"""

Support for plotting vector fields.

Presently this contains Quiver and Barb. Quiver plots an arrow in the

direction of the vector, with the size of the arrow related to the

magnitude of the vector.

Barbs are like quiver in that they point along a vector, but

the magnitude of the vector is given schematically by the presence of barbs

or flags on the barb.

This will also become a home for things such as standard

deviation ellipses, which can and will be derived very easily from

the Quiver code.

"""

import math

import numpy as np

from numpy import ma

from matplotlib import _api, cbook, docstring, font_manager

import matplotlib.artist as martist

import matplotlib.collections as mcollections

from matplotlib.patches import CirclePolygon

import matplotlib.text as mtext

import matplotlib.transforms as transforms

_quiver_doc = """

Plot a 2D field of arrows.

Call signature::

quiver([X, Y], U, V, [C], **kw)

*X*, *Y* define the arrow locations, *U*, *V* define the arrow directions, and

*C* optionally sets the color.

Each arrow is internally represented by a filled polygon with a default edge

linewidth of 0. As a result, an arrow is rather a filled area, not a line with

a head, and `.PolyCollection` properties like *linewidth*, *linestyle*,

*facecolor*, etc. act accordingly.

**Arrow size**

The default settings auto-scales the length of the arrows to a reasonable size.

To change this behavior see the *scale* and *scale_units* parameters.

**Arrow shape**

The defaults give a slightly swept-back arrow; to make the head a

triangle, make *headaxislength* the same as *headlength*. To make the

arrow more pointed, reduce *headwidth* or increase *headlength* and

*headaxislength*. To make the head smaller relative to the shaft,

scale down all the head parameters. You will probably do best to leave

minshaft alone.

**Arrow outline**

*linewidths* and *edgecolors* can be used to customize the arrow

outlines.

Parameters

----------

X, Y : 1D or 2D array-like, optional

The x and y coordinates of the arrow locations.

If not given, they will be generated as a uniform integer meshgrid based

on the dimensions of *U* and *V*.

If *X* and *Y* are 1D but *U*, *V* are 2D, *X*, *Y* are expanded to 2D

using ``X, Y = np.meshgrid(X, Y)``. In this case ``len(X)`` and ``len(Y)``

must match the column and row dimensions of *U* and *V*.

U, V : 1D or 2D array-like

The x and y direction components of the arrow vectors.

They must have the same number of elements, matching the number of arrow

locations. *U* and *V* may be masked. Only locations unmasked in

*U*, *V*, and *C* will be drawn.

C : 1D or 2D array-like, optional

Numeric data that defines the arrow colors by colormapping via *norm* and

*cmap*.

This does not support explicit colors. If you want to set colors directly,

use *color* instead. The size of *C* must match the number of arrow

locations.

units : {'width', 'height', 'dots', 'inches', 'x', 'y', 'xy'}, default: 'width'

The arrow dimensions (except for *length*) are measured in multiples of

this unit.

The following values are supported:

- 'width', 'height': The width or height of the axis.

- 'dots', 'inches': Pixels or inches based on the figure dpi.

- 'x', 'y', 'xy': *X*, *Y* or :math:`\\sqrt{X^2 + Y^2}` in data units.

The arrows scale differently depending on the units. For

'x' or 'y', the arrows get larger as one zooms in; for other

units, the arrow size is independent of the zoom state. For

'width or 'height', the arrow size increases with the width and

height of the axes, respectively, when the window is resized;

for 'dots' or 'inches', resizing does not change the arrows.

angles : {'uv', 'xy'} or array-like, default: 'uv'

Method for determining the angle of the arrows.

- 'uv': The arrow axis aspect ratio is 1 so that

if *U* == *V* the orientation of the arrow on the plot is 45 degrees

counter-clockwise from the horizontal axis (positive to the right).

Use this if the arrows symbolize a quantity that is not based on

*X*, *Y* data coordinates.

