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""" matplotlib includes a framework for arbitrary geometric transformations that is used determine the final position of all elements drawn on the canvas.
Transforms are composed into trees of :class:`TransformNode` objects whose actual value depends on their children. When the contents of children change, their parents are automatically invalidated. The next time an invalidated transform is accessed, it is recomputed to reflect those changes. This invalidation/caching approach prevents unnecessary recomputations of transforms, and contributes to better interactive performance.
For example, here is a graph of the transform tree used to plot data to the graph:
.. image:: ../_static/transforms.png
The framework can be used for both affine and non-affine transformations. However, for speed, we want use the backend renderers to perform affine transformations whenever possible. Therefore, it is possible to perform just the affine or non-affine part of a transformation on a set of data. The affine is always assumed to occur after the non-affine. For any transform::
full transform == non-affine part + affine part
The backends are not expected to handle non-affine transformations themselves. """
# Note: There are a number of places in the code where we use `np.min` or # `np.minimum` instead of the builtin `min`, and likewise for `max`. This is # done so that `nan`s are propagated, instead of being silently dropped.
affine_transform, count_bboxes_overlapping_bbox, update_path_extents)
return re.sub("(^|\n)", r"\1 ", str(obj))
""" :class:`TransformNode` is the base class for anything that participates in the transform tree and needs to invalidate its parents or be invalidated. This includes classes that are not really transforms, such as bounding boxes, since some transforms depend on bounding boxes to compute their values. """
# Invalidation may affect only the affine part. If the # invalidation was "affine-only", the _invalid member is set to # INVALID_AFFINE_ONLY
# Some metadata about the transform, used to determine whether an # invalidation is affine-only
""" If pass_through is True, all ancestors will always be invalidated, even if 'self' is already invalid. """
""" Creates a new :class:`TransformNode`.
Parameters ---------- shorthand_name : str A string representing the "name" of the transform. The name carries no significance other than to improve the readability of ``str(transform)`` when DEBUG=True. """
# TransformNodes start out as invalid until their values are # computed for the first time.
def __str__(self): # either just return the name of this TransformNode, or its repr return self._shorthand_name or repr(self)
# turn the dictionary with weak values into a normal dictionary return {**self.__dict__, '_parents': {k: v() for k, v in self._parents.items()}}
self.__dict__ = data_dict # turn the normal dictionary back into a dictionary with weak values self._parents = {k: weakref.ref(v) for k, v in self._parents.items() if v is not None}
raise NotImplementedError( "TransformNode instances can not be copied. " "Consider using frozen() instead.")
""" Invalidate this :class:`TransformNode` and triggers an invalidation of its ancestors. Should be called any time the transform changes. """
""" Called by :meth:`invalidate` and subsequently ascends the transform stack calling each TransformNode's _invalidate_internal method. """ # determine if this call will be an extension to the invalidation # status. If not, then a shortcut means that we needn't invoke an # invalidation up the transform stack as it will already have been # invalidated.
# N.B This makes the invalidation sticky, once a transform has been # invalidated as NON_AFFINE, then it will always be invalidated as # NON_AFFINE even when triggered with a AFFINE_ONLY invalidation. # In most cases this is not a problem (i.e. for interactive panning and # zooming) and the only side effect will be on performance.
# Dereference the weak reference value=value, invalidating_node=self)
""" Set the children of the transform, to let the invalidation system know which transforms can invalidate this transform. Should be called from the constructor of any transforms that depend on other transforms. """ # Parents are stored as weak references, so that if the # parents are destroyed, references from the children won't # keep them alive.
_set_children = set_children
def set_children(self, *children): self._set_children(*children) self._children = children set_children.__doc__ = _set_children.__doc__
""" Returns a frozen copy of this transform node. The frozen copy will not update when its children change. Useful for storing a previously known state of a transform where ``copy.deepcopy()`` might normally be used. """ return self
def write_graphviz(self, fobj, highlight=[]): """ For debugging purposes.
Writes the transform tree rooted at 'self' to a graphviz "dot" format file. This file can be run through the "dot" utility to produce a graph of the transform tree.
Affine transforms are marked in blue. Bounding boxes are marked in yellow.
*fobj*: A Python file-like object
Once the "dot" file has been created, it can be turned into a png easily with::
$> dot -Tpng -o $OUTPUT_FILE $DOT_FILE
""" seen = set()
def recurse(root): if root in seen: return seen.add(root) props = {} label = root.__class__.__name__ if root._invalid: label = '[%s]' % label if root in highlight: props['style'] = 'bold' props['shape'] = 'box' props['label'] = '"%s"' % label props = ' '.join(map('{0[0]}={0[1]}'.format, props.items()))
fobj.write('%s [%s];\n' % (hash(root), props))
if hasattr(root, '_children'): for child in root._children: name = next((key for key, val in root.__dict__.items() if val is child), '?') fobj.write('"%s" -> "%s" [label="%s", fontsize=10];\n' % (hash(root), hash(child), name)) recurse(child)
fobj.write("digraph G {\n") recurse(self) fobj.write("}\n")
""" This is the base class of all bounding boxes, and provides read-only access to its data. A mutable bounding box is provided by the :class:`Bbox` class.
The canonical representation is as two points, with no restrictions on their ordering. Convenience properties are provided to get the left, bottom, right and top edges and width and height, but these are not stored explicitly. """
def _check(points): if isinstance(points, np.ma.MaskedArray): warnings.warn("Bbox bounds are a masked array.") points = np.asarray(points) if (points[1, 0] - points[0, 0] == 0 or points[1, 1] - points[0, 1] == 0): warnings.warn("Singular Bbox.") _check = staticmethod(_check)
""" Returns True if the :class:`Bbox` is the unit bounding box from (0, 0) to (1, 1). """ return list(self.get_points().flatten()) == [0., 0., 1., 1.]
