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
(+1.54955842774115145448683046738593702, +1.74465342656027980173336158802661263), (+1.72548056685990962673066161062439592, +1.42260121145015867849996646986331565), (+1.04979861365467585328742294472595085, +1.21791446800168017082101208696823954), (+1.98495698107768848712879162046998461, +1.54863627369627560653427553366769674), (+1.64978366752093311045298560403431759, +1.08882731434545538767888819576935563), (+1.39647108457501725746590254726215871, +1.13424239241254335108004240402195428)
(+1.77819881040069919316326246325350725, +1.24233978485410341559705247090218826), (+1.79225443180755946010869917915491854, +1.25229244941914417192479124513889302), (+1.84576366793101192889205764503956624, +1.35626466655005092808379692115282438), (+1.07142307342073358447722477577059476, +1.48396609574200379924482047648415481), (+1.71577226864992527919986589771602389, +1.24048874000327796978346768379381214), (+1.88761620488969619481395146149179708, +1.18917296327052438399589747088310176)
(+1.93930872919297942949865811232473077, +1.89317590708054477723831893335264633), (+1.05509016134710617282959024699268602, +1.63245821127321351967229849533844537), (+1.81265889994836671556357584793745363, +1.68575692266863729068662410149468249), (+1.11966607628005457045350894762159147, +1.95942781982778490367195154605699013), (+1.63670210523877561235165755127073125, +1.08477932713035769794562218089666397), (+1.53151561588609425739137033926772227, +1.93289708581033138807955897187478361)
(+1.93090660551181321636755333488698727, +1.58603423225364729344291992321104305), (+1.19229105931779142152957061107728050, +1.75626919960245138522960973501938071), (+1.71150184253085231768925086131979428, +1.73575290476943202675544569456258810), (+1.45381909275848119675547641903086172, +1.40285764388921621157650993957519160), (+1.12387050983329458138014243266463827, +1.07227948457427350539495245787979381), (+1.76966663859745070453484688956288642, +1.23127569128862426341657500313605773)
(+1.63802911695712004266245712260468886, +1.11482500081113506174328111584410256), (+1.26056399547458674754596381740752724, +1.60716537620179181656388909011423686), (+1.48088400198368299254508103798431192, +1.52138307871086821774166761910349549), (+1.10951081460379884891385543562072748, +1.07699994609350035354399864257283816), (+1.67973626254179015863775709877338056, +1.76993555019789768832153536369746528), (+1.30327282947160519909261380634437656, +1.31016991075312462812327135004205056)
(+1.72583118722598551982057872647324152, +1.71405236139560166920897930634341167), (+1.58715515632145629755412099198309071, +1.15919150501418892202935340222099841), (+1.89645670380034029215519649574603326, +1.10227564622032814547328056943248470), (+1.85738385183124090429311677181830815, +1.92364211423200523363128721645792800), (+1.48678371725029334775263622052147749, +1.93268612454518468762922997448909329), (+1.61359978386598798690385954962481939, +1.99698600612101769679564442525076370)
det = getMatDet(mat)
det
-2.11316593362098571930925518602715363
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.969985558061137535560872381350647096, -0.170627006109704446357056273856460688)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.11875491720500375039047958666881500, +1.68363309595735620512651252116656670), (+1.61734229341886642930041302197347830, +1.26463219264193457645606544233429503), (+1.20197494052475197329708052482546770, +1.36345632838032965072039873931644414), (+1.99454759693642951076772650843523148, +1.29300506772015364067083058328789224), (+1.50423376828842529443157809228732342, +1.05613014268206212973881349512824059), (+1.00242716770115717992890433097765101, +1.48231908264589197619884362209196634), (+1.96914010305704890948679498271329131, +1.43402531195478935098189351057682797), (+1.26143733466779142832554157304178957, +1.51014611703136140456375705018126117)