- 'xy': Arrows point from (x, y) to (x+u, y+v).

Use this for plotting a gradient field, for example.

- Alternatively, arbitrary angles may be specified explicitly as an array

of values in degrees, counter-clockwise from the horizontal axis.

In this case *U*, *V* is only used to determine the length of the

arrows.

Note: inverting a data axis will correspondingly invert the

arrows only with ``angles='xy'``.

scale : float, optional

Number of data units per arrow length unit, e.g., m/s per plot width; a

smaller scale parameter makes the arrow longer. Default is *None*.

If *None*, a simple autoscaling algorithm is used, based on the average

vector length and the number of vectors. The arrow length unit is given by

the *scale_units* parameter.

scale_units : {'width', 'height', 'dots', 'inches', 'x', 'y', 'xy'}, optional

If the *scale* kwarg is *None*, the arrow length unit. Default is *None*.

e.g. *scale_units* is 'inches', *scale* is 2.0, and ``(u, v) = (1, 0)``,

then the vector will be 0.5 inches long.

If *scale_units* is 'width' or 'height', then the vector will be half the

width/height of the axes.

If *scale_units* is 'x' then the vector will be 0.5 x-axis

units. To plot vectors in the x-y plane, with u and v having

the same units as x and y, use

``angles='xy', scale_units='xy', scale=1``.

width : float, optional

Shaft width in arrow units; default depends on choice of units,

above, and number of vectors; a typical starting value is about

0.005 times the width of the plot.

headwidth : float, default: 3

Head width as multiple of shaft width.

headlength : float, default: 5

Head length as multiple of shaft width.

headaxislength : float, default: 4.5

Head length at shaft intersection.

minshaft : float, default: 1

Length below which arrow scales, in units of head length. Do not

set this to less than 1, or small arrows will look terrible!

minlength : float, default: 1

Minimum length as a multiple of shaft width; if an arrow length

is less than this, plot a dot (hexagon) of this diameter instead.

pivot : {'tail', 'mid', 'middle', 'tip'}, default: 'tail'

The part of the arrow that is anchored to the *X*, *Y* grid. The arrow

rotates about this point.

'mid' is a synonym for 'middle'.

color : color or color sequence, optional

Explicit color(s) for the arrows. If *C* has been set, *color* has no

effect.

This is a synonym for the `.PolyCollection` *facecolor* parameter.

Other Parameters

----------------

data : indexable object, optional

DATA_PARAMETER_PLACEHOLDER

**kwargs : `~matplotlib.collections.PolyCollection` properties, optional

All other keyword arguments are passed on to `.PolyCollection`:

%(PolyCollection:kwdoc)s

Returns

-------

`~matplotlib.quiver.Quiver`

See Also

--------

.Axes.quiverkey : Add a key to a quiver plot.

""" % docstring.interpd.params

docstring.interpd.update(quiver_doc=_quiver_doc)

class QuiverKey(martist.Artist):

"""Labelled arrow for use as a quiver plot scale key."""

halign = {'N': 'center', 'S': 'center', 'E': 'left', 'W': 'right'}

valign = {'N': 'bottom', 'S': 'top', 'E': 'center', 'W': 'center'}

pivot = {'N': 'middle', 'S': 'middle', 'E': 'tip', 'W': 'tail'}

def __init__(self, Q, X, Y, U, label,

*, angle=0, coordinates='axes', color=None, labelsep=0.1,

labelpos='N', labelcolor=None, fontproperties=None,

**kw):

"""

Add a key to a quiver plot.

The positioning of the key depends on *X*, *Y*, *coordinates*, and

*labelpos*. If *labelpos* is 'N' or 'S', *X*, *Y* give the position of

the middle of the key arrow. If *labelpos* is 'E', *X*, *Y* positions

the head, and if *labelpos* is 'W', *X*, *Y* positions the tail; in

either of these two cases, *X*, *Y* is somewhere in the middle of the

arrow+label key object.

