502 lines
18 KiB
Python
502 lines
18 KiB
Python
import numpy as _np
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def Bravais_to_Miller(*,uvtw=None,hkil=None):
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"""
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Transform 4 Miller–Bravais indices to 3 Miller indices of crystal direction [uvw] or plane normal (hkl).
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Parameters
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----------
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uvtw|hkil : numpy.ndarray of shape (...,4)
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Miller–Bravais indices of crystallographic direction [uvtw] or plane normal (hkil).
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Returns
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-------
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uvw|hkl : numpy.ndarray of shape (...,3)
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Miller indices of [uvw] direction or (hkl) plane normal.
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"""
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if (uvtw is not None) ^ (hkil is None):
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raise KeyError('Specify either "uvtw" or "hkil"')
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axis,basis = (_np.array(uvtw),_np.array([[1,0,-1,0],
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[0,1,-1,0],
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[0,0, 0,1]])) \
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if hkil is None else \
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(_np.array(hkil),_np.array([[1,0,0,0],
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[0,1,0,0],
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[0,0,0,1]]))
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return _np.einsum('il,...l',basis,axis)
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def Miller_to_Bravais(*,uvw=None,hkl=None):
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"""
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Transform 3 Miller indices to 4 Miller–Bravais indices of crystal direction [uvtw] or plane normal (hkil).
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Parameters
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----------
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uvw|hkl : numpy.ndarray of shape (...,3)
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Miller indices of crystallographic direction [uvw] or plane normal (hkl).
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Returns
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-------
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uvtw|hkil : numpy.ndarray of shape (...,4)
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Miller–Bravais indices of [uvtw] direction or (hkil) plane normal.
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"""
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if (uvw is not None) ^ (hkl is None):
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raise KeyError('Specify either "uvw" or "hkl"')
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axis,basis = (_np.array(uvw),_np.array([[ 2,-1, 0],
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[-1, 2, 0],
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[-1,-1, 0],
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[ 0, 0, 3]])/3) \
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if hkl is None else \
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(_np.array(hkl),_np.array([[ 1, 0, 0],
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[ 0, 1, 0],
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[-1,-1, 0],
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[ 0, 0, 1]]))
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return _np.einsum('il,...l',basis,axis)
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kinematics = {
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'cF': {
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'slip' : _np.array([
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[+0,+1,-1 , +1,+1,+1],
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[-1,+0,+1 , +1,+1,+1],
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[+1,-1,+0 , +1,+1,+1],
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[+0,-1,-1 , -1,-1,+1],
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[+1,+0,+1 , -1,-1,+1],
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[-1,+1,+0 , -1,-1,+1],
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[+0,-1,+1 , +1,-1,-1],
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[-1,+0,-1 , +1,-1,-1],
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[+1,+1,+0 , +1,-1,-1],
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[+0,+1,+1 , -1,+1,-1],
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[+1,+0,-1 , -1,+1,-1],
