"""
Matplotlib includes a framework for arbitrary geometric transformations that is used to
determine the final position of all elements drawn on the canvas.
Transforms are composed into trees of `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 figure:
.. graphviz:: /api/transforms.dot
:alt: Diagram of transform tree from data to figure coordinates.
The framework can be used for both affine and non-affine
transformations. However, for speed, we want to 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.
See the tutorial :ref:`transforms_tutorial` for examples
of how to use transforms.
"""
# 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.
import functools
import itertools
import textwrap
import weakref
import math
import numpy as np
from numpy.linalg import inv
from matplotlib import _api, _docstring
from matplotlib._path import affine_transform, count_bboxes_overlapping_bbox
from .path import Path
DEBUG = False
def _make_str_method(*args, **kwargs):
"""
Generate a ``__str__`` method for a `.Transform` subclass.
After ::
class T:
__str__ = _make_str_method("attr", key="other")
``str(T(...))`` will be
.. code-block:: text
{type(T).__name__}(
{self.attr},
key={self.other})
"""
indent = functools.partial(textwrap.indent, prefix=" " * 4)
def strrepr(x): return repr(x) if isinstance(x, str) else str(x)
return lambda self: (
type(self).__name__ + "("
+ ",".join([*(indent("\n" + strrepr(getattr(self, arg)))
for arg in args),
*(indent("\n" + k + "=" + strrepr(getattr(self, arg)))
for k, arg in kwargs.items())])
+ ")")
class TransformNode:
"""
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
# Possible values for the _invalid attribute.
_VALID, _INVALID_AFFINE_ONLY, _INVALID_FULL = range(3)
# Some metadata about the transform, used to determine whether an
# invalidation is affine-only
is_affine = False
pass_through = False
"""
If pass_through is True, all ancestors will always be
invalidated, even if 'self' is already invalid.
"""
def __init__(self, shorthand_name=None):
"""
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.
"""
self._parents = {}
# Initially invalid, until first computation.
self._invalid = self._INVALID_FULL
self._shorthand_name = shorthand_name or ''
if DEBUG:
def __str__(self):
# either just return the name of this TransformNode, or its repr
return self._shorthand_name or repr(self)
def __getstate__(self):
# turn the dictionary with weak values into a normal dictionary
return {**self.__dict__,
'_parents': {k: v() for k, v in self._parents.items()}}
def __setstate__(self, data_dict):
self.__dict__ = data_dict
# turn the normal dictionary back into a dictionary with weak values
# The extra lambda is to provide a callback to remove dead
# weakrefs from the dictionary when garbage collection is done.
self._parents = {
k: weakref.ref(v, lambda _, pop=self._parents.pop, k=k: pop(k))
for k, v in self._parents.items() if v is not None}
def __copy__(self):
cls = type(self)
other = cls.__new__(cls)
other.__dict__.update(self.__dict__)
# If `c = a + b; a1 = copy(a)`, then modifications to `a1` do not
# propagate back to `c`, i.e. we need to clear the parents of `a1`.
other._parents = {}
# If `c = a + b; c1 = copy(c)`, then modifications to `a` also need to
# be propagated to `c1`.
for key, val in vars(self).items():
if isinstance(val, TransformNode) and id(self) in val._parents:
other.set_children(val) # val == getattr(other, key)
return other
def invalidate(self):
"""
Invalidate this `TransformNode` and triggers an invalidation of its
ancestors. Should be called any time the transform changes.
"""
self._invalidate_internal(
level=self._INVALID_AFFINE_ONLY if self.is_affine else self._INVALID_FULL,
invalidating_node=self)
def _invalidate_internal(self, level, invalidating_node):
"""
Called by :meth:`invalidate` and subsequently ascends the transform
stack calling each TransformNode's _invalidate_internal method.
"""
# If we are already more invalid than the currently propagated invalidation,
# then we don't need to do anything.
if level 0 or height > 0) and width < np.inf and height < np.inf
def containsx(self, x):
"""
Return whether *x* is in the closed (:attr:`x0`, :attr:`x1`) interval.
"""
x0, x1 = self.intervalx
return x0 = x1
def containsy(self, y):
"""
Return whether *y* is in the closed (:attr:`y0`, :attr:`y1`) interval.
"""
y0, y1 = self.intervaly
return y0 = y1
def contains(self, x, y):
"""
Return whether ``(x, y)`` is in the bounding box or on its edge.
"""
return self.containsx(x) and self.containsy(y)
def overlaps(self, other):
"""
Return 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 y1
def fully_contains(self, x, y):
"""
Return whether ``x, y`` is in the bounding box, but not on its edge.
"""
return self.fully_containsx(x) and self.fully_containsy(y)
def fully_overlaps(self, other):
"""
Return 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
def transformed(self, transform):
"""
Construct a `Bbox` by statically transforming this one by *transform*.
"""
pts = self.get_points()
ll, ul, lr = transform.transform(np.array(
[pts[0], [pts[0, 0], pts[1, 1]], [pts[1, 0], pts[0, 1]]]))
return Bbox([ll, [lr[0], ul[1]]])
coefs = {'C': (0.5, 0.5),
'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)}
def anchored(self, c, container):
"""
Return a copy of the `Bbox` anchored to *c* within *container*.
Parameters
----------
c : (float, float) or {'C', 'SW', 'S', 'SE', 'E', 'NE', ...}
Either an (*x*, *y*) pair of relative coordinates (0 is left or
bottom, 1 is right or top), 'C' (center), or a cardinal direction
('SW', southwest, is bottom left, etc.).
container : `Bbox`
The box within which the `Bbox` is positioned.
See Also
--------
.Axes.set_anchor
"""
l, b, w, h = container.bounds
L, B, W, H = self.bounds
cx, cy = self.coefs[c] if isinstance(c, str) else c
return Bbox(self._points +
[(l + cx * (w - W)) - L,
(b + cy * (h - H)) - B])
def shrunk(self, mx, my):
"""
Return a copy of the `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]])
def shrunk_to_aspect(self, box_aspect, container=None, fig_aspect=1.0):
"""
Return a copy of the `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 (i.e.
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.