Parameters

----------

Q : `matplotlib.quiver.Quiver`

A `.Quiver` object as returned by a call to `~.Axes.quiver()`.

X, Y : float

The location of the key.

U : float

The length of the key.

label : str

The key label (e.g., length and units of the key).

angle : float, default: 0

The angle of the key arrow, in degrees anti-clockwise from the

x-axis.

coordinates : {'axes', 'figure', 'data', 'inches'}, default: 'axes'

Coordinate system and units for *X*, *Y*: 'axes' and 'figure' are

normalized coordinate systems with (0, 0) in the lower left and

(1, 1) in the upper right; 'data' are the axes data coordinates

(used for the locations of the vectors in the quiver plot itself);

'inches' is position in the figure in inches, with (0, 0) at the

lower left corner.

color : color

Overrides face and edge colors from *Q*.

labelpos : {'N', 'S', 'E', 'W'}

Position the label above, below, to the right, to the left of the

arrow, respectively.

labelsep : float, default: 0.1

Distance in inches between the arrow and the label.

labelcolor : color, default: :rc:`text.color`

Label color.

fontproperties : dict, optional

A dictionary with keyword arguments accepted by the

`~matplotlib.font_manager.FontProperties` initializer:

*family*, *style*, *variant*, *size*, *weight*.

**kwargs

Any additional keyword arguments are used to override vector

properties taken from *Q*.

"""

super().__init__()

self.Q = Q

self.X = X

self.Y = Y

self.U = U

self.angle = angle

self.coord = coordinates

self.color = color

self.label = label

self._labelsep_inches = labelsep

self.labelpos = labelpos

self.labelcolor = labelcolor

self.fontproperties = fontproperties or dict()

self.kw = kw

_fp = self.fontproperties

# boxprops = dict(facecolor='red')

self.text = mtext.Text(

text=label, # bbox=boxprops,

horizontalalignment=self.halign[self.labelpos],

verticalalignment=self.valign[self.labelpos],

fontproperties=font_manager.FontProperties._from_any(_fp))

if self.labelcolor is not None:

self.text.set_color(self.labelcolor)

self._dpi_at_last_init = None

self.zorder = Q.zorder + 0.1

@property

def labelsep(self):

return self._labelsep_inches * self.Q.axes.figure.dpi

def _init(self):

if True: # self._dpi_at_last_init != self.axes.figure.dpi

if self.Q._dpi_at_last_init != self.Q.axes.figure.dpi:

self.Q._init()

self._set_transform()

with cbook._setattr_cm(self.Q, pivot=self.pivot[self.labelpos],

# Hack: save and restore the Umask

Umask=ma.nomask):

u = self.U * np.cos(np.radians(self.angle))

v = self.U * np.sin(np.radians(self.angle))

angle = (self.Q.angles if isinstance(self.Q.angles, str)

else 'uv')

self.verts = self.Q._make_verts(

np.array([u]), np.array([v]), angle)

kw = self.Q.polykw

kw.update(self.kw)

self.vector = mcollections.PolyCollection(

self.verts,

offsets=[(self.X, self.Y)],

transOffset=self.get_transform(),

**kw)

if self.color is not None:

self.vector.set_color(self.color)

self.vector.set_transform(self.Q.get_transform())

self.vector.set_figure(self.get_figure())

self._dpi_at_last_init = self.Q.axes.figure.dpi

def _text_x(self, x):

if self.labelpos == 'E':

return x + self.labelsep

elif self.labelpos == 'W':

return x - self.labelsep

else:

return x

def _text_y(self, y):

if self.labelpos == 'N':

return y + self.labelsep

elif self.labelpos == 'S':

return y - self.labelsep

else:

return y

@martist.allow_rasterization

def draw(self, renderer):

self._init()

self.vector.draw(renderer)

x, y = self.get_transform().transform((self.X, self.Y))

self.text.set_x(self._text_x(x))