(+1.54494947051492435215501448314640962, +1.94248947765020044286784139350753254), (+1.33590807968769953952205089767868645, +1.90256542151450629299353896129512715), (+1.24824324769844107166216137350627771, +1.54552304664975007466075242652345597), (+1.91339150724366595986794099390745243, +1.65948727639692487501403670717384448), (+1.35872788510017192548406958383251413, +1.40982055461537253704046344534325618), (+1.92095807183358859187540614975952791, +1.66854008825443673471889416528714986), (+1.86383140000852305127333648551729382, +1.01106285874247451769199788821712889), (+1.26007823800348391983036472408856851, +1.06013326844684071578002738302748409)
(+1.38309524208604036088146148974713370, +1.02536814226917215512250428310879062), (+1.07660168288561875225003285784575006, +1.86401926712667171037015217655337680), (+1.40236836369122704670301093854541453, +1.97326456995819880337515765135489336), (+1.76329634492038574899606760941774409, +1.38280024067240666583385193063383170), (+1.28920938492553671651788371322158461, +1.81159491011068282594620355207549077), (+1.48013986147167212434926291013063206, +1.39545518534456664531322643055989355), (+1.27172184541376052012746662706262478, +1.24692585942649869343622668963258354), (+1.84973531155829943935895636352571332, +1.25945917991547805158875008218380945)
(+1.17884806967925293966076972151768480, +1.75859478815824249257004426943518714), (+1.68382809961116777082054529139114439, +1.53422881919510882100276965214713934), (+1.96869539306194027319449365696948863, +1.90961344176479158830333613626271225), (+1.71908348421525048682108635051283693, +1.79375758565382313344805440313488842), (+1.21659031578305744161502740925132656, +1.37570787764766541600469007945869606), (+1.18833361738515618075059112129741845, +1.74112739555342772756947718316454718), (+1.77748056363629535684674215948234433, +1.08938403865033019283553996495874817), (+1.37710477160122293811697514067967990, +1.15076328392884449233751787192546206)
(+1.46403747769479383338104839809820141, +1.20865601941165485919154615527390564), (+1.26700425457536206665609359681491596, +1.67696511468206090811852928159836589), (+1.91008427546506397464062898143434717, +1.73248468355321432975148177651675773), (+1.29836069947641758449994690612956708, +1.27313314121395817773425413528263054), (+1.87565935944715996518499930987264216, +1.58326649524470642393263957153110806), (+1.92036532966435752675147336780790659, +1.79679915707858424211934916762186985), (+1.68220487786200522799926189116403865, +1.03783006329928892048179235964196844), (+1.57119943977271473239837016971579294, +1.92886432390870730173668457623222305)
(+1.39628072981324569542970732863323542, +1.31283793865823489442001074593422564), (+1.46514042225502276308908110317086935, +1.90051344322372961745926025821644221), (+1.98124567105687081992133778281827930, +1.77130176567695500169080652741166570), (+1.49340730780563907617860324506974419, +1.88385550362054287723884585976746817), (+1.48395187529201861209853460727942822, +1.48013015910326296313079584070206899), (+1.12385946597769600482282079552697449, +1.12090606564590183577694087824504723), (+1.53127678201325028246611964493703431, +1.56137475132930757262406461565925550), (+1.20036270802441090143719925918452351, +1.13745571972087692724324601282196943)
