DAMASK_EICMD/python/damask/_grid.py

1152 lines
44 KiB
Python
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

import os
import copy
import warnings
import multiprocessing as mp
from functools import partial
import numpy as np
import pandas as pd
import h5py
from scipy import ndimage, spatial
from . import VTK
from . import util
from . import grid_filters
from . import Rotation
class Grid:
"""
Geometry definition for grid solvers.
Create and manipulate geometry definitions for storage as VTK
image data files ('.vti' extension). A grid contains the
material ID (referring to the entry in 'material.yaml') and
the physical size.
"""
def __init__(self,material,size,origin=[0.0,0.0,0.0],comments=[]):
"""
New geometry definition for grid solvers.
Parameters
----------
material : numpy.ndarray of shape (:,:,:)
Material indices. The shape of the material array defines
the number of cells.
size : list or numpy.ndarray of shape (3)
Physical size of grid in meter.
origin : list or numpy.ndarray of shape (3), optional
Coordinates of grid origin in meter.
comments : list of str, optional
Comments, e.g. history of operations.
"""
self.material = material
self.size = size
self.origin = origin
self.comments = comments
def __repr__(self):
"""Basic information on grid definition."""
mat_min = np.nanmin(self.material)
mat_max = np.nanmax(self.material)
mat_N = self.N_materials
return util.srepr([
f'cells : {util.srepr(self.cells, " x ")}',
f'size : {util.srepr(self.size, " x ")} / m³',
f'origin: {util.srepr(self.origin," ")} / m',
f'# materials: {mat_N}' + ('' if mat_min == 0 and mat_max+1 == mat_N else
f' (min: {mat_min}, max: {mat_max})')
])
def __copy__(self):
"""Create deep copy."""
return copy.deepcopy(self)
copy = __copy__
def __eq__(self,other):
"""
Test equality of other.
Parameters
----------
other : damask.Grid
Grid to compare self against.
"""
return (np.allclose(other.size,self.size)
and np.allclose(other.origin,self.origin)
and np.all(other.cells == self.cells)
and np.all(other.material == self.material))
@property
def material(self):
"""Material indices."""
return self._material
@material.setter
def material(self,material):
if len(material.shape) != 3:
raise ValueError(f'invalid material shape {material.shape}')
elif material.dtype not in np.sctypes['float'] + np.sctypes['int']:
raise TypeError(f'invalid material data type {material.dtype}')
else:
self._material = np.copy(material)
if self.material.dtype in np.sctypes['float'] and \
np.all(self.material == self.material.astype(int).astype(float)):
self._material = self.material.astype(int)
@property
def size(self):
"""Physical size of grid in meter."""
return self._size
@size.setter
def size(self,size):
if len(size) != 3 or any(np.array(size) < 0):
raise ValueError(f'invalid size {size}')
else:
self._size = np.array(size)
@property
def origin(self):
"""Coordinates of grid origin in meter."""
return self._origin
@origin.setter
def origin(self,origin):
if len(origin) != 3:
raise ValueError(f'invalid origin {origin}')
else:
self._origin = np.array(origin)
@property
def comments(self):
"""Comments, e.g. history of operations."""
return self._comments
@comments.setter
def comments(self,comments):
self._comments = [str(c) for c in comments] if isinstance(comments,list) else [str(comments)]
@property
def cells(self):
"""Number of cells in x,y,z direction."""
return np.asarray(self.material.shape)
@property
def N_materials(self):
"""Number of (unique) material indices within grid."""
return np.unique(self.material).size
@staticmethod
def load(fname):
"""
Load from VTK image data file.
Parameters
----------
fname : str or or pathlib.Path
Grid file to read. Valid extension is .vti, which will be appended
if not given.
Returns
-------
loaded : damask.Grid
Grid-based geometry from file.
"""
v = VTK.load(fname if str(fname).endswith(('.vti','.vtr')) else str(fname)+'.vti') # compatibility hack
comments = v.get_comments()
cells = np.array(v.vtk_data.GetDimensions())-1
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
return Grid(material = v.get('material').reshape(cells,order='F'),
size = bbox[1] - bbox[0],
origin = bbox[0],
comments=comments)
@staticmethod
def load_ASCII(fname):
"""
Load from geom file.
Storing geometry files in ASCII format is deprecated.
This function will be removed in a future version of DAMASK.
