# -*- coding: utf-8 -*-
"""
==================================================================
Custom NumPy Vector class (:mod:`sknano.core.math.vector`)
==================================================================
.. currentmodule:: sknano.core.math.vector
"""
from __future__ import absolute_import, division, print_function
from __future__ import unicode_literals
__docformat__ = 'restructuredtext en'
# import copy
import numbers
import warnings
import numpy as np
np.seterr(all='warn')
from sknano.core import Singleton
from .point import Point
from .transforms import rotate, transformation_matrix
__all__ = ['Vector', 'angle', 'cross', 'dot', 'scalar_triple_product',
'vector_triple_product', 'scalar_projection', 'vector_projection',
'vector_rejection', 'projection', 'rejection',
'e1', 'e2', 'e3', 'xhat', 'yhat', 'zhat', 'NullVector']
incompatible_shape_error_msg = \
"operands could not be broadcast together with shapes {}, {}"
different_shape_error_msg = "operand shape {} != {}"""
[docs]class Vector(np.ndarray):
"""Abstract object representation of a vector in :math:`R^n`
Parameters
----------
v : array_like, optional
components of vector
nd : {None, int}, optional
p0 : array_like, optional
Origin `Point` of vector in :math:`R^n` space.
p : array_like, optional
Terminating `Point` of vector.
:math:`x, y` coordinates of point in :math:`R^2` space.
:math:`x, y, z` coordinates of point in :math:`R^3` space.
dtype : data-type, optional
copy : bool, optional
Notes
-----
.. todo::
add new methods for coordinate transformations
Examples
--------
I began writing my own `Point` and `Vector` classes while trying to
teach myself about subclassing :class:`~numpy:numpy.ndarray`.
I still don't completely understand the machinery of it, but I ended
up with some code that's been useful for handling math operations involving
points and vectors. More testing is in order...
Here are some examples of their use.
"""
__array_priority__ = 20.0
def __new__(cls, v=None, nd=None, p0=None, p=None, dtype=None, copy=True):
if isinstance(v, Vector):
if nd is not None and isinstance(nd, numbers.Number) and \
len(v) < int(nd):
v = np.append(v, np.zeros(int(nd) - len(v)))
if dtype is None:
intype = v.dtype
else:
intype = np.dtype(dtype)
vec = v.view(cls)
if p0 is not None:
vec = Vector(np.asarray(vec), nd=nd,
p0=Point(p0, nd=nd, dtype=dtype, copy=copy))
if intype != v.dtype:
return vec.astype(intype)
if copy:
return vec.copy()
else:
return vec
dtype = np.dtype(dtype)
if isinstance(v, (tuple, list, np.ndarray)):
try:
for i, coord in enumerate(v[:]):
if coord is None:
v[i] = 0.0
except TypeError:
v = np.zeros(len(v), dtype=dtype)
else:
v = np.asarray(v, dtype=dtype)
if nd is not None and isinstance(nd, numbers.Number) and \
len(v) < int(nd):
v = np.append(v, np.zeros(int(nd) - len(v)))
nd = len(v)
if p0 is None:
p0 = Point(nd=nd, dtype=dtype)
else:
p0 = Point(p0, nd=nd, dtype=dtype, copy=copy)
p = p0 + v
else:
if p is None and p0 is None and \
(nd is None or not isinstance(nd, numbers.Number)):
nd = 3
if p is None:
p = Point(nd=nd, dtype=dtype)
else:
p = Point(p, nd=nd, dtype=dtype, copy=copy)
if p0 is None:
p0 = Point(nd=nd, dtype=dtype)
else:
p0 = Point(p0, nd=nd, dtype=dtype, copy=copy)
v = p - p0
arr = np.array(v, dtype=dtype, copy=copy).view(cls)
vec = np.ndarray.__new__(cls, arr.shape, arr.dtype, buffer=arr)
vec.nd = len(vec)
vec._p = p
vec._p0 = p0
return vec
def __array_finalize__(self, obj):
if obj is None:
return None
self.nd = len(obj)
self._p0 = getattr(obj, 'p0', None)
