06330765627038530229644578911476385, +1.72491581696371453393265048580047645)
(+1.43330572363220135758501892583703740, +1.97631115011094916405243098567994488), (+1.45584595846329463678181618791952814, +1.56913941699129182722688594852735034), (+1.73356958343510888980167634102425656, +1.98181045240106164922563232901629062), (+1.50301110626259103658708853978977525, +1.55801984135913203827953288258630154), (+1.14086666698820028509538120372828760, +1.30377674079596946009333827185433026)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.86144427969400098946374129081941198, +1.92107880161162291257520072171525329), (+1.03660096654733344148346839174375724, +1.29566284611996914414156632733454495), (+1.24490505322019504558370834100550105, +1.79385713726835067578075187459478314), (+1.08156086314887426952004169639019549, +1.01450066915222533057194429435854061), (+1.06330765627038530229644578911476385, +1.72491581696371453393265048580047645)
(+0.664018300932043688849967656202450804, +0.537165039549672872367638763396929966E-1), (+1.06417131397626203425282435094028284, +1.00073865589546896156433124261486254), (+0.776010385715902157418503791537531077, +0.731631845423557090527804313499060423), (+0.727738655900172490362275165043847142, +0.608639455454006367550393478165563963), (+0.946662477006932531277155866102687628, -0.579191124849980581053877359814888305E-1)
(+0.698269801153122590952871881108648734, +0.471976901730421361781347900392569742E-1), (+0.558631711406520279040009558777344377, +0.428156675267348213810723310033904579E-1), (+0.535589433869032428528557740594501535, -0.282874569864697935362128487086198521), (+0.874379904813412345072565731526661295E-1, +0.187798549241517872586434681909002089), (+0.758728544963659754061292504681799148, +0.510205433327379526189415351537340460)
(+0.805607630236709180350234274158514293, +0.159846465353061809839646490854721419), (+0.458017390250150357424905191539975470, -0.278510925798214816159787729185736382), (+0.404301316596835736990437329311862278, -0.349786228269276730755530580513603322), (+0.322155247613853058900952712185978896, +0.213486603720828187958065229095709148E-1), (+0.204347703956937922252967469410319305, -0.193602871876185718448787248541724570)
(+0.903452088674238546914756588965909391, +0.129312758331232388545862523208858017), (+0.466587810056189945713662882748288398, -0.190202529480903665631493038609447842), (+0.490830243253277925508921844513147424, +0.271171145575339168578456520713887939), (+0.697421634107649455989365612049295460, +0.699242285412858243276073834106440646), (-0.539357792767498428910910514667141735, -0.649054623197644424264124446754593811)
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.999999999999999999999999999999999230, +0.288889491658085377958396691387739098E-33)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.25662148436511230660824023518379153, +1.16021754989895564860391941307280311), (+1.10413180209203285048883377703868842, +1.03377524257232917509388104856877233), (+1.65237090140912452842095197526662582, +1.78429182049487658617846244066645156), (+1.37446965803747154597060066964014048, +1.36935185968520173573303795142323467), (+1.24948517485412737779337233039218545, +1.38802626245568403930397737702257895), (+1.49669066898675343831223483375820355, +1.64161065330108055190443461579443219)
(+1.92392940955708587701697430159712975, +1.63573407481525268001443677601741764), (+1.21707165536185136271111947358587262, +1.03613719658453481029085013269106655), (+1.21317155758739437780145959952344629, +1.86443465941799400912157352690253862), (+1.26110434941642868899730549956321405, +1.42734565613218235323745442561151633), (+1.54246129442100670961992526411120633, +1.27936394156927862183507058384490745), (+1.90443094774713070478664858837872020, +1.26597970632342400641916260192053158)
(+1.31940419112442513450791095098633121, +1.43958369451425000653392250939735889), (+1.73556126530556698417786693521675190, +1.89368896464068897763246628527511559), (+1.57865327869208432060959368364981966, +1.93972696222642093425739232439353659), (+1.20792186266011800659278192836712776, +1.21339627464212364209104310629688026), (+1.59778323219306731743152252206986491, +1.16587471525090471192182422098137822), (+1.33137869704635434287841853354459871, +1.05819287838129187181792898051304122)
(+1.68261431149351593892632428058631827, +1.23335274514161330599236725565587194), (+1.36547967237672313108570818718169247, +1.97772070400041516271887761909478296), (+1.67190058344484147357622425429445450, +1.71797913723021470954753721797092273), (+1.19950888354026710525688975694381918, +1.26652711605499750080612505130027397), (+1.91703230206239835267660894675064035, +1.36390207974799289641021423445771993), (+1.99572054103091152318345865791647505, +1.54479125951828817819106414084706157)
(+1.40071347159448571940299779493247365, +1.08278056499237074351340352037152567), (+1.23924400732573075979756532492080260, +1.61426153075539919235231700237985799), (+1.48302998379467813922087543262436368, +1.72330129294982776767939852672020574), (+1.60340103030573387044178155642672308, +1.73212732527114549032826963328584606), (+1.60915759234925094751823190978731407, +1.59636489122981769996210613436531713), (+1.94202293957200139865299076851628415, +1.76682940936788672590665709159601025)
