B ]t\#@sdZddlmZddlmZddlZddlZddlZddl Zddl Z ddl Z ddl mZddlmZddlmZddlmZddlmZddlmZddlmZddlmZddlmZddlTdd l m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&e'e(Z)ej*ej*ej+ej,ej-ej.ej/ej0ej1ej2ej3ej4ej5ej6ej7ej8ej9ej:d Z;ed+ddZ?ddZ@GdddejAejBZCGdddeCZDGdddeDZEGdddeDZFGdddeCZGGdddeCZHd,ddZId-d!d"ZJd#d$ZKd.d(d)ZLdS)/zR The image module supports basic image loading, rescaling and display operations. )BytesIO)ceilN)rcParams)allow_rasterization)FigureCanvasBase)*)Affine2DBboxBaseBbox BboxTransformIdentityTransformTransformedBbox)nonenearestbilinearZbicubicZspline16Zspline36ZhanningZhammingZhermiteZkaiserZquadricZcatromZgaussianZbesselZmitchellZsincZlanczosZblackman?c CsZt|dkr"tjdtjdddfSg}g}x|D]x}|||\}}}} |dk r0||9}||9}|||||ptdf|t||g||jd||jdggq0Wt|dkrtjdtjdddfSt |} tj t | j t | j dftjd} xH|D]@\}}}} t|| j|| j} tj|| | tjd| d qW| | j|| j|fS) aD Composite a number of RGBA images into one. The images are composited in the order in which they appear in the `images` list. Parameters ---------- images : list of Images Each must have a `make_image` method. For each image, `can_composite` should return `True`, though this is not enforced by this function. Each image must have a purely affine transformation with no shear. renderer : RendererBase instance magnification : float The additional magnification to apply for the renderer in use. Returns ------- tuple : image, offset_x, offset_y Returns the tuple: - image: A numpy array of the same type as the input images. - offset_x, offset_y: The offset of the image (left, bottom) in the output figure. r)rr)dtypeNg?rF)resamplealpha)lennpemptyuint8 make_imageappend get_alphar shapeunionzerosintheightwidthr translatex0y0_imagerNEAREST) Zimagesrenderer magnificationpartsZbboxesimagedataxytransbboxoutputrr3/lib/python3.7/site-packages/matplotlib/image.pycomposite_images>s,  .  r5cstdd|D}|dk r|n}|s.|sHxx|D]}|q4Wn`gfdd}x:|D]2}t|tr|r|ql||qlW|dS)a Draw a sorted list of artists, compositing images into a single image where possible. For internal matplotlib use only: It is here to reduce duplication between `Figure.draw` and `Axes.draw`, but otherwise should not be generally useful. css|]}t|tVqdS)N) isinstance _ImageBase).0r.r3r3r4 sz0_draw_list_compositing_images..Ncstdkrdnntdkrt\}}}|jdkr}|j| |t |t ||| dd=dS)Nrr) rdrawr5sizenew_gcZset_clip_rectangler1Z set_clip_pathZ get_clip_path draw_imagerroundrestore)r-lbgc) image_groupmagparentr)r3r4 flush_imagess    z3_draw_list_compositing_images..flush_images)anyZoption_image_nocompositer:get_image_magnificationr6r7 can_compositer)r)rEZartistsZsuppress_compositeZ has_imagesZ not_compositearFr3)rCrDrEr)r4_draw_list_compositing_imagesxs     rKcCsztj|jd|jddf|jd}||ddddddf<|jtjkr`d|dddddf<nd|dddddf<|S) z\ Convert an RGB image to RGBA, as required by the image resample C++ extension. rrr)rNg?)rr rrr)AZrgbar3r3r4 _rgb_to_rgbas " rOcseZdZdZddZd7dd Zfd d Zd d ZddZddZ d8ddZ d9ddZ ddZ ddZ eddZddZdd Zd!d"Zd#d$Zd%d&Zd'd(Zd)d*Zd+d,Zd-d.Zd/d0Zd1d2Zd3d4Zd5d6ZZS):r7rcCsdt|jjjS)NzAxesImage(%g,%g;%gx%g))tupleaxesr1bounds)selfr3r3r4__str__sz_ImageBase.