self._p = getattr(obj, 'p', None)
if self._p0 is not None and self._p is None:
try:
self._p = self._p0 + self.__array__()
except TypeError:
try:
self._p = self._p0 + np.asarray(obj)
except TypeError:
pass
# def __array_prepare__(self, obj, context=None):
# if self.__array_priority__ >= Vector.__array_priority__:
# res = obj if isinstance(obj, type(self)) \
# else obj.view(type(self))
# else:
# res = obj.view(Vector)
# if context is None:
# return res
# return super(Vector, self).__array_prepare__(obj, context)
def __array_wrap__(self, obj, context=None):
res = np.ndarray.__array_wrap__(self, obj, context)
return self.__class__(res.__array__(), p0=self.p0)
def __str__(self):
strrep = repr(self)
begin = len('Vector(')
end = -1
return strrep[begin:end]
def __repr__(self):
try:
if np.allclose(self.p0, np.zeros_like(self.p0)):
return "Vector({!r})".format(self.tolist())
else:
return "Vector({!r}, p0={!r}, p={!r})".format(
self.tolist(), self.p0.tolist(), self.p.tolist())
except AttributeError:
return "Vector({!r})".format(self.tolist())
def __getattr__(self, name):
try:
nd = len(self)
if nd == 2 and name in ('x', 'y'):
if name == 'x':
return self[0]
else:
return self[1]
elif nd == 3 and name in ('x', 'y', 'z'):
if name == 'x':
return self[0]
elif name == 'y':
return self[1]
else:
return self[2]
except TypeError:
pass
return np.ndarray.__getattribute__(self, name)
def __setattr__(self, name, value):
# nd = len(self)
nd = getattr(self, 'nd', None)
if nd is not None and nd == 2 and name in ('x', 'y'):
if name == 'x':
self[0] = value
try:
self._p.x = self._p0.x + value
except AttributeError:
pass
else:
self[1] = value
try:
self._p.y = self._p0.y + value
except AttributeError:
pass
elif nd is not None and nd == 3 and name in ('x', 'y', 'z'):
if name == 'x':
self[0] = value
try:
self._p.x = self._p0.x + value
except AttributeError:
pass
elif name == 'y':
self[1] = value
try:
self._p.y = self._p0.y + value
except AttributeError:
pass
else:
self[2] = value
try:
self._p.z = self._p0.z + value
except AttributeError:
pass
else:
np.ndarray.__setattr__(self, name, value)
# if name is not None and name.endswith('p'):
# try:
# self[:] = self._p.__array__() - self._p0.__array__()
# except (AttributeError, TypeError):
# pass
def __getitem__(self, index):
data = np.ndarray.__getitem__(np.ndarray.view(self, np.ndarray),
index)
p0 = np.ndarray.__getitem__(np.ndarray.view(
np.ndarray.__getattribute__(self, 'p0'),
np.ndarray), index)
p = np.ndarray.__getitem__(np.ndarray.view(
np.ndarray.__getattribute__(self, 'p'),
np.ndarray), index)
try:
data = data.view(type(self))
data._p0 = np.ndarray.view(p0, Point)
data._p = np.ndarray.view(p, Point)
data._nd = len(data)
except (AttributeError, TypeError):
pass
return data
def __setitem__(self, index, value):
data = np.ndarray.view(self, np.ndarray)
p0 = np.ndarray.view(np.ndarray.__getattribute__(self, 'p0'),
np.ndarray)
p = np.ndarray.view(np.ndarray.__getattribute__(self, 'p'),
np.ndarray)
np.ndarray.__setitem__(data, index, value)
np.ndarray.__setitem__(p, index, np.ndarray.__getitem__(p0, index) +
np.ndarray.__getitem__(data, index))
data = data.view(type(self))
data._p0 = np.ndarray.view(p0, Point)
data._p = np.ndarray.view(p, Point)
def __eq__(self, other):
try:
other = self.__cast(other)
return self is other or (np.allclose(self.__array__(),
other.__array__()) and
np.allclose(self.p0, other.p0) and
np.allclose(self.p, other.p))
except (TypeError, ValueError):
return NotImplemented
def __lt__(self, other):
