Enable open upper limits for the grids in interpolation code #440
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Hi Bharat, I do not understand why this PR is needed, could you clarify?
You want to interpolate the BMW field on the cylindrical domain [rmin, rmax] x [phimin, phimax] x [zmin, zmax]. If you do not include the endpoint, what does the field interpolator do on the interval [rmax-h, rmax)?
The field is periodic in phi on 0 to 2pi, so I'm not sure why you can't just always include the endpoint there. If you're interpolating on 0 to 2pi/nfp, then same question as above, what happens on the subinterval (2pi/nfp - h, 2pi/nfp)?
| phirange: a 3-tuple of the form ``(phimin, phimax, nphi)``. | ||
| zrange: a 3-tuple of the form ``(zmin, zmax, nz)``. | ||
| rrange: a 3-tuple of the form ``(rmin, rmax, nr)`` or a 4-tuple of the form ``(rmin, rmax, nr, include_endpoint)``. | ||
| The default for `include_endpoint` is True. This mean that the interval :math:`[rmin, rmax]` is |
| rrange: a 3-tuple of the form ``(rmin, rmax, nr)`` or a 4-tuple of the form ``(rmin, rmax, nr, include_endpoint)``. | ||
| The default for `include_endpoint` is True. This mean that the interval :math:`[rmin, rmax]` is | ||
| split into ``nr`` many subintervals. When `include_endpoint` is False, interval :math:`[rmin, rmax)` is | ||
| split into ``nr`` many subintervals. |
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what does it mean [rmin, rmax] is split into nr many subintervals as opposed to [rmin, rmax) is split into nr many subintervals ?
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To concretize this, lets suppose you want 5 points between 0 and 1. If you include the end point, the mesh would [0, 0.25, 0.5, 0.75, 1]. If you don't want to include the end point, the mesh generated would be [0, 0.2, 0.4, 0.6, 0.8]. So the mesh would be quite different. Unfortunately, BMW generates phi grid with end point not included.
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But then what happens on the small subinterval (2pi/nfp - h, 2pi/nfp)? I guess the behavior would be dictated by the extrapolate keyword argument.
Since the BMW field is nfp-periodic, you can just rotate the B-field values from B(R, phi=0, Z) to B(R, phi=2pi/nfp, Z) and obtain the endpoint value.
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My reaction is the same as @andrewgiuliani 's - to avoid extrapolating, the thing to do would be to rotate the BMW field from phi=0 by 2pi/nfp and add the result as a new grid point at phi=2pi/nfp. This could be done in whatever function you have that passes data from BMW to the InterpolatedField. It seems unlikely that a user would have |
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I agree with @landreman and @andrewgiuliani, BMW will interpolate between the last phi plane and the first (flipped and copied according to the relevant symmetry), and the equivalently functioning Technically |
This PR enables open endpoints for the upper limits of the meshes when doing interpolation. The main reason to enable this functionality is to allow for [0, phi_max) generated by BMW mesh.