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{"sheet":"Sheet1","index":0,"n_rows":32,"n_cols":21,"rows_kept":32,"cut":false,"hidden":false,"merged":[[1,12,1,15],[4,7,7,7],[4,8,7,10],[9,6,9,7],[19,12,19,17],[25,12,25,17],[9,4,9,5],[9,8,9,10],[2,16,2,18],[14,12,14,14],[14,15,14,17],[13,12,13,17],[8,8,8,10]]}
["Gauss-Newton, Gradient-Search and Levenberg-Marquardt algorithms"]
["Nonlinear regression algebra for y = Ae-Gx +B.  ",null,null,null,null,null,null,null,null,null,null,null,"parameters"]
["Change current solution in cells M4:M6 to see how the starting values affect current and next solution.",null,null,null,null,null,null,null,null,null,null,null,"current","change","next","sa","correlation matrix"]
["Change l-factor to affect gradient-search and Levenberg-Marquardt algorithm.. ",null,null,null,null,null,null,null,null,null,null,"A =",102.55423904502508,{"$f":"MMULT(MMULT(MMULT(P10:R12,TRANSPOSE(Jacobian_mat)),y_weight_mat),G12:G32)","v":1.89754159452733E-2},{"$f":"M4+N4","v":102.57321446097036},{"$f":"a_stddevs_vec","v":3.9189263870505942},{"$f":"P16:R18/P4:P6/TRANSPOSE(P4:P6)","v":0.99999999999999989},-0.35400710708216498,3.569995393174772E-2]
["Hit \"cntl + I\" to iterate solution.  Hit \"cntl + r\" to regenerate noise. ",null,null,null,null,null,null,"algorithm",null,null,null,"B =",3.7487777315208612,-9.9951174320372926E-2,{"$f":"M5+N5","v":3.6488265572004881},2.7451580862756697,-0.35400710708216437,1,0.83340652347482469]
[null,null,null,null,null,null,null,null,null,null,null,"G =",0.19079409114153967,-6.1059033846023666E-4,{"$f":"M6+N6","v":0.19018350080307944},1.9287034029316783E-2,3.5699953931748248E-2,0.83340652347482458,1.0000000000000002]
[null,null,null,null,"l =",1.0000000000000007,null,null,null,null,null,"c2=",{"$f":"MMULT(TRANSPOSE(G12:G32),MMULT(y_weight_mat,G12:G32))","v":27.519300950448116},{"$f":"O7-M7","v":-1.4491905035107777E-3},{"$f":"MMULT(TRANSPOSE(H12:H32),MMULT(y_weight_mat,H12:H32))","v":27.517851759944605}]
[null,"Atrue =",100,null,"l-factor =",10]
[null,"Btrue =",5,null,null,null,null,null,"Jacobian matrix",null,null,null,"[X] (l modified)",null,null,"[X]-1 (l modified)",null,null,"Marquardt multiplier"]
[null,"Gtrue =",0.2,null,"yfit",null,"Dy",null,"[Jya]",null,null,null,{"$f":"S10:U12*M16:O18","v":0.12605219491472761},0.22609592776640472,-27.733919100442794,{"$f":"MINVERSE(M10:O12)","v":15.357984027121422},-3.8084341096745025,2.6983619750556571E-3,1,1,1]
["noise","x","y","sy","current","next","current","next","dy/dA","dy/dB","dy/dG",null,0.22609592776640472,0.84000000000000019,-101.28107260384272,-3.8084341096744962,7.5358929186446968,4.4125506310326211E-2,1,1,1]
[4.9164164066314697,0,{"$f":"$C$8*EXP(-$C$10*B12)+$C$9+A12","v":109.91641640663147},5,{"$f":"$M$4*EXP(-$M$6*B12)+$M$5","v":106.30301677654595},{"$f":"$O$4*EXP(-$O$6*B12)+$O$5","v":106.22204101817086},{"$f":"C12-$M$4*EXP(-$M$6*B12)-$M$5","v":3.6133996300855236},{"$f":"C12-$O$4*EXP(-$O$6*B12)-$O$5","v":3.6943753884606192},{"$f":"EXP(-$M$6*B12)","v":1},1,{"$f":"-B12*$M$4*EXP(-$M$6*B12)","v":0},null,-27.733919100442794,-101.28107260384272,14903.41005281706,2.698361975055697E-3,4.4125506310326204E-2,3.7198968164802365E-4,1,1,1]
[-5.3628575801849365,1,81.510217727613252,5,88.489623754215842,{"$f":"$O$4*EXP(-$O$6*B13)+$O$5","v":88.457119335855779},-6.9794060266025904,-6.9469016082425217,0.82630271368393293,1,-84.740846022694981]
[4.6728098392486572,2,76.704814442812591,5,73.770368759946038,73.768950624940189,2.9344456828665519,2.9358638178724075,0.6827761746414317,1,-140.04318205685036,null,"Current"]
[1.117168664932251,3,60.998332274334892,5,61.607808414775128,61.624664039365747,-0.60947614044023712,-0.62633176503085686,0.56417980594494999,1,-173.5770920497628,null,"[X] (curvature matrix)",null,null,"[X]-1 (covariance matrix)"]
[2.5639688968658447,4,52.496865308587999,5,51.5578517962158,51.583678020260443,0.9390135123721981,0.91318728832755447,0.46618330465798685,1,-191.23629625877976,null,{"$f":"MMULT(MMULT(TRANSPOSE(Jacobian_mat),y_weight_mat),Jacobian_mat)","v":0.12605219491472761},0.22609592776640472,-27.733919100442794,{"$f":"MINVERSE(M16:O18)","v":15.357984027121422},-3.8084341096745025,2.6983619750556571E-3]
