σ šίΘ[c@`s,ddlmZmZmZmZddlZddlZddlm Z m Z m Z ddl m Z ddlmZddlmZmZd d d d d ddddddddddgZd„Zde fd„ƒYZde fd„ƒYZde fd„ƒYZde fd „ƒYZd!e fd"„ƒYZd#e fd$„ƒYZd%e fd&„ƒYZd'e fd(„ƒYZd)e fd*„ƒYZd+e fd,„ƒYZd-e fd.„ƒYZd/e fd0„ƒYZ d1e fd2„ƒYZ!d3e fd4„ƒYZ"d5e fd6„ƒYZ#d7e fd8„ƒYZ$dS(9i(tabsolute_importtdivisiontprint_functiontunicode_literalsNi(tKernel1DtKernel2DtKernel(tKernelSizeErrori(tmodels(tFittable1DModeltFittable2DModeluGaussian1DKerneluGaussian2DKernelu CustomKernelu Box1DKernelu Box2DKerneluTophat2DKerneluTrapezoid1DKerneluMexicanHat1DKerneluMexicanHat2DKerneluAiryDisk2DKerneluMoffat2DKernelu Model1DKernelu Model2DKerneluTrapezoidDisk2DKernelu Ring2DKernelcC`s5ttj|ƒƒ}|ddkr-|dS|SdS(Niii(tinttmathtceil(tvalueti((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyt_round_up_to_odd_integerstGaussian1DKernelcB`s#eZdZeZeZd„ZRS(u  1D Gaussian filter kernel. The Gaussian filter is a filter with great smoothing properties. It is isotropic and does not produce artifacts. Parameters ---------- stddev : number Standard deviation of the Gaussian kernel. x_size : odd int, optional Size of the kernel array. Default = 8 * stddev 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. Very slow. factor : number, optional Factor of oversampling. Default factor = 10. If the factor is too large, evaluation can be very slow. See Also -------- Box1DKernel, Trapezoid1DKernel, MexicanHat1DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Gaussian1DKernel gauss_1D_kernel = Gaussian1DKernel(10) plt.plot(gauss_1D_kernel, drawstyle='steps') plt.xlabel('x [pixels]') plt.ylabel('value') plt.show() cK`s|tjdtjdtjƒ|d|ƒ|_td|ƒ|_tt |ƒj |tj d|j j ƒƒ|_dS(Ngπ?iii(Rt Gaussian1Dtnptsqrttpit_modelRt _default_sizetsuperRt__init__tabst_arraytsumt _truncation(tselftstddevtkwargs((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRUs !(t__name__t __module__t__doc__tTruet _separabletFalset_is_boolR(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRs3tGaussian2DKernelcB`s#eZdZeZeZd„ZRS(uΑ 2D Gaussian filter kernel. The Gaussian filter is a filter with great smoothing properties. It is isotropic and does not produce artifacts. Parameters ---------- stddev : number Standard deviation of the Gaussian kernel. x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * stddev. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * stddev. 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. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Gaussian2DKernel gaussian_2D_kernel = Gaussian2DKernel(10) plt.imshow(gaussian_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() cK`s}tjddtj|ddd||ƒ|_td|ƒ|_tt|ƒj |tj d|j j ƒƒ|_ dS(Ngπ?iii(Rt Gaussian2DRRRRRRR(RRRRR(RRR ((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyR—s (R!R"R#R$R%R&R'R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyR(]s6t Box1DKernelcB`s#eZdZeZeZd„ZRS(uΊ 1D Box filter kernel. The Box filter or running mean is a smoothing filter. It is not isotropic and can produce artifacts, when applied repeatedly to the same data. By default the Box kernel uses the ``linear_interp`` discretization mode, which allows non-shifting, even-sized kernels. This is achieved by weighting the edge pixels with 1/2. E.g a Box kernel with an effective smoothing of 4 pixel would have the following array: [0.5, 1, 1, 1, 0.5]. Parameters ---------- width : number Width of the filter kernel. mode : str, optional One of the following discretization modes: * 'center' Discretize model by taking the value at the center of the bin. * 'linear_interp' (default) 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. See Also -------- Gaussian1DKernel, Trapezoid1DKernel, MexicanHat1DKernel Examples -------- Kernel response function: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Box1DKernel box_1D_kernel = Box1DKernel(9) plt.plot(box_1D_kernel, drawstyle='steps') plt.xlim(-1, 9) plt.xlabel('x [pixels]') plt.ylabel('value') plt.show() cK`sbtjd|d|ƒ|_t|ƒ|_d|dR(RR-R R?((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRœs (R!R"R#R&R'R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyR@[s>tAiryDisk2DKernelcB`seZdZeZd„ZRS(uΰ 2D Airy disk kernel. This kernel models the diffraction pattern of a circular aperture. This kernel is normalized to a peak value of 1. Parameters ---------- radius : float The radius of the Airy disk kernel (radius of the first zero). x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * radius. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * radius. 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. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Gaussian2DKernel, Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel, Moffat2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import AiryDisk2DKernel airydisk_2D_kernel = AiryDisk2DKernel(10) plt.imshow(airydisk_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() cK`s[tjddd|ƒ|_td|ƒ|_tt|ƒj||jƒd|_ dS(Niii( Rt AiryDisk2DRRRRRBRR,tNoneR(RR2R ((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRΫs  (R!R"R#R&R'R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRB€s4tMoffat2DKernelcB`seZdZeZd„ZRS(u€ 2D Moffat kernel. This kernel is a typical model for a seeing limited PSF. Parameters ---------- gamma : float Core width of the Moffat model. alpha : float Power index of the Moffat model. x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * radius. y_size : odd int, optional Size in y direction of the kernel array. Default = 8 * radius. 