a ضa_[ @s dZddlZddlZddlmZmZddlmZddl m Z ddl m ZddlmZdgZd&d dZGd d d ZGd ddZGdddZGdddZGdddeZGdddeZddZedddZGdddeZddZd d!Z d"d#Z!d$d%Z"dS)'z, Streamline plotting for 2D vector fields. N)_apicm streamplot-|>皙?@bothc4 Csdt||}t|}t||}|dur,tjj}| dur:|j} |durL|j}|dur^t j d}i}t | d| d}t j gd|d|dkr|d}t|tj}|r|j|jkrtd g}tj|}n||d <||d <t|tjr|j|jkrtd g|d <n||d <||d <||d <||d <|j|jksB|j|jkrJtdtj|}tj|}t|||| ||}g}|durt|jD]J\}}|||fdkr|||\}}|||}|dur||qntj|td} | D]d\}!}"|j|!kr|j|jkrDnn$|j|"krB|j|jksntd |!|"q| dddf|j8<| dddf|j8<| D]`\}!}"|!|!|"\}}t"|d|j#d}t"|d|j$d}|||}|dur||q|r | durt%&|'|(} t)*|}g}#g}$|D]t}|j+\}%}&|,|%|&\}'}(|'|j7}'|(|j7}(t-|'|(g.ddd})|#/t0|)dd|)ddgt1t2t3|'t3|(}*t4|*|*dd}+|'|+|(|+f},t5|'|+|+dt5|(|+|+df}-t|tjrFt6||%|&dd}.|d /|.|.|+|d <|r~t6||%|&dd}/||/|| |/|+|d <t7j8|,|-fd| i|}0|$|0q,t9j:|#fd| i|}1|j|j|jg|1j;jtj0||1?||1@| |A|1t jBC|$}2|$D]}0|D|0q<|EtF|1|2}3|3S)a^ Draw streamlines of a vector flow. Parameters ---------- x, y : 1D/2D arrays Evenly spaced strictly increasing arrays to make a grid. If 2D, all rows of *x* must be equal and all columns of *y* must be equal; i.e., they must be as if generated by ``np.meshgrid(x_1d, y_1d)``. u, v : 2D arrays *x* and *y*-velocities. The number of rows and columns must match the length of *y* and *x*, respectively. density : float or (float, float) 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 a tuple (density_x, density_y). linewidth : float or 2D array The width of the stream lines. With a 2D array the line width can be varied across the grid. The array must have the same shape as *u* and *v*. color : color or 2D array The streamline color. If given an array, its values are converted to colors using *cmap* and *norm*. The array must have the same shape as *u* and *v*. cmap : `~matplotlib.colors.Colormap` Colormap used to plot streamlines and arrows. This is only used if *color* is an array. norm : `~matplotlib.colors.Normalize` Normalize object used to scale luminance data to 0, 1. If ``None``, stretch (min, max) to (0, 1). This is only used if *color* is an array. arrowsize : float Scaling factor for the arrow size. arrowstyle : str Arrow style specification. See `~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 coordinates as the *x* and *y* arrays). zorder : int The zorder of the stream lines and arrows. Artists with lower zorder values are drawn first. maxlength : float Maximum length of streamline in axes coordinates. integration_direction : {'forward', 'backward', 'both'}, default: 'both' Integrate the streamline in forward, backward or both directions. data : indexable object, optional DATA_PARAMETER_PLACEHOLDER Returns ------- StreamplotSet Container object with attributes - ``lines``: `.LineCollection` of streamlines - ``arrows``: `.PatchCollection` containing `.FancyArrowPatch` objects representing the 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. Nzlines.linewidth ) arrowstyleZmutation_scale)r forwardbackward)integration_directionr g@z|jdkr|dddf}t||jstd|}ntdt|dkstdt|dkstd t||_t||_ |d|d|_ |d|d|_ |d|_ |d|_ |d |d|_|d |d|_tt||j|jds^td tt||j|j dstd dS) NrrrzThe rows of 'x' must be equalz$'x' can have at maximum 2 dimensionsz The columns of 'y' must be equalz$'y' can have at maximum 2 dimensionsz'x' must be strictly increasingz'y' must be strictly increasingrz!'x' values must be equally spacedz!'y' values must be equally spaced)ndimrZallcloserr3r7alllenr.r/rdrfr'r)r(r*)rZr<r=Zx_rowZy_colrVrVrWr[>s@           z Grid.