ó m[c@`s•dZddlmZmZmZmZddlZddlmZddl Z ddl Z ddl j Z ddljZddljZddljZddljZdgZdddddddddddd d d „ Zd efd „ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZ de!fd„ƒYZ"de!fd„ƒYZ#d„Z$d„Z%d„Z&d„Z'd„Z(dS(u, Streamline plotting for 2D vector fields. i(tabsolute_importtdivisiontprint_functiontunicode_literalsN(txrangeu streamplotiu-|>gš™™™™™¹?g@ubothc5C`sXt||ƒ}t|ƒ}t||ƒ}|dkrEtjj}n| dkr]|j} n|dkr{|jj ƒ}n|dkr—t j d}ni}t d| dd| ƒ}|dkrŪd|}t |ƒ‚n|dkrō|d }nt|tjƒ}|rH|j|jkr-t d ƒ‚ng}tjj|ƒ}n||d <||d |2ƒ|j?ƒt j@jA|%ƒ}3tB|2|3ƒ}4|4S(uĮ 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 30x30 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. *start_points*: Nx2 array Coordinates of starting points for the streamlines. In data coordinates, the same as the ``x`` and ``y`` arrays. *zorder* : int any number *maxlength* : float Maximum length of streamline in axes coordinates. *integration_direction* : ['forward', 'backward', 'both'] Integrate the streamline in forward, backward or both directions. 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. ulines.linewidtht arrowstyletmutation_scalei ubothuforwardubackwarduTIntegration direction '%s' not recognised. Expected 'both', 'forward' or 'backward'.g@u7If 'color' is given, must have the shape of 'Grid(x,y)'ucoloru;If 'linewidth' is given, must have the shape of 'Grid(x,y)'u linewidthuzorderu('u' and 'v' must be of shape 'Grid(x,y)'itdtypeu2Starting point ({}, {}) outside of data boundariesNiu image.cmapi’’’’it transform(ubothuforwardubackward(CtGridt StreamMaskt DomainMaptNonetmlinestLine2Dtzordert transDatat _get_linestget_next_colort matplotlibtrcParamstdictt ValueErrort isinstancetnptndarraytshapetmatmasked_invalidtget_integratort_gen_starting_pointst mask2gridtappendt asanyarraytfloattcopytx_origintwidthty_origintheighttformatt data2gridtmcolorst Normalizetmintmaxtcmtget_cmaptarrayt grid2datat transposetreshapetextendthstacktcumsumtsqrttdifft searchsortedtmeant interpgridtpatchestFancyArrowPatcht add_patcht mcollectionstLineCollectiont sticky_edgestxtyt set_arraytset_cmaptset_normtadd_collectiontautoscale_viewt collectionstPatchCollectiont StreamplotSet(5taxesRBRCtutvtdensityt linewidthtcolortcmaptnormt arrowsizeRt minlengthRRt start_pointst maxlengthtintegration_directiontgridtmasktdmaptline_kwtarrow_kwterrstrtuse_multicolor_linest line_colorst integratet trajectoriestxmtymtxgtygtttsp2txstyst streamlinestarrowsttgxttgyttxttytpointststnt arrow_tailt arrow_headt line_widthst color_valuestptlctactstream_container((s4lib/python2.7/site-packages/matplotlib/streamplot.pyt streamplotsŚ<                  $   ))   !    $$64       RKcB`seZd„ZRS(cK`s||_||_dS(N(tlinesRl(tselfR}Rltkwargs((s4lib/python2.7/site-packages/matplotlib/streamplot.pyt__init__ės (t__name__t __module__R€(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyRKésR cB`s_eZdZd„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z d „Z RS( uMap 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`. cC`s„||_||_|jd|j|_|jd|j|_d|j|_d|j|_d|j|_ d|j |_ dS(Nigš?