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[-1,-1,+0 , -1,+1,-1],
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[+1,+1,+0 , +1,-1,+0],
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[+1,-1,+0 , +1,+1,+0],
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[+1,+0,+1 , +1,+0,-1],
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[+1,+0,-1 , +1,+0,+1],
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[+0,+1,+1 , +0,+1,-1],
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[+0,+1,-1 , +0,+1,+1],
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],'d'),
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'twin' : _np.array([
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[-2, 1, 1, 1, 1, 1],
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[ 1,-2, 1, 1, 1, 1],
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[ 1, 1,-2, 1, 1, 1],
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[ 2,-1, 1, -1,-1, 1],
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[-1, 2, 1, -1,-1, 1],
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[-1,-1,-2, -1,-1, 1],
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[-2,-1,-1, 1,-1,-1],
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[ 1, 2,-1, 1,-1,-1],
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[ 1,-1, 2, 1,-1,-1],
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[ 2, 1,-1, -1, 1,-1],
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[-1,-2,-1, -1, 1,-1],
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[-1, 1, 2, -1, 1,-1],
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],dtype=float),
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},
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'cI': {
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'slip' : _np.array([
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[+1,-1,+1 , +0,+1,+1],
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[-1,-1,+1 , +0,+1,+1],
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[+1,+1,+1 , +0,-1,+1],
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[-1,+1,+1 , +0,-1,+1],
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[-1,+1,+1 , +1,+0,+1],
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[-1,-1,+1 , +1,+0,+1],
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[+1,+1,+1 , -1,+0,+1],
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[+1,-1,+1 , -1,+0,+1],
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[-1,+1,+1 , +1,+1,+0],
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[-1,+1,-1 , +1,+1,+0],
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[+1,+1,+1 , -1,+1,+0],
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[+1,+1,-1 , -1,+1,+0],
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[-1,+1,+1 , +2,+1,+1],
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[+1,+1,+1 , -2,+1,+1],
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[+1,+1,-1 , +2,-1,+1],
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[+1,-1,+1 , +2,+1,-1],
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[+1,-1,+1 , +1,+2,+1],
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[+1,+1,-1 , -1,+2,+1],
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[+1,+1,+1 , +1,-2,+1],
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[-1,+1,+1 , +1,+2,-1],
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[+1,+1,-1 , +1,+1,+2],
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[+1,-1,+1 , -1,+1,+2],
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[-1,+1,+1 , +1,-1,+2],
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[+1,+1,+1 , +1,+1,-2],
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[+1,+1,-1 , +1,+2,+3],
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[+1,-1,+1 , -1,+2,+3],
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[-1,+1,+1 , +1,-2,+3],
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[+1,+1,+1 , +1,+2,-3],
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[+1,-1,+1 , +1,+3,+2],
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[+1,+1,-1 , -1,+3,+2],
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[+1,+1,+1 , +1,-3,+2],
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[-1,+1,+1 , +1,+3,-2],
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[+1,+1,-1 , +2,+1,+3],
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[+1,-1,+1 , -2,+1,+3],
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[-1,+1,+1 , +2,-1,+3],
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[+1,+1,+1 , +2,+1,-3],
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[+1,-1,+1 , +2,+3,+1],
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[+1,+1,-1 , -2,+3,+1],
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[+1,+1,+1 , +2,-3,+1],
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[-1,+1,+1 , +2,+3,-1],
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[-1,+1,+1 , +3,+1,+2],
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[+1,+1,+1 , -3,+1,+2],