"""
if box_aspect 0: # Fast path for all-positive x values
minpos[0] = min(minpos[0], minx)
else:
minpos[0] = min(minpos[0], np.min(x[x > 0], initial=np.inf))
if updatey:
y = path.vertices[..., 1][valid_points]
miny = np.min(y, initial=np.inf)
points[0, 1] = min(points[0, 1], miny)
points[1, 1] = max(points[1, 1], np.max(y, initial=-np.inf))
if miny > 0: # Fast path for all-positive y values
minpos[1] = min(minpos[1], miny)
else:
minpos[1] = min(minpos[1], np.min(y[y > 0], initial=np.inf))
if np.any(points != self._points) or np.any(minpos != self._minpos):
self.invalidate()
if updatex:
self._points[:, 0] = points[:, 0]
self._minpos[0] = minpos[0]
if updatey:
self._points[:, 1] = points[:, 1]
self._minpos[1] = minpos[1]
def update_from_data_x(self, x, ignore=None):
"""
Update the x-bounds of the `Bbox` based on the passed in data. After
updating, the bounds will have positive *width*, and *x0* will be the
minimal value.
Parameters
----------
x : `~numpy.ndarray`
Array of x-values.
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
"""
x = np.ravel(x)
# The y-component in np.array([x, *y*]).T is not used. We simply pass
# x again to not spend extra time on creating an array of unused data
self.update_from_data_xy(np.array([x, x]).T, ignore=ignore, updatey=False)
def update_from_data_y(self, y, ignore=None):
"""
Update the y-bounds of the `Bbox` based on the passed in data. After
updating, the bounds will have positive *height*, and *y0* will be the
minimal value.
Parameters
----------
y : `~numpy.ndarray`
Array of y-values.
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
"""
y = np.ravel(y)
# The x-component in np.array([*x*, y]).T is not used. We simply pass
# y again to not spend extra time on creating an array of unused data
self.update_from_data_xy(np.array([y, y]).T, ignore=ignore, updatex=False)
def update_from_data_xy(self, xy, ignore=None, updatex=True, updatey=True):
"""
Update the `Bbox` bounds based on the passed in *xy* coordinates.
After updating, the bounds will have positive *width* and *height*;
*x0* and *y0* will be the minimal values.
Parameters
----------
xy : (N, 2) array-like
The (x, y) coordinates.
ignore : bool, optional
- When ``True``, ignore the existing bounds of the `Bbox`.
- When ``False``, include the existing bounds of the `Bbox`.
- When ``None``, use the last value passed to :meth:`ignore`.
updatex, updatey : bool, default: True
When ``True``, update the x/y values.
"""
if len(xy) == 0:
return
path = Path(xy)
self.update_from_path(path, ignore=ignore,
updatex=updatex, updatey=updatey)
@BboxBase.x0.setter
def x0(self, val):
self._points[0, 0] = val
self.invalidate()
@BboxBase.y0.setter
def y0(self, val):
self._points[0, 1] = val
self.invalidate()
@BboxBase.x1.setter
def x1(self, val):
self._points[1, 0] = val
self.invalidate()
@BboxBase.y1.setter
def y1(self, val):
self._points[1, 1] = val
self.invalidate()
@BboxBase.p0.setter
def p0(self, val):
self._points[0] = val
self.invalidate()
@BboxBase.p1.setter
def p1(self, val):
self._points[1] = val
self.invalidate()
@BboxBase.intervalx.setter
def intervalx(self, interval):
self._points[:, 0] = interval
self.invalidate()
@BboxBase.intervaly.setter
def intervaly(self, interval):
self._points[:, 1] = interval
self.invalidate()
@BboxBase.bounds.setter
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()
@property
def minpos(self):
"""
The minimum positive value in both directions within the Bbox.
This is useful when dealing with logarithmic scales and other scales
where negative bounds result in floating point errors, and will be used
as the minimum extent instead of *p0*.
"""
return self._minpos
@minpos.setter
def minpos(self, val):
self._minpos[:] = val
@property
def minposx(self):
"""
The minimum positive value in the *x*-direction within the Bbox.
This is useful when dealing with logarithmic scales and other scales
where negative bounds result in floating point errors, and will be used
as the minimum *x*-extent instead of *x0*.
"""
return self._minpos[0]
@minposx.setter
def minposx(self, val):
self._minpos[0] = val
@property
def minposy(self):
"""
The minimum positive value in the *y*-direction within the Bbox.
This is useful when dealing with logarithmic scales and other scales
where negative bounds result in floating point errors, and will be used
as the minimum *y*-extent instead of *y0*.
"""
return self._minpos[1]
@minposy.setter
def minposy(self, val):
self._minpos[1] = val
def get_points(self):
"""
Get the points of the bounding box as an array of the form
``[[x0, y0], [x1, y1]]``.
"""
self._invalid = 0
return self._points
def set_points(self, points):
"""
Set the points of the bounding box directly from an 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()
def set(self, other):
"""
Set this bounding box from the "frozen" bounds of another `Bbox`.
"""
if np.any(self._points != other.get_points()):
self._points = other.get_points()
self.invalidate()
def mutated(self):
"""Return whether the bbox has changed since init."""
return self.mutatedx() or self.mutatedy()
def mutatedx(self):
"""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])
def mutatedy(self):
"""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])
class TransformedBbox(BboxBase):
"""
A `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.
"""
def __init__(self, bbox, transform, **kwargs):
"""
Parameters
----------
bbox : `Bbox`
transform : `Transform`
"""
_api.check_isinstance(BboxBase, bbox=bbox)
_api.check_isinstance(Transform, transform=transform)
if transform.input_dims != 2 or transform.output_dims != 2:
raise ValueError(
"The input and output dimensions of 'transform' must be 2")
super().__init__(**kwargs)
self._bbox = bbox
self._transform = transform
self.set_children(bbox, transform)
self._points = None
__str__ = _make_str_method("_bbox", "_transform")
def get_points(self):
# docstring inherited
if self._invalid:
p = self._bbox.get_points()
# Transform all four points, then make a new bounding box
# from the result, taking care to make the orientation the
# same.
points = self._transform.transform(
[[p[0, 0], p[0, 1]],
[p[1, 0], p[0, 1]],
[p[0, 0], p[1, 1]],
[p[1, 0], p[1, 1]]])
points = np.ma.filled(points, 0.0)
xs = min(points[:, 0]), max(points[:, 0])
if p[0, 0] > p[1, 0]:
xs = xs[::-1]
ys = min(points[:, 1]), max(points[:, 1])
if p[0, 1] > p[1, 1]:
ys = ys[::-1]
self._points = np.array([
[xs[0], ys[0]],
[xs[1], ys[1]]
])
self._invalid = 0
return self._points
if DEBUG:
_get_points = get_points
def get_points(self):
points = self._get_points()
self._check(points)
return points
def contains(self, x, y):
# Docstring inherited.
return self._bbox.contains(*self._transform.inverted().transform((x, y)))
def fully_contains(self, x, y):
# Docstring inherited.
return self._bbox.fully_contains(*self._transform.inverted().transform((x, y)))
class LockableBbox(BboxBase):
"""
A `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.