def x0(self): """ :attr:`x0` is the first of the pair of *x* coordinates that define the bounding box. :attr:`x0` is not guaranteed to be less than :attr:`x1`. If you require that, use :attr:`xmin`. """
def y0(self): """ :attr:`y0` is the first of the pair of *y* coordinates that define the bounding box. :attr:`y0` is not guaranteed to be less than :attr:`y1`. If you require that, use :attr:`ymin`. """
def x1(self): """ :attr:`x1` is the second of the pair of *x* coordinates that define the bounding box. :attr:`x1` is not guaranteed to be greater than :attr:`x0`. If you require that, use :attr:`xmax`. """
def y1(self): """ :attr:`y1` is the second of the pair of *y* coordinates that define the bounding box. :attr:`y1` is not guaranteed to be greater than :attr:`y0`. If you require that, use :attr:`ymax`. """
def p0(self): """ :attr:`p0` is the first pair of (*x*, *y*) coordinates that define the bounding box. It is not guaranteed to be the bottom-left corner. For that, use :attr:`min`. """ return self.get_points()[0]
def p1(self): """ :attr:`p1` is the second pair of (*x*, *y*) coordinates that define the bounding box. It is not guaranteed to be the top-right corner. For that, use :attr:`max`. """
def xmin(self): """ :attr:`xmin` is the left edge of the bounding box. """
def ymin(self): """ :attr:`ymin` is the bottom edge of the bounding box. """
def xmax(self): """ :attr:`xmax` is the right edge of the bounding box. """
def ymax(self): """ :attr:`ymax` is the top edge of the bounding box. """
def min(self): """ :attr:`min` is the bottom-left corner of the bounding box. """
def max(self): """ :attr:`max` is the top-right corner of the bounding box. """
def intervalx(self): """ :attr:`intervalx` is the pair of *x* coordinates that define the bounding box. It is not guaranteed to be sorted from left to right. """
def intervaly(self): """ :attr:`intervaly` is the pair of *y* coordinates that define the bounding box. It is not guaranteed to be sorted from bottom to top. """
def width(self): """ The width of the bounding box. It may be negative if :attr:`x1` < :attr:`x0`. """
def height(self): """ The height of the bounding box. It may be negative if :attr:`y1` < :attr:`y0`. """
def size(self): """ The width and height of the bounding box. May be negative, in the same way as :attr:`width` and :attr:`height`. """
def bounds(self): """ Returns (:attr:`x0`, :attr:`y0`, :attr:`width`, :attr:`height`). """
def extents(self): """ Returns (:attr:`x0`, :attr:`y0`, :attr:`x1`, :attr:`y1`). """ return self.get_points().flatten().copy()
raise NotImplementedError
""" Returns whether *x* is in the closed (:attr:`x0`, :attr:`x1`) interval. """ x0, x1 = self.intervalx return x0 <= x <= x1 or x0 >= x >= x1
""" Returns whether *y* is in the closed (:attr:`y0`, :attr:`y1`) interval. """ y0, y1 = self.intervaly return y0 <= y <= y1 or y0 >= y >= y1
""" Returns whether ``(x, y)`` is in the bounding box or on its edge. """ return self.containsx(x) and self.containsy(y)
""" Returns whether this bounding box overlaps with the other bounding box.
Parameters ---------- other : BboxBase """ ax1, ay1, ax2, ay2 = self.extents bx1, by1, bx2, by2 = other.extents if ax2 < ax1: ax2, ax1 = ax1, ax2 if ay2 < ay1: ay2, ay1 = ay1, ay2 if bx2 < bx1: bx2, bx1 = bx1, bx2 if by2 < by1: by2, by1 = by1, by2 return ax1 <= bx2 and bx1 <= ax2 and ay1 <= by2 and by1 <= ay2
""" Returns whether *x* is in the open (:attr:`x0`, :attr:`x1`) interval. """ x0, x1 = self.intervalx return x0 < x < x1 or x0 > x > x1
""" Returns whether *y* is in the open (:attr:`y0`, :attr:`y1`) interval. """ y0, y1 = self.intervaly return y0 < y < y1 or y0 > y > y1
""" Returns whether ``x, y`` is in the bounding box, but not on its edge. """ return self.fully_containsx(x) and self.fully_containsy(y)
""" Returns whether this bounding box overlaps with the other bounding box, not including the edges.
Parameters ---------- other : BboxBase """ ax1, ay1, ax2, ay2 = self.extents bx1, by1, bx2, by2 = other.extents if ax2 < ax1: ax2, ax1 = ax1, ax2 if ay2 < ay1: ay2, ay1 = ay1, ay2 if bx2 < bx1: bx2, bx1 = bx1, bx2 if by2 < by1: by2, by1 = by1, by2 return ax1 < bx2 and bx1 < ax2 and ay1 < by2 and by1 < ay2
""" Return a new :class:`Bbox` object, statically transformed by the given transform. """ [pts[0, 0], pts[1, 1]], [pts[1, 0], pts[0, 1]]]))
""" Return a new :class:`Bbox` object, statically transformed by the inverse of the given transform. """
'SW': (0, 0), 'S': (0.5, 0), 'SE': (1.0, 0), 'E': (1.0, 0.5), 'NE': (1.0, 1.0), 'N': (0.5, 1.0), 'NW': (0, 1.0), 'W': (0, 0.5)}
""" Return a copy of the :class:`Bbox`, shifted to position *c* within a container.
Parameters ---------- c : May be either:
* A sequence (*cx*, *cy*) where *cx* and *cy* range from 0 to 1, where 0 is left or bottom and 1 is right or top
* a string: - 'C' for centered - 'S' for bottom-center - 'SE' for bottom-left - 'E' for left - etc.
