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
+9
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.49402272699495955229968775346136775, +1.85237859119052848993428623004310583, +1.59489728699916983445865862359433522, +1.93658818799610192464743346780798548, +1.81851967447870033398198584424662113, +1.02510588460616795213269813095252423, +1.92107084625127376423261551257252226, +1.16935554870566144873085922744295611, +1.50653656165577174144493849606245770
+1.94910385368816601100604329999531410, +1.10900538620702539375600446403730221, +1.75115739896550289923339469421091949, +1.66700273789256997737671367842785779, +1.28653975576022225524092921502559754, +1.91084292610287752425950255891319612, +1.09959050459096343005292445000894733, +1.07520707555084741847715945280574046, +1.35041877050326302274694067755651219
+1.73628509429831731194580962783870552, +1.72617137000275159495580901305968628, +1.31690247620684536201050162069941299, +1.31481071647990743940026843009048375, +1.21936741289044879340958013234744695, +1.63422218934515603877616470227566096, +1.50354141048215485501346040396057462, +1.41367681453036919564715351807178214, +1.86538914658007091786611610185211739
+1.20571703667906907595842337738863478, +1.32910856021534916504782623435891903, +1.13586542293268578165677633487674690, +1.09581420885105751688064640196691259, +1.55287724754859887435067450424926084, +1.99100462856035206026910550068809563, +1.42205015441976430803559907612724183, +1.23367864551498290524680351737066279, +1.01540296172634488168466320750798092
+1.37022057017961127143429219144238202, +1.24524331858503539985706542164274871, +1.72943312112610664246432932345478839, +1.55303166578794574789135712430431617, +1.75799713746101806862021047509304061, +1.72425049876420401906599487292017892, +1.93290629246226979854346233652419816, +1.37922722786235467664691080500019316, +1.75177954425251237005618181208882097
+1.94881843562449333965809146829395033, +1.16499575000018091065927234432881184, +1.10425283609488807097917500181457648, +1.82307157758049403366740893839272469, +1.28140125496685711142004437385900865, +1.87548308679940348205837224570248194, +1.38267277265784025537611475507036557, +1.29377868031281650203536566405624491, +1.69091257285227413487797073773976701
+1.62229802713976577359938748725710689, +1.29314249011570573121150381817749367, +1.31094645797093657886901034114757573, +1.97745165473330343709479750649538730, +1.01792341546566074045980039323035594, +1.18512771296780952612828100719259259, +1.95143763098583021413635778796290127, +1.58968919573004566475631043116911505, +1.87101395015098579114454791538859052
+1.32280911625412560936755934971457940, +1.27448769231685373711596585840053627, +1.93294986242146200704766964186452230, +1.61882478864143899376609321109564946, +1.07297791474644594876651255837406627, +1.20256116248010243912574904235601016, +1.16122521248699632836529341081077427, +1.63617033224710813799161311091865429, +1.18861491080196340992406956050104999
+1.76476994117808388757893381536740285, +1.70553202520638216677482644902068293, +1.17617918845810318720035153949871538, +1.72008499777548860090542344406581309, +1.26334385706709138524514788227367137, +1.16269025733283316062830031045647551, +1.20238658016550898022547189742924917, +1.16040329209635799725384869745558736, +1.04670786752624214872450610064660428
det = getMatDet(mat)
det
+0.700562546885857398778122954709650247E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000096
 
 
ndim = getUnifRand(1, 9)
ndim
+5
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.23628321006451491424024824364077714, +1.84564118143214438874265858541717766, +1.37224075357606449198863660046821652, +1.70901418995622989563344925962301498, +1.53803492122739706157749617579171243
+1.04068772105846838870366678069776326, +1.41361414960964293722946740851887823, +1.48040296032698150151233551752666894, +1.47900539669768120797759630589630084, +1.83860374735656624556907913738304227
+1.09597194752290804434366224650854273, +1.01895939544080508364105825577573706, +1.07395862568612990418172644417418630, +1.87428831780212705101319816316388340, +1.76372183426906124558799982120800557
+1.97340939837643406580666587462972107, +1.19898128769320963299795623747479212, +1.31744836887910296841994937915735759, +1.09317287664291150353135251631174046, +1.80677908897636311646299862040134433
+1.71530789234513759257461551664970883, +1.13600577517119037479142984717083108, +1.94004099746720844927539973436868659, +1.01875097310141377571417499785111112, +1.10757250517436206898587017783743247