"""
def __init__(self, bbox, x0=None, y0=None, x1=None, y1=None, **kwargs):
"""
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.
"""
_api.check_isinstance(BboxBase, bbox=bbox)
super().__init__(**kwargs)
self._bbox = bbox
self.set_children(bbox)
self._points = None
fp = [x0, y0, x1, y1]
mask = [val is None for val in fp]
self._locked_points = np.ma.array(fp, float, mask=mask).reshape((2, 2))
__str__ = _make_str_method("_bbox", "_locked_points")
def get_points(self):
# docstring inherited
if self._invalid:
points = self._bbox.get_points()
self._points = np.where(self._locked_points.mask,
points,
self._locked_points)
self._invalid = 0
return self._points
if DEBUG:
_get_points = get_points
def get_points(self):
points = self._get_points()
self._check(points)
return points
@property
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]
@locked_x0.setter
def locked_x0(self, x0):
self._locked_points.mask[0, 0] = x0 is None
self._locked_points.data[0, 0] = x0
self.invalidate()
@property
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]
@locked_y0.setter
def locked_y0(self, y0):
self._locked_points.mask[0, 1] = y0 is None
self._locked_points.data[0, 1] = y0
self.invalidate()
@property
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]
@locked_x1.setter
def locked_x1(self, x1):
self._locked_points.mask[1, 0] = x1 is None
self._locked_points.data[1, 0] = x1
self.invalidate()
@property
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]
@locked_y1.setter
def locked_y1(self, y1):
self._locked_points.mask[1, 1] = y1 is None
self._locked_points.data[1, 1] = y1
self.invalidate()
class Transform(TransformNode):
"""
The base class of all `TransformNode` instances that
actually perform a transformation.
All non-affine transformations should be subclasses of this class.
New affine transformations should be subclasses of `Affine2D`.
Subclasses of this class should override the following members (at
minimum):
- :attr:`input_dims`
- :attr:`output_dims`
- :meth:`transform`
- :meth:`inverted` (if an inverse exists)
The following attributes may be overridden if the default is unsuitable:
- :attr:`is_separable` (defaults to True for 1D -> 1D transforms, False
otherwise)
- :attr:`has_inverse` (defaults to True if :meth:`inverted` is overridden,
False otherwise)
If the transform needs to do something non-standard with
`matplotlib.path.Path` objects, such as adding curves
where there were once line segments, it should override:
- :meth:`transform_path`
"""
input_dims = None
"""
The number of input dimensions of this transform.
Must be overridden (with integers) in the subclass.
"""
output_dims = None
"""
The number of output dimensions of this transform.
Must be overridden (with integers) in the subclass.
"""
is_separable = False
"""True if this transform is separable in the x- and y- dimensions."""
has_inverse = False
"""True if this transform has a corresponding inverse transform."""
def __init_subclass__(cls):
# 1d transforms are always separable; we assume higher-dimensional ones
# are not but subclasses can also directly set is_separable -- this is
# verified by checking whether "is_separable" appears more than once in
# the class's MRO (it appears once in Transform).
if (sum("is_separable" in vars(parent) for parent in cls.__mro__) == 1
and cls.input_dims == cls.output_dims == 1):
cls.is_separable = True
# Transform.inverted raises NotImplementedError; we assume that if this
# is overridden then the transform is invertible but subclass can also
# directly set has_inverse.
if (sum("has_inverse" in vars(parent) for parent in cls.__mro__) == 1
and hasattr(cls, "inverted")
and cls.inverted is not Transform.inverted):
cls.has_inverse = True
def __add__(self, other):
"""
Compose two transforms together so that *self* is followed by *other*.
``A + B`` returns a transform ``C`` so that
``C.transform(x) == B.transform(A.transform(x))``.
"""
return (composite_transform_factory(self, other)
if isinstance(other, Transform) else
NotImplemented)
# 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.
def _iter_break_from_left_to_right(self):
"""
Return 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).
"""
yield IdentityTransform(), self
@property
def depth(self):
"""
Return 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 1
def contains_branch(self, other):
"""
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.
"""
if self.depth < other.depth:
return False
# check that a subtree is equal to other (starting from self)
for _, sub_tree in self._iter_break_from_left_to_right():
if sub_tree == other:
return True
return False
def contains_branch_separately(self, other_transform):
"""
Return 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_separately(ax.transData)
"""
if self.output_dims != 2:
raise ValueError('contains_branch_separately only supports '
'transforms with 2 output dimensions')
# for a non-blended transform each separate dimension is the same, so
# just return the appropriate shape.
return (self.contains_branch(other_transform), ) * 2
# Permanent alias for backwards compatibility (historical typo)
def contains_branch_seperately(self, other_transform):
""":meta private:"""
return self.contains_branch_separately(other_transform)
def __sub__(self, other):
"""
Compose *self* with the inverse of *other*, cancelling identical terms
if any::
# In general:
A - B == A + B.inverted()
# (but see note regarding frozen transforms below).
# If A "ends with" B (i.e. A == A' + B for some A') we can cancel
# out B:
(A' + B) - B == A'
# Likewise, if B "starts with" A (B = A + B'), we can cancel out A:
A - (A + B') == B'.inverted() == B'^-1
Cancellation (rather than naively returning ``A + B.inverted()``) is
important for multiple reasons:
- It avoids floating-point inaccuracies when computing the inverse of
B: ``B - B`` is guaranteed to cancel out exactly (resulting in the
identity transform), whereas ``B + B.inverted()`` may differ by a
small epsilon.
- ``B.inverted()`` always returns a frozen transform: if one computes
``A + B + B.inverted()`` and later mutates ``B``, then
``B.inverted()`` won't be updated and the last two terms won't cancel
out anymore; on the other hand, ``A + B - B`` will always be equal to
``A`` even if ``B`` is mutated.