container : Bbox, optional The box within which the :class:`Bbox` is positioned; it defaults to the initial :class:`Bbox`. """ container = self else: cx, cy = c [(l + cx * (w - W)) - L, (b + cy * (h - H)) - B])
""" Return a copy of the :class:`Bbox`, shrunk by the factor *mx* in the *x* direction and the factor *my* in the *y* direction. The lower left corner of the box remains unchanged. Normally *mx* and *my* will be less than 1, but this is not enforced. """ w, h = self.size return Bbox([self._points[0], self._points[0] + [mx * w, my * h]])
""" Return a copy of the :class:`Bbox`, shrunk so that it is as large as it can be while having the desired aspect ratio, *box_aspect*. If the box coordinates are relative---that is, fractions of a larger box such as a figure---then the physical aspect ratio of that figure is specified with *fig_aspect*, so that *box_aspect* can also be given as a ratio of the absolute dimensions, not the relative dimensions. """ raise ValueError("'box_aspect' and 'fig_aspect' must be positive") container = self else: self._points[0] + (W, H)])
""" e.g., ``bbox.splitx(f1, f2, ...)``
Returns a list of new :class:`Bbox` objects formed by splitting the original one with vertical lines at fractional positions *f1*, *f2*, ... """ xf = [0, *args, 1] x0, y0, x1, y1 = self.extents w = x1 - x0 return [Bbox([[x0 + xf0 * w, y0], [x0 + xf1 * w, y1]]) for xf0, xf1 in zip(xf[:-1], xf[1:])]
""" e.g., ``bbox.splitx(f1, f2, ...)``
Returns a list of new :class:`Bbox` objects formed by splitting the original one with horizontal lines at fractional positions *f1*, *f2*, ... """ yf = [0, *args, 1] x0, y0, x1, y1 = self.extents h = y1 - y0 return [Bbox([[x0, y0 + yf0 * h], [x1, y0 + yf1 * h]]) for yf0, yf1 in zip(yf[:-1], yf[1:])]
""" Count the number of vertices contained in the :class:`Bbox`. Any vertices with a non-finite x or y value are ignored.
Parameters ---------- vertices : Nx2 Numpy array. """ (vertices < self.max)).all(axis=1).sum())
""" Count the number of bounding boxes that overlap this one.
Parameters ---------- bboxes : sequence of :class:`BboxBase` objects """ self, np.atleast_3d([np.array(x) for x in bboxes]))
""" Return a new :class:`Bbox` which is this :class:`Bbox` expanded around its center by the given factors *sw* and *sh*. """ width = self.width height = self.height deltaw = (sw * width - width) / 2.0 deltah = (sh * height - height) / 2.0 a = np.array([[-deltaw, -deltah], [deltaw, deltah]]) return Bbox(self._points + a)
""" Return a new :class:`Bbox` that is padded on all four sides by the given value. """
""" Return a copy of the :class:`Bbox`, statically translated by *tx* and *ty*. """
""" Return an array of points which are the four corners of this rectangle. For example, if this :class:`Bbox` is defined by the points (*a*, *b*) and (*c*, *d*), :meth:`corners` returns (*a*, *b*), (*a*, *d*), (*c*, *b*) and (*c*, *d*). """ l, b, r, t = self.get_points().flatten() return np.array([[l, b], [l, t], [r, b], [r, t]])
""" Return a new bounding box that bounds a rotated version of this bounding box by the given radians. The new bounding box is still aligned with the axes, of course. """ corners = self.corners() corners_rotated = Affine2D().rotate(radians).transform(corners) bbox = Bbox.unit() bbox.update_from_data_xy(corners_rotated, ignore=True) return bbox
def union(bboxes): """ Return a :class:`Bbox` that contains all of the given bboxes. """ raise ValueError("'bboxes' cannot be empty")
def intersection(bbox1, bbox2): """ Return the intersection of the two bboxes or None if they do not intersect. """
""" A mutable bounding box. """
""" Parameters ---------- points : ndarray A 2x2 numpy array of the form ``[[x0, y0], [x1, y1]]``.
Notes ----- If you need to create a :class:`Bbox` object from another form of data, consider the static methods :meth:`unit`, :meth:`from_bounds` and :meth:`from_extents`. """ raise ValueError('Bbox points must be of the form ' '"[[x0, y0], [x1, y1]]".') # it is helpful in some contexts to know if the bbox is a # default or has been mutated; we store the orig points to # support the mutated methods ___init__ = __init__
def __init__(self, points, **kwargs): self._check(points) self.___init__(points, **kwargs)
def invalidate(self): self._check(self._points) TransformNode.invalidate(self)
def unit(): """ (staticmethod) Create a new unit :class:`Bbox` from (0, 0) to (1, 1). """
def null(): """ (staticmethod) Create a new null :class:`Bbox` from (inf, inf) to (-inf, -inf). """
def from_bounds(x0, y0, width, height): """ (staticmethod) Create a new :class:`Bbox` from *x0*, *y0*, *width* and *height*.
*width* and *height* may be negative. """
def from_extents(*args): """ (staticmethod) Create a new Bbox from *left*, *bottom*, *right* and *top*.
The *y*-axis increases upwards. """
return ( 'Bbox(x0={0.x0:{1}}, y0={0.y0:{1}}, x1={0.x1:{1}}, y1={0.y1:{1}})'. format(self, fmt))
def __str__(self): return format(self, '')
def __repr__(self): return 'Bbox([[{0.x0}, {0.y0}], [{0.x1}, {0.y1}]])'.format(self)
""" Set whether the existing bounds of the box should be ignored by subsequent calls to :meth:`update_from_data_xy`.
value : bool - When ``True``, subsequent calls to :meth:`update_from_data_xy` will ignore the existing bounds of the :class:`Bbox`.
- When ``False``, subsequent calls to :meth:`update_from_data_xy` will include the existing bounds of the :class:`Bbox`. """ self._ignore = value
""" Update the bounds of the :class:`Bbox` based on the passed in data. After updating, the bounds will have positive *width* and *height*; *x0* and *y0* will be the minimal values.
Parameters ---------- path : :class:`~matplotlib.path.Path`
ignore : bool, optional - when ``True``, ignore the existing bounds of the :class:`Bbox`. - when ``False``, include the existing bounds of the :class:`Bbox`. - when ``None``, use the last value passed to :meth:`ignore`.
updatex, updatey : bool, optional When ``True``, update the x/y values. """
return
path, None, self._points, self._minpos, ignore)
""" Update the bounds of the :class:`Bbox` based on the passed in data. After updating, the bounds will have positive *width* and *height*; *x0* and *y0* will be the minimal values.
