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{"sheet":"Sheet1","index":0,"n_rows":32,"n_cols":21,"rows_kept":32,"cut":false,"hidden":false,"merged":[[1,11,1,15],[19,12,19,17],[25,12,25,17],[2,16,2,18],[14,12,14,14],[14,15,14,17],[13,12,13,17],[9,4,9,5],[9,8,9,10],[8,8,8,10],[4,7,7,7],[4,8,7,10],[9,6,9,7]]}
["Gauss-Newton, Gradient-Search and Levenberg-Marquardt algorithms for Poisson distributed variables"]
["Nonlinear regression algebra for y = Ae-Gx +B.  ",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,"names","current","change","next","std. dev.","correlation matrix"]
["Change l-factor to affect gradient-search and Levenberg-Marquardt algorithm.. ",null,null,null,null,null,null,null,null,null,null,"A =",98.90434289260773,{"$f":"MMULT(MMULT(MMULT(P10:R12,TRANSPOSE(Jacobian_mat)),y_weight_mat),G12:G32)","v":-1.4022481072751263E-2},{"$f":"M4+N4","v":98.890320411534972},{"$f":"a_stddevs_vec","v":6.170799147786262},{"$f":"P16:R18/P4:P6/TRANSPOSE(P4:P6)","v":0.99999999999999989},0.15144097591724354,0.48580301230199618]
["Hit \"cntl + I\" to iterate solution.  Hit \"cntl + r\" to regenerate ymeas. ",null,null,null,null,null,null,"algorithm",null,null,null,"B =",3.2738837025076615,-3.103188561983334E-2,{"$f":"M5+N5","v":3.242851816887828},2.1032613338187667,0.15144097591724365,1.0000000000000002,0.86252625254478354]
[null,null,null,null,null,null,null,null,null,null,null,"G =",0.18094027153628819,3.884723938168009E-4,{"$f":"M6+N6","v":0.18132874393010501},2.0943020378604182E-2,0.48580301230199591,0.86252625254478354,0.99999999999999989]
[null,null,null,null,"l =",10,null,null,null,null,null,"L =",{"$f":"SUM(C12:C32*LN(E12:E32)-E12:E32)","v":1817.4650460406554},{"$f":"O7-M7","v":4.4651290692854673E-2},{"$f":"SUM(C12:C32*LN(F12:F32)-F12:F32)","v":1817.5096973313482}]
[null,"Atrue =",100,null,"l-factor =",10,null,null,null,null,null,"c2 =",{"$f":"MMULT(TRANSPOSE(G12:G32),MMULT(y_weight_mat,G12:G32))","v":24.57551764055081},{"$f":"O8-M8","v":-8.9028328195816187E-2},{"$f":"MMULT(TRANSPOSE(H12:H32),MMULT(y_weight_mat,H12:H32))","v":24.486489312354994}]
[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,{"$f":"S10:U12*M16:O18","v":0.59639178500939938},0.16623158456807638,-22.159953900891189,{"$f":"MINVERSE(M10:O12)","v":1.6879727634489676},-1.6647985193795539E-2,1.7715147330654417E-4,{"$f":"1+F7","v":11},1,1]
["ytrue","x","ymeas","sy","current","next","current","next","dy/dA","dy/dB","dy/dG",null,0.16623158456807638,15.317806776355607,-144.41746537110319,-1.6647985193795574E-2,6.5900706215259217E-2,4.6302317070197522E-5,1,{"$f":"1+F7","v":11},1]
[{"$f":"$C$8*EXP(-$C$10*B12)+$C$9","v":105},0,97,{"$f":"SQRT(E12)","v":10.108324618605963},{"$f":"$M$4*EXP(-$M$6*B12)+$M$5","v":102.17822659511539},{"$f":"$O$4*EXP(-$O$6*B12)+$O$5","v":102.13317222842279},{"$f":"C12-$M$4*EXP(-$M$6*B12)-$M$5","v":-5.1782265951153912},{"$f":"C12-$O$4*EXP(-$O$6*B12)-$O$5","v":-5.1331722284228007},{"$f":"EXP(-$M$6*x_vec)","v":1},1,{"$f":"-x_vec*$M$4*EXP(-$M$6*x_vec)","v":0},null,-22.159953900891189,-144.41746537110319,197577.46376853564,1.7715147330653899E-4,4.6302317070197597E-5,5.1150192561332795E-6,1,1,{"$f":"1+F7","v":11}]
[{"$f":"$C$8*EXP(-$C$10*B13)+$C$9","v":86.873075307798189},1,98,{"$f":"SQRT(E13)","v":9.2632658406763841},85.808094035041961,85.733309105936783,12.191905964958039,12.26669089406321,{"$f":"EXP(-$M$6*B13)","v":0.83448519972628055},1,-82.5342103325343]
[72.032004603563934,2,74,8.493966134621882,72.147460696103394,72.05318143700184,1.8525393038966049,1.9468185629981538,0.69636554856221033,1,-137.74715398719147,null,"Current"]
[59.881163609402641,3,58,7.7940916312211614,60.747864355871748,60.641751253675395,-2.7478643558717488,-2.6417512536753942,0.58110674387443695,1,-172.42194196009228,null,"[X] (curvature matrix)",null,null,"[X]-1 (covariance matrix)"]
[49.932896411722155,4,47,7.1578676941596635,51.235069927094578,51.122780233789257,-4.2350699270945791,-4.122780233789257,0.48492497722434807,1,-191.84474489834767,null,{"$f":"MMULT(MMULT(TRANSPOSE(Jacobian_mat),y_weight_mat),Jacobian_mat)","v":5.4217435000854491E-2},0.16623158456807638,-22.159953900891189,{"$f":"MINVERSE(M16:O18)","v":38.078762122319652},1.9655226298576578,6.2782836000826084E-2]
