Bio.PDB.vectors module¶
Vector class, including rotation-related functions.
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Bio.PDB.vectors.
m2rotaxis
(m)¶ Return angles, axis pair that corresponds to rotation matrix m.
The case where
m
is the identity matrix corresponds to a singularity where any rotation axis is valid. In that case,Vector([1, 0, 0])
, is returned.
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Bio.PDB.vectors.
vector_to_axis
(line, point)¶ Vector to axis method.
Return the vector between a point and the closest point on a line (ie. the perpendicular projection of the point on the line).
- Parameters
line (L{Vector}) – vector defining a line
point (L{Vector}) – vector defining the point
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Bio.PDB.vectors.
rotaxis2m
(theta, vector)¶ Calculate left multiplying rotation matrix.
Calculate a left multiplying rotation matrix that rotates theta rad around vector.
- Parameters
theta (float) – the rotation angle
vector (L{Vector}) – the rotation axis
- Returns
The rotation matrix, a 3x3 Numeric array.
Examples
>>> from numpy import pi >>> from Bio.PDB.vectors import rotaxis2m >>> from Bio.PDB.vectors import Vector >>> m = rotaxis2m(pi, Vector(1, 0, 0)) >>> Vector(1, 2, 3).left_multiply(m) <Vector 1.00, -2.00, -3.00>
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Bio.PDB.vectors.
rotaxis
(theta, vector)¶ Calculate left multiplying rotation matrix.
Calculate a left multiplying rotation matrix that rotates theta rad around vector.
- Parameters
theta (float) – the rotation angle
vector (L{Vector}) – the rotation axis
- Returns
The rotation matrix, a 3x3 Numeric array.
Examples
>>> from numpy import pi >>> from Bio.PDB.vectors import rotaxis2m >>> from Bio.PDB.vectors import Vector >>> m = rotaxis2m(pi, Vector(1, 0, 0)) >>> Vector(1, 2, 3).left_multiply(m) <Vector 1.00, -2.00, -3.00>
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Bio.PDB.vectors.
refmat
(p, q)¶ Return a (left multiplying) matrix that mirrors p onto q.
- Returns
The mirror operation, a 3x3 Numeric array.
Examples
>>> from Bio.PDB.vectors import refmat >>> p, q = Vector(1, 2, 3), Vector(2, 3, 5) >>> mirror = refmat(p, q) >>> qq = p.left_multiply(mirror) >>> print(q) <Vector 2.00, 3.00, 5.00> >>> print(qq) <Vector 1.21, 1.82, 3.03>
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Bio.PDB.vectors.
rotmat
(p, q)¶ Return a (left multiplying) matrix that rotates p onto q.
- Parameters
p (L{Vector}) – moving vector
q (L{Vector}) – fixed vector
- Returns
rotation matrix that rotates p onto q
- Return type
3x3 Numeric array
Examples
>>> from Bio.PDB.vectors import rotmat >>> p, q = Vector(1, 2, 3), Vector(2, 3, 5) >>> r = rotmat(p, q) >>> print(q) <Vector 2.00, 3.00, 5.00> >>> print(p) <Vector 1.00, 2.00, 3.00> >>> p.left_multiply(r) <Vector 1.21, 1.82, 3.03>
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Bio.PDB.vectors.
calc_angle
(v1, v2, v3)¶ Calculate angle method.
Calculate the angle between 3 vectors representing 3 connected points.
- Parameters
v2, v3 (v1,) – the tree points that define the angle
- Returns
angle
- Return type
float
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Bio.PDB.vectors.
calc_dihedral
(v1, v2, v3, v4)¶ Calculate dihedral angle method.
Calculate the dihedral angle between 4 vectors representing 4 connected points. The angle is in ]-pi, pi].
- Parameters
v2, v3, v4 (v1,) – the four points that define the dihedral angle
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class
Bio.PDB.vectors.
Vector
(x, y=None, z=None)¶ Bases:
object
3D vector.
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__init__
(self, x, y=None, z=None)¶ Initialize the class.
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__repr__
(self)¶ Return vector 3D coordinates.
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__neg__
(self)¶ Return Vector(-x, -y, -z).
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__add__
(self, other)¶ Return Vector+other Vector or scalar.
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__sub__
(self, other)¶ Return Vector-other Vector or scalar.
