σ šίΘ[c@`sίdZddlmZmZmZmZddlZddlZddlZ ddl m Z ddl m Z mZmZdZd d d d gZd efd„ƒYZdefd„ƒYZdefd„ƒYZd„ZdS(ul This module contains the convolution and filter functionalities of astropy. A few conceptual notes: A filter kernel is mainly characterized by its response function. In the 1D case we speak of "impulse response function", in the 2D case we call it "point spread function". This response function is given for every kernel by an astropy `FittableModel`, which is evaluated on a grid to obtain a filter array, which can then be applied to binned data. The model is centered on the array and should have an amplitude such that the array integrates to one per default. Currently only symmetric 2D kernels are supported. i(tabsolute_importtdivisiontprint_functiontunicode_literalsNi(tAstropyUserWarningi(tdiscretize_modeltadd_kernel_arrays_1Dtadd_kernel_arrays_2DiduKerneluKernel1DuKernel2Dukernel_arithmeticstKernelcB`sζeZdZeZeZdZd„Z e d„ƒZ e d„ƒZ e d„ƒZ e d„ƒZe d„ƒZdd„Ze d „ƒZe d „ƒZe d „ƒZd „Zd „Zd„Zd„Zd„Zdd„ZRS(uz Convolution kernel base class. Parameters ---------- array : `~numpy.ndarray` Kernel array. cC`stj|ƒ|_dS(N(tnpt asanyarrayt_array(tselftarray((s7lib/python2.7/site-packages/astropy/convolution/core.pyt__init__.scC`s|jS(u: Deviation from the normalization to one. (t _truncation(R ((s7lib/python2.7/site-packages/astropy/convolution/core.pyt truncation1scC`s|jS(uͺ Indicates if kernel is bool. If the kernel is bool the multiplication in the convolution could be omitted, to increase the performance. (t_is_bool(R ((s7lib/python2.7/site-packages/astropy/convolution/core.pytis_bool8scC`s|jS(u( Kernel response model. (t_model(R ((s7lib/python2.7/site-packages/astropy/convolution/core.pytmodelBscC`s |jjS(u# Kernel dimension. (R tndim(R ((s7lib/python2.7/site-packages/astropy/convolution/core.pyt dimensionIscC`s!g|jjD]}|d^q S(u- Index of the kernel center. i(R tshape(R t axes_size((s7lib/python2.7/site-packages/astropy/convolution/core.pytcenterPsuintegralcC`s–|dkr|jjƒ}n*|dkr<|jjƒ}n tdƒ‚|dkrgtjdtƒntj|j||jƒ|jjƒ|_ dS(ug Normalize the filter kernel. Parameters ---------- mode : {'integral', 'peak'} One of the following modes: * 'integral' (default) Kernel is normalized such that its integral = 1. * 'peak' Kernel is normalized such that its peak = 1. uintegralupeaku*invalid mode, must be 'integral' or 'peak'iu8The kernel cannot be normalized because it sums to zero.N( R tsumtmaxt ValueErrortwarningstwarnRR tdividet _kernel_sum(R tmodet normalization((s7lib/python2.7/site-packages/astropy/convolution/core.pyt normalizeWs      cC`s |jjS(u, Shape of the kernel array. (R R(R ((s7lib/python2.7/site-packages/astropy/convolution/core.pyRuscC`s|jS(uΊ Indicates if the filter kernel is separable. A 2D filter is separable, when its filter array can be written as the outer product of two 1D arrays. If a filter kernel is separable, higher dimension convolutions will be performed by applying the 1D filter array consecutively on every dimension. This is significantly faster, than using a filter array with the same dimension. (t _separable(R ((s7lib/python2.7/site-packages/astropy/convolution/core.pyt separable|s cC`s|jS(u& Filter kernel array. (R (R ((s7lib/python2.7/site-packages/astropy/convolution/core.pyR ‹scC`st||dƒS(u) Add two filter kernels. uadd(tkernel_arithmetics(R tkernel((s7lib/python2.7/site-packages/astropy/convolution/core.pyt__add__’scC`st||dƒS(u. Subtract two filter kernels. usub(R&(R R'((s7lib/python2.7/site-packages/astropy/convolution/core.pyt__sub__˜scC`st||dƒS(uF Multiply kernel with number or convolve two kernels. umul(R&(R tvalue((s7lib/python2.7/site-packages/astropy/convolution/core.pyt__mul__žscC`st||dƒS(uF Multiply kernel with number or convolve two kernels. umul(R&(R