import os
import copy
import warnings
import multiprocessing as mp
from functools import partial
import typing
from typing import Optional, Union, TextIO, Sequence, Dict
from pathlib import Path
import numpy as np
import pandas as pd
import h5py
from scipy import ndimage, spatial, interpolate
from . import VTK
from . import util
from . import grid_filters
from . import Rotation
from . import Table
from . import Colormap
from ._typehints import FloatSequence, IntSequence, NumpyRngSeed
try:
import numba as nb # type: ignore
except ImportError:
nb = False
def numba_njit_wrapper(**kwargs):
return (lambda function: nb.njit(function) if nb else function)
[docs]class GeomGrid:
"""
Geometry definition for grid solvers.
Create and manipulate geometry definitions for storage as VTK ImageData
files ('.vti' extension). A grid has a physical size, a coordinate origin,
and contains the material ID (indexing an entry in 'material.yaml')
as well as initial condition fields.
"""
def __init__(self,
material: np.ndarray,
size: FloatSequence,
origin: FloatSequence = np.zeros(3),
initial_conditions: Optional[Dict[str,np.ndarray]] = None,
comments: Union[None, str, Sequence[str]] = None):
"""
New geometry definition for grid solvers.
Parameters
----------
material : numpy.ndarray of int, shape (:,:,:)
Material indices. The shape of the material array defines
the number of cells.
size : sequence of float, len (3)
Physical size of grid in meter.
origin : sequence of float, len (3), optional
Coordinates of grid origin in meter. Defaults to [0.0,0.0,0.0].
initial_conditions : dictionary, optional
Initial condition label and field values at each grid point.
comments : (sequence of) str, optional
Additional, human-readable information, e.g. history of operations.
"""
self.material = material
self.size = size # type: ignore
self.origin = origin # type: ignore
self.initial_conditions = {} if initial_conditions is None else initial_conditions
self.comments = [] if comments is None else \
[comments] if isinstance(comments,str) else \
[str(c) for c in comments]
def __repr__(self) -> str:
"""
Return repr(self).
Give short, human-readable summary.
"""
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, " × ")}',
f'size: {util.srepr(self.size, " × ")} 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})')
]+(['initial_conditions:']+[f' - {f}' for f in self.initial_conditions] if self.initial_conditions else []))
def __copy__(self) -> 'GeomGrid':
"""
Return deepcopy(self).
Create deep copy.
"""
return copy.deepcopy(self)
copy = __copy__
def __eq__(self,
other: object) -> bool:
"""
Return self==other.
Test equality of other.
Parameters
----------
other : damask.GeomGrid
GeomGrid to compare self against.
"""
if not isinstance(other, GeomGrid):
return NotImplemented
return bool( 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) -> np.ndarray:
"""Material indices."""
return self._material
@material.setter
def material(self,
material: np.ndarray):
if len(material.shape) != 3:
raise ValueError(f'invalid material shape {material.shape}')
if material.dtype not in np.sctypes['float'] and material.dtype not in np.sctypes['int']:
raise TypeError(f'invalid material data type "{material.dtype}"')
self._material = np.copy(material)
if self.material.dtype in np.sctypes['float'] and \
np.all(self.material == self.material.astype(np.int64).astype(float)):
self._material = self.material.astype(np.int64)
@property
def size(self) -> np.ndarray:
"""Edge lengths of grid in meter."""
return self._size
@size.setter
def size(self,
size: FloatSequence):
if len(size) != 3 or any(np.array(size) < 0):
raise ValueError(f'invalid size {size}')
self._size = np.array(size)
@property
def origin(self) -> np.ndarray:
"""Vector to grid origin in meter."""
return self._origin
@origin.setter
def origin(self,
origin: FloatSequence):
if len(origin) != 3:
raise ValueError(f'invalid origin {origin}')
self._origin = np.array(origin)
@property
def initial_conditions(self) -> Dict[str,np.ndarray]:
"""Fields of initial conditions."""
self._ic = dict(zip(self._ic.keys(), # type: ignore
[v if isinstance(v,np.ndarray) else
np.broadcast_to(v,self.cells) for v in self._ic.values()])) # type: ignore
return self._ic
@initial_conditions.setter
def initial_conditions(self,
ic: Dict[str,np.ndarray]):
if not isinstance(ic,dict):
raise TypeError('initial conditions is not a dictionary')
self._ic = ic
@property
def cells(self) -> np.ndarray:
"""Cell counts along x,y,z direction."""
return np.asarray(self.material.shape)
@property
def N_materials(self) -> int:
"""Number of (unique) material indices within grid."""
return np.unique(self.material).size
@staticmethod
def _load(fname: Union[str, Path], label: str) -> 'GeomGrid':
"""
Load from VTK ImageData file.
