75 lines
1.6 KiB
Python
75 lines
1.6 KiB
Python
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"""
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Tensor operations.
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Notes
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-----
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This is not a tensor class, but a collection of routines
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to operate on numpy.ndarrays of shape (...,3,3).
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"""
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import numpy as _np
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def symmetric(T):
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"""
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Return the symmetrized tensor.
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Parameters
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----------
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T : numpy.ndarray of shape (...,3,3)
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Tensor of which the symmetrized values are computed.
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"""
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return (T+transpose(T))*0.5
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def transpose(T):
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"""
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Return the transpose of a tensor.
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Parameters
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----------
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T : numpy.ndarray of shape (...,3,3)
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Tensor of which the transpose is computed.
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"""
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return _np.swapaxes(T,axis2=-2,axis1=-1)
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def eigenvalues(T_sym):
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"""
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Return the eigenvalues, i.e. principal components, of a symmetric tensor.
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The eigenvalues are sorted in ascending order, each repeated according to
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its multiplicity.
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Parameters
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----------
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T_sym : numpy.ndarray of shape (...,3,3)
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Symmetric tensor of which the eigenvalues are computed.
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"""
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return _np.linalg.eigvalsh(symmetric(T_sym))
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def eigenvectors(T_sym,RHS=False):
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"""
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Return eigenvectors of a symmetric tensor.
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The eigenvalues are sorted in ascending order of their associated eigenvalues.
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Parameters
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----------
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T_sym : numpy.ndarray of shape (...,3,3)
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Symmetric tensor of which the eigenvectors are computed.
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RHS: bool, optional
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Enforce right-handed coordinate system. Default is False.
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"""
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(u,v) = _np.linalg.eigh(symmetric(T_sym))
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if RHS:
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v[_np.linalg.det(v) < 0.0,:,2] *= -1.0
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return v
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