det = getMatDet(mat)
det
+1.08881967688509821976451643585285958
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000039
 
 
ndim = getUnifRand(1, 9)
ndim
+7
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.47527565792525574667017148352325835, +1.21419205551870990028448565880994422, +1.72435042098148928149422949795493562, +1.79696534083779717684110587867641691, +1.07858384785475723151343860935150938, +1.98155654372547836517837417844227146, +1.56042489063917376975867551593182734
+1.75057181475874590286368197545039594, +1.82031583134333053373045131320528679, +1.25170085550157780901983011681940305, +1.80659455292972744199141350955166976, +1.41086109424444556966598101436130105, +1.94584308234005666673493040578709408, +1.77256202480427362666847666761647609
+1.35429786743591557746981173054130295, +1.22006772252613200021623407883123473, +1.76603172218536132344374290043900830, +1.69782697212912788560991950639670472, +1.48413600722401515290840052980668251, +1.88933018993906925781390102521567303, +1.60913149444224036167395287237948344
+1.87688679056718594963787862287071023, +1.91597431470881347689070874879192412, +1.12232358344368709750114733506195237, +1.43875957270364912033002978973779409, +1.44844380754626351918478984459957015, +1.81194226359468811376518013049763476, +1.94212557706730664369089630208773686
+1.45689785992368720245008322242812153, +1.76037626673364314242695395947767973, +1.87109316762600837604357631149627941, +1.28410517646925737238442764216233170, +1.37803913486648113693908150615793871, +1.01308318563294080200589575679728806, +1.84107909536913841382778015968089453
+1.80528953622066551657997338273072821, +1.46945158760877306483415751042032869, +1.10361958251621305798427518120635463, +1.59753617241573416011644864377008627, +1.74201191075276731418565910577111203, +1.24222360748065840745226539674912607, +1.61874521243065617709387909666007392
+1.14366788816464848300234706426329719, +1.23290487011265288516232261102352114, +1.76429681254086053455592117261892161, +1.23359440132908005930680588090422791, +1.08257015463123199938914708250987616, +1.40126496940344288214404806063185123, +1.00174284295301334099727318261505196
det = getMatDet(mat)
det
+0.110424511713007174716850546635810066
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000212
 
 
ndim = getUnifRand(1, 9)
ndim
+2
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.88468741031064195061527280926085988, +1.90933812281065576987472268757493805
+1.88494738962611675285928622008173685, +1.65807775142198677197725058462545178
det = getMatDet(mat)
det
-0.474043647084378947062219844005107912
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999615
 
 
ndim = getUnifRand(1, 9)
ndim
+6
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.81293055620438891001481559242059200, +1.49007730173726118588558701019122316, +1.70966001702866118901945676640664402, +1.21027724568738326461884867217913328, +1.52356527427679350120032689074562121, +1.15746047138956993309345324405246725
+1.00151251833628660226030226178904099, +1.59392166260873014506599392942146161, +1.23082826553472245368912761044096415, +1.50392605142046166537861260824736470, +1.79868133072827766696406467063738492, +1.98021207277300276586929365507408374
+1.87211074392861866807561487284325977, +1.40842562147537729625073403085469667, +1.46179160086059216258268712125986253, +1.70438052035864933019318468044427395, +1.00757235219674104234482347334728885, +1.83186686596344942791447568319973019
+1.86430802455765189249892848182982996, +1.15599678494655389688335165497534711, +1.65275883737122493676452571994840251, +1.35793041029692814676025802046909605, +1.07290980816270909987151865436386958, +1.07411373293010131707397585822052459
+1.52843074300684833121669083573336032, +1.75986021640685617244804314365561630, +1.50041296266782693787677156420085328, +1.61990588029672362314222661890584722, +1.89615135962545904329345461170779851, +1.46672908803170194833703567066288523
+1.15430894964600821989779197310838242, +1.88879109869998822376796313716395725, +1.82141932442100425871397448894263294, +1.88952415566039455049546287108493899, +1.89422906556484697994609086400578578, +1.98488145844739048046429993570108872
det = getMatDet(mat)
det
+0.905189558588608556314311073158766797E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000077
 
 
ndim = getUnifRand(1, 9)
ndim
+4