(+1.29704539940508884927871541035611300, +1.83654522853445232762729378152753614), (+1.62983972709637691972981614643140326, +1.33047210355486779339291487910707328), (+1.58400072916281085116759891141326832, +1.00288730872156141432060614523690192), (+1.14389686433272648718954365334644112, +1.53406370671052692138944416840692213), (+1.16598504866915062627572875328986499, +1.25582488025276429699171644888065155), (+1.10822994852171594144720856442013611, +1.55583251342656804474226028861596245)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.92392940955708587701697430159712975, +1.63573407481525268001443677601741764), (+1.21707165536185136271111947358587262, +1.03613719658453481029085013269106655), (+1.21317155758739437780145959952344629, +1.86443465941799400912157352690253862), (+1.26110434941642868899730549956321405, +1.42734565613218235323745442561151633), (+1.54246129442100670961992526411120633, +1.27936394156927862183507058384490745), (+1.90443094774713070478664858837872020, +1.26597970632342400641916260192053158)
(+0.767306981492689068316464435939020936, +0.958837253210294751170596836499151855E-1), (+0.901042381521767507902304171105292086, +0.981956295618386184771784190665590144), (+0.826547213569558810231887985069070669, +0.392809823123054944409766906567733973), (+0.377126909792839433679052859369086800, -0.273539535196336405730647238174186191E-2), (+0.536912093060637012499911504924583121, +0.363128959422091205395599889432301779E-1), (-0.851761450764482982265084162591086046E-2, -0.958061225953892917352874141882480003E-1)
(+0.862382154595135814307791485383116075, +0.221378887725743261380883516274000324), (+0.503338684224505288357026700575048437, -0.362651846730071648532897546033883487), (+0.392043303879515703038585314550010908, -0.771505946119005029938357120378952943), (+0.183496605683548322799756753095941941, +0.162107006828611039497594436794350523), (-0.164399444651134820199508871165200348, -0.125096410917931239992115093397582341E-1), (-0.214824624038593358784672256893982043, +0.876074007077961302860539175464293743E-1)
(+0.700317332786554848541284581437223899, -0.326167681197702575670874814807381487E-1), (+0.692382942322467480961447796666118751, +0.275729369353899945511095759255553807), (+0.100859070997481280275679774991200582, +0.895572761886972453429528988587853833E-1), (+0.407812490199635039546015835431593334, +0.638791128316766633245169391348817713), (+0.140941098704331060423395998445247039, +0.593514265074689423223929698797342588), (+0.576018552664254276919924785405083158, +1.02144444936730305403370864555481128)
(+0.823986337595766303447262265296942830, -0.594979129054212080636562004830414308E-1), (+0.814125490909164301931361650801847649, +0.440529092092549587674978198262484668), (+0.475167490226564579949362212145120410, -0.161789304158698015077173180162728587), (-0.296749552358110587080404215530195398, +0.352513094694014911950171113726064354), (+0.480015806474927500264485210024410400, +0.241195860325153712327966634235482706), (+0.934810860375607710073626047664422810, +0.720375993422281663387070246108417003)
(+0.676708516735166102811804031558780956, +0.277049511758478199469200006408395033E-1), (+0.322126747556997405013598992051631102, -0.193341864486762910804599990835986116E-1), (-0.709513607116088249098770819803709414E-1, +0.825696590470441387285501661995773881), (+0.679338268423490549818678696475149467, -0.483745405724869456512766309131994988), (-0.328762035031338220084631866845036491, +0.744464147996570340691751512326330054), (+0.262904965910974800295073780387752319, +0.720812268375403848865700992002478398E-1)
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.999999999999999999999999999999997496, +0.625927231925851652243192831340101379E-33)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.10596512531649260764630944417513346, +1.74990434199524069898170353387156351), (+1.06862406371943089969097073555961101, +1.46772893937515341770247768241660249), (+1.87255461496056049341868726083975884, +1.68487381257604645323176638691681923), (+1.87080736110516451163318799960598040, +1.01713505781341573831472608313194429), (+1.66031316337943732736785861582621008, +1.44194233008569092891337850952319570), (+1.84691867609159012905472911499955793, +1.40567897410800995117942458285952781), (+1.65427746546393812427048494031409866, +1.14597680029722141825027039342937661), (+1.70646596575399608474894897956479816, +1.33468446539314742379862407481491001)
(+1.95579832263043425908246799141546190, +1.68594050123056057900987755519747624), (+1.60466699838488906844432319170350210, +1.75465268920790462112001840957981172), (+1.91772036948424149440832977456879208, +1.19956878979612630861486453996357176), (+1.14668915706706059746578620976487300, +1.14716107584542432394386199004077223), (+1.02156669305952954478927578747209968, +1.61327443755750269295731605131332578), (+1.27633732345386699288197688156989321, +1.68892511681261276390641634431379644), (+1.86991251868586877009958073282458735, +1.85803476615481866141685780533788657), (+1.89403231290521286824575752028843596, +1.51846119318257510094725099435750367)
(+1.74028417887323076529875858772150839, +1.89021905856041993206262274910817703), (+1.07224415089623198087987210355219946, +1.61602297585419716422666069469943723), (+1.07533829443369414335188918300521823, +1.74153771943452755712368059397352240), (+1.78646828862474080609232750149611391, +1.20283929914680169598070075711351391), (+1.20938416070769442908221762375260494, +1.67570381741135131883030076254504200), (+1.91115906692672586432920636004333882, +1.50404822651456239717395352817866673), (+1.15723951649842126415025129073335342, +1.71916222061063867190052196716030848), (+1.55318522320036267991902046455741017, +1.67487685317068368228781312061815455)