__str__NT@Fc Ksztj|tj|||d|_|dkr2td}||_||| || || |||_ d|_ || dS)a interpolation and cmap default to their rc settings cmap is a colors.Colormap instance norm is a colors.Normalize instance to map luminance to 0-1 extent is data axes (left, right, bottom, top) for making image plots registered with data plots. Default is to label the pixel centers with the zero-based row and column indices. Additional kwargs are matplotlib.artist properties TNz image.origin)martistArtist__init__cmScalarMappableZ _mouseoverroriginset_filternorm set_filterradset_interpolation set_resamplerQ_imcacheupdate) rSaxcmapnorm interpolationr[ filternorm filterradrkwargsr3r3r4rXs     z_ImageBase.__init__cst}d|d<|S)Nr`)super __getstate__)rSstate) __class__r3r4rjs z_ImageBase.__getstate__cCs"|jdkrtd|jjddS)z+Get the numrows, numcols of the input imageNz"You must first set the image array)_A RuntimeErrorr)rSr3r3r4get_sizes z_ImageBase.get_sizecCstj||d|_dS)z Set the alpha value used for blending - not supported on all backends. Parameters ---------- alpha : float N)rVrW set_alphar`)rSrr3r3r4rqsz_ImageBase.set_alphacCsd|_d|_tj|dS)zb Call this whenever the mappable is changed so observers can update state N)r` _rgbacacherYrZchanged)rSr3r3r4rssz_ImageBase.changed?c$ Cs|dkrtd|jdkr"tdt||}|dkr:dS|j|} |j|} | dks^| dkrbdS|jdkrtd|j d  dd} nt } | t |j|j d|j|j d|j |j |7} | t|j |j  ||} | jrh|rh| d d ks| d d krhtt| } tt| }| | | }|| | }| t d |d |7} nt| } t| }|s|jd krtd |j |jd kr|j}|}|}|tjjkrtdtd}}|jdkr.|j}|jtjtjfkr^|jtjkr&t !d|jtj}n0|"tj|"tj}|dkrXtj}ntj}tj#|j |d}||dd<|j$%|t|j$j&t|j$j'}|j$j'|d }|tjkrdnd}|||}||krd}n t|}|||}||krd}n t|}|dk s&|dk r4t(|||}||8}|"|)}|"|)}||krr|||d}|d7}tj*|| f|jd}t+,||| t-|.|/d |0|1~|d8}||kr|||d9}||7}t2|j$t3j4r|"|j}tj#|j tjd}|j5j |j krLt6|j5ttj7td|dd<n d|dd<tj*|| f|jd}t+,||| t-|.dd|0|1~t8|}t9|}d||<|$tj:||} n|j d dkrt;|}n |j d dkrtd|j ftj*|| df|jd} |<}!|!dkr.d }!t+,|| | t-|.|/|!|0|1|j=| ddd} |jd kr|<}!|!dkrd}!| dddddf}"t>t>|"tj||!tj?|"dd<n|j@dkr|j=|d|jd kd|_@|j@} tA|| BCB}#| tt|#jDdtt|#jEd| j dtt|#jFdtt|#jGd| j df} ttt|#jFdtt|#jDd| } | |j |j | fS)ae Normalize, rescale and color the image `A` from the given in_bbox (in data space), to the given out_bbox (in pixel space) clipped to the given clip_bbox (also in pixel space), and magnified by the magnification factor. `A` may be a greyscale image (MxN) with a dtype of `float32`, `float64`, `float128`, `uint16` or `uint8`, or an RGBA image (MxNx4) with a dtype of `float32`, `float64`, `float128`, or `uint8`. If `unsampled` is True, the image will not be scaled, but an appropriate affine transformation will be returned instead. If `round_to_pixel_border` is True, the output image size will be rounded to the nearest pixel boundary. This makes the images align correctly with the axes. It should not be used in cases where you want exact scaling, however, such as FigureImage. Returns the resulting (image, x, y, trans), where (x, y) is the upper left corner of the result in pixel space, and `trans` is the affine transformation from the image to pixel space. Nz9You must first