( RYRZtnxt x_grid2masktnyt y_grid2maskt x_mask2gridt y_mask2gridtdxt x_data2gridtdyt y_data2grid(R~RYRZ((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR€s  cC`s,t||jdƒt||jdƒfS(u;Return nearest space in mask-coords from given grid-coords.gą?(tintR„R†(R~txityi((s4lib/python2.7/site-packages/matplotlib/streamplot.pyt grid2maskscC`s||j||jfS(N(R‡Rˆ(R~RcRd((s4lib/python2.7/site-packages/matplotlib/streamplot.pyRscC`s||j||jfS(N(RŠRŒ(R~txdtyd((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR)scC`s||j||jfS(N(RŠRŒ(R~ReRf((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR1scC`s/|j||ƒ\}}|jj||ƒdS(N(RRZt_start_trajectory(R~ReRfRcRd((s4lib/python2.7/site-packages/matplotlib/streamplot.pytstart_trajectory scC`s.|j||ƒ\}}||f|j_dS(N(RRZt _current_xy(R~ReRfRcRd((s4lib/python2.7/site-packages/matplotlib/streamplot.pytreset_start_point$scC`sM|jj||ƒst‚n|j||ƒ\}}|jj||ƒdS(N(RYt within_gridtInvalidIndexErrorRRZt_update_trajectory(R~ReRfRcRd((s4lib/python2.7/site-packages/matplotlib/streamplot.pytupdate_trajectory(s cC`s|jjƒdS(N(RZt_undo_trajectory(R~((s4lib/python2.7/site-packages/matplotlib/streamplot.pytundo_trajectory.s( RR‚t__doc__R€RRR)R1R”R–RšRœ(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR ós       R cB`s/eZdZd„Zed„ƒZd„ZRS(u Grid of data.cC`sm|jdkrn[|jdkra|ddd…f}tj||ƒsXtdƒ‚n|}n tdƒ‚|jdkrn^|jdkrŃ|dd…df}tj||jƒsČtdƒ‚n|}n tdƒ‚t|ƒ|_t|ƒ|_|d|d|_|d|d|_ |d|_ |d|_ |d|d|_ |d|d|_ dS( NiiiuThe rows of 'x' must be equalu$'x' can have at maximum 2 dimensionsu The columns of 'y' must be equalu$'y' can have at maximum 2 dimensionsi’’’’(tndimRtallcloseRtTtlenRƒR…R‰R‹R$R&R%R'(R~RBRCtx_rowty_col((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR€4s0      cC`s|j|jfS(N(R…Rƒ(R~((s4lib/python2.7/site-packages/matplotlib/streamplot.pyRVscC`s<|dko;||jdko;|dko;||jdkS(u.Return True if point is a valid index of grid.ii(RƒR…(R~RŽR((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR—Zs(RR‚RR€tpropertyRR—(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR 2s "R cB`s;eZdZd„Zd„Zd„Zd„Zd„ZRS(uIMask 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. cC`sŠtj|ƒrG|dkr*tdƒ‚ntd|ƒ|_|_nOt|ƒdkrhtdƒ‚ntd|dƒ|_td|dƒ|_tj|j|jfƒ|_|jj |_ d|_ dS(Niu'If a scalar, 'density' must be positiveiiu*'density' can have at maximum 2 dimensionsi( RtisscalarRRRƒR…R”tzerost_maskRR R•(R~RO((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR€js cG`s|jj|ŒS(N(R§t __getitem__(R~targs((s4lib/python2.7/site-packages/matplotlib/streamplot.pyRØyscC`sg|_|j||ƒdS(u%Start recording streamline trajectoryN(t_trajR™(R~RcRd((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR“|s cC`s+x$|jD]}|jj|dƒq WdS(u#Remove current trajectory from maskiN(RŖR§t __setitem__(R~Rg((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR›scC`ss|j||fkro|||fdkrf|jj||fƒd|j||f<||f|_qot‚ndS(u…Update current trajectory position in mask. If the new position has already been filled, raise `InvalidIndexError`. iiN(R•RŖR R§R˜(R~RcRd((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR™†s (RR‚RR€RØR“R›R™(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR as     R˜cB`seZRS((RR‚(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR˜”stTerminateTrajectorycB`seZRS((RR‚(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR¬˜sc `sœˆjˆˆƒ\‰‰ˆˆjj}ˆˆjj}tjj|d|dƒ‰‡‡‡fd†‰‡fd†‰‡‡‡‡‡‡fd†}|S(Nic`sjtˆ||ƒ}|dkr*tƒ‚nd|}tˆ||ƒ}tˆ||ƒ}||||fS(Nigš?