try:
other = self.__cast(other)
return self.norm < other.norm
except (TypeError, ValueError):
return NotImplemented
def __le__(self, other):
try:
other = self.__cast(other)
return self < other or self == other
except (TypeError, ValueError):
return NotImplemented
def __gt__(self, other):
try:
other = self.__cast(other)
return not (self < other or self == other)
except (TypeError, ValueError):
return NotImplemented
def __ge__(self, other):
try:
other = self.__cast(other)
return not (self < other)
except (TypeError, ValueError):
return NotImplemented
def __ne__(self, other):
try:
other = self.__cast(other)
return not (self == other)
except (TypeError, ValueError):
return NotImplemented
def __add__(self, other):
if np.isscalar(other):
return self.__class__(self.__array__() + other, p0=self.p0)
if isinstance(other, Vectors):
return other.__radd__(self)
try:
return self.__class__(self.__array__() +
self.__cast(other).__array__(),
p0=self.p0)
except (TypeError, ValueError):
return NotImplemented
def __radd__(self, other):
if np.isscalar(other):
return self.__add__(other)
if isinstance(other, Vectors):
return other.__add__(self)
try:
return self.__class__(self.__cast(other).__array__() +
self.__array__(),
p0=other.p0)
except (TypeError, ValueError):
return NotImplemented
def __iadd__(self, other):
"""Add other to self in-place."""
try:
other = self.__cast(other)
# self._validate_operand(other, shape='same')
except (TypeError, ValueError):
if not np.isscalar(other):
return NotImplemented
super().__iadd__(other)
self._update_p()
return self
def __sub__(self, other):
if np.isscalar(other):
return self.__class__(self.__array__() - other, p0=self.p0)
if isinstance(other, Vectors):
return other.__rsub__(self)
try:
return self.__class__(self.__array__() -
self.__cast(other).__array__(),
p0=self.p0)
except (TypeError, ValueError):
return NotImplemented
def __rsub__(self, other):
if np.isscalar(other):
return self.__class__(other - self.__array__())
if isinstance(other, Vectors):
return other.__sub__(self)
try:
return self.__class__(self.__cast(other).__array__() -
self.__array__(),
p0=other.p0)
except (TypeError, ValueError):
return NotImplemented
def __isub__(self, other):
"""Subtract other from self in-place."""
try:
other = self.__cast(other)
# self._validate_operand(other, shape='same')
except (TypeError, ValueError):
if not np.isscalar(other):
return NotImplemented
super().__isub__(other)
self._update_p()
return self
def _mul_warn_msg(self, other):
return "Computing *scalar product* of Vector's:\n" + \
"{!r}.{!r}".format(self, other)
def __mul__(self, other):
if np.isscalar(other):
return self.__class__(self.__array__() * other, p0=self.p0)
# elif isinstance(other, np.matrix):
# res = self.row_matrix * other
# if len(self) == res.shape[1]:
# return self.__class__(res.A.flatten(), p0=self.p0)
# elif res.shape == (1, 1):
# return res.A.flatten()[0]
try:
print(self._mul_warn_msg(other))
return self.dot(self.__cast(other))
except (TypeError, ValueError):
return NotImplemented
def __rmul__(self, other):
if np.isscalar(other):
return self.__class__(other * self.__array__(), p0=self.p0)
# elif isinstance(other, np.matrix):
# res = other * self.column_matrix
# if len(self) == res.shape[0]:
# return self.__class__(res.A.flatten(), p0=self.p0)
# elif res.shape == (1, 1):
# return res.A.flatten()[0]
try:
return self.__cast(other).__mul__(self)
except (TypeError, ValueError):
return NotImplemented
def __imul__(self, other):
"""Multiply self by other in-place."""