(+1.36416197850110618181521441738369378, +1.02520106840167450415433008985649884), (+1.96834804649237638716472680161013610, +1.51285176977238976234441576731577003), (+1.61523546073902201082607123527843568, +1.32664410375996571051744278568747917), (+1.33258130588464602792142030015784440, +1.89948471670806766492060184503393563), (+1.54688596078108790709077157831688901, +1.59582845798994700032531919021608707), (+1.65282471378001085847872434850279752, +1.03684752444280158807695059389322505), (+1.46461298707890798629595224551712905, +1.54261696602530274771769572193482080), (+1.67325039603506138082668227683868473, +1.57568432714043582470604877299912655)
(+1.70469296610665706612410556579006184, +1.03484578849383981062989514768637697), (+1.06018191059317661882551956832436178, +1.78107858714398470903505728318023172), (+1.26133868235604838669926587449480542, +1.26821853075971917737782368227550827), (+1.37569500462706721557177190133149749, +1.47689238784561907883027811864004562), (+1.47690720937597314402563818545488083, +1.73280929063980982024229943751601443), (+1.90792072971379677677442873285704587, +1.36065181635981399067331110309970713), (+1.10047423188815849333351923488774904, +1.61800378360614448199233725732120252), (+1.22678673278633052083521029710600895, +1.61309500537066992112558467865974315)
det = getMatDet(mat)
det
-1.40832478210538459299748053873297820
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.996071555587536680488005533702719122, +0.625540705067344537259902879471645170E-1)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.25267239574612790913892036720513476, +1.46815078754452930890439780404063249), (+1.27666559994773743638507648165072159, +1.00863350011243740274003226893641036), (+1.55474907760249492784566634198584017, +1.99057180796337613154758984174485458)
(+1.08122519811931624409386008326608788, +1.81458934963900846897579523042727395), (+1.07499460921328658993108387933553348, +1.17419895746976226169222876081828092), (+1.09064976521772819510832551688914831, +1.32615636299622793789780838413644333)
(+1.33477007020945269890644364869044937, +1.31027616501933064630114800416868699), (+1.16824756735261259188122828673919722, +1.86002898127295298081728359329492221), (+1.91201689280654938356266360368981550, +1.38205572453477562646758211365554446)
det = getMatDet(mat)
det
-1.62819255123497802831213448709592238
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.473398263246648132101833629321385701, -0.499291846119787308131048639828298352)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.07637938051456183359417166924681186, +1.82804495417634457404242265193078553), (+1.24526335381848456849984257037185199, +1.21468855421669474917027879003617568), (+1.84748773277655642054801246415667692, +1.49633382509259815012546011166987263), (+1.07367397538087543158965249545880486, +1.90533862964655907122411429176673633), (+1.04530439303137007609052378461852717, +1.24610887433454530533234621759546213), (+1.70294123258501984364944539456262219, +1.63988396160360249052656759740827195), (+1.40205302000883780784913417484607051, +1.69285563005052469385786237113979455)
(+1.99328037739040801102907465245410610, +1.89510884214615568158167686954691305), (+1.81595373789167857868647127390332916, +1.58374197705284008515454119798272665), (+1.66893435918398536563824458084052587, +1.20676861184648273693442836866789594), (+1.82629532698096595712167518126020624, +1.15262315680609053124397572933105830), (+1.16541210604846629516160233238667856, +1.82508987194037925569031251590219639), (+1.70119840898430233943438724038141076, +1.54481489364811258142414182433395484), (+1.77937291356672201308937545086836466, +1.36970444602626653486485690051109859)
