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� ��L]c @ sL d Z d d l m Z d d l Z d d l Z d d l j Z d d l j Z d d l j Z d d l j Z d g Z d d d d d d d d d d � Z d e f d � � YZ d e f d � � YZ d e f d � � YZ d e f d � � YZ d e f d � � YZ d e f d � � YZ d � Z d � Z d � Z d � Z d � Z d S( s, Streamline plotting for 2D vector fields. i����( t divisionNt streamploti s -|>g�������?c - C s� t | | � } t | � } t | | � } | d k rB | j } n | d k rc | j j j � } n | d k r t j d } n i } t d | d d | � } t | t j � } | r� | j | j k s� t � g } n | | d <| | d <t | t j � r"| j | j k st � g | d <n | | d <| | d <| j | j k sNt � | j | j k sft � t j t j | � � r�t j j | d t j | � �} n t j t j | � � r�t j j | d t j | � �} n t | | | | � } g } xy t | j � D]h \ } } | | | f d k r | j | | � \ } } | | | � } | d k rq| j | � qqq q W| r�| d k r�t j | j � | j � � } n | d k r�t j t j d � } q�t j | � } n g } g } x| D]} t j | d � } t j | d � } t j | d � | j | j } t j | d � | j | j! }! t j" | |! g � j# d d d � }" | j$ t j% |" d |" d g � � t j& t j' t j( | � d t j( |! � d � � }# t j) |# |# d d � }$ | |$ |! |$ f }% t j* | |$ |$ d !� t j* |! |$ |$ d !� f }& t | t j � r�t+ | | | � d }' | d j$ |' � |' |$ | d <n | r�t+ | | | � d }( | j$ |( � | | |( |$ � � | d <n t, j- |% |& d | | �}) | j. |) � | j |) � q�Wt/ j0 | d | | �}* | rZ|* j1 t j2 | � � |* j3 | � |* j4 | � n | j5 |* � | j6 | j � | j � f | j � | j � f f � | j7 d t8 � t j9 j: | � }+ t; |* |+ � }, |, S( s' Draws streamlines of a vector flow. *x*, *y* : 1d arrays an *evenly spaced* grid. *u*, *v* : 2d arrays x and y-velocities. Number of rows should match length of y, and the number of columns should match x. *density* : float or 2-tuple Controls the closeness of streamlines. When `density = 1`, the domain is divided into a 25x25 grid---*density* linearly scales this grid. Each cell in the grid can have, at most, one traversing streamline. For different densities in each direction, use [density_x, density_y]. *linewidth* : numeric or 2d array vary linewidth when given a 2d array with the same shape as velocities. *color* : matplotlib color code, or 2d array Streamline color. When given an array with the same shape as velocities, *color* values are converted to colors using *cmap*. *cmap* : :class:`~matplotlib.colors.Colormap` Colormap used to plot streamlines and arrows. Only necessary when using an array input for *color*. *norm* : :class:`~matplotlib.colors.Normalize` Normalize object used to scale luminance data to 0, 1. If None, stretch (min, max) to (0, 1). Only necessary when *color* is an array. *arrowsize* : float Factor scale arrow size. *arrowstyle* : str Arrow style specification. See :class:`~matplotlib.patches.FancyArrowPatch`. *minlength* : float Minimum length of streamline in axes coordinates. Returns: *stream_container* : StreamplotSet Container object with attributes lines: `matplotlib.collections.LineCollection` of streamlines arrows: collection of `matplotlib.patches.FancyArrowPatch` objects representing arrows half-way along stream lines. This container will probably change in the future to allow changes to the colormap, alpha, etc. for both lines and arrows, but these changes should be backward compatible. s lines.linewidtht arrowstylet mutation_scalei t colort linewidtht maski s image.cmapi i����i g @t transformt tightN(< t Gridt StreamMaskt DomainMapt Nonet transDatat _get_linest color_cyclet nextt matplotlibt rcParamst dictt isinstancet npt ndarrayt shapet AssertionErrort anyt isnant mat arrayt get_integratort _gen_starting_pointst mask2gridt appendt mcolorst normalizet mint maxt cmt get_cmapt dxt x_origint dyt y_origint transposet reshapet extendt hstackt cumsumt sqrtt difft searchsortedt meant interpgridt patchest FancyArrowPatcht add_patcht mcollectionst LineCollectiont set_arrayt asarrayt set_cmapt set_normt add_collectiont update_datalimt autoscale_viewt Truet collectionst PatchCollectiont StreamplotSet(- t axest xt yt ut vt densityR R t cmapt normt arrowsizeR t minlengthR t gridR t dmapt line_kwt arrow_kwt use_multicolor_linest line_colorst integratet trajectoriest xmt ymt xgt ygt tt streamlinest arrowst tgxt tgyt txt tyt pointst st nt arrow_tailt arrow_headt line_widthst color_valuest pt lct act stream_container( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR s� / $$ ! !!