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.86559456936248834255673093831364183, +1.75476368714460352177828079228086916, +1.07003209423701922329460032284313780, +1.42546658708880837154822497991362323
+1.35801607670792111265320019509967099, +1.91908215319550306930897304042086610, +1.94270227299446275650293933257168133, +1.91759872833595806187451461753861460
+1.75104336381645529428245054446538434, +1.01907734992091147410982121675371167, +1.71528826569417497851499891448324421, +1.10841050570674471367813097605239152
+1.48678359068235510494531164532874052, +1.84290097213465622126555392431494796, +1.04850639953056002130060433110318841, +1.60496011024375950637472028112372489
det = getMatDet(mat)
det
+0.150266533305688629329157149336841886
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999996533
 
 
ndim = getUnifRand(1, 9)
ndim
+2
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.99757713786968863752969967051320807, +1.33958468740009192952524589497147777
+1.78460885591087350517180469990237456, +1.08798329800989520490351191226111259
det = getMatDet(mat)
det
-0.217304133888172211748907133914927470
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999904
 
 
ndim = getUnifRand(1, 9)
ndim
+8
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.60269983323099500570846048802758953, +1.62605304523476135966038240944529508, +1.05022987743180314151714321272729531, +1.08900708002345482222660109762003156, +1.53634482076540808743621690019305291, +1.84167662070769746107044904019642088, +1.65593889186301863286351660006002563, +1.08055412010872429658888459550900420
+1.22115412354344771817675231785067815, +1.08317810205078653726832785675409255, +1.52887383436064778156697273546619648, +1.51516390508645130531832137844585966, +1.99576206921663285391311896185007710, +1.79531574618682160518763462742437298, +1.14133966996429009584131465573974551, +1.88539486745994435270371864925095638
+1.69764014873453629913820309426782221, +1.20453217645677274024584343787090621, +1.66765883971482309347417880185827803, +1.80369755338428181324056702181468934, +1.54847880343360366243954668151449927, +1.45696822285245721813699504129759351, +1.10869501096545274203437834086263193, +1.31954535027185258552332496491655088
+1.34263623858029472886974338822018266, +1.02145069480617944913692359675946319, +1.46643090928428249785317197103700874, +1.58877543730618735820908642187942634, +1.18191612490851928633204076957102206, +1.57480352274292405466219172061764241, +1.49343113771888871634959705705554982, +1.21850248883643327212565577766298202
+1.47086278442947895411993392701443361, +1.35777923908711141721314001305186820, +1.01655159283145072867309526953331423, +1.53870330103500862828815896387620252, +1.50454917446560033255200119420487211, +1.05942676672727537320701802584856586, +1.27653221508844736030828598944158321, +1.11603982363155022646822273858837539
+1.74031255621943012603660145137724168, +1.71649682447799306596663050698330714, +1.53089619729045209024148667930494682, +1.42975217947975862317221088010884003, +1.28081948487323861939168888336240113, +1.56295593572043292012079592117577020, +1.60652591583781463515272823447387364, +1.12085872961580197086398452826508153
+1.64332364058743872005356661007275084, +1.78592790670253758147817310927057316, +1.01970646830484670542223416410462339, +1.85781019558278594188371282778868332, +1.91221640907958754701687422910988019, +1.45150143064013894480752612824737849, +1.84667524529797815045135889921254245, +1.06029720583604871504972961538912628
+1.02852054627682343446246457006503420, +1.09227250595424578896353189518680036, +1.20115741991838601618438097246241245, +1.57455041662602953181116306478246176, +1.90512324109672623399983438587608513, +1.28488815793589217006470523514919480, +1.78428484839273336135210642262005188, +1.85954485027202267428411774825665883
det = getMatDet(mat)
det
-0.268467422128554905869938763845753700E-1
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999519
 
 
ndim = getUnifRand(1, 9)
ndim
+3
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.14790522786343246643465110126513324, +1.57126836941055412725025774889943759, +1.95731625754478066726984501998275719
+1.21310362335246663877465282291482305, +1.16503835442665402298715813168970849, +1.41299128532707752200348933868498512
+1.15383206876649788711257255351213541, +1.39455327035131978923930336099648064, +1.14523197485734820391873822969113459
det = getMatDet(mat)
det
+0.328553848201798241432649896895990211
det * getMatDet(getMatInv(mat)) ! must be one.