(+1.82961321171472664492057024766807051, +1.91788237409912239068249751786345056), (+1.19064900710962735178477237335758612, +1.58021945977486564000919240461459809), (+1.08167037826974616123252834145436456, +1.81138834741674535789730321375696194), (+1.80292126172909668234636454455765492, +1.08237973900773632604867875443025447), (+1.80958451736594471248744033967272477, +1.39389078699279800099209932711052974), (+1.67974994965859326988092264260622144, +1.34808901106025563050109126429627089), (+1.68012333501119489741986934073767272, +1.95858969806355041230383965598116708), (+1.23648682783017797841444794297211721, +1.72887509804306857811110820766562993)
(+1.54522009757329018402374759618420850, +1.53988930827923776262708905606317309), (+1.89576602686805320302781462259541081, +1.98314112486296662980759739967630732), (+1.62860768354997023418459579210713325, +1.10603285773199225165427546503836573), (+1.78589353258472729170983360034188667, +1.06489694559020850042814870538976613), (+1.82377556356998732272931736486121275, +1.24585448957041144761077567231633560), (+1.39672041814174378250800053280010045, +1.86295401734084561488602025304666924), (+1.18853775011500214619036415878344045, +1.68064069201125307391545357059071556), (+1.27730619027997852270451539862694746, +1.54703575771060262433494845047624816)
(+1.78721331652684356487015044437644811, +1.40063641926148084665925770585749732), (+1.74971010693912392332718994418815957, +1.28073326035075755305326060293169973), (+1.47072974833534132055390681785826665, +1.66342940653027218683547771602855617), (+1.24802307423150425255056466649090466, +1.30591617058969042648121513641429665), (+1.27178574222051155191696913182980069, +1.92730031973277223761422059881362546), (+1.34607949131778486096451943232854606, +1.42626032113016051279276862316406957), (+1.29895417358129084857711452848749436, +1.78409328683685932433536660824302864), (+1.84639110032785953193881484059920673, +1.91958456850974515043864749344862272)
(+1.46074601674034828864851673254732729, +1.82311732763575117648940764681792307), (+1.18941454185004750609139436757938341, +1.78097646398864950400449043673093216), (+1.71573066329980100997960119334680376, +1.29979143690022957465366954382874678), (+1.52159363875252877134237500036935578, +1.83661711576242835698830257808354773), (+1.78004777168701633633050874727248310, +1.96223720380623578169056863496321051), (+1.53868341494708999738336459207461340, +1.94183260221869103274733796979240810), (+1.20038144556364529150943271451908292, +1.77550739580042364943591527043695410), (+1.69190192953952409948778671544776359, +1.83867141683996525538191194167266933)
(+1.85462131569401058983791398461870959, +1.24570755221259384695062114329339240), (+1.84341874290304300109192797469567630, +1.82991517085169235721991214624393537), (+1.57512805911476108915925550157134712, +1.14774472359144696665244391480995519), (+1.65241572603967546932610152931586038, +1.94881850023606192703067789526743731), (+1.09638207556418515462930308120491990, +1.89395140743530846221240397139071084), (+1.41568203702061882452827250816722765, +1.08152612346951932830021031055578890), (+1.42164120901314921587764320215601187, +1.57105491544364933872959018633872445), (+1.96339777769072190733276971314852178, +1.92457253325042663018143377163472191)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.82961321171472664492057024766807051, +1.91788237409912239068249751786345056), (+1.19064900710962735178477237335758612, +1.58021945977486564000919240461459809), (+1.08167037826974616123252834145436456, +1.81138834741674535789730321375696194), (+1.80292126172909668234636454455765492, +1.08237973900773632604867875443025447), (+1.80958451736594471248744033967272477, +1.39389078699279800099209932711052974), (+1.67974994965859326988092264260622144, +1.34808901106025563050109126429627089), (+1.68012333501119489741986934073767272, +1.95858969806355041230383965598116708), (+1.23648682783017797841444794297211721, +1.72887509804306857811110820766562993)
(+0.822755671268166806798572185926688182, -0.208018239004743799386705741205223408E-1), (+0.883281356852455925295655878601243606, +0.707774273458046270827620381258110113), (+0.700977063967418877811572912583312468, -0.361796461247080651846181254983531039), (+0.280014366922873741908625557212258300, +0.211866927448744955315526861153757473), (+0.305934168580569998192693721444342526, +0.136665597906909919121922069329609626), (-0.133460894625216206860258110836029859E-1, +0.788748000766354608805182099519963340), (-0.234535490187845876272181554684870943, +0.104149539988041106229127660433438034), (+0.224015884898906950916528616098029906, +0.150315147129139581014537987151679457)
(+0.765696687920312605240252549761840504, +0.153796528427490827630266769327785040), (+0.317005341864414883356473578485977783, -0.169510853353381184819952762416309314), (+1.16202338144872999645500818974544211, +0.365057236518089399708904751377100534), (+0.532102974935198594980904332222261709, -0.108620027976256458033222171923191093), (+0.368946788142871979730494442934747463, +0.104872391896113716428255738727978115), (+0.638600547977951635702087815051793619, -0.137187664207876202327998659271354237), (+0.725731414570859166515689039730562248, -0.684878252371950000276115211454816241), (+0.929092804153859872662009116717143871, -0.188954433362084018922013986044372721)
