vectorized
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@ -22,35 +22,16 @@ def shapeMismatch(size,F,nodes,centres):
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the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
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the initial volume element with the current deformation gradient.
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"""
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sMismatch = np.empty(F.shape[:3])
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#--------------------------------------------------------------------------------------------------
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# initial positions
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delta = size/grid*.5
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coordsInitial = np.vstack((delta * np.array((-1,-1,-1)),
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delta * np.array((+1,-1,-1)),
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delta * np.array((+1,+1,-1)),
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delta * np.array((-1,+1,-1)),
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delta * np.array((-1,-1,+1)),
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delta * np.array((+1,-1,+1)),
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delta * np.array((+1,+1,+1)),
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delta * np.array((-1,+1,+1))))
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#--------------------------------------------------------------------------------------------------
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# compare deformed original and deformed positions to actual positions
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for k in range(grid[0]):
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for j in range(grid[1]):
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for i in range(grid[2]):
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sMismatch[k,j,i] = \
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+ np.linalg.norm(nodes[k, j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[0,0:3]))\
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+ np.linalg.norm(nodes[k+1,j, i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[1,0:3]))\
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+ np.linalg.norm(nodes[k+1,j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[2,0:3]))\
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+ np.linalg.norm(nodes[k, j+1,i ,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[3,0:3]))\
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+ np.linalg.norm(nodes[k, j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[4,0:3]))\
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+ np.linalg.norm(nodes[k+1,j, i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[5,0:3]))\
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+ np.linalg.norm(nodes[k+1,j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[6,0:3]))\
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+ np.linalg.norm(nodes[k ,j+1,i+1,0:3] - centres[k,j,i,0:3] - np.dot(F[k,j,i,:,:], coordsInitial[7,0:3]))
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return sMismatch
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return + np.linalg.norm(nodes[:-1,:-1,:-1] -centres - np.dot(F,delta * np.array((-1,-1,-1))),axis=-1)\
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+ np.linalg.norm(nodes[+1:,:-1,:-1] -centres - np.dot(F,delta * np.array((+1,-1,-1))),axis=-1)\
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+ np.linalg.norm(nodes[+1:,+1:,:-1] -centres - np.dot(F,delta * np.array((+1,+1,-1))),axis=-1)\
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+ np.linalg.norm(nodes[:-1,+1:,:-1] -centres - np.dot(F,delta * np.array((-1,+1,-1))),axis=-1)\
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+ np.linalg.norm(nodes[:-1,:-1,+1:] -centres - np.dot(F,delta * np.array((-1,-1,+1))),axis=-1)\
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+ np.linalg.norm(nodes[+1:,:-1,+1:] -centres - np.dot(F,delta * np.array((+1,-1,+1))),axis=-1)\
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+ np.linalg.norm(nodes[+1:,+1:,+1:] -centres - np.dot(F,delta * np.array((+1,+1,+1))),axis=-1)\
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+ np.linalg.norm(nodes[:-1,+1:,+1:] -centres - np.dot(F,delta * np.array((-1,+1,+1))),axis=-1)
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# --------------------------------------------------------------------
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