MATLAB Newsgroup

Hi,

I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

Initial point is a local minimum.

Optimization completed because the size of the gradient at the initial point

is less than the default value of the function tolerance.

The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

My function is the following :

function F = myfun(x,T)

%UNTITLED2 Summary of this function goes here

% Detailed explanation goes here

F=exp(-x(1)./T)./(x(2).*T.^(1/2)+x(3).*T.^(3/2));

end

I can' t really provide you my data but there is about 200 points.

Thanks for your help.

Kevin

"Kevin " <kevheritier@gmail.com> wrote in message <kaoe1i$4ar$1@newscl01ah.mathworks.com>...

> Hi,

>

> I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

>

> Initial point is a local minimum.

>

> Optimization completed because the size of the gradient at the initial point

> is less than the default value of the function tolerance.

>

> The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

===============

Perhaps, but what evidence do you see that the outcome is bad? The message you displayed doesn't indicate that anything is wrong.

"Kevin " <kevheritier@gmail.com> wrote in message <kaoe1i$4ar$1@newscl01ah.mathworks.com>...

> Hi,

>

> I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

>

> Initial point is a local minimum.

>

> Optimization completed because the size of the gradient at the initial point

> is less than the default value of the function tolerance.

>

> The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

>

> My function is the following :

>

> function F = myfun(x,T)

> %UNTITLED2 Summary of this function goes here

> % Detailed explanation goes here

> F=exp(-x(1)./T)./(x(2).*T.^(1/2)+x(3).*T.^(3/2));

> end

>

> I can' t really provide you my data but there is about 200 points.

>

> Thanks for your help.

>

> Kevin

If the components of the vector F become very small, you should adjust the parameter 'TolFun' in the options for lsqcurvefit (or multiply F by a large constant).

Best wishes

Torsten.

"Torsten" wrote in message <kapb6v$nho$1@newscl01ah.mathworks.com>...

> "Kevin " <kevheritier@gmail.com> wrote in message <kaoe1i$4ar$1@newscl01ah.mathworks.com>...

> > Hi,

> >

> > I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

> >

> > Initial point is a local minimum.

> >

> > Optimization completed because the size of the gradient at the initial point

> > is less than the default value of the function tolerance.

> >

> > The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

> >

> > My function is the following :

> >

> > function F = myfun(x,T)

> > %UNTITLED2 Summary of this function goes here

> > % Detailed explanation goes here

> > F=exp(-x(1)./T)./(x(2).*T.^(1/2)+x(3).*T.^(3/2));

> > end

> >

> > I can' t really provide you my data but there is about 200 points.

> >

> > Thanks for your help.

> >

> > Kevin

>

> If the components of the vector F become very small, you should adjust the parameter 'TolFun' in the options for lsqcurvefit (or multiply F by a large constant).

>

> Best wishes

> Torsten.

Hi,

Thanks for your help, I changed the value of TolFun and tried a lot of values. The algorithm now starts but the result is still very bad. For example, the scale of the fitted points is about 10^-5 whereas as I said my ydata is around 10^-10. The fitted points are very far from the data points.

Any idea of which parameters could I change?

Thanks

On 18 Dez., 17:53, "Kevin " <kevherit...@gmail.com> wrote:

> "Torsten" wrote in message <kapb6v$nh...@newscl01ah.mathworks.com>...

> > "Kevin " <kevherit...@gmail.com> wrote in message <kaoe1i$4a...@newscl01ah.mathworks.com>...

> > > Hi,

>

> > > I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

>

> > > Initial point is a local minimum.

>

> > > Optimization completed because the size of the gradient at the initial point

> > > is less than the default value of the function tolerance.

>

> > > The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

>

> > > My function is the following :

>

> > > function F = myfun(x,T)

> > > %UNTITLED2 Summary of this function goes here

> > > % Detailed explanation goes here

> > > F=exp(-x(1)./T)./(x(2).*T.^(1/2)+x(3).*T.^(3/2));

> > > end

>

> > > I can' t really provide you my data but there is about 200 points.

>

> > > Thanks for your help.

>

> > > Kevin

>

> > If the components of the vector F become very small, you should adjust the parameter 'TolFun' in the options for lsqcurvefit (or multiply F by a large constant).

>

> > Best wishes

> > Torsten.