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[+1,+1,-1 , +3,-1,+2],
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[+1,-1,+1 , +3,+1,-2],
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[-1,+1,+1 , +3,+2,+1],
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[+1,+1,+1 , -3,+2,+1],
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[+1,+1,-1 , +3,-2,+1],
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[+1,-1,+1 , +3,+2,-1],
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],'d'),
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'twin' : _np.array([
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[-1, 1, 1, 2, 1, 1],
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[ 1, 1, 1, -2, 1, 1],
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[ 1, 1,-1, 2,-1, 1],
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[ 1,-1, 1, 2, 1,-1],
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[ 1,-1, 1, 1, 2, 1],
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[ 1, 1,-1, -1, 2, 1],
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[ 1, 1, 1, 1,-2, 1],
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[-1, 1, 1, 1, 2,-1],
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[ 1, 1,-1, 1, 1, 2],
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[ 1,-1, 1, -1, 1, 2],
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[-1, 1, 1, 1,-1, 2],
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[ 1, 1, 1, 1, 1,-2],
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],dtype=float),
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},
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'hP': {
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'slip' : _np.array([
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[+2,-1,-1,+0 , +0,+0,+0,+1],
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[-1,+2,-1,+0 , +0,+0,+0,+1],
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[-1,-1,+2,+0 , +0,+0,+0,+1],
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[+2,-1,-1,+0 , +0,+1,-1,+0],
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[-1,+2,-1,+0 , -1,+0,+1,+0],
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[-1,-1,+2,+0 , +1,-1,+0,+0],
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[-1,+1,+0,+0 , +1,+1,-2,+0],
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[+0,-1,+1,+0 , -2,+1,+1,+0],
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[+1,+0,-1,+0 , +1,-2,+1,+0],
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[-1,+2,-1,+0 , +1,+0,-1,+1],
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[-2,+1,+1,+0 , +0,+1,-1,+1],
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[-1,-1,+2,+0 , -1,+1,+0,+1],
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[+1,-2,+1,+0 , -1,+0,+1,+1],
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[+2,-1,-1,+0 , +0,-1,+1,+1],
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[+1,+1,-2,+0 , +1,-1,+0,+1],
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[-2,+1,+1,+3 , +1,+0,-1,+1],
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[-1,-1,+2,+3 , +1,+0,-1,+1],
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[-1,-1,+2,+3 , +0,+1,-1,+1],
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[+1,-2,+1,+3 , +0,+1,-1,+1],
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[+1,-2,+1,+3 , -1,+1,+0,+1],
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[+2,-1,-1,+3 , -1,+1,+0,+1],
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[+2,-1,-1,+3 , -1,+0,+1,+1],
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[+1,+1,-2,+3 , -1,+0,+1,+1],
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[+1,+1,-2,+3 , +0,-1,+1,+1],
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[-1,+2,-1,+3 , +0,-1,+1,+1],
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[-1,+2,-1,+3 , +1,-1,+0,+1],
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[-2,+1,+1,+3 , +1,-1,+0,+1],
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[-1,-1,+2,+3 , +1,+1,-2,+2],
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[+1,-2,+1,+3 , -1,+2,-1,+2],
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[+2,-1,-1,+3 , -2,+1,+1,+2],
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[+1,+1,-2,+3 , -1,-1,+2,+2],
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[-1,+2,-1,+3 , +1,-2,+1,+2],
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[-2,+1,+1,+3 , +2,-1,-1,+2],
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],'d'),
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'twin' : _np.array([
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[-1, 0, 1, 1, 1, 0, -1, 2], # shear = (3-(c/a)^2)/(sqrt(3) c/a) <-10.1>{10.2}
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[ 0, -1, 1, 1, 0, 1, -1, 2],
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[ 1, -1, 0, 1, -1, 1, 0, 2],
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[ 1, 0, -1, 1, -1, 0, 1, 2],