set the image array or the image attributerzk_make_image must get a non-empty image. Your Artist's draw method must filter before this method is called.)NrrNupperrg?g)rmrLzInvalid dimensions, got {}rmfz4Casting input data from '{0}' to 'float64'for imshowgחA)rgcAg@g?g?TrLrzInvalid dimensions, got %sF)bytesrd)Hror;r intersectionr#r"r[rr$rscaler r%r& get_transform is_affiner!rndim ValueErrorformatrminmaxrZmaZmaskedZint32Zkindfloat32Zfloat16float64warningswarnastyperrdZautoscale_Nonevmaxvminclipitemr r'r _interpd_get_interpolation get_resampleget_filternorm get_filterradr6mcolorsZNoNormmaskwherenanarrayisnanZ masked_arrayrOrto_rgbaasarrayrr`r frozeninvertedyminymaxxminxmax)$rSrNZin_bboxZout_bboxZ clip_bboxr* unsampledround_to_pixel_borderZ clipped_bboxZout_width_baseZout_height_baseZt0tZ out_widthZ out_heightZ extra_widthZ extra_heightZ inp_dtypeZa_minZa_maxZ scaled_dtypeZdaZA_scaledZdvZvmidZfactZnewminZnewmaxZ A_resampledrZout_maskZ out_alphar2rZ alpha_channelZsubsetr3r3r4 _make_images"                                                 $z_ImageBase._make_imagecCs tddS)Nz)The make_image method must be overridden.)ro)rSr)r*rr3r3r4rsz_ImageBase.make_imagecCsV|j|dd\}}}}|dkr"dSt|jd|jd|}||||||dS)zu draw unsampled image. The renderer should support a draw_image method with scale parameter. T)rNrr)rrrzrr=)rSr)rBimr@rAr0r3r3r4_draw_unsampled_images z _ImageBase._draw_unsampled_imagecCsdS)z{ return True if the image is better to be drawn unsampled. The derived class needs to override it. Fr3)rSr)r3r3r4_check_unsampled_image)sz!_ImageBase._check_unsampled_imagec Os|sd|_dS|jdkr*d|_dS|}|||||| | | | |r| jr|||n0|||\}}}}|dk r||||||d|_dS)NFr) get_visiblestale get_arrayr;r<Z _set_gc_cliprqrZset_urlZget_urlZset_gidZget_gidrr{r|rrrHr=r?) rSr)argsrhrBrr@rAr0r3r3r4r:0s(   z_ImageBase.drawc Cst|jr|||S|j|j}}|\}}}}||krF||}}||krX||}}|dk r|dk r||koz|kno||ko|kn}nd}|ifS)zI Test whether the mouse event occurred within the image. NF)callable _containsxdataydata get_extent) rS mouseeventr.r/rrrrinsider3r3r4containsNs    2z_ImageBase.containscCs<|j|jdkr|jdddn|jddd}t||dS)z&Write the image to png file with fnamelowerNrvT)rxrd)rr[rn_png write_png)rSfnamerr3r3r4rfs" z_ImageBase.write_pngcCs tj|dd|_|jjtjkr8t|jjtds8td|jj dksh|jj dkr`|jj ddkshtd |jj dkrt |jjtj rd nd }|j d ks||jkrtd t|jd ||_|jjtjkrt |jjtj r|jtj|_d|_d|_d|_dS)z Set the image array. Note that this function does *not* update the normalization used. Parameters ---------- A : array-like T)copyZ same_kindz'Image data cannot be converted to floatrmrLrv)rLrz!Invalid dimensions for image datarMrrzmClipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).N)cbooksafe_masked_invalidrnrrrZcan_castfloat TypeErrorr}rZ issubdtypeZintegerrr_logZwarningrrr`rrr)rSrNZhighr3r3r4set_datals&   z_ImageBase.set_datacCs||dS)z Retained for backwards compatibility - use set_data instead. 