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  377. 3.506170420950347`*^8}, {63.9`, 3.519154600804556`*^8}, {64.`,
  378.  
  379. 3.5322981180072695`*^8}, {64.1`, 3.545289680868335`*^8}, {64.2`,
  380.  
  381. 3.5581905592917013`*^8}, {64.30000000000001`,
  382.  
  383. 3.5704211897827905`*^8}, {64.4`, 3.582551007439326`*^8}, {64.5`,
  384.  
  385. 3.5944058332260954`*^8}, {64.6`, 3.605756569776652`*^8}, {64.7`,
  386.  
  387. 3.6164205471404`*^8}, {64.80000000000001`,
  388.  
  389. 3.6267334190372324`*^8}, {64.9`, 3.636912133768186`*^8}, {65.`,
  390.  
  391. 3.6463633306688815`*^8}, {65.1`, 3.655268696122972`*^8}, {65.2`,
  392.  
  393. 3.6635543329660434`*^8}, {65.30000000000001`,
  394.  
  395. 3.6713083830029327`*^8}, {65.4`, 3.6786690749869096`*^8}, {65.5`,
  396.  
  397. 3.6855780815393907`*^8}, {65.6`, 3.691908229707714`*^8}, {65.7`,
  398.  
  399. 3.697965049602041`*^8}, {65.80000000000001`,
  400.  
  401. 3.703591469341711`*^8}, {65.9`, 3.708577605620679`*^8}, {66.`,
  402.  
  403. 3.713301150699523`*^8}, {66.1`, 3.7174966664643246`*^8}, {66.2`,
  404.  
  405. 3.72155464312756`*^8}, {66.30000000000001`,
  406.  
  407. 3.725194219931153`*^8}, {66.4`, 3.728704857414911`*^8}, {66.5`,
  408.  
  409. 3.7319707439847356`*^8}, {66.6`, 3.735130511447414`*^8}, {66.7`,
  410.  
  411. 3.738044033955617`*^8}, {66.80000000000001`,
  412.  
  413. 3.740787563024863`*^8}, {66.9`, 3.743872606550009`*^8}, {67.`,
  414.  
  415. 3.7466644826032037`*^8}, {67.1`, 3.7494796011228526`*^8}, {67.2`,
  416.  
  417. 3.752567597003231`*^8}, {67.30000000000001`,
  418.  
  419. 3.755528597048888`*^8}, {67.4`, 3.758867756212609`*^8}, {67.5`,
  420.  
  421. 3.762253642893481`*^8}, {67.6`, 3.765563102468596`*^8}, {67.7`,
  422.  
  423. 3.76929418561745`*^8}, {67.80000000000001`,
  424.  
  425. 3.7734675463116574`*^8}, {67.9`, 3.777793327652246`*^8}, {68.`,
  426.  
  427. 3.78229775978888`*^8}, {68.1`, 3.786886041650724`*^8}, {68.2`,
  428.  
  429. 3.7921789819393176`*^8}, {68.30000000000001`,
  430.  
  431. 3.797400500297583`*^8}, {68.4`, 3.803015063139415`*^8}, {68.5`,
  432.  
  433. 3.809133938161798`*^8}, {68.6`, 3.815470864869022`*^8}, {68.7`,
  434.  
  435. 3.8222110275067735`*^8}, {68.80000000000001`,
  436.  
  437. 3.829037876579778`*^8}, {68.9`, 3.835887650962112`*^8}, {69.`,
  438.  
  439. 3.8435872719788545`*^8}, {69.1`, 3.851099881198329`*^8}, {69.2`,
  440.  
  441. 3.859342022241043`*^8}, {69.30000000000001`,
  442.  
  443. 3.867606783579225`*^8}, {69.4`, 3.8759238864472085`*^8}, {69.5`,
  444.  
  445. 3.8845543983685386`*^8}, {69.6`, 3.89349742833892`*^8}, {69.7`,
  446.  
  447. 3.9029700599955183`*^8}, {69.80000000000001`,
  448.  
  449. 3.912164360108417`*^8}, {69.9`, 3.9216870483815044`*^8}, {70.`,
  450.  
  451. 3.931483602407363`*^8}, {70.1`, 3.9410969655725956`*^8}, {70.2`,
  452.  
  453. 3.9513894195117193`*^8}, {70.30000000000001`,
  454.  
  455. 3.9616302770693266`*^8}, {70.4`, 3.9716179276966923`*^8}, {70.5`,
  456.  
  457. 3.982128004055699`*^8}, {70.6`, 3.9927235371773595`*^8}, {70.7`,
  458.  
  459. 4.003509165551405`*^8}, {70.80000000000001`,
  460.  
  461. 4.014030954849812`*^8}, {70.9`, 4.024962310210849`*^8}, {71.`,
  462.  