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. factor : number, optional Factor of oversampling. Default factor = 10. See Also -------- Gaussian2DKernel, Box2DKernel, Tophat2DKernel, MexicanHat2DKernel, Ring2DKernel, TrapezoidDisk2DKernel, AiryDisk2DKernel Examples -------- Kernel response: .. plot:: :include-source: import matplotlib.pyplot as plt from astropy.convolution import Moffat2DKernel moffat_2D_kernel = Moffat2DKernel(3, 2) plt.imshow(moffat_2D_kernel, interpolation='none', origin='lower') plt.xlabel('x [pixels]') plt.ylabel('y [pixels]') plt.colorbar() plt.show() cK`stj|dtj||dd||ƒ|_d|dd|dd}td|ƒ|_tt|ƒj ||j ƒd|_ dS(Ngπ?ig@gΰ?g@( RtMoffat2DRRRRRRRERR,RDR(RtgammatalphaR tfwhm((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRs (R!R"R#R&R'R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyREγs5t Model1DKernelcB`s#eZdZeZeZd„ZRS(uk Create kernel from 1D model. The model has to be centered on x = 0. Parameters ---------- model : `~astropy.modeling.Fittable1DModel` Kernel response function model x_size : odd int, optional Size in x direction of the kernel array. Default = 8 * width. 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. Raises ------ TypeError If model is not an instance of `~astropy.modeling.Fittable1DModel` See also -------- Model2DKernel : Create kernel from `~astropy.modeling.Fittable2DModel` CustomKernel : Create kernel from list or array Examples -------- Define a Gaussian1D model: >>> from astropy.modeling.models import Gaussian1D >>> from astropy.convolution.kernels import Model1DKernel >>> gauss = Gaussian1D(1, 0, 2) And create a custom one dimensional kernel from it: >>> gauss_kernel = Model1DKernel(gauss, x_size=9) This kernel can now be used like a usual Astropy kernel. cK`sAt|tƒr||_n tdƒ‚tt|ƒj|dS(NuMust be Fittable1DModel(t isinstanceR Rt TypeErrorRRJR(RtmodelR ((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyR]s  (R!R"R#R&R%R'R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRJ%s4t Model2DKernelcB`s#eZdZeZeZd„ZRS(uξ Create kernel from 2D model. The model has to be centered on x = 0 and y = 0. Parameters ---------- model : `~astropy.modeling.Fittable2DModel` Kernel response function model 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. 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. factor : number, optional Factor of oversampling. Default factor = 10. Raises ------ TypeError If model is not an instance of `~astropy.modeling.Fittable2DModel` See also -------- Model1DKernel : Create kernel from `~astropy.modeling.Fittable1DModel` CustomKernel : Create kernel from list or array Examples -------- Define a Gaussian2D model: >>> from astropy.modeling.models import Gaussian2D >>> from astropy.convolution.kernels import Model2DKernel >>> gauss = Gaussian2D(1, 0, 0, 2, 2) And create a custom two dimensional kernel from it: >>> gauss_kernel = Model2DKernel(gauss, x_size=9) This kernel can now be used like a usual astropy kernel. cK`sJt|_t|tƒr$||_n tdƒ‚tt|ƒj|dS(NuMust be Fittable2DModel( R&R%RKR RRLRRNR(RRMR ((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyR s    (R!R"R#R&R'R%R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRNes7t PSFKernelcB`seZdZeZd„ZRS(u= Initialize filter kernel from astropy PSF instance. cC`stdƒ‚dS(NuNot yet implemented(tNotImplementedError(R((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyR―s(R!R"R#R&R%R(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRO©st CustomKernelcB`s8eZdZd„Zed„ƒZejd„ƒZRS(u' Create filter kernel from list or array. Parameters ---------- array : list or array Filter kernel array. Size must be odd. Raises ------ TypeError If array is not a list or array. KernelSizeError If array size is even. See also -------- Model2DKernel, Model1DKernel Examples -------- Define one dimensional array: >>> from astropy.convolution.kernels import CustomKernel >>> import numpy as np >>> array = np.array([1, 2, 3, 2, 1]) >>> kernel = CustomKernel(array) >>> kernel.dimension 1 Define two dimensional array: >>> array = np.array([[1, 1, 1], [1, 2, 1], [1, 1, 1]]) >>> kernel = CustomKernel(array) >>> kernel.dimension 2 cC`s&||_tt|ƒj|jƒdS(N(tarrayRRQRR(RRR((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRΩs cC`s|jS(u& Filter kernel array. (R(R((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRRέscC`sΰt|tjƒr*|jtjƒ|_n9t|tƒrWtj|dtjƒ|_n tdƒ‚t d„|j Dƒƒ}|s‘t dƒ‚n|jdk}|jdk}t tj tj ||ƒƒƒ|_d|_dS( u, Filter kernel array setter tdtypeuMust be list or array.cs`s|]}|ddkVqdS(iiN((t.0t axes_size((s:lib/python2.7/site-packages/astropy/convolution/kernels.pys ρsu$Kernel size must be odd in all axes.gπ?igN(RKRtndarraytastypetfloat64RtlistRRRLtalltshapeRtboolt logical_orR'R(RRRtoddtonestzeros((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRRδs $(R!R"R#RtpropertyRRtsetter(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyRQ³s% (%t __future__RRRRR tnumpyRtcoreRRRtutilsRtmodelingRt modeling.coreR R t__all__RRR(R*R.R0R3R7R:R<R@RBRERJRNRORQ(((s:lib/python2.7/site-packages/astropy/convolution/kernels.pyts8"       ?BDF:<:<FI?B@D