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1200 lines
45 KiB
1200 lines
45 KiB
"""
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Support for plotting vector fields.
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Presently this contains Quiver and Barb. Quiver plots an arrow in the
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direction of the vector, with the size of the arrow related to the
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magnitude of the vector.
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Barbs are like quiver in that they point along a vector, but
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the magnitude of the vector is given schematically by the presence of barbs
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or flags on the barb.
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This will also become a home for things such as standard
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deviation ellipses, which can and will be derived very easily from
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the Quiver code.
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"""
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import math
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import weakref
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import numpy as np
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from numpy import ma
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import matplotlib.collections as mcollections
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import matplotlib.transforms as transforms
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import matplotlib.text as mtext
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import matplotlib.artist as martist
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from matplotlib.artist import allow_rasterization
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from matplotlib import docstring
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import matplotlib.font_manager as font_manager
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from matplotlib.cbook import delete_masked_points
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from matplotlib.patches import CirclePolygon
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_quiver_doc = """
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Plot a 2-D field of arrows.
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Call signatures::
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quiver(U, V, **kw)
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quiver(U, V, C, **kw)
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quiver(X, Y, U, V, **kw)
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quiver(X, Y, U, V, C, **kw)
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*U* and *V* are the arrow data, *X* and *Y* set the location of the
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arrows, and *C* sets the color of the arrows. These arguments may be 1-D or
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2-D arrays or sequences.
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If *X* and *Y* are absent, they will be generated as a uniform grid.
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If *U* and *V* are 2-D arrays and *X* and *Y* are 1-D, and if ``len(X)`` and
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``len(Y)`` match the column and row dimensions of *U*, then *X* and *Y* will be
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expanded with :func:`numpy.meshgrid`.
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The default settings auto-scales the length of the arrows to a reasonable size.
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To change this behavior see the *scale* and *scale_units* kwargs.
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The defaults give a slightly swept-back arrow; to make the head a
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triangle, make *headaxislength* the same as *headlength*. To make the
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arrow more pointed, reduce *headwidth* or increase *headlength* and
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*headaxislength*. To make the head smaller relative to the shaft,
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scale down all the head parameters. You will probably do best to leave
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minshaft alone.
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*linewidths* and *edgecolors* can be used to customize the arrow
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outlines.
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Parameters
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----------
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X : 1D or 2D array, sequence, optional
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The x coordinates of the arrow locations
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Y : 1D or 2D array, sequence, optional
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The y coordinates of the arrow locations
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U : 1D or 2D array or masked array, sequence
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The x components of the arrow vectors
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V : 1D or 2D array or masked array, sequence
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The y components of the arrow vectors
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C : 1D or 2D array, sequence, optional
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The arrow colors
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units : [ 'width' | 'height' | 'dots' | 'inches' | 'x' | 'y' | 'xy' ]
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The arrow dimensions (except for *length*) are measured in multiples of
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this unit.
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'width' or 'height': the width or height of the axis
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'dots' or 'inches': pixels or inches, based on the figure dpi
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'x', 'y', or 'xy': respectively *X*, *Y*, or :math:`\\sqrt{X^2 + Y^2}`
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in data units
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The arrows scale differently depending on the units. For
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'x' or 'y', the arrows get larger as one zooms in; for other
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units, the arrow size is independent of the zoom state. For
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'width or 'height', the arrow size increases with the width and
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height of the axes, respectively, when the window is resized;
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for 'dots' or 'inches', resizing does not change the arrows.
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angles : [ 'uv' | 'xy' ], array, optional
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Method for determining the angle of the arrows. Default is 'uv'.
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'uv': the arrow axis aspect ratio is 1 so that
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if *U*==*V* the orientation of the arrow on the plot is 45 degrees
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counter-clockwise from the horizontal axis (positive to the right).
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'xy': arrows point from (x,y) to (x+u, y+v).
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Use this for plotting a gradient field, for example.
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Alternatively, arbitrary angles may be specified as an array
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of values in degrees, counter-clockwise from the horizontal axis.
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Note: inverting a data axis will correspondingly invert the
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arrows only with ``angles='xy'``.
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scale : None, float, optional
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Number of data units per arrow length unit, e.g., m/s per plot width; a
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smaller scale parameter makes the arrow longer. Default is *None*.
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If *None*, a simple autoscaling algorithm is used, based on the average
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vector length and the number of vectors. The arrow length unit is given by
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the *scale_units* parameter
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scale_units : [ 'width' | 'height' | 'dots' | 'inches' | 'x' | 'y' | 'xy' ], \
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None, optional
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If the *scale* kwarg is *None*, the arrow length unit. Default is *None*.
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e.g. *scale_units* is 'inches', *scale* is 2.0, and
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``(u,v) = (1,0)``, then the vector will be 0.5 inches long.
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If *scale_units* is 'width'/'height', then the vector will be half the
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width/height of the axes.
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If *scale_units* is 'x' then the vector will be 0.5 x-axis
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units. To plot vectors in the x-y plane, with u and v having
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the same units as x and y, use
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``angles='xy', scale_units='xy', scale=1``.
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width : scalar, optional
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Shaft width in arrow units; default depends on choice of units,
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above, and number of vectors; a typical starting value is about
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0.005 times the width of the plot.
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headwidth : scalar, optional
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Head width as multiple of shaft width, default is 3
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headlength : scalar, optional
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Head length as multiple of shaft width, default is 5
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headaxislength : scalar, optional
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Head length at shaft intersection, default is 4.5
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minshaft : scalar, optional
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Length below which arrow scales, in units of head length. Do not
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set this to less than 1, or small arrows will look terrible!
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Default is 1
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minlength : scalar, optional
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Minimum length as a multiple of shaft width; if an arrow length
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is less than this, plot a dot (hexagon) of this diameter instead.
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Default is 1.
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pivot : [ 'tail' | 'mid' | 'middle' | 'tip' ], optional
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The part of the arrow that is at the grid point; the arrow rotates
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about this point, hence the name *pivot*.
