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Streamline plotting for 2D vector fields.
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� r�t+ | | | � d }' | d j$ |' � |' |$ | d <n | r�t+ | | | � d }( | j$ |( � | | |( |$ � � | d <n t, j- |% |& d |
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| �}* | 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.
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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`.
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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
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If the new position has already been filled, raise `InvalidIndexError`.
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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`.
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| 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.
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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.
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