self.text.set_y(self._text_y(y))

self.text.draw(renderer)

self.stale = False

def _set_transform(self):

self.set_transform(_api.check_getitem({

"data": self.Q.axes.transData,

"axes": self.Q.axes.transAxes,

"figure": self.Q.axes.figure.transFigure,

"inches": self.Q.axes.figure.dpi_scale_trans,

}, coordinates=self.coord))

def set_figure(self, fig):

super().set_figure(fig)

self.text.set_figure(fig)

def contains(self, mouseevent):

inside, info = self._default_contains(mouseevent)

if inside is not None:

return inside, info

# Maybe the dictionary should allow one to

# distinguish between a text hit and a vector hit.

if (self.text.contains(mouseevent)[0] or

self.vector.contains(mouseevent)[0]):

return True, {}

return False, {}

def _parse_args(*args, caller_name='function'):

"""

Helper function to parse positional parameters for colored vector plots.

This is currently used for Quiver and Barbs.

Parameters

----------

*args : list

list of 2-5 arguments. Depending on their number they are parsed to::

U, V

U, V, C

X, Y, U, V

X, Y, U, V, C

caller_name : str

Name of the calling method (used in error messages).

"""

X = Y = C = None

len_args = len(args)

if len_args == 2:

# The use of atleast_1d allows for handling scalar arguments while also

# keeping masked arrays

U, V = np.atleast_1d(*args)

elif len_args == 3:

U, V, C = np.atleast_1d(*args)

elif len_args == 4:

X, Y, U, V = np.atleast_1d(*args)

elif len_args == 5:

X, Y, U, V, C = np.atleast_1d(*args)

else:

raise TypeError(f'{caller_name} takes 2-5 positional arguments but '

f'{len_args} were given')

nr, nc = (1, U.shape[0]) if U.ndim == 1 else U.shape

if X is not None:

X = X.ravel()

Y = Y.ravel()

if len(X) == nc and len(Y) == nr:

X, Y = [a.ravel() for a in np.meshgrid(X, Y)]

elif len(X) != len(Y):

raise ValueError('X and Y must be the same size, but '

f'X.size is {X.size} and Y.size is {Y.size}.')

else:

indexgrid = np.meshgrid(np.arange(nc), np.arange(nr))

X, Y = [np.ravel(a) for a in indexgrid]

# Size validation for U, V, C is left to the set_UVC method.

return X, Y, U, V, C

def _check_consistent_shapes(*arrays):

all_shapes = {a.shape for a in arrays}

if len(all_shapes) != 1:

raise ValueError('The shapes of the passed in arrays do not match')

class Quiver(mcollections.PolyCollection):

"""

Specialized PolyCollection for arrows.

The only API method is set_UVC(), which can be used

to change the size, orientation, and color of the

arrows; their locations are fixed when the class is

instantiated. Possibly this method will be useful

in animations.

Much of the work in this class is done in the draw()

method so that as much information as possible is available

about the plot. In subsequent draw() calls, recalculation

is limited to things that might have changed, so there

should be no performance penalty from putting the calculations

in the draw() method.

"""

_PIVOT_VALS = ('tail', 'middle', 'tip')

@docstring.Substitution(_quiver_doc)

def __init__(self, ax, *args,

scale=None, headwidth=3, headlength=5, headaxislength=4.5,

minshaft=1, minlength=1, units='width', scale_units=None,

angles='uv', width=None, color='k', pivot='tail', **kw):

"""

The constructor takes one required argument, an Axes

instance, followed by the args and kwargs described

by the following pyplot interface documentation:

%s

"""

self._axes = ax # The attr actually set by the Artist.axes property.

