Merge branch '256-grid-geometry-displacement-reconstruction' into 'development'
Resolve "grid geometry/displacement reconstruction" Closes #256 See merge request damask/DAMASK!762
This commit is contained in:
Sharan Roongta
commit
f424d54f5e
2
PRIVATE
2
PRIVATE
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@ -1 +1 @@
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Subproject commit 4cd6c7350b0a9d4ad3efcb5fe6c6cfffa99c426f
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Subproject commit 486e66396f57abe970f01337b9b3967993dd601f
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@ -186,8 +186,6 @@ def displacement_fluct_point(size: _FloatSequence,
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Fluctuating part of the cell center displacements.
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"""
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integrator = 0.5j*_np.array(size,float)/_np.pi
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k_s = _ks(size,F.shape[:3],False)
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k_s_squared = _np.einsum('...l,...l',k_s,k_s)
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k_s_squared[0,0,0] = 1.0
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@ -195,8 +193,8 @@ def displacement_fluct_point(size: _FloatSequence,
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displacement = -_np.einsum('ijkml,ijkl,l->ijkm',
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_np.fft.rfftn(F,axes=(0,1,2)),
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k_s,
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integrator,
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) / k_s_squared[...,_np.newaxis]
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_np.array([0.5j/_np.pi]*3),
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) / k_s_squared[...,_np.newaxis]
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return _np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
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@ -2,98 +2,153 @@ import pytest
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import numpy as np
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from damask import grid_filters
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from damask import mechanics
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from damask import Grid
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from damask import seeds
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class TestGridFilters:
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def test_coordinates0_point(self):
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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coord = grid_filters.coordinates0_point(cells,size)
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assert np.allclose(coord[0,0,0],size/cells*.5) and coord.shape == tuple(cells) + (3,)
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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coord = grid_filters.coordinates0_point(cells,size)
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assert np.allclose(coord[0,0,0],size/cells*.5) and coord.shape == tuple(cells) + (3,)
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def test_coordinates0_node(self):
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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coord = grid_filters.coordinates0_node(cells,size)
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assert np.allclose(coord[-1,-1,-1],size) and coord.shape == tuple(cells+1) + (3,)
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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coord = grid_filters.coordinates0_node(cells,size)
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assert np.allclose(coord[-1,-1,-1],size) and coord.shape == tuple(cells+1) + (3,)
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def test_coord0(self):
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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c = grid_filters.coordinates0_point(cells+1,size+size/cells)
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n = grid_filters.coordinates0_node(cells,size) + size/cells*.5
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assert np.allclose(c,n)
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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c = grid_filters.coordinates0_point(cells+1,size+size/cells)
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n = grid_filters.coordinates0_node(cells,size) + size/cells*.5
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assert np.allclose(c,n)
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@pytest.mark.parametrize('mode',['point','node'])
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def test_grid_DNA(self,mode):
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"""Ensure that cellsSizeOrigin_coordinates0_xx is the inverse of coordinates0_xx.""" # noqa
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cells = np.random.randint(8,32,(3))
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size = np.random.random(3)
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origin = np.random.random(3)
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coord0 = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)') # noqa
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_cells,_size,_origin = eval(f'grid_filters.cellsSizeOrigin_coordinates0_{mode}(coord0.reshape(-1,3,order="F"))')
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assert np.allclose(cells,_cells) and np.allclose(size,_size) and np.allclose(origin,_origin)
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"""Ensure that cellsSizeOrigin_coordinates0_xx is the inverse of coordinates0_xx.""" # noqa
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cells = np.random.randint(8,32,(3))
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size = np.random.random(3)
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origin = np.random.random(3)
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coord0 = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)') # noqa
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_cells,_size,_origin = eval(f'grid_filters.cellsSizeOrigin_coordinates0_{mode}(coord0.reshape(-1,3,order="F"))')
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assert np.allclose(cells,_cells) and np.allclose(size,_size) and np.allclose(origin,_origin)
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def test_displacement_fluct_equivalence(self):