Parameters
----------
fname : str, pathlib.Path, or file handle
Geometry file to read.
Returns
-------
loaded : damask.Grid
Grid-based geometry from file.
"""
warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
try:
f = open(fname)
except TypeError:
f = fname
f.seek(0)
try:
header_length,keyword = f.readline().split()[:2]
header_length = int(header_length)
except ValueError:
header_length,keyword = (-1, 'invalid')
if not keyword.startswith('head') or header_length < 3:
raise TypeError('header length information missing or invalid')
comments = []
content = f.readlines()
for i,line in enumerate(content[:header_length]):
items = line.split('#')[0].lower().strip().split()
key = items[0] if items else ''
if key == 'grid':
cells = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']])
elif key == 'size':
size = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']])
elif key == 'origin':
origin = np.array([float(dict(zip(items[1::2],items[2::2]))[i]) for i in ['x','y','z']])
else:
comments.append(line.strip())
material = np.empty(cells.prod()) # initialize as flat array
i = 0
for line in content[header_length:]:
items = line.split('#')[0].split()
if len(items) == 3:
if items[1].lower() == 'of':
items = np.ones(int(items[0]))*float(items[2])
elif items[1].lower() == 'to':
items = np.linspace(int(items[0]),int(items[2]),
abs(int(items[2])-int(items[0]))+1,dtype=float)
else: items = list(map(float,items))
else: items = list(map(float,items))
material[i:i+len(items)] = items
i += len(items)
if i != cells.prod():
raise TypeError(f'invalid file: expected {cells.prod()} entries, found {i}')
if not np.any(np.mod(material,1) != 0.0): # no float present
material = material.astype('int') - (1 if material.min() > 0 else 0)
return Grid(material.reshape(cells,order='F'),size,origin,comments)
@staticmethod
def load_Neper(fname):
"""
Load from Neper VTK file.
Parameters
----------
fname : str, pathlib.Path, or file handle
Geometry file to read.
Returns
-------
loaded : damask.Grid
Grid-based geometry from file.
"""
v = VTK.load(fname,'vtkImageData')
cells = np.array(v.vtk_data.GetDimensions())-1
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
return Grid(v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe') - 1,
bbox[1] - bbox[0], bbox[0],
util.execution_stamp('Grid','load_Neper'))
@staticmethod
def load_DREAM3D(fname,
feature_IDs=None,cell_data=None,
phases='Phases',Euler_angles='EulerAngles',
base_group=None):
"""
Load DREAM.3D (HDF5) file.
Data in DREAM.3D files can be stored per cell ('CellData') and/or
per grain ('Grain Data'). Per default, cell-wise data is assumed.
damask.ConfigMaterial.load_DREAM3D gives the corresponding material definition.
Parameters
----------
fname : str
Filename of the DREAM.3D (HDF5) file.
feature_IDs : str
Name of the dataset containing the mapping between cells and
grain-wise data. Defaults to 'None', in which case cell-wise
data is used.
cell_data : str
Name of the group (folder) containing cell-wise data. Defaults to
None in wich case it is automatically detected.
phases : str
Name of the dataset containing the phase ID. It is not used for
grain-wise data, i.e. when feature_IDs is not None.
Defaults to 'Phases'.
Euler_angles : str
Name of the dataset containing the crystallographic orientation as
Euler angles in radians It is not used for grain-wise data, i.e.
when feature_IDs is not None. Defaults to 'EulerAngles'.
base_group : str
Path to the group (folder) that contains geometry (_SIMPL_GEOMETRY),
and grain- or cell-wise data. Defaults to None, in which case
it is set as the path that contains _SIMPL_GEOMETRY/SPACING.
Returns
-------
loaded : damask.Grid
Grid-based geometry from file.
"""
b = util.DREAM3D_base_group(fname) if base_group is None else base_group
c = util.DREAM3D_cell_data_group(fname) if cell_data is None else cell_data
f = h5py.File(fname, 'r')
cells = f['/'.join([b,'_SIMPL_GEOMETRY','DIMENSIONS'])][()]
size = f['/'.join([b,'_SIMPL_GEOMETRY','SPACING'])] * cells
origin = f['/'.join([b,'_SIMPL_GEOMETRY','ORIGIN'])][()]
if feature_IDs is None:
phase = f['/'.join([b,c,phases])][()].reshape(-1,1)
O = Rotation.from_Euler_angles(f['/'.join([b,c,Euler_angles])]).as_quaternion().reshape(-1,4) # noqa
unique,unique_inverse = np.unique(np.hstack([O,phase]),return_inverse=True,axis=0)
ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \
np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse]
else:
ma = f['/'.join([b,c,feature_IDs])][()].flatten()
return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','load_DREAM3D'))
@staticmethod
def from_table(table,coordinates,labels):
"""
Create grid from ASCII table.