(+0.823023051932045209819437101584782063, -0.181871146554130431911834096909271652), (+0.809270584779879844077673603291334239, +0.195998621385269823941533770240693562), (-0.219233831739358608329881191024875491, +0.766667722428378338756267530582868841E-1), (-0.105038014962342535541361469636902481, +1.09494647642311559368447179148835118), (-0.778327621123175195399462504965545705, +0.900001862153405819872282398686959533), (+0.829098409435125829896177547167535748E-1, -0.437214520166946087735767948035635611), (-0.536666413095248343871142281267999533E-3, +0.205519069507826628977045963817051589E-1), (+0.668682263073963424660055259894752785, +0.448341568240568587111291668874597731)
(+0.847761278709118329393054707661560261, -0.123124381249600913118493272036642384), (+0.424718136264329485171109085662781066, -0.241058249322586102534640056736791175), (+0.237760249504029498325456074908674464, +0.427552691110140246851513342211236910), (+0.415126621387956011315488664279967827, +0.651210088136853414692060074506380282), (+0.269500358136768484557888853620191406, +0.934682643104084303252820843828863250), (-0.958021354254191457936858220397250749, +0.390981168659094563459640129541061149E-1), (-0.743799335923629031012764629182766070, +0.741362565285750127166093792624567033E-1), (+0.166587884121922932232469909882762917, -0.377569243251951634582125620474177565)
(+0.969185874981460029709855861758578854, +0.171809820274425410845968993885525992E-1), (-0.224138016517790755733601195274898525E-2, +0.742984866444265783563846981632831687E-1), (+0.465767413659262530556690448326192674E-2, -0.750511717706936057514378830529507317E-1), (+0.122438832847733156329395889976607325, -0.845724039365849301146740558485514162E-1), (-0.214862357908178481337984409353850090E-1, +0.528808253169317468988299853452272685), (+0.399141239144837153955076802446744245, +0.787959408622012463270588923067199181), (-0.360678627656882268106107487749807773, +0.259732982974347308996715023296542785), (+0.901551744131604770218552201106569537E-1, -0.622140071203683013864888129264454563E-1)
(+0.969545306728170819336058959879625085, -0.948470159281856015515510851160793021E-1), (+0.392455879345763726815044036069844392, +0.653445908359842571772496654272820014E-1), (+0.224024315339998806374261653216791048, -0.378356140749313011267953774574325239), (+0.431845046011978964660389367385413238, +0.760567687542386763940827890446839407), (+0.648737142694276565285635206433112562, +0.270452187094069701677560925557625325), (+0.744690783653635011815118633337204135, +0.695455495427522195517855933610145889), (+1.21825750846095256834750515207549821, +0.722929167382742946579997185045758877), (+0.481183006489814876947793822107316303E-1, -0.238928179463612833033884899931386562)
(+0.878072573766192314049197329103253042, +0.760146539931110002038822356684911830E-1), (+0.349408824248283502957912715937477219, +0.629694563033367375079924326344959341E-1), (+0.426570899368068412653510848093065752, -0.384165981710496934490999648089134518), (+0.843543120849468165787919804790589346, +0.146464810261117324379828601668401922), (+0.210558461722325487789608617389659950, -0.783926599779419644202076657451622819), (+0.278900569618703159450164824832069329, +0.931336895443557795058238513554543555E-1), (+0.227435529796952017876880031043811174E-1, -0.159165428815389012386512506510186331), (+0.113564848627802687672011789061306493, +0.353510295697537936060542962611975300)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000077, -0.794446102059734789385590901316282519E-33)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.40249967291683242234294815801581119, +1.23422196164731345241187845331337299)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.40249967291683242234294815801581119, +1.23422196164731345241187845331337299)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000000, +0.00000000000000000000000000000000000)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.80099879744533496662648020979936737, +1.99165323133682864126956948513121339), (+1.77229834187419408199516377667061507, +1.60375732034298376775410155620774957), (+1.62439946473626063311405783040927052, +1.62309992880764288163806328337825425), (+1.20949646375003889655126765572484716, +1.92327259107643464187320072305190707), (+1.83739752881116261925512445771340936, +1.44104933080147004396777167468746570)
(+1.62647289262319555598490494262480100, +1.01135961879297475215955044887042147), (+1.30448293549352624582362643899329725, +1.54375681356484435823644915587453756), (+1.26192509899407251029759460508982693, +1.36510852821579939630217008208264043), (+1.74405190551966634919890120040185620, +1.84867708477607360255917086001541106), (+1.57241712712096757223933331536000563, +1.65981824229558798189688944602980602)
(+1.26919009580137632120861318457475707, +1.92014471026214165923662411492877534), (+1.49128692042757565170514979530911719, +1.77864134326495466605631742901690743), (+1.70480849912106222323897476971441949, +1.84144397138700159982354311371419731), (+1.44180867830362860652858079102629586, +1.93506345545653656828456521651025573), (+1.87820736150076200147795813850992783, +1.08118180744736274089408716481447683)
(+1.59966311919535595964689020079622916, +1.25982868442594601080015686839075518), (+1.90668764684577928619423835872484695, +1.98729106506864612421944776913241691), (+1.41925173635022816165991408165329596, +1.66658284016983931198679918338270260), (+1.33231078558821607411206633749476181, +1.93629381018168576909201998062565081), (+1.67049986975189300367893372807458130, +1.62166793073235264567303091612727190)