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color : [ color | color sequence ], optional
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This is a synonym for the
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:class:`~matplotlib.collections.PolyCollection` facecolor kwarg.
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If *C* has been set, *color* has no effect.
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Notes
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-----
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Additional :class:`~matplotlib.collections.PolyCollection`
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keyword arguments:
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%(PolyCollection)s
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See Also
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--------
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quiverkey : Add a key to a quiver plot
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""" % docstring.interpd.params
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_quiverkey_doc = """
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Add a key to a quiver plot.
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Call signature::
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quiverkey(Q, X, Y, U, label, **kw)
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Arguments:
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*Q*:
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The Quiver instance returned by a call to quiver.
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*X*, *Y*:
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The location of the key; additional explanation follows.
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*U*:
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The length of the key
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*label*:
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A string with the length and units of the key
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Keyword arguments:
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*angle* = 0
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The angle of the key arrow. Measured in degrees anti-clockwise from the
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x-axis.
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*coordinates* = [ 'axes' | 'figure' | 'data' | 'inches' ]
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Coordinate system and units for *X*, *Y*: 'axes' and 'figure' are
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normalized coordinate systems with 0,0 in the lower left and 1,1
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in the upper right; 'data' are the axes data coordinates (used for
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the locations of the vectors in the quiver plot itself); 'inches'
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is position in the figure in inches, with 0,0 at the lower left
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corner.
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*color*:
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overrides face and edge colors from *Q*.
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*labelpos* = [ 'N' | 'S' | 'E' | 'W' ]
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Position the label above, below, to the right, to the left of the
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arrow, respectively.
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*labelsep*:
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Distance in inches between the arrow and the label. Default is
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0.1
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*labelcolor*:
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defaults to default :class:`~matplotlib.text.Text` color.
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*fontproperties*:
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A dictionary with keyword arguments accepted by the
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:class:`~matplotlib.font_manager.FontProperties` initializer:
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*family*, *style*, *variant*, *size*, *weight*
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Any additional keyword arguments are used to override vector
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properties taken from *Q*.
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The positioning of the key depends on *X*, *Y*, *coordinates*, and
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*labelpos*. If *labelpos* is 'N' or 'S', *X*, *Y* give the position
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of the middle of the key arrow. If *labelpos* is 'E', *X*, *Y*
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positions the head, and if *labelpos* is 'W', *X*, *Y* positions the
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tail; in either of these two cases, *X*, *Y* is somewhere in the
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middle of the arrow+label key object.
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"""
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class QuiverKey(martist.Artist):
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""" Labelled arrow for use as a quiver plot scale key."""
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halign = {'N': 'center', 'S': 'center', 'E': 'left', 'W': 'right'}
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valign = {'N': 'bottom', 'S': 'top', 'E': 'center', 'W': 'center'}
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pivot = {'N': 'middle', 'S': 'middle', 'E': 'tip', 'W': 'tail'}
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def __init__(self, Q, X, Y, U, label,
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*, angle=0, coordinates='axes', color=None, labelsep=0.1,
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labelpos='N', labelcolor=None, fontproperties=None,
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**kw):
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martist.Artist.__init__(self)
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self.Q = Q
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self.X = X
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self.Y = Y
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self.U = U
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self.angle = angle
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self.coord = coordinates
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self.color = color
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self.label = label
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self._labelsep_inches = labelsep
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self.labelsep = (self._labelsep_inches * Q.ax.figure.dpi)
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# try to prevent closure over the real self
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weak_self = weakref.ref(self)
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def on_dpi_change(fig):
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self_weakref = weak_self()
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if self_weakref is not None:
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self_weakref.labelsep = (self_weakref._labelsep_inches*fig.dpi)
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self_weakref._initialized = False # simple brute force update
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# works because _init is
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# called at the start of
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# draw.
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self._cid = Q.ax.figure.callbacks.connect('dpi_changed',
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on_dpi_change)
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self.labelpos = labelpos
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self.labelcolor = labelcolor
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self.fontproperties = fontproperties or dict()
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self.kw = kw
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_fp = self.fontproperties
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# boxprops = dict(facecolor='red')
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self.text = mtext.Text(
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text=label, # bbox=boxprops,
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horizontalalignment=self.halign[self.labelpos],
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verticalalignment=self.valign[self.labelpos],
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fontproperties=font_manager.FontProperties(**_fp))
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if self.labelcolor is not None:
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self.text.set_color(self.labelcolor)
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self._initialized = False
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self.zorder = Q.zorder + 0.1
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def remove(self):
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"""
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Overload the remove method
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"""
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self.Q.ax.figure.callbacks.disconnect(self._cid)
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self._cid = None
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# pass the remove call up the stack
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martist.Artist.remove(self)
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__init__.__doc__ = _quiverkey_doc
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def _init(self):
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if True: # not self._initialized:
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if not self.Q._initialized:
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self.Q._init()
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self._set_transform()
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_pivot = self.Q.pivot
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self.Q.pivot = self.pivot[self.labelpos]
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# Hack: save and restore the Umask
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_mask = self.Q.Umask
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self.Q.Umask = ma.nomask
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self.verts = self.Q._make_verts(np.array([self.U]),
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np.zeros((1,)),
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self.angle)
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self.Q.Umask = _mask
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self.Q.pivot = _pivot
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kw = self.Q.polykw
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kw.update(self.kw)
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self.vector = mcollections.PolyCollection(
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self.verts,
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offsets=[(self.X, self.Y)],
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transOffset=self.get_transform(),
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**kw)
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if self.color is not None:
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self.vector.set_color(self.color)
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self.vector.set_transform(self.Q.get_transform())
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self.vector.set_figure(self.get_figure())
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self._initialized = True
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def _text_x(self, x):
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if self.labelpos == 'E':
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return x + self.labelsep
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elif self.labelpos == 'W':
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return x - self.labelsep
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else:
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return x
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def _text_y(self, y):
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if self.labelpos == 'N':
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return y + self.labelsep
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elif self.labelpos == 'S':
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return y - self.labelsep
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else:
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return y
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@allow_rasterization
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def draw(self, renderer):
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self._init()
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self.vector.draw(renderer)
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x, y = self.get_transform().transform_point((self.X, self.Y))
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self.text.set_x(self._text_x(x))
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self.text.set_y(self._text_y(y))
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self.text.draw(renderer)
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self.stale = False
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def _set_transform(self):
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if self.coord == 'data':
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self.set_transform(self.Q.ax.transData)
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elif self.coord == 'axes':
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self.set_transform(self.Q.ax.transAxes)
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elif self.coord == 'figure':
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self.set_transform(self.Q.ax.figure.transFigure)
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elif self.coord == 'inches':
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self.set_transform(self.Q.ax.figure.dpi_scale_trans)
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else:
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raise ValueError('unrecognized coordinates')
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def set_figure(self, fig):
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martist.Artist.set_figure(self, fig)
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self.text.set_figure(fig)
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def contains(self, mouseevent):
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# Maybe the dictionary should allow one to
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# distinguish between a text hit and a vector hit.