Parameters ---------- xy : ndarray A numpy array of 2D points.
ignore : bool, optional - When ``True``, ignore the existing bounds of the :class:`Bbox`. - When ``False``, include the existing bounds of the :class:`Bbox`. - When ``None``, use the last value passed to :meth:`ignore`.
updatex, updatey : bool, optional When ``True``, update the x/y values. """ return
updatex=updatex, updatey=updatey)
def x0(self, val): self._points[0, 0] = val self.invalidate()
def y0(self, val): self._points[0, 1] = val self.invalidate()
def x1(self, val): self._points[1, 0] = val self.invalidate()
def y1(self, val): self._points[1, 1] = val self.invalidate()
def p0(self, val): self._points[0] = val self.invalidate()
def p1(self, val):
def intervalx(self, interval):
def intervaly(self, interval):
def bounds(self, bounds): l, b, w, h = bounds points = np.array([[l, b], [l + w, b + h]], float) if np.any(self._points != points): self._points = points self.invalidate()
def minpos(self): return self._minpos
def minposx(self):
def minposy(self):
""" Get the points of the bounding box directly as a numpy array of the form: ``[[x0, y0], [x1, y1]]``. """
""" Set the points of the bounding box directly from a numpy array of the form: ``[[x0, y0], [x1, y1]]``. No error checking is performed, as this method is mainly for internal use. """ if np.any(self._points != points): self._points = points self.invalidate()
""" Set this bounding box from the "frozen" bounds of another :class:`Bbox`. """
'Return whether the bbox has changed since init.' return self.mutatedx() or self.mutatedy()
'Return whether the x-limits have changed since init.' return (self._points[0, 0] != self._points_orig[0, 0] or self._points[1, 0] != self._points_orig[1, 0])
'Return whether the y-limits have changed since init.' return (self._points[0, 1] != self._points_orig[0, 1] or self._points[1, 1] != self._points_orig[1, 1])
""" A :class:`Bbox` that is automatically transformed by a given transform. When either the child bounding box or transform changes, the bounds of this bbox will update accordingly. """ """ Parameters ---------- bbox : :class:`Bbox`
transform : :class:`Transform` """ raise ValueError("'bbox' is not a bbox") raise ValueError("'transform' must be an instance of " "'matplotlib.transform.Transform'") raise ValueError( "The input and output dimensions of 'transform' must be 2")
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._bbox), _indent_str(self._transform)))
# Transform all four points, then make a new bounding box # from the result, taking care to make the orientation the # same. [[p[0, 0], p[0, 1]], [p[1, 0], p[0, 1]], [p[0, 0], p[1, 1]], [p[1, 0], p[1, 1]]])
xs = xs[::-1]
[xs[0], ys[0]], [xs[1], ys[1]] ])
_get_points = get_points
def get_points(self): points = self._get_points() self._check(points) return points
""" A :class:`Bbox` where some elements may be locked at certain values.
When the child bounding box changes, the bounds of this bbox will update accordingly with the exception of the locked elements. """ """ Parameters ---------- bbox : Bbox The child bounding box to wrap.
x0 : float or None The locked value for x0, or None to leave unlocked.
y0 : float or None The locked value for y0, or None to leave unlocked.
x1 : float or None The locked value for x1, or None to leave unlocked.
y1 : float or None The locked value for y1, or None to leave unlocked.
""" raise ValueError("'bbox' is not a bbox")
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._bbox), _indent_str(self._locked_points)))
points, self._locked_points)
_get_points = get_points
def get_points(self): points = self._get_points() self._check(points) return points
def locked_x0(self): """ float or None: The value used for the locked x0. """ if self._locked_points.mask[0, 0]: return None else: return self._locked_points[0, 0]
def locked_x0(self, x0): self._locked_points.mask[0, 0] = x0 is None self._locked_points.data[0, 0] = x0 self.invalidate()
def locked_y0(self): """ float or None: The value used for the locked y0. """ if self._locked_points.mask[0, 1]: return None else: return self._locked_points[0, 1]
def locked_y0(self, y0):
def locked_x1(self): """ float or None: The value used for the locked x1. """ if self._locked_points.mask[1, 0]: return None else: return self._locked_points[1, 0]
def locked_x1(self, x1): self._locked_points.mask[1, 0] = x1 is None self._locked_points.data[1, 0] = x1 self.invalidate()
def locked_y1(self): """ float or None: The value used for the locked y1. """ if self._locked_points.mask[1, 1]: return None else: return self._locked_points[1, 1]
def locked_y1(self, y1): self._locked_points.mask[1, 1] = y1 is None self._locked_points.data[1, 1] = y1 self.invalidate()
""" The base class of all :class:`TransformNode` instances that actually perform a transformation.
All non-affine transformations should be subclasses of this class. New affine transformations should be subclasses of :class:`Affine2D`.
Subclasses of this class should override the following members (at minimum):
- :attr:`input_dims` - :attr:`output_dims` - :meth:`transform` - :attr:`is_separable` - :attr:`has_inverse` - :meth:`inverted` (if :attr:`has_inverse` is True)
If the transform needs to do something non-standard with :class:`matplotlib.path.Path` objects, such as adding curves where there were once line segments, it should override:
- :meth:`transform_path` """ """ The number of input dimensions of this transform. Must be overridden (with integers) in the subclass. """
""" The number of output dimensions of this transform. Must be overridden (with integers) in the subclass. """
"""True if this transform has a corresponding inverse transform."""
"""True if this transform is separable in the x- and y- dimensions."""
""" Composes two transforms together such that *self* is followed by *other*. """ raise TypeError( "Can not add Transform to object of type '%s'" % type(other))
""" Composes two transforms together such that *self* is followed by *other*. """ if isinstance(other, Transform): return composite_transform_factory(other, self) raise TypeError( "Can not add Transform to object of type '%s'" % type(other))
# Equality is based on object identity for `Transform`s (so we don't # override `__eq__`), but some subclasses, such as TransformWrapper & # AffineBase, override this behavior.
""" Returns an iterator breaking down this transform stack from left to right recursively. If self == ((A, N), A) then the result will be an iterator which yields I : ((A, N), A), followed by A : (N, A), followed by (A, N) : (A), but not ((A, N), A) : I.
This is equivalent to flattening the stack then yielding ``flat_stack[:i], flat_stack[i:]`` where i=0..(n-1).
