IR-e&~dZddlZddlmZmZmZddlmZddgZ dZ d Z d Z d Z d Zd ZdZdZeee 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_matrixc|jdkr/|jdkr$tjdg|jzj}|St |}|d}tj|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_matrixs :lib/python3.11/site-packages/astropy/modeling/separable.pyrrs<Q9#6#:#:x)*= =>>@ !),,#''**L8LA-ud;;L c|jdkr7|jdkr,tj|j|jftjSt |}tj|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)dtyperTF)r r r onesbool_rr)rrs rr r Aso>Q9#6#:#:w +Y-?@QQQQ!),,x 0A 5tUCC rct|tr|j}n |jd}t|tr|j}n |jd}||z}|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)leftrightlnoutrnoutnoutps r_compute_n_outputsr#gs^$ 1 % A EME Lrc d}||\}}||\}}||ks||krtd|d|d|d|d tj||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. cft|tr|j|j}}n |j\}}||fS)N)rrr r r)inputr r s r_n_inputs_outputsz&_arith_oper.._n_inputs_outputss: eU # # ."'/5>xII"'+ Ix""rz=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)rrr' left_inputs left_outputs right_inputs right_outputsresults r _arith_operr-s$###!2 1$ 7 7K"3"3E":":L-l""lm&C&C" K% K K3? K K& K K4A K K K   WlK0 1 1F Mrct|trg}|jD]6}tj|jf}d||<||7tj|}tj||jf}|dkr||d|jd|jf<n|||j d|j df<|S|j sOtj||jf}|dkrd|d|jd|jf<ntd||j d|j df<n\tj||jf}t|jD] }d|||f< |dkrtj |||jz }|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 appendvstackr separablerangeroll)modelposr"axesiaxismmats r _coord_matrixr=s$%!!   A8U^-..DDG KK     IdOOhu~.// &==78C!%/!#3U^#33 4 49:C ""U^O$5$55 6 ? :hu~.// &==78C!%/!#3U^#33 4 49:C ""U^O$5$55 6 6hu~.//u~&&  AC1II '>>'# 799C Jrct||}t|trt|d|}nBt j||jdf}||d|jdd|jdf<t|trt|d|}nDt j||jdf}|||jd d|jd df<t j||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)r#rrr=r r0rhstack)rrr"cleftcrights r_cstackrBs tU + +E$7dFE22%A/0026o 1 oA./%=ugu555%+a.1227< A  5;q>/"3"334 9eV_ % %%rc||}}d}||d}||d} tj||}n##t$rtd|d|wxYw|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. cbt|trt|||j}n|}|S)zQ Return ``n_inputs``, ``n_outputs`` for a model or coord_matrix. )rrr=r )r&positioncoordss rr'z _cdot.._n_inputs_outputss5 eU # # "5(EODDFFF rrrzFModels cannot be combined with the "|" operator; left coord_matrix is z, right coord_matrix is )r dot ValueErrorr)rrr'r@rAr,s r_cdotrIs%D  dF + +E  ug . .F v&&    " L$* L LDI L L    Ms 7 AcJ|x}tur|St|trCt |j}t |j}t|j||St|trt|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) _calculate_separability_matrixNotImplementedrrrrr _operatorsoprr=r )rtransform_matrixsepleftseprights rrrs&DDFFF   I} - -EY^,,io..),'::: Iu % %EY 0CDDDEEr)&|+-*/z**)__doc__numpyr corerrrmappingsr__all__rr r#r-r=rBrIrrMrrr^s  <<<<<<<<<< 0 1$$$N###L2&&&R---`&&&>$$$NEEE:        r