"""
# we only know how to do this operation if other is a Transform.
if not isinstance(other, Transform):
return NotImplemented
for remainder, sub_tree in self._iter_break_from_left_to_right():
if sub_tree == other:
return remainder
for remainder, sub_tree in other._iter_break_from_left_to_right():
if sub_tree == self:
if not remainder.has_inverse:
raise ValueError(
"The shortcut cannot be computed since 'other' "
"includes a non-invertible component")
return remainder.inverted()
# if we have got this far, then there was no shortcut possible
if other.has_inverse:
return self + other.inverted()
else:
raise ValueError('It is not possible to compute transA - transB '
'since transB cannot be inverted and there is no '
'shortcut possible.')
def __array__(self, *args, **kwargs):
"""Array interface to get at this Transform's affine matrix."""
return self.get_affine().get_matrix()
def transform(self, values):
"""
Apply this transformation on the given array of *values*.
Parameters
----------
values : array-like
The input values as an array of length :attr:`~Transform.input_dims` or
shape (N, :attr:`~Transform.input_dims`).
Returns
-------
array
The output values as an array of length :attr:`~Transform.output_dims` or
shape (N, :attr:`~Transform.output_dims`), depending on the input.
"""
# Ensure that values is a 2d array (but remember whether
# we started with a 1d or 2d array).
values = np.asanyarray(values)
ndim = values.ndim
values = values.reshape((-1, self.input_dims))
# Transform the values
res = self.transform_affine(self.transform_non_affine(values))
# Convert the result back to the shape of the input values.
if ndim == 0:
assert not np.ma.is_masked(res) # just to be on the safe side
return res[0, 0]
if ndim == 1:
return res.reshape(-1)
elif ndim == 2:
return res
raise ValueError(
"Input values must have shape (N, {dims}) or ({dims},)"
.format(dims=self.input_dims))
def transform_affine(self, values):
"""
Apply 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)``.
Parameters
----------
values : array
The input values as an array of length :attr:`~Transform.input_dims` or
shape (N, :attr:`~Transform.input_dims`).
Returns
-------
array
The output values as an array of length :attr:`~Transform.output_dims` or
shape (N, :attr:`~Transform.output_dims`), depending on the input.
"""
return self.get_affine().transform(values)
def transform_non_affine(self, values):
"""
Apply only the non-affine part of this 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.
Parameters
----------
values : array
The input values as an array of length
:attr:`~matplotlib.transforms.Transform.input_dims` or
shape (N, :attr:`~matplotlib.transforms.Transform.input_dims`).
Returns
-------
array
The output values as an array of length
:attr:`~matplotlib.transforms.Transform.output_dims` or shape
(N, :attr:`~matplotlib.transforms.Transform.output_dims`),
depending on the input.
"""
return values
def transform_bbox(self, bbox):
"""
Transform the given bounding box.
For smarter transforms including caching (a common requirement in
Matplotlib), see `TransformedBbox`.
"""
return Bbox(self.transform(bbox.get_points()))
def get_affine(self):
"""Get the affine part of this transform."""
return IdentityTransform()
def get_matrix(self):
"""Get the matrix for the affine part of this transform."""
return self.get_affine().get_matrix()
def transform_point(self, point):
"""
Return a transformed point.
This function is only kept for backcompatibility; the more general
`.transform` method is capable of transforming both a list of points
and 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`.
"""
if len(point) != self.input_dims:
raise ValueError("The length of 'point' must be 'self.input_dims'")
return self.transform(point)
def transform_path(self, path):
"""
Apply the transform to `.Path` *path*, returning a new `.Path`.
In some cases, this transform may insert curves into the path
that began as line segments.
"""
return self.transform_path_affine(self.transform_path_non_affine(path))
def transform_path_affine(self, path):
"""
Apply the affine part of this transform to `.Path` *path*, returning a
new `.Path`.
``transform_path(path)`` is equivalent to
``transform_path_affine(transform_path_non_affine(values))``.
"""
return self.get_affine().transform_path_affine(path)
def transform_path_non_affine(self, path):
"""
Apply the non-affine part of this transform to `.Path` *path*,
returning a new `.Path`.
``transform_path(path)`` is equivalent to
``transform_path_affine(transform_path_non_affine(values))``.
"""
x = self.transform_non_affine(path.vertices)
return Path._fast_from_codes_and_verts(x, path.codes, path)
def transform_angles(self, angles, pts, radians=False, pushoff=1e-5):
"""
Transform a set of angles anchored at specific locations.
Parameters
----------
angles : (N,) array-like
The angles to transform.
pts : (N, 2) array-like
The points where the angles are anchored.
radians : bool, default: False
Whether *angles* are radians or degrees.
pushoff : float
For each point in *pts* and angle in *angles*, the transformed
angle is computed by transforming a segment of length *pushoff*
starting at that point and making that angle relative to the
horizontal axis, and measuring the angle between the horizontal
axis and the transformed segment.
Returns
-------
(N,) array
"""
# Must be 2D
if self.input_dims != 2 or self.output_dims != 2:
raise NotImplementedError('Only defined in 2D')
angles = np.asarray(angles)
pts = np.asarray(pts)
_api.check_shape((None, 2), pts=pts)
_api.check_shape((None,), angles=angles)
if len(angles) != len(pts):
raise ValueError("There must be as many 'angles' as 'pts'")
# Convert to radians if desired
if not radians:
angles = np.deg2rad(angles)
# Move a short distance away
pts2 = pts + pushoff * np.column_stack([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
def inverted(self):
"""
Return the corresponding inverse transformation.
It holds ``x == self.inverted().transform(self.transform(x))``.
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.
"""
raise NotImplementedError()
class TransformWrapper(Transform):
"""
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.
`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.
"""
pass_through = True
def __init__(self, child):
"""
*child*: A `Transform` instance. This child may later
be replaced with :meth:`set`.
"""
_api.check_isinstance(Transform, child=child)
super().__init__()
self.set(child)
def __eq__(self, other):
return self._child.__eq__(other)
__str__ = _make_str_method("_child")
def frozen(self):
# docstring inherited
return self._child.frozen()
def set(self, child):
"""
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.
