معرفی شرکت ها

تبلیغات ما

مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.

مشاهده بیشتر

تبلیغات ما

مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.

مشاهده بیشتر

تبلیغات ما

مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.

مشاهده بیشتر

تبلیغات ما

مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.

مشاهده بیشتر

تبلیغات ما

مشتریان به طور فزاینده ای آنلاین هستند. تبلیغات می تواند به آنها کمک کند تا کسب و کار شما را پیدا کنند.

مشاهده بیشتر

توضیحات

A package for frequency-domain ghost imaging

ویژگی	مقدار
سیستم عامل	-
نام فایل	FDGI-0.9.3
نام	FDGI
نسخه کتابخانه	0.9.3
نگهدارنده	[]
ایمیل نگهدارنده	[]
نویسنده	Jun Wang
ایمیل نویسنده	junwang9@stanford.edu
آدرس صفحه اصلی	https://github.com/congzlwag/spook
آدرس اینترنتی	https://pypi.org/project/FDGI/
مجوز	-

# Spooktroscopy: Spectral-Domain Ghost Imaging ## Target Problem Solve <img src="https://render.githubusercontent.com/render/math?math=(A \otimes G)X = B"> in the least-square way, under [regularizations](#Regularizations). A, G are matrices acting on the two dimensions of X, i.e. ![(AG)X=B](https://latex.codecogs.com/svg.latex?\normalsize&space;\sum_{w,b}A_{iw}G_{bq}X_{wb}=B_{iq}) . For spectral-domain ghost imaging, the dimension indexed by <img src="https://render.githubusercontent.com/render/math?math=w"> is photon energy, and the other dimension can be properties of the photoproduct, such as the electron kinetic energy. `G` is the (optional) linear operator on the dimension indexed by <img src="https://render.githubusercontent.com/render/math?math=b">. By default (`G=None`), it is the identity, in which case this is the conventional Spooktroscopy, i.e. to solve <img src="https://render.githubusercontent.com/render/math?math=AX=B"> under regularizations. `G` can accommodate other linear operations on the $b$ dimension, to solve the two linear inversions in one step. With `mode='raw'`, pass in matrix ![G](https://latex.codecogs.com/svg.latex?\normalsize&space;G_{bq}) to G, and with `mode='contracted'`, pass in matrix ![GtG](https://latex.codecogs.com/svg.latex?\normalsize&space;\sum_qG_{bq}G_{b'q}). For example, for Abel transform in Velocity Map Imaging, [pBasex](https://github.com/e-champenois/CPBASEX) offers this G with `loadG`. ### Key Advantages The key advantages of this package are 1. Efficient optimization: Contraction over shots is decoupled from optimization. It is **recommended** to input precontracted results when instantiating, or to save the caches using method `save_prectr` of a solver created with raw inputs. Once instantiated, the precontracted results are cached to be reused every time solving with a different hyperparameter. See `spook.contraction_utils.adaptive_contraction` . 2. Support dimension reduction on the dependent variable B, through basis functions in G. In that case, it is also recommended to contract (B,G) over the dependent variable space (index q) prior to instantiating a spook solver. 3. Support multiple combinations of regularizations. See [Solvers](#Solvers) . 4. Support time-dependent measurement (Beta): when each entry in the raw input A is a pair of (photon spectrum, delay bin), index w is the flattened axis of (<img src="https://render.githubusercontent.com/render/math?math=\omega">, <img src="https://render.githubusercontent.com/render/math?math=\tau">). In this case, the third smoothness hyperparameter is for the delay axis. At the very bottom level, this package depends on either [OSQP](https://osqp.org) to solve a quadratic programming or LAPACK gesv through `numpy.linalg.solve` . ### Regularizations Common regularizations are the following three types, all of which optional, depending on what _a prior_ knowledge one wants to enforce on the problem solving. 1. Nonnegativity: To constrain <img src="https://render.githubusercontent.com/render/math?math=X\succeq 0"> 2. Sparsity: To penalize on <img src="https://render.githubusercontent.com/render/math?math=\|X\|_1"> or <img src="https://render.githubusercontent.com/render/math?math=\|X\|_2^2"> 3. Smoothness: To penalize on roughness of X , along the two indices, independently. For <img src="https://render.githubusercontent.com/render/math?math=\omega">-axis, which is the photon energy axis, the form is fixed <img src="https://render.githubusercontent.com/render/math?math=\|(L_{N_w}\otimes I)X\|_2^2"> where <img src="https://render.githubusercontent.com/render/math?math=L_{N_w}"> is the [laplacian](https://en.wikipedia.org/wiki/Laplace_operator). Roughness along the second axis of X is customizable through parameter `Bsmoother`, which by