DAMASK_EICMD/python/damask/_grid.py

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Python
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import os
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import copy
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import warnings
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import multiprocessing as mp
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from functools import partial
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import typing
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from typing import Optional, Union, TextIO, List, Sequence, Dict
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from pathlib import Path
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import numpy as np
import pandas as pd
import h5py
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from scipy import ndimage, spatial, interpolate
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from . import VTK
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from . import util
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from . import grid_filters
from . import Rotation
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from . import Table
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from . import Colormap
from ._typehints import FloatSequence, IntSequence, IntCollection, NumpyRngSeed
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class Grid:
"""
Geometry definition for grid solvers.
Create and manipulate geometry definitions for storage as VTK
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image data files ('.vti' extension). A grid contains the
material ID (referring to the entry in 'material.yaml') and
the physical size.
"""
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def __init__(self,
material: np.ndarray,
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size: FloatSequence,
origin: FloatSequence = np.zeros(3),
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initial_conditions: Optional[Dict[str,np.ndarray]] = None,
comments: Union[None, str, Sequence[str]] = None):
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"""
New geometry definition for grid solvers.
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Parameters
----------
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material : numpy.ndarray of int, shape (:,:,:)
Material indices. The shape of the material array defines
the number of cells.
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size : sequence of float, len (3)
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Physical size of grid in meter.
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origin : sequence of float, len (3), optional
Coordinates of grid origin in meter. Defaults to [0.0,0.0,0.0].
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initial_conditions : dictionary, optional
Labels and values of the inital conditions at each material point.
comments : (sequence of) str, optional
Additional, human-readable information, e.g. history of operations.
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"""
self.material = material
self.size = size # type: ignore
self.origin = origin # type: ignore
self.initial_conditions = {} if initial_conditions is None else initial_conditions
comments_ = [comments] if isinstance(comments,str) else comments
self.comments = [] if comments_ is None else [str(c) for c in comments_]
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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
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return util.srepr([
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f'cells: {util.srepr(self.cells, " × ")}',
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f'size: {util.srepr(self.size, " × ")}',
f'origin: {util.srepr(self.origin," ")} m',
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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 []))
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def __copy__(self) -> 'Grid':
"""
Return deepcopy(self).
Create deep copy.
"""
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return copy.deepcopy(self)
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copy = __copy__
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def __eq__(self,
other: object) -> bool:
"""
Return self==other.
Test equality of other.
Parameters
----------
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other : damask.Grid
Grid to compare self against.
"""
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if not isinstance(other, Grid):
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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))
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@property
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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
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def size(self) -> np.ndarray:
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"""Physical size 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
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def origin(self) -> np.ndarray:
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"""Coordinates of 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."""
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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
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def comments(self) -> List[str]:
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"""Comments, e.g. history of operations."""
return self._comments
@comments.setter
def comments(self,
comments: Union[str, Sequence[str]]):
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self._comments = [str(c) for c in comments] if isinstance(comments,Sequence) else [str(comments)]
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@property
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def cells(self) -> np.ndarray:
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"""Number of cells in x,y,z direction."""
return np.asarray(self.material.shape)
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@property
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def N_materials(self) -> int:
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"""Number of (unique) material indices within grid."""
return np.unique(self.material).size
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@staticmethod
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def load(fname: Union[str, Path]) -> 'Grid':
"""
Load from VTK image data file.
Parameters
----------
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fname : str or pathlib.Path
Grid file to read.
Valid extension is .vti, which will be appended if not given.
Returns
-------
loaded : damask.Grid
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Grid-based geometry from file.
"""
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v = VTK.load(fname if str(fname).endswith('.vti') else str(fname)+'.vti')
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cells = np.array(v.vtk_data.GetDimensions())-1
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
comments = v.comments
ic = {label:v.get(label).reshape(cells,order='F') for label in set(v.labels['Cell Data']) - {'material'}}
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return Grid(material = v.get('material').reshape(cells,order='F'),
size = bbox[1] - bbox[0],
origin = bbox[0],
initial_conditions = ic,
comments = comments,
)
@typing.no_type_check
@staticmethod
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def load_ASCII(fname)-> 'Grid':
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"""
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Load from geom file.
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Storing geometry files in ASCII format is deprecated.
This function will be removed in a future version of DAMASK.
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Parameters
----------
fname : str, pathlib.Path, or file handle
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Geometry file to read.