Parameters
----------
table : damask.Table
Table that contains material information.
coordinates : str
Label of the vector column containing the spatial coordinates.
Need to be ordered (1./x fast, 3./z slow).
labels : str or list of str
Label(s) of the columns containing the material definition.
Each unique combination of values results in one material ID.
Returns
-------
new : damask.Grid
Grid-based geometry from values in table.
"""
cells,size,origin = grid_filters.cellsSizeOrigin_coordinates0_point(table.get(coordinates))
labels_ = [labels] if isinstance(labels,str) else labels
unique,unique_inverse = np.unique(np.hstack([table.get(l) for l in labels_]),return_inverse=True,axis=0)
ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \
np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse]
return Grid(ma.reshape(cells,order='F'),size,origin,util.execution_stamp('Grid','from_table'))
@staticmethod
def _find_closest_seed(seeds, weights, point):
return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
@staticmethod
def from_Laguerre_tessellation(cells,size,seeds,weights,material=None,periodic=True):
"""
Create grid from Laguerre tessellation.
Parameters
----------
cells : int numpy.ndarray of shape (3)
Number of cells in x,y,z direction.
size : list or numpy.ndarray of shape (3)
Physical size of the grid in meter.
seeds : numpy.ndarray of shape (:,3)
Position of the seed points in meter. All points need to lay within the box.
weights : numpy.ndarray of shape (seeds.shape[0])
Weights of the seeds. Setting all weights to 1.0 gives a standard Voronoi tessellation.
material : numpy.ndarray of shape (seeds.shape[0]), optional
Material ID of the seeds.
Defaults to None, in which case materials are consecutively numbered.
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
new : damask.Grid
Grid-based geometry from tessellation.
"""
if periodic:
weights_p = np.tile(weights,27) # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
seeds_p = np.vstack((seeds -np.array([size[0],0.,0.]),seeds, seeds +np.array([size[0],0.,0.])))
seeds_p = np.vstack((seeds_p-np.array([0.,size[1],0.]),seeds_p,seeds_p+np.array([0.,size[1],0.])))
seeds_p = np.vstack((seeds_p-np.array([0.,0.,size[2]]),seeds_p,seeds_p+np.array([0.,0.,size[2]])))
else:
weights_p = weights
seeds_p = seeds
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
pool = mp.Pool(int(os.environ.get('OMP_NUM_THREADS',4)))
result = pool.map_async(partial(Grid._find_closest_seed,seeds_p,weights_p), coords)
pool.close()
pool.join()
material_ = np.array(result.get()).reshape(cells)
if periodic: material_ %= len(weights)
return Grid(material = material_ if material is None else material[material_],
size = size,
comments = util.execution_stamp('Grid','from_Laguerre_tessellation'),
)
@staticmethod
def from_Voronoi_tessellation(cells,size,seeds,material=None,periodic=True):
"""
Create grid from Voronoi tessellation.
Parameters
----------
cells : int numpy.ndarray of shape (3)
Number of cells in x,y,z direction.
size : list or numpy.ndarray of shape (3)
Physical size of the grid in meter.
seeds : numpy.ndarray of shape (:,3)
Position of the seed points in meter. All points need to lay within the box.
material : numpy.ndarray of shape (seeds.shape[0]), optional
Material ID of the seeds.
Defaults to None, in which case materials are consecutively numbered.
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
new : damask.Grid
Grid-based geometry from tessellation.