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"""Ensure that fluctuations are periodic.""" # noqa
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size = np.random.random(3)
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cells = np.random.randint(8,32,(3))
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F = np.random.random(tuple(cells)+(3,3))
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assert np.allclose(grid_filters.displacement_fluct_node(size,F),
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grid_filters.point_to_node(grid_filters.displacement_fluct_point(size,F)))
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def test_displacement_fluct_periodic(self):
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"""Ensure that fluctuations are periodic.""" # noqa
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size = np.random.random(3)
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cells = np.random.randint(8,32,(3))
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F = np.random.random(tuple(cells)+(3,3))
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assert np.allclose(grid_filters.displacement_fluct_node(size,F),
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grid_filters.point_to_node(grid_filters.displacement_fluct_point(size,F)))
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def test_interpolation_to_node(self):
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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F = np.random.random(tuple(cells)+(3,3))
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assert np.allclose(grid_filters.coordinates_node(size,F) [1:-1,1:-1,1:-1],
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grid_filters.point_to_node(grid_filters.coordinates_point(size,F))[1:-1,1:-1,1:-1])
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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F = np.random.random(tuple(cells)+(3,3))
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assert np.allclose(grid_filters.coordinates_node(size,F) [1:-1,1:-1,1:-1],
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grid_filters.point_to_node(grid_filters.coordinates_point(size,F))[1:-1,1:-1,1:-1])
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def test_interpolation_to_cell(self):
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cells = np.random.randint(1,30,(3)) # noqa
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cells = np.random.randint(1,30,(3)) # noqa
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coordinates_node_x = np.linspace(0,np.pi*2,num=cells[0]+1)
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node_field_x = np.cos(coordinates_node_x)
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node_field = np.broadcast_to(node_field_x.reshape(-1,1,1),cells+1)
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coordinates_node_x = np.linspace(0,np.pi*2,num=cells[0]+1)
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node_field_x = np.cos(coordinates_node_x)
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node_field = np.broadcast_to(node_field_x.reshape(-1,1,1),cells+1)
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coordinates0_point_x = coordinates_node_x[:-1]+coordinates_node_x[1]*.5
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cell_field_x = np.interp(coordinates0_point_x,coordinates_node_x,node_field_x,period=np.pi*2.)
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cell_field = np.broadcast_to(cell_field_x.reshape(-1,1,1),cells)
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coordinates0_point_x = coordinates_node_x[:-1]+coordinates_node_x[1]*.5
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cell_field_x = np.interp(coordinates0_point_x,coordinates_node_x,node_field_x,period=np.pi*2.)
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cell_field = np.broadcast_to(cell_field_x.reshape(-1,1,1),cells)
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assert np.allclose(cell_field,grid_filters.node_to_point(node_field))
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assert np.allclose(cell_field,grid_filters.node_to_point(node_field))
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@pytest.mark.parametrize('mode',['point','node'])
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def test_coordinates0_origin(self,mode):
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origin= np.random.random(3) # noqa
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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shifted = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)')
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unshifted = eval(f'grid_filters.coordinates0_{mode}(cells,size)')
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if mode == 'cell':
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origin= np.random.random(3) # noqa
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size = np.random.random(3) # noqa
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cells = np.random.randint(8,32,(3))
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shifted = eval(f'grid_filters.coordinates0_{mode}(cells,size,origin)')
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unshifted = eval(f'grid_filters.coordinates0_{mode}(cells,size)')
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if mode == 'cell':
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assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(cells) +(3,)))
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elif mode == 'node':
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elif mode == 'node':
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assert np.allclose(shifted,unshifted+np.broadcast_to(origin,tuple(cells+1)+(3,)))
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@pytest.mark.parametrize('function',[grid_filters.displacement_avg_point,
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grid_filters.displacement_avg_node])
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def test_displacement_avg_vanishes(self,function):
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"""Ensure that random fluctuations in F do not result in average displacement.""" # noqa
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size = np.random.random(3)
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cells = np.random.randint(8,32,(3))
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F = np.random.random(tuple(cells)+(3,3))
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F += np.eye(3) - np.average(F,axis=(0,1,2))
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assert np.allclose(function(size,F),0.0)