Parameters
----------
fname : str or pathlib.Path
VTK ImageData file to read.
Valid extension is .vti, which will be appended if not given.
label : str
Label of the dataset containing the material IDs.
Returns
-------
loaded : damask.GeomGrid
GeomGrid-based geometry from file.
"""
v = VTK.load(fname if str(fname).endswith('.vti') else str(fname)+'.vti')
cells = np.array(v.vtk_data.GetDimensions())-1
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
ic = {l:v.get(l).reshape(cells,order='F') for l in set(v.labels['Cell Data']) - {label}}
return GeomGrid(material = v.get(label).reshape(cells,order='F'),
size = bbox[1] - bbox[0],
origin = bbox[0],
initial_conditions = ic,
comments = v.comments,
)
[docs] @staticmethod
def load(fname: Union[str, Path]) -> 'GeomGrid':
"""
Load from VTK ImageData file with material IDs stored as 'material'.
Parameters
----------
fname : str or pathlib.Path
GeomGrid file to read.
Valid extension is .vti, which will be appended if not given.
Returns
-------
loaded : damask.GeomGrid
GeomGrid-based geometry from file.
"""
return GeomGrid._load(fname,'material')
[docs] @staticmethod
def load_SPPARKS(fname: Union[str, Path]) -> 'GeomGrid':
"""
Load from SPPARKS VTK dump.
Parameters
----------
fname : str or pathlib.Path
SPPARKS VTK dump file to read.
Valid extension is .vti, which will be appended if not given.
Returns
-------
loaded : damask.GeomGrid
GeomGrid-based geometry from file.
Notes
-----
A SPPARKS VTI dump is equivalent to a DAMASK VTI file,
but stores the materialID information as 'Spin' rather than 'material'.
"""
return GeomGrid._load(fname,'Spin')
[docs] @typing.no_type_check
@staticmethod
def load_ASCII(fname)-> 'GeomGrid':
"""
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.GeomGrid
GeomGrid-based geometry from file.
"""
warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
if isinstance(fname, (str, Path)):
f = open(fname)
elif isinstance(fname, TextIO):
f = fname
else:
raise TypeError
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('invalid or missing header length information')
comments = []
content = f.readlines()
for i,line in enumerate(content[:header_length]):
items = line.split('#')[0].lower().strip().split()
if (key := items[0] if items else '') == '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:]:
if len(items := line.split('#')[0].split()) == 3:
if items[1].lower() == 'of':
material_entry = np.ones(int(items[0]))*float(items[2])
elif items[1].lower() == 'to':
material_entry = np.linspace(int(items[0]),int(items[2]),
abs(int(items[2])-int(items[0]))+1,dtype=float)
else: material_entry = list(map(float, items))
else: material_entry = list(map(float, items))
material[i:i+len(material_entry)] = material_entry
i += len(items)
if i != cells.prod():
raise TypeError(f'mismatch between {cells.prod()} expected entries and {i} found')
if not np.any(np.mod(material,1) != 0.0): # no float present
material = material.astype(np.int64) - (1 if material.min() > 0 else 0)
return GeomGrid(material = material.reshape(cells,order='F'),
size = size,
origin = origin,
comments = comments,
)
[docs] @staticmethod
def load_Neper(fname: Union[str, Path]) -> 'GeomGrid':
"""
Load from Neper VTK file.
Parameters
----------
fname : str or pathlib.Path
Geometry file to read.
Returns
-------
loaded : damask.GeomGrid
GeomGrid-based geometry from file.
Notes
-----
Material indices in Neper usually start at 1 unless
a buffer material with index 0 is added.
Examples
--------
Read a periodic polycrystal generated with Neper.