"""
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
tree = spatial.cKDTree(seeds,boxsize=size) if periodic else \
spatial.cKDTree(seeds)
try:
material_ = tree.query(coords, workers = int(os.environ.get('OMP_NUM_THREADS',4)))[1]
except TypeError:
material_ = tree.query(coords, n_jobs = int(os.environ.get('OMP_NUM_THREADS',4)))[1] # scipy <1.6
return Grid(material = (material_ if material is None else material[material_]).reshape(cells),
size = size,
comments = util.execution_stamp('Grid','from_Voronoi_tessellation'),
)
_minimal_surface = \
{'Schwarz P': lambda x,y,z: np.cos(x) + np.cos(y) + np.cos(z),
'Double Primitive': lambda x,y,z: ( 0.5 * (np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x))
+ 0.2 * (np.cos(2*x) + np.cos(2*y) + np.cos(2*z)) ),
'Schwarz D': lambda x,y,z: ( np.sin(x)*np.sin(y)*np.sin(z)
+ np.sin(x)*np.cos(y)*np.cos(z)
+ np.cos(x)*np.cos(y)*np.sin(z)
+ np.cos(x)*np.sin(y)*np.cos(z) ),
'Complementary D': lambda x,y,z: ( np.cos(3*x+y)*np.cos(z) - np.sin(3*x-y)*np.sin(z) + np.cos(x+3*y)*np.cos(z)
+ np.sin(x-3*y)*np.sin(z) + np.cos(x-y)*np.cos(3*z) - np.sin(x+y)*np.sin(3*z) ),
'Double Diamond': lambda x,y,z: 0.5 * (np.sin(x)*np.sin(y)
+ np.sin(y)*np.sin(z)
+ np.sin(z)*np.sin(x)
+ np.cos(x) * np.cos(y) * np.cos(z) ),
'Dprime': lambda x,y,z: 0.5 * ( np.cos(x)*np.cos(y)*np.cos(z)
+ np.cos(x)*np.sin(y)*np.sin(z)
+ np.sin(x)*np.cos(y)*np.sin(z)
+ np.sin(x)*np.sin(y)*np.cos(z)
- np.sin(2*x)*np.sin(2*y)
- np.sin(2*y)*np.sin(2*z)
- np.sin(2*z)*np.sin(2*x) ) - 0.2,
'Gyroid': lambda x,y,z: np.cos(x)*np.sin(y) + np.cos(y)*np.sin(z) + np.cos(z)*np.sin(x),
'Gprime': lambda x,y,z : ( np.sin(2*x)*np.cos(y)*np.sin(z)
+ np.sin(2*y)*np.cos(z)*np.sin(x)
+ np.sin(2*z)*np.cos(x)*np.sin(y) ) + 0.32,
'Karcher K': lambda x,y,z: ( 0.3 * ( np.cos(x) + np.cos(y) + np.cos(z)
+ np.cos(x)*np.cos(y) + np.cos(y)*np.cos(z) + np.cos(z)*np.cos(x) )
- 0.4 * ( np.cos(2*x) + np.cos(2*y) + np.cos(2*z) ) ) + 0.2,
'Lidinoid': lambda x,y,z: 0.5 * ( np.sin(2*x)*np.cos(y)*np.sin(z)
+ np.sin(2*y)*np.cos(z)*np.sin(x)
+ np.sin(2*z)*np.cos(x)*np.sin(y)
- np.cos(2*x)*np.cos(2*y)
- np.cos(2*y)*np.cos(2*z)
- np.cos(2*z)*np.cos(2*x) ) + 0.15,
'Neovius': lambda x,y,z: ( 3 * (np.cos(x)+np.cos(y)+np.cos(z))
+ 4 * np.cos(x)*np.cos(y)*np.cos(z) ),
'Fisher-Koch S': lambda x,y,z: ( np.cos(2*x)*np.sin( y)*np.cos( z)
+ np.cos( x)*np.cos(2*y)*np.sin( z)
+ np.sin( x)*np.cos( y)*np.cos(2*z) ),
}
@staticmethod
def from_minimal_surface(cells,size,surface,threshold=0.0,periods=1,materials=(0,1)):
"""
Create grid from definition of triply periodic minimal surface.
Parameters
----------
cells : int numpy.ndarray of shape (3)
Number of cells in x,y,z direction.
size : list or numpy.ndarray of shape (3)
Physical size of the grid in meter.
surface : str
Type of the minimal surface. See notes for details.
threshold : float, optional.
Threshold of the minimal surface. Defaults to 0.0.
periods : integer, optional.
Number of periods per unit cell. Defaults to 1.
materials : (int, int), optional
Material IDs. Defaults to (0,1).
Returns
-------
new : damask.Grid
Grid-based geometry from definition of minimal surface.
