U e{j&@sdZddlZddlmZmZmZddlmZddgZ ddZ d dZ d d Z d d Z ddZddZddZddZeee e e e e dZdS)a Functions to determine if a model is separable, i.e. if the model outputs are independent. It analyzes ``n_inputs``, ``n_outputs`` and the operators in a compound model by stepping through the transforms and creating a ``coord_matrix`` of shape (``n_outputs``, ``n_inputs``). Each modeling operator is represented by a function which takes two simple models (or two ``coord_matrix`` arrays) and returns an array of shape (``n_outputs``, ``n_inputs``). N) CompoundModelModelModelDefinitionError)Mapping is_separableseparability_matrixcCsT|jdkr,|jdkr,tdg|jj}|St|}|d}t|dkdd}|S)a A separability test for the outputs of a transform. Parameters ---------- transform : `~astropy.modeling.core.Model` A (compound) model. Returns ------- is_separable : ndarray A boolean array with size ``transform.n_outputs`` where each element indicates whether the output is independent and the result of a separable transform. Examples -------- >>> from astropy.modeling.models import Shift, Scale, Rotation2D, Polynomial2D >>> is_separable(Shift(1) & Shift(2) | Scale(1) & Scale(2)) array([ True, True]...) >>> is_separable(Shift(1) & Shift(2) | Rotation2D(2)) array([False, False]...) >>> is_separable(Shift(1) & Shift(2) | Mapping([0, 1, 0, 1]) | Polynomial2D(1) & Polynomial2D(2)) array([False, False]...) >>> is_separable(Shift(1) & Shift(2) | Mapping([0, 1, 0, 1])) array([ True, True, True, True]...) rFT)n_inputs n_outputsnparrayT _separablesumwhere) transformrseparable_matrixrY/var/www/html/bwave/python/venv/lib/python3.8/site-packages/astropy/modeling/separable.pyrs cCsJ|jdkr,|jdkr,tj|j|jftjdSt|}t|dkdd}|S)at Compute the correlation between outputs and inputs. Parameters ---------- transform : `~astropy.modeling.core.Model` A (compound) model. Returns ------- separable_matrix : ndarray A boolean correlation matrix of shape (n_outputs, n_inputs). Indicates the dependence of outputs on inputs. For completely independent outputs, the diagonal elements are True and off-diagonal elements are False. Examples -------- >>> from astropy.modeling.models import Shift, Scale, Rotation2D, Polynomial2D >>> separability_matrix(Shift(1) & Shift(2) | Scale(1) & Scale(2)) array([[ True, False], [False, True]]...) >>> separability_matrix(Shift(1) & Shift(2) | Rotation2D(2)) array([[ True, True], [ True, True]]...) >>> separability_matrix(Shift(1) & Shift(2) | Mapping([0, 1, 0, 1]) | Polynomial2D(1) & Polynomial2D(2)) array([[ True, True], [ True, True]]...) >>> separability_matrix(Shift(1) & Shift(2) | Mapping([0, 1, 0, 1])) array([[ True, False], [False, True], [ True, False], [False, True]]...) r)ZdtyperTF)r r r onesZbool_rr)rrrrrrAs cCsDt|tr|j}n |jd}t|tr.|j}n |jd}||}|S)aB Compute the number of outputs of two models. The two models are the left and right model to an operation in the expression tree of a compound model. Parameters ---------- left, right : `astropy.modeling.Model` or ndarray If input is of an array, it is the output of `coord_matrix`. r) isinstancerr shape)leftrightZlnoutZrnoutnoutprrr_compute_n_outputsgs    rc Csddd}||\}}||\}}||ks0||krRtd|d|d|d|d t||f}|S)a Function corresponding to one of the arithmetic operators ['+', '-'. '*', '/', '**']. This always returns a nonseparable output. Parameters ---------- left, right : `astropy.modeling.Model` or ndarray If input is of an array, it is the output of `coord_matrix`. Returns ------- result : ndarray Result from this operation. cSs,t|tr|j|j}}n |j\}}||fS)N)rrr r r)inputr r rrr_n_inputs_outputss  z&_arith_oper.._n_inputs_outputsz=Unsupported operands for arithmetic operator: left (n_inputs=z , n_outputs=z) and right (n_inputs=zO); models must have the same n_inputs and the same n_outputs for this operator.)rr r)rrrZ left_inputsZ left_outputsZ right_inputsZ right_outputsresultrrr _arith_opers  rcCs:t|trg}|jD]$}t|jf}d||<||qt|}t||jf}|dkrv||d|jd|jf<n|||j d|j df<|S|j st||jf}|dkrd|d|jd|jf<nd||j d|j df<nJt||jf}t |jD]}d|||f<q|dkr6t |||j}|S)a Create an array representing inputs and outputs of a simple model. The array has a shape (noutp, model.n_inputs). Parameters ---------- model : `astropy.modeling.Model` model pos : str Position of this model in the expression tree. One of ['left', 'right']. noutp : int Number of outputs of the compound model of which the input model is a left or right child. rrNr) rrmappingr zerosr appendZvstackr Z separablerangeZroll)modelposrZaxesiZaxismZmatrrr _coord_matrixs.     r(cCst||}t|tr"t|d|}n4t||jdf}||d|jdd|jdf<t|trnt|d|}n8t||jdf}|||jd d|jd df<t||gS)a Function corresponding to '&' operation. Parameters ---------- left, right : `astropy.modeling.Model` or ndarray If input is of an array, it is the output of `coord_matrix`. Returns ------- result : ndarray Result from this operation. rrNrr)rrrr(r r!rZhstack)rrrcleftcrightrrr_cstacks    $r+cCsd||}}dd}||d}||d}zt||}Wn(tk r^td|d|YnX|S)a Function corresponding to "|" operation. Parameters ---------- left, right : `astropy.modeling.Model` or ndarray If input is of an array, it is the output of `coord_matrix`. Returns ------- result : ndarray Result from this operation. cSs"t|trt|||j}n|}|S)zQ Return ``n_inputs``, ``n_outputs`` for a model or coord_matrix. )rrr(r )rpositionZcoordsrrrr s z _cdot.._n_inputs_outputsrrzFModels cannot be combined with the "|" operator; left coord_matrix is z, right coord_matrix is )r dot ValueErrorr)rrrr)r*rrrr_cdots    r/cCs^|}tk r|St|trBt|j}t|j}t|j||St|t rZt |d|j SdS)aq Calculate the separability of outputs. Parameters ---------- transform : `astropy.modeling.Model` A transform (usually a compound model). Returns : is_separable : ndarray of dtype np.bool An array of shape (transform.n_outputs,) of boolean type Each element represents the separablity of the corresponding output. rN) Z_calculate_separability_matrixNotImplementedrrrrr _operatorsoprr(r )rZtransform_matrixZsepleftZseprightrrrr s     r)&|+-*/z**)__doc__numpyr corerrrZmappingsr__all__rrrrr(r+r/rr1rrrrs( '&)0(