>

> Hi,

>

> Thanks for your help, I changed the value of TolFun and tried a lot of values. The algorithm now starts but the result is still very bad. For example, the scale of the fitted points is about 10^-5 whereas as I said my ydata is around 10^-10. The fitted points are very far from the data points.

>

> Any idea of which parameters could I change?

>

> Thanks

If your y-data are around 10^(-10), TolFun should be in the order of

10^(-14) or so.

Further, you should try several initial guesses for the parameters

x(1)-x(3).

I think nothing more can be said unless you give us more detailed

information about your data points (T,y(T)).

Best wishes

Torsten.

"Torsten" wrote in message <0a2dafb2-7b73-49fb-afa5-923dbd9520ce@f8g2000yqa.googlegroups.com>...

> On 18 Dez., 17:53, "Kevin " <kevherit...@gmail.com> wrote:

> > "Torsten" wrote in message <kapb6v$nh...@newscl01ah.mathworks.com>...

> > > "Kevin " <kevherit...@gmail.com> wrote in message <kaoe1i$4a...@newscl01ah.mathworks.com>...

> > > > Hi,

> >

> > > > I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

> >

> > > > Initial point is a local minimum.

> >

> > > > Optimization completed because the size of the gradient at the initial point

> > > > is less than the default value of the function tolerance.

> >

> > > > The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

> >

> > > > My function is the following :

> >

> > > > function F = myfun(x,T)

> > > > %UNTITLED2 Summary of this function goes here

> > > > % Detailed explanation goes here

> > > > F=exp(-x(1)./T)./(x(2).*T.^(1/2)+x(3).*T.^(3/2));

> > > > end

> >

> > > > I can' t really provide you my data but there is about 200 points.

> >

> > > > Thanks for your help.

> >

> > > > Kevin

> >

> > > If the components of the vector F become very small, you should adjust the parameter 'TolFun' in the options for lsqcurvefit (or multiply F by a large constant).

> >

> > > Best wishes

> > > Torsten.

> >

> > Hi,

> >

> > Thanks for your help, I changed the value of TolFun and tried a lot of values. The algorithm now starts but the result is still very bad. For example, the scale of the fitted points is about 10^-5 whereas as I said my ydata is around 10^-10. The fitted points are very far from the data points.

> >

> > Any idea of which parameters could I change?

> >

> > Thanks

>

> If your y-data are around 10^(-10), TolFun should be in the order of

> 10^(-14) or so.

> Further, you should try several initial guesses for the parameters

> x(1)-x(3).

>

> I think nothing more can be said unless you give us more detailed

> information about your data points (T,y(T)).

>

> Best wishes

> Torsten.

Hi Torsten,

Thank you very much for your help.

I tried with many starting values and I reached a results which is not too bad but unfortunately, I would have expected more accuracy from a LS method.

I am gonna give you my data if you have time to check and figure out what's wrong it would be great.

The function has a bit changed because I added a proportional parameters it is :

function [F] = myfun(x,T)

F=x(1)*exp(-x(4)./T)./(x(3).*T.^(1/2)+x(2).*T.^(3/2));

end

Values of T (this is not an uniform distribution so I have to display everything sorry):

0.100034482758621 0.200068965517241 0.300103448275862 0.400137931034483 0.500172413793103 0.600206896551724 0.700241379310345 0.800275862068966 0.900310344827586 1.00034482758621 1.10037931034483 1.20041379310345 1.30044827586207 1.40048275862069 1.50051724137931 1.60055172413793 1.70058620689655 1.80062068965517 1.90065517241379 2.00068965517241 2.10072413793103 2.20075862068966 2.30079310344828 2.40082758620690 2.50086206896552 2.60089655172414 2.70093103448276 2.80096551724138 2.90100000000000 3.00103448275862 3.10106896551724 3.20110344827586 3.30113793103448 3.40117241379310 3.50120689655172 3.60124137931035 3.70127586206897 3.80131034482759 3.90134482758621 4.00137931034483 4.10141379310345 4.20144827586207 4.30148275862069 4.40151724137931 4.50155172413793 4.60158620689655 4.70162068965517 4.80165517241379 4.90168965517241 5.00172413793104 5.10175862068966 5.20179310344828 5.30182