"""
def depth(self): """ Returns the number of transforms which have been chained together to form this Transform instance.
.. note::
For the special case of a Composite transform, the maximum depth of the two is returned.
"""
""" Return whether the given transform is a sub-tree of this transform.
This routine uses transform equality to identify sub-trees, therefore in many situations it is object id which will be used.
For the case where the given transform represents the whole of this transform, returns True.
"""
# check that a subtree is equal to other (starting from self)
""" Returns whether the given branch is a sub-tree of this transform on each separate dimension.
A common use for this method is to identify if a transform is a blended transform containing an axes' data transform. e.g.::
x_isdata, y_isdata = trans.contains_branch_seperately(ax.transData)
""" raise ValueError('contains_branch_seperately only supports ' 'transforms with 2 output dimensions') # for a non-blended transform each separate dimension is the same, so # just return the appropriate shape.
""" Returns a transform stack which goes all the way down self's transform stack, and then ascends back up other's stack. If it can, this is optimised::
# normally A - B == a + b.inverted()
# sometimes, when A contains the tree B there is no need to # descend all the way down to the base of A (via B), instead we # can just stop at B.
(A + B) - (B)^-1 == A
# similarly, when B contains tree A, we can avoid decending A at # all, basically: A - (A + B) == ((B + A) - A).inverted() or B^-1
For clarity, the result of ``(A + B) - B + B == (A + B)``.
""" # we only know how to do this operation if other is a Transform. return NotImplemented
return remainder
raise ValueError("The shortcut cannot be computed since " "other's transform includes a non-invertable component.")
# if we have got this far, then there was no shortcut possible else: raise ValueError('It is not possible to compute transA - transB ' 'since transB cannot be inverted and there is no ' 'shortcut possible.')
""" Array interface to get at this Transform's affine matrix. """
""" Performs the transformation on the given array of values.
Accepts a numpy array of shape (N x :attr:`input_dims`) and returns a numpy array of shape (N x :attr:`output_dims`).
Alternatively, accepts a numpy array of length :attr:`input_dims` and returns a numpy array of length :attr:`output_dims`. """ # Ensure that values is a 2d array (but remember whether # we started with a 1d or 2d array).
# Transform the values
# Convert the result back to the shape of the input values. assert not np.ma.is_masked(res) # just to be on the safe side return res[0, 0] raise ValueError( "Input values must have shape (N x {dims}) " "or ({dims}).".format(dims=self.input_dims))
""" Performs only the affine part of this transformation on the given array of values.
``transform(values)`` is always equivalent to ``transform_affine(transform_non_affine(values))``.
In non-affine transformations, this is generally a no-op. In affine transformations, this is equivalent to ``transform(values)``.
Accepts a numpy array of shape (N x :attr:`input_dims`) and returns a numpy array of shape (N x :attr:`output_dims`).
Alternatively, accepts a numpy array of length :attr:`input_dims` and returns a numpy array of length :attr:`output_dims`. """
""" Performs only the non-affine part of the transformation.
``transform(values)`` is always equivalent to ``transform_affine(transform_non_affine(values))``.
In non-affine transformations, this is generally equivalent to ``transform(values)``. In affine transformations, this is always a no-op.
Accepts a numpy array of shape (N x :attr:`input_dims`) and returns a numpy array of shape (N x :attr:`output_dims`).
Alternatively, accepts a numpy array of length :attr:`input_dims` and returns a numpy array of length :attr:`output_dims`. """ return values
""" Transform the given bounding box.
Note, for smarter transforms including caching (a common requirement for matplotlib figures), see :class:`TransformedBbox`. """ return Bbox(self.transform(bbox.get_points()))
""" Get the affine part of this transform. """
""" Get the Affine transformation array for the affine part of this transform.
"""
""" A convenience function that returns the transformed copy of a single point.
The point is given as a sequence of length :attr:`input_dims`. The transformed point is returned as a sequence of length :attr:`output_dims`. """ raise ValueError("The length of 'point' must be 'self.input_dims'")
""" Returns a transformed path.
*path*: a :class:`~matplotlib.path.Path` instance.
In some cases, this transform may insert curves into the path that began as line segments. """
""" Returns a path, transformed only by the affine part of this transform.
*path*: a :class:`~matplotlib.path.Path` instance.
``transform_path(path)`` is equivalent to ``transform_path_affine(transform_path_non_affine(values))``. """
""" Returns a path, transformed only by the non-affine part of this transform.
*path*: a :class:`~matplotlib.path.Path` instance.
``transform_path(path)`` is equivalent to ``transform_path_affine(transform_path_non_affine(values))``. """ {'interpolation_steps': path._interpolation_steps, 'should_simplify': path.should_simplify})
""" Performs transformation on a set of angles anchored at specific locations.
The *angles* must be a column vector (i.e., numpy array).
The *pts* must be a two-column numpy array of x,y positions (angle transforms currently only work in 2D). This array must have the same number of rows as *angles*.
*radians* indicates whether or not input angles are given in radians (True) or degrees (False; the default).
*pushoff* is the distance to move away from *pts* for determining transformed angles (see discussion of method below).
The transformed angles are returned in an array with the same size as *angles*.
The generic version of this method uses a very generic algorithm that transforms *pts*, as well as locations very close to *pts*, to find the angle in the transformed system. """ # Must be 2D if self.input_dims != 2 or self.output_dims != 2: raise NotImplementedError('Only defined in 2D')
if pts.shape[1] != 2: raise ValueError("'pts' must be array with 2 columns for x,y")
if angles.ndim != 1 or angles.shape[0] != pts.shape[0]: raise ValueError("'angles' must be a column vector and have same " "number of rows as 'pts'")
# Convert to radians if desired if not radians: angles = angles / 180.0 * np.pi
# Move a short distance away pts2 = pts + pushoff * np.c_[np.cos(angles), np.sin(angles)]
# Transform both sets of points tpts = self.transform(pts) tpts2 = self.transform(pts2)
# Calculate transformed angles d = tpts2 - tpts a = np.arctan2(d[:, 1], d[:, 0])
# Convert back to degrees if desired if not radians: a = np.rad2deg(a)
return a
""" Return the corresponding inverse transformation.