X, Y, U, V, C = _parse_args(*args, caller_name='quiver()')

self.X = X

self.Y = Y

self.XY = np.column_stack((X, Y))

self.N = len(X)

self.scale = scale

self.headwidth = headwidth

self.headlength = float(headlength)

self.headaxislength = headaxislength

self.minshaft = minshaft

self.minlength = minlength

self.units = units

self.scale_units = scale_units

self.angles = angles

self.width = width

if pivot.lower() == 'mid':

pivot = 'middle'

self.pivot = pivot.lower()

_api.check_in_list(self._PIVOT_VALS, pivot=self.pivot)

self.transform = kw.pop('transform', ax.transData)

kw.setdefault('facecolors', color)

kw.setdefault('linewidths', (0,))

super().__init__([], offsets=self.XY, transOffset=self.transform,

closed=False, **kw)

self.polykw = kw

self.set_UVC(U, V, C)

self._dpi_at_last_init = None

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: # self._dpi_at_last_init != self.axes.figure.dpi

trans = self._set_transform()

self.span = trans.inverted().transform_bbox(self.axes.bbox).width

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 (self._dpi_at_last_init != self.axes.figure.dpi

and self.scale is None):

self._make_verts(self.U, self.V, self.angles)

self._dpi_at_last_init = self.axes.figure.dpi

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

@martist.allow_rasterization

def draw(self, renderer):

self._init()

verts = self._make_verts(self.U, self.V, self.angles)

self.set_verts(verts, closed=False)

super().draw(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()

if C is not None:

C = ma.masked_invalid(C, copy=True).ravel()

for name, var in zip(('U', 'V', 'C'), (U, V, C)):

if not (var is None or var.size == self.N or var.size == 1):

raise ValueError(f'Argument {name} has a size {var.size}'

f' which does not match {self.N},'

' the number of arrow positions')

mask = ma.mask_or(U.mask, V.mask, copy=False, shrink=True)

if C is not None:

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.stale = True

def _dots_per_unit(self, units):

"""

Return a scale factor for converting from units to pixels

"""

if units in ('x', 'y', 'xy'):

if units == 'x':

dx0 = self.axes.viewLim.width

dx1 = self.axes.bbox.width

elif units == 'y':

dx0 = self.axes.viewLim.height

dx1 = self.axes.bbox.height

else: # 'xy' is assumed

dxx0 = self.axes.viewLim.width

dxx1 = self.axes.bbox.width

dyy0 = self.axes.viewLim.height

dyy1 = self.axes.bbox.height

dx1 = np.hypot(dxx1, dyy1)

dx0 = np.hypot(dxx0, dyy0)

dx = dx1 / dx0

else:

if units == 'width':

dx = self.axes.bbox.width

elif units == 'height':

dx = self.axes.bbox.height

elif units == 'dots':

dx = 1.0

elif units == 'inches':

dx = self.axes.figure.dpi

else:

raise ValueError('unrecognized units')

return dx

def _set_transform(self):

"""

Set the PolyCollection 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.axes.transData.transform(self.XY)

uv = np.column_stack((U, V))

xyp = self.axes.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.axes.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[:, ii]

Y = y[:, ii]

Y[:, 3:-1] *= -1

X0 = x0[ii]

Y0 = y0[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':

# numpy bug? using -= does not work here unless we multiply by a

# float first, as with 'mid'.

X = X - X[:, 3, np.newaxis]

elif self.pivot != 'tail':

_api.check_in_list(["middle", "tip", "tail"], pivot=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 2D field of barbs.

Call signature::

barbs([X, Y], U, V, [C], **kw)

Where *X*, *Y* define the barb locations, *U*, *V* define the barb

directions, and *C* optionally sets the color.

All arguments may be 1D or 2D. *U*, *V*, *C* may be masked arrays, but masked

*X*, *Y* are not supported at present.

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::

: /\ \

: / \ \

: / \ \ \

: / \ \ \

: ------------------------------

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.

See also https://en.wikipedia.org/wiki/Wind_barb.

Parameters

----------

X, Y : 1D or 2D array-like, optional

The x and y coordinates of the barb locations. See *pivot* for how the

barbs are drawn to the x, y positions.