758620690 5.40186206896552 5.50189655172414 5.60193103448276 5.70196551724138 5.80200000000000 5.90203448275862 6.00206896551724 6.10210344827586 6.20213793103448 6.30217241379310 6.40220689655173 6.50224137931035 6.60227586206897 6.70231034482759 6.80234482758621 6.90237931034483 7.00241379310345 7.10244827586207 7.20248275862069 7.30251724137931 7.40255172413793 7.50258620689655 7.60262068965517 7.70265517241379 7.80268965517241 7.90272413793104 8.00275862068965 8.10279310344828 8.20282758620690 8.30286206896552 8.40289655172414 8.50293103448276 8.60296551724138 8.70300000000000 8.80303448275862 8.90306896551724 9.00310344827586 9.10313793103448 9.20317241379310 9.30320689655173 9.40324137931035 9.50327586206897 9.60331034482759 9.70334482758621 9.80337931034483 9.90341379310345 10.0034482758621 10.1034827586207 10.1034827586207 11.1038275862069 12.1041724137931 13.1045172413793 14.104

8620689655 15.1052068965517 16.1055517241379 17.1058965517241 18.1062413793103 19.1065862068966 20.1069310344828 21.1072758620690 22.1076206896552 23.1079655172414 24.1083103448276 25.1086551724138 26.1090000000000 27.1093448275862 28.1096896551724 29.1100344827586 30.1103793103448 31.1107241379310 32.1110689655172 33.1114137931035 34.1117586206897 35.1121034482759 36.1124482758621 37.1127931034483 38.1131379310345 39.1134827586207 40.1138275862069 41.1141724137931 42.1145172413793 43.1148620689655 44.1152068965517 45.1155517241379 46.1158965517241 47.1162413793103 48.1165862068966 49.1169310344828 50.1172758620690 51.1176206896552 52.1179655172414 53.1183103448276 54.1186551724138 55.1190000000000 56.1193448275862 57.1196896551724 58.1200344827586 59.1203793103448 60.1207241379310 61.1210689655172 62.1214137931035 63.1217586206897 64.1221034482759 65.1224482758621 66.1227931034483 67.12

31379310345 68.1234827586207 69.1238275862069 70.1241724137931 71.1245172413793 72.1248620689655 73.1252068965517 74.1255517241379 75.1258965517241 76.1262413793103 77.1265862068966 78.1269310344828 79.1272758620690 80.1276206896552 81.1279655172414 82.1283103448276 83.1286551724138 84.1290000000000 85.1293448275862 86.1296896551724 87.1300344827586 88.1303793103448 89.1307241379310 90.1310689655172 91.1314137931034 92.1317586206897 93.1321034482759 94.1324482758621 95.1327931034483 96.1331379310345 97.1334827586207 98.1338275862069 99.1341724137931 100.134517241379 101.134862068966 102.135206896552 103.135551724138 104.135896551724 105.136241379310 106.136586206897 107.136931034483 108.137275862069 109.137620689655 110.137965517241

Values of ydata:

1.24600000000000e-12 1.87100000000000e-11 2.28800000000000e-10 8.53900000000000e-10 1.81700000000000e-09 2.91200000000000e-09 3.97400000000000e-09 4.91400000000000e-09 5.69900000000000e-09 6.32700000000000e-09 6.81100000000000e-09 7.17000000000000e-09 7.42500000000000e-09 7.59400000000000e-09 7.69400000000000e-09 7.73700000000000e-09 7.73600000000000e-09 7.70000000000000e-09 7.63600000000000e-09 7.55100000000000e-09 7.44900000000000e-09 7.33600000000000e-09 7.21300000000000e-09 7.08400000000000e-09 6.95100000000000e-09 6.81500000000000e-09 6.67700000000000e-09 6.54000000000000e-09 6.40300000000000e-09 6.26700000000000e-09 6.13300000000000e-09 6.00100000000000e-09 5.87200000000000e-09 5.74500000000000e-09 5.62200000000000e-09 5.50100000000000e-09 5.38300000000000e-09 5.26800000000000e-09 5.15600000000000e-09 5.04700000000000e-09 4.94100000000000e-09 4.83900000000000e-09 4.73900000000000e-