R*((s7lib/python2.7/site-packages/astropy/convolution/core.pyt__rmul__€scC`s|jS(u5 Array representation of the kernel. (R (R ((s7lib/python2.7/site-packages/astropy/convolution/core.pyt __array__ͺscC`s%t|dƒtjkrtS|SdS(u? Wrapper for multiplication with numpy arrays. iN(ttypeR tufunctNotImplemented(R R tcontext((s7lib/python2.7/site-packages/astropy/convolution/core.pyt__array_wrap__°sN(t__name__t __module__t__doc__tFalseR$tTrueRtNoneRRtpropertyRRRRRR#RR%R R(R)R+R,R-R2(((s7lib/python2.7/site-packages/astropy/convolution/core.pyR!s(        tKernel1DcB`s eZdZdddd„ZRS(uω Base class for 1D filter kernels. Parameters ---------- model : `~astropy.modeling.FittableModel` Model to be evaluated. x_size : odd int, optional Size of the kernel array. Default = 8 * width. array : `~numpy.ndarray` Kernel array. width : number Width of the filter kernel. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by linearly interpolating between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. factor : number, optional Factor of oversampling. Default factor = 10. cK`s|dkrδ|jdkr*tdƒ‚n|dkrB|j}n!|t|ƒkrctdƒ‚n|ddkrŸt|ƒ ddt|ƒddf}n-t|ƒd dt|ƒdddf}t|j||}n|dk rόd|_ntt|ƒj|ƒdS(Nu#Must specify either array or model.ux_size should be an integeriigΰ?i( R8Rt TypeErrort _default_sizetintRtsuperR:R(R Rtx_sizeR tkwargstx_range((s7lib/python2.7/site-packages/astropy/convolution/core.pyRΪs   ,-  N(R3R4R5R8R(((s7lib/python2.7/site-packages/astropy/convolution/core.pyR:ΊstKernel2DcB`s#eZdZddddd„ZRS(uz Base class for 2D filter kernels. Parameters ---------- model : `~astropy.modeling.FittableModel` Model to be evaluated. x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * width. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * width. array : `~numpy.ndarray` Kernel array. mode : str, optional One of the following discretization modes: * 'center' (default) Discretize model by taking the value at the center of the bin. * 'linear_interp' Discretize model by performing a bilinear interpolation between the values at the corners of the bin. * 'oversample' Discretize model by taking the average on an oversampled grid. * 'integrate' Discretize model by integrating the model over the bin. width : number Width of the filter kernel. factor : number, optional Factor of oversampling. Default factor = 10. cK`sΈ|dkr†|jdkr*tdƒ‚n|dkrB|j}n!|t|ƒkrctdƒ‚n|dkrx|}n!|t|ƒkr™tdƒ‚n|ddkrΥt|ƒ ddt|ƒddf}n-t|ƒd dt|ƒdddf}|ddkr>t|ƒ ddt|ƒddf}n-t|ƒd dt|ƒdddf}t|j|||}n|dk ržd|_ntt|ƒj|ƒdS(Nu#Must specify either array or model.ux_size should be an integeruy_size should be an integeriigΰ?i( R8RR;R<R=RR>RBR(R RR?ty_sizeR R@RAty_range((s7lib/python2.7/site-packages/astropy/convolution/core.pyRs*     ,-,-  N(R3R4R5R8R(((s7lib/python2.7/site-packages/astropy/convolution/core.pyRBυs cC`sυt|tƒrΎt|tƒrΎ|dkrBt|j|jƒ}n|dkrgt|j|j ƒ}n|dkr‚tdƒ‚ntd|ƒ}|jo |j|_|jp΅|j|_n3t|tƒr|t|tƒr||dkrt|j|jƒ}n|dkr%t|j|j ƒ}n|dkr@tdƒ‚ntd|ƒ}|jo^|j|_|jps|j|_nut|tƒsšt|tƒrεt j |ƒrε|dkrΦt j |ƒ}|j |9_ qρtdƒ‚n tdƒ‚|S(uε Add, subtract or multiply two kernels. Parameters ---------- kernel : `astropy.convolution.Kernel` Kernel instance value : kernel, float or int Value to operate with operation : {'add', 'sub', 'mul'} One of the following operations: * 'add' Add two kernels * 'sub' Subtract two kernels * 'mul' Multiply kernel with number or convolve two kernels. uaddusubumuluYKernel operation not supported. Maybe you want to use convolve(kernel1, kernel2) instead.R uKernel operation not supported.( t isinstanceR:RR t ExceptionR$RRBRR tisscalartcopyR (R'R*t operationt new_arrayt new_kernel((s7lib/python2.7/site-packages/astropy/convolution/core.pyR&=s8        (R5t __future__RRRRRRHtnumpyR tutils.exceptionsRtutilsRRRtMAX_NORMALIZATIONt__all__tobjectRR:RBR&(((s7lib/python2.7/site-packages/astropy/convolution/core.pyts"   ™;H