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if (self.text.contains(mouseevent)[0] or
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self.vector.contains(mouseevent)[0]):
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return True, {}
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return False, {}
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quiverkey_doc = _quiverkey_doc
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# This is a helper function that parses out the various combination of
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# arguments for doing colored vector plots. Pulling it out here
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# allows both Quiver and Barbs to use it
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def _parse_args(*args):
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X, Y, U, V, C = [None] * 5
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args = list(args)
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# The use of atleast_1d allows for handling scalar arguments while also
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# keeping masked arrays
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if len(args) == 3 or len(args) == 5:
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C = np.atleast_1d(args.pop(-1))
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V = np.atleast_1d(args.pop(-1))
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U = np.atleast_1d(args.pop(-1))
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if U.ndim == 1:
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nr, nc = 1, U.shape[0]
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else:
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nr, nc = U.shape
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if len(args) == 2: # remaining after removing U,V,C
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X, Y = [np.array(a).ravel() for a in args]
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if len(X) == nc and len(Y) == nr:
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X, Y = [a.ravel() for a in np.meshgrid(X, Y)]
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else:
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indexgrid = np.meshgrid(np.arange(nc), np.arange(nr))
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X, Y = [np.ravel(a) for a in indexgrid]
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return X, Y, U, V, C
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def _check_consistent_shapes(*arrays):
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all_shapes = {a.shape for a in arrays}
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if len(all_shapes) != 1:
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raise ValueError('The shapes of the passed in arrays do not match')
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class Quiver(mcollections.PolyCollection):
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"""
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Specialized PolyCollection for arrows.
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The only API method is set_UVC(), which can be used
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to change the size, orientation, and color of the
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arrows; their locations are fixed when the class is
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instantiated. Possibly this method will be useful
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in animations.
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Much of the work in this class is done in the draw()
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method so that as much information as possible is available
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about the plot. In subsequent draw() calls, recalculation
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is limited to things that might have changed, so there
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should be no performance penalty from putting the calculations
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in the draw() method.
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"""
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_PIVOT_VALS = ('tail', 'middle', 'tip')
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@docstring.Substitution(_quiver_doc)
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def __init__(self, ax, *args,
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scale=None, headwidth=3, headlength=5, headaxislength=4.5,
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minshaft=1, minlength=1, units='width', scale_units=None,
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angles='uv', width=None, color='k', pivot='tail', **kw):
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"""
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The constructor takes one required argument, an Axes
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instance, followed by the args and kwargs described
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by the following pyplot interface documentation:
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%s
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"""
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self.ax = ax
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X, Y, U, V, C = _parse_args(*args)
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self.X = X
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self.Y = Y
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self.XY = np.column_stack((X, Y))
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self.N = len(X)
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self.scale = scale
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self.headwidth = headwidth
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self.headlength = float(headlength)
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self.headaxislength = headaxislength
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self.minshaft = minshaft
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self.minlength = minlength
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self.units = units
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self.scale_units = scale_units
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self.angles = angles
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self.width = width
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self.color = color
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if pivot.lower() == 'mid':
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pivot = 'middle'
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self.pivot = pivot.lower()
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if self.pivot not in self._PIVOT_VALS:
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raise ValueError(
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'pivot must be one of {keys}, you passed {inp}'.format(
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keys=self._PIVOT_VALS, inp=pivot))
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self.transform = kw.pop('transform', ax.transData)
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kw.setdefault('facecolors', self.color)
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kw.setdefault('linewidths', (0,))
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mcollections.PolyCollection.__init__(self, [], offsets=self.XY,
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transOffset=self.transform,
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closed=False,
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**kw)
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self.polykw = kw
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self.set_UVC(U, V, C)
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self._initialized = False
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self.keyvec = None
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self.keytext = None
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# try to prevent closure over the real self
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weak_self = weakref.ref(self)
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def on_dpi_change(fig):
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self_weakref = weak_self()
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if self_weakref is not None:
|
|
self_weakref._new_UV = True # vertices depend on width, span
|
|
# which in turn depend on dpi
|
|
self_weakref._initialized = False # simple brute force update
|
|
# works because _init is
|
|
# called at the start of
|
|
# draw.
|
|
|
|
self._cid = self.ax.figure.callbacks.connect('dpi_changed',
|
|
on_dpi_change)
|
|
|
|
def remove(self):
|
|
"""
|
|
Overload the remove method
|
|
"""
|
|
# disconnect the call back
|
|
self.ax.figure.callbacks.disconnect(self._cid)
|
|
self._cid = None
|
|
# pass the remove call up the stack
|
|
mcollections.PolyCollection.remove(self)
|
|
|
|
def _init(self):
|
|
"""
|
|
Initialization delayed until first draw;
|
|
allow time for axes setup.