try:
self = self.__mul__(self.__cast(other))
# other = self.__cast(other)
except (TypeError, ValueError):
if not np.isscalar(other):
return NotImplemented
super().__imul__(other)
self._update_p()
return self
def __truediv__(self, other):
if not np.isscalar(other):
return NotImplemented
return self.__class__(self.__array__() / other, p0=self.p0)
__div__ = __truediv__
def __itruediv__(self, other):
if not np.isscalar(other):
return NotImplemented
super().__itruediv__(other)
self._update_p()
return self
__idiv__ = __itruediv__
def __floordiv__(self, other):
if not np.isscalar(other):
return NotImplemented
return self.__class__(self.__array__() // other, p0=self.p0)
def __ifloordiv__(self, other):
if not np.isscalar(other):
return NotImplemented
super().__ifloordiv__(other)
self._update_p()
return self
def __pow__(self, other, *modulo):
if not np.isscalar(other):
return NotImplemented
return self.__class__(self.__array__() ** other, p0=self.p0)
def __ipow__(self, other):
if not np.isscalar(other):
return NotImplemented
super().__ipow__(other)
self._update_p()
return self
def __neg__(self):
return self.__class__(-self.__array__(), p0=self.p0)
def __abs__(self):
# return self.__class__(np.abs(self.__array__()), p0=self.p0)
return self.norm
def __copy__(self):
try:
return self.__class__(self.__array__(), p0=self.p0.__array__())
except AttributeError:
return self.__class__(self.__array__())
def __deepcopy__(self, memo):
return self.__copy__()
[docs] def copy(self):
"""Return a copy of the `Vector`."""
return self.__copy__()
[docs] def tolist(self):
"""List of `Vector` coordinates with values formatted for *pretty*
output.
"""
return np.around(self.__array__(), decimals=10).tolist()
def __cast(self, other):
if isinstance(other, (self.__class__, Vectors)):
return other
try:
self._validate_operand(other, shape='same')
except ValueError as e:
if not self._is_compatible_shape(other):
raise e
return self.__class__(other)
def _is_valid_operand(self, other):
return isinstance(other, (tuple, list, np.ndarray, self.__class__,
Vectors))
def _is_same_shape(self, other):
other = np.asarray(other)
return len(self) == len(other) and self.ndim == other.ndim
def _is_compatible_shape(self, other):
other = np.asarray(other)
return len(self) == len(other) if other.ndim == 1 else \
len(self) == other.shape[-1]
def _validate_operand(self, other, shape='compatible'):
valid = self._is_valid_operand(other)
if not valid:
raise TypeError('Invalid operand type {!r}.'.format(type(other)))
compatible = self._is_compatible_shape(other)
same = self._is_same_shape(other)
other_shape = np.asarray(other).shape
if shape.startswith('compat') and not compatible:
raise ValueError(incompatible_shape_error_msg.format(self.shape,
other_shape))
elif shape == 'same' and not same:
raise ValueError(different_shape_error_msg.format(other_shape,
self.shape))
def _update_p(self):
self._p[:] = self._p0[:] + self.__array__()
def _update_vector(self):
self[:] = self._p - self._p0
def _translate_p0(self, t, fix_components=False):
if fix_components:
self.translate(t)
else:
self.p0.translate(t)
def _translate_p(self, t, fix_components=False):
if fix_components:
self.translate(t)
else:
self.p.translate(t)
@property
def norm(self):
"""Return the vector norm."""
return np.sqrt((self.__array__() ** 2).sum())
@property
def length(self):
"""Alias for :attr:`Vector.norm`."""
return self.norm
@property
def magnitude(self):
"""Alias for :attr:`Vector.norm`."""
return self.norm
@property
def mag(self):
"""Alias for :attr:`Vector.norm`."""
return self.norm
@property
def unit_vector(self):
"""Return unit vector."""
