Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

Hello . i try to curve fit nonliner equation by lsqcurvefit and get error.

function F = myfunp(a,data)
zdata=[2370.1776112981,26665.5436328856,33999.0700566522,43581.3827551805,56913.3992480947,88844.7226527384,130991.934524133,15112.911231467,176285.501029454,223360.820798491,294455.827929450,35478.787278946,411258.878280649,422702.346106183,511111.835129998,633910.342810244,780340.236378774,619555.134715430,633756.837052416,788803.530398270,777517.401792431,773693.310713579,844333.304097923,150471.6450798029,20517.8541413645,28176.4764184613,29779.9220185300,584153.2552467975,757318.1239141541,984123.5255855076,127002.474102260,157119.325006092,211544.282909359,281369.717982640,271505.093553462,327050.316856829,344420.741097441,374147.438486281,421984.526771006,432866.381682883,554318.948982768,471859.782416242,584014.198110098,622301.344956696]
ydata=[473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000];
xdata=[1.08768000000,4.56728200000,4.99472000000,5.392799100000,6.791900000,8.11234546400000,11.3288295200000,15.2542138200000,23.7895322600000,38.9844910700000,70.9384511000000,100.361732800000,139.249301900000,168.187221200000,275.463489000000,323.697079700000,380.152481600000,511.387441300000,718.018141700000,852.617257800000,927.814899300000,1311.46673800000,1594.53133400000,2.170800000,3.2341306200000,4.161204900000,6.9362766600000,7.13110839100000,12.3316076700000,15.1135745800000,26.7895322600000,37.2653961400000,50.5485060700000,80.8837167700000,89.4791805100000,115.361732800000,129.025620400000,135.094336600000,219.59504900000,258.623830500000,333.908380200000,328.757892400000,444.190385600000,630.380891400000,751.682901300000,871.212537500000,1157.09126200000,1521.09905800000,4.75969298600000,7.91421685000000,10.4898360300000,13.7855398600000,23.1085904900000,30.23414500000,44.5823445700000,67.94350200000,92.278451600000,120.278265300000,122.956453700000,281.618343800000,333.757892400000,419.290040000000,555.402383500000,628.192380300000,831.755300000];
data = [xdata ; ydata];
x=data(1,1);
y=data(2,1);
fun= @(a,data)(1./a(1)).*(((x.*exp(a(2)./(8.314.*y))./a(3)).^(1./a(4)))+sqrt((((x.*exp(a(2)./(8.314.*y))./a(3)).^(2./a(4)))+1)));
a0 = [3; 66666; 2e+10; 2];
lb=[0; 5555; 1e+10 ; 0];
ub=[258; 205588; 1e+15 ; 4];
a = lsqcurvefit(@myfun, a0, data, zdata,lb ,ub)

thank you .

Best regards

Answer 1

[Walter Roberson]

format long g
zdata=[2370.1776112981,26665.5436328856,33999.0700566522,43581.3827551805,56913.3992480947,88844.7226527384,130991.934524133,15112.911231467,176285.501029454,223360.820798491,294455.827929450,35478.787278946,411258.878280649,422702.346106183,511111.835129998,633910.342810244,780340.236378774,619555.134715430,633756.837052416,788803.530398270,777517.401792431,773693.310713579,844333.304097923,150471.6450798029,20517.8541413645,28176.4764184613,29779.9220185300,584153.2552467975,757318.1239141541,984123.5255855076,127002.474102260,157119.325006092,211544.282909359,281369.717982640,271505.093553462,327050.316856829,344420.741097441,374147.438486281,421984.526771006,432866.381682883,554318.948982768,471859.782416242,584014.198110098,622301.344956696]

zdata = 1×44

2370.1776112981 26665.5436328856 33999.0700566522 43581.3827551805 56913.3992480947 88844.7226527384 130991.934524133 15112.911231467 176285.501029454 223360.820798491 294455.82792945 35478.787278946 411258.878280649 422702.346106183 511111.835129998 633910.342810244 780340.236378774 619555.13471543 633756.837052416 788803.53039827 777517.401792431 773693.310713579 844333.304097923 150471.645079803 20517.8541413645 28176.4764184613 29779.92201853 584153.255246797 757318.123914154 984123.525585508

ydata=[473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,473.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,483.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000,493.150000000000];
xdata=[1.08768000000,4.56728200000,4.99472000000,5.392799100000,6.791900000,8.11234546400000,11.3288295200000,15.2542138200000,23.7895322600000,38.9844910700000,70.9384511000000,100.361732800000,139.249301900000,168.187221200000,275.463489000000,323.697079700000,380.152481600000,511.387441300000,718.018141700000,852.617257800000,927.814899300000,1311.46673800000,1594.53133400000,2.170800000,3.2341306200000,4.161204900000,6.9362766600000,7.13110839100000,12.3316076700000,15.1135745800000,26.7895322600000,37.2653961400000,50.5485060700000,80.8837167700000,89.4791805100000,115.361732800000,129.025620400000,135.094336600000,219.59504900000,258.623830500000,333.908380200000,328.757892400000,444.190385600000,630.380891400000,751.682901300000,871.212537500000,1157.09126200000,1521.09905800000,4.75969298600000,7.91421685000000,10.4898360300000,13.7855398600000,23.1085904900000,30.23414500000,44.5823445700000,67.94350200000,92.278451600000,120.278265300000,122.956453700000,281.618343800000,333.757892400000,419.290040000000,555.402383500000,628.192380300000,831.755300000];
size(xdata)

ans = 1×2

1 65

size(ydata)

ans = 1×2

1 61

N = min([length(xdata), length(ydata), length(zdata)]);
data = [xdata(1:N); ydata(1:N)].';  %x y must be columns
fun= @(a,data)(1./a(1)).*(((data(:,1).*exp(a(2)./(8.314.*data(:,2)))./a(3)).^(1./a(4)))+sqrt((((data(:,1).*exp(a(2)./(8.314.*data(:,2)))./a(3)).^(2./a(4)))+1)));
a0 = [3; 66666; 2e+10; 2];
lb=[0; 5555; 1e+10 ; 0];
ub=[258; 205588; 1e+15 ; 4];
a = lsqcurvefit(fun, a0, data, reshape(zdata(1:N), [], 1),lb ,ub)

Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.

a = 4×1

7.36857657624095e-06 76932.5702990955 18995165527.3496 2.83794699233607

[Walter Roberson]

Your X, Y, and Z are all different lengths.

Your data has to be arranged in columns.

You were asking for function @myfun after naming your anonymous function fun

You were extracting only one x and one y and using those in your fitting, instead of using all of the x and all of the y

You cannot just use your x and y as constants in your fitting: the fitting process passes in some trial data of different size, so you have to use the data passed in.