Notes
-----
The following triply-periodic minimal surfaces are implemented:
- Schwarz P
- Double Primitive
- Schwarz D
- Complementary D
- Double Diamond
- Dprime
- Gyroid
- Gprime
- Karcher K
- Lidinoid
- Neovius
- Fisher-Koch S
References
----------
S.B.G. Blanquer et al., Biofabrication 9(2):025001, 2017
https://doi.org/10.1088/1758-5090/aa6553
M. Wohlgemuth et al., Macromolecules 34(17):6083-6089, 2001
https://doi.org/10.1021/ma0019499
M.-T. Hsieh and L. Valdevit, Software Impacts 6:100026, 2020
https://doi.org/10.1016/j.simpa.2020.100026
Examples
--------
Minimal surface of 'Gyroid' type.
>>> import numpy as np
>>> import damask
>>> damask.Grid.from_minimal_surface(np.array([64]*3,int),np.ones(3),
... 'Gyroid')
cells a b c: 64 x 64 x 64
size x y z: 1.0 x 1.0 x 1.0
origin x y z: 0.0 0.0 0.0
# materials: 2
Minimal surface of 'Neovius' type. non-default material IDs.
>>> import numpy as np
>>> import damask
>>> damask.Grid.from_minimal_surface(np.array([80]*3,int),np.ones(3),
... 'Neovius',materials=(1,5))
cells a b c: 80 x 80 x 80
size x y z: 1.0 x 1.0 x 1.0
origin x y z: 0.0 0.0 0.0
# materials: 2 (min: 1, max: 5)
"""
x,y,z = np.meshgrid(periods*2.0*np.pi*(np.arange(cells[0])+0.5)/cells[0],
periods*2.0*np.pi*(np.arange(cells[1])+0.5)/cells[1],
periods*2.0*np.pi*(np.arange(cells[2])+0.5)/cells[2],
indexing='ij',sparse=True)
return Grid(material = np.where(threshold < Grid._minimal_surface[surface](x,y,z),materials[1],materials[0]),
size = size,
comments = util.execution_stamp('Grid','from_minimal_surface'),
)
def save(self,fname,compress=True):
"""
Save as VTK image data file.
Parameters
----------
fname : str or pathlib.Path
Filename to write. Valid extension is .vti, it will be appended if not given.
compress : bool, optional
Compress with zlib algorithm. Defaults to True.
"""
v = VTK.from_image_data(self.cells,self.size,self.origin)
v.add(self.material.flatten(order='F'),'material')
v.add_comments(self.comments)
v.save(fname if str(fname).endswith('.vti') else str(fname)+'.vti',parallel=False,compress=compress)
def save_ASCII(self,fname):
"""
Save as geom file.
Storing geometry files in ASCII format is deprecated.
This function will be removed in a future version of DAMASK.
Parameters
----------
fname : str or file handle
Geometry file to write with extension '.geom'.
compress : bool, optional
Compress geometry with 'x of y' and 'a to b'.
"""
warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
header = [f'{len(self.comments)+4} header'] + self.comments \
+ ['grid a {} b {} c {}'.format(*self.cells),
'size x {} y {} z {}'.format(*self.size),
'origin x {} y {} z {}'.format(*self.origin),
'homogenization 1',
]
format_string = '%g' if self.material.dtype in np.sctypes['float'] else \
'%{}i'.format(1+int(np.floor(np.log10(np.nanmax(self.material)))))
np.savetxt(fname,
self.material.reshape([self.cells[0],np.prod(self.cells[1:])],order='F').T,
header='\n'.join(header), fmt=format_string, comments='')
def show(self):
"""Show on screen."""
VTK.from_rectilinear_grid(self.cells,self.size,self.origin).show()
def add_primitive(self,dimension,center,exponent,
fill=None,R=Rotation(),inverse=False,periodic=True):
"""
Insert a primitive geometric object at a given position.
Parameters
----------
dimension : int or float numpy.ndarray of shape (3)
Dimension (diameter/side length) of the primitive. If given as
integers, cell centers are addressed.
If given as floats, coordinates are addressed.
center : int or float numpy.ndarray of shape (3)
Center of the primitive. If given as integers, cell centers are addressed.
If given as floats, coordinates in space are addressed.
exponent : numpy.ndarray of shape (3) or float
Exponents for the three axes.
0 gives octahedron (ǀxǀ^(2^0) + ǀyǀ^(2^0) + ǀzǀ^(2^0) < 1)
1 gives sphere (ǀxǀ^(2^1) + ǀyǀ^(2^1) + ǀzǀ^(2^1) < 1)
fill : int, optional
Fill value for primitive. Defaults to material.max()+1.
