Numerical Function Fitting
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In summary I have a program that numerically integrates a function with multiple parameters, and would like to fit it against some data. Now, if I had the analytic form of the function I could of course find the minimum of my fit criteria (say Chi Square.) So, for the 3 parameters I care about, I could simply try a bunch of values for each parameter, but that could take forever! The integration takes at least 1.2s (bare minimum), and if I were to try 10 values for each parameter... More importantly however, this isn't smart! Is there a robust way to look for minimums in a non-analytic evaluation?
algorithms
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
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add a comment |
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In summary I have a program that numerically integrates a function with multiple parameters, and would like to fit it against some data. Now, if I had the analytic form of the function I could of course find the minimum of my fit criteria (say Chi Square.) So, for the 3 parameters I care about, I could simply try a bunch of values for each parameter, but that could take forever! The integration takes at least 1.2s (bare minimum), and if I were to try 10 values for each parameter... More importantly however, this isn't smart! Is there a robust way to look for minimums in a non-analytic evaluation?
algorithms
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
$endgroup$
add a comment |
$begingroup$
In summary I have a program that numerically integrates a function with multiple parameters, and would like to fit it against some data. Now, if I had the analytic form of the function I could of course find the minimum of my fit criteria (say Chi Square.) So, for the 3 parameters I care about, I could simply try a bunch of values for each parameter, but that could take forever! The integration takes at least 1.2s (bare minimum), and if I were to try 10 values for each parameter... More importantly however, this isn't smart! Is there a robust way to look for minimums in a non-analytic evaluation?
algorithms
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
$endgroup$
In summary I have a program that numerically integrates a function with multiple parameters, and would like to fit it against some data. Now, if I had the analytic form of the function I could of course find the minimum of my fit criteria (say Chi Square.) So, for the 3 parameters I care about, I could simply try a bunch of values for each parameter, but that could take forever! The integration takes at least 1.2s (bare minimum), and if I were to try 10 values for each parameter... More importantly however, this isn't smart! Is there a robust way to look for minimums in a non-analytic evaluation?
algorithms
algorithms
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
asked Jun 22 '18 at 0:07
Captain MorganCaptain Morgan
37918
37918
add a comment |
add a comment |
2 Answers
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Any numerical analysis book will have a section on multidimensional minimization. There are a number of methods. The fact that you don't have a functional form is not important. These methods just call your routine to evaluate the function (and maybe the gradient, if you can) at various points. They have clever ways to choose the points to evaluate the function at. Sections 10.4 through 10.7 in Numerical Recipes has routines in C. Others will have other favorites.
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
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Ever heard of the Nelder and Mead Simplex Method for Function Minimization? Give it a try. Seems to me like the thing you are looking for. Here is a Python implementation. But you can find it also in C++, Fortran and other languages...if you care to Google around.
answered Dec 15 '18 at 16:38
agcalaagcala
1112
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2 Answers
2
active
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votes
2 Answers
2
active
oldest
votes
active
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active
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$begingroup$
Any numerical analysis book will have a section on multidimensional minimization. There are a number of methods. The fact that you don't have a functional form is not important. These methods just call your routine to evaluate the function (and maybe the gradient, if you can) at various points. They have clever ways to choose the points to evaluate the function at. Sections 10.4 through 10.7 in Numerical Recipes has routines in C. Others will have other favorites.
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
$endgroup$
add a comment |
$begingroup$
Any numerical analysis book will have a section on multidimensional minimization. There are a number of methods. The fact that you don't have a functional form is not important. These methods just call your routine to evaluate the function (and maybe the gradient, if you can) at various points. They have clever ways to choose the points to evaluate the function at. Sections 10.4 through 10.7 in Numerical Recipes has routines in C. Others will have other favorites.
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
$endgroup$
add a comment |
$begingroup$
Any numerical analysis book will have a section on multidimensional minimization. There are a number of methods. The fact that you don't have a functional form is not important. These methods just call your routine to evaluate the function (and maybe the gradient, if you can) at various points. They have clever ways to choose the points to evaluate the function at. Sections 10.4 through 10.7 in Numerical Recipes has routines in C. Others will have other favorites.
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
$endgroup$
Any numerical analysis book will have a section on multidimensional minimization. There are a number of methods. The fact that you don't have a functional form is not important. These methods just call your routine to evaluate the function (and maybe the gradient, if you can) at various points. They have clever ways to choose the points to evaluate the function at. Sections 10.4 through 10.7 in Numerical Recipes has routines in C. Others will have other favorites.
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
answered Jun 22 '18 at 2:18
Ross MillikanRoss Millikan
296k23198371
296k23198371
add a comment |
add a comment |
$begingroup$
Ever heard of the Nelder and Mead Simplex Method for Function Minimization? Give it a try. Seems to me like the thing you are looking for. Here is a Python implementation. But you can find it also in C++, Fortran and other languages...if you care to Google around.
answered Dec 15 '18 at 16:38
agcalaagcala
1112
$endgroup$
add a comment |
$begingroup$
Ever heard of the Nelder and Mead Simplex Method for Function Minimization? Give it a try. Seems to me like the thing you are looking for. Here is a Python implementation. But you can find it also in C++, Fortran and other languages...if you care to Google around.
answered Dec 15 '18 at 16:38
agcalaagcala
1112
$endgroup$
add a comment |
$begingroup$
Ever heard of the Nelder and Mead Simplex Method for Function Minimization? Give it a try. Seems to me like the thing you are looking for. Here is a Python implementation. But you can find it also in C++, Fortran and other languages...if you care to Google around.
answered Dec 15 '18 at 16:38
agcalaagcala
1112
$endgroup$
Ever heard of the Nelder and Mead Simplex Method for Function Minimization? Give it a try. Seems to me like the thing you are looking for. Here is a Python implementation. But you can find it also in C++, Fortran and other languages...if you care to Google around.
answered Dec 15 '18 at 16:38
agcalaagcala
1112
edited Dec 16 '18 at 2:03
answered Dec 15 '18 at 16:38
agcalaagcala
1112
answered Dec 15 '18 at 16:38
agcalaagcala
1112
answered Dec 15 '18 at 16:38
agcalaagcala
1112
1112
add a comment |
add a comment |
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