+1.00000000000000000000000000000000077
 
 
ndim = getUnifRand(1, 9)
ndim
+5
mat = getUnifRand(1._TKG, 2._TKG, ndim, ndim)
mat
+1.75571710613527834119994960928349205, +1.50783385627270486931830478935720769, +1.90212632398114560450235556520201743, +1.23915050245782621028885933597950763, +1.89353926923229995331242446173799277
+1.87876068567007193633886960549990256, +1.84869256021181684545075341247889814, +1.42406538656046392709920729147999937, +1.35782137028737440668590302452781664, +1.92495649828840898346925834219764296
+1.67938791926268679870245694647940605, +1.27494273963575576326522659146057983, +1.21116091803017584602791895811822360, +1.29172724437231936392634699684168920, +1.80158291102987095790071646209911745
+1.08654435590444428833755876398765491, +1.43025761680209612672344565838438054, +1.04496635968775443228631418288105220, +1.60921006110457382424790864144744309, +1.76272904937242836794142074926537224
+1.77190293722902740327867258664836626, +1.29630735154871431808492253980180035, +1.31093905452671343854248611214451437, +1.24303975958450343692437005559245200, +1.50969525888793072828267122964822106
det = getMatDet(mat)
det
+0.121786965454092241529072773292377479
det * getMatDet(getMatInv(mat)) ! must be one.
+0.999999999999999999999999999999999133
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.20707850960389843998120110654120468, +1.02050693443003742580992094967893223), (+1.22297492272994639207581835712234290, +1.17576541498844453569941118055873125), (+1.41607902894809750924945669330589076, +1.92429902182844620910981913527982019), (+1.74458810286163165210426881464950725, +1.52873371921086710526745376489958838)
(+1.76961398813810651825733087405318131, +1.83953242475030836236312374177812312), (+1.58542589586188076296094162911026772, +1.94682279964190602809837520132273744), (+1.76996342810911639196102945026401702, +1.01103954558947755303940519460243369), (+1.40721457769363294901632365879260670, +1.75826989093689732327289432846527901)
(+1.57840577123474554740497750351386693, +1.92278427685307777846364217342382703), (+1.20338908011089784085557492562415930, +1.57778887160788508076424330259417516), (+1.27938062500195494048593896722946110, +1.33644998883371742144492730299177240), (+1.25954654041150771430037490750405139, +1.97106041130941220242839194015011083)
(+1.98748552944362033449326879555796323, +1.83770812546567443572273777198096130), (+1.04546598934871812321753864825681759, +1.83978357563200149281393249043626326), (+1.38060404782833860572602967062069486, +1.42854866600487292246928339606505030), (+1.71627556390745559674276294064309990, +1.78828808709852570980740522332924227)
det = getMatDet(mat)
det
+0.507220704467218365775744149531454406
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.705804614838700766631101242390287292, +0.455680217379572039964673677461129913)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.97748598421393153280157914183232854, +1.71767092627039753764424209127714231), (+1.87474308310767480516423945794550155, +1.89410210904297308475404858591917165), (+1.62090498520067496300153991746945154, +1.49016925145638431099369136570781806), (+1.63007243041324414092218321033975108, +1.94529292188401842992591404867297216)
(+1.29290680985654570915349233843108584, +1.92611632931753627462645668067859941), (+1.68729390007332759874435133047014683, +1.44015285650387973106079437635476534), (+1.26710504794451909415396229036790958, +1.88849459836338446072022401333363815), (+1.17437732155022577585422091452754573, +1.23610266212384388094351409469590369)
(+1.33299561904211138237551696562031810, +1.34807333956249440446310431726041578), (+1.66052753592048811653276375785969946, +1.01443222227950335427439353109952394), (+1.05734643227877642834572816012245780, +1.62934155933155601363244880977382091), (+1.75619292442578145000850630341914158, +1.20202405453105740640182253214596899)