"""
if hasattr(self, "_child"): # Absent during init.
self.invalidate()
new_dims = (child.input_dims, child.output_dims)
old_dims = (self._child.input_dims, self._child.output_dims)
if new_dims != old_dims:
raise ValueError(
f"The input and output dims of the new child {new_dims} "
f"do not match those of current child {old_dims}")
self._child._parents.pop(id(self), None)
self._child = child
self.set_children(child)
self.transform = child.transform
self.transform_affine = child.transform_affine
self.transform_non_affine = child.transform_non_affine
self.transform_path = child.transform_path
self.transform_path_affine = child.transform_path_affine
self.transform_path_non_affine = child.transform_path_non_affine
self.get_affine = child.get_affine
self.inverted = child.inverted
self.get_matrix = child.get_matrix
# 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.
self._invalid = 0
self.invalidate()
self._invalid = 0
input_dims = property(lambda self: self._child.input_dims)
output_dims = property(lambda self: self._child.output_dims)
is_affine = property(lambda self: self._child.is_affine)
is_separable = property(lambda self: self._child.is_separable)
has_inverse = property(lambda self: self._child.has_inverse)
class AffineBase(Transform):
"""
The base class of all affine transformations of any number of dimensions.
"""
is_affine = True
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
self._inverted = None
def __array__(self, *args, **kwargs):
# optimises the access of the transform matrix vs. the superclass
return self.get_matrix()
def __eq__(self, other):
if getattr(other, "is_affine", False) and hasattr(other, "get_matrix"):
return (self.get_matrix() == other.get_matrix()).all()
return NotImplemented
def transform(self, values):
# docstring inherited
return self.transform_affine(values)
def transform_affine(self, values):
# docstring inherited
raise NotImplementedError('Affine subclasses should override this '
'method.')
def transform_non_affine(self, values):
# docstring inherited
return values
def transform_path(self, path):
# docstring inherited
return self.transform_path_affine(path)
def transform_path_affine(self, path):
# docstring inherited
return Path(self.transform_affine(path.vertices),
path.codes, path._interpolation_steps)
def transform_path_non_affine(self, path):
# docstring inherited
return path
def get_affine(self):
# docstring inherited
return self
class Affine2DBase(AffineBase):
"""
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 `Affine2D`.
Subclasses of this class will generally only need to override a
constructor and `~.Transform.get_matrix` that generates a custom 3x3 matrix.
"""
input_dims = 2
output_dims = 2
def frozen(self):
# docstring inherited
return Affine2D(self.get_matrix().copy())
@property
def is_separable(self):
mtx = self.get_matrix()
return mtx[0, 1] == mtx[1, 0] == 0.0
def to_values(self):
"""
Return the values of the matrix as an ``(a, b, c, d, e, f)`` tuple.
"""
mtx = self.get_matrix()
return tuple(mtx[:2].swapaxes(0, 1).flat)
def transform_affine(self, values):
mtx = self.get_matrix()
if isinstance(values, np.ma.MaskedArray):
tpoints = affine_transform(values.data, mtx)
return np.ma.MaskedArray(tpoints, mask=np.ma.getmask(values))
return affine_transform(values, mtx)
if DEBUG:
_transform_affine = transform_affine
def transform_affine(self, values):
# docstring inherited
# 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(values, np.ndarray):
_api.warn_external(
f'A non-numpy array of type {type(values)} was passed in '
f'for transformation, which results in poor performance.')
return self._transform_affine(values)
def inverted(self):
# docstring inherited
if self._inverted is None or self._invalid:
mtx = self.get_matrix()
shorthand_name = None
if self._shorthand_name:
shorthand_name = '(%s)-1' % self._shorthand_name
self._inverted = Affine2D(inv(mtx), shorthand_name=shorthand_name)
self._invalid = 0
return self._inverted
class Affine2D(Affine2DBase):
"""
A mutable 2D affine transformation.
"""
def __init__(self, matrix=None, **kwargs):
"""
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.
"""
super().__init__(**kwargs)
if matrix is None:
# A bit faster than np.identity(3).
matrix = IdentityTransform._mtx
self._mtx = matrix.copy()
self._invalid = 0
_base_str = _make_str_method("_mtx")
def __str__(self):
return (self._base_str()
if (self._mtx != np.diag(np.diag(self._mtx))).any()
else f"Affine2D().scale({self._mtx[0, 0]}, {self._mtx[1, 1]})"
if self._mtx[0, 0] != self._mtx[1, 1]
else f"Affine2D().scale({self._mtx[0, 0]})")
@staticmethod
def from_values(a, b, c, d, e, f):
"""
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)))
def get_matrix(self):
"""
Get the underlying transformation matrix as a 3x3 array::
a c e
b d f
0 0 1
.
"""
if self._invalid:
self._inverted = None
self._invalid = 0
return self._mtx
def set_matrix(self, mtx):
"""
Set the underlying transformation matrix from a 3x3 array::
a c e
b d f
0 0 1
.
"""
self._mtx = mtx
self.invalidate()
def set(self, other):
"""
Set this transformation from the frozen copy of another
`Affine2DBase` object.
"""
_api.check_isinstance(Affine2DBase, other=other)
self._mtx = other.get_matrix()
self.invalidate()
def clear(self):
"""
Reset the underlying matrix to the identity transform.
"""
# A bit faster than np.identity(3).
self._mtx = IdentityTransform._mtx.copy()
self.invalidate()
return self
def rotate(self, theta):
"""
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`.
"""
a = math.cos(theta)
b = math.sin(theta)
mtx = self._mtx
# Operating and assigning one scalar at a time is much faster.
(xx, xy, x0), (yx, yy, y0), _ = mtx.tolist()
# mtx = [[a -b 0], [b a 0], [0 0 1]] * mtx
mtx[0, 0] = a * xx - b * yx
mtx[0, 1] = a * xy - b * yy
mtx[0, 2] = a * x0 - b * y0
mtx[1, 0] = b * xx + a * yx
mtx[1, 1] = b * xy + a * yy
mtx[1, 2] = b * x0 + a * y0
self.invalidate()
return self
def rotate_deg(self, degrees):
"""
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`.
"""
return self.rotate(math.radians(degrees))
def rotate_around(self, x, y, theta):
"""
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)
def rotate_deg_around(self, x, y, degrees):
"""
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
x, y = float(x), float(y)
return self.translate(-x, -y).rotate_deg(degrees).translate(x, y)
def translate(self, tx, ty):
"""
Add 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`.