with warnings.catch_warnings():
warnings.filterwarnings('ignore')
return self / self.norm
@property
def p(self):
""":class:`Point` of `Vector` *head*."""
return self._p
@p.setter
def p(self, value=np.ndarray):
"""Set new terminating :class:`Point` of `Vector`."""
self._p[:] = value
self._update_vector()
@property
def p0(self):
""":class:`Point` of `Vector` *tail*."""
return self._p0
@p0.setter
def p0(self, value=np.ndarray):
"""Set new origin :class:`Point` of vector."""
self._p0[:] = value
self.p = self._p0 + self.__array__()
# self[:] = self._p - self._p0
@property
def column_matrix(self):
"""Return column matrix representation of `Vector` coordinates."""
return np.matrix(self.__array__().reshape(self.shape[0], 1))
@property
def row_matrix(self):
"""Return row matrix representation of `Vector` coordinates."""
return np.matrix(self.__array__())
[docs] def angle(self, other):
"""Angle between two `Vector`\ s."""
self._validate_operand(other)
if isinstance(other, Vectors):
return other.angle(self)
other = self.__cast(other)
return np.arccos(np.dot(self.__array__(), other.__array__()) /
(self.norm * other.norm))
[docs] def cross(self, other):
"""Cross product of two `Vector`\ s."""
self._validate_operand(other)
if isinstance(other, Vectors):
return -other.cross(self)
other = self.__cast(other)
val = np.cross(self.__array__(), other.__array__())
if val.shape == ():
return val[()]
return Vector(val, p0=self.p0)
[docs] def dot(self, other, out=None):
"""Dot product of two `Vector`\ s."""
self._validate_operand(other)
if isinstance(other, Vectors):
return other.dot(self)
other = self.__cast(other)
return self.__array__().dot(other.__array__())
[docs] def normalize(self):
"""Normalize the `Vector` to a :attr:`~Vector.unit_vector`."""
self[:] = self.unit_vector
[docs] def projection(self, other):
"""Vector projection onto `Vector` `other`."""
self._validate_operand(other)
if isinstance(other, Vectors):
return other.projection(self)
return dot(self, other) / dot(other, other) * other
[docs] def rejection(self, other):
"""Vector rejection onto `Vector` `other`."""
self._validate_operand(other)
if isinstance(other, Vectors):
return other.rejection(self)
return self - self.projection(other)
[docs] def rezero_components(self, epsilon=1.0e-10):
"""Alias for :meth:`Vector.rezero`"""
self.rezero(epsilon=epsilon)
[docs] def rezero(self, epsilon=1.0e-10):
"""Re-zero `Vector` coordinates near zero.
Set `Vector` coordinates with absolute value less than `epsilon` to
zero.
Parameters
----------
epsilon : float, optional
Smallest allowed absolute value of any :math:`x,y,z` coordinate.
"""
self[np.where(np.abs(self.__array__()) <= epsilon)] = 0.0
[docs] def rotate(self, angle=None, axis=None, anchor_point=None,
rot_point=None, from_vector=None, to_vector=None,
degrees=False, transform_matrix=None,
fix_anchor_point=False, verbose=False, **kwargs):
"""Rotate `Vector` coordinates.
Parameters
----------
angle : float
Rotation angle in radians, unless `degrees` is `True`.
axis : :class:`~sknano.core.math.Vector`, optional
anchor_point : :class:`~sknano.core.math.Point`, optional
rot_point : :class:`~sknano.core.math.Point`, optional
from_vector, to_vector : :class:`~sknano.core.math.Vector`, optional
degrees : :class:`~python:bool`, optional
If `True`, you are saying that the `angle` is in degrees.
transform_matrix : :class:`~numpy:numpy.ndarray`
fix_anchor_point : :class:`~python:bool`, optional
If `True`, leave the *tail* of the vector (:attr:`Vector.p0`)
fixed (default: `False`).