|
|
"""
|
|
# It seems that there are not enough event notifications
|
|
# available to have this work on an as-needed basis at present.
|
|
if True: # not self._initialized:
|
|
trans = self._set_transform()
|
|
ax = self.ax
|
|
sx, sy = trans.inverted().transform_point(
|
|
(ax.bbox.width, ax.bbox.height))
|
|
self.span = sx
|
|
if self.width is None:
|
|
sn = np.clip(math.sqrt(self.N), 8, 25)
|
|
self.width = 0.06 * self.span / sn
|
|
|
|
# _make_verts sets self.scale if not already specified
|
|
if not self._initialized and self.scale is None:
|
|
self._make_verts(self.U, self.V, self.angles)
|
|
|
|
self._initialized = True
|
|
|
|
def get_datalim(self, transData):
|
|
trans = self.get_transform()
|
|
transOffset = self.get_offset_transform()
|
|
full_transform = (trans - transData) + (transOffset - transData)
|
|
XY = full_transform.transform(self.XY)
|
|
bbox = transforms.Bbox.null()
|
|
bbox.update_from_data_xy(XY, ignore=True)
|
|
return bbox
|
|
|
|
@allow_rasterization
|
|
def draw(self, renderer):
|
|
self._init()
|
|
verts = self._make_verts(self.U, self.V, self.angles)
|
|
self.set_verts(verts, closed=False)
|
|
self._new_UV = False
|
|
mcollections.PolyCollection.draw(self, renderer)
|
|
self.stale = False
|
|
|
|
def set_UVC(self, U, V, C=None):
|
|
# We need to ensure we have a copy, not a reference
|
|
# to an array that might change before draw().
|
|
U = ma.masked_invalid(U, copy=True).ravel()
|
|
V = ma.masked_invalid(V, copy=True).ravel()
|
|
mask = ma.mask_or(U.mask, V.mask, copy=False, shrink=True)
|
|
if C is not None:
|
|
C = ma.masked_invalid(C, copy=True).ravel()
|
|
mask = ma.mask_or(mask, C.mask, copy=False, shrink=True)
|
|
if mask is ma.nomask:
|
|
C = C.filled()
|
|
else:
|
|
C = ma.array(C, mask=mask, copy=False)
|
|
self.U = U.filled(1)
|
|
self.V = V.filled(1)
|
|
self.Umask = mask
|
|
if C is not None:
|
|
self.set_array(C)
|
|
self._new_UV = True
|
|
self.stale = True
|
|
|
|
def _dots_per_unit(self, units):
|
|
"""
|
|
Return a scale factor for converting from units to pixels
|
|
"""
|
|
ax = self.ax
|
|
if units in ('x', 'y', 'xy'):
|
|
if units == 'x':
|
|
dx0 = ax.viewLim.width
|
|
dx1 = ax.bbox.width
|
|
elif units == 'y':
|
|
dx0 = ax.viewLim.height
|
|
dx1 = ax.bbox.height
|
|
else: # 'xy' is assumed
|
|
dxx0 = ax.viewLim.width
|
|
dxx1 = ax.bbox.width
|
|
dyy0 = ax.viewLim.height
|
|
dyy1 = ax.bbox.height
|
|
dx1 = np.hypot(dxx1, dyy1)
|
|
dx0 = np.hypot(dxx0, dyy0)
|
|
dx = dx1 / dx0
|
|
else:
|
|
if units == 'width':
|
|
dx = ax.bbox.width
|
|
elif units == 'height':
|
|
dx = ax.bbox.height
|
|
elif units == 'dots':
|
|
dx = 1.0
|
|
elif units == 'inches':
|
|
dx = ax.figure.dpi
|
|
else:
|
|
raise ValueError('unrecognized units')
|
|
return dx
|
|
|
|
def _set_transform(self):
|
|
"""
|
|
Sets the PolygonCollection transform to go
|
|
from arrow width units to pixels.
|
|
"""
|
|
dx = self._dots_per_unit(self.units)
|
|
self._trans_scale = dx # pixels per arrow width unit
|
|
trans = transforms.Affine2D().scale(dx)
|
|
self.set_transform(trans)
|
|
return trans
|
|
|
|
def _angles_lengths(self, U, V, eps=1):
|
|
xy = self.ax.transData.transform(self.XY)
|
|
uv = np.column_stack((U, V))
|
|
xyp = self.ax.transData.transform(self.XY + eps * uv)
|
|
dxy = xyp - xy
|
|
angles = np.arctan2(dxy[:, 1], dxy[:, 0])
|
|
lengths = np.hypot(*dxy.T) / eps
|
|
return angles, lengths
|
|
|
|
def _make_verts(self, U, V, angles):
|
|
uv = (U + V * 1j)
|
|
str_angles = angles if isinstance(angles, str) else ''
|
|
if str_angles == 'xy' and self.scale_units == 'xy':
|
|
# Here eps is 1 so that if we get U, V by diffing
|
|
# the X, Y arrays, the vectors will connect the
|
|
# points, regardless of the axis scaling (including log).
|
|
angles, lengths = self._angles_lengths(U, V, eps=1)
|
|
elif str_angles == 'xy' or self.scale_units == 'xy':
