[WIP] add HOEDMD #408
[WIP] add HOEDMD #408
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Hi @jieli-matrix, thanks a lot for your contribution! Could you please format your code with black ? |
pydmd/hoedmd.py
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| As a reference consult this work by Weiyang and Jie: | ||
| https://doi.org/10.1137/21M1463665 | ||
| """ | ||
| from __future__ import division |
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Please remove this import
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Code format & remove import done. cc: @fAndreuzzi @mtezzele |
reformat
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Hi @jieli-matrix, I've left some comments. They are mainly related to code style, for instance in PyDMD we try to simplify indexing expressions (you've some quite complex ones) by skipping the trailing : when not needed. Could you please fix all the occurrences in your code?
I'll finish reviewing the PR after you're ready for the next round. Thanks!
pydmd/hoedmd.py
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| self._compute_modes(U, V, inprodUV) | ||
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| else: | ||
| raise ValueError("Invalid value for alg_type: {}".format(alg_type)) |
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| raise ValueError("Invalid value for alg_type: {}".format(alg_type)) | |
| raise ValueError(f"Invalid value for alg_type: {alg_type}") |
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| :param numpy.ndarray Psi: the time-delay data matrix containing the snapshots x0,..x{n} by column. | ||
| :param int d: order in HOEDMD. | ||
| :param string alg_type: Algorithm type in HOEDMD. Default is 'stls'. |
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Please document briefly all possible values for alg_type.
pydmd/hoedmd.py
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| Px = P[:-d, :] | ||
| Py = P[d:, :] |
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You don't need the trailing :
| Px = P[:-d, :] | |
| Py = P[d:, :] | |
| Px = P[:-d] | |
| Py = P[d:] |
pydmd/hoedmd.py
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| self._compute_eigenquantities() | ||
| U = self.eigenvectors_r | ||
| V = self.eigenvectors_l | ||
| inprodUV = self.eigenvalues.conj() * ((U.conj() * V).sum(0)) |
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| inprodUV = self.eigenvalues.conj() * ((U.conj() * V).sum(0)) | |
| inprodUV = self.eigenvalues.conj() * (U.conj() * V).sum(0) |
pydmd/hoedmd.py
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| U = self.eigenvectors_r | ||
| V = self.eigenvectors_l | ||
| inprodUV = self.eigenvalues.conj() * ((U.conj() * V).sum(0)) | ||
| U = P[m : 2 * m, :].dot(U) |
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You don't need the trailing :
| U = P[m : 2 * m, :].dot(U) | |
| U = P[m : 2 * m].dot(U) |
pydmd/hoedmd.py
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| Gxx = np.dot(Psi[:-d, :].T.conj(), Psi[:-d, :]) | ||
| Gxy = np.dot(Psi[:-d, :].T.conj(), Psi[d:, :]) | ||
| Gpp = np.dot(Psi[m * d :, :].T.conj(), Psi[m * d :, :]) |
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Same as above:
| Gxx = np.dot(Psi[:-d, :].T.conj(), Psi[:-d, :]) | |
| Gxy = np.dot(Psi[:-d, :].T.conj(), Psi[d:, :]) | |
| Gpp = np.dot(Psi[m * d :, :].T.conj(), Psi[m * d :, :]) | |
| Gxx = np.dot(Psi[:-d].T.conj(), Psi[:-d]) | |
| Gxy = np.dot(Psi[:-d].T.conj(), Psi[d:]) | |
| Gpp = np.dot(Psi[m * d :].T.conj(), Psi[m * d :]) |
pydmd/hoedmd.py
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| Gpp = np.dot(Psi[m * d :, :].T.conj(), Psi[m * d :, :]) | ||
| sigma, Q = np.linalg.eig(Gxx Gpp) | ||
| ind = np.sort(-sigma) | ||
| sigma = sigma(ind) |
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Could you please clarify what this part is doing? Why are you using round brackets to index sigma? Is it running without errors?
pydmd/hoedmd.py
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| self._compute_eigenquantities() | ||
| U = self.eigenvectors_r | ||
| V = self.eigenvectors_l | ||
| inprodUV = self.eigenvalues.conj() * ((U.conj() * V).sum(0)) |
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| inprodUV = self.eigenvalues.conj() * ((U.conj() * V).sum(0)) | |
| inprodUV = self.eigenvalues.conj() * (U.conj() * V).sum(0) |
pydmd/hoedmd.py
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| U = Psi[m : 2 * m, :] * (Q * U) | ||
| V = Psi[: m * d, :] * ( |
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| U = Psi[m : 2 * m, :] * (Q * U) | |
| V = Psi[: m * d, :] * ( | |
| U = Psi[m : 2 * m] * (Q * U) | |
| V = Psi[: m * d] * ( |
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Hi @jieli-matrix, I suggest focusing on the tests as the main priority so we can merge this PR. Later you can add the Guassian kernel option and the tutorial showcasing your method. |
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Hi @jieli-matrix, could you please update us on this PR? |
Sorry for late response! I will update this PR in this week. cc: @mtezzele |
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@jieli-matrix you need to rebase this branch and fix the conflicts (see |
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@jieli-matrix Do you have any updates on this PR? |
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Sorry for update. I will add all tests in this week. |
Description:
Add a new dmd-variant for pyDMD, HOEDMD. Here is the paper link and the Matlab implementation version can be found in jieli-matrix/HOEDMD. We extended HODMD to HOEDMD and designed efficient numerical implementation by solving the Structured Total Least Squares problem. Thus, the implementation of HOEDMD is quite similar to HODMD overall while we need to rewrite the DMDOperator part.
ToDo:
Help:
Weiyang Ding and I want to thank PyDMD because it is convenient to compare our method with the existing DMD variants. We hope to add HOEDMD to PyDMD though we have developed HOEDMD in Matlab. Since I am a new developer at PyDMD, please feel free to comment on the bugs and give guidelines. Thanks!