This is also known as Interpolative Butterfly Factorization [1].
The current implementation supports any dimension Fourier integral operators with/without singularity at the origin.
Fourier integral operatiors without singularity could be solved via fastBF
in the src
folder, whereas the Fourier integral operators with singularity at the origin
could be solved via either fastBF
with polar transform or fastMBF
.
The former adopts fast butterfly factorization with the idea given in [2]
and the later adopts the idea of multiscale domain decomposition [3] together
with the interpolative butterfly factorization.
-
The example for
fastBF
can be found intest/test_fastbf_1D
andtest/test_fastbf_2D
, -
The example for
fastBF
with polar transform can be found intest/test_fastpbf_2D
, -
The example for
fastMBF
can be found intest/test_fastmbf_2D
.
More examples of special function transforms can be found in test
folder as well.
[1] Y. Li and H. Yang. Interpolative Butterfly Factorization. Submitted. PDF
[2] E. Candes, L. Demanet and L. Ying. A fast butterfly algorithm for the computation of Fourier integral operators. SIAM Multiscale Modeling and Simulation 7 (2009). PDF
[3] Y. Li, H. Yang, and L. Ying. Multidimensional butterfly factorization. Submitted. PDF