>>> import damask
>>> N_grains = 20
>>> cells = (32,32,32)
>>> damask.util.run(f'neper -T -n {N_grains} -tesrsize {cells[0]}:{cells[1]}:{cells[2]} -periodicity all -format vtk')
>>> damask.GeomGrid.load_Neper(f'n{N_grains}-id1.vtk').renumber()
cells: 32 × 32 × 32
size: 1.0 × 1.0 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 20
"""
v = VTK.load(fname,'ImageData')
cells = np.array(v.vtk_data.GetDimensions())-1
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
return GeomGrid(material = v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe'),
size = bbox[1] - bbox[0],
origin = bbox[0],
comments = util.execution_stamp('GeomGrid','load_Neper'),
)
[docs] @staticmethod
def load_DREAM3D(fname: Union[str, Path],
feature_IDs: Optional[str] = None,
cell_data: Optional[str] = None,
phases: str = 'Phases',
Euler_angles: str = 'EulerAngles',
base_group: Optional[str] = None) -> 'GeomGrid':
"""
Load DREAM.3D (HDF5) file.
Data in DREAM.3D files can be stored per cell ('CellData')
and/or per grain ('Grain Data'). Per default, i.e. if
'feature_IDs' is None, cell-wise data is assumed.
Parameters
----------
fname : str or pathlib.Path
Filename of the DREAM.3D (HDF5) file.
feature_IDs : str, optional
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, optional
Name of the group (folder) containing cell-wise data. Defaults to
None in wich case it is automatically detected.
phases : str, optional
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, optional
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, optional
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.GeomGrid
GeomGrid-based geometry from file.
Notes
-----
damask.ConfigMaterial.load_DREAM3D gives the corresponding
material definition.
For cell-wise data, only unique combinations of
orientation and phase are considered.
"""
with h5py.File(fname, 'r') as f:
b = util.DREAM3D_base_group(f) if base_group is None else base_group
c = util.DREAM3D_cell_data_group(f) if cell_data is None else cell_data
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 GeomGrid(material = ma.reshape(cells,order='F'),
size = size,
origin = origin,
comments = util.execution_stamp('GeomGrid','load_DREAM3D'),
)
[docs] @staticmethod
def from_table(table: Table,
coordinates: str,
labels: Union[str, Sequence[str]]) -> 'GeomGrid':
"""
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 : (sequence of) str
Label(s) of the columns containing the material definition.
Each unique combination of values results in one material ID.
Returns
-------
new : damask.GeomGrid
GeomGrid-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 GeomGrid(material = ma.reshape(cells,order='F'),
size = size,
origin = origin,
comments = util.execution_stamp('GeomGrid','from_table'),
)
@staticmethod
def _find_closest_seed(seeds: np.ndarray,
weights: np.ndarray,
point: np.ndarray) -> np.integer:
return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
[docs] @staticmethod
def from_Laguerre_tessellation(cells: IntSequence,
size: FloatSequence,
seeds: np.ndarray,
weights: FloatSequence,
material: Optional[IntSequence] = None,
periodic: bool = True):
"""
Create grid from Laguerre tessellation.
Parameters
----------
cells : sequence of int, len (3)
Cell counts along x,y,z direction.
size : sequence of float, len (3)
Edge lengths of the grid in meter.
seeds : numpy.ndarray of float, shape (:,3)
Position of the seed points in meter. All points need
to lay within the box [(0,0,0),size].
weights : sequence of float, len (seeds.shape[0])
Weights of the seeds. Setting all weights to 1.0 gives a
standard Voronoi tessellation.
material : sequence of int, len (seeds.shape[0]), optional
Material ID of the seeds.
Defaults to None, in which case materials are consecutively numbered.
periodic : bool, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
new : damask.GeomGrid
GeomGrid-based geometry from tessellation.
"""
weights_p: FloatSequence
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 = np.array(weights,float)
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(GeomGrid._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 GeomGrid(material = material_ if material is None else np.array(material)[material_],
size = size,
comments = util.execution_stamp('GeomGrid','from_Laguerre_tessellation'),
)
[docs] @staticmethod
def from_Voronoi_tessellation(cells: IntSequence,
size: FloatSequence,
seeds: np.ndarray,
material: Optional[IntSequence] = None,
periodic: bool = True) -> 'GeomGrid':
"""
Create grid from Voronoi tessellation.
Parameters
----------
cells : sequence of int, len (3)
Cell counts along x,y,z direction.
size : sequence of float, len (3)
Edge lengths of the grid in meter.
seeds : numpy.ndarray of float, shape (:,3)
Position of the seed points in meter. All points need
to lay within the box [(0,0,0),size].
material : sequence of int, len (seeds.shape[0]), optional
Material ID of the seeds.
