#13273: extension of sage.numerical.optimize.find_fit
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Reporter: hackstein | Owner:
Type: enhancement | Status:
needs_review
Priority: major | Milestone:
sage-5.6
Component: numerical | Resolution:
Keywords: fitting, interpolation, two-dimensional | Work issues:
enhancement
Report Upstream: N/A | Reviewers:
evanandel, was, ncohen
Authors: Urs Hackstein | Merged in:
Dependencies: | Stopgaps:
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Description changed by ncohen:
Old description:
> There is no routine in Sage to interpolate points
> ((x,y),(f_1,f_2))\in\mathbb{R}^{2} \times \mathbb{R}^{2} by an arbitrary
> class of functions f\colon\mathbb{R}^{2}\to \mathbb{R}^{2} other than
> splines. Until now, a similar routine exists only for interpolating
> functions \mathbb{R}^{k} \to \mathbb{R}, called
> sage.numerical.optimize.find_fit. It seems to me as one could extend the
> routine "find_fit" to the two-dimensional case with not too much work as
> the underlying routine scipy.optimize.leastsq (see line 645/655) is not
> restricted to the one-dimensional case. The new "model" (cp. line 527
> ff.) should be a pair of symbolic expressions, of symbolic functions, or
> of python functions. model has to be a function of the variables '(x_1,
> x_2)` and free parameters `(a_1, a_2, \ldots, a_l)'. Thus I want to
> propose to extend the routine find_fit to the two-dimensional case.
New description:
There is no routine in Sage to interpolate points
`((x,y),(f_1,f_2))\in\mathbb{R}^{2} \times \mathbb{R}^{2}` by an arbitrary
class of functions `f\colon\mathbb{R}^{2}\to \mathbb{R}^{2}` other than
splines. Until now, a similar routine exists only for interpolating
functions `\mathbb{R}^{k} \to \mathbb{R}`, called
`sage.numerical.optimize.find_fit`. It seems to me as one could extend the
routine "find_fit" to the two-dimensional case with not too much work as
the underlying routine scipy.optimize.leastsq (see line 645/655) is not
restricted to the one-dimensional case. The new "model" (cp. line 527 ff.)
should be a pair of symbolic expressions, of symbolic functions, or of
python functions. model has to be a function of the variables `(x_1, x_2)`
and free parameters `(a_1, a_2, \ldots, a_l)`. Thus I want to propose to
extend the routine find_fit to the two-dimensional case.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13273#comment:8>
Sage <http://www.sagemath.org>
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