Vector

class sknano.core.math.Vector

Bases: numpy.ndarray

Abstract object representation of a vector in \(R^n\)

Parameters:

• v (array_like, optional) – components of vector
• nd ({None, int}, optional) –
• p0 (array_like, optional) – Origin Point of vector in \(R^n\) space.
• p (array_like, optional) – Terminating Point of vector. \(x, y\) coordinates of point in \(R^2\) space. \(x, y, z\) coordinates of point in \(R^3\) 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 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.

Attributes

T	Same as self.transpose(), except that self is returned if self.ndim < 2.
base	Base object if memory is from some other object.
column_matrix	Return column matrix representation of Vector coordinates.
ctypes	An object to simplify the interaction of the array with the ctypes module.
data	Python buffer object pointing to the start of the array’s data.
dtype	Data-type of the array’s elements.
flags	Information about the memory layout of the array.
flat	A 1-D iterator over the array.
imag	The imaginary part of the array.
itemsize	Length of one array element in bytes.
length	Alias for Vector.norm.
mag	Alias for Vector.norm.
magnitude	Alias for Vector.norm.
nbytes	Total bytes consumed by the elements of the array.
ndim	Number of array dimensions.
norm	Return the vector norm.
p	Point of Vector head.
p0	Point of Vector tail.
real	The real part of the array.
row_matrix	Return row matrix representation of Vector coordinates.
shape	Tuple of array dimensions.
size	Number of elements in the array.
strides	Tuple of bytes to step in each dimension when traversing an array.
unit_vector	Return unit vector.

Methods

all([axis, out, keepdims])	Returns True if all elements evaluate to True.
angle(other)	Angle between two Vectors.
any([axis, out, keepdims])	Returns True if any of the elements of a evaluate to True.
argmax([axis, out])	Return indices of the maximum values along the given axis.
argmin([axis, out])	Return indices of the minimum values along the given axis of a.
argpartition(kth[, axis, kind, order])	Returns the indices that would partition this array.
argsort([axis, kind, order])	Returns the indices that would sort this array.
astype(dtype[, order, casting, subok, copy])	Copy of the array, cast to a specified type.
byteswap(inplace)	Swap the bytes of the array elements
choose(choices[, out, mode])	Use an index array to construct a new array from a set of choices.
clip([min, max, out])	Return an array whose values are limited to [min, max].
compress(condition[, axis, out])	Return selected slices of this array along given axis.
conj()	Complex-conjugate all elements.
conjugate()	Return the complex conjugate, element-wise.
copy()	Return a copy of the Vector.
cross(other)	Cross product of two Vectors.
cumprod([axis, dtype, out])	Return the cumulative product of the elements along the given axis.
cumsum([axis, dtype, out])	Return the cumulative sum of the elements along the given axis.
diagonal([offset, axis1, axis2])	Return specified diagonals.
dot(other[, out])	Dot product of two Vectors.
dump(file)	Dump a pickle of the array to the specified file.
dumps()	Returns the pickle of the array as a string.
fill(value)	Fill the array with a scalar value.
flatten([order])	Return a copy of the array collapsed into one dimension.
getfield(dtype[, offset])	Returns a field of the given array as a certain type.
item(*args)	Copy an element of an array to a standard Python scalar and return it.
itemset(*args)	Insert scalar into an array (scalar is cast to array’s dtype, if possible)
max([axis, out])	Return the maximum along a given axis.
mean([axis, dtype, out, keepdims])	Returns the average of the array elements along given axis.
min([axis, out, keepdims])	Return the minimum along a given axis.
newbyteorder([new_order])	Return the array with the same data viewed with a different byte order.
nonzero()	Return the indices of the elements that are non-zero.
normalize()	Normalize the Vector to a unit_vector.
partition(kth[, axis, kind, order])	Rearranges the elements in the array in such a way that value of the element in kth position is in the position it would be in a sorted array.
prod([axis, dtype, out, keepdims])	Return the product of the array elements over the given axis
projection(other)	Vector projection onto Vector other.
ptp([axis, out])	Peak to peak (maximum - minimum) value along a given axis.
put(indices, values[, mode])	Set a.flat[n] = values[n] for all n in indices.
ravel([order])	Return a flattened array.
rejection(other)	Vector rejection onto Vector other.
repeat(repeats[, axis])	Repeat elements of an array.
reshape(shape[, order])	Returns an array containing the same data with a new shape.
resize(new_shape[, refcheck])	Change shape and size of array in-place.
rezero([epsilon])	Re-zero Vector coordinates near zero.
rezero_components([epsilon])	Alias for Vector.rezero
rotate([angle, axis, anchor_point, ...])	Rotate Vector coordinates.
round([decimals, out])	Return a with each element rounded to the given number of decimals.
scale()
searchsorted(v[, side, sorter])	Find indices where elements of v should be inserted in a to maintain order.
setfield(val, dtype[, offset])	Put a value into a specified place in a field defined by a data-type.
setflags([write, align, uic])	Set array flags WRITEABLE, ALIGNED, and UPDATEIFCOPY, respectively.
sort([axis, kind, order])	Sort an array, in-place.
squeeze([axis])	Remove single-dimensional entries from the shape of a.
std([axis, dtype, out, ddof, keepdims])	Returns the standard deviation of the array elements along given axis.
sum([axis, dtype, out, keepdims])	Return the sum of the array elements over the given axis.
swapaxes(axis1, axis2)	Return a view of the array with axis1 and axis2 interchanged.
take(indices[, axis, out, mode])	Return an array formed from the elements of a at the given indices.
tobytes([order])	Construct Python bytes containing the raw data bytes in the array.
tofile(fid[, sep, format])	Write array to a file as text or binary (default).
tolist()	List of Vector coordinates with values formatted for pretty output.
tostring([order])	Construct Python bytes containing the raw data bytes in the array.
trace([offset, axis1, axis2, dtype, out])	Return the sum along diagonals of the array.
translate(t[, fix_anchor_point])	Translate Vector coordinates by Vector t.
transpose(*axes)	Returns a view of the array with axes transposed.
var([axis, dtype, out, ddof, keepdims])	Returns the variance of the array elements, along given axis.
view([dtype, type])	New view of array with the same data.

