EVOLUTION-MANAGER

Edit File: quiver.py

""" 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 weakref import numpy as np from numpy import ma from matplotlib import 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. **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 ---------------- **kwargs : `~matplotlib.collections.PolyCollection` properties, optional All other keyword arguments are passed on to `.PolyCollection`: %(PolyCollection)s See Also -------- .Axes.quiverkey : Add a key to a quiver plot. """ % docstring.interpd.params 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*. """ martist.Artist.__init__(self) 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.labelsep = (self._labelsep_inches * Q.axes.figure.dpi) # try to prevent closure over the real self weak_self = weakref.ref(self) def on_dpi_change(fig): self_weakref = weak_self() if self_weakref is not None: self_weakref.labelsep = self_weakref._labelsep_inches * fig.dpi # simple brute force update works because _init is called at # the start of draw. self_weakref._initialized = False self._cid = Q.axes.figure.callbacks.connect( 'dpi_changed', on_dpi_change) 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._initialized = False self.zorder = Q.zorder + 0.1 def remove(self): # docstring inherited self.Q.axes.figure.callbacks.disconnect(self._cid) self._cid = None super().remove() # pass the remove call up the stack def _init(self): if True: # not self._initialized: if not self.Q._initialized: 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._initialized = True 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(cbook._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): martist.Artist.set_figure(self, 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, {} @cbook.deprecated("3.2") @property def quiverkey_doc(self): return self.__init__.__doc__ 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() cbook._check_in_list(self._PIVOT_VALS, pivot=self.pivot) self.transform = kw.pop('transform', ax.transData) kw.setdefault('facecolors', color) kw.setdefault('linewidths', (0,)) mcollections.PolyCollection.__init__(self, [], offsets=self.XY, transOffset=self.transform, closed=False, **kw) self.polykw = kw self.set_UVC(U, V, C) self._initialized = False weak_self = weakref.ref(self) # Prevent closure over the real self. def on_dpi_change(fig): self_weakref = weak_self() if self_weakref is not None: # vertices depend on width, span which in turn depend on dpi self_weakref._new_UV = True # simple brute force update works because _init is called at # the start of draw. self_weakref._initialized = False self._cid = ax.figure.callbacks.connect('dpi_changed', on_dpi_change) @cbook.deprecated("3.3", alternative="axes") def ax(self): return self.axes def remove(self): # docstring inherited self.axes.figure.callbacks.disconnect(self._cid) self._cid = None super().remove() # pass the remove call up the stack 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() 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 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 @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) 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() 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._new_UV = True 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': cbook._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 ---------------- **kwargs The barbs can further be customized using `.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 = 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 mcollections.PolyCollection.__init__(self, [], (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 many points from the origin. sizes : dict 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). - *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 : bool Whether the circle representing an empty barb should be filled or not (this changes the drawing of the polygon). flip : list of bool Whether the features should be flipped to the other side of the barb (useful for winds in the southern hemisphere). Returns ------- list of arrays of vertices Polygon vertices for each of the wind barbs. These polygons have been rotated to properly align with the vector direction. """ # These control the spacing and size of barb elements relative to the # length of the shaft spacing = length * sizes.get('spacing', 0.125) full_height = length * sizes.get('height', 0.4) full_width = length * sizes.get('width', 0.25) 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.) endx = 0.0 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 # Handle if this barb should be flipped barb_height = -full_height if flip[index] else full_height # 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 + barb_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 + barb_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 + barb_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() # Flip needs to have the same number of entries as everything else. # Use broadcast_to to avoid a bloated array of identical values. # (can't rely on actual broadcasting) if len(self.flip) == 1: flip = np.broadcast_to(self.flip, self.u.shape) else: flip = self.flip if C is not None: c = ma.masked_invalid(C, copy=False).ravel() x, y, u, v, c, flip = cbook.delete_masked_points( self.x.ravel(), self.y.ravel(), self.u, self.v, c, flip.ravel()) _check_consistent_shapes(x, y, u, v, c, flip) else: x, y, u, v, flip = cbook.delete_masked_points( self.x.ravel(), self.y.ravel(), self.u, self.v, flip.ravel()) _check_consistent_shapes(x, y, u, v, flip) 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, 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 masks them as appropriate for the existing U/V data. Parameters ---------- xy : sequence of pairs of floats """ self.x = xy[:, 0] self.y = xy[:, 1] x, y, u, v = cbook.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 barbs_doc = _barbs_doc