|
|
# Calculate eps based on the extents of the plot
|
|
# so that we don't end up with roundoff error from
|
|
# adding a small number to a large.
|
|
eps = np.abs(self.ax.dataLim.extents).max() * 0.001
|
|
angles, lengths = self._angles_lengths(U, V, eps=eps)
|
|
if str_angles and self.scale_units == 'xy':
|
|
a = lengths
|
|
else:
|
|
a = np.abs(uv)
|
|
if self.scale is None:
|
|
sn = max(10, math.sqrt(self.N))
|
|
if self.Umask is not ma.nomask:
|
|
amean = a[~self.Umask].mean()
|
|
else:
|
|
amean = a.mean()
|
|
# crude auto-scaling
|
|
# scale is typical arrow length as a multiple of the arrow width
|
|
scale = 1.8 * amean * sn / self.span
|
|
if self.scale_units is None:
|
|
if self.scale is None:
|
|
self.scale = scale
|
|
widthu_per_lenu = 1.0
|
|
else:
|
|
if self.scale_units == 'xy':
|
|
dx = 1
|
|
else:
|
|
dx = self._dots_per_unit(self.scale_units)
|
|
widthu_per_lenu = dx / self._trans_scale
|
|
if self.scale is None:
|
|
self.scale = scale * widthu_per_lenu
|
|
length = a * (widthu_per_lenu / (self.scale * self.width))
|
|
X, Y = self._h_arrows(length)
|
|
if str_angles == 'xy':
|
|
theta = angles
|
|
elif str_angles == 'uv':
|
|
theta = np.angle(uv)
|
|
else:
|
|
theta = ma.masked_invalid(np.deg2rad(angles)).filled(0)
|
|
theta = theta.reshape((-1, 1)) # for broadcasting
|
|
xy = (X + Y * 1j) * np.exp(1j * theta) * self.width
|
|
XY = np.stack((xy.real, xy.imag), axis=2)
|
|
if self.Umask is not ma.nomask:
|
|
XY = ma.array(XY)
|
|
XY[self.Umask] = ma.masked
|
|
# This might be handled more efficiently with nans, given
|
|
# that nans will end up in the paths anyway.
|
|
|
|
return XY
|
|
|
|
def _h_arrows(self, length):
|
|
""" length is in arrow width units """
|
|
# It might be possible to streamline the code
|
|
# and speed it up a bit by using complex (x,y)
|
|
# instead of separate arrays; but any gain would be slight.
|
|
minsh = self.minshaft * self.headlength
|
|
N = len(length)
|
|
length = length.reshape(N, 1)
|
|
# This number is chosen based on when pixel values overflow in Agg
|
|
# causing rendering errors
|
|
# length = np.minimum(length, 2 ** 16)
|
|
np.clip(length, 0, 2 ** 16, out=length)
|
|
# x, y: normal horizontal arrow
|
|
x = np.array([0, -self.headaxislength,
|
|
-self.headlength, 0],
|
|
np.float64)
|
|
x = x + np.array([0, 1, 1, 1]) * length
|
|
y = 0.5 * np.array([1, 1, self.headwidth, 0], np.float64)
|
|
y = np.repeat(y[np.newaxis, :], N, axis=0)
|
|
# x0, y0: arrow without shaft, for short vectors
|
|
x0 = np.array([0, minsh - self.headaxislength,
|
|
minsh - self.headlength, minsh], np.float64)
|
|
y0 = 0.5 * np.array([1, 1, self.headwidth, 0], np.float64)
|
|
ii = [0, 1, 2, 3, 2, 1, 0, 0]
|
|
X = x.take(ii, 1)
|
|
Y = y.take(ii, 1)
|
|
Y[:, 3:-1] *= -1
|
|
X0 = x0.take(ii)
|
|
Y0 = y0.take(ii)
|
|
Y0[3:-1] *= -1
|
|
shrink = length / minsh if minsh != 0. else 0.
|
|
X0 = shrink * X0[np.newaxis, :]
|
|
Y0 = shrink * Y0[np.newaxis, :]
|
|
short = np.repeat(length < minsh, 8, axis=1)
|
|
# Now select X0, Y0 if short, otherwise X, Y
|
|
np.copyto(X, X0, where=short)
|
|
np.copyto(Y, Y0, where=short)
|
|
if self.pivot == 'middle':
|
|
X -= 0.5 * X[:, 3, np.newaxis]
|
|
elif self.pivot == 'tip':
|
|
X = X - X[:, 3, np.newaxis] # numpy bug? using -= does not
|
|
# work here unless we multiply
|
|
# by a float first, as with 'mid'.
|
|
elif self.pivot != 'tail':
|
|
raise ValueError(("Quiver.pivot must have value in {{'middle', "
|
|
"'tip', 'tail'}} not {0}").format(self.pivot))
|
|
|
|
tooshort = length < self.minlength
|
|
if tooshort.any():
|
|
# Use a heptagonal dot:
|
|
th = np.arange(0, 8, 1, np.float64) * (np.pi / 3.0)
|
|
x1 = np.cos(th) * self.minlength * 0.5
|
|
y1 = np.sin(th) * self.minlength * 0.5
|
|
X1 = np.repeat(x1[np.newaxis, :], N, axis=0)
|
|
Y1 = np.repeat(y1[np.newaxis, :], N, axis=0)
|
|
tooshort = np.repeat(tooshort, 8, 1)
|
|
np.copyto(X, X1, where=tooshort)
|
|
np.copyto(Y, Y1, where=tooshort)
|
|
# Mask handling is deferred to the caller, _make_verts.
|
|
return X, Y
|
|
|
|
quiver_doc = _quiver_doc
|
|
|
|
|
|
_barbs_doc = r"""
|
|
Plot a 2-D field of barbs.
|
|
|
|
Call signatures::
|
|
|
|
barb(U, V, **kw)
|
|
barb(U, V, C, **kw)
|
|
barb(X, Y, U, V, **kw)
|
|
barb(X, Y, U, V, C, **kw)
|
|
|
|
Arguments:
|
|
|
|
*X*, *Y*:
|
|
The x and y coordinates of the barb locations
|
|
(default is head of barb; see *pivot* kwarg)
|
|
|
|
*U*, *V*:
|
|
Give the x and y components of the barb shaft
|
|
|
|
*C*:
|
|
An optional array used to map colors to the barbs
|
|
|
|
All arguments may be 1-D or 2-D arrays or sequences. If *X* and *Y*
|
|
are absent, they will be generated as a uniform grid. If *U* and *V*
|
|
are 2-D arrays but *X* and *Y* are 1-D, and if ``len(X)`` and ``len(Y)``
|
|
match the column and row dimensions of *U*, then *X* and *Y* will be
|
|
expanded with :func:`numpy.meshgrid`.
