def compute_centroid(coords):
"""Compute the centroid of coordinates.
.. math::
\\mathbf{C} =
\\frac{\\sum_{i=1}^{N}m_i\\mathbf{r}_i}{\\sum_{i=1}^{N}m_i}
Returns
-------
C : `~sknano.core.math.Vector`
The position vector of the centroid coordinates.
"""
C = Vector(np.mean(coords, axis=0))
C.rezero()
return C
def centroid(self):
"""Centroid of `Atoms`.
Computes the position vector of the centroid of the `Atoms`
coordinates.
.. math::
\\mathbf{C} =
\\frac{\\sum_{i=1}^{N_{\\mathrm{atoms}}}
\\mathbf{r}_i}{N_{\\mathrm{atoms}}}
Returns
-------
C : :class:`~sknano.core.math.Vector`
The position vector of the centroid coordinates.
"""
C = Vector(np.mean(self.coords, axis=0))
C.rezero()
return C
def centroid(self):
"""Centroid of `Atoms`.
Computes the position vector of the centroid of the `Atoms`
coordinates.
.. math::
\\mathbf{C} =
\\frac{\\sum_{i=1}^{N_{\\mathrm{atoms}}}
\\mathbf{r}_i}{N_{\\mathrm{atoms}}}
Returns
-------
C : :class:`~sknano.core.math.Vector`
The position vector of the centroid coordinates.
"""
C = Vector(np.mean(self.coords, axis=0))
C.rezero()
return C
def center_of_mass(self):
"""Center-of-Mass coordinates of `Atoms`.
Computes the position vector of the center-of-mass coordinates:
.. math::
\\mathbf{R}_{COM} = \\frac{1}{M}\\sum_{i=1}^{N_{\\mathrm{atoms}}}
m_i\\mathbf{r}_i
Returns
-------
com : :class:`~sknano.core.math.Vector`
The position vector of the center of mass coordinates.
"""
masses = np.asarray([self.masses])
coords = self.coords
MxR = masses.T * coords
com = Vector(np.sum(MxR, axis=0) / np.sum(masses))
com.rezero()
return com
def center_of_mass(self):
"""Center-of-Mass coordinates of `Atoms`.
Computes the position vector of the center-of-mass coordinates:
.. math::
\\mathbf{R}_{COM} = \\frac{1}{M}\\sum_{i=1}^{N_{\\mathrm{atoms}}}
m_i\\mathbf{r}_i
Returns
-------
com : :class:`~sknano.core.math.Vector`
The position vector of the center of mass coordinates.
"""
masses = np.asarray([self.masses])
coords = self.coords
MxR = masses.T * coords
com = Vector(np.sum(MxR, axis=0) / np.sum(masses))
com.rezero()
return com