Defaults to None, in which case materials are consecutively numbered.
periodic : bool, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
new : damask.GeomGrid
GeomGrid-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 GeomGrid(material = (material_ if material is None else np.array(material)[material_]).reshape(cells),
size = size,
comments = util.execution_stamp('GeomGrid','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) ),
}
[docs] @staticmethod
def from_minimal_surface(cells: IntSequence,
size: FloatSequence,
surface: str,
threshold: float = 0.0,
periods: int = 1,
materials: IntSequence = (0,1)) -> 'GeomGrid':
"""
Create grid from definition of triply-periodic minimal surface.
Parameters
----------
cells : sequence of int, len (3)
Cell counts along x,y,z direction.
size : sequence of float, len (3)
Edge lengths 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 : sequence of int, len (2)
Material IDs. Defaults to (0,1).
Returns
-------
new : damask.GeomGrid
GeomGrid-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.GeomGrid.from_minimal_surface([64]*3,np.ones(3)*1.e-4,'Gyroid')
cells : 64 × 64 × 64
size : 0.0001 × 0.0001 × 0.0001 m³
origin: 0.0 0.0 0.0 m
# materials: 2
Minimal surface of 'Neovius' type with specific material IDs.
>>> import numpy as np
>>> import damask
>>> damask.GeomGrid.from_minimal_surface([80]*3,np.ones(3)*5.e-4,
... 'Neovius',materials=(1,5))
cells : 80 × 80 × 80
size : 0.0005 × 0.0005 × 0.0005 m³
origin: 0.0 0.0 0.0 m
# 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 GeomGrid(material = np.where(threshold < GeomGrid._minimal_surface[surface](x,y,z),materials[1],materials[0]),
size = size,
comments = util.execution_stamp('GeomGrid','from_minimal_surface'),
)
[docs] def save(self,
fname: Union[str, Path],
compress: bool = True):
"""
Save as VTK ImageData file.
Parameters
----------
fname : str or pathlib.Path
Filename to write.
Valid extension is .vti, which 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)\
.set('material',self.material.flatten(order='F'))
for label,data in self.initial_conditions.items():
v = v.set(label,data.flatten(order='F'))
v.comments = self.comments
v.save(fname,parallel=False,compress=compress)
[docs] def save_ASCII(self,
fname: Union[str, TextIO]):
"""
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 using '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='')
[docs] def show(self,
colormap: Union[Colormap, str] = 'cividis') -> None:
"""
Show on screen.
Parameters
----------
colormap : damask.Colormap or str, optional
Colormap for visualization of material IDs. Defaults to 'cividis'.
"""
VTK.from_image_data(self.cells,self.size,self.origin) \
.set('material',self.material.flatten('F'),) \
.show('material',colormap)
[docs] def canvas(self,
cells: Optional[IntSequence] = None,
offset: Optional[IntSequence] = None,
fill: Optional[int] = None) -> 'GeomGrid':
"""
Crop or enlarge/pad grid.
Parameters
----------
cells : sequence of int, len (3), optional
Cell counts along x,y,z direction.
offset : sequence of int, len (3), optional
Offset (measured in cells) from old to new grid.
Defaults to [0,0,0].
fill : int, optional
Material ID to fill the background.
Defaults to material.max()+1.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Examples
--------
Remove lower 1/2 of the microstructure in z-direction.
>>> import numpy as np
>>> import damask
>>> g = damask.GeomGrid(np.zeros([32]*3,int),np.ones(3)*1e-3)
>>> g.canvas([32,32,16],[0,0,16])
cells: 32 × 32 × 16
size: 0.001 × 0.001 × 0.0005 m³
origin: 0.0 0.0 0.0005 m
# materials: 1
"""
offset_ = np.array(offset,np.int64) if offset is not None else np.zeros(3,np.int64)
cells_ = np.array(cells,np.int64) if cells is not None else self.cells
canvas = np.full(cells_,np.nanmax(self.material) + 1 if fill is None else fill,self.material.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 GeomGrid(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('GeomGrid','canvas')],
)
[docs] def mirror(self,
directions: Sequence[str],
reflect: bool = False) -> 'GeomGrid':
"""
Mirror grid along given directions.
Parameters
----------
directions : (sequence of) {'x', 'y', 'z'}
Direction(s) along which the grid is mirrored.
reflect : bool, optional
Reflect (include) outermost layers. Defaults to False.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Examples
--------
Mirror along y-direction.