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Parameters ---------- s : {'nearest', 'bilinear', 'bicubic', 'spline16', 'spline36', 'hanning', 'hamming', 'hermite', 'kaiser', 'quadric', 'catrom', 'gaussian', 'bessel', 'mitchell', 'sinc', 'lanczos', 'none'} Nzimage.interpolationzIllegal interpolation stringT)rrrr~rr)rSsr3r3r4r^sz_ImageBase.set_interpolationcCs|}|jdko|jo|jS)zS Returns `True` if the image can be composited with its neighbors. r)r{rr|Z is_separable)rSr0r3r3r4rIs z_ImageBase.can_compositecCs |dkrtd}||_d|_dS)zv Set whether or not image resampling is used. Parameters ---------- v : bool Nzimage.resampleT)r _resampler)rSvr3r3r4r_sz_ImageBase.set_resamplecCs|jS)z"Return the image resample boolean.)r)rSr3r3r4rsz_ImageBase.get_resamplecCst||_d|_dS)z Set whether the resize filter normalizes the weights. See help for `~.Axes.imshow`. 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N)autoT) rrQZupdate_datalimZ sticky_edgesr.r/Z _autoscaleXonZset_xlimZ _autoscaleYonZset_ylimr)rSrrrrrZcornersr3r3r4 set_extentHs  zAxesImage.set_extentcCsV|jdk r|jS|}|\}}|jdkr>d|d|ddfSd|dd|dfSdS)z.Get the image extent: left, right, bottom, topNrugg?)rrpr[)rSZsznumrowsnumcolsr3r3r4r\s  zAxesImage.get_extentcCs|\}}}}|jdkr$||}}|}t||g||gg}tddg|jddg}t||d} |j|j} } | | | g} t t | rdS| t \} }d| kr|jdkrnnd|kr|jdksndS|| |fSdS)z%Get the cursor data for a given eventrurNrm)ZboxinZboxoutr)rr[rr rr rrZtransform_pointrGrrrr!)rSeventrrrrarrZ data_extentZ array_extentr0r/r.Zpointijr3r3r4get_cursor_datahs   :zAxesImage.get_cursor_data)NNNNNrrF)N)rF) rrrrTrXrrrrrrrr3r3)rlr4rs   rcs|eZdZddfdd ZddZdd d Zd d Zd dZddZddZ ddZ ddZ fddZ fddZ ZS)NonUniformImager)rec stj|f|||dS)z kwargs are identical to those for AxesImage, except that 'nearest' and 'bilinear' are the only supported 'interpolation' options. N)rirXr^)rSrbrerh)rlr3r4rX~szNonUniformImage.__init__cCsdS)z; return False. Do not use unsampled image. Fr3)rSr)r3r3r4rsz&NonUniformImage._check_unsampled_image?Fc Cs|jdkrtd|rtd|j}|jdkr|jtjkrV|j|dd}|j |_ n>t |ddddtj fdd}d|dddddf<d|_ n|jtjkrd| tj}|jddkrtt|jd dd tj}||ddddd df<d|dddddf<|}d |_ |jjj\}}}} |jjj\} } } } t| d t| d }t| d t| d }||9}||9}t|j|j|t|t||||||| ft|j}|| | tfS) Nz"You must first set the image arrayz*unsampled not supported on NonUniformImagermT)rxrrMrLrFg?)r)rnror~r}rrrrrcis_gray is_grayscalerepeatZnewaxisrrr rPrQviewLimrRr1extentsr>r'Zpcolor_Ax_Ayr!rrr )rSr)r*rrNBr%r&Zv_widthZv_heightr@rArrr#r"rr3r3r4rs>   "    zNonUniformImage.make_imagecCst|tj}t|tj}tj|dd}|j|jkrBdkr`nn|jdd|j|jkshtd|jdkrztd|jd kr|jdd krtd |jd kr|jddkr|jdd|_||_||_ ||_ d |_ d|_ d S) a^ Set the grid for the pixel centers, and the pixel values. *x* and *y* are monotonic 1-D ndarrays of lengths N and M, respectively, specifying pixel centers *A* is an (M,N) ndarray or masked array of values to be colormapped, or a (M,N,3) RGB array, or a (M,N,4) RGBA array. T)rrrrmzAxes don't match array shape)rmrLzCan only plot 2D or 3D datarL)rrLrz?3D arrays must have three (RGB) or four (RGBA) color componentsN) rrrrrr}rrrnrrr`r)rSr.r/rNr3r3r4rs 6 zNonUniformImage.set_datacGs tddS)NzMethod not supported)NotImplementedError)rSrr3r3r4rszNonUniformImage.set_arraycCs(|dk r|dkrtdt||dS)z| Parameters ---------- s : str, None Either 'nearest', 'bilinear', or ``None``. N)rrz?Only