(+1.34294792835065059740908092628642087, +1.84429948268273750108356017826586733), (+1.93756801850549091863538717928101346, +1.89043648985658425134755241178699139), (+1.15318415176520422591420021740077005, +1.53582013514531108069938361357911228), (+1.83111510978812272362176186676647877, +1.72640978849183631983744109027570136)
det = getMatDet(mat)
det
-0.398875188878261928666590201784560301
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.469545180283952262105374588860601237, +0.499071642107686809792529418165774628)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.30207803872331615372243050108015355, +1.84722132841251073650217840030155274), (+1.51844647458436711522327537816129510, +1.27743118706545433132664534919122027), (+1.21179807927738505934047126132264737, +1.99721162848284068390349833001438938), (+1.77409294730113762131531733331281227, +1.95874049415849800199520942789552477), (+1.52838927609664797351703157480524520, +1.84787337305397383423155397127184877), (+1.70527958750887746116730074722052216, +1.83205386067314882443054540082489585), (+1.74601672567646814851177310982080947, +1.65352891979249530139089902856142072), (+1.08489980990638755072423008235269198, +1.87118876369478039526454266256953862), (+1.38196978769012870003076930672119083, +1.00657642485850128781223911525458241)
(+1.66406369963884232782584612955629088, +1.08089097408354867928673840415885992), (+1.10105384083480200911680768331595941, +1.73674030764226863581862889219855294), (+1.63421412991366636174843321459194917, +1.56112652232331625318617264833103834), (+1.69832581967562096611395941294505798, +1.79900377084754869389412036922081202), (+1.41298666489759178598414269785669620, +1.89239554126757321124999429410815350), (+1.11712824955107448345706371500331598, +1.22971608817368503193796949772291038), (+1.00911879849401049564863893875443125, +1.97101806291571936215292255477731819), (+1.78572005658089816685383222626927894, +1.71037542498432640884272134432725154), (+1.48596666469699226983777919861780060, +1.65740586084632489198030869428504634)
(+1.36026764498284347249175580379893137, +1.70401947235145237658322028200210778), (+1.40461028365915680935530958175333840, +1.63507584839228621745804821172546214), (+1.61124034494867976464317979116882304, +1.78550044566404134913840336797866161), (+1.93690968532578361068496582130637855, +1.87472521923937082413042160990528973), (+1.69438148922664249911715510069473311, +1.70486228769972106771916756315311450), (+1.71196692677333696387787557282509366, +1.03489029599566732352527723945427164), (+1.16596286598214812753671776439042007, +1.57390388330659840645909433839083183), (+1.76137963640653862002862131548347405, +1.79353578978374428524577635264198697), (+1.21783780898631728219311389014020729, +1.50714343060348773887480847568491972)
(+1.53964082860682838260967660983847561, +1.35981489433667542049117893237790569), (+1.46296224760651941344671775695064678, +1.85798981183886944500581415554836269), (+1.21980408608144304782355318062589921, +1.11894275726421486598930419433070128), (+1.60495171564514121996546762950743483, +1.51421454689565681881121323372631638), (+1.01541924513000051321518768838862148, +1.17954483944108911908950403217874870), (+1.69848392343589262809225597920342923, +1.39647005854797790451876312866564006), (+1.70167581902383716752621406740945247, +1.67104455141727648048047537816498221), (+1.07644923614379805789080126377990943, +1.18508634754614549273858604836433135), (+1.74859744873104850925924176969046180, +1.63178813938915152471132336667023388)