R : damask.Rotation, optional
Rotation of primitive. Defaults to no rotation.
inverse : Boolean, optional
Retain original materials within primitive and fill outside.
Defaults to False.
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
Examples
--------
Add a sphere at the center.
>>> import numpy as np
>>> import damask
>>> g = damask.Grid(np.zeros([64]*3,int), np.ones(3)*1e-4)
>>> g.add_primitive(np.ones(3)*5e-5,np.ones(3)*5e-5,1)
cells a b c: 64 x 64 x 64
size x y z: 0.0001 x 0.0001 x 0.0001
origin x y z: 0.0 0.0 0.0
# materials: 2
Add a cube at the origin.
>>> import numpy as np
>>> import damask
>>> g = damask.Grid(np.zeros([64]*3,int), np.ones(3)*1e-4)
>>> g.add_primitive(np.ones(3,int)*32,np.zeros(3),np.inf)
cells a b c: 64 x 64 x 64
size x y z: 0.0001 x 0.0001 x 0.0001
origin x y z: 0.0 0.0 0.0
# materials: 2
"""
# radius and center
r = np.array(dimension)/2.0*self.size/self.cells if np.array(dimension).dtype in np.sctypes['int'] else \
np.array(dimension)/2.0
c = (np.array(center) + .5)*self.size/self.cells if np.array(center).dtype in np.sctypes['int'] else \
(np.array(center) - self.origin)
coords = grid_filters.coordinates0_point(self.cells,self.size,
-(0.5*(self.size + (self.size/self.cells
if np.array(center).dtype in np.sctypes['int'] else
0)) if periodic else c))
coords_rot = R.broadcast_to(tuple(self.cells))@coords
with np.errstate(all='ignore'):
mask = np.sum(np.power(coords_rot/r,2.0**np.array(exponent)),axis=-1) > 1.0
if periodic: # translate back to center
mask = np.roll(mask,((c/self.size-0.5)*self.cells).round().astype(int),(0,1,2))
return Grid(material = np.where(np.logical_not(mask) if inverse else mask,
self.material,
np.nanmax(self.material)+1 if fill is None else fill),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','add_primitive')],
)
def mirror(self,directions,reflect=False):
"""
Mirror grid along given directions.
Parameters
----------
directions : iterable containing str
Direction(s) along which the grid is mirrored.
Valid entries are 'x', 'y', 'z'.
reflect : bool, optional
Reflect (include) outermost layers. Defaults to False.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
Examples
--------
Mirror along x- and y-direction.
>>> import numpy as np
>>> import damask
>>> g = damask.Grid(np.zeros([32]*3,int), np.ones(3)*1e-4)
>>> g.mirror('xy',True)
cells a b c: 64 x 64 x 32
size x y z: 0.0002 x 0.0002 x 0.0001
origin x y z: 0.0 0.0 0.0
# materials: 1
"""
valid = ['x','y','z']
if not set(directions).issubset(valid):
raise ValueError(f'invalid direction {set(directions).difference(valid)} specified')
limits = [None,None] if reflect else [-2,0]
mat = self.material.copy()
if 'x' in directions:
mat = np.concatenate([mat,mat[limits[0]:limits[1]:-1,:,:]],0)
if 'y' in directions:
mat = np.concatenate([mat,mat[:,limits[0]:limits[1]:-1,:]],1)
if 'z' in directions:
mat = np.concatenate([mat,mat[:,:,limits[0]:limits[1]:-1]],2)
return Grid(material = mat,
size = self.size/self.cells*np.asarray(mat.shape),
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','mirror')],
)
def flip(self,directions):
"""
Flip grid along given directions.
Parameters
----------
directions : iterable containing str
Direction(s) along which the grid is flipped.
Valid entries are 'x', 'y', 'z'.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
valid = ['x','y','z']
if not set(directions).issubset(valid):
raise ValueError(f'invalid direction {set(directions).difference(valid)} specified')
mat = np.flip(self.material, (valid.index(d) for d in directions if d in valid))
return Grid(material = mat,
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','flip')],
)
def scale(self,cells,periodic=True):
"""
Scale grid to new cells.
Parameters
----------
cells : numpy.ndarray of shape (3)
Number of cells in x,y,z direction.
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
Examples
--------
Double resolution.
