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1 | 1 | .. _realinterp1d: |
2 | 2 |
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3 | | -Fast Fourier interpolation of 1D real-valued function at arbitrary points |
4 | | -========================================================================= |
| 3 | +Fast Fourier interpolation of a real-valued function at arbitrary points |
| 4 | +======================================================================== |
| 5 | + |
| 6 | +1D |
| 7 | +~~ |
| 8 | + |
5 | 9 |
|
6 | 10 | This is a Python variant of the previous 1D MATLAB demo, but illustrating |
7 | 11 | a trick for **real-valued** functions. |
@@ -63,13 +67,21 @@ When run this gives: |
63 | 67 |
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64 | 68 | which shows that both schemes work. |
65 | 69 | See the full code `tutorial/realinterp1d.py <https://github.com/flatironinstitute/finufft/blob/master/tutorial/realinterp1d.py>`_. |
66 | | -See the full code `tutorial/realinterp2d.py <https://github.com/flatironinstitute/finufft/blob/master/tutorial/realinterp2d.py>`_. |
67 | 70 | This arose from Discussion https://github.com/flatironinstitute/finufft/discussions/720 |
68 | 71 |
|
69 | | - |
70 | 72 | .. note:: |
71 | 73 |
|
72 | 74 | Complex-valued spreading/interpolation is still used under the hood in FINUFFT, so that there is no |
73 | 75 | efficiency gain on the nonuniform point side, |
74 | 76 | possibly motivating real-valued NUFFT variants. Since the decisions about |
75 | 77 | real-valued interfaces become elaborate, we leave this for future work. |
| 78 | + |
| 79 | +2D |
| 80 | +~~ |
| 81 | + |
| 82 | +A demo (including a ``pytest`` framework) for the 2D version of the above |
| 83 | +1D code has been written by Kaya Unalmis, arising from the above discussion. |
| 84 | +The idea in 2D is to use the above trick for one of the dimensions, then |
| 85 | +perform the usual complex evaluation in the other dimension; |
| 86 | +this is somewhat neater than using Hermitian inversion symmetry in 2D. |
| 87 | +The code is at `tutorial/realinterp2d.py <https://github.com/flatironinstitute/finufft/blob/master/tutorial/realinterp2d.py>`_. |
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