(+1.32774585559112027433887037162105393, +1.56366526880987175472332257125277716), (+1.63966350018754944580175490087009750, +1.25647282719482704833854490858825293), (+1.09335369647711975627345686021975516, +1.14591390396565299317402020165960840), (+1.30390434045211133746135301959090638, +1.01561140736271911161909121075185685), (+1.63965337582360733181062233177656629, +1.31219770502412560610781801590445167)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.80099879744533496662648020979936737, +1.99165323133682864126956948513121339), (+1.77229834187419408199516377667061507, +1.60375732034298376775410155620774957), (+1.62439946473626063311405783040927052, +1.62309992880764288163806328337825425), (+1.20949646375003889655126765572484716, +1.92327259107643464187320072305190707), (+1.83739752881116261925512445771340936, +1.44104933080147004396777167468746570)
(+0.747562338180693762477817399702750096, -0.127182906708354005735416730251704091), (+0.377813636784518686379478557018282828, +1.01378854747259739216799622362646852), (-0.151869247135671463504529156886717207E-2, +0.659810307870132232759903506884853144), (+0.183529382600347812394021409311604012, +0.652354930950950260253620539521589724), (+0.113653834344932307682704274828813271, +0.778079282057631947086043281676135534)
(+0.847411318039820546434695796268789660, +0.129036854853194804753850955117198992), (+0.228728571723731903528279689821530544, -0.108452866132345730620165469163641831), (+0.466502766979190971138665791189206750, +0.105321147571974434621210554410941707), (+0.552312556421848955346370394257115349, +0.198829504133911063345001461537222532E-1), (+0.396743565764718308449575733457827315, -0.542714582351567321226435711584675996)
(+0.763569270247013842203583469001776661, +0.238201515924135964705410101436402199E-1), (+0.958298271372263333606024935930818055E-1, -0.284464523027509472500578969950777875), (-0.693634052293545523397429885972651963, -0.263098017610679521824053477028466269), (+0.600894861451805866748046347914095635, -0.332954462427950062033411035898333076), (+0.456753697948446959756143781783845006, -0.146205957221996960780054449185371058)
(+0.685625784615118283208468245168350172, -0.196651541981012362445182219056211655), (+0.613610092702100426840677476309360765, +0.451634729518058161767268796344731557), (+0.338087275008715844677678286816613489, +0.282789139083171456905603097510711450), (+0.598426517795955197533201483495237343, +0.534269757745520517157239833570938622), (-0.328120768762900278536302247649775867, +0.419111359506963701602499089188818273)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000116, -0.770371977754894341222391177033970927E-33)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.92474838334527815687916548217204222, +1.09471535865777783381148643574301439), (+1.42185735333306672741169640460936467, +1.31500771223371881112534644290550592), (+1.28586390475841898491488697599013489, +1.72481396206496603871353359514969536), (+1.43477748444879376074585454145173871, +1.69382689091741559520212609127895202), (+1.87192163704299481769931885297695035, +1.69891718330988773305091021668471909), (+1.10296735470677371691882048614070839, +1.94182841517588495966753797186476553), (+1.78863680219885132783363902131366020, +1.70016492628221828500581451947501464), (+1.47815262016733804891821548831266056, +1.57716944575694604086655249007495239)
(+1.18508295422401778261268905025846779, +1.60395435453876597941427314165888581), (+1.15048356960534345925309329676151077, +1.70064422241596601580206330497111756), (+1.77090325628737126621875285328963495, +1.31104896979383522715474586220883540), (+1.75202141093168329111153648520063471, +1.40886304521921109958020246122445700), (+1.11972544784828486358351789108534949, +1.68847460663903989008833536159186503), (+1.68445517851940230080189068149809625, +1.40810166484223229381842223289787894), (+1.81892776099845613560520595136183646, +1.20490072633693901729336601352501954), (+1.46306870048762656191549298090465782, +1.02389407888292384989786600555578399)
(+1.03902167426597859082748574105866335, +1.45802175001294614829076304700468891), (+1.73157022601738010730494467102313276, +1.02425699911924310516389359783469292), (+1.58687732382052142357972493038874093, +1.39346556630749284762746882861783000), (+1.97315713983147504301068552978280193, +1.19886591539936414119328647653779480), (+1.02456372196285333798389805567276307, +1.53966231337751039080967798477661647), (+1.33346681450977687126634616070670520, +1.35345379290126227438444471362732293), (+1.79957851735248965373717708878331291, +1.20732137426131128716641999983786779), (+1.36878613937369872166832134952720833, +1.38611186433430544674653343741029097)
(+1.56584864939046463157718267353061247, +1.05696482659952074438503985469975719), (+1.68097374587100649115857067432404329, +1.26293034742564844567839734513788674), (+1.41310013890190263588700047452200136, +1.64395517942144987658902767752282705), (+1.91481532383641263599435690952417312, +1.55981567120066233612182775838011813), (+1.74210914215443189363775612507195752, +1.84642598110077150395222530316623493), (+1.62889270004548454937431651211860641, +1.25850695938672459645247589062010566), (+1.00798593641048994730409307701794828, +1.82188059100742765989246588841031984), (+1.34556138452607982404402900312770930, +1.50741846426490818104588429753963692)