|
|
|
|
*U*, *V*, *C* may be masked arrays, but masked *X*, *Y* are not
|
|
supported at present.
|
|
|
|
Keyword arguments:
|
|
|
|
*length*:
|
|
Length of the barb in points; the other parts of the barb
|
|
are scaled against this.
|
|
Default is 7.
|
|
|
|
*pivot*: [ 'tip' | 'middle' | float ]
|
|
The part of the arrow that is at the grid point; the arrow rotates
|
|
about this point, hence the name *pivot*. Default is 'tip'. Can
|
|
also be a number, which shifts the start of the barb that many
|
|
points from the origin.
|
|
|
|
*barbcolor*: [ color | color sequence ]
|
|
Specifies the color all parts of the barb except any flags. This
|
|
parameter is analogous to the *edgecolor* parameter for polygons,
|
|
which can be used instead. However this parameter will override
|
|
facecolor.
|
|
|
|
*flagcolor*: [ color | color sequence ]
|
|
Specifies the color of any flags on the barb. This parameter is
|
|
analogous to the *facecolor* parameter for polygons, which can be
|
|
used instead. However this parameter will override facecolor. If
|
|
this is not set (and *C* has not either) then *flagcolor* will be
|
|
set to match *barbcolor* so that the barb has a uniform color. If
|
|
*C* has been set, *flagcolor* has no effect.
|
|
|
|
*sizes*:
|
|
A dictionary of coefficients specifying the ratio of a given
|
|
feature to the length of the barb. Only those values one wishes to
|
|
override need to be included. These features include:
|
|
|
|
- 'spacing' - space between features (flags, full/half barbs)
|
|
|
|
- 'height' - height (distance from shaft to top) of a flag or
|
|
full barb
|
|
|
|
- 'width' - width of a flag, twice the width of a full barb
|
|
|
|
- 'emptybarb' - radius of the circle used for low magnitudes
|
|
|
|
*fill_empty*:
|
|
A flag on whether the empty barbs (circles) that are drawn should
|
|
be filled with the flag color. If they are not filled, they will
|
|
be drawn such that no color is applied to the center. Default is
|
|
False
|
|
|
|
*rounding*:
|
|
A flag to indicate whether the vector magnitude should be rounded
|
|
when allocating barb components. If True, the magnitude is
|
|
rounded to the nearest multiple of the half-barb increment. If
|
|
False, the magnitude is simply truncated to the next lowest
|
|
multiple. Default is True
|
|
|
|
*barb_increments*:
|
|
A dictionary of increments specifying values to associate with
|
|
different parts of the barb. Only those values one wishes to
|
|
override need to be included.
|
|
|
|
- 'half' - half barbs (Default is 5)
|
|
|
|
- 'full' - full barbs (Default is 10)
|
|
|
|
- 'flag' - flags (default is 50)
|
|
|
|
*flip_barb*:
|
|
Either a single boolean flag or an array of booleans. Single
|
|
boolean indicates whether the lines and flags should point
|
|
opposite to normal for all barbs. An array (which should be the
|
|
same size as the other data arrays) indicates whether to flip for
|
|
each individual barb. Normal behavior is for the barbs and lines
|
|
to point right (comes from wind barbs having these features point
|
|
towards low pressure in the Northern Hemisphere.) Default is
|
|
False
|
|
|
|
Barbs are traditionally used in meteorology as a way to plot the speed
|
|
and direction of wind observations, but can technically be used to
|
|
plot any two dimensional vector quantity. As opposed to arrows, which
|
|
give vector magnitude by the length of the arrow, the barbs give more
|
|
quantitative information about the vector magnitude by putting slanted
|
|
lines or a triangle for various increments in magnitude, as show
|
|
schematically below::
|
|
|
|
: /\ \\
|
|
: / \ \\
|
|
: / \ \ \\
|
|
: / \ \ \\
|
|
: ------------------------------
|
|
|
|
.. note the double \\ at the end of each line to make the figure
|
|
.. render correctly
|
|
|
|
The largest increment is given by a triangle (or "flag"). After those
|
|
come full lines (barbs). The smallest increment is a half line. There
|
|
is only, of course, ever at most 1 half line. If the magnitude is
|
|
small and only needs a single half-line and no full lines or
|
|
triangles, the half-line is offset from the end of the barb so that it
|
|
can be easily distinguished from barbs with a single full line. The
|
|
magnitude for the barb shown above would nominally be 65, using the
|
|
standard increments of 50, 10, and 5.
|
|
|
|
linewidths and edgecolors can be used to customize the barb.
|
|
Additional :class:`~matplotlib.collections.PolyCollection` keyword
|
|
arguments:
|
|
|
|
%(PolyCollection)s
|
|
""" % docstring.interpd.params
|
|
|
|
docstring.interpd.update(barbs_doc=_barbs_doc)
|
|
|
|
|
|
class Barbs(mcollections.PolyCollection):
|
|
'''
|
|
Specialized PolyCollection for barbs.
|
|
|
|
The only API method is :meth:`set_UVC`, which can be used to
|
|
change the size, orientation, and color of the arrows. Locations
|
|
are changed using the :meth:`set_offsets` collection method.
|
|
Possibly this method will be useful in animations.
|
|
|
|
There is one internal function :meth:`_find_tails` which finds
|
|
exactly what should be put on the barb given the vector magnitude.
|
|
From there :meth:`_make_barbs` is used to find the vertices of the
|
|
polygon to represent the barb based on this information.