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[ 0, 1, -1, 1, 0, -1, 1, 2],
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[-1, 1, 0, 1, 1, -1, 0, 2],
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[-1, -1, 2, 6, 1, 1, -2, 1], # shear = 1/(c/a) <11.6>{-1-1.1}
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[ 1, -2, 1, 6, -1, 2, -1, 1],
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[ 2, -1, -1, 6, -2, 1, 1, 1],
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[ 1, 1, -2, 6, -1, -1, 2, 1],
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[-1, 2, -1, 6, 1, -2, 1, 1],
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[-2, 1, 1, 6, 2, -1, -1, 1],
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[ 1, 0, -1, -2, 1, 0, -1, 1], # shear = (4(c/a)^2-9)/(4 sqrt(3) c/a) <10.-2>{10.1}
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[ 0, 1, -1, -2, 0, 1, -1, 1],
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[-1, 1, 0, -2, -1, 1, 0, 1],
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[-1, 0, 1, -2, -1, 0, 1, 1],
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[ 0, -1, 1, -2, 0, -1, 1, 1],
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[ 1, -1, 0, -2, 1, -1, 0, 1],
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[ 1, 1, -2, -3, 1, 1, -2, 2], # shear = 2((c/a)^2-2)/(3 c/a) <11.-3>{11.2}
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[-1, 2, -1, -3, -1, 2, -1, 2],
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[-2, 1, 1, -3, -2, 1, 1, 2],
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[-1, -1, 2, -3, -1, -1, 2, 2],
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[ 1, -2, 1, -3, 1, -2, 1, 2],
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[ 2, -1, -1, -3, 2, -1, -1, 2],
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],dtype=float),
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},
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}
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# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
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# from S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
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# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
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relations = {
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'KS': {
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'cF' : _np.array([
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[[ -1, 0, 1],[ 1, 1, 1]],
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[[ -1, 0, 1],[ 1, 1, 1]],
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[[ 0, 1, -1],[ 1, 1, 1]],
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[[ 0, 1, -1],[ 1, 1, 1]],
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[[ 1, -1, 0],[ 1, 1, 1]],
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[[ 1, -1, 0],[ 1, 1, 1]],
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[[ 1, 0, -1],[ 1, -1, 1]],
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[[ 1, 0, -1],[ 1, -1, 1]],
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[[ -1, -1, 0],[ 1, -1, 1]],
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[[ -1, -1, 0],[ 1, -1, 1]],
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[[ 0, 1, 1],[ 1, -1, 1]],
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[[ 0, 1, 1],[ 1, -1, 1]],
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[[ 0, -1, 1],[ -1, 1, 1]],
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[[ 0, -1, 1],[ -1, 1, 1]],
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[[ -1, 0, -1],[ -1, 1, 1]],
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[[ -1, 0, -1],[ -1, 1, 1]],
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[[ 1, 1, 0],[ -1, 1, 1]],
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[[ 1, 1, 0],[ -1, 1, 1]],
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[[ -1, 1, 0],[ 1, 1, -1]],
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[[ -1, 1, 0],[ 1, 1, -1]],
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[[ 0, -1, -1],[ 1, 1, -1]],
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[[ 0, -1, -1],[ 1, 1, -1]],
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[[ 1, 0, 1],[ 1, 1, -1]],
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[[ 1, 0, 1],[ 1, 1, -1]],
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],dtype=float),
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'cI' : _np.array([
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, -1],[ 0, 1, 1]],
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],dtype=float),
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},
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'GT': {
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'cF' : _np.array([
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[[ -5,-12, 17],[ 1, 1, 1]],