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__mul__
(self, other)¶ Return Vector.Vector (dot product).
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__truediv__
(self, x)¶ Return Vector(coords/a).
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__pow__
(self, other)¶ Return VectorxVector (cross product) or Vectorxscalar.
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__getitem__
(self, i)¶ Return value of array index i.
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__setitem__
(self, i, value)¶ Assign values to array index i.
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__contains__
(self, i)¶ Validate if i is in array.
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norm
(self)¶ Return vector norm.
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normsq
(self)¶ Return square of vector norm.
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normalize
(self)¶ Normalize the Vector object.
Changes the state of
self
and doesn’t return a value. If you need to chain function calls or create a new object use thenormalized
method.
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normalized
(self)¶ Return a normalized copy of the Vector.
To avoid allocating new objects use the
normalize
method.
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angle
(self, other)¶ Return angle between two vectors.
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get_array
(self)¶ Return (a copy of) the array of coordinates.
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left_multiply
(self, matrix)¶ Return Vector=Matrix x Vector.
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right_multiply
(self, matrix)¶ Return Vector=Vector x Matrix.
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copy
(self)¶ Return a deep copy of the Vector.
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Bio.PDB.vectors.
homog_rot_mtx
(angle_rads: float, axis: str) → <built-in function array>¶ Generate a 4x4 single-axis numpy rotation matrix.
- Parameters
angle_rads (float) – the desired rotation angle in radians
axis (char) – character specifying the rotation axis
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Bio.PDB.vectors.
set_Z_homog_rot_mtx
(angle_rads: float, mtx: numpy.ndarray)¶ Update existing Z rotation matrix to new angle.
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Bio.PDB.vectors.
set_Y_homog_rot_mtx
(angle_rads: float, mtx: numpy.ndarray)¶ Update existing Y rotation matrix to new angle.
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Bio.PDB.vectors.
set_X_homog_rot_mtx
(angle_rads: float, mtx: numpy.ndarray)¶ Update existing X rotation matrix to new angle.
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Bio.PDB.vectors.
homog_trans_mtx
(x: float, y: float, z: float) → <built-in function array>¶ Generate a 4x4 numpy translation matrix.
- Parameters
y, z (x,) – translation in each axis
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Bio.PDB.vectors.
set_homog_trans_mtx
(x: float, y: float, z: float, mtx: numpy.ndarray)¶ Update existing translation matrix to new values.
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Bio.PDB.vectors.
homog_scale_mtx
(scale: float) → <built-in function array>¶ Generate a 4x4 numpy scaling matrix.
- Parameters
scale (float) – scale multiplier
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Bio.PDB.vectors.
get_spherical_coordinates
(xyz: <built-in function array>) → Tuple[float, float, float]¶ Compute spherical coordinates (r, azimuth, polar_angle) for X,Y,Z point.
- Parameters
xyz (array) – column vector (3 row x 1 column numpy array)
- Returns
tuple of r, azimuth, polar_angle for input coordinate
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Bio.PDB.vectors.
coord_space
(a0: numpy.ndarray, a1: numpy.ndarray, a2: numpy.ndarray, rev: bool = False) → Tuple[numpy.ndarray, Union[numpy.ndarray, NoneType]]¶ Generate transformation matrix to coordinate space defined by 3 points.
- New coordinate space will have:
acs[0] on XZ plane acs[1] origin acs[2] on +Z axis
- Parameters
column array x3 acs (numpy) – X,Y,Z column input coordinates x3
rev (bool) – if True, also return reverse transformation matrix (to return from coord_space)
- Returns
4x4 numpy array, x2 if rev=True
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Bio.PDB.vectors.
multi_rot_Z
(angle_rads: numpy.ndarray) → numpy.ndarray¶ Create [entries] numpy Z rotation matrices for [entries] angles.
- Parameters
entries – int number of matrices generated.
angle_rads – numpy array of angles
- Returns
entries x 4 x 4 homogeneous rotation matrices
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Bio.PDB.vectors.
multi_rot_Y
(angle_rads: numpy.ndarray) → numpy.ndarray¶ Create [entries] numpy Y rotation matrices for [entries] angles.
- Parameters
entries – int number of matrices generated.
angle_rads – numpy array of angles
- Returns
entries x 4 x 4 homogeneous rotation matrices