fitting using lsqcurve fit always giving initial value or one of the boundary conditions vale

I am working on fitting a function with 5 parameters. After giving the initial and boundary condition values, the lsqcurve fit function always gives either the initial value of the boundary values for the parameters. How can this be avoided and why does it happen ?

[Matt J]

Often, it happens when your objective function contains rounding or table-lookup operations, making it piece-wise flat, but we would need to see the code and data to have a clearer idea.

[Sahithya S Iyer]

the objective function code is as given below:

{ f=@(ini,x)fitng_func(ini,lt(:),ut(:),v1(:),v,l0,total_obs); [ini error]=lsqcurvefit(f,ini0,x,y,lb,ub,Optimset('Display','iter','TolFun',5.89e-009))

function q = fitng_func(ini,lt,ut,v1,v,l0,total_obs)

function nl = nl_func() function b = b_func() b = (-1)*(ini(1).*(lt+ut.*ini(2))+1); end

    function a = a_func()
        a=ini(1);
    end

    function c = c_func()
        c = ini(1).*lt.*ut.*ini(2);
    end

nl=(((-1)*b_func())-sqrt((b_func().*b_func())-(4.*a_func().*c_func())))./(2.*a_func()); end

n1=nl_func(); less_data=total_obs-1; q1 = ini(3).*v1(2:total_obs).*(n1(2:total_obs)-n1(1:less_data).*(1-v./v1(2:total_obs)))./(l0.*v); q=[0;q1]; end }

the data given are: X =

   0.159872102318145
   0.318594104308390
   0.476174451540647
   0.632621634384072
   0.787944180832135
   0.942150649734476
   1.095249624414796
   1.247249706655237
   1.398159511028487
   1.547987659559872
   1.696742776702832
   1.844433484611361
   1.991068398694775
   2.136656123440044
   2.281205248487944
   2.424724344950467
   2.567221961956482
   2.708706623414810
   2.849186824982533
   2.988671031228817
   3.127167672983912
   3.264685144863550
   3.401231802959949
   3.536815962690838
   3.671445896798316
   3.805129833489193
   3.937875954710451
   4.069692394552330
   4.200587237771377
   4.330568518429607
y =

                   0
 -11.970875328024491
 -11.305605271727272
 -12.218396970670840
 -11.387129995703109
 -11.432748162939383
  -4.397173478750450
  -0.025496126081728
  -0.027108056729776
  -0.029691693130599
  -0.032555302627605
  -0.036551892597730
  -0.039672059543856
  -0.040486745035987
  -0.046715729788864
  -0.049819373907396
  -0.049959641162103
  -0.051637573088091
  -0.056719840652825
  -0.056449110514077
  -0.058280823358226
  -0.060832824181501
  -0.062812338642387
  -0.064036739343408
  -0.071236931426518
  -0.068107023462374
  -0.070676809332754
  -0.072729699581921
  -0.079068823782647
  -0.077542242878192

[Sahithya S Iyer]

ini0=[10^(14) 1 -7] lb=[10^(13) 1 -10]; ub=[10^(15) 3 -1];

[Matt J]

Please highlight your code and apply the

toolbar button to format it. Please also attach your x,y in a .mat file so that we have the exact data.

[Sahithya S Iyer]

clc
  clear all
  hold on;

    y_tot=[
      -3.497458577973105
      -3.422672959194234
      -3.334843843563475
      -3.228646460386137
      -3.097941203805021
      -2.935215102618057
      -2.733090162927215
      -2.483701318876909
      -2.193254124181070
      -1.872215056983354
      -1.548347821734015
      -1.252567035390769
      -0.998499577686843
      -0.794119627382786
      -0.636861783802723
      -0.516695298177893
      -0.425872830644377
      -0.356490471923106
      -0.302358266913845
      -0.260317229611995
      -0.228615827053601
      -0.203095348981863
      -0.180955142570347
      -0.163439577226996
      -0.150576733922086
      -0.137981420111499
      -0.129705004841609
      -0.121459333418920
      -0.114092870358963  
    ];

