B |‹dXã@s2ddlmZddlZddgZdd„Zd d d„ZdS) é)ÚexpNÚsolve_corrections_sgdÚdetermine_offset_matrixc Cs¨t|ƒ}t ||f¡tj}x†t|ƒD]z\}}xpt|ƒD]d\}}||krJq8| |¡r8||}t |j¡r8|j|j}t  |¡|||f<|||f |||f<q8Wq&W|S)ze Given a list of ReprojectedArraySubset, determine the offset matrix between all arrays. ) ÚlenÚnpZonesÚnanÚ enumerateÚoverlapsÚanyZ footprintÚarrayZmedian) ZarraysÚNÚ offset_matrixÚi1Zarray1Úi2Zarray2Ú differenceÚvalues©rúl/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/reproject/mosaicking/background.pyr s   ééd绽×Ùß|Û=c Cs&|jdks|jd|jdkr&tdƒ‚|jd}t |¡}t |¡}d}xØtt|dƒƒD]Ä} tj  |¡|t | |ƒ} xj|D]b} t  || ¡r–q‚t  || dd…f¡} || || } || | t  || | f| ¡7<q‚W|t  |¡8}|dk rtj||||drP| ¡}qZW|S)aî Given a matrix of offsets from each image to each other image, find the optimal offsets to use using Stochastic Gradient Descent. Given N images, we can construct an NxN matrix Oij giving the typical (e.g. mean, median, or other statistic) offset from each image to each other image. This can be a reasonably sparse matrix since not all images necessarily overlap. From this we then want to find a vector of N corrections Ci to apply to each image to minimize the differences. We do this by using the Stochastic Gradient Descent algorithm: https://en.wikipedia.org/wiki/Stochastic_gradient_descent Essentially what we are trying to minimize is the difference between Dij and a matrix of the same shape constructed from the Oi values. The learning rate is decreased using a decaying exponential: $$\eta = \eta_{\rm initial} * \exp{(-i/t_{\eta})}$$ Parameters ---------- offset_matrix : `~numpy.ndarray` The NxN matrix giving the offsets between all images (or NaN if an offset could not be determined) eta_initial : float The initial learning rate to use eta_half_life : float The number of iterations after which the learning rate should be decreased by a factor $e$. rtol : float The relative tolerance to use to determine if the corrections have converged. atol : float The absolute tolerance to use to determine if the corrections have converged. érrz+offset_matrix should be a square NxN matrixNé )ÚrtolÚatol)ÚndimÚshapeÚ ValueErrorrZarangeZzerosÚrangeÚintÚrandomÚshufflerÚisnanZmeanZnanmeanZallcloseÚcopy)r Z eta_initialZ eta_half_liferrr ÚindicesZ correctionsZprevious_correctionsÚ iterationÚetaÚiZkeepZfitted_offset_matrix_rowrrrr$s0)         )rrrr)ÚmathrÚnumpyrÚ__all__rrrrrrÚs