See Also
--------
core.math.rotate
"""
if transform_matrix is None:
transform_matrix = \
transformation_matrix(angle=angle, axis=axis,
anchor_point=anchor_point,
rot_point=rot_point,
from_vector=from_vector,
to_vector=to_vector, degrees=degrees,
verbose=verbose, **kwargs)
self._p = rotate(self.p, transform_matrix=transform_matrix)
if not fix_anchor_point:
self._p0 = rotate(self.p0, transform_matrix=transform_matrix)
self._update_vector()
[docs] def scale(self):
return NotImplemented
[docs] def translate(self, t, fix_anchor_point=False):
"""Translate `Vector` coordinates by :class:`Vector` `t`.
Parameters
----------
t : :class:`Vector`
fix_anchor_point : bool, optional
See Also
--------
core.math.translate
"""
if not fix_anchor_point:
self.p0 += t
else:
self.p += t
[docs]def angle(u, v, degrees=False):
"""Compute the angle between two Cartesian `Vector`\ s.
Parameters
----------
u, v : array_like
degrees : :class:`~python:bool`, optional
Returns
-------
:class:`~numpy:numpy.number`
"""
u, v = map(Vector, (u, v))
angle = np.arccos(dot(u, v) / (u.norm * v.norm))
if degrees:
angle = np.degrees(angle)
return angle
[docs]def cross(u, v, p0=None):
"""Vector cross product of two `Vector`\ s.
Parameters
----------
u, v : array_like
p0 : `Point`, optional
Returns
-------
:class:`~numpy:numpy.number` or :class:`Vector`
"""
u, v = map(Vector, (u, v))
val = np.cross(np.asarray(u), np.asarray(v))
if p0 is None:
p0 = u.p0
if val.shape == ():
return val[()]
else:
return Vector(val, p0=p0)
[docs]def dot(u, v):
"""Dot product of two `Vector`\ s.
Parameters
----------
u, v : array_like
Returns
-------
:class:`~numpy:numpy.number`
"""
return np.dot(np.asarray(u), np.asarray(v))
[docs]def scalar_triple_product(u, v, w):
"""Compute scalar triple product of three `Vector`\ s.
Parameters
----------
u, v, w : array_like
Returns
-------
:class:`~numpy:numpy.number`
"""
return dot(u, cross(v, w))
[docs]def vector_triple_product(u, v, w):
"""Compute vector triple product of three `Vector`\ s.
Parameters
----------
u, v, w : array_like
Returns
-------
:class:`Vector`
"""
return cross(u, cross(v, w))
[docs]def scalar_projection(a, b):
"""Compute the scalar projection of :math:`\\mathbf{a}` onto \
:math:`\\mathbf{b}`.
Parameters
----------
a, b : array_like
Returns
-------
:class:`~numpy:numpy.number`
"""
a, b = map(Vector, (a, b))
return dot(a, b) / b.norm
[docs]def vector_projection(a, b):
"""Compute the vector projection of :math:`\\mathbf{a}` onto \
:math:`\\mathbf{b}`.
Parameters
----------
a, b : array_like
Returns
-------
:class:`Vector`
"""
a, b = map(Vector, (a, b))
return dot(a, b) / dot(b, b) * b
projection = vector_projection
[docs]def vector_rejection(a, b):
"""Compute the vector rejection of :math:`\\mathbf{a}` onto \
:math:`\\mathbf{b}`.
Parameters
----------
a, b : array_like
Returns
-------
:class:`Vector`
"""
a, b = map(Vector, (a, b))
a1 = vector_projection(a, b)
return a - a1
rejection = vector_rejection
e1 = xhat = Vector([1, 0, 0])
e2 = yhat = Vector([0, 1, 0])
e3 = zhat = Vector([0, 0, 1])
[docs]class NullVector(Vector, metaclass=Singleton):
""":class:`~sknano.core.Singleton` class for a 3D null vector."""
def __init__(self):
self.__instance = Vector([0, 0, 0])
def __repr__(self):
return '{}({})'.format(self.__class__.__name__,
self.__instance.tolist())
from .vectors import Vectors