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Returns
-------
loaded : damask.Grid
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Grid-based geometry from file.
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"""
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warnings.warn('Support for ASCII-based geom format will be removed in DAMASK 3.0.0', DeprecationWarning,2)
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if isinstance(fname, (str, Path)):
f = open(fname)
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elif isinstance(fname, TextIO):
f = fname
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else:
raise TypeError
f.seek(0)
try:
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header_length_,keyword = f.readline().split()[:2]
header_length = int(header_length_)
except ValueError:
header_length,keyword = (-1, 'invalid')
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if not keyword.startswith('head') or header_length < 3:
raise TypeError('invalid or missing header length information')
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comments = []
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content = f.readlines()
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for i,line in enumerate(content[:header_length]):
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items = line.split('#')[0].lower().strip().split()
if (key := items[0] if items else '') == 'grid':
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cells = np.array([ int(dict(zip(items[1::2],items[2::2]))[i]) for i in ['a','b','c']])
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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
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i = 0
for line in content[header_length:]:
if len(items := line.split('#')[0].split()) == 3:
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if items[1].lower() == 'of':
material_entry = np.ones(int(items[0]))*float(items[2])
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elif items[1].lower() == 'to':
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material_entry = np.linspace(int(items[0]),int(items[2]),
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abs(int(items[2])-int(items[0]))+1,dtype=float)
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else: material_entry = list(map(float, items))
else: material_entry = list(map(float, items))
material[i:i+len(material_entry)] = material_entry
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i += len(items)
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if i != cells.prod():
raise TypeError(f'mismatch between {cells.prod()} expected entries and {i} found')
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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)
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return Grid(material = material.reshape(cells,order='F'),
size = size,
origin = origin,
comments = comments)
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@staticmethod
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def load_Neper(fname: Union[str, Path]) -> 'Grid':
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"""
Load from Neper VTK file.
Parameters
----------
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fname : str or pathlib.Path
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Geometry file to read.
Returns
-------
loaded : damask.Grid
Grid-based geometry from file.
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Examples
--------
Read a periodic polycrystal generated with Neper.
>>> import damask
>>> N_grains = 20
>>> cells = (32,32,32)
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>>> damask.util.run(f'neper -T -n {N_grains} -tesrsize {cells[0]}:{cells[1]}:{cells[2]} -periodicity all -format vtk')
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>>> damask.Grid.load_Neper(f'n{N_grains}-id1.vtk')
cells: 32 × 32 × 32
size: 1.0 × 1.0 × 1.0
origin: 0.0 0.0 0.0 m
# materials: 20
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"""
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v = VTK.load(fname,'ImageData')
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cells = np.array(v.vtk_data.GetDimensions())-1
bbox = np.array(v.vtk_data.GetBounds()).reshape(3,2).T
return Grid(material = v.get('MaterialId').reshape(cells,order='F').astype('int32',casting='unsafe') - 1,
size = bbox[1] - bbox[0],
origin = bbox[0],
comments = util.execution_stamp('Grid','load_Neper'),
)
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@staticmethod
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def load_DREAM3D(fname: Union[str, Path],
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feature_IDs: Optional[str] = None,
cell_data: Optional[str] = None,
phases: str = 'Phases',
Euler_angles: str = 'EulerAngles',
base_group: Optional[str] = None) -> 'Grid':
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"""
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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.
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damask.ConfigMaterial.load_DREAM3D gives the corresponding material definition.
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Parameters
----------
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fname : str or or pathlib.Path
Filename of the DREAM.3D (HDF5) file.
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feature_IDs : str, optional
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Name of the dataset containing the mapping between cells and
grain-wise data. Defaults to 'None', in which case cell-wise
data is used.
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cell_data : str, optional
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Name of the group (folder) containing cell-wise data. Defaults to
None in wich case it is automatically detected.
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phases : str, optional
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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'.
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Euler_angles : str, optional
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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'.
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base_group : str, optional
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Path to the group (folder) that contains geometry (_SIMPL_GEOMETRY),
and grain- or cell-wise data. Defaults to None, in which case
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it is set as the path that contains _SIMPL_GEOMETRY/SPACING.
Returns
-------
loaded : damask.Grid
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Grid-based geometry from file.