09 4.64100000000000e-09 4.54700000000000e-09 4.45500000000000e-09 4.36700000000000e-09 4.28000000000000e-09 4.19600000000000e-09 4.11500000000000e-09 4.03600000000000e-09 3.95900000000000e-09 3.88400000000000e-09 3.81100000000000e-09 3.74100000000000e-09 3.67200000000000e-09 3.60600000000000e-09 3.54100000000000e-09 3.47800000000000e-09 3.41700000000000e-09 3.35700000000000e-09 3.29900000000000e-09 3.24300000000000e-09 3.18800000000000e-09 3.13400000000000e-09 3.08200000000000e-09 3.03100000000000e-09 2.98200000000000e-09 2.93400000000000e-09 2.88700000000000e-09 2.84100000000000e-09 2.79700000000000e-09 2.75300000000000e-09 2.71100000000000e-09 2.66900000000000e-09 2.62900000000000e-09 2.59000000000000e-09 2.55100000000000e-09 2.51400000000000e-09 2.47700000000000e-09 2.44100000000000e-09 2.40600000000000e-09 2.37200000000000e-09 2.33900000000000e-09 2.30600000000000e-09 2.2740000000000

0e-09 2.24300000000000e-09 2.21300000000000e-09 2.18300000000000e-09 2.15400000000000e-09 2.12500000000000e-09 2.09700000000000e-09 2.07000000000000e-09 2.04300000000000e-09 2.01700000000000e-09 1.99100000000000e-09 1.96600000000000e-09 1.94200000000000e-09 1.91800000000000e-09 1.89400000000000e-09 1.87100000000000e-09 1.87100000000000e-09 1.66300000000000e-09 1.49000000000000e-09 1.34500000000000e-09 1.22200000000000e-09 1.11600000000000e-09 1.02500000000000e-09 9.45700000000000e-10 8.75900000000000e-10 8.14200000000000e-10 7.59400000000000e-10 7.10500000000000e-10 6.66600000000000e-10 6.27100000000000e-10 5.91300000000000e-10 5.58700000000000e-10 5.29000000000000e-10 5.01900000000000e-10 4.77000000000000e-10 4.54100000000000e-10 4.33000000000000e-10 4.13400000000000e-10 3.95300000000000e-10 3.78500000000000e-10 3.62800000000000e-10 3.48200000000000e-10 3.34500000000000e-10 3.2170000000

0000e-10 3.09700000000000e-10 2.98400000000000e-10 2.87800000000000e-10 2.77800000000000e-10 2.68400000000000e-10 2.59500000000000e-10 2.51000000000000e-10 2.43100000000000e-10 2.35500000000000e-10 2.28300000000000e-10 2.21500000000000e-10 2.15000000000000e-10 2.08800000000000e-10 2.02900000000000e-10 1.97300000000000e-10 1.91900000000000e-10 1.86800000000000e-10 1.81900000000000e-10 1.77200000000000e-10 1.72700000000000e-10 1.68400000000000e-10 1.64300000000000e-10 1.60300000000000e-10 1.56500000000000e-10 1.52900000000000e-10 1.49300000000000e-10 1.46000000000000e-10 1.42700000000000e-10 1.39600000000000e-10 1.36500000000000e-10 1.33600000000000e-10 1.30800000000000e-10 1.28100000000000e-10 1.25500000000000e-10 1.22900000000000e-10 1.20500000000000e-10 1.18100000000000e-10 1.15800000000000e-10 1.13600000000000e-10 1.11400000000000e-10 1.09300000000000e-10 1.07300000000000e-10 1.0540000

0000000e-10 1.03500000000000e-10 1.01600000000000e-10 9.98200000000000e-11 9.80800000000000e-11 9.63900000000000e-11 9.47500000000000e-11 9.31600000000000e-11 9.16100000000000e-11 9.01000000000000e-11 8.86300000000000e-11 8.72000000000000e-11 8.58100000000000e-11 8.44600000000000e-11 8.31400000000000e-11 8.18600000000000e-11 8.06100000000000e-11 7.93900000000000e-11 7.82000000000000e-11 7.70400000000000e-11 7.59100000000000e-11 7.48000000000000e-11 7.37300000000000e-11 7.26700000000000e-11 7.16500000000000e-11 7.06400000000000e-11 6.96600000000000e-11 6.87100000000000e-11 6.77700000000000e-11 6.68600000000000e-11 6.59600000000000e-11

Sorry for the lenght of the message and thanks for your help.

Best wishes

Kevin

"Kevin " <kevheritier@gmail.com> wrote in message <kb25f3$6om$1@newscl01ah.mathworks.com>...