|
|
'''
|
|
# This may be an abuse of polygons here to render what is essentially maybe
|
|
# 1 triangle and a series of lines. It works fine as far as I can tell
|
|
# however.
|
|
@docstring.interpd
|
|
def __init__(self, ax, *args,
|
|
pivot='tip', length=7, barbcolor=None, flagcolor=None,
|
|
sizes=None, fill_empty=False, barb_increments=None,
|
|
rounding=True, flip_barb=False, **kw):
|
|
"""
|
|
The constructor takes one required argument, an Axes
|
|
instance, followed by the args and kwargs described
|
|
by the following pyplot interface documentation:
|
|
%(barbs_doc)s
|
|
"""
|
|
self.sizes = sizes or dict()
|
|
self.fill_empty = fill_empty
|
|
self.barb_increments = barb_increments or dict()
|
|
self.rounding = rounding
|
|
self.flip = flip_barb
|
|
transform = kw.pop('transform', ax.transData)
|
|
self._pivot = pivot
|
|
self._length = length
|
|
barbcolor = barbcolor
|
|
flagcolor = flagcolor
|
|
|
|
# Flagcolor and barbcolor provide convenience parameters for
|
|
# setting the facecolor and edgecolor, respectively, of the barb
|
|
# polygon. We also work here to make the flag the same color as the
|
|
# rest of the barb by default
|
|
|
|
if None in (barbcolor, flagcolor):
|
|
kw['edgecolors'] = 'face'
|
|
if flagcolor:
|
|
kw['facecolors'] = flagcolor
|
|
elif barbcolor:
|
|
kw['facecolors'] = barbcolor
|
|
else:
|
|
# Set to facecolor passed in or default to black
|
|
kw.setdefault('facecolors', 'k')
|
|
else:
|
|
kw['edgecolors'] = barbcolor
|
|
kw['facecolors'] = flagcolor
|
|
|
|
# Explicitly set a line width if we're not given one, otherwise
|
|
# polygons are not outlined and we get no barbs
|
|
if 'linewidth' not in kw and 'lw' not in kw:
|
|
kw['linewidth'] = 1
|
|
|
|
# Parse out the data arrays from the various configurations supported
|
|
x, y, u, v, c = _parse_args(*args)
|
|
self.x = x
|
|
self.y = y
|
|
xy = np.column_stack((x, y))
|
|
|
|
# Make a collection
|
|
barb_size = self._length ** 2 / 4 # Empirically determined
|
|
mcollections.PolyCollection.__init__(self, [], (barb_size,),
|
|
offsets=xy,
|
|
transOffset=transform, **kw)
|
|
self.set_transform(transforms.IdentityTransform())
|
|
|
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self.set_UVC(u, v, c)
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def _find_tails(self, mag, rounding=True, half=5, full=10, flag=50):
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'''
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Find how many of each of the tail pieces is necessary. Flag
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specifies the increment for a flag, barb for a full barb, and half for
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half a barb. Mag should be the magnitude of a vector (i.e., >= 0).
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|
|
|
This returns a tuple of:
|
|
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(*number of flags*, *number of barbs*, *half_flag*, *empty_flag*)
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|
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*half_flag* is a boolean whether half of a barb is needed,
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|
since there should only ever be one half on a given
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barb. *empty_flag* flag is an array of flags to easily tell if
|
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a barb is empty (too low to plot any barbs/flags.
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|
'''
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|
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# If rounding, round to the nearest multiple of half, the smallest
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# increment
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if rounding:
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mag = half * (mag / half + 0.5).astype(int)
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|
|
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num_flags = np.floor(mag / flag).astype(int)
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mag = np.mod(mag, flag)
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num_barb = np.floor(mag / full).astype(int)
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mag = np.mod(mag, full)
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half_flag = mag >= half
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empty_flag = ~(half_flag | (num_flags > 0) | (num_barb > 0))
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return num_flags, num_barb, half_flag, empty_flag
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def _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,
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pivot, sizes, fill_empty, flip):
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'''
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|
This function actually creates the wind barbs. *u* and *v*
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are components of the vector in the *x* and *y* directions,
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|
respectively.
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|
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*nflags*, *nbarbs*, and *half_barb*, empty_flag* are,
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|
*respectively, the number of flags, number of barbs, flag for
|
|
*half a barb, and flag for empty barb, ostensibly obtained
|
|
*from :meth:`_find_tails`.
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|
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|
*length* is the length of the barb staff in points.
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|
|
|
*pivot* specifies the point on the barb around which the
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|
entire barb should be rotated. Right now, valid options are
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'tip' and 'middle'. Can also be a number, which shifts the start
|
|
of the barb that many points from the origin.
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|
|
|
*sizes* is a dictionary of coefficients specifying the ratio
|
|
of a given feature to the length of the barb. These features
|
|
include:
|
|
|
|
- *spacing*: space between features (flags, full/half
|
|
barbs)
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|
|
|
- *height*: distance from shaft of top of a flag or full
|
|
barb
|
|
|
|
- *width* - width of a flag, twice the width of a full barb
|
|
|
|
- *emptybarb* - radius of the circle used for low
|
|
magnitudes
|
|
|
|
*fill_empty* specifies whether the circle representing an
|
|
empty barb should be filled or not (this changes the drawing
|
|
of the polygon).
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|
|
|
*flip* is a flag indicating whether the features should be flipped to
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|
the other side of the barb (useful for winds in the southern
|
|
hemisphere).
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|
|
|
This function returns list of arrays of vertices, defining a polygon
|
|
for each of the wind barbs. These polygons have been rotated to
|
|
properly align with the vector direction.
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|
'''
|
|
|
|
# These control the spacing and size of barb elements relative to the
|
|
# length of the shaft
|
|
spacing = length * sizes.get('spacing', 0.125)
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|
full_height = length * sizes.get('height', 0.4)
|
|
full_width = length * sizes.get('width', 0.25)
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|
empty_rad = length * sizes.get('emptybarb', 0.15)
|
|
|
|
# Controls y point where to pivot the barb.
|
|
pivot_points = dict(tip=0.0, middle=-length / 2.)