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[[ 17, -5,-12],[ 1, 1, 1]],
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[[-12, 17, -5],[ 1, 1, 1]],
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[[ 5, 12, 17],[ -1, -1, 1]],
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[[-17, 5,-12],[ -1, -1, 1]],
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[[ 12,-17, -5],[ -1, -1, 1]],
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[[ -5, 12,-17],[ -1, 1, 1]],
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[[ 17, 5, 12],[ -1, 1, 1]],
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[[-12,-17, 5],[ -1, 1, 1]],
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[[ 5,-12,-17],[ 1, -1, 1]],
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[[-17, -5, 12],[ 1, -1, 1]],
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[[ 12, 17, 5],[ 1, -1, 1]],
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[[ -5, 17,-12],[ 1, 1, 1]],
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[[-12, -5, 17],[ 1, 1, 1]],
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[[ 17,-12, -5],[ 1, 1, 1]],
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[[ 5,-17,-12],[ -1, -1, 1]],
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[[ 12, 5, 17],[ -1, -1, 1]],
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[[-17, 12, -5],[ -1, -1, 1]],
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[[ -5,-17, 12],[ -1, 1, 1]],
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[[-12, 5,-17],[ -1, 1, 1]],
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[[ 17, 12, 5],[ -1, 1, 1]],
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[[ 5, 17, 12],[ 1, -1, 1]],
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[[ 12, -5,-17],[ 1, -1, 1]],
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[[-17,-12, 5],[ 1, -1, 1]],
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],dtype=float),
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'cI' : _np.array([
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[[-17, -7, 17],[ 1, 0, 1]],
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[[ 17,-17, -7],[ 1, 1, 0]],
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[[ -7, 17,-17],[ 0, 1, 1]],
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[[ 17, 7, 17],[ -1, 0, 1]],
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[[-17, 17, -7],[ -1, -1, 0]],
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[[ 7,-17,-17],[ 0, -1, 1]],
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[[-17, 7,-17],[ -1, 0, 1]],
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[[ 17, 17, 7],[ -1, 1, 0]],
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[[ -7,-17, 17],[ 0, 1, 1]],
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[[ 17, -7,-17],[ 1, 0, 1]],
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[[-17,-17, 7],[ 1, -1, 0]],
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[[ 7, 17, 17],[ 0, -1, 1]],
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[[-17, 17, -7],[ 1, 1, 0]],
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[[ -7,-17, 17],[ 0, 1, 1]],
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[[ 17, -7,-17],[ 1, 0, 1]],
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[[ 17,-17, -7],[ -1, -1, 0]],
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[[ 7, 17, 17],[ 0, -1, 1]],
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[[-17, 7,-17],[ -1, 0, 1]],
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[[-17,-17, 7],[ -1, 1, 0]],
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[[ -7, 17,-17],[ 0, 1, 1]],
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[[ 17, 7, 17],[ -1, 0, 1]],
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[[ 17, 17, 7],[ 1, -1, 0]],
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[[ 7,-17,-17],[ 0, -1, 1]],
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[[-17, -7, 17],[ 1, 0, 1]],
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],dtype=float),
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},
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'GT_prime': {
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'cF' : _np.array([
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[[ 0, 1, -1],[ 7, 17, 17]],
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[[ -1, 0, 1],[ 17, 7, 17]],
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[[ 1, -1, 0],[ 17, 17, 7]],
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[[ 0, -1, -1],[ -7,-17, 17]],
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[[ 1, 0, 1],[-17, -7, 17]],
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[[ 1, -1, 0],[-17,-17, 7]],
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[[ 0, 1, -1],[ 7,-17,-17]],
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[[ 1, 0, 1],[ 17, -7,-17]],
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[[ -1, -1, 0],[ 17,-17, -7]],
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[[ 0, -1, -1],[ -7, 17,-17]],