[41.787944117144235,5,44,6.5800291616558511,43.296783768241404,43.182425009093066,0.70321623175859482,0.81757499090693431,0.40466271647132213,1,-200.11450032866873,null,0.16623158456807638,1.3925278887596007,-144.41746537110319,1.9655226298576591,4.423708238337098,3.7993112680563233E-2]
[35.119421191220198,6,43,6.0557742244478083,36.672401457486451,36.558889653996019,6.3275985425135479,6.4411103460039811,0.3376850477763505,1,-200.39110652987279,null,-22.159953900891189,-144.41746537110319,17961.587615321423,6.2782836000826056E-2,3.7993112680563233E-2,4.3861010257863003E-4]
[29.659696394160644,7,23,5.5807215001138397,31.144452461832866,31.033794194315341,-8.1444524618328664,-8.033794194315341,0.28179317453822644,1,-195.09398131527644]
[25.189651799465537,8,31,5.1508699110070904,26.531460840118189,26.424974553140988,4.4685391598818098,4.5750254468590121,0.23515223353603451,1,-186.06061710088423,null,"True value (evaluated at 100,5,0.2)"]
[21.529888822158654,9,25,4.7625610342898446,22.681987605335955,22.580476545842828,2.3180123946640441,2.4195234541571726,0.1962310585683987,1,-174.67293512545464,null,"[X]",null,null,"[X]-1"]
[18.533528323661272,10,23,4.41244367263399,19.469659164167734,19.373545904409994,3.5303408358322654,3.6264540955900064,0.16375191410194964,1,-161.95775461660074,null,4.720442113207849E-2,0.14269760411703461,-17.056809263987599,42.661319098158877,1.9436569418126717,7.5697514206694877E-2]
[16.080315836233389,11,8,4.0974404966214042,16.789018623353062,16.698449150701823,-8.7890186233530621,-8.6984491507018245,0.13664854874492618,1,-148.66648412929939,null,0.14269760411703461,1.3460479176593072,-114.98294883480831,1.9436569418126666,3.4916643249784514,3.4590369467204105E-2]
[14.071795328941247,12,11,3.814716734733651,14.552063766256968,14.466987531531082,-3.5520637662569667,-3.4669875315310814,0.11403119149171613,1,-135.33816076499167,null,-17.056809263987603,-114.98294883480831,12565.186578031016,7.569751420669478E-2,3.4590369467204111E-2,4.9887526184179496E-4]
[12.427357821433388,13,14,3.5616510280422555,12.685358045554455,12.60558907895933,1.3146419544455439,1.3944109210406705,9.5157341606990478E-2,1,-122.34916645960834]
[11.081006262521795,14,10,3.3358087099508311,11.127619749383829,11.052882920148443,-1.1276197493838298,-1.0528829201484435,7.9407393216331348E-2,1,-109.95230465626636,null,"Fractional difference of current from true value"]
[9.9787068367863938,15,3,3.1349178930528003,9.8277101961826094,9.7576758610266854,-6.8277101961826094,-6.7576758610266854,6.6264294387873554E-2,1,-98.30739740512422,null,"[X]",null,null,"[X]-1"]
[9.0762203978366216,16,6,2.9568488147102463,8.7429549130533886,8.6772645311176415,-2.7429549130533895,{"$f":"C28-$O$4*EXP(-$O$6*B28)-$O$5","v":-2.677264531117642},5.5296572936985713E-2,1,-87.505139368731648,null,{"$f":"(M16-M22)/M22","v":0.14856688633366588},0.16492204334236882,0.29918518510246617,-0.10741714210231706,1.1249767165492685E-2,-0.17060901327096137]
[8.3373269960326066,17,11,2.7995968788304437,7.8377426839571633,7.7760274404339835,3.1622573160428367,3.223972559566016,4.6144171711499357E-2,1,-77.585602684641529,null,{"$f":"(M17-M23)/M23","v":0.16492204334236882},3.4530695743075178E-2,0.25599027364120175,1.1249767165496027E-2,0.26693399668778262,9.837256050662728E-2]
[7.7323722447292553,18,10,2.6612697112778947,7.0823564761651294,7.0242505281238135,2.9176435238348715,2.975749471876187,3.8506628346874329E-2,1,-68.552509925834414,null,{"$f":"(M18-M24)/M24","v":0.29918518510246589},0.25599027364120175,0.42947241601055725,-0.17060901327096067,9.8372560506627058E-2,-0.12080205989904633]
[7.2370771856165597,19,10,2.5400783188093463,6.4519978656853141,6.3971474808514373,3.548002134314685,3.6028525191485632,3.2133211446827077E-2,1,-60.384169100375402]
[6.8315638888734176,20,3,2.43433213319791,5.9259729347198862,5.8740425205117566,-2.9259729347198862,-2.8740425205117566,2.6814689372052298E-2,1,-53.041784644244494]