"""
self._mtx[0, 2] += tx
self._mtx[1, 2] += ty
self.invalidate()
return self
def scale(self, sx, sy=None):
"""
Add 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`.
"""
if sy is None:
sy = sx
# explicit element-wise scaling is fastest
self._mtx[0, 0] *= sx
self._mtx[0, 1] *= sx
self._mtx[0, 2] *= sx
self._mtx[1, 0] *= sy
self._mtx[1, 1] *= sy
self._mtx[1, 2] *= sy
self.invalidate()
return self
def skew(self, xShear, yShear):
"""
Add 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`.
"""
rx = math.tan(xShear)
ry = math.tan(yShear)
mtx = self._mtx
# Operating and assigning one scalar at a time is much faster.
(xx, xy, x0), (yx, yy, y0), _ = mtx.tolist()
# mtx = [[1 rx 0], [ry 1 0], [0 0 1]] * mtx
mtx[0, 0] += rx * yx
mtx[0, 1] += rx * yy
mtx[0, 2] += rx * y0
mtx[1, 0] += ry * xx
mtx[1, 1] += ry * xy
mtx[1, 2] += ry * x0
self.invalidate()
return self
def skew_deg(self, xShear, yShear):
"""
Add 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(math.radians(xShear), math.radians(yShear))
class IdentityTransform(Affine2DBase):
"""
A special class that does one thing, the identity transform, in a
fast way.
"""
_mtx = np.identity(3)
def frozen(self):
# docstring inherited
return self
__str__ = _make_str_method()
def get_matrix(self):
# docstring inherited
return self._mtx
def transform(self, values):
# docstring inherited
return np.asanyarray(values)
def transform_affine(self, values):
# docstring inherited
return np.asanyarray(values)
def transform_non_affine(self, values):
# docstring inherited
return np.asanyarray(values)
def transform_path(self, path):
# docstring inherited
return path
def transform_path_affine(self, path):
# docstring inherited
return path
def transform_path_non_affine(self, path):
# docstring inherited
return path
def get_affine(self):
# docstring inherited
return self
def inverted(self):
# docstring inherited
return self
class _BlendedMixin:
"""Common methods for `BlendedGenericTransform` and `BlendedAffine2D`."""
def __eq__(self, other):
if isinstance(other, (BlendedAffine2D, BlendedGenericTransform)):
return (self._x == other._x) and (self._y == other._y)
elif self._x == self._y:
return self._x == other
else:
return NotImplemented
def contains_branch_separately(self, transform):
return (self._x.contains_branch(transform),
self._y.contains_branch(transform))
__str__ = _make_str_method("_x", "_y")
class BlendedGenericTransform(_BlendedMixin, Transform):
"""
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.
"""
input_dims = 2
output_dims = 2
is_separable = True
pass_through = True
def __init__(self, x_transform, y_transform, **kwargs):
"""
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
`blended_transform_factory` function instead, which can determine
automatically which kind of blended transform to create.
"""
Transform.__init__(self, **kwargs)
self._x = x_transform
self._y = y_transform
self.set_children(x_transform, y_transform)
self._affine = None
@property
def depth(self):
return max(self._x.depth, self._y.depth)
def contains_branch(self, other):
# A blended transform cannot possibly contain a branch from two
# different transforms.
return False
is_affine = property(lambda self: self._x.is_affine and self._y.is_affine)
has_inverse = property(
lambda self: self._x.has_inverse and self._y.has_inverse)
def frozen(self):
# docstring inherited
return blended_transform_factory(self._x.frozen(), self._y.frozen())
def transform_non_affine(self, values):
# docstring inherited
if self._x.is_affine and self._y.is_affine:
return values
x = self._x
y = self._y
if x == y and x.input_dims == 2:
return x.transform_non_affine(values)
if x.input_dims == 2:
x_points = x.transform_non_affine(values)[:, 0:1]
else:
x_points = x.transform_non_affine(values[:, 0])
x_points = x_points.reshape((len(x_points), 1))
if y.input_dims == 2:
y_points = y.transform_non_affine(values)[:, 1:]
else:
y_points = y.transform_non_affine(values[:, 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)
def inverted(self):
# docstring inherited
return BlendedGenericTransform(self._x.inverted(), self._y.inverted())
def get_affine(self):
# docstring inherited
if self._invalid or self._affine is None:
if self._x == self._y:
self._affine = self._x.get_affine()
else:
x_mtx = self._x.get_affine().get_matrix()
y_mtx = self._y.get_affine().get_matrix()
# We already know the transforms are separable, so we can skip
# setting b and c to zero.
mtx = np.array([x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0]])
self._affine = Affine2D(mtx)
self._invalid = 0
return self._affine
class BlendedAffine2D(_BlendedMixin, Affine2DBase):
"""
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 `Affine2DBase`.
"""
is_separable = True
def __init__(self, x_transform, y_transform, **kwargs):
"""
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
`blended_transform_factory` function instead, which can determine
automatically which kind of blended transform to create.
"""
is_affine = x_transform.is_affine and y_transform.is_affine
is_separable = x_transform.is_separable and y_transform.is_separable
is_correct = is_affine and is_separable
if not is_correct:
raise ValueError("Both *x_transform* and *y_transform* must be 2D "
"affine transforms")
Transform.__init__(self, **kwargs)
self._x = x_transform
self._y = y_transform
self.set_children(x_transform, y_transform)
Affine2DBase.__init__(self)
self._mtx = None
def get_matrix(self):
# docstring inherited
if self._invalid:
if self._x == self._y:
self._mtx = self._x.get_matrix()
else:
x_mtx = self._x.get_matrix()
y_mtx = self._y.get_matrix()
# We already know the transforms are separable, so we can skip
# setting b and c to zero.
self._mtx = np.array([x_mtx[0], y_mtx[1], [0.0, 0.0, 1.0]])
self._inverted = None
self._invalid = 0
return self._mtx
def blended_transform_factory(x_transform, y_transform):
"""
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.
"""
if (isinstance(x_transform, Affine2DBase) and
isinstance(y_transform, Affine2DBase)):
return BlendedAffine2D(x_transform, y_transform)
return BlendedGenericTransform(x_transform, y_transform)
class CompositeGenericTransform(Transform):
"""
A composite transform formed by applying transform *a* then
transform *b*.