> "Torsten" wrote in message <0a2dafb2-7b73-49fb-afa5-923dbd9520ce@f8g2000yqa.googlegroups.com>...

> > On 18 Dez., 17:53, "Kevin " <kevherit...@gmail.com> wrote:

> > > "Torsten" wrote in message <kapb6v$nh...@newscl01ah.mathworks.com>...

> > > > "Kevin " <kevherit...@gmail.com> wrote in message <kaoe1i$4a...@newscl01ah.mathworks.com>...

> > > > > Hi,

> > >

> > > > > I am trying to fit a curve with the non linear LS method. When I try with the examples provided by Mathworks everything works fine but when I try with my data, the algorithm stop at the first iteration and I obtain the following message :

> > >

> > > > > Initial point is a local minimum.

> > >

> > > > > Optimization completed because the size of the gradient at the initial point

> > > > > is less than the default value of the function tolerance.

> > >

> > > > > The difference between my data and the examples is that my data is composed of very small values (between e-12 and e-9) So I was wondering if it could be due to the condition of convergence that I should change but I don't know how to do that.

> > >

> > > > > My function is the following :

> > >

> > > > > function F = myfun(x,T)

> > > > > %UNTITLED2 Summary of this function goes here

> > > > > % Detailed explanation goes here

> > > > > F=exp(-x(1)./T)./(x(2).*T.^(1/2)+x(3).*T.^(3/2));

> > > > > end

> > >

> > > > > I can' t really provide you my data but there is about 200 points.

> > >

> > > > > Thanks for your help.

> > >

> > > > > Kevin

> > >

> > > > If the components of the vector F become very small, you should adjust the parameter 'TolFun' in the options for lsqcurvefit (or multiply F by a large constant).

> > >

> > > > Best wishes

> > > > Torsten.

> > >

> > > Hi,

> > >

> > > Thanks for your help, I changed the value of TolFun and tried a lot of values. The algorithm now starts but the result is still very bad. For example, the scale of the fitted points is about 10^-5 whereas as I said my ydata is around 10^-10. The fitted points are very far from the data points.

> > >

> > > Any idea of which parameters could I change?

> > >

> > > Thanks

> >

> > If your y-data are around 10^(-10), TolFun should be in the order of

> > 10^(-14) or so.

> > Further, you should try several initial guesses for the parameters

> > x(1)-x(3).

> >

> > I think nothing more can be said unless you give us more detailed

> > information about your data points (T,y(T)).

> >

> > Best wishes

> > Torsten.

>

> Hi Torsten,

>

> Thank you very much for your help.

> I tried with many starting values and I reached a results which is not too bad but unfortunately, I would have expected more accuracy from a LS method.

> I am gonna give you my data if you have time to check and figure out what's wrong it would be great.

>

> The function has a bit changed because I added a proportional parameters it is :

>

> function [F] = myfun(x,T)

> F=x(1)*exp(-x(4)./T)./(x(3).*T.^(1/2)+x(2).*T.^(3/2));

> end

>

> Values of T (this is not an uniform distribution so I have to display everything sorry):

>

0.100034482758621 0.200068965517241 0.300103448275862 0.400137931034483 0.500172413793103 0.600206896551724 0.700241379310345 0.800275862068966 0.900310344827586 1.00034482758621 1.10037931034483 1.20041379310345 1.30044827586207 1.40048275862069 1.50051724137931 1.60055172413793 1.70058620689655 1.80062068965517 1.90065517241379 2.00068965517241 2.10072413793103 2.20075862068966 2.30079310344828 2.40082758620690 2.50086206896552 2.60089655172414 2.70093103448276 2.80096551724138 2.90100000000000 3.00103448275862 3.10106896551724 3.20110344827586 3.30113793103448 3.40117241379310 3.50120689655172 3.60124137931035 3.70127586206897 3.80131034482759 3.90134482758621 4.00137931034483 4.10141379310345 4.20144827586207 4.30148275862069 4.40151724137931 4.50155172413793 4.60158620689655 4.70162068965517 4.80165517241379 4.90168965517241 5.00172413793104 5.10175862068966 5.20179310344828 5.30182