    q=[
          -3.498555531811177
      -3.423624056709905
      -3.335433396853431
      -3.229149366019616
      -3.098444615640528
      -2.935611121616155
      -2.732635543386978
      -2.484124329747534
      -2.192343141143736
      -1.871961931004800
      -1.549022861809153
      -1.251541670523438
      -0.998326644944361
      -0.794941572898976
      -0.637258704637672
      -0.517033078376788
      -0.425708767366708
      -0.356046505438913
      -0.302453351208873
      -0.260785926207760
      -0.228026577976551
      -0.201985307313793
      -0.181066611360143
      -0.164098912643618
      -0.150213340442235
      -0.138758498278120
      -0.129240590393676
      -0.121281175280005
      -0.114587134782998
      ];

    x=[
          0.179209183673469
       0.267848128991614
       0.355849669341040
       0.443218601718076
       0.529959740475643
       0.616077913733323
       0.701577959993571
       0.786464724953524
       0.870743058502428
       0.954417811895343
       1.037493835093891
       1.119975974265811
       1.201869069435025
       1.283177952274469
       1.363907444034638
       1.444062353600521
       1.523647475670831
       1.602667589052675
       1.681127455066209
       1.759031816053450
       1.836385393985747
       1.913192889164972
       1.989458979013596
       2.065188316949052
       2.140385531337671
       2.215055224524629
       2.289201971935686
       2.362830321246400
       2.435944791616654
       ];

    format long
    v=10;
    l0=5*10^4;
    u0=40*10^2;
    data=29;
    total_obs=data;
    v_upper=1400+total_obs-1;
    v1=[1400:v_upper];
    i=[1:total_obs];
    lt=(1-(1-v./v1).^i)*l0;
    ut=((1-v./v1).^i)*u0;
    less_data=total_obs-1;
    f=@(ini,x)model1_fitng_func(ini,lt(:),ut(:),v1(:),v,l0,total_obs,Optimset());

     ini0=[0.005 1 -3.76];
    lb=[ 0.003 0  -6];
    ub=[ 0.009 2  0];

    param=3;
    sum=0;
    sq_resi=(y_tot-q).*(y_tot-q);
    for i = 1:data
        sum=sum + sq_resi(i:i);
    end
    rmssr=sqrt(sum/(data-param));
    sd=1.5*rmssr;
    mean=0;
    sim_num=1000;

    for j = 1:sim_num
        R=normrnd(mean,sd,[data,1]);
        y1=q+R;
         f=@(ini,x)model1_fitng_func(ini,lt(:),ut(:),v1(:),v,l0,total_obs);
        [ini resnorm residual]=lsqcurvefit(f,ini0,x,y1,lb,ub);  
        new_p(j,:)=ini;
        new_error(j,:)=resnorm;
    end

    fid1=fopen('confi1','w');
    fid2=fopen('confi2','w');
    fid3=fopen('confi3','w');

    for z = 1:sim_num
        new_p(z,:)
        new_error(z,:);

        fprintf(fid1,'%f\n',new_p(z,1));
        fprintf(fid2,'%f\n',new_p(z,2));
        fprintf(fid3,'%f\n',new_p(z,3));

    end

    fclose(fid1);
    fclose(fid2);
    fclose(fid3);
--------------------------------------------------------------------------

The function is --

function q = model1_fitng_func(ini,lt,ut,v1,v,l0,total_obs)

function  nl = nl_func()
    function b = b_func()
        b = (-1)*(ini(1).*(lt+ut.*ini(2))+1);
    end

      function a = a_func()
          a=ini(1);
      end

      function c = c_func()
          c = ini(1).*lt.*ut.*ini(2);
      end

nl=(((-1)*b_func())-sqrt((b_func().*b_func())-(4.*a_func().*c_func())))./(2.*a_func());
end

n1=nl_func();
less_data=total_obs-1;
q1 = ini(3).*v1(2:total_obs).*(n1(2:total_obs)-n1(1:less_data).*(1-v./v1(2:total_obs)))./(l0.*v);
q=[0;q1];
end