(+1.35147473164136686356972975736234501, +1.33542897136855299243006587039799716), (+1.65963916751057904153622909307971793, +1.69998097380421590431579123628944901), (+1.13360207674599042295128439033673108, +1.92415623836444720446317290477137641), (+1.47378115565851557334147122470881816, +1.68671611228494316448446201011887613), (+1.69328416870352483418638918549370535, +1.60691497140180416686717053754394744), (+1.95529942422249832445097607104174579, +1.66456341758331667616718482531064042), (+1.29586589527687921751606415101840882, +1.31629562473260951115936154121903844)
(+1.30608705987281534801891747921034171, +1.81585294295926018879450208926012207), (+1.50340673168502336746128827898749893, +1.05112604851620197149279530835286864), (+1.91414009983392034877712465686588232, +1.24128419822682242722467398051039972), (+1.71726068544426017574787661643563409, +1.49818990091196678428708127433135949), (+1.26561845814880956182398121432849740, +1.41154804241831142869438265253720507), (+1.98306603739867148685873873765725699, +1.39284903598715399516299542920347200), (+1.32336898638223017938954943989511635, +1.35136044625347738138059304484913784)
(+1.61686560131207313759100831490155726, +1.13882960315004146150713833418333845), (+1.75912313681676211900974635613949148, +1.36141389289512459262312853804785931), (+1.24873509616684682939057520661016955, +1.53860051697298502628759329016837008), (+1.22413507191871141979078478601181699, +1.86719568375371648200971708438740051), (+1.23530667340823393351032031450787277, +1.31170902867988528248532368283871408), (+1.21060156016203801490755984813424602, +1.55616433253294116478150478462739361), (+1.25766426298851490912502495275970886, +1.94638096301340974740013540369586956)
(+1.46539631868679456479910171592782545, +1.31740799326068103021325401297838194), (+1.00491742524087322701067588848019005, +1.50604275598658005368981478379452861), (+1.47584806717726384541436538073872011, +1.27063802458263306769745539994288893), (+1.97077510349766452267593634016778802, +1.57386244928970086414010762862757705), (+1.18818893716146671793363231659574480, +1.68647163823463294735329882654081521), (+1.79659300010456173652213498433798487, +1.64945358218677091619766122889229462), (+1.27732556409308612125683606361625276, +1.79142620392925470375816089240361503)
(+1.50869314881970947115256930454809987, +1.10580363474657904262414574260631715), (+1.07519000860011288387503204689611505, +1.68178164927350817002847257464847945), (+1.26641072689965266623044723309328686, +1.66130344730066834334060905512927526), (+1.32413733543110507115605750621447160, +1.44105396692119755218053907563574076), (+1.57337220095823639555958620942204190, +1.06607851709643459972453285345827019), (+1.26300412480243771699845435148519202, +1.90320766861097641083033763418879181), (+1.13751255434861548946383699016382330, +1.11829471077114679111485966986369519)
det = getMatDet(mat)
det
-1.30087387279669735392057173046625931
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.965238182508372266275985136217914395, -0.183175963314804210308798753216280193)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.71451789092775882288811456147596802, +1.61429413346254774970940308008917735), (+1.44584586002201030853369615538979530, +1.44070856432777351442621852257791543), (+1.82836563402139994413972914774554460, +1.31365196583403494960949222586461509), (+1.06109854876037877130927324250201778, +1.78157253503954751449540962642901949), (+1.21805446675885153027840060285409834, +1.58133109093811861575014258210825858)
(+1.19610209005374509618337382516296796, +1.19969659984222703640046457902684905), (+1.11880355987276998075137545425451806, +1.98363788562503401851713296523431991), (+1.55285653033260844394085644816042090, +1.56528195728216835341093985395318395), (+1.32008971163130062336084676438840025, +1.61639372145836541254674234595769162), (+1.46326249988688486881226243900675487, +1.99641953413640984365549516306029610)