>>> import numpy as np
>>> import damask
>>> (g := damask.GeomGrid(np.arange(4*5*6).reshape([4,5,6]),np.ones(3)))
cells: 4 × 5 × 6
size: 1.0 × 1.0 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 120
>>> g.mirror('y')
cells: 4 × 8 × 6
size: 1.0 × 1.6 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 120
Reflect along x- and y-direction.
>>> g.mirror('xy',reflect=True)
cells: 8 × 10 × 6
size: 2.0 × 2.0 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 120
Independence of mirroring order.
>>> g.mirror('xy') == g.mirror(['y','x'])
True
"""
if not set(directions).issubset(valid := ['x', 'y', 'z']):
raise ValueError(f'invalid direction "{set(directions).difference(valid)}" specified')
limits: Sequence[Optional[int]] = [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 GeomGrid(material = mat,
size = self.size/self.cells*np.asarray(mat.shape),
origin = self.origin,
comments = self.comments+[util.execution_stamp('GeomGrid','mirror')],
)
[docs] def flip(self,
directions: Sequence[str]) -> 'GeomGrid':
"""
Flip grid along given directions.
Parameters
----------
directions : (sequence of) {'x', 'y', 'z'}
Direction(s) along which the grid is flipped.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Examples
--------
Invariance of flipping order.
>>> import numpy as np
>>> import damask
>>> (g := damask.GeomGrid(np.arange(4*5*6).reshape([4,5,6]),np.ones(3)))
cells: 4 × 5 × 6
size: 1.0 × 1.0 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 120
>>> g.flip('xyz') == g.flip(['x','z','y'])
True
Invariance of flipping a (fully) mirrored grid.
>>> g.mirror('x',True) == g.mirror('x',True).flip('x')
True
"""
if not set(directions).issubset(valid := ['x', 'y', 'z']):
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 GeomGrid(material = mat,
size = self.size,
origin = self.origin,
comments = self.comments+[util.execution_stamp('GeomGrid','flip')],
)
[docs] def rotate(self,
R: Rotation,
fill: Optional[int] = None) -> 'GeomGrid':
"""
Rotate grid (possibly extending its bounding box).
Parameters
----------
R : damask.Rotation
Rotation to apply to the grid.
fill : int, optional
Material ID to fill enlarged bounding box.
Defaults to material.max()+1.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Examples
--------
Rotation by 180° (π) is equivalent to twice flipping.
>>> import numpy as np
>>> import damask
>>> (g := damask.GeomGrid(np.arange(4*5*6).reshape([4,5,6]),np.ones(3)))
cells: 4 × 5 × 6
size: 1.0 × 1.0 × 1.0 m³
origin: 0.0 0.0 0.0 m
# materials: 120
>>> g.rotate(damask.Rotation.from_axis_angle([0,0,1,180],degrees=True)) == g.flip('xy')
True
"""
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=self.material.dtype,
cval=np.nanmax(self.material) + 1 if fill is None else 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(np.int64),axes=axes)
origin = self.origin-(np.asarray(material.shape)-self.cells)*.5 * self.size/self.cells
return GeomGrid(material = material,
size = self.size/self.cells*np.asarray(material.shape),
origin = origin,
comments = self.comments+[util.execution_stamp('GeomGrid','rotate')],
)
[docs] def scale(self,
cells: IntSequence) -> 'GeomGrid':
"""
Scale grid to new cell counts.
Parameters
----------
cells : sequence of int, len (3)
Cell counts along x,y,z direction.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Examples
--------
Double grid resolution.
>>> import numpy as np
>>> import damask
>>> (g := damask.GeomGrid(np.zeros([32]*3,int),np.ones(3)*1e-4))
cells: 32 × 32 × 32
size: 0.0001 × 0.0001 × 0.0001 m³
origin: 0.0 0.0 0.0 m
# materials: 1
>>> g.scale(g.cells*2)
cells : 64 × 64 × 64
size : 0.0001 × 0.0001 × 0.0001 m³
origin: 0.0 0.0 0.0 m
# materials: 1
"""
orig = tuple(map(np.linspace,self.origin + self.size/self.cells*.5,
self.origin + self.size - self.size/self.cells*.5,self.cells))
interpolator = partial(interpolate.RegularGridInterpolator,
points=orig,method='nearest',bounds_error=False,fill_value=None)
new = grid_filters.coordinates0_point(cells,self.size,self.origin)
return GeomGrid(material = interpolator(values=self.material)(new).astype(int),
size = self.size,
origin = self.origin,
initial_conditions = {k: interpolator(values=v)(new)
for k,v in self.initial_conditions.items()},
comments = self.comments+[util.execution_stamp('GeomGrid','scale')],
)
[docs] def assemble(self,
idx: np.ndarray) -> 'GeomGrid':
"""
Assemble new grid from index map.