default is laplacian squared too. Sparsity and Smoothness are enforced through penalties in the total obejctive function, and the penalties are weighted by hyperparameters `lsparse` and `lsmooth`. `lsmooth` is a 2-tuple that weight roughness penalty along the two axes of X respectively. The hyperparameters can be passed in during instantiation and also updated afterwards. It is recommended to call method `getXopt` with the hyperparameter(s) to be updated, because it will update, solve, and return the optimal X in one step. Calling `solve` with the hyperparameter(s) to be updated and then calling `getXopt()` without input is effectively the same, and the problem will be solved once as long as there is no update. ## Solvers Different combinations of regularizations can lead to different forms of objective function. Solvers in package always formalize the specific problem into either a [Quadratic Programming](https://en.wikipedia.org/wiki/Quadratic_programming) or a linear equation. Examples can be found in [unit tests](#UnitTests) | Nonnegativity | Sparsity | Smoothness | Solver | Notes | | ------------- | ------------------- | ---------- | ------------------- | ------------------------------------------------------------ | | True | L1 or False | Quadratic | `SpookPosL1` | This solver can serve tasks like in [Li _et al_](https://iopscience.iop.org/article/10.1088/1361-6455/abcdf1) | | True | L2 squared | Quadratic | `SpookPosL2` | | | False | L2 squared or False | Quadratic | `SpookLinSolve` | This solver is so far the work-horse for SpookVMI | | False | L1 | Quadratic | `SpookL1` | | ### Quadratic Programming For cases where it can be formalized into a [Quadratic Programming](https://en.wikipedia.org/wiki/Quadratic_programming) , [OSQP](https://osqp.org) does the job. Thus the root numerical method is alternating direction method of multipliers (ADMM). Looking into the [solver settings of OSQP](https://osqp.org/docs/interfaces/solver_settings.html) is always encouraged, but the default settings usually work fine for `spook` . If one needs to pass in settings, the OSQP solver is `SpookQPBase._prob` . ### Linear Equation A rare case that it can be formalized into a linear equation is the third line in the table above: no nonnegativity constraint, and the sparsity is L2 norm squared. This is implemented in `SpookLinSolve` , which calls `numpy.linalg.solve` or `scipy.sparse.linalg.spsolve` . ## Normalization Convention The entries in <img src="https://render.githubusercontent.com/render/math?math=A^TA, G^TG"> are preferred to be on the order of unity, because regularization-related quadratic form matrices have their entries around unity. The scale factors are set as ![normalization](https://latex.codecogs.com/svg.latex?&space;s_a=\sqrt{\frac{1}{N_w}\mathrm{tr}(A^TA)},s_g=\sqrt{\frac{1}{N_q}\mathrm{tr}(G^TG)}) where <img src="https://render.githubusercontent.com/render/math?math=N_w, N_q"> are the dimensions along w-axis and q-axis, respectively. <img src="https://render.githubusercontent.com/render/math?math=s_as_g"> is an accessible property of the solver `AGscale`. To normalize or not is controlled by parameter `pre_normalize` in instanciation. **By default** `pre_normalize=True`, i.e. `self._AtA` =<img src="https://render.githubusercontent.com/render/math?math=A^TA/s_a^2">, `self._GtG` =<img src="https://render.githubusercontent.com/render/math?math=G^TG/s_g^2">, and `self._Bcontracted` = <img src="https://render.githubusercontent.com/render/math?math=(A^T \otimes G^T)B/(s_as_g)">. In this case, the direct solution `self.res` is scaled as <img src="https://render.githubusercontent.com/render/math?math=s_as_g X_\mathrm{opt}"> , but in `getXopt` the final result of <img src="https://render.githubusercontent.com/render/math?math=X_\mathrm{opt}"> is scaled back before returned. The entries in B are not always accessible, because of the option to pass in precontracted results and in `mode='contracted'`. Therefore B is not normalized. ## Unit Tests `unittest/testPosL1.py` is a good example to play with `SpookPosL1`. `unittest/testL1L2.ipynb` include good examples to play with `SpookPosL1`, `SpookPosL2`, and `SpookL1`. ## Dependencies See `requirements.txt` ## Acknowledgement This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES), Chemical Sciences, Geosciences, and Biosciences Division (CSGB).

نیازمندی

مقدار	نام
>=1.19	numpy
>=1.7	scipy
>=0.6.2	osqp

زبان مورد نیاز

مقدار	نام
>=3.7	Python

نحوه نصب

نصب پکیج whl FDGI-0.9.3:

pip install FDGI-0.9.3.whl

نصب پکیج tar.gz FDGI-0.9.3:

pip install FDGI-0.9.3.tar.gz