>>> import numpy as np
>>> import damask
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
>>> g.scale(g.cells*2)
cells a b c: 64 x 64 x 64
size x y z: 0.0001 x 0.0001 x 0.0001
origin x y z: 0.0 0.0 0.0
# materials: 1
"""
return Grid(material = ndimage.interpolation.zoom(
self.material,
cells/self.cells,
output=self.material.dtype,
order=0,
mode=('wrap' if periodic else 'nearest'),
prefilter=False
),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','scale')],
)
def clean(self,stencil=3,selection=None,periodic=True):
"""
Smooth grid by selecting most frequent material index within given stencil at each location.
Parameters
----------
stencil : int, optional
Size of smoothing stencil.
selection : list, optional
Field values that can be altered. Defaults to all.
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
def mostFrequent(arr,selection=None):
me = arr[arr.size//2]
if selection is None or me in selection:
unique, inverse = np.unique(arr, return_inverse=True)
return unique[np.argmax(np.bincount(inverse))]
else:
return me
return Grid(material = ndimage.filters.generic_filter(
self.material,
mostFrequent,
size=(stencil if selection is None else stencil//2*2+1,)*3,
mode=('wrap' if periodic else 'nearest'),
extra_keywords=dict(selection=selection),
).astype(self.material.dtype),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','clean')],
)
def renumber(self):
"""
Renumber sorted material indices as 0,...,N-1.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
_,renumbered = np.unique(self.material,return_inverse=True)
return Grid(material = renumbered.reshape(self.cells),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','renumber')],
)
def rotate(self,R,fill=None):
"""
Rotate grid (pad if required).
Parameters
----------
R : damask.Rotation
Rotation to apply to the grid.
fill : int or float, optional
Material index to fill the corners. Defaults to material.max() + 1.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
if fill is None: fill = np.nanmax(self.material) + 1
dtype = float if isinstance(fill,float) or self.material.dtype in np.sctypes['float'] else int
material = self.material
# These rotations are always applied in the reference coordinate system, i.e. (z,x,z) not (z,x',z'')
# see https://www.cs.utexas.edu/~theshark/courses/cs354/lectures/cs354-14.pdf
for angle,axes in zip(R.as_Euler_angles(degrees=True)[::-1], [(0,1),(1,2),(0,1)]):
material_temp = ndimage.rotate(material,angle,axes,order=0,prefilter=False,output=dtype,cval=fill)
# avoid scipy interpolation errors for rotations close to multiples of 90°
material = material_temp if np.prod(material_temp.shape) != np.prod(material.shape) else \
np.rot90(material,k=np.rint(angle/90.).astype(int),axes=axes)
origin = self.origin-(np.asarray(material.shape)-self.cells)*.5 * self.size/self.cells
return Grid(material = material,
size = self.size/self.cells*np.asarray(material.shape),
origin = origin,
comments = self.comments+[util.execution_stamp('Grid','rotate')],
)
def canvas(self,cells=None,offset=None,fill=None):
"""
Crop or enlarge/pad grid.
Parameters
----------
cells : numpy.ndarray of shape (3)
Number of cells x,y,z direction.
offset : numpy.ndarray of shape (3)
Offset (measured in cells) from old to new grid [0,0,0].
fill : int or float, optional
Material index to fill the background. Defaults to material.max() + 1.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
Examples
--------
Remove 1/2 of the microstructure in z-direction.
>>> import numpy as np
>>> import damask
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
>>> g.canvas(np.array([32,32,16],int))
cells a b c: 33 x 32 x 16
size x y z: 0.0001 x 0.0001 x 5e-05
origin x y z: 0.0 0.0 0.0
# materials: 1
"""
if offset is None: offset = 0
if fill is None: fill = np.nanmax(self.material) + 1
dtype = float if int(fill) != fill or self.material.dtype in np.sctypes['float'] else int
canvas = np.full(self.cells if cells is None else cells,fill,dtype)
LL = np.clip( offset, 0,np.minimum(self.cells, cells+offset))
UR = np.clip( offset+cells, 0,np.minimum(self.cells, cells+offset))
ll = np.clip(-offset, 0,np.minimum( cells,self.cells-offset))
ur = np.clip(-offset+self.cells,0,np.minimum( cells,self.cells-offset))
canvas[ll[0]:ur[0],ll[1]:ur[1],ll[2]:ur[2]] = self.material[LL[0]:UR[0],LL[1]:UR[1],LL[2]:UR[2]]
return Grid(material = canvas,
size = self.size/self.cells*np.asarray(canvas.shape),
origin = self.origin+offset*self.size/self.cells,
comments = self.comments+[util.execution_stamp('Grid','canvas')],
)
def substitute(self,from_material,to_material):
"""
Substitute material indices.