Attributes Summary

column_matrix	Return column matrix representation of Vector coordinates.
length	Alias for Vector.norm.
mag	Alias for Vector.norm.
magnitude	Alias for Vector.norm.
norm	Return the vector norm.
p	Point of Vector head.
p0	Point of Vector tail.
row_matrix	Return row matrix representation of Vector coordinates.
unit_vector	Return unit vector.

Methods Summary

angle(other)	Angle between two Vectors.
copy()	Return a copy of the Vector.
cross(other)	Cross product of two Vectors.
dot(other[, out])	Dot product of two Vectors.
normalize()	Normalize the Vector to a unit_vector.
projection(other)	Vector projection onto Vector other.
rejection(other)	Vector rejection onto Vector other.
rezero([epsilon])	Re-zero Vector coordinates near zero.
rezero_components([epsilon])	Alias for Vector.rezero
rotate([angle, axis, anchor_point, ...])	Rotate Vector coordinates.
scale()
tolist()	List of Vector coordinates with values formatted for pretty output.
translate(t[, fix_anchor_point])	Translate Vector coordinates by Vector t.

Attributes Documentation

column_matrix

Return column matrix representation of Vector coordinates.

length

Alias for Vector.norm.

mag

Alias for Vector.norm.

magnitude

Alias for Vector.norm.

norm

Return the vector norm.

p

Point of Vector head.

p0

Point of Vector tail.

row_matrix

Return row matrix representation of Vector coordinates.

unit_vector

Return unit vector.

Methods Documentation

angle(other)

Angle between two Vectors.

copy()

Return a copy of the Vector.

cross(other)

Cross product of two Vectors.

dot(other, out=None)

Dot product of two Vectors.

normalize()

Normalize the Vector to a unit_vector.

projection(other)

Vector projection onto Vector other.

rejection(other)

Vector rejection onto Vector other.

rezero(epsilon=1e-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 \(x,y,z\) coordinate.

rezero_components(epsilon=1e-10)

Alias for Vector.rezero

rotate(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 (Vector, optional) –
• anchor_point (Point, optional) –
• rot_point (Point, optional) –
• to_vector (from_vector,) –
• degrees (bool, optional) – If True, you are saying that the angle is in degrees.
• transform_matrix (ndarray) –
• fix_anchor_point (bool, optional) – If True, leave the tail of the vector (Vector.p0) fixed (default: False).

See also

core.math.rotate

scale()

tolist()

List of Vector coordinates with values formatted for pretty output.

translate(t, fix_anchor_point=False)

Translate Vector coordinates by Vector t.

Parameters:

• t (Vector) –
• fix_anchor_point (bool, optional) –

See also

core.math.translate