"""
Vector class used for SSF and PSF Calculation
This module defines the Vector datatype that's used to
store position (x,y,z) information for the atoms and residues
in an MD Simulation. Documentation is provided for reference.
"""
import numpy as np
[docs]
class Vector:
"""
Represents a 3D vector with x, y, and z components.
This class defines a data type 'Vector' that represents a 3D vector with
x, y, and z components, assuming the vector originates at the origin (0,0,0).
Expands the numpy.array object.
Attributes
----------
x : float
The x-component of the vector.
y : float
The y-component of the vector.
z : float
The z-component of the vector.
"""
[docs]
def __init__(self, x: float, y: float, z: float) -> None:
"""
Initialize a Vector instance.
Parameters
----------
x : float
The x-component of the vector.
y : float
The y-component of the vector.
z : float
The z-component of the vector.
"""
self.x = x
self.y = y
self.z = z
self.components = np.array([x, y, z])
def __add__(self, other: 'Vector') -> 'Vector':
"""
Add two vectors element-wise.
Parameters
----------
other : Vector
Another Vector to add to this vector.
Returns
-------
Vector
A new Vector representing the element-wise sum of the two vectors.
"""
return Vector(*(self.components + other.components))
def __sub__(self, other: 'Vector') -> 'Vector':
"""
Subtract another vector element-wise from this vector.
Parameters
----------
other : Vector
Another Vector to subtract from this vector.
Returns
-------
Vector
A new Vector representing the element-wise difference of the two vectors.
"""
return Vector(*(self.components - other.components))
def __eq__(self, other: 'Vector') -> bool:
"""
Check if two Vectors are equal.
Parameters
----------
other : Vector
Vector to check equality to.
Returns
-------
bool
True if vectors are equal, False otherwise.
"""
return np.array_equal(self.components, other.components)
[docs]
def calculate_cross_product(self, b: 'Vector') -> 'Vector':
"""
Calculate the cross product of two vectors.
Calculates the cross product of two vectors, which is the unit vector that is
perpendicular to both vectors.
Parameters
----------
b : Vector
The second vector to calculate the cross product with.
Returns
-------
Vector
The resulting vector from the cross product.
"""
c = np.cross(self.components, b.components)
return Vector(*c)
[docs]
def magnitude(self) -> float:
"""
Calculate the magnitude (length) of the vector.
Returns
-------
float
The magnitude (length) of the vector.
"""
return np.linalg.norm(self.components)
[docs]
def calculate_projection(self, b: 'Vector') -> 'Vector':
"""
Calculate the projection of this vector onto vector b.
Parameters
----------
b : Vector
The vector to project onto.
Returns
-------
Vector
The resulting vector from the projection.
"""
b_np = b.components
projected_vector = (np.dot(self.components, b_np) / np.dot(b_np, b_np)) * b_np
return Vector(*projected_vector)
def __str__(self) -> str:
"""
Redefine the string representation of the Vector.
Redefines the output of print(Vector()) to display the x, y, z attributes.
Returns
-------
str
The string representation of the vector.
"""
x, y, z = self.components
return "[ " + str(x) + "\n " + str(y) + "\n " + str(z) + " ]"
[docs]
def scale(self, a: float) -> 'Vector':
"""
Scale the vector by a scalar a.
Parameters
----------
a : float
The scalar to scale the vector by.
Returns
-------
Vector
The scaled vector.
"""
scaled_vector = a * self.components
return Vector(*scaled_vector)
if __name__ == "__main__":
assert (Vector(1,2,3) + Vector(3,2,1) == Vector(4,4,4))
assert (Vector(1,2,3).y == 2)
assert (Vector(1,2,3) - Vector(-1,0,4) == Vector(2,2,-1))
assert (Vector(1,0,0).calculate_cross_product(Vector(0,1,0)) == Vector(0,0,1))
assert (Vector(1,0,0).calculate_cross_product(Vector(0,0,0)) == Vector(0,0,0))
assert (Vector(1,0,0).magnitude() == 1)
assert (Vector(0,3,4).magnitude() == 5)
assert (Vector(-1,-2,-2).magnitude() == 3)
assert (Vector(3,1,0).calculate_projection(Vector(1,0,0)) == Vector(3,0,0))
assert (Vector(1,2,3).calculate_projection(Vector(0,0,0)) == Vector(0,0,0))