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|
|
|
# Check for flip
|
|
if flip:
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|
full_height = -full_height
|
|
|
|
endx = 0.0
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try:
|
|
endy = float(pivot)
|
|
except ValueError:
|
|
endy = pivot_points[pivot.lower()]
|
|
|
|
# Get the appropriate angle for the vector components. The offset is
|
|
# due to the way the barb is initially drawn, going down the y-axis.
|
|
# This makes sense in a meteorological mode of thinking since there 0
|
|
# degrees corresponds to north (the y-axis traditionally)
|
|
angles = -(ma.arctan2(v, u) + np.pi / 2)
|
|
|
|
# Used for low magnitude. We just get the vertices, so if we make it
|
|
# out here, it can be reused. The center set here should put the
|
|
# center of the circle at the location(offset), rather than at the
|
|
# same point as the barb pivot; this seems more sensible.
|
|
circ = CirclePolygon((0, 0), radius=empty_rad).get_verts()
|
|
if fill_empty:
|
|
empty_barb = circ
|
|
else:
|
|
# If we don't want the empty one filled, we make a degenerate
|
|
# polygon that wraps back over itself
|
|
empty_barb = np.concatenate((circ, circ[::-1]))
|
|
|
|
barb_list = []
|
|
for index, angle in np.ndenumerate(angles):
|
|
# If the vector magnitude is too weak to draw anything, plot an
|
|
# empty circle instead
|
|
if empty_flag[index]:
|
|
# We can skip the transform since the circle has no preferred
|
|
# orientation
|
|
barb_list.append(empty_barb)
|
|
continue
|
|
|
|
poly_verts = [(endx, endy)]
|
|
offset = length
|
|
|
|
# Add vertices for each flag
|
|
for i in range(nflags[index]):
|
|
# The spacing that works for the barbs is a little to much for
|
|
# the flags, but this only occurs when we have more than 1
|
|
# flag.
|
|
if offset != length:
|
|
offset += spacing / 2.
|
|
poly_verts.extend(
|
|
[[endx, endy + offset],
|
|
[endx + full_height, endy - full_width / 2 + offset],
|
|
[endx, endy - full_width + offset]])
|
|
|
|
offset -= full_width + spacing
|
|
|
|
# Add vertices for each barb. These really are lines, but works
|
|
# great adding 3 vertices that basically pull the polygon out and
|
|
# back down the line
|
|
for i in range(nbarbs[index]):
|
|
poly_verts.extend(
|
|
[(endx, endy + offset),
|
|
(endx + full_height, endy + offset + full_width / 2),
|
|
(endx, endy + offset)])
|
|
|
|
offset -= spacing
|
|
|
|
# Add the vertices for half a barb, if needed
|
|
if half_barb[index]:
|
|
# If the half barb is the first on the staff, traditionally it
|
|
# is offset from the end to make it easy to distinguish from a
|
|
# barb with a full one
|
|
if offset == length:
|
|
poly_verts.append((endx, endy + offset))
|
|
offset -= 1.5 * spacing
|
|
poly_verts.extend(
|
|
[(endx, endy + offset),
|
|
(endx + full_height / 2, endy + offset + full_width / 4),
|
|
(endx, endy + offset)])
|
|
|
|
# Rotate the barb according the angle. Making the barb first and
|
|
# then rotating it made the math for drawing the barb really easy.
|
|
# Also, the transform framework makes doing the rotation simple.
|
|
poly_verts = transforms.Affine2D().rotate(-angle).transform(
|
|
poly_verts)
|
|
barb_list.append(poly_verts)
|
|
|
|
return barb_list
|
|
|
|
def set_UVC(self, U, V, C=None):
|
|
self.u = ma.masked_invalid(U, copy=False).ravel()
|
|
self.v = ma.masked_invalid(V, copy=False).ravel()
|
|
if C is not None:
|
|
c = ma.masked_invalid(C, copy=False).ravel()
|
|
x, y, u, v, c = delete_masked_points(self.x.ravel(),
|
|
self.y.ravel(),
|
|
self.u, self.v, c)
|
|
_check_consistent_shapes(x, y, u, v, c)
|
|
else:
|
|
x, y, u, v = delete_masked_points(self.x.ravel(), self.y.ravel(),
|
|
self.u, self.v)
|
|
_check_consistent_shapes(x, y, u, v)
|
|
|
|
magnitude = np.hypot(u, v)
|
|
flags, barbs, halves, empty = self._find_tails(magnitude,
|
|
self.rounding,
|
|
**self.barb_increments)
|
|
|
|
# Get the vertices for each of the barbs
|
|
|
|
plot_barbs = self._make_barbs(u, v, flags, barbs, halves, empty,
|
|
self._length, self._pivot, self.sizes,
|
|
self.fill_empty, self.flip)
|
|
self.set_verts(plot_barbs)
|
|
|
|
# Set the color array
|
|
if C is not None:
|
|
self.set_array(c)
|
|
|
|
# Update the offsets in case the masked data changed
|
|
xy = np.column_stack((x, y))
|
|
self._offsets = xy
|
|
self.stale = True
|
|
|
|
def set_offsets(self, xy):
|
|
"""
|
|
Set the offsets for the barb polygons. This saves the offsets passed
|
|
in and actually sets version masked as appropriate for the existing
|
|
U/V data. *offsets* should be a sequence.
|
|
|
|
Parameters
|
|
----------
|
|
offsets : sequence of pairs of floats
|
|
"""
|
|
self.x = xy[:, 0]
|
|
self.y = xy[:, 1]
|
|
x, y, u, v = delete_masked_points(self.x.ravel(), self.y.ravel(),
|
|
self.u, self.v)
|
|
_check_consistent_shapes(x, y, u, v)
|
|
xy = np.column_stack((x, y))
|
|
mcollections.PolyCollection.set_offsets(self, xy)
|
|
self.stale = True
|
|
|
|
set_offsets.__doc__ = mcollections.PolyCollection.set_offsets.__doc__
|
|
|
|
barbs_doc = _barbs_doc
|