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"""
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
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f = h5py.File(fname, 'r')
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cells = f['/'.join([b,'_SIMPL_GEOMETRY','DIMENSIONS'])][()]
size = f['/'.join([b,'_SIMPL_GEOMETRY','SPACING'])] * cells
origin = f['/'.join([b,'_SIMPL_GEOMETRY','ORIGIN'])][()]
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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()
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return Grid(material = ma.reshape(cells,order='F'),
size = size,
origin = origin,
comments = util.execution_stamp('Grid','load_DREAM3D'),
)
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@staticmethod
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def from_table(table: Table,
coordinates: str,
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labels: Union[str, Sequence[str]]) -> 'Grid':
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"""
Create grid from ASCII table.
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Parameters
----------
table : damask.Table
Table that contains material information.
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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
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Label(s) of the columns containing the material definition.
Each unique combination of values results in one material ID.
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Returns
-------
new : damask.Grid
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Grid-based geometry from values in table.
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"""
cells,size,origin = grid_filters.cellsSizeOrigin_coordinates0_point(table.get(coordinates))
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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)
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ma = np.arange(cells.prod()) if len(unique) == cells.prod() else \
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np.arange(unique.size)[np.argsort(pd.unique(unique_inverse))][unique_inverse]
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return Grid(material = ma.reshape(cells,order='F'),
size = size,
origin = origin,
comments = util.execution_stamp('Grid','from_table'),
)
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@staticmethod
def _find_closest_seed(seeds: np.ndarray,
weights: np.ndarray,
point: np.ndarray) -> np.integer:
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return np.argmin(np.sum((np.broadcast_to(point,(len(seeds),3))-seeds)**2,axis=1) - weights)
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@staticmethod
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def from_Laguerre_tessellation(cells: IntSequence,
size: FloatSequence,
seeds: np.ndarray,
weights: FloatSequence,
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material: Optional[IntSequence] = None,
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periodic: bool = True):
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"""
Create grid from Laguerre tessellation.
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Parameters
----------
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cells : sequence of int, len (3)
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Number of cells in x,y,z direction.
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size : sequence of float, len (3)
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Physical size of the grid in meter.
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seeds : numpy.ndarray of float, shape (:,3)
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Position of the seed points in meter. All points need to lay within the box.
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weights : sequence of float, len (seeds.shape[0])
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Weights of the seeds. Setting all weights to 1.0 gives a standard Voronoi tessellation.
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material : sequence of int, len (seeds.shape[0]), optional
Material ID of the seeds.
Defaults to None, in which case materials are consecutively numbered.
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periodic : bool, optional
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Assume grid to be periodic. Defaults to True.
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Returns
-------
new : damask.Grid
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Grid-based geometry from tessellation.
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"""
weights_p: FloatSequence
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if periodic:
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weights_p = np.tile(weights,27) # Laguerre weights (1,2,3,1,2,3,...,1,2,3)
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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:
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weights_p = np.array(weights,float)
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seeds_p = seeds
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
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pool = mp.Pool(int(os.environ.get('OMP_NUM_THREADS',4)))
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result = pool.map_async(partial(Grid._find_closest_seed,seeds_p,weights_p), coords)
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pool.close()
pool.join()
material_ = np.array(result.get()).reshape(cells)
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if periodic: material_ %= len(weights)
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return Grid(material = material_ if material is None else np.array(material)[material_],
size = size,
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comments = util.execution_stamp('Grid','from_Laguerre_tessellation'),
)
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@staticmethod
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def from_Voronoi_tessellation(cells: IntSequence,
size: FloatSequence,
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seeds: np.ndarray,
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material: Optional[IntSequence] = None,
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periodic: bool = True) -> 'Grid':
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"""
Create grid from Voronoi tessellation.
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Parameters
----------
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cells : sequence of int, len (3)
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Number of cells in x,y,z direction.
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size : sequence of float, len (3)
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Physical size of the grid in meter.
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seeds : numpy.ndarray of float, shape (:,3)
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Position of the seed points in meter. All points need to lay within the box.
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material : sequence of int, len (seeds.shape[0]), optional
Material ID of the seeds.
Defaults to None, in which case materials are consecutively numbered.
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periodic : bool, optional
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Assume grid to be periodic. Defaults to True.
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Returns
-------
new : damask.Grid
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Grid-based geometry from tessellation.