  463. 4.0358209453883123`*^8}, {71.1`, 4.0467931066218626`*^8}, {71.2`,
  464.  
  465. 4.057559335818988`*^8}, {71.30000000000001`,
  466.  
  467. 4.068661360490459`*^8}, {71.4`, 4.080052928244571`*^8}, {71.5`,
  468.  
  469. 4.091169005766451`*^8}, {71.6`, 4.102270502761557`*^8}, {71.7`,
  470.  
  471. 4.1138578091937834`*^8}, {71.80000000000001`,
  472.  
  473. 4.1251155210459965`*^8}, {71.9`, 4.1364941770349723`*^8}, {72.`,
  474.  
  475. 4.1479014369837517`*^8}, {72.1`, 4.1593269639449173`*^8}, {72.2`,
  476.  
  477. 4.170742870689594`*^8}, {72.30000000000001`,
  478.  
  479. 4.1822452256960845`*^8}, {72.4`, 4.19377280532779`*^8}, {72.5`,
  480.  
  481. 4.2054366824108684`*^8}, {72.6`, 4.2166842641395384`*^8}, {72.7`,
  482.  
  483. 4.2283143004773027`*^8}, {72.80000000000001`,
  484.  
  485. 4.240186452268878`*^8}, {72.9`, 4.251858930902198`*^8}, {73.`,
  486.  
  487. 4.2632043093512297`*^8}, {73.1`, 4.2749669162602633`*^8}, {73.2`,
  488.  
  489. 4.286488051759319`*^8}, {73.30000000000001`,
  490.  
  491. 4.2984178745028996`*^8}, {73.4`, 4.310295223728404`*^8}, {73.5`,
  492.  
  493. 4.321735402830664`*^8}, {73.6`, 4.333782728263144`*^8}, {73.7`,
  494.  
  495. 4.345358988467979`*^8}, {73.80000000000001`,
  496.  
  497. 4.357223893549589`*^8}, {73.9`, 4.368848682802905`*^8}, {74.`,
  498.  
  499. 4.381027789385323`*^8}, {74.1`, 4.392741358383033`*^8}, {74.2`,
  500.  
  501. 4.404523585717674`*^8}, {74.30000000000001`,
  502.  
  503. 4.4165790947883683`*^8}, {74.4`, 4.428364190545716`*^8}, {74.5`,
  504.  
  505. 4.4402239358321327`*^8}, {74.6`, 4.4520446091178155`*^8}, {74.7`,
  506.  
  507. 4.4640519786811954`*^8}, {74.80000000000001`,
  508.  
  509. 4.476036989583306`*^8}, {74.9`, 4.488212002259784`*^8}, {75.`,
  510.  
  511. 4.50016702284048`*^8}, {75.1`, 4.511972553212277`*^8}, {75.2`,
  512.  
  513. 4.524220942450661`*^8}, {75.30000000000001`,
  514.  
  515. 4.535864223500876`*^8}, {75.4`, 4.548080748479822`*^8}, {75.5`,
  516.  
  517. 4.5601746125887114`*^8}, {75.6`, 4.572276632620131`*^8}, {75.7`,
  518.  
  519. 4.5842204294312906`*^8}, {75.80000000000001`,
  520.  
  521. 4.596595601715562`*^8}, {75.9`, 4.6086719915453845`*^8}, {76.`,
  522.  
  523. 4.621003597526813`*^8}, {76.1`, 4.633181225397551`*^8}, {76.2`,
  524.  
  525. 4.645075736797058`*^8}, {76.30000000000001`,
  526.  
  527. 4.6572917749778366`*^8}, {76.4`, 4.669677776682115`*^8}, {76.5`,
  528.  
  529. 4.6817393303444105`*^8}, {76.6`, 4.694097331758887`*^8}, {76.7`,
  530.  
  531. 4.7063634216148126`*^8}, {76.80000000000001`,
  532.  
  533. 4.718550648902903`*^8}, {76.9`, 4.730765984916197`*^8}, {77.`,
  534.  
  535. 4.743005877022079`*^8}, {77.1`, 4.7555780128627634`*^8}, {77.2`,
  536.  
  537. 4.767942632996616`*^8}, {77.30000000000001`,
  538.  
  539. 4.7802375760961807`*^8}, {77.4`, 4.7925397668717337`*^8}, {77.5`,
  540.  
  541. 4.8048861965555114`*^8}, {77.6`, 4.8175653709807914`*^8}, {77.7`,
  542.  
  543. 4.829827580688622`*^8}, {77.80000000000001`,
  544.  
  545. 4.8422945178250486`*^8}, {77.9`, 4.8547249122644436`*^8}, {78.`,
  546.  
  547. 4.8672796681303275`*^8}, {78.1`, 4.8798126343066156`*^8}, {78.2`,
  548.  