>

758620690 5.40186206896552 5.50189655172414 5.60193103448276 5.70196551724138 5.80200000000000 5.90203448275862 6.00206896551724 6.10210344827586 6.20213793103448 6.30217241379310 6.40220689655173 6.50224137931035 6.60227586206897 6.70231034482759 6.80234482758621 6.90237931034483 7.00241379310345 7.10244827586207 7.20248275862069 7.30251724137931 7.40255172413793 7.50258620689655 7.60262068965517 7.70265517241379 7.80268965517241 7.90272413793104 8.00275862068965 8.10279310344828 8.20282758620690 8.30286206896552 8.40289655172414 8.50293103448276 8.60296551724138 8.70300000000000 8.80303448275862 8.90306896551724 9.00310344827586 9.10313793103448 9.20317241379310 9.30320689655173 9.40324137931035 9.50327586206897 9.60331034482759 9.70334482758621 9.80337931034483 9.90341379310345 10.0034482758621 10.1034827586207 10.1034827586207 11.1038275862069 12.1041724137931 13.1045172413793 14.104

>

8620689655 15.1052068965517 16.1055517241379 17.1058965517241 18.1062413793103 19.1065862068966 20.1069310344828 21.1072758620690 22.1076206896552 23.1079655172414 24.1083103448276 25.1086551724138 26.1090000000000 27.1093448275862 28.1096896551724 29.1100344827586 30.1103793103448 31.1107241379310 32.1110689655172 33.1114137931035 34.1117586206897 35.1121034482759 36.1124482758621 37.1127931034483 38.1131379310345 39.1134827586207 40.1138275862069 41.1141724137931 42.1145172413793 43.1148620689655 44.1152068965517 45.1155517241379 46.1158965517241 47.1162413793103 48.1165862068966 49.1169310344828 50.1172758620690 51.1176206896552 52.1179655172414 53.1183103448276 54.1186551724138 55.1190000000000 56.1193448275862 57.1196896551724 58.1200344827586 59.1203793103448 60.1207241379310 61.1210689655172 62.1214137931035 63.1217586206897 64.1221034482759 65.1224482758621 66.1227931034483 67.12

> 31379310345 68.1234827586207 69.1238275862069 70.1241724137931 71.1245172413793 72.1248620689655 73.1252068965517 74.1255517241379 75.1258965517241 76.1262413793103 77.1265862068966 78.1269310344828 79.1272758620690 80.1276206896552 81.1279655172414 82.1283103448276 83.1286551724138 84.1290000000000 85.1293448275862 86.1296896551724 87.1300344827586 88.1303793103448 89.1307241379310 90.1310689655172 91.1314137931034 92.1317586206897 93.1321034482759 94.1324482758621 95.1327931034483 96.1331379310345 97.1334827586207 98.1338275862069 99.1341724137931 100.134517241379 101.134862068966 102.135206896552 103.135551724138 104.135896551724 105.136241379310 106.136586206897 107.136931034483 108.137275862069 109.137620689655 110.137965517241

>

> Values of ydata:

>

>

1.24600000000000e-12 1.87100000000000e-11 2.28800000000000e-10 8.53900000000000e-10 1.81700000000000e-09 2.91200000000000e-09 3.97400000000000e-09 4.91400000000000e-09 5.69900000000000e-09 6.32700000000000e-09 6.81100000000000e-09 7.17000000000000e-09 7.42500000000000e-09 7.59400000000000e-09 7.69400000000000e-09 7.73700000000000e-09 7.73600000000000e-09 7.70000000000000e-09 7.63600000000000e-09 7.55100000000000e-09 7.44900000000000e-09 7.33600000000000e-09 7.21300000000000e-09 7.08400000000000e-09 6.95100000000000e-09 6.81500000000000e-09 6.67700000000000e-09 6.54000000000000e-09 6.40300000000000e-09 6.26700000000000e-09 6.13300000000000e-09 6.00100000000000e-09 5.87200000000000e-09 5.74500000000000e-09 5.62200000000000e-09 5.50100000000000e-09 5.38300000000000e-09 5.26800000000000e-09 5.15600000000000e-09 5.04700000000000e-09 4.94100000000000e-09 4.83900000000000e-09 4.73900000000000e-