(R;R¬(RŽRtds_dttdt_dstuitvi(tspeedRMRN(s4lib/python2.7/site-packages/matplotlib/streamplot.pyt forward_time©s   c`s!ˆ||ƒ\}}| | fS(N((RŽRtdxitdyi(R²(s4lib/python2.7/site-packages/matplotlib/streamplot.pyt backward_time²sc`sTdgg}}}yˆj||ƒWntk r<dSXˆd kr„t||ˆˆˆƒ\}}}||7}||ddd…7}||ddd…7}nˆd kr,ˆj||ƒt||ˆˆˆƒ\}}}t|ƒdkr |d}|d}n||7}||7}||7}n|ˆkrB||fSˆjƒdSdS( u™Return x, y grid-coordinates of trajectory based on starting point. Integrate both forward and backward in time from starting point in grid coordinates. Integration is terminated when a trajectory reaches a domain boundary or when it crosses into an already occupied cell in the StreamMask. The resulting trajectory is None if it is shorter than `minlength`. gubothubackwardNi’’’’uforwardii(ubothubackward(ubothuforward(R”R˜R t_integrate_rk12R–R”Rœ(tx0ty0tstotaltx_trajty_trajRrtxttyt(RµR[R²RXRWRU(s4lib/python2.7/site-packages/matplotlib/streamplot.pyRa¶s.   !  !        (R)RYRƒR…RRR7( RMRNR[RURWRXtu_axtv_axRa(( RµR[R²RXRWRUR±RMRNs4lib/python2.7/site-packages/matplotlib/streamplot.pyRŸs 'cC`s2d}td|jjd|jjdƒ}|}d}|} |} g} g} xŅ|jj| | ƒr$| j| ƒ| j| ƒy>|| | ƒ\} }|| || | ||ƒ\}}WnKtk rüt| | ||ƒ\}} } ||7}Pnt k r PnX|| }||}|d| |}|d||}|jj \}}t j |||d|||dƒ}||krķ| |7} | |7} y|j | | ƒWntk rĖPnX|||krąPn||7}n|dkr|}qSt|d|||dƒ}qSW|| | fS(uA2nd-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. gś~j¼t“h?gš?gš™™™™™¹?igą?ig333333ė?(R,RZRƒR…RYR—R t IndexErrort _euler_stepR¬RRR7RšR˜(R·RøR[tfRWtmaxerrortmaxdstdsR¹RŽRtxf_trajtyf_trajtk1xtk1ytk2xtk2ytdx1tdy1tdx2tdy2RƒR…terror((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR¶ąsR&       +       #c C`s |jj\}}|d}|d}|||ƒ\}} |dkrStj} n,|dkrm|| } n|d||} | dkr—tj} n,| dkr±|| } n|d|| } t| | ƒ} |j||| ƒ|j|| | ƒ| ||fS(uBSimple Euler integration step that extends streamline to boundary.i’’’’ii(RYRRtinfR,R ( RĘRĒR[RĀR…RƒRŽRtcxtcytdsxtdsyRÅ((s4lib/python2.7/site-packages/matplotlib/streamplot.pyRĮ9s$        cC`sŖtj|ƒ\}}t|tjƒr‚|jtƒ}|jtƒ}tj|dd|dƒ}tj|dd|dƒ}n^t|ƒ}t|ƒ}||dkr³|}n |d}||dkrÖ|}n |d}|||f} |||f} |||f} |||f} ||} ||}| d| | | }| d| | | }|d|||}t|tjƒs¦tjj|ƒr¦t ‚q¦n|S(u0Fast 2D, linear interpolation on an integer gridiii( RRRRtastypeRtclipRt is_maskedR¬(taRŽRtNytNxRBRCtxntynta00ta01ta10ta11R¼R½ta0ta1tai((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR;Ts6          c c`sN|\}}d}d}|d}|d}d\}}d} d} xt||ƒD]ń} ||fV| dkrž|d7}||krF|d8}d} qFqU| dkrÖ|d7}||krF|d8}d} qFqU| dkr|d8}||krF|d7}d} qFqU| dkrU|d8}||krF|d7}d} qFqUqUWdS( uYield 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. iiurightuupuleftudownN(ii(R( RR…RƒtxfirsttyfirsttxlasttylastRBRCtit direction((s4lib/python2.7/site-packages/matplotlib/streamplot.pyR|s<                        ()Rt __future__RRRRtsixt six.movesRtnumpyRRt matplotlib.cmR.tmatplotlib.colorstcolorsR*tmatplotlib.collectionsRIR?tmatplotlib.linesR}R tmatplotlib.patchesR<t__all__R R|tobjectRKR R R t ExceptionR˜R¬RR¶RĮR;R(((s4lib/python2.7/site-packages/matplotlib/streamplot.pyts4"       Ļ ?/3 A Y  (