This "generic" version can handle any two arbitrary
transformations.
"""
pass_through = True
def __init__(self, a, b, **kwargs):
"""
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 write ``a +
b`` instead, which will automatically choose the best kind of composite
transform instance to create.
"""
if a.output_dims != b.input_dims:
raise ValueError("The output dimension of 'a' must be equal to "
"the input dimensions of 'b'")
self.input_dims = a.input_dims
self.output_dims = b.output_dims
super().__init__(**kwargs)
self._a = a
self._b = b
self.set_children(a, b)
def frozen(self):
# docstring inherited
self._invalid = 0
frozen = composite_transform_factory(
self._a.frozen(), self._b.frozen())
if not isinstance(frozen, CompositeGenericTransform):
return frozen.frozen()
return frozen
def _invalidate_internal(self, level, invalidating_node):
# When the left child is invalidated at AFFINE_ONLY level and the right child is
# non-affine, the composite transform is FULLY invalidated.
if invalidating_node is self._a and not self._b.is_affine:
level = Transform._INVALID_FULL
super()._invalidate_internal(level, invalidating_node)
def __eq__(self, other):
if isinstance(other, (CompositeGenericTransform, CompositeAffine2D)):
return self is other or (self._a == other._a
and self._b == other._b)
else:
return False
def _iter_break_from_left_to_right(self):
for left, right in self._a._iter_break_from_left_to_right():
yield left, right + self._b
for left, right in self._b._iter_break_from_left_to_right():
yield self._a + left, right
def contains_branch_separately(self, other_transform):
# docstring inherited
if self.output_dims != 2:
raise ValueError('contains_branch_separately only supports '
'transforms with 2 output dimensions')
if self == other_transform:
return (True, True)
return self._b.contains_branch_separately(other_transform)
depth = property(lambda self: self._a.depth + self._b.depth)
is_affine = property(lambda self: self._a.is_affine and self._b.is_affine)
is_separable = property(
lambda self: self._a.is_separable and self._b.is_separable)
has_inverse = property(
lambda self: self._a.has_inverse and self._b.has_inverse)
__str__ = _make_str_method("_a", "_b")
def transform_affine(self, values):
# docstring inherited
return self.get_affine().transform(values)
def transform_non_affine(self, values):
# docstring inherited
if self._a.is_affine and self._b.is_affine:
return values
elif not self._a.is_affine and self._b.is_affine:
return self._a.transform_non_affine(values)
else:
return self._b.transform_non_affine(self._a.transform(values))
def transform_path_non_affine(self, path):
# docstring inherited
if self._a.is_affine and self._b.is_affine:
return path
elif not self._a.is_affine and self._b.is_affine:
return self._a.transform_path_non_affine(path)
else:
return self._b.transform_path_non_affine(
self._a.transform_path(path))
def get_affine(self):
# docstring inherited
if not self._b.is_affine:
return self._b.get_affine()
else:
return Affine2D(np.dot(self._b.get_affine().get_matrix(),
self._a.get_affine().get_matrix()))
def inverted(self):
# docstring inherited
return CompositeGenericTransform(
self._b.inverted(), self._a.inverted())
class CompositeAffine2D(Affine2DBase):
"""
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.
"""
def __init__(self, a, b, **kwargs):
"""
Create a new composite transform that is the result of
applying `Affine2DBase` *a* then `Affine2DBase` *b*.
You will generally not call this constructor directly but write ``a +
b`` instead, which will automatically choose the best kind of composite
transform instance to create.
"""
if not a.is_affine or not b.is_affine:
raise ValueError("'a' and 'b' must be affine transforms")
if a.output_dims != b.input_dims:
raise ValueError("The output dimension of 'a' must be equal to "
"the input dimensions of 'b'")
self.input_dims = a.input_dims
self.output_dims = b.output_dims
super().__init__(**kwargs)
self._a = a
self._b = b
self.set_children(a, b)
self._mtx = None
@property
def depth(self):
return self._a.depth + self._b.depth
def _iter_break_from_left_to_right(self):
for left, right in self._a._iter_break_from_left_to_right():
yield left, right + self._b
for left, right in self._b._iter_break_from_left_to_right():
yield self._a + left, right
__str__ = _make_str_method("_a", "_b")
def get_matrix(self):
# docstring inherited
if self._invalid:
self._mtx = np.dot(
self._b.get_matrix(),
self._a.get_matrix())
self._inverted = None
self._invalid = 0
return self._mtx
def composite_transform_factory(a, b):
"""
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.
if isinstance(a, IdentityTransform):
return b
elif isinstance(b, IdentityTransform):
return a
elif isinstance(a, Affine2D) and isinstance(b, Affine2D):
return CompositeAffine2D(a, b)
return CompositeGenericTransform(a, b)
class BboxTransform(Affine2DBase):
"""
`BboxTransform` linearly transforms points from one `Bbox` to another.
"""
is_separable = True
def __init__(self, boxin, boxout, **kwargs):
"""
Create a new `BboxTransform` that linearly transforms
points from *boxin* to *boxout*.
"""
_api.check_isinstance(BboxBase, boxin=boxin, boxout=boxout)
super().__init__(**kwargs)
self._boxin = boxin
self._boxout = boxout
self.set_children(boxin, boxout)
self._mtx = None
self._inverted = None
__str__ = _make_str_method("_boxin", "_boxout")
def get_matrix(self):
# docstring inherited
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(Affine2DBase):
"""
`BboxTransformTo` is a transformation that linearly transforms points from
the unit bounding box to a given `Bbox`.
"""
is_separable = True
def __init__(self, boxout, **kwargs):
"""
Create a new `BboxTransformTo` that linearly transforms
points from the unit bounding box to *boxout*.
"""
_api.check_isinstance(BboxBase, boxout=boxout)
super().__init__(**kwargs)
self._boxout = boxout
self.set_children(boxout)
self._mtx = None
self._inverted = None
__str__ = _make_str_method("_boxout")
def get_matrix(self):
# docstring inherited
if self._invalid:
outl, outb, outw, outh = self._boxout.bounds
if DEBUG and (outw == 0 or outh == 0):
raise ValueError("Transforming to a singular bounding box.")
self._mtx = np.array([[outw, 0.0, outl],
[ 0.0, outh, outb],
[ 0.0, 0.0, 1.0]],
float)
self._inverted = None
self._invalid = 0
return self._mtx
class BboxTransformFrom(Affine2DBase):
"""
`BboxTransformFrom` linearly transforms points from a given `Bbox` to the
unit bounding box.
