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NonlinearModelFit and assumptions on fit parameters
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Niles
Sep 23, 2012, 3:00:50 AM9/23/12
to
Hi
I have a set of data (x, y) that I can succesfully fit a nonlinear function to using NonlinearModelFit:
data = {{1, 1}, {2, 2}, {3, 3.2}};
fitFuncExactNoLosses[a_, b_, x_] := a*x^2 + b + x;
nlm = NonlinearModelFit[data, fitFuncExactNoLosses[a, b, x],
{
{a, 1},
{b, 1}},
x]
However, the paramter "b" comes out negative and it *must* be positive. Is there a way to utilize assumptions such that b is constrained to be grater than zero?
Best,
Niels.
I have a set of data (x, y) that I can succesfully fit a nonlinear function to using NonlinearModelFit:
data = {{1, 1}, {2, 2}, {3, 3.2}};
fitFuncExactNoLosses[a_, b_, x_] := a*x^2 + b + x;
nlm = NonlinearModelFit[data, fitFuncExactNoLosses[a, b, x],
{
{a, 1},
{b, 1}},
x]
However, the paramter "b" comes out negative and it *must* be positive. Is there a way to utilize assumptions such that b is constrained to be grater than zero?
Best,
Niels.
Bob Hanlon
Sep 24, 2012, 12:41:17 AM9/24/12
to
As shown in the documentation
data = {{1, 1}, {2, 2}, {3, 3.2}};
fitFuncExactNoLosses[a_, b_, x_] =
a*x^2 + b + x;
(nlm1 = NonlinearModelFit[data,
{fitFuncExactNoLosses[a, b, x], b > 0},
{{a, 1}, {b, 1}}, x]) // Normal
7.890764227861177*^-7 + x +
0.018364206486339258*x^2
nlm1["FitResiduals"]
{-0.018365, -0.0734576, 0.0347214}
(nlm2 = NonlinearModelFit[data,
{fitFuncExactNoLosses[a, b, x], b > 0},
{a, b}, x]) // Normal
0.011226160044776182 + x +
0.016760582112590634*x^2
nlm2["FitResiduals"]
{-0.0279867, -0.0782685, 0.0379286}
Plot[{nlm1[x], nlm2[x]}, {x, 0, 4},
Epilog -> {Red,
AbsolutePointSize[4],
Point[data]}]
Bob Hanlon
data = {{1, 1}, {2, 2}, {3, 3.2}};
fitFuncExactNoLosses[a_, b_, x_] =
a*x^2 + b + x;
{fitFuncExactNoLosses[a, b, x], b > 0},
{{a, 1}, {b, 1}}, x]) // Normal
7.890764227861177*^-7 + x +
0.018364206486339258*x^2
nlm1["FitResiduals"]
{-0.018365, -0.0734576, 0.0347214}
(nlm2 = NonlinearModelFit[data,
{fitFuncExactNoLosses[a, b, x], b > 0},
{a, b}, x]) // Normal
0.011226160044776182 + x +
0.016760582112590634*x^2
nlm2["FitResiduals"]
{-0.0279867, -0.0782685, 0.0379286}
Plot[{nlm1[x], nlm2[x]}, {x, 0, 4},
Epilog -> {Red,
AbsolutePointSize[4],
Point[data]}]
Bob Hanlon
DC
Sep 24, 2012, 12:47:47 AM9/24/12
to
You can include contraints on the parameters as in :
nlm = NonlinearModelFit[data,
{fitFuncExactNoLosses[a, b, x],b>0}, {{a, 1}, {b, 1}}, x]
nlm = NonlinearModelFit[data,
{fitFuncExactNoLosses[a, b, x],b>0}, {{a, 1}, {b, 1}}, x]
Frank K
Sep 24, 2012, 12:48:32 AM9/24/12
to
Bill Rowe
Sep 24, 2012, 12:48:42 AM9/24/12
to
On 9/23/12 at 3:01 AM, niels.m...@gmail.com (Niles) wrote:
>I have a set of data (x, y) that I can succesfully fit a nonlinear
>function to using NonlinearModelFit:
>data = {{1, 1}, {2, 2}, {3, 3.2}}; fitFuncExactNoLosses[a_, b_,
>x_]:= a*x^2 + b + x; nlm =
>NonlinearModelFit[data,fitFuncExactNoLosses[a, b, x],
>I have a set of data (x, y) that I can succesfully fit a nonlinear
>function to using NonlinearModelFit:
>data = {{1, 1}, {2, 2}, {3, 3.2}}; fitFuncExactNoLosses[a_, b_,
>x_]:= a*x^2 + b + x; nlm =
>{ {a, 1}, {b, 1}}, x]
>However, the paramter "b" comes out negative and it *must* be
>positive. Is there a way to utilize assumptions such that b is
>constrained to be grater than zero?
Look up NonlinearModelFit in the Documentation Center and you
>However, the paramter "b" comes out negative and it *must* be
>positive. Is there a way to utilize assumptions such that b is
>constrained to be grater than zero?
will find the second argument can be given in the form {model,
constrainte}. So, all you need do is
nlm = NonlinearModelFit[
data, {fitFuncExactNoLosses[a, b, x], b > 0}, {{a, 1}, {b,
1}}, x]
Alexei Boulbitch
Sep 25, 2012, 4:49:54 AM9/25/12
to
Hi
I have a set of data (x, y) that I can succesfully fit a nonlinear function to using NonlinearModelFit:
data = {{1, 1}, {2, 2}, {3, 3.2}};
fitFuncExactNoLosses[a_, b_, x_] := a*x^2 + b + x;
nlm = NonlinearModelFit[data, fitFuncExactNoLosses[a, b, x],
Niels.
Hi, Niels,
Try this:
ff = FindFit[data, {a*x^2 + b + x, b > 0.05}, {{a, 1}, {b, 1}}, x]
Show[{ListPlot[data, PlotStyle -> Red],
Plot[(a*x^2 + b + x) /. ff, {x, 0, 3}]}]
Have fun, Alexei
Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44
e-mail: alexei.b...@iee.lu
I have a set of data (x, y) that I can succesfully fit a nonlinear function to using NonlinearModelFit:
data = {{1, 1}, {2, 2}, {3, 3.2}};
fitFuncExactNoLosses[a_, b_, x_] := a*x^2 + b + x;
{
{a, 1},
{b, 1}},
x]
However, the paramter "b" comes out negative and it *must* be positive. Is there a way to utilize assumptions such that b is constrained to be grater than zero?
Best,
{a, 1},
{b, 1}},
x]
However, the paramter "b" comes out negative and it *must* be positive. Is there a way to utilize assumptions such that b is constrained to be grater than zero?
Niels.
Hi, Niels,
Try this:
ff = FindFit[data, {a*x^2 + b + x, b > 0.05}, {{a, 1}, {b, 1}}, x]
Show[{ListPlot[data, PlotStyle -> Red],
Plot[(a*x^2 + b + x) /. ff, {x, 0, 3}]}]
Have fun, Alexei
Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
Office fax: +352-2454-3566
mobile phone: +49 151 52 40 66 44
e-mail: alexei.b...@iee.lu
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