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"""Ensure that random fluctuations in F do not result in average displacement.""" # noqa
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size = np.random.random(3) + 1.0
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cells = np.random.randint(8,32,(3))
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F = np.random.random(tuple(cells)+(3,3))
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F += np.eye(3) - np.average(F,axis=(0,1,2))
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assert np.allclose(function(size,F),0.0)
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@pytest.mark.parametrize('function',[grid_filters.displacement_avg_point,
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grid_filters.displacement_avg_node])
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def test_displacement_avg_vanishes_simple(self,function):
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F = np.eye(3)
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size = np.random.random(3) + 1.0
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F_c = F.copy()
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F_t = F.copy()
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F_c[0,0] = 0.8
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F_t[0,0] = 1.2
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F_no_avg = np.concatenate([np.broadcast_to(_,(10,20,20,3,3)) for _ in [F_t,F_c]])
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assert np.allclose(function(size,F_no_avg),0.0)
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@pytest.mark.parametrize('function',[grid_filters.displacement_fluct_point,
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grid_filters.displacement_fluct_node])
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def test_displacement_fluct_vanishes(self,function):
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"""Ensure that constant F does not result in fluctuating displacement.""" # noqa
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size = np.random.random(3)
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cells = np.random.randint(8,32,(3))
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F = np.broadcast_to(np.random.random((3,3)), tuple(cells)+(3,3))
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assert np.allclose(function(size,F),0.0)
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def test_displacement_fluct_vanishes_avg(self,function):
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"""Ensure that constant F does not result in fluctuating displacement.""" # noqa
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size = np.random.random(3)
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cells = np.random.randint(8,32,(3))
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F = np.broadcast_to(np.random.random((3,3)), tuple(cells)+(3,3))
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assert np.allclose(function(size,F),0.0)
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displacement_fluct_test_data = [
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(['np.sin(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0',
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'0.0', '0.0', '0.0',
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'0.0', '0.0', '0.0'],
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['-np.cos(np.pi*2*nodes[...,0]/size[0])/np.pi/2*size[0]', '0.0', '0.0']),
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(['np.cos(np.pi*2*nodes[...,0]/size[0])', '0.0', '0.0',
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'0.0', '0.0', '0.0',
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'0.0', '0.0', 'np.cos(np.pi*2*nodes[...,2]/size[2])'],
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['np.sin(np.pi*2*nodes[...,0]/size[0])/np.pi/2*size[0]',
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'0.0',
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'np.sin(np.pi*2*nodes[...,2]/size[2])/np.pi/2*size[2]'])]
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@pytest.mark.parametrize('F_def,u_def',displacement_fluct_test_data)
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def test_displacment_fluct_analytic(self,F_def,u_def):
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size = np.random.random(3)+1.0
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cells = np.random.randint(8,32,(3))
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nodes = grid_filters.coordinates0_point(cells,size)
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my_locals = locals() # needed for list comprehension
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F = np.stack([np.broadcast_to(eval(F,globals(),my_locals),cells) for F in F_def],axis=-1).reshape(tuple(cells) + (3,3))
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u = np.stack([np.broadcast_to(eval(u,globals(),my_locals),cells) for u in u_def],axis=-1).reshape(tuple(cells) + (3,))
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assert np.allclose(u,grid_filters.displacement_fluct_point(size,F))
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def test_coordinates(self):
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cells = np.array([np.random.randint(40,100)*2,2,2])
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size = (np.random.rand(3)+0.8)*cells
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F = np.broadcast_to(np.eye(3),tuple(cells)+(3,3)).copy()
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F[...,0,0] += np.expand_dims(0.1*np.sin(np.linspace(0,2*np.pi,cells[0],False))+
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np.random.rand(cells[0])*0.05,(-1,-2))
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c_n = grid_filters.coordinates_node(size,F)[:,0,0,0]
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l_0 = (size/cells)[0]
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l = c_n[1:] - c_n[:-1]
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epsilon_reconstructed = (l-l_0)/l_0
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epsilon_direct = mechanics.strain(F,'V',1)[:,0,0,0,0]
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assert np.corrcoef(epsilon_reconstructed,epsilon_direct)[0,1] > 0.99
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@pytest.mark.parametrize('function',[grid_filters.cellsSizeOrigin_coordinates0_point,
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grid_filters.cellsSizeOrigin_coordinates0_node])
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