$$64 7RD c B s e Z d � Z RS( c K s | | _ | | _ d S( N( t linesR] ( t selfRm R] t kwargs( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt __init__� s ( t __name__t __module__Rp ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyRD � s R c B sV e Z d Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z d � Z RS( s Map representing different coordinate systems. Coordinate definitions: * axes-coordinates goes from 0 to 1 in the domain. * data-coordinates are specified by the input x-y coordinates. * grid-coordinates goes from 0 to N and 0 to M for an N x M grid, where N and M match the shape of the input data. * mask-coordinates goes from 0 to N and 0 to M for an N x M mask, where N and M are user-specified to control the density of streamlines. This class also has methods for adding trajectories to the StreamMask. Before adding a trajectory, run `start_trajectory` to keep track of regions crossed by a given trajectory. Later, if you decide the trajectory is bad (e.g. if the trajectory is very short) just call `undo_trajectory`. c C s� | | _ | | _ t | j d � | j | _ t | j d � | j | _ d | j | _ d | j | _ | j | j | _ | j | j | _ d S( Ni g �?( RO R t floatt nxt x_grid2maskt nyt y_grid2maskt x_mask2gridt y_mask2gridt widtht x_data2gridt heightt y_data2grid( Rn RO R ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyRp � s c C s, t | | j d � t | | j d � f S( s; Return nearest space in mask-coords from given grid-coords.g �?( t intRu Rw ( Rn t xit yi( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt grid2mask� s c C s | | j | | j f S( N( Rx Ry ( Rn RW RX ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR � s c C s | | j | | j f S( N( R{ R} ( Rn t xdt yd( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt data2grid� s c C s/ | j | | � \ } } | j j | | � d S( N( R� R t _start_trajectory( Rn RY RZ RW RX ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt start_trajectory� s c C s. | j | | � \ } } | | f | j _ d S( N( R� R t _current_xy( Rn RY RZ RW RX ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt reset_start_point� s c C sM | j j | | � s t � n | j | | � \ } } | j j | | � d S( N( RO t within_gridt InvalidIndexErrorR� R t _update_trajectory( Rn RY RZ RW RX ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt update_trajectory� s c C s | j j � d S( N( R t _undo_trajectory( Rn ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt undo_trajectory� s ( Rq Rr t __doc__Rp R� R R� R� R� R� R� ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR � s R c B s/ e Z d Z d � Z e d � � Z d � Z RS( s Grid of data.c C sU t | j � d k r@ | d } t j | | � s7 t � | } n t | j � d k s[ t � t | j � d k r� | d d � d f } t j | | j � s� t � | } n t | j � d k s� t � t | � | _ t | � | _ | d | d | _ | d | d | _ | d | _ | d | _ | d | d | _ | d | d | _ d S( Ni i i i����( t lenR R t allcloseR t TRt Rv R' R) R( R* Rz R| ( Rn RF RG t x_rowt y_col( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyRp � s$ c C s | j | j f S( N( Rv Rt ( Rn ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR s c C s< | d k o; | | j d k o; | d k o; | | j d k S( s. Return True if point is a valid index of grid.i i ( Rt Rv ( Rn R R� ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� s ( Rq Rr R� Rp t propertyR R� ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR � s R c B s; e Z d Z d � Z d � Z d � Z d � Z d � Z RS( sI Mask to keep track of discrete regions crossed by streamlines. The resolution of this grid determines the approximate spacing between trajectories. Streamlines are only allowed to pass through zeroed cells: When a streamline enters a cell, that cell is set to 1, and no new streamlines are allowed to enter. c C s� t j | � r> | d k s! t � t d | � | _ | _ nF t | � d k sV t � t d | d � | _ t d | d � | _ t j | j | j f � | _ | j j | _ d | _ d S( Ni i i i i ( R t isscalarR R~ Rt Rv R� t zerost _maskR R R� ( Rn RJ ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyRp ' s c G s | j j | � S( N( R� t __getitem__( Rn t args( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� 4 s c C s g | _ | j | | � d S( s% Start recording streamline trajectoryN( t _trajR� ( Rn RW RX ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� 7 s c C s+ x$ | j D] } | j j | d � q Wd S( s# Remove current trajectory from maski N( R� R� t __setitem__( Rn R[ ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� < s c C ss | j | | f k ro | | | f d k rf | j j | | f � d | j | | f <| | f | _ qo t � n d S( s� Update current trajectory position in mask. If the new position has already been filled, raise `InvalidIndexError`. i i N( R� R� R R� R� ( Rn RW RX ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� A s ( Rq Rr R� Rp R� R� R� R� ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR s R� c B s e Z RS( ( Rq Rr ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� O s t TerminateTrajectoryc B s e Z RS( ( Rq Rr ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� S s c s� � j � � � \ � � � � j j } � � j j } t j j | d | d � � � � � f d � � � f d � � � � � � f d � } | S( Ni c sj t � | | � } | d k r* t � � n d | } t � | | � } t � | | � } | | | | f S( Ni g �?