nearest neighbor and bilinear interpolations are supported)rrr^)rSrr3r3r4r^sz!NonUniformImage.set_interpolationcCs6|jdkrtd|jd|jd|jd|jdfS)NzMust set data firstrrv)rnrorr)rSr3r3r4rs zNonUniformImage.get_extentcCsdS)Nr3)rSrr3r3r4r\szNonUniformImage.set_filternormcCsdS)Nr3)rSrr3r3r4r]szNonUniformImage.set_filterradcs"|jdk rtdt|dS)Nz'Cannot change colors after loading data)rnroriset_norm)rSrd)rlr3r4rs zNonUniformImage.set_normcs"|jdk rtdt|dS)Nz'Cannot change colors after loading data)rnroriset_cmap)rSrc)rlr3r4rs zNonUniformImage.set_cmap)rF)rrrrXrrrrr^rr\r]rrrr3r3)rlr4r}s  '  rcsLeZdZdZdfdd ZdddZd d Zd d Zd dZddZ Z S) PcolorImagez Make a pcolor-style plot with an irregular rectangular grid. This uses a variation of the original irregular image code, and it is used by pcolorfast for the corresponding grid type. Nc s6tj|||d|||dk r2||||dS)z cmap defaults to its rc setting cmap is a colors.Colormap instance norm is a colors.Normalize instance to map luminance to 0-1 Additional kwargs are matplotlib.artist properties )rdrcN)rirXrar)rSrbr.r/rNrcrdrh)rlr3r4rXs zPcolorImage.__init__?Fc Cs:|jdkrtd|rtd|jj}t|d}t |d tj }|jj j \}}}} t|dt|d} t| dt|d} tt| |} tt| |} |jdkr|j|jdd} | |_|jjdkr|j|_n|j} |jj} t|j|j| | | | j| j| j| jf|}|||tfS) Nz"You must first set the image arrayz&unsampled not supported on PColorImagerrMg?T)rxrm)rnror~rQZpatchZ get_facecolorrrrrrrr1rr>r!rrr}rcrrrr'Zpcolor2rrr%rr&rr )rSr)r*rZfcZbgr@rArrr#r"rNZvlrr3r3r4rs2     zPcolorImage.make_imagecCsdS)NFr3)rSr)r3r3r4r0sz"PcolorImage._check_unsampled_imagecCs$tj|dd}|dkr4tjd|jddtjd}nt|tj}|dkrltjd|jddtjd}nt|tj}|jdd|jd|jdfkrt d|jdd|jd|jdff|j d krt d |j d kr|jddkr|jdd|_d |_ |j d kr|jdd kr|dddddf|dddddfk r|dddddf|dddddfk rd|_ nt d|d|dkr|ddd}|dddddf}|d|dkr|ddd}|ddd}||_ ||_||_d|_d|_dS)a Set the grid for the rectangle boundaries, and the data values. *x* and *y* are monotonic 1-D ndarrays of lengths N+1 and M+1, respectively, specifying rectangle boundaries. If None, they will be created as uniform arrays from 0 through N and 0 through M, respectively. *A* is an (M,N) ndarray or masked array of values to be colormapped, or a (M,N,3) RGB array, or a (M,N,4) RGBA array. T)rNrr)rrmz2Axes don't match array shape. Got %s, expected %s.)rmrLzA must be 2D or 3DrLF)rLrz+3D arrays must have RGB or RGBA as last dimrv)rrrZarangerrrZravelr;r~r}rallrnrrrrr)rSr.r/rNr3r3r4r3sB"&  22zPcolorImage.set_datacGs tddS)NzMethod not supported)r)rSrr3r3r4rjszPcolorImage.set_arraycCs|j|j}}||jdksF||jdksF||jdksF||jdkrJdSt|j|d}t|j|d}y|j||fStk rdSXdS)z%Get the cursor data for a given eventrrvNr)rrrrrZ searchsortedrn IndexError)rSrr.r/rrr3r3r4rmszPcolorImage.get_cursor_data)NNNNN)rF) rrr__doc__rXrrrrrrr3r3)rlr4rs 7rcs@eZdZdZdZdfdd ZddZdd d Zd d ZZ S) FigureImagerrNc s:tjd|||d||_||_||_||d|_dS)z cmap is a colors.Colormap instance norm is a colors.Normalize instance to map luminance to 0-1 kwargs are an optional list of Artist keyword args N)rdrcr[g?)rirXfigureoxoyrar*)rSfigrcrdZoffsetxZoffsetyr[rh)rlr3r4rXs zFigureImage.