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"""
coords = grid_filters.coordinates0_point(cells,size).reshape(-1,3)
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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
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return Grid(material = (material_ if material is None else np.array(material)[material_]).reshape(cells),
size = size,
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comments = util.execution_stamp('Grid','from_Voronoi_tessellation'),
)
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_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) ),
}
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@staticmethod
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def from_minimal_surface(cells: IntSequence,
size: FloatSequence,
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surface: str,
threshold: float = 0.0,
periods: int = 1,
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materials: IntSequence = (0,1)) -> 'Grid':
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"""
Create grid from definition of triply periodic minimal surface.
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Parameters
----------
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cells : sequence of int, len (3)
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Number of cells in x,y,z direction.
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size : sequence of float, len (3)
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Physical size of the grid in meter.
surface : str
Type of the minimal surface. See notes for details.
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threshold : float, optional.
Threshold of the minimal surface. Defaults to 0.0.
periods : integer, optional.
Number of periods per unit cell. Defaults to 1.
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materials : sequence of int, len (2)
Material IDs. Defaults to (0,1).
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Returns
-------
new : damask.Grid
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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
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References
----------
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S.B.G. Blanquer et al., Biofabrication 9(2):025001, 2017
https://doi.org/10.1088/1758-5090/aa6553
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M. Wohlgemuth et al., Macromolecules 34(17):6083-6089, 2001
https://doi.org/10.1021/ma0019499
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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
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>>> damask.Grid.from_minimal_surface([64]*3,np.ones(3)*1.e-4,'Gyroid')
cells : 64 x 64 x 64
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size : 0.0001 x 0.0001 x 0.0001
origin: 0.0 0.0 0.0 m
# materials: 2
Minimal surface of 'Neovius' type with non-default material IDs.
>>> import numpy as np
>>> import damask
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>>> damask.Grid.from_minimal_surface([80]*3,np.ones(3)*5.e-4,
... 'Neovius',materials=(1,5))
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cells : 80 x 80 x 80
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size : 0.0005 x 0.0005 x 0.0005
origin: 0.0 0.0 0.0 m
# materials: 2 (min: 1, max: 5)
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"""
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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],
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indexing='ij',sparse=True)
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return Grid(material = np.where(threshold < Grid._minimal_surface[surface](x,y,z),materials[1],materials[0]),
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size = size,
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comments = util.execution_stamp('Grid','from_minimal_surface'),
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)
def save(self,
fname: Union[str, Path],
compress: bool = True):
"""
Save as VTK image data file.
Parameters
----------
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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.
"""
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v = VTK.from_image_data(self.cells,self.size,self.origin)\
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.set('material',self.material.flatten(order='F'))
for label,data in self.initial_conditions.items():
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v = v.set(label,data.flatten(order='F'))
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v.comments = self.comments
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v.save(fname,parallel=False,compress=compress)
def save_ASCII(self,
fname: Union[str, TextIO]):
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"""
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Save as geom file.
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Storing geometry files in ASCII format is deprecated.
This function will be removed in a future version of DAMASK.
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Parameters
----------
fname : str or file handle
Geometry file to write with extension '.geom'.
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compress : bool, optional
Compress geometry with 'x of y' and 'a to b'.
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"""
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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 \
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+ ['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,
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self.material.reshape([self.cells[0],np.prod(self.cells[1:])],order='F').T,
header='\n'.join(header), fmt=format_string, comments='')
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def show(self,
colormap: Union[Colormap, str] = 'cividis') -> None:
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"""
Show on screen.
Parameters
----------
colormap : damask.Colormap or str, optional
Colormap for visualization of material IDs. Defaults to 'cividis'.
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"""
VTK.from_image_data(self.cells,self.size,self.origin) \
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.set('material',self.material.flatten('F'),) \
.show('material',colormap)
def canvas(self,
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cells: Optional[IntSequence] = None,
offset: Optional[IntSequence] = None,
fill: Optional[int] = None) -> 'Grid':
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"""
Crop or enlarge/pad grid.
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Parameters
----------
cells : sequence of int, len (3), optional
Number of cells 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].
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fill : int, optional
Material ID to fill the background.
Defaults to material.max() + 1.
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Returns
-------
updated : damask.Grid
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Updated grid-based geometry.
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Examples
--------
Remove lower 1/2 of the microstructure in z-direction.