  549. 4.892411314706424`*^8}, {78.30000000000001`,
  550.  
  551. 4.9046098222035885`*^8}, {78.4`, 4.9171998456332064`*^8}, {78.5`,
  552.  
  553. 4.92980620158521`*^8}, {78.6`, 4.9423632445393294`*^8}, {78.7`,
  554.  
  555. 4.954999596248343`*^8}, {78.80000000000001`,
  556.  
  557. 4.967454296502248`*^8}, {78.9`, 4.97999207575818`*^8}, {79.`,
  558.  
  559. 4.992957422144184`*^8}, {79.1`, 5.005565145880107`*^8}, {79.2`,
  560.  
  561. 5.0182334144736385`*^8}, {79.30000000000001`,
  562.  
  563. 5.0308015555361265`*^8}, {79.4`, 5.043309905755629`*^8}, {79.5`,
  564.  
  565. 5.0560503568740994`*^8}, {79.6`, 5.068821803821288`*^8}, {79.7`,
  566.  
  567. 5.0815950435918`*^8}, {79.80000000000001`,
  568.  
  569. 5.094525165929398`*^8}, {79.9`, 5.1070616158582973`*^8}, {80.`,
  570.  
  571. 5.12012990408671`*^8}}
  572.  
  573.  
  574.  
  575.  
  576. peakfunc[A_, \[Mu]_, \[Sigma]_, x_] =
  577.  
  578. A^2 E^(-((x - \[Mu])^2/(2 \[Sigma]^2)))
  579.  
  580. Clear[model]
  581.  
  582.  
  583.  
  584.  
  585. model[data_, n_] :=
  586.  
  587. Module[{dataconfig, modelfunc, objfunc, fitvar, fitres},
  588.  
  589. dataconfig = {A[#], \[Mu][#], \[Sigma][#]} & /@ Range[n];
  590.  
  591. modelfunc = peakfunc[##, fitvar] & @@@ dataconfig // Total;
  592.  
  593. objfunc =
  594.  
  595. Total[((Sqrt[data[[All, 2]]])/
  596.  
  597. data[[All,
  598.  
  599. 1]]) (data[[All, 2]] - (modelfunc /. fitvar -> # &) /@
  600.  
  601. data[[All, 1]])^2];
  602.  
  603. FindMinimum[objfunc, Flatten@dataconfig]]
  604.  
  605.  
  606.  
  607.  
  608. Clear[modelvalue]
  609.  
  610. modelvalue[data_, n_] /; NumericQ[n] :=
  611.  
  612. If[n >= 1, model[data, n][[1]], 0]
  613.  
  614.  
  615.  
  616.  
  617. fitres = ReleaseHold[
  618.  
  619. Hold[{Round[n], model[data, Round[n]]}] /.
  620.  
  621. FindMinimum[modelvalue[data, Round[n]], {n, 3},
  622.  
  623. Method -> "PrincipalAxis"][[2]]] // Quiet
  624.  
  625.  
  626.  
  627.  
  628. resfunc =
  629.  
  630. peakfunc[A[#], \[Mu][#], \[Sigma][#], x] & /@ Range[fitres[[1]]] /.
  631.  
  632. fitres[[2, 2]];
  633.  
  634.  
  635.  
  636.  
  637. Show@{Plot[Evaluate[resfunc], {x, 30, 80},
  638.  
  639. PlotStyle -> ({Directive[Dashed, Thick,
  640.  
  641. ColorData["Rainbow"][#]]} & /@
  642.  
  643. Rescale[Range[Length[resfunc]]]), PlotRange -> All,
  644.  
  645. Frame -> True, Axes -> False],
  646.  
  647. Plot[Evaluate[Total@resfunc], {x, 30, 80},
  648.  
  649. PlotStyle -> Directive[Thick, Red], PlotRange -> All,
  650.  
  651. Frame -> True, Axes -> False],
  652.  
  653. Graphics[{PointSize[.003], Gray, Line@data}]}
  654.  
  655.  
  656.  
  657.  
  658. {#, modelvalue[data, #]} & /@ Range[1, 13] //
  659.  
  660. ListLogPlot[#, Joined -> True] & // Quiet
  661.  
  662.  
  663.  
  664.  
  665. dataflat = Flatten@data;
  666.  
  667. (*Residuals plot*)
  668.  
  669. ListPlot[Transpose[{dataflat[[
  670.  
  671. 1 ;; -1 ;;
  672.  
  673. 2]], (dataflat[[2 ;; -1 ;; 2]] -
  674.  
  675. Table[Evaluate[Total@resfunc], {x, 30, 80, 0.1}])/
  676.  
  677. Sqrt[data[[All, 2]]]}], Filling -> Axis]
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