(+1.62682985058935047758993248613540724, +1.37143733044612606929132711408834999), (+1.01447626479823247419020127963133016, +1.50569722407890212082415011856280396), (+1.47667892576744238286373125697629015, +1.19938638828973052707530350292654605), (+1.30483868014942525077838372220317451, +1.23946419850676966801776658356462960), (+1.56786751898226697954140874435031157, +1.05313402132111306131237776879114365), (+1.16294291737992652239064765712171933, +1.83471799186481420788626503826862168), (+1.18631514931850227993277045620712290, +1.21588964053499306119393386822120266), (+1.90666252655312373635400588333101672, +1.52248242307472189592462198742946612)
(+1.25714243463020582740148675260680593, +1.15212046917003073297297110738058582), (+1.30923762210989158489119905333801847, +1.51353212836463035860703281969493041), (+1.13800110730817915220340868959675906, +1.48999708028361461235011326668516748), (+1.81973662983320280878928132916386527, +1.51643669241704341228464036836747681), (+1.22025010368488041836609503147549892, +1.58087394323667693546285882664750148), (+1.09677346387570722452671284176229558, +1.58838463999601167854623682925142370), (+1.32006974660479011386383167403517581, +1.40820564293229703418117027642874208), (+1.79039142918277897987322622065308577, +1.28422812287130234067705013464582885)
(+1.27125925799138127714039786595413968, +1.23403103877847474101341469977774378), (+1.06056004763594678015016498345009762, +1.07924311002768499999448427610308638), (+1.22192736923291587694097366814530800, +1.27041387856522517313183900961255275), (+1.51010774247647934787609000354951115, +1.50298948832271646499666299317137855), (+1.75892817296362552553028520680416298, +1.84089074338815261235703987324104345), (+1.84921377293129930032180340629960623, +1.18136127793110266926375847435550920), (+1.20369498996335903428859646948794410, +1.84502175121238453765594314817514909), (+1.88278527596852977420041756517416374, +1.79185970369465138935154658192994528)
(+1.08591835486387764615360558455262693, +1.85205334307121493399896195356616684), (+1.18388925610027086039685150289653179, +1.44921610974576076760343133520694970), (+1.72243243302784932180969965823405387, +1.09072720664990971709979379396826853), (+1.16153177302050799182498671688805042, +1.22980930249814446096398306868048261), (+1.89028829878647136232994673546298668, +1.76255398249949045161937016405233479), (+1.91232038274361634037840494397239249, +1.51135364737288721454416369372319925), (+1.94283558236103224792847361910539003, +1.90925279913234170205549137441400356), (+1.55137764396945121890792045677178793, +1.01339751712304029059629330294185820)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.92474838334527815687916548217204222, +1.09471535865777783381148643574301439), (+1.42185735333306672741169640460936467, +1.31500771223371881112534644290550592), (+1.28586390475841898491488697599013489, +1.72481396206496603871353359514969536), (+1.43477748444879376074585454145173871, +1.69382689091741559520212609127895202), (+1.87192163704299481769931885297695035, +1.69891718330988773305091021668471909), (+1.10296735470677371691882048614070839, +1.94182841517588495966753797186476553), (+1.78863680219885132783363902131366020, +1.70016492628221828500581451947501464), (+1.47815262016733804891821548831266056, +1.57716944575694604086655249007495239)
(+0.733414544549570896973733181620985234, +0.340377781065010434548514196698399244), (+1.13635876998163965737453640325220206, -0.424157434146300737068994196492361072), (+1.23089438291701497736005946690059492, -0.309217582766385640648161535687258192), (+1.49741150318319932331517329116276434, -0.531777738827365859133842243049938019), (+0.229942828166715298516234057799279984, -0.343508791991427188640677181076378943), (+1.18548976157101696987434498188187881, -0.446136990590610387460137724197367199), (+1.06646463675571667833527605375008810, -0.648416536670777606657110893115893391), (+0.821520944989197251249871554556511761, -0.273737455331014013566180112850398227)
(+0.823335135120988031437610590587899396, +0.365053813204423657801108256157251519), (+0.326684980287198422542207984072083940, +0.208968849097261688424418660674680335), (+0.875124688825745899618361783501049296, -0.734662331043441916715205250527379189), (+0.588749832884553813069675153382537585, -0.648683697002929954505802461215145324), (+0.518012847593177090818601766022560762E-1, -0.329487458883156459592273428674580174), (+1.00470483719358260911591384646447267, -0.695300511539681860133243979661704395), (+0.483035090954174262360979792366140432, -0.858883422297637873230736160608908166), (+0.496224278761137758432561297329777262, -0.896496561523269150002817448217544154)
(+0.839800547113619126609450312371542716, +0.484588424132430364792013341498252699), (+0.583546058557054465752875901076830739, -0.850332696753315035999636628398577218E-1), (+0.918645777612614289982018907516118879, -0.238630469867544977036507406120134808E-1), (-0.576548998938996606884641235071577573, +0.159662496489867385295020169285528199), (+0.996826072304513418282372739669804119, -0.473847622037376489571688935175864068E-1), (+0.366808108008518512816891198810380674, +0.369977620484794894661494411908843251), (+0.274180831253259746653407208942459972, +0.884302882295126906119505345995739064), (+0.183722603671866022873619238407166159, +0.375933342160347697232830726177431547E-1)