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>>> import numpy as np
>>> import damask
>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
>>> g.canvas([32,32,16],[0,0,16])
cells : 33 x 32 x 16
size : 0.0001 x 0.0001 x 5e-05
origin: 0.0 0.0 5e-05 m
# materials: 1
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"""
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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
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canvas = np.full(cells_,np.nanmax(self.material) + 1 if fill is None else fill,self.material.dtype)
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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_))
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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]]
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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')],
)
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def mirror(self,
directions: Sequence[str],
reflect: bool = False) -> 'Grid':
"""
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Mirror grid along given directions.
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Parameters
----------
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directions : (sequence of) {'x', 'y', 'z'}
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Direction(s) along which the grid is mirrored.
reflect : bool, optional
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Reflect (include) outermost layers. Defaults to False.
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Returns
-------
updated : damask.Grid
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Updated grid-based geometry.
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Examples
--------
Mirror along x- and y-direction.
>>> import numpy as np
>>> import damask
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>>> g = damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4)
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>>> g.mirror('xy',True)
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cells : 64 x 64 x 32
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size : 0.0002 x 0.0002 x 0.0001
origin: 0.0 0.0 0.0 m
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# materials: 1
"""
if not set(directions).issubset(valid := ['x', 'y', 'z']):
raise ValueError(f'invalid direction "{set(directions).difference(valid)}" specified')
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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)
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return Grid(material = mat,
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size = self.size/self.cells*np.asarray(mat.shape),
origin = self.origin,
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comments = self.comments+[util.execution_stamp('Grid','mirror')],
)
def flip(self,
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directions: Sequence[str]) -> 'Grid':
"""
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Flip grid along given directions.
Parameters
----------
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directions : (sequence of) {'x', 'y', 'z'}
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Direction(s) along which the grid is flipped.
Returns
-------
updated : damask.Grid
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Updated grid-based geometry.
"""
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])
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return Grid(material = mat,
size = self.size,
origin = self.origin,
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comments = self.comments+[util.execution_stamp('Grid','flip')],
)
def rotate(self,
R: Rotation,
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fill: Optional[int] = None) -> 'Grid':
"""
Rotate grid (and pad if required).
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.Grid
Updated grid-based geometry.
"""
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 Grid(material = material,
size = self.size/self.cells*np.asarray(material.shape),
origin = origin,
comments = self.comments+[util.execution_stamp('Grid','rotate')],
)
def scale(self,
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cells: IntSequence) -> 'Grid':
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"""
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Scale grid to new cell count.
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Parameters
----------
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cells : sequence of int, len (3)
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Number of cells in x,y,z direction.
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Returns
-------
updated : damask.Grid
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Updated grid-based geometry.
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Examples
--------
Double resolution.
>>> import numpy as np
>>> import damask
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>>> (g := damask.Grid(np.zeros([32]*3,int),np.ones(3)*1e-4))
cells: 32 × 32 × 32
size: 0.0001 × 0.0001 × 0.0001
origin: 0.0 0.0 0.0 m
# materials: 1
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>>> g.scale(g.cells*2)
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cells : 64 x 64 x 64
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size : 0.0001 x 0.0001 x 0.0001
origin: 0.0 0.0 0.0 m
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# materials: 1
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"""
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orig = tuple(map(np.linspace,self.origin + self.size/self.cells*.5,
self.origin + self.size - self.size/self.cells*.5,self.cells))
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interpolator = partial(interpolate.RegularGridInterpolator,
points=orig,method='nearest',bounds_error=False,fill_value=None)
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new = grid_filters.coordinates0_point(cells,self.size,self.origin)
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return Grid(material = interpolator(values=self.material)(new).astype(int),
size = self.size,
origin = self.origin,
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initial_conditions = {k: interpolator(values=v)(new)
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for k,v in self.initial_conditions.items()},
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comments = self.comments+[util.execution_stamp('Grid','scale')],
)
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def assemble(self,
idx: np.ndarray) -> 'Grid':
"""
Assemble new grid from index map.
Parameters
----------
idx : numpy.ndarray of int, shape (:,:,:) or (:,:,:,3)
Grid of flat indices or coordinate indices.
Returns
-------
updated : damask.Grid
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 Grid(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('Grid','assemble')],
)
def renumber(self) -> 'Grid':
"""
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,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('Grid','renumber')],
)
def substitute(self,
from_material: Union[int,IntSequence],
to_material: Union[int,IntSequence]) -> 'Grid':
"""
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.Grid
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 Grid(material = material,
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('Grid','substitute')],
)
def sort(self) -> 'Grid':
"""
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,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('Grid','sort')],
)
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def clean(self,
distance: float = np.sqrt(3),
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selection: Optional[IntCollection] = None,
invert_selection: bool = False,
periodic: bool = True,
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rng_seed: Optional[NumpyRngSeed] = None) -> 'Grid':
"""
Smooth grid by selecting most frequent material ID within given stencil at each location.