(+1.00961306211039967436980971160270002, +1.46481168763436696628045883898690672), (+1.04723470901870991190602949862171118, +1.71576568250770808886546931091334937), (+1.72096773431531669657062431594557460, +1.34781561075969207144533179679328695), (+1.77217201270747823238421452521086907, +1.32271747419456204324172476893838929), (+1.23199383646653288817425714491482102, +1.88820648278807417124453018075467487)
(+1.06831530783399163443440940420174032, +1.74362782612757156040288259188927928), (+1.26174985008024947095971185824788865, +1.07477307380017550784998494928699832), (+1.18553174865331643642861611877029289, +1.11178182437787935558133359214159484), (+1.49697809212527956706614065102181944, +1.06533368656750263464538121148213396), (+1.26169003164573291554350262182102225, +1.43619879022701369881860082430600463)
(+1.09913191701373685037372343761231766, +1.17050446788992151119432376301476969), (+1.01096320166771308900038169153176864, +1.34510293758627538314331134598058927), (+1.89986948292383074032141969285810875, +1.12994552604359200785280415566930773), (+1.69690302328559454310948718915313147, +1.25248779754070106108619763100549116), (+1.49053557212958092801753100933722747, +1.35179349482363812629338620295556837)
det = getMatDet(mat)
det
+0.260419736502192860905767393788832323E-1
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.176703705571384749185459733927141794E-2, -0.419989837467239393784010716627429994E-1)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.79071029132262462105987878714305824, +1.24876605969933320896962581106429512), (+1.05952887534920250705558564715616252, +1.36862351578957397090842593377903480), (+1.51506166366701353123069017704680546, +1.64366095687662123816507722658798000), (+1.69008767944350227168575016115130207, +1.53666034185958673831902051826842890), (+1.77457931010636722182124527323578681, +1.20106611288736644206952857778855511)
(+1.14886976938242052146518005888128293, +1.99619024247197331082563238992110976), (+1.79758668270625102313017766194670073, +1.67730320405191139419405371912890013), (+1.71084802476098981392019674893821350, +1.86152775159804063274922106029176630), (+1.27675570800269654652144406475343790, +1.66302343414131858111098533735920315), (+1.25173323913204347994737166893269394, +1.64081879317796869970477446984508274)
(+1.89048327604071160960291729048110364, +1.02515660563752227140429959129375227), (+1.03505902852539549209965678322206185, +1.21344037260162222526060706833205735), (+1.35983798934595712451943904672835551, +1.18658488875596237013326235531950420), (+1.70524605907448158311438450968155208, +1.27665147397232533679968712904025117), (+1.30574188273158566857273096474295016, +1.16612491167416898782021319529102359)
(+1.87913122446300636562772382523030805, +1.27191229016373741872113743985587928), (+1.89433087332978056238358976467824703, +1.32002985950323441023208321780244909), (+1.65212212576661707404750586326854098, +1.39753309979904383050008283461312678), (+1.88828048394724740694583066043714974, +1.97053453376338333929144815183700296), (+1.83559081121334363711790430575694050, +1.80976542354764012008547450370799256)
(+1.16807311065086028610529638264645665, +1.31212407908680086846162030888366915), (+1.36974970878190970003802440827729178, +1.75109504417917870501337023993901609), (+1.08362002678953007187309899422567398, +1.22452950779003552007554961444096339), (+1.39385303869849543199898533026146656, +1.73843917031048160647340932651937006), (+1.88180792891925055704954321223312621, +1.39461999409445656760671955314853887)
det = getMatDet(mat)
det
+1.03382574497047033260332666432988549
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.877492449892455682146738732442503967, +0.327871087890030090174272260613547373)
 