(+0.774571071711024471257844331037023830, +0.200595669306838394031421814309405914), (+0.236991408863450614593025539568421931, -0.109138579974976658861637242360450174), (+0.275663974955291485630275443031719584, +0.989848235585602078703569517751251308E-1), (-0.206958726236662028454745047818129628, -0.600516390748698497977191028833238227), (+0.820646015376559709077301608484292546, +0.930467519300957571578379298077862975), (+0.660100792357379233964917962141157475, +0.802031396189782875649383824167729777E-1), (-0.715127367059915572968668748262786455, +0.976006326584538094739082627835684892), (+0.679323159933268259648115873291308851, +0.744373752623034597593656700027572637)
(+0.944833118713958196327018540127616360, +0.175147051395628625174140062492519781), (-0.802687420708116491992195506799953350E-1, -0.174648367649736029507333267366788995E-1), (+0.818517329994575278201343937325501036, -0.656815264235327111556578556267530585E-1), (+0.766124769927426639592481375843593715E-1, +0.123758740327578111778617403474032119), (-0.443725272419940601048345712837378636, -0.410954287139648568739989762307815395), (+0.648073791601777328873482888925856102E-1, +0.659951109305607946135383906773621437), (-1.07788035174037438254595947526918142, +0.350716550114138039627663318445313095E-1), (+0.495836207426317590034906352948227130, +1.11604314657563912317937834436342067)
(+0.850681398906260999026444019749759267, +0.653128663362550035970108257608998350E-1), (+0.415641720447723707209148197863216535, +0.200385388512135463096906991276151683), (-0.806621811234845912104527000640543574E-1, -0.967684035843053810690720532086844435E-1), (-0.321926522242545738304576025894182996, -0.384455147942041792217767063316439700E-2), (+0.448860559074455254258964342404479368, -0.914025193305461951700539927613375767E-1), (-0.468587511280006112260545929615574656, -0.344023276044969489628687650520692365), (-1.05415380140020721465428650033607190, -0.280073249316099433100922160699927590), (-0.543958913938198812055000830284935149, +0.428392274577850463270154563059237115)
(+0.750741027236227333838053849886572647, +0.171592681483898856817738349775180919), (+0.279650051480843957738561510202739946, +0.352826264555674092221959793606748875), (+0.220344919103899093496154905622276204, -0.241652882012004354097453069401266684), (-0.773914556164233119631476145401253537, -0.481693353862114319280079496499900818E-1), (+0.464536631093282901672733175176033462, -0.410190618332269171539878301833881648), (+0.870383896293159487359079497853423233, +0.106443499299915755096759817188605274), (-0.778645295829905491847439759600282733, +0.234388865487112080638410104315368425), (-0.384151165225567235302873107057569744, -0.641602887370152882541047642603289609)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000173, -0.105926146941297971918078786842171003E-32)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.24457568550838670309386292129707489, +1.11901764359731211857783587789997764), (+1.81356570623683253525803317619958588, +1.57659699350368487885207959456077107), (+1.97983724415368319133076171448322507, +1.67663338719167981906528203151395624), (+1.84065552371997079857544793895566661, +1.52181938613869914008892738983468143), (+1.51839632215120097449467617706424026, +1.44761082315733080284235770163166712), (+1.75736889627385056809504551464303834, +1.75972894299238925221600471839891100)
(+1.37285674625083383758896844760965488, +1.00122337318151186130645201000044515), (+1.00029055221608096427739961164712453, +1.63302820983920953145961413891591132), (+1.67772750108655047041046845238904738, +1.56290333492994346160154641028882417), (+1.85255860738629612653203186171096564, +1.94320561392835273190779805353893544), (+1.32384436959619839987425036471585883, +1.22155719388276079867622611768766414), (+1.19825018199547262284827405864235407, +1.77962615870029307983877364494639736)
(+1.45949802377174024114329583400379233, +1.41978711323309171452899408546490102), (+1.73491255378016363472239399344647840, +1.19862565831474198256071363977794998), (+1.96294125077685629926992447368945290, +1.50804588150893001257039277934752405), (+1.08068362802466128566480401996712376, +1.02115863019358364027075613317147026), (+1.37948642699542812445415865360428184, +1.25306156948589712159645221986885504), (+1.69604044448959889079729205198885126, +1.82535659919048876366093539693075980)
(+1.68801027027974808486184890460796342, +1.26823656339798894150874081188440068), (+1.89573339065671490115814429334277978, +1.73355089856309450602263475109394562), (+1.80174424723209726710330647262280539, +1.04969244529407243260562268453432427), (+1.77093128091241309616156344289959997, +1.60097076260481827848686046995035759), (+1.68633222092579597928328730406224466, +1.11226045889380174819188329815470509), (+1.85855039196821331039203202426686579, +1.46520205664028916761411452772825150)
(+1.80551670948289656293871404547722698, +1.36251511025978631281301103412127949), (+1.76142994808384924145762536597237227, +1.60224825110040678866833602246453608), (+1.04597253050026736821396375030637403, +1.52644298160858788426497706085332427), (+1.34218655118373871776270760015002396, +1.71089352481257249519808666171254956), (+1.79114673706335384898271000944434489, +1.81040213279090975472903179098662423), (+1.95124948512133841313517133789269275, +1.41248785477548080186355840702952937)