The return value of this method should be treated as temporary. An update to *self* does not cause a corresponding update to its inverted copy.
``x === self.inverted().transform(self.transform(x))`` """ raise NotImplementedError()
""" A helper class that holds a single child transform and acts equivalently to it.
This is useful if a node of the transform tree must be replaced at run time with a transform of a different type. This class allows that replacement to correctly trigger invalidation.
Note that :class:`TransformWrapper` instances must have the same input and output dimensions during their entire lifetime, so the child transform may only be replaced with another child transform of the same dimensions. """
""" *child*: A class:`Transform` instance. This child may later be replaced with :meth:`set`. """ raise ValueError("'child' must be an instance of " "'matplotlib.transform.Transform'")
def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._child)))
# note we do not wrap other properties here since the transform's # child can be changed with WrappedTransform.set and so checking # is_affine and other such properties may be dangerous.
""" Replace the current child of this transform with another one.
The new child must have the same number of input and output dimensions as the current child. """ child.output_dims != self.output_dims): raise ValueError( "The new child must have the same number of input and output " "dimensions as the current child")
return self._child.is_separable
""" The base class of all affine transformations of any number of dimensions. """
# optimises the access of the transform matrix vs the superclass
def _concat(a, b): """ Concatenates two transformation matrices (represented as numpy arrays) together. """ return np.dot(b, a)
return NotImplemented
raise NotImplementedError('Affine subclasses should override this ' 'method.')
path.codes, path._interpolation_steps)
""" The base class of all 2D affine transformations.
2D affine transformations are performed using a 3x3 numpy array::
a c e b d f 0 0 1
This class provides the read-only interface. For a mutable 2D affine transformation, use :class:`Affine2D`.
Subclasses of this class will generally only need to override a constructor and :meth:`get_matrix` that generates a custom 3x3 matrix. """
""" Return the values of the matrix as a sequence (a,b,c,d,e,f) """ mtx = self.get_matrix() return tuple(mtx[:2].swapaxes(0, 1).flatten())
def matrix_from_values(a, b, c, d, e, f): """ (staticmethod) Create a new transformation matrix as a 3x3 numpy array of the form::
a c e b d f 0 0 1 """ return np.array([[a, c, e], [b, d, f], [0.0, 0.0, 1.0]], float)
tpoints = affine_transform(points.data, mtx) return np.ma.MaskedArray(tpoints, mask=np.ma.getmask(points))
_transform_affine = transform_affine
def transform_affine(self, points): # The major speed trap here is just converting to the # points to an array in the first place. If we can use # more arrays upstream, that should help here. if not isinstance(points, (np.ma.MaskedArray, np.ndarray)): warnings.warn( ('A non-numpy array of type %s was passed in for ' + 'transformation. Please correct this.') % type(points)) return self._transform_affine(points)
shorthand_name = '(%s)-1' % self._shorthand_name
""" A mutable 2D affine transformation. """
""" Initialize an Affine transform from a 3x3 numpy float array::
a c e b d f 0 0 1
If *matrix* is None, initialize with the identity transform. """ # A bit faster than np.identity(3).
def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._mtx)))
def from_values(a, b, c, d, e, f): """ (staticmethod) Create a new Affine2D instance from the given values::
a c e b d f 0 0 1
. """ return Affine2D( np.array([a, c, e, b, d, f, 0.0, 0.0, 1.0], float).reshape((3, 3)))
""" Get the underlying transformation matrix as a 3x3 numpy array::
a c e b d f 0 0 1
. """
""" Set the underlying transformation matrix from a 3x3 numpy array::
a c e b d f 0 0 1
. """ self._mtx = mtx self.invalidate()
""" Set this transformation from the frozen copy of another :class:`Affine2DBase` object. """ if not isinstance(other, Affine2DBase): raise ValueError("'other' must be an instance of " "'matplotlib.transform.Affine2DBase'") self._mtx = other.get_matrix() self.invalidate()
def identity(): """ (staticmethod) Return a new :class:`Affine2D` object that is the identity transform.
Unless this transform will be mutated later on, consider using the faster :class:`IdentityTransform` class instead. """ return Affine2D()
""" Reset the underlying matrix to the identity transform. """ # A bit faster than np.identity(3).
""" Add a rotation (in radians) to this transform in place.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ float)
""" Add a rotation (in degrees) to this transform in place.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """
""" Add a rotation (in radians) around the point (x, y) in place.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ return self.translate(-x, -y).rotate(theta).translate(x, y)
""" Add a rotation (in degrees) around the point (x, y) in place.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ # Cast to float to avoid wraparound issues with uint8's
""" Adds a translation in place.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ [[1.0, 0.0, tx], [0.0, 1.0, ty], [0.0, 0.0, 1.0]], float)
""" Adds a scale in place.
If *sy* is None, the same scale is applied in both the *x*- and *y*-directions.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ [[sx, 0.0, 0.0], [0.0, sy, 0.0], [0.0, 0.0, 1.0]], float)
""" Adds a skew in place.
*xShear* and *yShear* are the shear angles along the *x*- and *y*-axes, respectively, in radians.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ rotX = np.tan(xShear) rotY = np.tan(yShear) skew_mtx = np.array( [[1.0, rotX, 0.0], [rotY, 1.0, 0.0], [0.0, 0.0, 1.0]], float) self._mtx = np.dot(skew_mtx, self._mtx) self.invalidate() return self
""" Adds a skew in place.
*xShear* and *yShear* are the shear angles along the *x*- and *y*-axes, respectively, in degrees.
Returns *self*, so this method can easily be chained with more calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate` and :meth:`scale`. """ return self.skew(np.deg2rad(xShear), np.deg2rad(yShear))
""" A special class that does one thing, the identity transform, in a fast way. """
def __str__(self): return ("{}()" .format(type(self).__name__))
""" A "blended" transform uses one transform for the *x*-direction, and another transform for the *y*-direction.
This "generic" version can handle any given child transform in the *x*- and *y*-directions. """
""" Create a new "blended" transform using *x_transform* to transform the *x*-axis and *y_transform* to transform the *y*-axis.