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Parameters
----------
distance : float, optional
Voxel distance checked for presence of other materials.
Defaults to sqrt(3).
selection : (collection 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.
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periodic : bool, optional
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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.Grid
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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,set],
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rng):
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 \
set(self.material.flatten()) - set(util.aslist(selection)) if invert_selection else \
set(self.material.flatten()) & set(util.aslist(selection))
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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 Grid(material = material,
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
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comments = self.comments+[util.execution_stamp('Grid','clean')],
)
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def add_primitive(self,
dimension: Union[FloatSequence, IntSequence],
center: Union[FloatSequence, IntSequence],
exponent: Union[FloatSequence, float],
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fill: Optional[int] = None,
R: Rotation = Rotation(),
inverse: bool = False,
periodic: bool = True) -> 'Grid':
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"""
Insert a primitive geometric object at a given position.
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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)
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fill : int, optional
Fill value for primitive. Defaults to material.max()+1.
R : damask.Rotation, optional
Rotation of 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.
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Returns
-------
updated : damask.Grid
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Updated grid-based geometry.
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Examples
--------
Add a sphere at the center.
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>>> 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 : 64 x 64 x 64
size : 0.0001 x 0.0001 x 0.0001
origin: 0.0 0.0 0.0 m
# materials: 2
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Add a cube at the origin.
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>>> 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 : 64 x 64 x 64
size : 0.0001 x 0.0001 x 0.0001
origin: 0.0 0.0 0.0 m
# materials: 2
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"""
# 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)
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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'):
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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 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,
initial_conditions = self.initial_conditions,
comments = self.comments+[util.execution_stamp('Grid','add_primitive')],
)
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def vicinity_offset(self,
distance: float = np.sqrt(3),
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offset: Optional[int] = None,
selection: Optional[IntCollection] = None,
invert_selection: bool = False,
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periodic: bool = True) -> 'Grid':
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"""
Offset material ID of points in the vicinity of selected (or just other) material IDs.
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Trigger points are variations in material ID, i.e. grain/phase
boundaries or explicitly given material IDs.
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Parameters
----------
distance : float, optional
Voxel distance checked for presence of other materials.
Defaults to sqrt(3).
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offset : int, optional
Offset (positive or negative) to tag material IDs.
Defaults to material.max()+1.
selection : (collection 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.
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periodic : bool, optional
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Assume grid to be periodic. Defaults to True.
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Returns
-------
updated : damask.Grid
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Updated grid-based geometry.
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"""
def tainted_neighborhood(stencil: np.ndarray, selection: Union[None,set]):
me = stencil[stencil.size//2]
return np.any(stencil != me if selection is None else
np.in1d(stencil,np.array(list(selection - {me}))))
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 \
set(self.material.flatten()) - set(util.aslist(selection)) if invert_selection else \
set(self.material.flatten()) & set(util.aslist(selection))
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mask = ndimage.generic_filter(self.material,
tainted_neighborhood,
footprint=footprint,
mode='wrap' if periodic else 'nearest',
extra_keywords=dict(selection=selection_),
)
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return Grid(material = np.where(mask, self.material + offset_,self.material),
size = self.size,
origin = self.origin,
initial_conditions = self.initial_conditions,
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comments = self.comments+[util.execution_stamp('Grid','vicinity_offset')],
)
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def get_grain_boundaries(self,
periodic: bool = True,
directions: Sequence[str] = 'xyz') -> VTK:
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"""
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Create VTK unstructured grid containing grain boundaries.
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Parameters
----------
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periodic : bool, optional
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Assume grid to be periodic. Defaults to True.
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directions : (sequence of) {'x', 'y', 'z'}, optional
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Direction(s) along which the boundaries are determined.
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Defaults to 'xyz'.
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Returns
-------
grain_boundaries : damask.VTK
VTK-based geometry of grain boundary network.
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"""
if not set(directions).issubset(valid := ['x', 'y', 'z']):
raise ValueError(f'invalid direction "{set(directions).difference(valid)}" specified')
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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
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connectivity = []
for i,d in enumerate(['x','y','z']):
if d not in directions: continue
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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
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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')