Parameters
----------
from_material : iterable of ints
Material indices to be substituted.
to_material : iterable of ints
New material indices.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
def mp(entry,mapper):
return mapper[entry] if entry in mapper else entry
mp = np.vectorize(mp)
mapper = dict(zip(from_material,to_material))
return Grid(material = mp(self.material,mapper).reshape(self.cells),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','substitute')],
)
def sort(self):
"""
Sort material indices such that min(material) is located at (0,0,0).
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
a = self.material.flatten(order='F')
from_ma = pd.unique(a)
sort_idx = np.argsort(from_ma)
ma = np.unique(a)[sort_idx][np.searchsorted(from_ma,a,sorter = sort_idx)]
return Grid(material = ma.reshape(self.cells,order='F'),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','sort')],
)
def vicinity_offset(self,vicinity=1,offset=None,trigger=[],periodic=True):
"""
Offset material index of points in the vicinity of xxx.
Different from themselves (or listed as triggers) within a given (cubic) vicinity,
i.e. within the region close to a grain/phase boundary.
ToDo: use include/exclude as in seeds.from_grid
Parameters
----------
vicinity : int, optional
Voxel distance checked for presence of other materials.
Defaults to 1.
offset : int, optional
Offset (positive or negative) to tag material indices,
defaults to material.max()+1.
trigger : list of ints, optional
List of material indices that trigger a change.
Defaults to [], meaning that any different neighbor triggers a change.
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
updated : damask.Grid
Updated grid-based geometry.
"""
def tainted_neighborhood(stencil,trigger):
me = stencil[stencil.shape[0]//2]
return np.any(stencil != me if len(trigger) == 0 else
np.in1d(stencil,np.array(list(set(trigger) - {me}))))
offset_ = np.nanmax(self.material)+1 if offset is None else offset
mask = ndimage.filters.generic_filter(self.material,
tainted_neighborhood,
size=1+2*vicinity,
mode='wrap' if periodic else 'nearest',
extra_keywords={'trigger':trigger})
return Grid(material = np.where(mask, self.material + offset_,self.material),
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('Grid','vicinity_offset')],
)
def get_grain_boundaries(self,periodic=True,directions='xyz'):
"""
Create VTK unstructured grid containing grain boundaries.
Parameters
----------
periodic : Boolean, optional
Assume grid to be periodic. Defaults to True.
directions : iterable containing str, optional
Direction(s) along which the boundaries are determined.
Valid entries are 'x', 'y', 'z'. Defaults to 'xyz'.
Returns
-------
grain_boundaries : damask.VTK
VTK-based geometry of grain boundary network.
"""
valid = ['x','y','z']
if not set(directions).issubset(valid):
raise ValueError(f'invalid direction {set(directions).difference(valid)} specified')
o = [[0, self.cells[0]+1, np.prod(self.cells[:2]+1)+self.cells[0]+1, np.prod(self.cells[:2]+1)],
[0, np.prod(self.cells[:2]+1), np.prod(self.cells[:2]+1)+1, 1],
[0, 1, self.cells[0]+1+1, self.cells[0]+1]] # offset for connectivity
connectivity = []
for i,d in enumerate(['x','y','z']):
if d not in directions: continue
mask = self.material != np.roll(self.material,1,i)
for j in [0,1,2]:
mask = np.concatenate((mask,np.take(mask,[0],j)*(i==j)),j)
if i == 0 and not periodic: mask[0,:,:] = mask[-1,:,:] = False
if i == 1 and not periodic: mask[:,0,:] = mask[:,-1,:] = False
if i == 2 and not periodic: mask[:,:,0] = mask[:,:,-1] = False
base_nodes = np.argwhere(mask.flatten(order='F')).reshape(-1,1)
connectivity.append(np.block([base_nodes + o[i][k] for k in range(4)]))
coords = grid_filters.coordinates0_node(self.cells,self.size,self.origin).reshape(-1,3,order='F')
return VTK.from_unstructured_grid(coords,np.vstack(connectivity),'QUAD')