You will generally not call this constructor directly but use the :func:`blended_transform_factory` function instead, which can determine automatically which kind of blended transform to create. """ # Here we ask: "Does it blend?"
# Note, this is an exact copy of BlendedAffine2D.__eq__ return (self._x == other._x) and (self._y == other._y) else:
# Note, this is an exact copy of BlendedAffine2D.contains_branch_seperately
def depth(self): return max(self._x.depth, self._y.depth)
# a blended transform cannot possibly contain a branch from two different transforms. return False
return self._x.has_inverse and self._y.has_inverse
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._x), _indent_str(self._y)))
x = self._x y = self._y
if x == y and x.input_dims == 2: return x.transform_non_affine(points)
if x.input_dims == 2: x_points = x.transform_non_affine(points)[:, 0:1] else: x_points = x.transform_non_affine(points[:, 0]) x_points = x_points.reshape((len(x_points), 1))
if y.input_dims == 2: y_points = y.transform_non_affine(points)[:, 1:] else: y_points = y.transform_non_affine(points[:, 1]) y_points = y_points.reshape((len(y_points), 1))
if (isinstance(x_points, np.ma.MaskedArray) or isinstance(y_points, np.ma.MaskedArray)): return np.ma.concatenate((x_points, y_points), 1) else: return np.concatenate((x_points, y_points), 1)
return BlendedGenericTransform(self._x.inverted(), self._y.inverted())
self._affine = self._x.get_affine() else: # This works because we already know the transforms are # separable, though normally one would want to set b and # c to zero.
""" A "blended" transform uses one transform for the *x*-direction, and another transform for the *y*-direction.
This version is an optimization for the case where both child transforms are of type :class:`Affine2DBase`. """
""" Create a new "blended" transform using *x_transform* to transform the *x*-axis and *y_transform* to transform the *y*-axis.
Both *x_transform* and *y_transform* must be 2D affine transforms.
You will generally not call this constructor directly but use the :func:`blended_transform_factory` function instead, which can determine automatically which kind of blended transform to create. """ raise ValueError("Both *x_transform* and *y_transform* must be 2D " "affine transforms")
# Note, this is an exact copy of BlendedGenericTransform.__eq__ return (self._x == other._x) and (self._y == other._y) else: return NotImplemented
# Note, this is an exact copy of BlendedTransform.contains_branch_seperately return self._x.contains_branch(transform), self._y.contains_branch(transform)
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._x), _indent_str(self._y)))
else: # This works because we already know the transforms are # separable, though normally one would want to set b and # c to zero.
""" Create a new "blended" transform using *x_transform* to transform the *x*-axis and *y_transform* to transform the *y*-axis.
A faster version of the blended transform is returned for the case where both child transforms are affine. """ and isinstance(y_transform, Affine2DBase)):
""" A composite transform formed by applying transform *a* then transform *b*.
This "generic" version can handle any two arbitrary transformations. """
""" Create a new composite transform that is the result of applying transform *a* then transform *b*.
You will generally not call this constructor directly but use the :func:`composite_transform_factory` function instead, which can automatically choose the best kind of composite transform instance to create. """ raise ValueError("The output dimension of 'a' must be equal to " "the input dimensions of 'b'")
return frozen
# In some cases for a composite transform, an invalidating call to AFFINE_ONLY needs # to be extended to invalidate the NON_AFFINE part too. These cases are when the right # hand transform is non-affine and either: # (a) the left hand transform is non affine # (b) it is the left hand node which has triggered the invalidation and not self._b.is_affine \ and (not self._a.is_affine or invalidating_node is self._a):
invalidating_node=invalidating_node)
and self._b == other._b) else:
def depth(self):
return self._a.is_separable and self._b.is_separable
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._a), _indent_str(self._b)))
else: self._a.transform(points))
else: self._a.transform_path(path))
else: self._a.get_affine().get_matrix()))
""" A composite transform formed by applying transform *a* then transform *b*.
This version is an optimization that handles the case where both *a* and *b* are 2D affines. """ """ Create a new composite transform that is the result of applying transform *a* then transform *b*.
Both *a* and *b* must be instances of :class:`Affine2DBase`.
You will generally not call this constructor directly but use the :func:`composite_transform_factory` function instead, which can automatically choose the best kind of composite transform instance to create. """ raise ValueError("'a' and 'b' must be affine transforms") raise ValueError("The output dimension of 'a' must be equal to " "the input dimensions of 'b'")
def depth(self):
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._a), _indent_str(self._b)))
self._b.get_matrix(), self._a.get_matrix())
""" Create a new composite transform that is the result of applying transform a then transform b.
Shortcut versions of the blended transform are provided for the case where both child transforms are affine, or one or the other is the identity transform.
Composite transforms may also be created using the '+' operator, e.g.::
c = a + b """ # check to see if any of a or b are IdentityTransforms. We use # isinstance here to guarantee that the transforms will *always* # be IdentityTransforms. Since TransformWrappers are mutable, # use of equality here would be wrong.