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[[ -1, 0, 1],[-17, 7,-17]],
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[[ -1, -1, 0],[-17, 17, -7]],
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[[ 0, -1, 1],[ 7, 17, 17]],
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[[ 1, 0, -1],[ 17, 7, 17]],
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[[ -1, 1, 0],[ 17, 17, 7]],
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[[ 0, 1, 1],[ -7,-17, 17]],
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[[ -1, 0, -1],[-17, -7, 17]],
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[[ -1, 1, 0],[-17,-17, 7]],
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[[ 0, -1, 1],[ 7,-17,-17]],
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[[ -1, 0, -1],[ 17, -7,-17]],
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[[ 1, 1, 0],[ 17,-17, -7]],
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[[ 0, 1, 1],[ -7, 17,-17]],
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[[ 1, 0, -1],[-17, 7,-17]],
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[[ 1, 1, 0],[-17, 17, -7]],
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],dtype=float),
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'cI' : _np.array([
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[[ 1, 1, -1],[ 12, 5, 17]],
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[[ -1, 1, 1],[ 17, 12, 5]],
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[[ 1, -1, 1],[ 5, 17, 12]],
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[[ -1, -1, -1],[-12, -5, 17]],
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[[ 1, -1, 1],[-17,-12, 5]],
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[[ 1, -1, -1],[ -5,-17, 12]],
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[[ -1, 1, -1],[ 12, -5,-17]],
|
||
[[ 1, 1, 1],[ 17,-12, -5]],
|
||
[[ -1, -1, 1],[ 5,-17,-12]],
|
||
[[ 1, -1, -1],[-12, 5,-17]],
|
||
[[ -1, -1, 1],[-17, 12, -5]],
|
||
[[ -1, -1, -1],[ -5, 17,-12]],
|
||
[[ 1, -1, 1],[ 12, 17, 5]],
|
||
[[ 1, 1, -1],[ 5, 12, 17]],
|
||
[[ -1, 1, 1],[ 17, 5, 12]],
|
||
[[ -1, 1, 1],[-12,-17, 5]],
|
||
[[ -1, -1, -1],[ -5,-12, 17]],
|
||
[[ -1, 1, -1],[-17, -5, 12]],
|
||
[[ -1, -1, 1],[ 12,-17, -5]],
|
||
[[ -1, 1, -1],[ 5,-12,-17]],
|
||
[[ 1, 1, 1],[ 17, -5,-12]],
|
||
[[ 1, 1, 1],[-12, 17, -5]],
|
||
[[ 1, -1, -1],[ -5, 12,-17]],
|
||
[[ 1, 1, -1],[-17, 5,-12]],
|
||
],dtype=float),
|
||
},
|
||
'NW': {
|
||
'cF' : _np.array([
|
||
[[ 2, -1, -1],[ 1, 1, 1]],
|
||
[[ -1, 2, -1],[ 1, 1, 1]],
|
||
[[ -1, -1, 2],[ 1, 1, 1]],
|
||
[[ -2, -1, -1],[ -1, 1, 1]],
|
||
[[ 1, 2, -1],[ -1, 1, 1]],
|
||
[[ 1, -1, 2],[ -1, 1, 1]],
|
||
[[ 2, 1, -1],[ 1, -1, 1]],
|
||
[[ -1, -2, -1],[ 1, -1, 1]],
|
||
[[ -1, 1, 2],[ 1, -1, 1]],
|
||
[[ 2, -1, 1],[ -1, -1, 1]],
|
||
[[ -1, 2, 1],[ -1, -1, 1]],
|
||
[[ -1, -1, -2],[ -1, -1, 1]],
|
||
],dtype=float),
|
||
'cI' : _np.array([
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
[[ 0, -1, 1],[ 0, 1, 1]],
|
||
],dtype=float),
|
||
},
|
||
'Pitsch': {
|
||
'cF' : _np.array([
|
||
[[ 1, 0, 1],[ 0, 1, 0]],
|
||
[[ 1, 1, 0],[ 0, 0, 1]],
|
||
[[ 0, 1, 1],[ 1, 0, 0]],
|
||
[[ 0, 1, -1],[ 1, 0, 0]],
|
||
[[ -1, 0, 1],[ 0, 1, 0]],
|
||
[[ 1, -1, 0],[ 0, 0, 1]],
|
||
[[ 1, 0, -1],[ 0, 1, 0]],
|
||
[[ -1, 1, 0],[ 0, 0, 1]],
|
||
[[ 0, -1, 1],[ 1, 0, 0]],
|
||
[[ 0, 1, 1],[ 1, 0, 0]],
|
||
[[ 1, 0, 1],[ 0, 1, 0]],
|
||
[[ 1, 1, 0],[ 0, 0, 1]],
|
||
],dtype=float),
|
||
'cI' : _np.array([
|
||
[[ 1, -1, 1],[ -1, 0, 1]],
|
||
[[ 1, 1, -1],[ 1, -1, 0]],
|
||
[[ -1, 1, 1],[ 0, 1, -1]],
|
||
[[ -1, 1, -1],[ 0, -1, -1]],
|
||
[[ -1, -1, 1],[ -1, 0, -1]],
|
||
[[ 1, -1, -1],[ -1, -1, 0]],
|
||
[[ 1, -1, -1],[ -1, 0, -1]],
|
||
[[ -1, 1, -1],[ -1, -1, 0]],
|
||
[[ -1, -1, 1],[ 0, -1, -1]],
|
||
[[ -1, 1, 1],[ 0, -1, 1]],
|
||
[[ 1, -1, 1],[ 1, 0, -1]],
|
||
[[ 1, 1, -1],[ -1, 1, 0]],
|
||
],dtype=float),
|
||
},
|
||
'Bain': {
|
||
'cF' : _np.array([
|
||
[[ 0, 1, 0],[ 1, 0, 0]],
|
||
[[ 0, 0, 1],[ 0, 1, 0]],
|
||
[[ 1, 0, 0],[ 0, 0, 1]],
|
||
],dtype=float),
|
||
'cI' : _np.array([
|
||
[[ 0, 1, 1],[ 1, 0, 0]],
|
||
[[ 1, 0, 1],[ 0, 1, 0]],
|
||
[[ 1, 1, 0],[ 0, 0, 1]],
|
||
],dtype=float),
|
||
},
|
||
'Burgers' : {
|
||
'cI' : _np.array([
|
||
[[ -1, 1, 1],[ 1, 1, 0]],
|
||
[[ -1, 1, -1],[ 1, 1, 0]],
|
||
[[ 1, 1, 1],[ 1, -1, 0]],
|
||
[[ 1, 1, -1],[ 1, -1, 0]],
|
||
|
||
[[ 1, 1, -1],[ 1, 0, 1]],
|
||
[[ -1, 1, 1],[ 1, 0, 1]],
|
||
[[ 1, 1, 1],[ -1, 0, 1]],
|
||
[[ 1, -1, 1],[ -1, 0, 1]],
|
||
|
||
[[ -1, 1, -1],[ 0, 1, 1]],
|
||
[[ 1, 1, -1],[ 0, 1, 1]],
|
||
[[ -1, 1, 1],[ 0, -1, 1]],
|
||
[[ 1, 1, 1],[ 0, -1, 1]],
|
||
],dtype=float),
|
||
'hP' : _np.array([
|
||
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
|
||
|
||
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
|
||
|
||
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, 2, -1, 0],[ 0, 0, 0, 1]],
|
||
[[ -1, -1, 2, 0],[ 0, 0, 0, 1]],
|
||
],dtype=float),
|
||
},
|
||
}
|