[2.6069605350494385,5,44.394904652193674,5,43.253545369894425,43.281716474357161,1.1413592822992475,1.1131881778365109,0.38520852971303821,1,-197.52383819186784,null,0.22609592776640472,0.84000000000000019,-101.28107260384272,-3.8084341096744962,7.5358929186446968,4.4125506310326211E-2]
[-0.16010642051696777,6,34.95931477070323,5,36.391674434562155,36.417593232026604,-1.432359663858926,-1.4582784613233759,0.31829885343608139,1,-195.85738021824776,null,-27.733919100442794,-101.28107260384272,14903.41005281706,2.698361975055697E-3,4.4125506310326204E-2,3.7198968164802365E-4]
[0.35651803016662598,7,30.01621442432727,5,30.721691859748191,30.742285339381326,-0.70547743542092167,-0.72607091505405386,0.26301120635671849,1,-188.81039889759131]
[-7.2494161128997803,8,17.940235686565757,5,26.0365698716388,26.049898775327449,-8.0963341850730437,-8.1096630887616907,0.21732687354184141,1,-178.30233712094352,null,"True value (evaluated at 100,5,0.2)"]
[13.115841150283813,9,34.645729972442467,5,22.165240858923749,22.170198839567583,12.480489113518718,12.475531132874886,0.17957778536406852,1,-165.748168146626,null,"[X]",null,null,"[X]-1"]
[-4.9539601802825928,10,13.57956814337868,5,18.966351190153958,18.962434222124976,-5.3867830467752773,-5.3828660787462983,0.14838561136368064,1,-152.17573458633095,null,0.12130250816328365,0.21735720535172093,-24.606474651689062,15.468076263938588,-3.3145045632782151,6.3351211615485783E-3]
[4.634929895401001,11,20.71524573163439,5,16.32309997607398,16.310230698322975,4.3921457555604091,4.4050150333114129,0.12261143334145876,1,-138.31754469008433,null,0.21735720535172093,0.84,-91.223826822912088,-3.31450456327822,6.7236728595502493,4.3052937919899885E-2]
[0.47626137733459473,12,14.548056706275842,5,14.138974324931347,14.11736919800637,0.40908238134449437,0.43068750826947166,0.10131416009872403,1,-124.68235912092582,null,-24.606474651689062,-91.223826822912088,12352.255658457734,6.3351211615485931E-3,4.3052937919899885E-2,4.1153121274808903E-4]
[-1.3362157344818115,13,11.091142086951576,5,12.334225372365506,12.304295081930425,-1.2430832854139284,-1.2131529949788487,8.3716165424184127E-2,1,-111.61081933098035]
[2.7912485599517822,14,13.872254822473577,5,10.842956415342108,10.805231985647344,3.0292984071314697,3.0670228368262329,6.9174894669216364E-2,1,-99.318501573497457,null,"Fractional difference of current from true value"]
[-1.047595739364624,15,8.9311110974217698,5,9.6107168293210705,9.5657955242734261,-0.67960573189929985,-0.63468442685165627,5.7159403183973716E-2,1,-87.929086467003131,null,"[X]",null,null,"[X]-1"]
[5.7410013675689697,16,14.817221765405591,5,8.5925139154831207,8.5410202859314914,6.2247078499224715,{"$f":"C28-$O$4*EXP(-$O$6*B28)-$O$5","v":6.2762014794741017},4.7230969963471522E-2,1,-77.499778943396137,null,{"$f":"(M16-M22)/M22","v":3.915571758046802E-2},4.0204429388678659E-2,0.12709843620524708,-7.1173838904472903E-3,0.14902062645156408,-0.57406308320769983]
[-13.249210119247437,17,-4.9118831232148299,5,7.7511700846979341,7.6937285353284262,-12.663053207912764,-12.605611658543255,3.9027078650740857E-2,1,-68.040670004010238,null,{"$f":"(M17-M23)/M23","v":4.0204429388678659E-2},2.6433881538694203E-16,0.11024801448479266,0.1490206264515605,0.12080005616882102,2.4912780456977007E-2]
[3.0755198001861572,18,10.807892044915413,5,7.0559653941788989,6.9931814458012047,3.7519266507365137,3.8147105991142078,3.2248180996263455E-2,1,-59.529377927844671,null,{"$f":"(M18-M24)/M24","v":0.12709843620524708},0.11024801448479266,0.20653348383479422,-0.5740630832076945,2.4912780456976844E-2,-9.6083917513858114E-2]
[-9.191058874130249,19,-1.9539816885136894,5,6.481515871837221,6.4139639279913681,-8.4354975603509104,-8.3679456165050574,2.6646759468583123E-2,1,-51.922024666010827]
[6.0448038578033447,20,12.876367746676763,5,6.0068466726518537,5.935062597940588,6.8695210740249086,6.9413051487361752,2.2018289659773274E-2,1,-45.161378822619852]