>

09 4.64100000000000e-09 4.54700000000000e-09 4.45500000000000e-09 4.36700000000000e-09 4.28000000000000e-09 4.19600000000000e-09 4.11500000000000e-09 4.03600000000000e-09 3.95900000000000e-09 3.88400000000000e-09 3.81100000000000e-09 3.74100000000000e-09 3.67200000000000e-09 3.60600000000000e-09 3.54100000000000e-09 3.47800000000000e-09 3.41700000000000e-09 3.35700000000000e-09 3.29900000000000e-09 3.24300000000000e-09 3.18800000000000e-09 3.13400000000000e-09 3.08200000000000e-09 3.03100000000000e-09 2.98200000000000e-09 2.93400000000000e-09 2.88700000000000e-09 2.84100000000000e-09 2.79700000000000e-09 2.75300000000000e-09 2.71100000000000e-09 2.66900000000000e-09 2.62900000000000e-09 2.59000000000000e-09 2.55100000000000e-09 2.51400000000000e-09 2.47700000000000e-09 2.44100000000000e-09 2.40600000000000e-09 2.37200000000000e-09 2.33900000000000e-09 2.30600000000000e-09 2.2740000000000

>

0e-09 2.24300000000000e-09 2.21300000000000e-09 2.18300000000000e-09 2.15400000000000e-09 2.12500000000000e-09 2.09700000000000e-09 2.07000000000000e-09 2.04300000000000e-09 2.01700000000000e-09 1.99100000000000e-09 1.96600000000000e-09 1.94200000000000e-09 1.91800000000000e-09 1.89400000000000e-09 1.87100000000000e-09 1.87100000000000e-09 1.66300000000000e-09 1.49000000000000e-09 1.34500000000000e-09 1.22200000000000e-09 1.11600000000000e-09 1.02500000000000e-09 9.45700000000000e-10 8.75900000000000e-10 8.14200000000000e-10 7.59400000000000e-10 7.10500000000000e-10 6.66600000000000e-10 6.27100000000000e-10 5.91300000000000e-10 5.58700000000000e-10 5.29000000000000e-10 5.01900000000000e-10 4.77000000000000e-10 4.54100000000000e-10 4.33000000000000e-10 4.13400000000000e-10 3.95300000000000e-10 3.78500000000000e-10 3.62800000000000e-10 3.48200000000000e-10 3.34500000000000e-10 3.2170000000

>

0000e-10 3.09700000000000e-10 2.98400000000000e-10 2.87800000000000e-10 2.77800000000000e-10 2.68400000000000e-10 2.59500000000000e-10 2.51000000000000e-10 2.43100000000000e-10 2.35500000000000e-10 2.28300000000000e-10 2.21500000000000e-10 2.15000000000000e-10 2.08800000000000e-10 2.02900000000000e-10 1.97300000000000e-10 1.91900000000000e-10 1.86800000000000e-10 1.81900000000000e-10 1.77200000000000e-10 1.72700000000000e-10 1.68400000000000e-10 1.64300000000000e-10 1.60300000000000e-10 1.56500000000000e-10 1.52900000000000e-10 1.49300000000000e-10 1.46000000000000e-10 1.42700000000000e-10 1.39600000000000e-10 1.36500000000000e-10 1.33600000000000e-10 1.30800000000000e-10 1.28100000000000e-10 1.25500000000000e-10 1.22900000000000e-10 1.20500000000000e-10 1.18100000000000e-10 1.15800000000000e-10 1.13600000000000e-10 1.11400000000000e-10 1.09300000000000e-10 1.07300000000000e-10 1.0540000

> 0000000e-10 1.03500000000000e-10 1.01600000000000e-10 9.98200000000000e-11 9.80800000000000e-11 9.63900000000000e-11 9.47500000000000e-11 9.31600000000000e-11 9.16100000000000e-11 9.01000000000000e-11 8.86300000000000e-11 8.72000000000000e-11 8.58100000000000e-11 8.44600000000000e-11 8.31400000000000e-11 8.18600000000000e-11 8.06100000000000e-11 7.93900000000000e-11 7.82000000000000e-11 7.70400000000000e-11 7.59100000000000e-11 7.48000000000000e-11 7.37300000000000e-11 7.26700000000000e-11 7.16500000000000e-11 7.06400000000000e-11 6.96600000000000e-11 6.87100000000000e-11 6.77700000000000e-11 6.68600000000000e-11 6.59600000000000e-11

>

>

> Sorry for the lenght of the message and thanks for your help.

>

> Best wishes

> Kevin

Oh and I forgot to give a x0 not too bad is : x0=[0.1;0.1;0.1;1];

Can someone help me with this ? Thanks

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