"""
is_separable = True
def __init__(self, boxin, **kwargs):
_api.check_isinstance(BboxBase, boxin=boxin)
super().__init__(**kwargs)
self._boxin = boxin
self.set_children(boxin)
self._mtx = None
self._inverted = None
__str__ = _make_str_method("_boxin")
def get_matrix(self):
# docstring inherited
if self._invalid:
inl, inb, inw, inh = self._boxin.bounds
if DEBUG and (inw == 0 or inh == 0):
raise ValueError("Transforming from a singular bounding box.")
x_scale = 1.0 / inw
y_scale = 1.0 / inh
self._mtx = np.array([[x_scale, 0.0, -inl*x_scale],
[ 0.0, y_scale, -inb*y_scale],
[ 0.0, 0.0, 1.0]],
float)
self._inverted = None
self._invalid = 0
return self._mtx
class ScaledTranslation(Affine2DBase):
"""
A transformation that translates by *xt* and *yt*, after *xt* and *yt*
have been transformed by *scale_trans*.
"""
def __init__(self, xt, yt, scale_trans, **kwargs):
super().__init__(**kwargs)
self._t = (xt, yt)
self._scale_trans = scale_trans
self.set_children(scale_trans)
self._mtx = None
self._inverted = None
__str__ = _make_str_method("_t")
def get_matrix(self):
# docstring inherited
if self._invalid:
# A bit faster than np.identity(3).
self._mtx = IdentityTransform._mtx.copy()
self._mtx[:2, 2] = self._scale_trans.transform(self._t)
self._invalid = 0
self._inverted = None
return self._mtx
class _ScaledRotation(Affine2DBase):
"""
A transformation that applies rotation by *theta*, after transform by *trans_shift*.
"""
def __init__(self, theta, trans_shift):
super().__init__()
self._theta = theta
self._trans_shift = trans_shift
self._mtx = None
def get_matrix(self):
if self._invalid:
transformed_coords = self._trans_shift.transform([[self._theta, 0]])[0]
adjusted_theta = transformed_coords[0]
rotation = Affine2D().rotate(adjusted_theta)
self._mtx = rotation.get_matrix()
return self._mtx
class AffineDeltaTransform(Affine2DBase):
r"""
A transform wrapper for transforming displacements between pairs of points.
This class is intended to be used to transform displacements ("position
deltas") between pairs of points (e.g., as the ``offset_transform``
of `.Collection`\s): given a transform ``t`` such that ``t =
AffineDeltaTransform(t) + offset``, ``AffineDeltaTransform``
satisfies ``AffineDeltaTransform(a - b) == AffineDeltaTransform(a) -
AffineDeltaTransform(b)``.
This is implemented by forcing the offset components of the transform
matrix to zero.
This class is experimental as of 3.3, and the API may change.
"""
pass_through = True
def __init__(self, transform, **kwargs):
super().__init__(**kwargs)
self._base_transform = transform
self.set_children(transform)
__str__ = _make_str_method("_base_transform")
def get_matrix(self):
if self._invalid:
self._mtx = self._base_transform.get_matrix().copy()
self._mtx[:2, -1] = 0
return self._mtx
class TransformedPath(TransformNode):
"""
A `TransformedPath` caches a non-affine transformed copy of the
`~.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.
"""
def __init__(self, path, transform):
"""
Parameters
----------
path : `~.path.Path`
transform : `Transform`
"""
_api.check_isinstance(Transform, transform=transform)
super().__init__()
self._path = path
self._transform = transform
self.set_children(transform)
self._transformed_path = None
self._transformed_points = None
def _revalidate(self):
# only recompute if the invalidation includes the non_affine part of
# the transform
if (self._invalid == self._INVALID_FULL
or self._transformed_path is None):
self._transformed_path = \
self._transform.transform_path_non_affine(self._path)
self._transformed_points = \
Path._fast_from_codes_and_verts(
self._transform.transform_non_affine(self._path.vertices),
None, self._path)
self._invalid = 0
def get_transformed_points_and_affine(self):
"""
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()
def get_transformed_path_and_affine(self):
"""
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.
"""
self._revalidate()
return self._transformed_path, self.get_affine()
def get_fully_transformed_path(self):
"""
Return a fully-transformed copy of the child path.
"""
self._revalidate()
return self._transform.transform_path_affine(self._transformed_path)
def get_affine(self):
return self._transform.get_affine()
class TransformedPatchPath(TransformedPath):
"""
A `TransformedPatchPath` caches a non-affine transformed copy of the
`~.patches.Patch`. This cached copy is automatically updated when the
non-affine part of the transform or the patch changes.
"""
def __init__(self, patch):
"""
Parameters
----------
patch : `~.patches.Patch`
"""
# Defer to TransformedPath.__init__.
super().__init__(patch.get_path(), patch.get_transform())
self._patch = patch
def _revalidate(self):
patch_path = self._patch.get_path()
# Force invalidation if the patch path changed; otherwise, let base
# class check invalidation.
if patch_path != self._path:
self._path = patch_path
self._transformed_path = None
super()._revalidate()
def _nonsingular(vmin, vmax, expander=0.001, tiny=1e-15, increasing=True):
"""
Modify the endpoints of a range as needed to avoid singularities.
Parameters
----------
vmin, vmax : float
The initial endpoints.
expander : float, default: 0.001
Fractional amount by which *vmin* and *vmax* are expanded if
the original interval is too small, based on *tiny*.
tiny : float, 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, 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*.
"""
if (not np.isfinite(vmin)) or (not np.isfinite(vmax)):
return -expander, expander
swapped = False
if vmax < vmin:
vmin, vmax = vmax, vmin
swapped = True
# Expand vmin, vmax to float: if they were integer types, they can wrap
# around in abs (abs(np.int8(-128)) == -128) and vmax - vmin can overflow.
vmin, vmax = map(float, [vmin, vmax])
maxabsvalue = max(abs(vmin), abs(vmax))
if maxabsvalue < (1e6 / tiny) * np.finfo(float).tiny:
vmin = -expander
vmax = expander
elif vmax - vmin b:
a, b = b, a
return a