Parameters
----------
idx : numpy.ndarray of int, shape (:,:,:) or (:,:,:,3)
GeomGrid of flat indices or coordinate indices.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Cell count of resulting grid matches shape of index map.
"""
cells = idx.shape[:3]
flat = (idx if len(idx.shape)==3 else grid_filters.ravel_index(idx)).flatten(order='F')
ic = {k: v.flatten(order='F')[flat].reshape(cells,order='F') for k,v in self.initial_conditions.items()}
return GeomGrid(material = self.material.flatten(order='F')[flat].reshape(cells,order='F'),
size = self.size,
origin = self.origin,
initial_conditions = ic,
comments = self.comments+[util.execution_stamp('GeomGrid','assemble')],
)
[docs] def renumber(self) -> 'GeomGrid':
"""
Renumber sorted material indices as 0,...,N-1.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
"""
_,renumbered = np.unique(self.material,return_inverse=True)
return GeomGrid(material = renumbered.reshape(self.cells),
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('GeomGrid','renumber')],
)
[docs] def substitute(self,
from_material: Union[int,IntSequence],
to_material: Union[int,IntSequence]) -> 'GeomGrid':
"""
Substitute material indices.
Parameters
----------
from_material : (sequence of) int
Material indices to be substituted.
to_material : (sequence of) int
New material indices.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
"""
material = self.material.copy()
for f,t in zip(from_material if isinstance(from_material,(Sequence,np.ndarray)) else [from_material],
to_material if isinstance(to_material,(Sequence,np.ndarray)) else [to_material]): # ToDo Python 3.10 has strict mode for zip
material[self.material==f] = t
return GeomGrid(material = material,
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('GeomGrid','substitute')],
)
[docs] def sort(self) -> 'GeomGrid':
"""
Sort material indices such that min(material ID) is located at (0,0,0).
Returns
-------
updated : damask.GeomGrid
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 GeomGrid(material = ma.reshape(self.cells,order='F'),
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('GeomGrid','sort')],
)
[docs] def clean(self,
distance: float = np.sqrt(3),
selection: Optional[IntSequence] = None,
invert_selection: bool = False,
periodic: bool = True,
rng_seed: Optional[NumpyRngSeed] = None) -> 'GeomGrid':
"""
Smooth grid by selecting most frequent material ID within given stencil at each location.
Parameters
----------
distance : float, optional
Voxel distance checked for presence of other materials.
Defaults to sqrt(3).
selection : (sequence of) int, optional
Material IDs to consider. Defaults to all.
invert_selection : bool, optional
Consider all material IDs except those in selection. Defaults to False.
periodic : bool, optional
Assume grid to be periodic. Defaults to True.
rng_seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional
A seed to initialize the BitGenerator. Defaults to None.
If None, then fresh, unpredictable entropy will be pulled from the OS.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Notes
-----
If multiple material IDs are most frequent within a stencil, a random choice is taken.
"""
def most_frequent(stencil: np.ndarray,
selection: Union[None,np.ndarray],
rng: np.random.Generator):
me = stencil[stencil.size//2]
if selection is None or me in selection:
unique, counts = np.unique(stencil,return_counts=True)
return rng.choice(unique[counts==np.max(counts)])
else:
return me
rng = np.random.default_rng(rng_seed)
d = np.floor(distance).astype(np.int64)
ext = np.linspace(-d,d,1+2*d,dtype=float),
xx,yy,zz = np.meshgrid(ext,ext,ext)
footprint = xx**2+yy**2+zz**2 <= distance**2+distance*1e-8
selection_ = None if selection is None else \
np.setdiff1d(self.material,selection) if invert_selection else \
np.intersect1d(self.material,selection)
material = ndimage.generic_filter(
self.material,
most_frequent,
footprint=footprint,
mode='wrap' if periodic else 'nearest',
extra_keywords=dict(selection=selection_,rng=rng),
).astype(self.material.dtype)
return GeomGrid(material = material,
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('GeomGrid','clean')],
)
[docs] def add_primitive(self,
dimension: Union[FloatSequence, IntSequence],
center: Union[FloatSequence, IntSequence],
exponent: Union[FloatSequence, float],
fill: Optional[int] = None,
R: Rotation = Rotation(),
inverse: bool = False,
periodic: bool = True) -> 'GeomGrid':
"""
Insert a primitive geometric object at a given position.