""" :class:`BboxTransform` linearly transforms points from one :class:`Bbox` to another :class:`Bbox`. """
""" Create a new :class:`BboxTransform` that linearly transforms points from *boxin* to *boxout*. """ if not boxin.is_bbox or not boxout.is_bbox: raise ValueError("'boxin' and 'boxout' must be bbox")
Affine2DBase.__init__(self, **kwargs) self._boxin = boxin self._boxout = boxout self.set_children(boxin, boxout) self._mtx = None self._inverted = None
def __str__(self): return ("{}(\n" "{},\n" "{})" .format(type(self).__name__, _indent_str(self._boxin), _indent_str(self._boxout)))
if self._invalid: inl, inb, inw, inh = self._boxin.bounds outl, outb, outw, outh = self._boxout.bounds x_scale = outw / inw y_scale = outh / inh if DEBUG and (x_scale == 0 or y_scale == 0): raise ValueError("Transforming from or to a singular bounding box.") self._mtx = np.array([[x_scale, 0.0 , (-inl*x_scale+outl)], [0.0 , y_scale, (-inb*y_scale+outb)], [0.0 , 0.0 , 1.0 ]], float) self._inverted = None self._invalid = 0 return self._mtx
""" :class:`BboxTransformTo` is a transformation that linearly transforms points from the unit bounding box to a given :class:`Bbox`. """
""" Create a new :class:`BboxTransformTo` that linearly transforms points from the unit bounding box to *boxout*. """ raise ValueError("'boxout' must be bbox")
def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._boxout)))
raise ValueError("Transforming to a singular bounding box.") [ 0.0, outh, outb], [ 0.0, 0.0, 1.0]], float)
""" :class:`BboxTransformTo` is a transformation that linearly transforms points from the unit bounding box to a given :class:`Bbox` with a fixed upper left of (0, 0). """ if self._invalid: xmax, ymax = self._boxout.max if DEBUG and (xmax == 0 or ymax == 0): raise ValueError("Transforming to a singular bounding box.") self._mtx = np.array([[xmax, 0.0, 0.0], [ 0.0, ymax, 0.0], [ 0.0, 0.0, 1.0]], float) self._inverted = None self._invalid = 0 return self._mtx
""" :class:`BboxTransformFrom` linearly transforms points from a given :class:`Bbox` to the unit bounding box. """
raise ValueError("'boxin' must be bbox")
def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._boxin)))
raise ValueError("Transforming from a singular bounding box.") [0.0 , y_scale, (-inb*y_scale)], [0.0 , 0.0 , 1.0 ]], float)
""" A transformation that translates by *xt* and *yt*, after *xt* and *yt* have been transformad by the given transform *scale_trans*. """
def __str__(self): return ("{}(\n" "{})" .format(type(self).__name__, _indent_str(self._t)))
[0.0, 1.0, yt], [0.0, 0.0, 1.0]], float)
""" A :class:`TransformedPath` caches a non-affine transformed copy of the :class:`~matplotlib.path.Path`. This cached copy is automatically updated when the non-affine part of the transform changes.
.. note::
Paths are considered immutable by this class. Any update to the path's vertices/codes will not trigger a transform recomputation.
""" """ Create a new :class:`TransformedPath` from the given :class:`~matplotlib.path.Path` and :class:`Transform`. """ raise ValueError("'transform' must be an instance of " "'matplotlib.transform.Transform'")
# only recompute if the invalidation includes the non_affine part of the transform or self._transformed_path is None): self._transform.transform_path_non_affine(self._path) Path._fast_from_codes_and_verts( self._transform.transform_non_affine(self._path.vertices), None, {'interpolation_steps': self._path._interpolation_steps, 'should_simplify': self._path.should_simplify})
""" Return a copy of the child path, with the non-affine part of the transform already applied, along with the affine part of the path necessary to complete the transformation. Unlike :meth:`get_transformed_path_and_affine`, no interpolation will be performed. """ self._revalidate() return self._transformed_points, self.get_affine()
""" Return a copy of the child path, with the non-affine part of the transform already applied, along with the affine part of the path necessary to complete the transformation. """
""" Return a fully-transformed copy of the child path. """ self._revalidate() return self._transform.transform_path_affine(self._transformed_path)
""" A :class:`TransformedPatchPath` caches a non-affine transformed copy of the :class:`~matplotlib.path.Patch`. This cached copy is automatically updated when the non-affine part of the transform or the patch changes. """ """ Create a new :class:`TransformedPatchPath` from the given :class:`~matplotlib.path.Patch`. """
# Only recompute if the invalidation includes the non_affine part of # the transform, or the Patch's Path has changed. (self._invalid & self.INVALID_NON_AFFINE == self.INVALID_NON_AFFINE)): self._transform.transform_path_non_affine(patch_path) Path._fast_from_codes_and_verts( self._transform.transform_non_affine(patch_path.vertices), None, {'interpolation_steps': patch_path._interpolation_steps, 'should_simplify': patch_path.should_simplify})
""" Modify the endpoints of a range as needed to avoid singularities.
Parameters ---------- vmin, vmax : float The initial endpoints. expander : float, optional, default: 0.001 Fractional amount by which *vmin* and *vmax* are expanded if the original interval is too small, based on *tiny*. tiny : float, optional, default: 1e-15 Threshold for the ratio of the interval to the maximum absolute value of its endpoints. If the interval is smaller than this, it will be expanded. This value should be around 1e-15 or larger; otherwise the interval will be approaching the double precision resolution limit. increasing : bool, optional, default: True If True, swap *vmin*, *vmax* if *vmin* > *vmax*.
Returns ------- vmin, vmax : float Endpoints, expanded and/or swapped if necessary. If either input is inf or NaN, or if both inputs are 0 or very close to zero, it returns -*expander*, *expander*. """
return -expander, expander
if vmax == 0 and vmin == 0: vmin = -expander vmax = expander else: vmin -= expander*abs(vmin) vmax += expander*abs(vmax)
""" Check, inclusively, whether an interval includes a given value.
Parameters ---------- interval : sequence of scalar A 2-length sequence, endpoints that define the interval. val : scalar Value to check is within interval.
Returns ------- bool Returns true if given val is within the interval. """
""" Check, excluding endpoints, whether an interval includes a given value.
Parameters ---------- interval : sequence of scalar A 2-length sequence, endpoints that define the interval. val : scalar Value to check is within interval.
Returns ------- bool Returns true if given val is within the interval. """ a, b = interval return a < val < b or a > val > b
""" Return a new transform with an added offset.
Parameters ---------- trans : :class:`Transform` instance Any transform, to which offset will be applied. fig : :class:`~matplotlib.figure.Figure`, optional, default: None Current figure. It can be None if *units* are 'dots'. x, y : float, optional, default: 0.0 Specifies the offset to apply. units : {'inches', 'points', 'dots'}, optional Units of the offset.
Returns ------- trans : :class:`Transform` instance Transform with applied offset. """ if units == 'dots': return trans + Affine2D().translate(x, y) if fig is None: raise ValueError('For units of inches or points a fig kwarg is needed') if units == 'points': x /= 72.0 y /= 72.0 elif not units == 'inches': raise ValueError('units must be dots, points, or inches') return trans + ScaledTranslation(x, y, fig.dpi_scale_trans) |