__init__cCs |j|jfSrX)r/r.rzrVrVrWrjsz Grid.shapecCs<d|ko|jdkno:d|ko6|jdkSS)z9Return whether (*xi*, *yi*) is a valid index of the grid.rr)r.r/rjrVrVrWrunszGrid.within_gridN)r\r]r^r|r[propertyrrurVrVrVrWr<s , rc@s8eZdZdZddZddZddZdd Zd d Zd S) raN Mask to keep track of discrete regions crossed by streamlines. The resolution of this grid determines the approximate spacing between trajectories. Streamlines are only allowed to pass through zeroed cells: When a streamline enters a cell, that cell is set to 1, and no new streamlines are allowed to enter. c Csz"dt|dt\|_|_Wn.tyP}ztd|WYd}~n d}~00|jdksf|jdkrntdt|j|jf|_|jj |_ d|_ dS)Nrz,'density' must be a scalar or be of length 2rz'density' must be positive) rZ broadcast_toastyperir.r/rZzeros_maskrrs)rZrBerrrVrVrWr[s" zStreamMask.__init__cCs |j|SrX)r)rZargsrVrVrW __getitem__szStreamMask.__getitem__cCsg|_|||dS)z%Start recording streamline trajectoryN)_trajrwrnrVrVrWrpszStreamMask._start_trajectorycCs|jD]}d|j|<qdS)z#Remove current trajectory from maskrN)rr)rZrMrVrVrWrys zStreamMask._undo_trajectorycCsP|j||fkrL|||fdkrH|j||fd|j||f<||f|_ntdS)z Update current trajectory position in mask. If the new position has already been filled, raise `InvalidIndexError`. rrN)rsrr$rrvrnrVrVrWrws  zStreamMask._update_trajectoryN) r\r]r^r|r[rrpryrwrVrVrVrWrus   rc@s eZdZdS)rvNr\r]r^rVrVrVrWrvsrvc@s eZdZdS)TerminateTrajectoryNrrVrVrVrWrsrc s\jjd}jjd}tj|d|dfddfddfdd}|S) Nrrcs\j||stt||}|dkr,td|}t||}t||}||||fS)Nrr_)rEru OutOfBoundsr9r)rkrlZds_dtZdt_dsZuivi)rGspeedr@rArVrW forward_times   z%_get_integrator..forward_timecs||\}}| | fSrXrV)rkrlZdxiZdyi)rrVrW backward_timesz&_get_integrator..backward_timecsdg}}z||Wnty.YdS0dvrft||\}}||7}||ddd7}dvr||t||\}}||7}||dd7}|krt|tddSdSdS) a Return (N, 2) 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`. gN)r r r)r r r)rrr)rrrv_integrate_rk12rtrZbroadcast_arraysemptyr{)x0y0stotalxy_trajrQZxyt)rrGrrrDrCrVrWrHs$   z"_get_integrator..integrate)r,rEr.r/rr sqrt) r@rArGrCrDrZu_axZv_axrHrV) rrGrrrDrCrr@rArWr!s #r!z3.5cCs:t||||||}|durdSt|s.ggfSgt|SrX)r!rzip)r@rArGrCrDrrrVrVrWget_integrators   rc@s eZdZdS)rNrrVrVrVrWrsrcCsd}td|jjd|jjd}|}d}|} |} g} zR|j| | rT| | | fnt|| | \} } || || | || \}}WnJty| rt| ||\}} ||7}YqYnt yYqYn0|| }|| }|d| |}|d| |}|jj \}}t |||d|||d}||kr| |7} | |7} z| | | WntyvYqYn0|||krq||7}|dkr|}q4t|d|||d}q4|| fS)a 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 RK4 and RK45 solvers (using similar Python implementations) in most setups. g~jth?r_rrrhrg333333?)r1rFr.r/rErur$r _euler_steprrrr6rxrv)rrrGfrDZmaxerrorZmaxdsdsrrkrlxyf_trajZk1xZk1yZk2xZk2yZdx1Zdy1Zdx2Zdy2r/r.errorrVrVrWrsP"     $   rc Cs|jj\}}|d\}}|||\}}|dkr6tj} n$|dkrJ|| } n|d||} |dkrjtj} n$|dkr~|| } n|d||} t| | } |||| ||| f| |fS)zBSimple Euler integration step that extends streamline to boundary.rrr)rErrinfr1r$) rrGrr/r.rkrlZcxcyZdsxZdsyrrVrVrWr_s      rcCs@t|\}}t|tjr\|t}|t}t|dd|d}t|dd|d}nDt|}t|}||dkr~|}n|d}||dkr|}n|d}|||f} |||f} |||f} |||f} ||} ||}| d| | | }| d| | | }|d|||}t|tjsr;Zmatplotlib.linesrYrZmatplotlib.patchesr:__all__rr?rrr Exceptionrvrr! deprecatedr IndexErrorrrrr9r"rVrVrVrWs8     ` @93? `(