If not given, they will be generated as a uniform integer meshgrid based

on the dimensions of *U* and *V*.

If *X* and *Y* are 1D but *U*, *V* are 2D, *X*, *Y* are expanded to 2D

using ``X, Y = np.meshgrid(X, Y)``. In this case ``len(X)`` and ``len(Y)``

must match the column and row dimensions of *U* and *V*.

U, V : 1D or 2D array-like

The x and y components of the barb shaft.

C : 1D or 2D array-like, optional

Numeric data that defines the barb colors by colormapping via *norm* and

*cmap*.

This does not support explicit colors. If you want to set colors directly,

use *barbcolor* instead.

length : float, default: 7

Length of the barb in points; the other parts of the barb

are scaled against this.

pivot : {'tip', 'middle'} or float, default: 'tip'

The part of the arrow that is anchored to the *X*, *Y* grid. The barb

rotates about this point. This can also be a number, which shifts the

start of the barb that many points away from grid point.

barbcolor : color or color sequence

The color of all parts of the barb except for the flags. This parameter

is analogous to the *edgecolor* parameter for polygons, which can be used

instead. However this parameter will override facecolor.

flagcolor : color or color sequence

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 : dict, optional

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 : bool, default: False

Whether the empty barbs (circles) that are drawn should be filled with

the flag color. If they are not filled, the center is transparent.

rounding : bool, default: True

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.

barb_increments : dict, optional

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 : bool or array-like of bool, default: False

Whether the lines and flags should point opposite to normal.

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).

A single value is applied to all barbs. Individual barbs can be flipped by

passing a bool array of the same size as *U* and *V*.

Returns

-------

barbs : `~matplotlib.quiver.Barbs`

Other Parameters

----------------

data : indexable object, optional

DATA_PARAMETER_PLACEHOLDER

**kwargs

The barbs can further be customized using `.PolyCollection` keyword

arguments:

%(PolyCollection:kwdoc)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 = np.atleast_1d(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, caller_name='barbs()')

self.x = x

self.y = y

xy = np.column_stack((x, y))

# Make a collection

barb_size = self._length ** 2 / 4 # Empirically determined

super().__init__([], (barb_size,), offsets=xy, transOffset=transform,

**kw)

self.set_transform(transforms.IdentityTransform())

self.set_UVC(u, v, c)

def _find_tails(self, mag, rounding=True, half=5, full=10, flag=50):

"""

Find how many of each of the tail pieces is necessary. Flag

specifies the increment for a flag, barb for a full barb, and half for

half a barb. Mag should be the magnitude of a vector (i.e., >= 0).

This returns a tuple of:

(*number of flags*, *number of barbs*, *half_flag*, *empty_flag*)

The bool *half_flag* indicates whether half of a barb is needed,

since there should only ever be one half on a given

barb. *empty_flag* flag is an array of flags to easily tell if

a barb is empty (too low to plot any barbs/flags.

"""

# If rounding, round to the nearest multiple of half, the smallest

# increment

if rounding:

mag = half * (mag / half + 0.5).astype(int)

num_flags = np.floor(mag / flag).astype(int)

mag = mag % flag

num_barb = np.floor(mag / full).astype(int)

mag = mag % full

half_flag = mag >= half

empty_flag = ~(half_flag | (num_flags > 0) | (num_barb > 0))

return num_flags, num_barb, half_flag, empty_flag

def _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,

pivot, sizes, fill_empty, flip):

"""

Create the wind barbs.

Parameters

----------

u, v

Components of the vector in the x and y directions, respectively.

nflags, nbarbs, half_barb, empty_flag

Respectively, the number of flags, number of barbs, flag for

half a barb, and flag for empty barb, ostensibly obtained from

:meth:`_find_tails`.

length

The length of the barb staff in points.

pivot : {"tip", "middle"} or number

The point on the barb around which the entire barb should be

rotated. If a number, the start of the barb is shifted by that