 
ndim = getUnifRand(1, 9)
mat = getUnifRand((1._TKG, 1._TKG), (2._TKG, 2._TKG), ndim, ndim)
mat
(+1.45433103351622737975024302633435279, +1.96167420093126855120205570972336016), (+1.67886893726511480743697038394480436, +1.99703734005751237586105764099244481), (+1.96161188591653500071647828598051434, +1.20987068317899544654014233212992192), (+1.58332055482237487546093475537301285, +1.88944436604047646053348793849559032), (+1.97348976283938683528428120003274640, +1.50874297780029741069679819108438330), (+1.50318470161048472424376657031564253, +1.44713852334704040859489903456227776), (+1.52334794736279387497975553721889154, +1.29026030842749774902603022955883862), (+1.52213800272141001292765125679825574, +1.11917038271302538450890674111208503)
(+1.13944213286680464711835497958124227, +1.82060259419930505660989374133408118), (+1.99461393418662889718627290136947771, +1.42220293388516852034254935951165098), (+1.24914053777632989986119199763468868, +1.44086718249094883615384548223827684), (+1.28927684312568586155523179858555577, +1.08957707952516436796409820858068625), (+1.16244582333779528364845953172350775, +1.65481361208564846970150546527029860), (+1.52142125601204489210002973957302836, +1.49565910090371094460718885276069475), (+1.92020496322269154318980907978497087, +1.79094311649494993424117813125553019), (+1.47328835362600499374561582745442308, +1.92298583532750807672590354647450860)
(+1.20545970024662935350674834448594198, +1.85047305314265330587415480321223539), (+1.45751765725610953448911248195094697, +1.65993523846001585710263717126682175), (+1.80426485775658887252744355181760757, +1.77930290184779663332634593454376020), (+1.43291138768640200649291998326362465, +1.92765670462987462929089487958255700), (+1.75936821472529647448333912210443396, +1.24860635706449865409641472256416661), (+1.13262788766481863812118823820223165, +1.50909421896607260418104057156400646), (+1.52933368077238448620860740556923676, +1.29369983480271755602114755845785893), (+1.21761180089099689810911110209989676, +1.52450135491711145903561513119195012)
(+1.82004209939985366653962927303192256, +1.08501692672420750657951822402975672), (+1.92511181730440661472980731500683112, +1.82147542577250647280792138131795021), (+1.79349544447586960165653430895730125, +1.67678697035870160694791907966180215), (+1.49798761978504375180798672255350393, +1.82922989222581021041193397093403058), (+1.36530039899955080497494225349175960, +1.60464127023186881382868571259514760), (+1.42593247642154185203217353954129785, +1.88048295556475707416003743612651558), (+1.72012559931989335031540306724585947, +1.94372346704713625056246341382421783), (+1.02766107291597456562527640721225596, +1.66473791704819582905542164524684594)
(+1.29448010116214862977152218510426301, +1.42209978383191246578701549620569706), (+1.35323638868103217468710733273238229, +1.77549010961172250659304871738683604), (+1.45405159926759997538619570195020632, +1.07134793210013567400223137080367077), (+1.50121690011526952794745389905485591, +1.20175477002367738648412158573716558), (+1.16151372049876580655723594310821063, +1.05959487300493111588363707490334858), (+1.23388694495955072251142328350457326, +1.12967829109289852820355674893315083), (+1.97120480450181046486202774194901588, +1.53896032648780989776600518791366018), (+1.95150773286275386935046895195983884, +1.56265626211491445151517817643713813)
(+1.32286504857168912486573816457104972, +1.41135230974453292437537262837644470), (+1.25157031755128018238960604300978579, +1.79455330607605637092605890809868511), (+1.76392919208005486043510700089835675, +1.89903049110575588211241055505269575), (+1.65588634517281180778543315537346793, +1.93213307513294190122671733985797983), (+1.10230051302150640188474049869511597, +1.69440150925879980888927481398015476), (+1.79001974875576499049480798400843426, +1.83945473776280653970808203892748682), (+1.44304571764637918955021090101643473, +1.43227168875035189603118445522037301), (+1.46738068950167890910323992390573684, +1.88470832241579825732607560117847546)
(+1.50731081214868602004683537348562804, +1.55680850798563583631927240208878037), (+1.49097179565739760399727634577260642, +1.15225318432062705791673358863968336), (+1.55177427836127567846921162797591121, +1.23839146116184171366122576959606213), (+1.43105125159279318137504090653172035, +1.55251072814815096287837297557809729), (+1.94569677654248577463410453399492692, +1.91729455416640403824975850097039724), (+1.92928173387579642202150225602111170, +1.86190996250397832590403714913542945), (+1.46869585968346388866449441370410405, +1.39293490146200368520964462962440504), (+1.04062680641685504976952650044111984, +1.27326094700835445976470149541001572)
(+1.62943749135387718987176464664616133, +1.94805399084656367937490446962073346), (+1.02542655454675841075558917907628687, +1.39001030781984488966136025832798783), (+1.48521747858131561777442038914418164, +1.16262198622034623880639152899937166), (+1.48699692637968745339203666259326942, +1.28169102749850034670383772894440838), (+1.83029670956955764818629420884240230, +1.41413363441978259847846657238882998), (+1.81414961619105219872731929863675602, +1.94415739782160531661711562319308585), (+1.11945576937972748264951640064076787, +1.73024606280092619134389223553164378), (+1.94507572809505970309803877702349293, +1.69106849600382252675585088095896949)
det = getMatDet(mat)
det
-2.14177964864417656767470995705969837
det * getMatDet(getMatInv(mat)) ! must be one.
(+0.975197992696582001322687464871253796, +0.155521277441831729994711215952724046)
 
 

Test:

test_pm_matrixDet

Bug:

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

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

yielding the following error message,

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

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

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

Todo:

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

Todo:

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

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

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

Final Remarks ⛓

---

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

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

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

Definition at line 216 of file pm_matrixDet.F90.

---

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

• src/fortran/main/pm_matrixDet.F90