( R4 R� ( R R� t ds_dtt dt_dst uit vi( t speedRH RI ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt forward_timed s c s! � | | � \ } } | | f S( N( ( R R� t dxit dyi( R� ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt backward_timem s c s� � j | | � t | | � � � \ } } } � j | | � t | | � � � \ } } } | | } | d d d � | d } | d d d � | d } | � k r� | | f S� j � d Sd S( s� Return x, y grid-coordinates of trajectory based on starting point. Integrate both forward and backward in time from starting point in grid coordinates. Integration is terminated when a trajectory reaches a domain boundary or when it crosses into an already occupied cell in the StreamMask. The resulting trajectory is None if it is shorter than `minlength`. Ni����i ( R� t _integrate_rk12R� R� R ( t x0t y0t sft xf_trajt yf_trajt sbt xb_trajt yb_trajt stotalt x_trajt y_traj( R� RP R� RN ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyRU q s ( R� RO Rt Rv R R R0 ( RH RI RP RN t u_axt v_axRU ( ( R� RP R� RN R� RH RI s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR Z s c C s2 d } t d | j j d | j j d � } | } d } | } | } g } g } x�| j j | | � r$| j | � | j | � y> | | | � \ } } | | | | | | | � \ } } WnK t k r� t | | | | � \ } } } | | 7} Pn t k r Pn X| | } | | } | d | | } | d | | } | j j \ } } t j | | | d | | | d � } | | k r�| | 7} | | 7} y | j | | � Wn t k r�Pn X| | d k r�Pn | | 7} n | d k r| } qS t | d | | | d � } qS W| | | f S( sA 2nd-order Runge-Kutta algorithm with adaptive step size. This method is also referred to as the improved Euler's method, or Heun's method. This method is favored over higher-order methods because: 1. To get decent looking trajectories and to sample every mask cell on the trajectory we need a small timestep, so a lower order solver doesn't hurt us unless the data is *very* high resolution. In fact, for cases where the user inputs data smaller or of similar grid size to the mask grid, the higher order corrections are negligible because of the very fast linear interpolation used in `interpgrid`. 2. For high resolution input data (i.e. beyond the mask resolution), we must reduce the timestep. Therefore, an adaptive timestep is more suited to the problem as this would be very hard to judge automatically otherwise. This integrator is about 1.5 - 2x as fast as both the RK4 and RK45 solvers in most setups on my machine. I would recommend removing the other two to keep things simple. g�~j�t�h?g �?g�������?i g �?i g333333�?( R# R Rt Rv RO R� R t IndexErrort _euler_stepR� R R R0 R� R� ( R� R� RP t ft maxerrort maxdst dsR� R R� R� R� t k1xt k1yt k2xt k2yt dx1t dy1t dx2t dy2Rt Rv t error( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� � sR & + #c C s | j j \ } } | d } | d } | | | � \ } } | d k rS t j } n, | d k rm | | } n | d | | } | d k r� t j } n, | d k r� | | } n | d | | } t | | � } | j | | | � | j | | | � | | | f S( sB Simple Euler integration step that extends streamline to boundary.i����i i ( RO R R t infR# R ( R� R� RP R� Rv Rt R R� t cxt cyt dsxt dsyR� ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR� � s$ c C s� t j | � \ } } t | t j � r� | j t j � } | j t j � } t j | d d | d � } t j | d d | d � } nd t j | � } t j | � } | | d k r� | } n | d } | | d k r� | } n | d } | | | f } | | | f } | | | f } | | | f } | | } | | } | d | | | } | d | | | } | d | | | } t | t j � s�t j j | � r�t � q�n | S( s0 Fast 2D, linear interpolation on an integer gridi i i ( R R R R t astypeR~ t clipR t is_maskedR� ( t aR R� t Nyt NxRF RG t xnt ynt a00t a01t a10t a11t xtt ytt a0t a1t ai( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR4 s6 c c sN | \ } } d } d } | d } | d } d \ } } d } d } xt | | � D]� } | | f V| d k r� | d 7} | | k rF| d 8} d } qFqU | d k r� | d 7} | | k rF| d 8} d } qFqU | d k r| d 8} | | k rF| d 7} d } qFqU | d k rU | d 8} | | k rF| d 7} d } qFqU qU Wd S( s Yield starting points for streamlines. Trying points on the boundary first gives higher quality streamlines. This algorithm starts with a point on the mask corner and spirals inward. This algorithm is inefficient, but fast compared to rest of streamplot. i i t rightt upt leftt downN( i i ( t xrange( R Rv Rt t xfirstt yfirstt xlastt ylastRF RG t it direction( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyR * s< ( R� t __future__R t numpyR R t matplotlib.cmR% t matplotlib.colorst colorsR! t matplotlib.collectionsRB R8 t matplotlib.patchesR5 t __all__R R t objectRD R R R t ExceptionR� R� R R� R� R4 R ( ( ( s; /usr/lib64/python2.7/site-packages/matplotlib/streamplot.pyt <module> s, � <)1 4 Y (
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