Parameters
----------
dimension : sequence of int or float, len (3)
Dimension (diameter/side length) of the primitive.
If given as integers, cell centers are addressed.
If given as floats, physical coordinates are addressed.
center : sequence of int or float, len (3)
Center of the primitive.
If given as integers, cell centers are addressed.
If given as floats, physical coordinates are addressed.
exponent : (sequence of) float, len (3)
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 the primitive. Defaults to no rotation.
inverse : bool, optional
Retain original materials within primitive and fill outside.
Defaults to False.
periodic : bool, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
Examples
--------
Add a sphere at the center.
>>> import numpy as np
>>> import damask
>>> g = damask.GeomGrid(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 : 64 × 64 × 64
size : 0.0001 × 0.0001 × 0.0001 m³
origin: 0.0 0.0 0.0 m
# materials: 2
Add a cube at the origin.
>>> import numpy as np
>>> import damask
>>> g = damask.GeomGrid(np.zeros([64]*3,int), np.ones(3)*1e-4)
>>> g.add_primitive(np.ones(3,int)*32,np.zeros(3),np.inf)
cells : 64 × 64 × 64
size : 0.0001 × 0.0001 × 0.0001 m³
origin: 0.0 0.0 0.0 m
# 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(np.abs(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(np.int64),(0,1,2))
return GeomGrid(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,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('GeomGrid','add_primitive')],
)
[docs] def vicinity_offset(self,
distance: float = np.sqrt(3),
offset: Optional[int] = None,
selection: Optional[IntSequence] = None,
invert_selection: bool = False,
periodic: bool = True) -> 'GeomGrid':
"""
Offset material ID of points in the vicinity of selected (or just other) material IDs.
Trigger points are variations in material ID, i.e. grain/phase
boundaries or explicitly given material IDs.
Parameters
----------
distance : float, optional
Voxel distance checked for presence of other materials.
Defaults to sqrt(3).
offset : int, optional
Offset (positive or negative) to tag material IDs.
Defaults to material.max()+1.
selection : (sequence of) int, optional
Material IDs that trigger an offset.
Defaults to any other than own material ID.
invert_selection : bool, optional
Consider all material IDs except those in selection.
Defaults to False.
periodic : bool, optional
Assume grid to be periodic. Defaults to True.
Returns
-------
updated : damask.GeomGrid
Updated grid-based geometry.
"""
@numba_njit_wrapper()
def tainted_neighborhood(stencil: np.ndarray,
selection: Optional[np.ndarray] = None):
me = stencil[stencil.size//2]
if selection is None:
return np.any(stencil != me)
elif not len(selection)==0:
for stencil_item in stencil:
for selection_item in selection:
if stencil_item==selection_item and selection_item!=me:
return True
return False
d = np.floor(distance).astype(np.int64)
ext = np.linspace(-d,d,1+2*d,dtype=float),
xx,yy,zz = np.meshgrid(ext,ext,ext)
footprint = xx**2+yy**2+zz**2 <= distance**2+distance*1e-8
offset_ = np.nanmax(self.material)+1 if offset is None else offset
selection_ = None if selection is None else \
np.setdiff1d(self.material,selection) if invert_selection else \
np.intersect1d(self.material,selection)
mask = ndimage.generic_filter(self.material,
tainted_neighborhood,
footprint=footprint,
mode='wrap' if periodic else 'nearest',
extra_keywords=dict(selection=selection_),
)
return GeomGrid(material = np.where(mask, self.material + offset_,self.material),
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('GeomGrid','vicinity_offset')],
)
[docs] def get_grain_boundaries(self,
periodic: bool = True,
directions: Sequence[str] = 'xyz') -> VTK:
"""
Create VTK unstructured grid containing grain boundaries.
Parameters
----------
periodic : bool, optional
Assume grid to be periodic. Defaults to True.
directions : (sequence of) {'x', 'y', 'z'}, optional
Direction(s) along which the boundaries are determined.
Defaults to 'xyz'.
Returns
-------
grain_boundaries : damask.VTK
VTK-based geometry of grain boundary network.
"""
if not set(directions).issubset(valid := ['x', 'y', 'z']):
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')