(+1.93016297647656983239856212264831925, +1.83742067837491679973733754023325909), (+1.82132816046906261411382861883244697, +1.02290763538567620179905306725952427), (+1.06762017360704875803084418872439009, +1.61303406167107283737165767267974598), (+1.25901173412717569152576475226072992, +1.13446381887085410887712349343193935), (+1.53006579386658568455301567080241940, +1.99011091861295297132009521312804910), (+1.45351247345139147604673707095790465, +1.59815521342741033728914725706000517)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.93016297647656983239856212264831925, +1.83742067837491679973733754023325909), (+1.82132816046906261411382861883244697, +1.02290763538567620179905306725952427), (+1.06762017360704875803084418872439009, +1.61303406167107283737165767267974598), (+1.25901173412717569152576475226072992, +1.13446381887085410887712349343193935), (+1.53006579386658568455301567080241940, +1.99011091861295297132009521312804910), (+1.45351247345139147604673707095790465, +1.59815521342741033728914725706000517)
(+0.632178391154013645428433281270214546, -0.830781012282078277695423267226650825E-1), (-0.236094978112428144833239605570022469, +1.13768059188717068628378468795748410), (+0.868793290312021028136065997198873218, +0.631873913802303819723350295217876662), (+0.962389494877861374277646016610937873, +1.33061840638745681813800687843250017), (+0.191235201317943005874457338312179586, +0.905670360446543773151336113914665571E-1), (+0.146599304407170506233394667667395322, +0.890062023467210950973968451908386593)
(+0.627789868388829691481970752999639633, -0.178722950730113229919499537055061189E-1), (+0.700864278988217383017567066335977885, -0.718429386443824611645795783479881806), (+0.217904523955468290011294188448163461, +0.864376544173964530828986912898420554), (-0.600474543993443559770297571816076752, +0.590941908134469562663355761257189618), (+0.323172727601511094087212025591771824, +0.299498926763011525447073169829946910), (+0.741128611174299948268173174451402156E-1, +0.263909465693893452456984529171713310)
(+0.786919074010948548540041194214834828, -0.920465357395306803061458628687469286E-1), (+0.859386552100595418761800214490628233, -0.502106892051584652429301542608094185), (-0.316950717020956108454060265864181370, +0.210201389633749821579118208950524642), (-0.885513820832388741412505727076729420, +0.477354092219245077688292881421255285), (+0.254677072487461314346305780000366772, -0.267775063686005341638741111827559378), (+0.737215651333285124553413471726333763E-1, -0.281857120607058325024054329651869774)
(+0.764022436713396354099459670381737260, +0.826691293324563577458102407911274358E-2), (+0.277271185217108521457304971581928870, -0.366795039227296303579322754391555119), (+0.634952838781693976784889594294193062, -0.635801193034921266060234327814095499), (+0.246891965195087295045205039474843346, +0.843358192127900791318043670484642555), (-0.543638878217748286632644151520432684, -0.368410822560014994026459564448784619), (-0.239141883428895455040986555919179183, +0.286262996776500401166810973314398787)
(+0.843249120628116575919633667267288328, -0.968251195787291708230821457086119950E-1), (+0.749800313237093906325632521278397655, -0.266838966038531586845228032275794827), (-0.197640074922479102109428688077180293, +0.910995167408843470134636706844829078), (+0.802454080305675560764757543268076245, -0.469823565249333753701626911430686991), (-0.812687405523992316601122974218407619, -0.116668090599899099883714712317866326), (+0.323998877811030260939671313458735331, +0.275292768289228545170421728252353190E-1)
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.999999999999999999999999999999999037, +0.962964972193617926527988971292463659E-34)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
lup = mat
lup ! matrix.
(+1.74349686056219870624506720628251335, +1.06503421965591386431069904018127988), (+1.70307174532941198089315511153511156, +1.49550626034484380415246650216212714), (+1.93651324970948079248786800595090255, +1.79654693346542096792337633634610664)
(+1.98075388974614448462609704505924335, +1.79841222455118682844286868889606196), (+1.85662190591441796309481975260312396, +1.39092718137245506981233036232155427), (+1.75438473541343252345480267764226188, +1.83401917471000345709814809959722124)
(+1.43765686165524940063836263877196342, +1.39463370922806623336409301717282279), (+1.65952298144091512015955614602699872, +1.54864352429474856221499895143859416), (+1.79380878080339566898071673918562360, +1.34275839907095152238703904089356854)
call setMatDet(lup, det, info)
if (info /= 0) error stop 'determinant computation failed.'
lup ! lup factorization.
(+1.98075388974614448462609704505924335, +1.79841222455118682844286868889606196), (+1.85662190591441796309481975260312396, +1.39092718137245506981233036232155427), (+1.75438473541343252345480267764226188, +1.83401917471000345709814809959722124)
(+0.750077451524009168266742451712484675, -0.143336453859722680815605636402152671), (+0.111090947942449603484764315515466754, +0.718324745037571782948241008875498931), (+0.357707013564283127403435109012446167, +0.672357791532564302675427146311715434)
(+0.748255907408880423598533273538843978, +0.247184359979066476811697814777546196E-1), (+0.692177621286907859308821227607174790, -0.317101075114702450265486279988982560), (+0.656119559280396098640915850648590776E-1, -0.424884667724414838914319725550007644)
det * getMatDet(getMatInv(mat)) ! must be one.
(+1.00000000000000000000000000000000019, -0.625927231925851652243192831340101379E-33)
 
 

Test:

test_pm_matrixDet

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 395 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