__init__cCs8|\}}d|j|d|jd|j|d|jfS)z.Get the image extent: left, right, bottom, topgg?)rprr)rSrrr3r3r4rs zFigureImage.get_extent?Fc Cs|j|jj}t|j||j|g|j||jjd|j||jjdgg}|j\}}||j9}||j9}tddg||gg}|j|j||||||ddS)NrrF)r*rr) dpirr rrrnrZget_size_inchesr) rSr)r*rZfacr1r#r"rr3r3r4rs  zFigureImage.make_imagecCs"tj|tj|ddd|_dS)zSet the image array.T)rN)rYrZrrrr)rSrNr3r3r4rszFigureImage.set_data)NNrrN)rF) rrrrrrXrrrrr3r3)rlr4r{s rcsFeZdZdZdfdd Zd d Zdd d Zd dZdddZZ S) BboxImagez;The Image class whose size is determined by the given bbox.Nr@FTc s:tjd|||||||d| ||_| |_t|_dS)aG cmap is a colors.Colormap instance norm is a colors.Normalize instance to map luminance to 0-1 interp_at_native is a flag that determines whether or not interpolation should still be applied when the image is displayed at its native resolution. A common use case for this is when displaying an image for annotational purposes; it is treated similarly to Photoshop (interpolation is only used when displaying the image at non-native resolutions). kwargs are an optional list of Artist keyword args N)rcrdrer[rfrgr)N)rirXr1interp_at_nativer _transform) rSr1rcrdrer[rfrgrrrh)rlr3r4rXszBboxImage.__init__cCs|jS)N)r)rSr3r3r4r{szBboxImage.get_transformcCsD|dkr|j}t|jtr$|jSt|jr8||StddS)Nzunknown type of bbox)Z get_figureZ_cachedRendererr6r1r rr~)rSr)r3r3r4rs    zBboxImage.get_window_extentcCsLt|jr|||S|s&difS|j|j}}|||}|ifS)z7Test whether the mouse event occurred within the image.F)rrrr.r/rr)rSrr.r/rr3r3r4rs  zBboxImage.contains?c Cs~|\}}||}|j||g_||}tddg||gg}ttddgddgg||_|j|j|||||dS)Nrr)r) Zget_canvas_width_heightrrZ_pointsr r rrrn) rSr)r*rr#r"Zbbox_inZbbox_outrr3r3r4rs  zBboxImage.make_image)NNNNrrFT)N)rF) rrrrrXr{rrrrr3r3)rlr4rs"  rc Csbdtji}|dkrt|tr^tj|}t|jdkru2z`_ installed. thumbfile : str or file-like The thumbnail filename. scale : float, optional The scale factor for the thumbnail. interpolation : str, optional The interpolation scheme used in the resampling. See the *interpolation* parameter of `~.Axes.imshow` for possible values. preview : bool, optional If True, the default backend (presumably a user interface backend) will be used which will cause a figure to be raised if `~matplotlib.pyplot.show` is called. If it is False, the figure is created using `FigureCanvasBase` and the drawing backend is selected as `~matplotlib.figure.savefig` would normally do. Returns ------- figure : `~.figure.Figure` The figure instance containing the thumbnail. r rN)Zfigsizer)rrrF)aspectrZxticksZyticksT)rrre)r) r rZmatplotlib.pyplotZpyplotrrrrZadd_axesZimshowr)ZinfileZ thumbfilerzreZpreviewrZrowsZcolsZdepthrr"r#Zpltrrrbr3r3r4 thumbnails $      r)r)N)N)NNNNNr )rrF)MriorZmathrrZloggingZ urllib.parserZurllib.requestrZnumpyrZ matplotlibrZmatplotlib.artistZartistrVrZmatplotlib.backend_basesrZmatplotlib.colorsZcolorsrZ matplotlib.cmrYZmatplotlib.cbookrZmatplotlib._imager'Zmatplotlib._pngrZmatplotlib.transformsrr r r r r Z getLoggerrrr(ZBILINEARZBICUBICZSPLINE16ZSPLINE36ZHANNINGZHAMMINGZHERMITEZKAISERZQUADRICZCATROMZGAUSSIANZBESSELZMITCHELLZSINCZLANCZOSZBLACKMANrsetZinterpolations_namesr5rKrOrWrZr7rrrrrr rrrr3r3r3r4sv               ; -Uxz=U O 8#