(+1.37307938480156771525035364207533540, +1.77402070128317939871306297065835929), (+1.59214403441636854587188706250090059, +1.97793792733644431745451110399621457), (+1.65591837447100096477532321967623369, +1.38648608538987052683857994287697217), (+1.17890338251861831393823224035265362, +1.60569854732749711477805100768627248), (+1.98034661900404106396291036915127833, +1.38868551355655356297601277183863915), (+1.79361441685347859274552799998396794, +1.16583047949112620718920922769239860), (+1.40994636569754454237018867751658355, +1.83202557180262915167931327630787679), (+1.43331803081566708999256896779460216, +1.29216109514668335337745414038899193), (+1.25011961467554133898315063037067941, +1.02931826746318697909512757239200126)
(+1.73366873467149039459503683066205153, +1.95381854253945354901878129074838683), (+1.99798128555593097999486279891761772, +1.50640795207089697756913373725474420), (+1.76728391290101965837086833342167979, +1.63679555276936757773044638746240678), (+1.39307528139361310732896247029044107, +1.20963691185552658417783496274629460), (+1.67443642419532898242150099242627305, +1.38255973963375844927141980911404135), (+1.96881229302076751089806943002749327, +1.14551202353690982294315377488479728), (+1.13031410102217213646878399097030420, +1.56505661300639680840803996164569385), (+1.91359621738914716063545002325222636, +1.97157789631157267431501619489440429), (+1.88099667649566421931369344530067800, +1.77818892496428480705331464900948316)
(+1.35481600585037608522112079156519145, +1.51536967562618570443329206525877227), (+1.41499308782045465593961663925465037, +1.09304576855813618466503008432371840), (+1.12638681502884000577551789341460233, +1.45292880371961817202041574683061202), (+1.54903235677872169705052024883992249, +1.87469090072727297688447556488906733), (+1.04433802283209702127383414600005242, +1.75780875697652070775484406834188052), (+1.53976750462980717328644854104697915, +1.37709148745376314484157278948464486), (+1.03361265910734897518406985053034462, +1.46297074421621765559339869643888843), (+1.12263485046985256410253406393675991, +1.40060886071634019564874543507780201), (+1.07167112245719915715197035915651634, +1.42819812520772059597213757782826050)
(+1.55449028716365428781148444599858238, +1.56865414782221571534601976790975859), (+1.90650477468281391768445455938525365, +1.61963436176064954731279394393157519), (+1.78900857377034936544419636630828854, +1.59739729451208801710642626664865284), (+1.78901344599632086165463396095931738, +1.67365528794873830073933837173596875), (+1.05958157414770646515464416948655515, +1.54859508035354083288767175912870063), (+1.88304131581130248563721248849900506, +1.81568790680715331515776926268721445), (+1.39175993970052167734128797970729752, +1.69150717890762628171212793062343565), (+1.17730098864905455610238700764657013, +1.93624486859930733945938463981183255), (+1.85285503176602848927062477803743763, +1.06741835959765334879040547675106065)
(+1.47853166244849858246401176005747891, +1.62040024830904031405267253157396728), (+1.89276434544984154978070355382037745, +1.26989776267908478127866394376500579), (+1.88382111674231839731728571331536735, +1.11947224404721267983282654133467886), (+1.57099860680684644220814923212264716, +1.96779558357084381315020297129376505), (+1.29800446132867683247717624515807785, +1.06012286887517704325135386939556421), (+1.43264057243239047545871314736315044, +1.40520765216348999112862300190751277), (+1.59386698624812153560912215762737308, +1.94783572093682563039491246410994265), (+1.82199071289727141529134936650862931, +1.00114300817680588964722268228925347), (+1.63360773461433494332882099929709832, +1.92798654697872380425178983679558635)
det = getMatDet(mat)
det
+1.23619850600300303900879252007315528
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.438549949253286386558873967385021776, +0.496209523551519838903785924797996017)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.54955842774115145448683046738